Systems and methods for automated neuroimaging signal processing

Abstract

The present disclosure relates to techniques for automated neuroimaging signal processing. In particular, the techniques can be used for cognitive impairment prediction using machine learning models and processed neuroimaging data. Aspects of the present disclosure are directed to accessing structural neuroimaging signals and functional neuroimaging signals for a brain of a subject, inputting the structural neuroimaging signals and the functional neuroimaging signals into a structure-function model, determining an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, inputting the scores into a cognitive impairment model, and generating a measure of cognitive impairment for the subject using the cognitive impairment model based on an estimation of relationships between the scores and cognitive performance.

Description

Attorney Docket No.: 081906-1447535-320210WO Client Reference No.: SF2023-091-2-PCT SYSTEMS AND METHODS FOR AUTOMATED NEUROIMAGING SIGNAL PROCESSING CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims priority and benefit from U.S. Provisional Application No.63 / 508,654, filed June 16, 2023, the entire contents of which are incorporated herein by reference for all purposes. FIELD

[0002] The present disclosure relates to automated neuroimaging signal processing, and in particular to machine learning techniques for making cognitive impairment predictions using structural neuroimaging signals (e.g., structural magnetic resonance imaging (sMRI) signals) and functional neuroimaging signals (e.g., functional magnetic resonance imaging (fMRI) signals). GOVERNMENT SUPPORT

[0003] This invention was made with government support under K01 AG055698 awarded by the National Institutes of Health. The government has certain rights in the invention. BACKGROUND

[0004] Cognitive impairment affects people’s daily life. It has been estimated that around 20% of global population are suffering from some kind of cognitive impairment. Cognitive impairment can interfere with daily activities, including self-care and work, and can lead to increased dependence on others. In addition to its effects on individuals and their families, cognitive impairment also has significant societal and economic impacts, including increased healthcare costs and decreased productivity. By understanding the underlying causes of cognitive impairment, such as in Alzheimer’s disease dementia and frontotemporal dementia, means can be developed to improve diagnosis, treatment, and prevention of cognitive impairment.

[0005] It is known that in dementia diseases such as Alzheimer’s disease (AD) and frontotemporal dementia (FTD), cognitive impairments are linked to the atrophy of gray matter in specific brain regions. Additionally, alterations in brain functional connectivity are prevalent in both AD and FTD, known to result in both reduced and increased connectivity compared to individuals without cognitive impairments. However, the connection betweenstructural and functional changes in dementia diseases such as AD and FTD and their unique or shared contributions to cognitive impairment remains unclear. SUMMARY

[0006] The techniques described herein process neuroimaging signals use machine learning to explore the connection between structural and functional changes in dementia diseases, realize their unique or shared contributions to cognitive impairment, and use that realization to make predictions concerning the cognitive impairment of a subject.

[0007] In various embodiments, a computer-implemented method is provided that includes accessing structural neuroimaging signals and functional neuroimaging signals for a brain of a subject; inputting the structural neuroimaging signals and the functional neuroimaging signals into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; and generating, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and cognitive performance.

[0008] In some embodiments, the computer-implemented method further comprises outputting a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment.

[0009] In some embodiments, the structural neuroimaging signals are structural magnetic resonance imaging (sMRI) data generated using a Magnetic Resonance Imaging (MRI) scanner, and the functional neuroimaging signals are functional magnetic resonance imaging (fMRI) data generated using the same MRI scanner or a different MRI scanner, wherein the subject is instructed to perform different tasks during sMRI and fMRI data acquisition.

[0010] In some embodiments, the structural neuroimaging signals and / or the functional neuroimaging signals are obtained using one or more of the following techniques: Computed Tomography (CT), Magnetic Resonance Imaging (MRI), diffusion-based MRI, PositronEmission Tomography (PET), Magnetoencephalography (MEG), Transcranial Electrical Stimulation (TES), Photoacoustic Imaging, and Molecular Imaging.

[0011] In some embodiments, the computer-implemented method further comprises preprocessing the structural neuroimaging signals and the functional neuroimaging signals to generate structural neuroimaging data and functional neuroimaging data, wherein the structural neuroimaging data and the functional neuroimaging data are input into the structure-function model, and wherein the structural neuroimaging data comprises W-scores as a measurement of gray matter atrophy within the brain, and the functional neuroimaging data comprises functional connectivity patterns across multiple regions of the brain.

[0012] In various embodiments, a computer-implemented method is provided that includes accessing structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject; inputting the sMRI data and the fMRI data into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; predicting, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and cognitive performance; and generating a treatment or clinical trial protocol for the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment.

[0013] In some embodiments, the sMRI data comprises W-scores as a measurement of gray matter atrophy within the brain, and the fMRI data comprises functional connectivity patterns across multiple regions of the brain.

[0014] In some embodiments, the predetermined number is 3.

[0015] In some embodiments, a first principal structure-function component of the three principal structure-function components captures a relationship between global atrophy and a distributed functional connectivity pattern of decreases and increases.

[0016] In some embodiments, a second principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in a left- predominant temporal pole versus right-predominant dorsal parietal cortex.

[0017] In some embodiments, a third principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in left- predominant temporal-occipital lobe versus prefrontal-insula-cingulate areas.

[0018] In some embodiments, the generating the treatment or clinical trial protocol comprises stratifying the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment, wherein the stratifying is a pattern recognition process based on a two-dimensional matrix and comprises generating a matrix-pattern graph corresponding to weights associated with the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components.

[0019] In some embodiments, the computer-implemented method further comprises rendering the treatment or clinical trial protocol and the matrix-pattern graph in a graphical user interface.

[0020] In some embodiments, the graphical user interface comprises the atrophy score and the functional connectivity score for the subject within a correlation plot, an atrophy pattern reflecting the atrophy score, and relationships between the treatment or clinical trial protocol and the matrix-pattern graph based on the stratifying.

[0021] In some embodiments, the computer-implemented method further comprises determining an expected response of the subject to a therapeutic agent based on (i) the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components, (ii) the measure of cognitive impairment, (iii) the matrix-pattern graph, or (iv) a combination thereof.

[0022] In some embodiments, the computer-implemented method further comprises comparing the matrix-pattern graph of the subject with a matrix-pattern graph of the subject prior to a treatment with a therapeutic agent and updating the treatment or clinical trial protocol for the subject based on the comparing.

[0023] In some embodiments, the computer-implemented method further comprises inputting the fMRI data into a dynamic systems model; determining, using the dynamicsystems model, a set of eigenmodes for the subject based on the fMRI data and simulated gradient dynamic activity for the subject, wherein each eigenmode of the set of eigenmodes represents one spatio-temporal component of a system, oscillating at a single fixed frequency, and wherein on a given eigenmode, each gradient has a specific amplitude and phase angle; measuring a cumulative amplitude of each gradient and an average phase angle between each pair of the gradients based on the set of eigenmodes for the subject; comparing the cumulative amplitude of each gradient and the average phase angle between each pair of the gradients to the functional connectivity score for each of the predetermined number of principal structure-function components; and validating or explaining the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and the measure of cognitive impairment based on the comparing.

[0024] In some embodiments, the validating or explaining comprises determining an accuracy of the structure-function model, determining the accuracy is greater than a predetermined threshold, and in response to determining the accuracy is greater than the predetermined threshold, generating the treatment or clinical trial protocol for the subject.

[0025] In some embodiments, the treatment or clinical trial protocol comprises monitoring the subject or administering a monitor of the subject regarding a progress of the cognitive impairment.

[0026] In some embodiments, a system is provided that includes one or more data processors and a non-transitory computer readable storage medium containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform part or all of one or more methods or processes disclosed herein.

[0027] In some embodiments, a non-transitory computer readable storage medium is provided that stores instructions that, when executed by one or more processors of a computing system, cause the computing system to perform part or all of one or more methods disclosed herein.

[0028] The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the disclosure claimed. Thus, it should be understood that although the present disclosure has been specifically disclosed by embodiments and optional features, modification and variationof the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this disclosure as defined by the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present disclosure will be better understood in view of the following non- limiting figures, in which:

[0030] FIG.1 is a block diagram of a system for training and deploying machine learning models capable of making cognitive impairment predictions in accordance with various embodiments.

[0031] FIG.2 is an exemplary flowchart showing a process of generating a treatment or clinical trial protocol for a subject based on sMRI and fMRI data for a brain of the subject in accordance with various embodiments.

[0032] FIG.3 is an exemplary flowchart showing a process of validating or explaining the atrophy score and the functional connectivity score for each of the three principal structure- function components and the measure of cognitive impairment based on a dynamic systems model in accordance with various embodiments.

[0033] FIG.4A is a matrix-pattern graph showing the partial least squares functional connectivity weights for a component in accordance with various embodiments.

[0034] FIG.4B is a violin plot showing PLSR structure component reliability using split- half analysis in accordance with various embodiments.

[0035] FIGS.5A-5B illustrate correlations using three structure-function components across the AD-FTD spectrum in accordance with various embodiments.

[0036] FIGS.6A-6C are boxplots showing statistics regarding functional connectivity edge weights for the bottom / top 1% of edges on each component in accordance with various embodiments.

[0037] FIG.7 shows the atrophy and functional connectivity patterns for each clinical syndrome in accordance with various embodiments.

[0038] FIG.8A is a violin plot showing out-of-sample correlation coefficients between atrophy component scores and ridge regression-derived functional connectivity scores in accordance with various embodiments.

[0039] FIG.8B are three violin plots showing correlation coefficients between ridge regression functional connectivity edge weights derived separately for each cross-validation fold versus partial least square regression-derived weights in accordance with various embodiments.

[0040] FIGS.9A-9B illustrate the correlation of brain structure-function component scores and neuropsychological test scores in accordance with various embodiments.

[0041] FIG.10 are longitudinal relationship effect plots showing the partial relationship of CDR-SB with components in accordance with various embodiments.

[0042] FIGS.11A-11F illustrate low-dimensional gradient activity correlates with structure-function components in accordance with various embodiments.

[0043] FIG.12 is a matrix-pattern graph showing spatial correlations between the PCA spatial components derived from the independent cognitively normal cohort and the main combined patient and control cohort in accordance with various embodiments.

[0044] FIGS.13A-13C illustrate eigenmode derivation and properties in low and high atrophy subjects in accordance with various embodiments.

[0045] FIG.14 illustrates correlations between each subject's actual FC matrix (rows) and the simulated FC matrix in accordance with various embodiments.

[0046] FIG.15 illustrates correlations between observed gradient variance / covariance and coupling parameter-derived gradient amplitude / angles in accordance with various embodiments.

[0047] FIGS.16A-16D illustrate eigenmode relationships with gradient activity and different structure-function components in accordance with various embodiments.

[0048] In the appended figures, similar components and / or features can have the same reference label. Further, various components of the same type can be distinguished by following the reference label by a dash and a second label that distinguishes among the similar components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.DETAILED DESCRIPTION

[0049] The ensuing description provides preferred exemplary embodiments only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the ensuing description of the preferred exemplary embodiments will provide those skilled in the art with an enabling description for implementing various embodiments. It is understood that various changes may be made in the function and arrangement of elements without departing from the spirit and scope as set forth in the appended claims.

[0050] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be understood that the embodiments may be practiced without these specific details. For example, circuits, systems, networks, processes, and other components may be shown as components in block diagram form in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments.

[0051] Also, it is noted that individual embodiments may be described as a process which is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart or diagram may describe the operations as a sequential process, many of the operations may be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed but could have additional steps not included in a figure. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, its termination may correspond to a return of the function to the calling function or the main function. INTRODUCTION

[0052] The brain is one of the most complex organs of human beings that regulate and control our daily activities and enable us to think, reason, and perceive the world. There are about 100 billion neurons in the human brain that process and transmit information throughout the brain and control the cognition of the human. Understanding the relationship between the brain, neurons, and cognition is thus essential to advancing our knowledge of the human mind and improving our ability to predict, diagnose and treat cognitive disorders.

[0053] With the development of technology, people are able to study the structure and functioning of neurons using neuroimaging technology. Some work has been done in researching the relationship between neurons and cognition of patients diagnosed with dementia, the functional patterns of neural activities in the brain, and cognitive impairment. For example, it has been found that cognitive deficits in Alzheimer’s disease (AD) and frontotemporal dementia (FTD) depend on gray matter atrophy in specific brain regions. Also, it is recognized that brain functional connectivity alterations are common in dementia such as AD and FTD, which involves both decreases and increases in connectivity when compared to cognitively unimpaired individuals. However, because of the complexity of neural activities, it is still unclear how structural and functional alterations are related to cognitive impairment and what overlapping or unique contributions they make to cognitive impairment. For example, one challenge that remains unresolved in neuroimaging is how to accurately map patterns of structural degeneration, such as atrophy, that are associated with cognitive impairment, to disruptions in normal brain activity.

[0054] Neuroimaging technology enables the study of the structure and functioning of neurons by providing detailed visualizations and measurements of brain activity and connectivity. Techniques such as fMRI and positron emission tomography (PET) scans allow the observation of neuronal interactions and brain regions in real time, facilitating a deeper understanding of neural processes. However, automated processing and analyzing neuroimaging signals presents significant challenges, primarily due to the sheer volume and complexity of the data involved. Neuroimaging techniques, such as fMRI and PET, generate vast amounts of data that capture brain activity with high temporal and spatial resolution. For example, a clinical MRI scan typically has a resolution ranging from 1 mm to 5 mm per voxel, and ranges from a few megabytes (MB) to several hundred MB in size. High- resolution scans can go down to sub-millimeter resolution, such as 0.5 mm per voxel or finer, and can easily exceed 100 MB or more. For a 10-minute fMRI session, the number of scans can range from approximately 300 to 600, depending on the repetition time (TR) used in the scanning protocol.

[0055] This large data size necessitates robust computational resources and sophisticated algorithms to process and interpret the signals effectively. Moreover, neuroimaging data is often noisy and requires meticulous preprocessing steps, such as motion correction, normalization, and artifact removal, to ensure accuracy and reliability. The intricate nature of brain connectivity and the need to discern subtle patterns amidst the data further complicatethe analysis. Additionally, integrating data across different modalities and subjects adds layers of complexity, necessitating advanced statistical and machine learning techniques to draw meaningful conclusions. Consequently, researchers and clinicians must navigate these challenges to harness the full potential of neuroimaging in understanding brain function and diagnosing neurological conditions.

[0056] To address these challenges and others, techniques described herein are directed to methods and systems to automated processing neuroimaging signals for a brain of a subject, in order to predict a medical condition of the subject, such as cognitive impairment, by capturing a structure-function connectivity relationship with cognitive impairment using machine learning models, and predicting a measure of cognitive impairment based on the structure-function connectivity relationship. The methods and systems may be further used to generate a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment and / or a treatment or clinical trial protocol based on the predicted measure of cognitive impairment. The machine learning models use features from structural neuroimaging signals (e.g., structural magnetic resonance imaging (sMRI) data) and functional neuroimaging signals (e.g., functional magnetic resonance imaging (fMRI) data) and algorithms to map structural patterns in the structural neuroimaging signals to functional patterns (including hypo and hyper-connectivity) in the functional neuroimaging signals. For the convenience of description, as used hereinafter, the term “sMRI data” may be used interchangeably with “structural neuroimaging signals,” and the term “fMRI data” may be used interchangeably with “functional neuroimaging signals.” There are various advantages associated with and achieved by the techniques described herein. First, the disclosed techniques enable an automated processing of complex neuroimaging signals within a relatively shorter time. For example, the whole process from accessing neuroimaging signals to generate a measure of cognitive impairment can be automatically performed within a few minutes to several hours, e.g., about 10 minutes to 5 hours, depending on the specific setup and resources available. For example, high-end Graphics Processing Unit (GPU) or Tensor Processing Unit (TPU) outperforms a CPU (Central Processing Unit). Second, the disclosed techniques enable an accurate cognitive impairment prediction using sMRI data and fMRI data for a brain of a subject. Comparing with the subjective clinical evaluation methods such as neuropsychological testing and screening test, the disclosed techniques provide an objective method to evaluate biological basis of cognitive impairment with improved accuracy and to provide biomarkers forcognitive impairment diagnosis and potential treatments. Third, the disclosed techniques solve the long-term unsolved problem in mapping brain structural atrophy to function connectivity alterations. To achieve the mappability of structure-function connectivity, algorithms such as partial least squares regression (PLSR) can be used to identify principal structure-function components and by using the reduced-dimension algorithms, the computing complexity is decreased, and computing efficiency is achieved. Additionally, the disclosed techniques can be used in early-stage diagnosis and prediction of cognitive impairment, even before an acute development of permanent structural change relating to the cognitive impairment. The early-stage diagnosis and prediction enables treatments that are specific to prevent or slow down the acute development of permanent structural change of the brain. Furthermore, an individual’s structure and function scores can be tracked at multiple timepoints to monitor disease progression, for example in response to a treatment.

[0058] In various embodiments, a computer-implemented method comprises: accessing structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject; inputting the sMRI data and the fMRI data into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of three principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the three principal structure-function components into a cognitive impairment model; and predicting, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the three principal structure- function components and cognitive performance. In some embodiments, the computer- implemented method further comprises generating a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment and / or generating a treatment or clinical trial protocol for the subject based on the atrophy score and the functional connectivity score for each of the three principal structure-function components and the measure of cognitive impairment.

[0059] As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / orcomponents, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0060] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0061] As used herein, the term “functional connectivity” refers to the correlation between neural activities in different brain regions, measured using functional magnetic resonance imaging (fMRI) data. The different brain regions may be predetermined or determined using an algorithm or a machine learning model.

[0062] As used herein, the term “gradient” may refer to spatial patterns of continuous spatial variation in regional brain activity. Latent fMRI BOLD activity dimensions represent dynamic spatial activity gradients. The term “gradient” or “gradient of an oscillator” may refer to the rate of change of its displacement with respect to time or space. Mathematically, the gradient of the oscillator can be described by its velocity, which is the derivative of its displacement with respect to time or space.

[0063] As used herein, the term “neuroimaging signals” refer to data obtained from various neuroimaging techniques used to visualize the structure, function, or pharmacology of the brain. Types of neuroimaging signals include but is not limited to Magnetic Resonance Imaging (MRI) signals (e.g., structural MRI (sMRI), functional MRI (fMRI), diffusion-based MRI), Positron Emission Tomography (PET) signals, Magnetoencephalography (MEG) signals, Computed Tomography (CT) signals, Near-Infrared Spectroscopy (NIRS) signals, Transcranial Electrical Stimulation (TES) signals, photoacoustic imaging signals, and molecular imaging signals.

[0064] As used herein, the terms “substantially,” “approximately” and “about” are defined as being largely but not necessarily wholly what is specified (and include wholly what is specified) as understood by one of ordinary skill in the art. In any disclosed embodiment, the term “substantially,” “approximately,” or “about” may be substituted with “within [a percentage] of” what is specified, where the percentage includes 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, and 90 percent.

[0065] As used herein, when an action is “based on” something or “using” something, it means the action is based at least in part on at least a part of the something.II. NEUROIMAGING OVERVIEW

[0066] Neuroimaging refers to the application of computational techniques for the study of the structure and function of the brain and the central nervous system. It serves as a non- invasive and objective method for scientific research and clinical applications on the human brain and brain diseases. Nowadays, neuroimaging is increasingly being used to study brain diseases and cognitive impairment.

[0067] Neuroimaging is also an important tool for the diagnosis and management of cognitive impairment (e.g., dementia). Several neuroimaging techniques are used to study changes in brain structure and function in people with dementia, including structural magnetic resonance imaging (sMRI) and functional magnetic resonance imaging (fMRI). A. Structural MRI and Its Application in Neurodegenerative Diseases

[0068] Structural magnetic resonance imaging (sMRI) is a non-invasive medical imaging technique that uses a strong magnetic field and radio waves to generate detailed images of the brain's structure. It is widely used in clinical and research settings to study changes in brain structure that occur in various neurodegenerative disease, such as Alzheimer's disease (AD), multiple sclerosis, and schizophrenia. By providing high-resolution images of the brain's anatomy, sMRI has been used to identify changes in brain structure in people with dementia, including atrophy (shrinkage) of the hippocampus and other brain regions and helped clinicians and researchers better understand the underlying causes of these disorders and develop more effective treatments.

[0069] For example, sMRI studies have shown that AD patients have significant hippocampal atrophy, which is associated with memory impairment. In multiple sclerosis, sMRI can detect changes in the brain's white matter that are associated with cognitive impairment. sMRI has also been used to study structural changes in the brains of individuals with schizophrenia, with studies suggesting that the disorder is associated with reduced gray matter volume in certain regions of the brain.

[0070] Although sMRI can be a powerful tool for studying the relationship between brain structure and cognitive impairment, there are limitations and problems with using sMRI to diagnose cognitive impairment. First, the finding using sMRI lacks specificity. For example, brain atrophy can be caused by normal aging or by other medical conditions such as stroke or brain tumors. It is not always a specific index relating to cognitive impairment. Secondly, asdiscussed above, sMRI is not sensitive enough to detect early changes in brain structure associated with cognitive impairment. For example, in the context of neurodegenerative disorders such as Alzheimer's disease, where brain changes can begin many years before clinical symptoms appear. Additionally, brain structure varies across individuals and so it is difficult to establish “normal” or “abnormal” brain structure. There is also the variability in the location and extent of brain damage or atrophy, which may affect cognitive function in different ways. B. Functional MRI and Its Application in Neurodegenerative Diseases

[0071] Functional Magnetic Resonance Imaging (fMRI) measures changes in blood flow in the brain, providing information about brain and neural activities. It is widely used in both research and clinical settings to investigate how the brain processes information and to study changes in brain and neural activities associated with various neurodegenerative diseases. There are different types of fMRI that are widely used in the field of neuroscience. For examples, in task-based fMRI studies, brain activities are measured when participants are asked to perform specific tasks. In contrast, in task-free fMRI studies, activities in different brain regions and patterns of functional connectivity between these regions are measured while participants are asked to remain still without performing a specific task (i.e., stay awake in a resting state). By identifying which regions of the brain are active during specific tasks, in response to stimuli, or in the resting state, fMRI can help researchers and clinicians better understand how the brain works and develop more effective treatments for the neurodegenerative diseases. Additionally, fMRI can be used to study the activity of different brain regions in real time to understand the neural basis of cognitive processes such as attention, memory, and decision-making.

[0072] When a particular region of the brain becomes active, it requires more oxygenated blood to fuel its increased metabolic demand. The resulting increased blood flow to that region causes a small but detectable change in the local magnetic field, which can be measured using specialized MRI machine. To perform an fMRI scan, the individual lies down in the specialized MRI machine, which uses a strong magnetic field and radio waves to create images of the brain. During the scan, the individual is asked to perform a specific task (such as viewing images or performing a memory test), is presented with a specific stimulus (such as an auditory or visual cue), or is asked to remain still in a resting state with eyesclosed or open (may be referred as a “resting” task). The MRI machine then captures images of the brain at various time points, typically over a period of several minutes.

[0073] The fMRI images are then analyzed to identify regions of the brain that show increased blood flow or oxygenation during the task or stimulus. These regions are considered to be active and are thought to be involved in processing the information associated with the task or stimulus. Studies have shown that neurodegenerative diseases are associated with changes in functional connectivity between brain regions and changes in the activation of specific brain networks. Research has also shown that the patterns of fMRI brain activity are altered in different ways in different types of cognitive impairment, for example, patients of Alzheimer’s disease show changes in the hippocampus and in the parietal lobe, while frontotemporal dementia patients are more affected in the frontal lobe and in the temporal lobe.

[0074] Although it is promising in identifying changes in brain function associated with neurodegenerative diseases using fMRI, the research is still limited by multiple reasons. One challenge is the complexity of data. Because fMRI data is like a movie in which the oxygen consumption of each region changes over time and tremendous data is collected as a time series. For example, if 100,000 voxels and 60 fMRI images are captured per minute, then studying the temporal correlation between different brain regions using traditional methods could be computationally demanding. Another challenge is that fMRI measures changes in brain activities but does not directly measure the underlying pathology of the disease. The fMRI also may not reflect structural changes in the brain. Additionally, the interpretation of fMRI data requires specialized expertise and may be subject to variability across different researchers or clinicians. C. Other Molecular Imaging Modalities and Their Applications in Neurodegenerative Diseases

[0075] Other molecular imaging modalities, such as positron emission tomography (PET), single-photon emission computed tomography (SPECT), diffusion magnetic resonance imaging (dMRI), and computed tomography (CT), can also be used to visualize and track molecular and cellular events in the body. For example, dMRI can be informative with regard to the structural connectivity of the brain and to understand how different brain regions communicate with each other. It can be used to diagnose and monitor neurological conditions, such as neurodegenerative diseases. PET, which measures physiological functionby looking at blood flow, metabolism, and / or neurotransmitters, can be also useful in monitoring brain activities and diagnosing neurodegenerative diseases.

[0076] Similar to the sMRI and fMRI techniques, these molecular imaging modalities have their limitations in providing objective and accurate disease diagnosis. They may have limited abilities to detect and distinguish small structures and interpretation of changes may also be challenging by merely reviewing the resulting images. D. Cognitive Screening and Assessment

[0077] Cognitive screening tests are a widely used clinical tool to evaluate a person's cognitive abilities without the use of neuroimaging techniques. The cognitive screening tests have to be administered by healthcare providers or other trained professionals. Commonly used cognitive screening tests include Mini-Mental State Examination (MMSE), Montreal Cognitive Assessment (MoCA), and Clinical Dementia Rating (CDR). Sometimes the Stroop test is also used to evaluate the severity of a patient’s cognitive impairment.

[0078] MMSE, also known as “Mini,” is a standardized test used to assess cognitive impairment and dementia, especially sensitive for Alzheimer’s disease. It evaluates various cognitive domains such as orientation, attention, memory, language, and visuospatial skills, with a maximum score of 30 points. A score of 24 or lower may be indicative of cognitive impairment. MOCA is a more comprehensive test than the MMSE, which includes additional cognitive domains such as visuospatial and executive functioning. MOCA may be more sensitive than MMSE in detecting mild cognitive impairment and early dementia.

[0079] CDR is a clinical tool used to stage the severity of dementia that is said to be more comprehensive than other cognitive screening tools . It is based on a structured interview with the patient and their caregiver and evaluates cognitive and functional performance in several domains. The scores may range from 0 (no dementia) to 3 (severe dementia). CDR may also be used to guide treatment and care decisions for individuals with dementia. Stroop is a neuropsychological test that evaluates an individual's ability to inhibit cognitive interference. It involves naming the ink color of a word while ignoring the word itself, which is either congruent (matching color and word) or incongruent (mismatched color and word). The Stroop test measures executive functioning, attention, and processing speed, and is usually used in conjunction with other assessment tools and clinical evaluations to make accurate diagnoses and guide treatment decisions.

[0080] Like sMRI and fMRI techniques, cognitive screening tests such as MMSE and CDR have limitations when it comes to diagnosing dementia. First, cognitive screening tests can easily produce false positive results, meaning that an individual may score poorly on the test but not actually have dementia. Also, cognitive screening tests only assess specific cognitive domains, such as memory, attention, and language, and may not be able to detect cognitive deficits in other areas such as behavior and personality. Additionally, cognitive screening tests may not be sensitive enough to detect early stages of dementia or mild cognitive impairment, which can delay diagnosis and treatment. Moreover, cognitive screening tests are sometimes subjectively dependent on the professionals who administer the tests. The training and expertise of the professionals may adversely affect the accuracy of the test results. III. COGNITIVE IMPAIRMENT MACHINE LEARNING PIPELINE

[0081] The disclosed techniques overcome the problem associated with the status quo of using neuroimaging techniques and cognitive screening tests to evaluate cognitive impairment. More specifically, the present disclosure is directed to systems and methods of predicting cognitive impairment using sMRI and fMRI data and machine learning models. The techniques provide an objective assessment of cognitive impairment using objective data and principal component analysis that substantially reduces the computational complexity and increase a prediction accuracy. In various embodiments, the disclosed techniques can be performed in a cognitive impairment machine learning pipeline.

[0082] One or more embodiments described herein can be implemented using operative, actionable, or programmatic systems, subsystems, modules, blocks, or components. An operative or actionable system, subsystem, module, block, or component can include in silico operations or actions that can be performed by an operator (e.g., a researcher or a practitioner) using a machine (e.g., a computing device, an MRI machine) or automatically triggered by the machine or an algorithm stored in the machine. A programmatic system, subsystem, module, block, or component can include a program, a sub-routine, a portion of a program, or a software component or a hardware component capable of performing one or more stated tasks or functions. As used herein, a system, subsystem, module, block, or component can exist on a hardware component independently of other systems, subsystems, modules, blocks, or components. Alternatively, a system, subsystem, module, block, or component can be a shared element or process of other systems, subsystems, modules, blocks, or components.A. System Overview

[0083] FIG.1 is a block diagram of a system 100 for training and deploying machine learning models capable of making cognitive impairment predictions in accordance with various embodiments. The system 100 may be a cognitive impairment machine learning pipeline that comprises a data accessing subsystem 110, a modeling subsystem 120, a reporting subsystem 130, and an interactive subsystem 140. The system and subsystems, modules, blocks, or components (e.g., program, code, or instructions) illustrated in FIG.1 may be executable by an operator, a machine (e.g., a computing device), one or more processors, or any combination thereof according to various embodiments. The system 100 or part thereof (e.g., the modeling subsystem 120, the reporting subsystem 130, and / or the interactive subsystem 140) can be performed using one or more GPUs and / or TPUs.

[0084] The data accessing subsystem 110 executes the function of data gathering, data obtaining, data pre-processing, and / or data providing. One or more blocks, modules, or services may be comprised by the data accessing subsystem 110. As shown in FIG.1, a data accessing subsystem 110 may comprise a data acquisition module 112, an MRI database module 114, and / or a pre-processing block 116.

[0085] In the data acquisition module 112, structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject are acquired. The sMRI and fMRI data may be acquired using a specialized MRI machine / scanner. The sMRI and fMRI data are multi-dimensional data. In some instances, the multi-dimensional data are stored as multi-dimensional matrices. The size of matrices may vary and depend on factors such as the specialized MRI machine / scanner, software prerequisites, acquisition methods, a field of view, and image resolutions. A standard two- dimensional (2-D) sMRI matrix may be a size of 240 x 240, resulting in a total of 57,600 pixels per image. A standard three-dimensional (3-D) sMRI matrix may be a size of 160 x 240 x 256, resulting in a total of 9,830,400 pixels per image. A standard 2-D fMRI matrix may be a size of 92 x 92, resulting in a total of 8,468 pixels per slice. Because fMRI data are taken for a period of time, with each time hundreds of slices, the final data collected is big data. In some instances, demographic data including a medical record of the subject may also be acquired in the data acquisition module 112. The medical record may comprise demographic data (e.g., name, date of birth, sex) and medical history (e.g., diagnoses, treatment plan, medications, and clinical testing results). In some instances, other molecularimaging data (e.g., PET data or dMRI data) is acquired in the data acquisition module 112. The other molecular imaging data may be used in auxiliary with the sMRI and fMRI data in subsequent analyses or may substitute the sMRI and fMRI data in the subsequent analyses.

[0086] In the MRI database module 114, structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject are stored and can be obtained. The sMRI and fMRI data may be pre-acquired using the data acquisition module 112 or acquired from another database. In some instances, demographic data including a medical record of the subject may also be obtained in the MRI database module 114. The medical record may comprise demographic data (e.g., name, date of birth, sex) and medical history (e.g., diagnoses, treatment plan, medications, and clinical testing results). In some instances, the MRI database module 114 stores other molecular imaging data. The other molecular imaging data may be used in auxiliary with the sMRI and fMRI data in subsequent analyses or may substitute the sMRI and fMRI data in the subsequent analyses.

[0087] At the pre-processing block 116, acquired or obtained sMRI and fMRI data is pre- processed. In some instances, the pre-processing comprises filtering and may be conducted by a trained technician. For example, MPRAGE (Magnetization Prepared RApid Gradient Echo) scans can be visually assessed by trained technicians, and scans with excessive motion artifact (ringing or blurring) are filtered out and excluded from further processes. In some instances, the pre-processing comprises regularization and normalization using a computing device. For example, the MPRAGE scans that passed quality control are pre-processed for warping regularization and bias regularization using default parameters or predetermined parameters, and then unified normalization / segmentation are applied to each scan based on a predetermined standard / procedure. In some instances, the pre-processing comprises correcting for intensity uniformity and is conducted using a software. In some instances, the pre-processing comprises segmenting cerebrospinal fluid (CSF), white-matter (WM) and gray-matter (GM).

[0088] The modeling subsystem 120 executes the function of model training and / or model execution. One or more blocks, modules, or services may be comprised by the modeling subsystem 120. As shown in FIG.1, a modeling subsystem 120 may comprise data 121, an optional model training block 122, one or more trained structure-function model 123, a structure-function model block 124, one or more trained cognitive impairment model 125, acognitive impairment model block 126, one or more trained dynamic systems model 127, and / or an optional dynamic systems model block 128.

[0089] The data 121 comprises structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject. The data 121 may be accessed using the data acquisition module 112 or the MRI database module 114, and be further pre-processed using the pre-processing block 116, as shown in FIG.1. The data 121 may be used to predict a measure of cognitive impairment for the subject and generate a treatment or clinical trial protocol for the subject. In some instances, the data 121 comprises W-scores that measures gray matter atrophy within the brain and functional connectivity patterns across multiple regions of the brain.

[0090] At the optional model training block 122, models are trained for predicting measures of cognitive impairment and / or for validating or explaining the predicted measures. Input data for the optional model training block 122 may be data accessed using the data accessing subsystem 110. Input data may be grouped based on imaging modalities (e.g., sMRI or fMRI). In some instances, specific patterns of gray matter atrophy are learned using sMRI data and a machine learning model, specific patterns of functional connectivity alterations are learned using the fMRI data using the same or a different machine learning model, and a linkage of specific patterns of gray matter atrophy and the specific patterns of functional connectivity alterations is learning using the same or third machine learning model. In some instances, one or more structure-function model is trained to link specific patterns of gray matter atrophy to specific patterns of functional connectivity alteration using the input data. In some instances, the input data is further categorized based on a measure of cognitive impairment for the subject from whom the input data are accessed. One or more cognitive impairment model may be trained based on the input data and their corresponding measures of cognitive impairment.

[0091] One or more specific type of models may be designated at the optional model training block 122. In some instances, a principal component analysis (PCA) model is designated as the structure-function model. Eigenvectors and eigenvalues are calculated and sorted using the input data and a number of principal components (PCs) is chosen. In some instances, the number of PCs is predetermined. In some instances, the number of PCs is determined based on a predetermined rule or a scree plot. In some instances, a least number of PCs are chosen that can explain at least a percentage of variance. In some instances, thepercentage is at least about 50%, 60%, 70%, 80%, or 90%. PCA models are advantageous for dimensionality reduction and feature selection, and they also provide noise reduction and computational efficiency.

[0092] In some instances, a partial least squares regression (PLSR) model is designated as the structure-function model. PLSR models use predictor variables to correlate with response variables using components. In some instances, parameters of the PLSR model such as a number of components and a type of regression are pre-determined. PLSR models can effectively handle high-dimensional data and identify and select the most important variables for prediction. They also outperform traditional regression models by taking into account the relationship between the predictor variables and the response variables. Additionally, PLSR models produce interpretable components that can be used to understand the underlying structure of the data. The components can also be visualized and analyzed to gain insights into the relationships between the predictor variables and the response variable.

[0093] In some instances, an artificial neural network (ANN) model is designated as the structure-function model. An architecture of the ANN model may be predetermined, and an optimization algorithm may be chosen to train the ANN model. ANN models can capture nonlinear relationship and are robust to noise and missing data. In some instances, PCA models or ANN models may be designated as the cognitive impairment model or the dynamic systems model. Other models may also be designated, such as a generalized additive model.

[0094] In some instances, more than one type of models is designated as the structure- function model. For example, a first type of models is designated to determine the structure components, and a second type of models is designated to link the structure component with associated functional connectivity alterations (e.g., function components). In some instances, one type of models (e.g., a PLSR model) is capable of determining the joint structure- function components.

[0095] The training at the optional model training block 122 can be supervised or unsupervised. The input data may also be split into training, validation, and test sets. The trained models may be further tested, evaluated, and adjusted using appropriate methods or algorithms. The trained structure-function model may be output and used at the structure- function model block 124, the trained cognitive impairment model may be output and used at the cognitive impairment model block 126, and the trained dynamic systems model may be output and used at the optional dynamic systems model block 128.

[0096] At the structure-function model block 124, a model is used to determine a structure- function relationship using the data 121. In some instances, the model used at the structure- function model block 124 is the one or more trained structure-function model 123 output by the optional model training block 122. In some instances, the model is a PCA model, a PLSR model, or an ANN model (e.g., an CNN model).

[0097] The structure-function relationship may be defined using scores from the PCA model. In some instances, scores for a number of PCs are determined at the structure-function model block 124. For example, an atrophy score and a functional connectivity score are determined for each of three PCs of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations. In some instances, a partial least squares regression (PLSR) algorithm is used to determine the PCs. In some instances, three structure PCs are determined using the PCA model and linked to specific functional connectivity alterations using ridge regression. The three PCs may capture a relationship between global atrophy and a distributed functional connectivity pattern of decreases and increases, opposing focal atrophy patterns in the left-predominant temporal pole versus right-predominant dorsal parietal cortex, and opposing focal atrophy patterns in left-predominant temporal-occipital lobe versus prefrontal-insula-cingulate areas. The PCs and / or the PC scores may be output to be used in a cognitive impairment model.

[0098] At the cognitive impairment model block 126, a model is used to determine a measure of cognitive impairment for the subject based on output of the structure-function model block 124. In some instances, the measure is a predicted score of a cognitive screening test, for example, an MMSE score or a CDR score. In some instances, other measures such as covariance, linearity, a percentage of variance are also determined at the cognitive impairment model block 126. In some instances, the model used at the cognitive impairment model block 126 is the one or more trained cognitive impairment model 125 output by the optional model training block 122.

[0099] At the optional dynamic systems model block 128, a model is used to validate or explain the structure-function relationship determined at the structure-function model block 124 and / or the measure of cognitive impairment determined at the cognitive impairment model block 126. The model may use a system of linear coupled harmonic oscillators. In some instances, a data-driven predictive model like an ANN may be used. In some instances,the model used at the optional dynamic systems model block 128 is the one or more trained dynamic systems model 127 output by the optional model training block 122.

[0100] A set of eigenmodes for the subject based on the fMRI data in the data 121 and simulated gradient dynamic activity for the subject are determined at the optional dynamic systems model block 128. In some instances, each eigenmode of the set of eigenmodes represents one spatio-temporal component of a system, oscillating at a single fixed frequency. The atrophy score and the functional connectivity score for each of the PCs determined at the structure-function model block 124 and the measure of cognitive impairment determined at the cognitive impairment model block 126 may be validated or explained based on the set of eigenmodes. In some instances, an accuracy of the structure-function model used at the structure-function model block 124 is determined at the optional dynamic systems model block 128 based on the set of eigenmodes.

[0101] The reporting subsystem 130 executes the function of generating visualization of cognitive impairment results, generating treatments or clinical trial protocols, reporting, and / or storing. One or more blocks, modules, or services may be comprised by the reporting subsystem 130. As shown in FIG.1, a reporting subsystem 130 may comprise a report block 132.

[0102] At the report block 132, a treatment or clinical trial protocol for the subject is be generated. The generation of the treatment or clinical trial protocol may be based on the atrophy score and the functional connectivity score for each of the PCs determined at the structure-function model block 124 and / or the measure of cognitive impairment determined at the cognitive impairment model block 126. A report regarding the treatment or clinical trial protocol for the subject may also be generated at the report block 132. The report may further comprise the validation / explanation information, including the accuracy of the structure- function model used at the structure-function model block 124, determined at the optional dynamic systems model block 128. In some instances, the report is stored at the report block 132 and output to the interactive subsystem 140.

[0103] In some instances, the generation of the treatment or clinical trial protocol comprises stratifying the subject based on the atrophy score and the functional connectivity score for each of the PCs determined at the structure-function model block 124 and / or the measure of cognitive impairment determined at the cognitive impairment model block 126. In some instances, the stratifying is a two-dimensional decision-making process and comprisesgenerating a matrix-pattern graph corresponding to weights associated with the atrophy score and the functional connectivity score for each of the PCs. In some instances, the matrix- pattern graph may be generated independently and may be reported to a user as part of a diagnostic report.

[0104] In some instances, the generation of the treatment or clinical trial protocol further comprises determining an expected response of the subject to a therapeutic agent based on the atrophy score and the functional connectivity score for each of the PCs determined at the structure-function model block 124, the measure of cognitive impairment determined at the cognitive impairment model block 126, and / or the matrix-pattern graph. In some instances, the matrix-pattern graph of the subject is compared with a matrix-pattern graph of the subject prior to a treatment with a therapeutic agent, and the treatment or clinical trial protocol for the subject or the report may be updated based on the comparison.

[0105] In some instances, a report, an analysis report, or a diagnostic report is generated at the report block 132. The report may comprise the measure of cognitive impairment determined at the cognitive impairment model block 126, a matrix-pattern graph (e.g., showing spatial correlations between the PCA spatial components or function connectivity weights), and / or a projected brain scan showing impaired areas (e.g., based on gradient spatial weights) or atrophy pattern. In some instances, the report is generated as part of the treatment or clinical trial protocol.

[0106] The interactive subsystem 140 executes the function of rendering visualization and / or downstream application. One or more blocks, modules, or services may be comprised by the interactive subsystem 140. As shown in FIG.1, an interactive subsystem 140 may comprise a visualization block 142 and a downstream application block 144.

[0107] At the visualization block 142, the treatment or clinical trial protocol for the subject or the report generated at the report block 132 is rendered to a user in a graphical user interface (GUI). In some instances, the matrix-pattern graph of the subject is also rendered. The treatment or clinical trial protocol for the subject, the matrix-pattern graph, and / or the report may be rendered in one single interface or multiple interfaces. The user may interact to acquire desired information using the GUI. The user may choose to visualize one or more of the treatment or clinical trial protocol for the subject, the matrix-pattern graph, and the report. The user may choose to visualize multiple treatments or clinical trial protocols, matrix- pattern graphs, and reports for multiple subjects. An electronic device may be used tovisualize the GUI. The electronic device may be a monitor, a computing device, or a device using augmented reality techniques.

[0108] At the downstream application block 144, information acquired from the reporting subsystem 130 and the visualization block 142 may be used in downstream applications. For example, the atrophy score and the functional connectivity score for the subject are used to generate a correlation plot, an atrophy pattern is generated to reflect the atrophy score, and relationships between the treatment or clinical trial protocol and the matrix-pattern graph are also generated. The downstream applications may also be rendered in the GUI at the visualization block 142 to provide further information to the used of the GUI.

[0109] FIG.2 is an exemplary flowchart showing a process 200 of generating a treatment or clinical trial protocol for a subject based on sMRI and fMRI data for a brain of the subject in accordance with various embodiments. In certain embodiments, the processing or a portion of the processing depicted in FIG.2 may be performed by system 100 as described with respect to FIG.1. Process 200 begins at block 210, where sMRI and fMRI data for a brain of a subject is accessed. The subject may be diagnosed with cognitive impairment using clinical methods such as cognitive screening tests, PET scans, and / or biological tests, or may be a person suspected to have a cognitive impairment. Details regarding sMRI and fMRI data access are illustrated in subsection C. In some instances, other molecular imaging data (e.g., PET data or dMRI data) is accessed at block 210. The other molecular imaging data may be used in auxiliary with the sMRI and fMRI data in subsequent analyses or may substitute the sMRI and fMRI data in the subsequent analyses. The process 200 is preferred to be performed using a GPU or a TPU.

[0110] At block 220, the sMRI and the fMRI data are input into a structure-function model. The structure-function model may be a PLSR- or PCA-based model and capable of providing a number of biomarkers, which comprise principal structure-function components. The biomarkers have a measurable biological characteristic that can be used to determine a presence or a progression of a cognitive impairment. The biomarkers may be associated with different brain regions. The measurements (e.g., atrophy scores and / or functional connectivity scores) of the biomarkers may also be fed into a machine learning model for cognitive impairment prediction. In some embodiments, the number of biomarkers (e.g., principal structure-function components) is predetermined (e.g., three), and the three biomarkers or principal structure-function components capture a relationship between global atrophy and adistributed functional connectivity pattern of decreases and increases, opposing focal atrophy patterns in the left-predominant temporal pole versus right-predominant dorsal parietal cortex, and opposing focal atrophy patterns in left-predominant temporal-occipital lobe versus prefrontal-insula-cingulate areas. As used herein, the term “biomarker” may be used interchangeably with the term “principal structure-function component.”

[0111] At block 230, an atrophy score and a functional connectivity score for each of three principal structure-function components of the structure-function model are determined. In some embodiments, the atrophy scores are determined using the sMRI data and the functional connectivity scores are determined using the fMRI data. Details regarding the atrophy score and the functional connectivity score determination are illustrated in subsection D.

[0112] At block 240, the atrophy score and the functional connectivity score for each of the three principal structure-function components are input into a cognitive impairment model. The cognitive impairment model may be a trained generalized additive model and capable of providing a measure of cognitive impairment based on the atrophy scores and the functional connectivity scores.

[0113] At block 250, a measure of cognitive impairment for the subject is predicted using the cognitive impairment model based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the three principal structure-function components and / or cognitive performance. The measure may be a predicted cognitive screening test score. Details regarding the measure of cognitive impairment determination is illustrated in subsection E.

[0114] At block 260, a treatment or clinical trial protocol for the subject is generated based on the atrophy score and the functional connectivity score for each of the three principal structure-function components and / or the measure of cognitive impairment. Further details are illustrated in subsection E.

[0115] FIG.3 is an exemplary flowchart showing a process 300 of validating or explaining the atrophy score and the functional connectivity score for each of the three principal structure-function components and the measure of cognitive impairment based on a dynamic systems model in accordance with various embodiments. In certain embodiments, the processing or a portion of the processing depicted in FIG.3 may be performed by system 100 as described with respect to FIG.1. The the processing or a portion of the processing depictedin FIG.3 may be optionally performed based on the process 200 depicted in FIG.2. Details regarding process 300 are further illustrated in subsection F.

[0116] Process 300 begins at block 310, where the fMRI data for the brain of the subject is input into a dynamic systems model. A system of linear coupled harmonic oscillators may be used to generate the dynamic system model. In some instances, other molecular imaging data (e.g., PET data or dMRI data) is input into a dynamic systems model at block 310. The other molecular imaging data may be used in auxiliary with the fMRI data in subsequent analyses or may substitute the fMRI data in the subsequent analyses.

[0117] At block 320, a set of eigenmodes for the subject based on the fMRI data and simulated gradient dynamic activity for the subject are determined using the dynamic systems model. Each eigenmode may represent one spatio-temporal component of the system of linear coupled harmonic oscillators, oscillating at a single fixed frequency. Each gradient of the eigenmode may have a specific phase angle and amplitude. In some embodiments, six gradients are simulated for each eigenmode. In some embodiments, the dynamic systems model is trained using groups of subjects with similar atrophy scores or other groupings based on other target metrics, for example from molecular imaging (e.g., ultrasound, MRI, CT, PET). The target metrics such as atrophy scores are sorted for a given component (e.g., from lowest to highest), and subjects then are sequentially ordered based on the sorting to determine similarity for the grouping.

[0118] At block 330, a cumulative amplitude of each gradient and an average phase angle between each pair of the gradients are measured based on the set of eigenmodes for the subject. In some embodiments, a correlation between the cumulative amplitude of each gradient or the average phase angle between each pair of the gradients and the gradient variance or covariance is also determined.

[0119] At block 340, the cumulative amplitude of each gradient and the average phase angle between each pair of the gradients are compared to the functional connectivity score from each subject for each of the three principal structure-function components. In various embodiments, it is found that an atrophy-associated functional connectivity alteration could be linked to a specific gradient amplitude or phase angle change.

[0120] At block 350, the atrophy score and the functional connectivity score for each of the three principal structure-function components and / or the measure of cognitive impairment arevalidated or explained based on the comparison. In some instances, the comparison is to be used independently to determine the measure of cognitive impairment. B. Pipeline Preparation / Model Training Processes

[0121] The disclosed techniques are directed to pipelines, methods and systems of using sMRI data, fMRI data, and machine learning models to predict a measure of cognitive impairment of a subject and to generate a treatment plan or clinical trial protocol for the subject. The machine learning models may be trained using historical sMRI and fMRI data, and then packed for use in the pipelines, methods, and systems. The training of the machine learning models is preferred to be performed using a GPU or a TPU.

[0122] A primary purpose of machine learning model training processes is to ensure that the machine learning model can learn better from input data and make more accurate predictions or decisions based on the input data, comparing with using a preset model with determined parameters. The training processes also allows the model to make accurate predictions or decisions on new data, which can be used in downstream applications and improve the efficiency and accuracy of the downstream applications. Different types of machine learning models, including but not limited to supervised learning, unsupervised learning, and reinforcement learning can be used for the training processes. In some embodiments, a machine learning model is trained to select an optimal type and / or algorithm, or a set of hyperparameters of machine learning models. Once a model is trained, it can be deployed to make predictions or decisions in real-time, which leads to significant improvements in efficiency, accuracy, and decision-making in a variety of fields and downstream applications.

[0123] Once input data is obtained and a specific machine learning model is set to be trained, the input data is run on the machine learning model and an optimal set of parameters of the machine learning model are determined. The optimal set of parameters may be determined based on a loss function, a preset number of runs, or a preset hyperparameter. The optimal set of parameters may be further optimized by adjusting hyperparameters or improve the quality of input data. In some embodiments, separate machine learning models are trained for different purposes and / or parameters, and an ensemble of trained models is provided to and used in the cognitive impairment machine learning pipeline for making predictions and decisions.(i) Structure-Function Model

[0124] A structure-function model is trained for capturing structure-function relationships in a brain using sMRI and fMRI data. As brain activity is distributed across different discrete regions, in various embodiments, a brain image (sMRI or fMRI) is analyzed based on a number of cortical and subcortical regions. In some embodiments, an analysis is based on 246 cortical and subcortical regions.

[0125] Training data are sMRI scans and fMRI scans from patient and control groups. Demographic data other than sMRI and fMRI may also be collected from the training subjects, for example, age, sex, education, and / or race / ethnicity. A cognitive screening testing score for each patient is also collected. In some embodiments, environmental factors such as MRI scanner types (e.g., Trio or Prisma) and fMRI head motions are also collected. To establish a comparison and following the standard scoring system, all subjects in the control group have a score of 0 in all cognitive screening tests, although not all prospective subjects with a 0 in all tests may be included based on other criteria such as presence of other disease or other demographic factors. In some embodiments, the patient group comprises more than one type of patients. For example, subjects with FTD and subjects with AD can be grouped together to train the structure-function model. The training data may come from an MRI dataset, an MRI library, clinical records, or subjects who are recruited through ongoing studies. The training data may be pre-processed before the training.

[0126] In various embodiments, a W-score for each region is determined using the sMRI data. The W-score measures the gray matter atrophy. In some embodiments, the W-score is a relative measurement with respect to a reference population. In some embodiments, the reference population is a control group. In some embodiments, the reference population is a group with respect to a geographic location, a predetermined age or age range, or a group with a predetermined number of subjects. In some embodiments, the predetermined number is a number of at least 10, 100, 1,000, 10,000, or 100,000. In some embodiments, the W- scores are normalized based on a total volume of a brain or a total volume of gray matter in the brain. Normalization may be based on other measurements that are used in the art. In some embodiments, a voxel W-score is determined for estimating a gray matter volume in each voxel.

[0127] In various embodiments, a functional connectivity (FC) score for each pair of regions is determined using the fMRI data. For example, if there are 246 different regions,then 30,135 FC scores are determined (246 x 245 / 2 = 30,135). In some embodiments, a FC score is be determined for multiple regions. In some embodiments, region timeseries (i.e., signals that are measured at each voxel across an entire run) are first normalized per voxel across time per subject to obtain the FC scores.

[0128] Functional connectivity is a measure of the temporal correlation between different regions of the brain. A variety of methods for calculating FC scores could be used, including: (i) correlation-based methods that calculate a pairwise correlation between time series of two brain regions; (ii) graph theory-based methods that construct a graph of a brain network, wherein nodes represent brain regions and edges represent the FC between them so that degree centrality or clustering coefficient can be used to summarize the FC scores; and (iii) machine learning-based methods that involve training a machine learning algorithm to estimate the FC scores between two brain regions based on their time series. The correlation- based methods to calculate the FC scores can use a statistical association of two regions with regard to times, for example, a correlation, a covariance, or mutual information.

[0129] A structure-function model can be trained based on the W-scores and the FC scores to provide principal structure-function components. In some embodiments, the structure- function model is a partial least squares regression (PLSR) model. PLSR models can be used to maximally covary two sets of variables and derive a number of components. The first several components may be determined to sufficient reliability to be used as principal structure-function components. PLSR models can efficiently identify a small set of latent variables (i.e., components) that capture information in predictor variables and their relationship with response variables. These components are used to build a predictive model that can be used to make predictions for new observations. In some embodiments, the first three components are used as the principal structure-function components. In some embodiments, the structure-function model is a principal component analysis (PCA) model. In some embodiments, the structure-function model is an ANN model.

[0130] The training process may also comprise a validating process and / or a testing process. For example, the training data is be split into five subsets. In each training cycle, four subsets are used as the training data and one subset as the validation data. Five models may be trained separately and the model with the best performance on the validation data may be chosen as the structure-function model. In some embodiments, an algorithm used bythe validating process is a ridge regression. The ridge regression is advantageous by shrinking coefficient weights, thereby reducing variances coming from redundant predictor variables.

[0131] In some embodiments, the structure-function model uses algorithms including PLSR to identify three principal structure-function components. A first principal structure- function component captures a relationship between global atrophy and a distributed functional connectivity pattern of decreases and increases. A second and a third principal structure-function components captured syndrome-specific atrophy patterns. Each of the components has a structure and function piece to them. Thus, the training outputs 6 structural and functional scores for each set of MRI scans for a subject. The 6 scores put the subject on a spectrum and relationships between the scores, spectrum, and cognitive impairment can be determined. Consequently, the 6 scores for the subject can be used to better understand the cognitive impairment of the subject and used to drive treatment / clinical trials downstream. (ii) Cognitive Impairment Model

[0132] A cognitive impairment model is trained for capturing a relationship with a measure of cognitive impairment of a subject with the structure-function relationships in the brain of the subject. In various embodiments, the cognitive impairment model is trained using the principal structure-function components to predict a measure of cognitive impairment of a subject. In some embodiments, the demographic data (e.g., age, sex, education, and / or race / ethnicity) and the environment factors are also used to train the cognitive impairment model.

[0133] In various embodiments, the cognitive impairment model is a generalized additive model. Generalized additive models use smooth functions to predict a relationship. They advance in handling nonlinear relationships and other complex structures that are difficult to capture with traditional linear models. They also advance in allowing for interpretation of the relationships between response and predictor variables. In some instances, hyperparameters of the cognitive impairment model are predetermined. For example, each smooth function can be limited to have a non-linear basis no greater than 3, reducing the risk of overfitting.

[0134] The training process of the cognitive impairment model may take a similar process as that of the structure-function model. In some instances, only data of patients are used in the training process. In some instances, the cognitive impairment model is trained on a cognitive screening test basis and different cognitive impairment models are be trained for predicting a measure of cognitive impairment based on different cognitive screening tests. In someinstances, a unified cognitive impairment model is trained that is suitable for predicting a measure of cognitive impairment of multiple cognitive screening tests.

[0135] Practically, the 6 scores generated by the structure-function model and their statistical interactions can be correlated using the cognitive impairment model with a measure of cognitive impairment such as a CDR score and predict a measure of cognitive impairment for a subject. The predicted measure of cognitive impairment may be used to determine whether the subject is getting better or worse with treatment, or whether they would be a good or poor candidate for a clinical trial.

[0136] Alternatively, the 6 scores could be used by themselves to drive treatments or downstream decisions. Because functional impairment is believed to be more recoverable from that of structure, and a subject with more functional damage may be a better candidate for a clinical trial as opposed to a subject with a lot of atrophy. Moreover, functional impairment may be observed earlier than physical, and thus treatment may be started earlier to reduce or prevent further impairment.

[0137] A dynamic systems model is trained for validating or explaining relationships of the structure-function relationships in the brain and the measure of cognitive impairment. The dynamic systems model can explain causal relationships. The dynamic systems model can also simulate gradient dynamic activities in different groups of subjects.

[0138] In various embodiments, the dynamic systems model is modeling a system of linear coupled harmonic oscillators. Other similar systems can also be modeled by the dynamic systems model.

[0139] In a dynamic systems model with a system of linear coupled harmonic oscillators, linear regression is used to measure the coupling strength of spatial gradients. In some instances, the number of the gradients is six. In some instances, the number of gradients can also be trained during the training of the dynamic systems model.

[0140] The dynamic systems model can be trained to perform gradient timeseries simulations using the gradients from a given subject or group of subjects. A larger number of timepoints (e.g., > 1000) can increase model parameter estimations. In some embodiments, subjects are grouped by atrophy scores. For example, subjects are ranked by atrophy scores and data of every five subjects are combined to create a new data to perform the training ofthe dynamic systems model. Gradient timeseries for the five subjects in each group may be concatenated into a matrix, and coupling parameters may be estimated based on the matrices.

[0141] Eigen decomposition is then performed on the coupling parameters to yield a set of eigenmodes that completely describe the system. Each eigenmode in the system of linear coupled harmonic oscillators represents one spatio-temporal component of the system, oscillating at a single fixed frequency. On a given eigenmode, each gradient has a specific phase angle and amplitude. An overall brain activity at each timepoint can be represented by the summed activity of the gradients across eigenmodes. Validation can be performed by comparing the simulated gradient timeseries based on subject-specific eigenmodes to actual functional connectivity patterns or the FC patterns derived by the structure-function model.

[0142] Eigenmode analysis could be used to model and explain patterns in a functional matrix with hyper- and hypo-FC patterns (increased activity versus decreased activity). Machine learning approach may offer understanding to why the patterns are seen. More atrophy may result in or be associated with more synchronization that gives rise to the patterns. This trained dynamic systems model could be used to explain and validate the patterns observed in the functional connectivity matrix (or matrix-pattern graph). These mathematical explanations could be used help drive the treatment and clinical trial decisions.

[0143] The three models can be trained as separate models and implemented in the pipelines, methods and systems of using sMRI data, fMRI data, and machine learning models to predict a measure of cognitive impairment of a subject and to generate a treatment plan or clinical trial protocol for the subject. In some embodiments, multiple models can be trained jointly. C. Data Acquisition, Pre-processing, and Accessing

[0144] The pipelines, methods and systems are capable of predicting a measure of cognitive impairment of a subject and generating a treatment plan or clinical trial protocol for the subject. The sMRI and fMRI data, or other molecular imaging data, of the subject are acquired, pre-processed, and accessed. In some embodiments, demographic data of the control subjects (e.g., age, sex, dominant hand) are also acquired. The data preprocessing and / or accessing can be performed using a GPU or a TPU.

[0145] In some embodiments, the subject is put in an MRI scanner. Parameters of the MRI scanner, e.g., acquisition time, slice orientation, and voxel resolution, may be predetermined.The subject is administered to take a structural MRI scan and a functional MRI scan. In some embodiments, a time-length is also administered. For example, a subject is given an about eight-minute (e.g., 8.53 minutes) structural MRI scan and an about ten-minute fMRI scan. A plurality of images may be generated for an sMRI scan or an fMRI scan. The scans or images can be pre-processed, and sMRI and fMRI data are extracted based on the pre-processing. In some embodiments, sMRI scans are pre-processed separately from fMRI scans. In some embodiments, other molecular imaging scanner (e.g., PET-CT scanner, CT scanner, or the like) is used to obtain molecular imaging data for the subject. Obtained molecular imaging data may be subsequently pre-processed using similar methods as illustrated below.

[0146] In some embodiments, an sMRI scan is a magnetization-prepared rapid gradient echo (MPRAGE) sMRI scan. The MPRAGE scan may be visually assessed by trained technicians and scans with excessive motion artifact (ringing or blurring) may be excluded from measurement and prediction. MPRAGE scans for all time points for a given subject that passed quality control may be pre-processed. The pre-processing comprises warping regularization, bias regularization, normalization, and / or segmentation. Other types of sMRI scans (e.g., T1-weighted, T2-weighted, diffusion-weighted) may also be used here.

[0147] In some embodiments, a voxel-wise gray matter probability map is be generated using sMRI scans from control subjects. Demographic data of the control subjects (e.g., age, sex, dominant hand) may also be acquired and used to generate the map. A multiple regression model may be executed for each voxel to estimate gray matter volume as a function of the demographic data. A voxel W-score may be calculated as a difference between actual gray matter volume and the estimated gray matter volume, divided by a standard deviation of the model fit in controls.

[0148] In some embodiments, an fMRI scan is pre-processed using following procedures. To allow for scanner equilibration, a first number of images or volumes are removed. The fMRI images may be aligned to the corresponding sMRI images by composing transformations. Images may also be spatially smoothed with a kernel. In some embodiments, images are standardized voxel-wise to have mean=0 and standard deviation=1 across time. In some embodiments, the pre-processing comprises filtering based on framewise displacement (FD). In some embodiments, subjects with greater than 0.55 mm mean FD are excluded from subsequent analysis.

[0149] In some embodiments, the filtering further comprises removing scans with implausible functional connectivity patterns using a PCA model. The PCA model may be trained using functional connectivity matrices. In some embodiments, the fMRI images may be aligned to the corresponding sMRI images after the pre-processing.

[0150] In some embodiments, the sMRI data, the fMRI data, and the demographic data of the subject are obtained and accessed from a database or a third party. The sMRI data and the fMRI data may be pre-processed before the obtaining and accessing. D. Structure-Function Relationship Determination

[0151] Once the sMRI data and fMRI data have been accessed and pre-processed, they can be input into a structure-function model in the pipelines as disclosed, for example, the modeling subsystem 120 as shown in FIG.1. Structure-function relationships can be determined using the structure-function model. In some embodiments, the structure-function relationships are captured using a set of scores for principal structure-function components. In some embodiments, an atrophy score and a functional connectivity score are determined for each of three principal structure-function components. The scores may be output to a report and further to a GUI for review. In some embodiments, explanations of the scores are generated and can be reported together with the scores. E. Stratification and Cognitive Impairment Prediction

[0152] The structure-function relationships can be used to stratify the subject and predict a measure of cognitive impairment of the subject. The structure-function relationships can be input into a cognitive impairment model in the pipelines as disclosed, for example, the modeling subsystem 120 as shown in FIG.1. A predicted measure of cognitive impairment can be determined using the cognitive impairment model.

[0153] A predicted cognitive screening test score can be determined using the cognitive impairment model based on the scores generated to capture the structure-function relationships. The subject can be stratified based on the predicted measure of impairment, e.g., the predicted CDR score. The subjects may be stratified into one of cognitive groups including (i) a group with no cognitive impairment, (ii) a group with mild cognitive impairment, (iii) a group with moderate cognitive impairment, and (iv) a group with severe cognitive impairment.

[0154] In some embodiments, a treatment or clinical trial protocol is generated and assigned to the subject based on the structure-function relationships and the measure of cognitive impairment. In some embodiments, different treatments or clinical trial protocols are generated for subjects that are stratified into different cognitive groups. For example, a subject stratified into the group with no cognitive impairment is assigned a protocol to administer MRI scanning every one year after the initial scanning, a subject stratified into the group with mild cognitive impairment is assigned a treatment of therapeutic agents comprising cholinesterase inhibitors such as donepezil, galantamine, and rivastigmine, a subject stratified into the group with moderate cognitive impairment is assigned a treatment of therapeutic agents comprising cholinesterase inhibitors or glutamate regulators such as memantine, or a subject stratified into the group with severe cognitive impairment is assigned a treatment of therapeutic agents comprising cholinesterase inhibitors and glutamate regulators such as memantine, a treatment of supportive care and / or symptom management. The treatments or clinical trial protocols regarding the time interval between each scan may vary from one week to a number of years, e.g., 3 years.

[0155] In some embodiments, a treatment or clinical trial protocol comprises monitoring the subject regarding the progress of cognitive impairment. For example, the subject may be administered to receive a brain scan in a period of time and / or take cognitive impairment tests in the same period of time, to monitor the progress of the cognitive impairment. Further treatments may be generated based on the monitored progress. In some embodiments, brain imaging data obtained in the subsequent brain scanners may be used to further determine measurements of biomarkers (e.g., atrophy scores and / or functional connectivity scores), and the measurements of biomarkers may be further fed into the machine learning models (e.g., models in subsection B) to predict a subsequent measure of cognitive impairment and / or generate a subsequent treatment / clinical trial protocol. In some embodiments, the subsequent measure of cognitive impairment may use to modify the original treatment / clinical trial protocol for the subject.

[0156] In some embodiments, the stratifying is a two-dimensional decision-making process and comprises generating a matrix-pattern graph corresponding to weights associated with atrophy score and a functional connectivity score for each of three principal structure- function components. The generation of the matrix-pattern graph is illustrated in subsection E.

[0157] In some embodiments, an expected response of the subject to a therapeutic agent is determined based on (i) the atrophy score and the functional connectivity score for each of the three principal structure-function components, (ii) the measure of cognitive impairment, and / or (iii) the matrix-pattern graph. In some embodiments, the treatment or clinical trial protocol is adjusted based on the expected response.

[0158] A likelihood of recovery may be generated based on the scores generated to capture the structure-function relationships, the measure of cognitive impairment, and / or the expected response of the subject to a therapeutic agent. A subject with relatively higher W-scores and lower FC scores may be assigned a higher likelihood of recovery comparing with a subject with relatively lower W-scores and higher FC scores. The likelihood of recovery may be used to choose candidates for a drug testing or clinical research event. In some embodiments, the treatment or clinical trial protocol is adjusted based on the likelihood of recovery. F. Pattern Prediction and Cause Determination

[0159] Matrix-pattern graphs are useful to visualize and analyze correlations or causations of diseases. They can also be used to validate or explain the structure-function relationships and / or the measure of cognitive impairment.

[0160] In various embodiments, a matrix-pattern graph is a graph showing FC patterns associated with atrophy. In some embodiments, the atrophy is a global atrophy level. In some embodiments, each entry in the matrix represents a connection strength between two regions in the brain. In some embodiments, each entry in the matrix is a weight of a component for each brain region. The weight may be normalized, and a spectrum may be generated associated with the normalized weight. In some embodiments, negative and positive weights indicate a decrease or increase in FC with an increase in the positive atrophy pattern.

[0161] In some embodiments, the atrophy score and the functional connectivity score for each of the three principal structure-function components are used to generate the matrix- pattern graph. Matrix-pattern graphs generated from training data of patient and control subjects may be used for predicting a measure of cognitive impairment and determining an expected response to a therapeutic agent. A graph-based machine learning model may be trained using methods illustrated in subsection B for the prediction and determination. In some embodiments, the machine learning model is an ANN model (e.g., a Convolutional Neural Network (CNN) model, a Recurrent Neural Network (RNN) model). In someembodiments, the machine learning model is a Support Vector Machine (SVM) model. Other algorithms such as decision trees and random forests may also be used to in a machine learning model to learn the graph pattern. 1. Pattern and Pattern Recognition

[0162] The matrix-pattern graph, like X-ray scans or MRI scans, can be used as a new index for clinical diagnosis. It is similarly intuitive as the X-ray and MRI scans that information can be directly read from the graph. FIG.4A is an exemplary matrix-pattern graph showing the partial least squares function connectivity weights for a component. For example, in FIG.4A, it can be read from the matrix-pattern graph that FC scores are associated with greater global atrophy included prominent reductions between primary visual, somatomotor, and auditory regions of the brain.

[0163] Explanations can be generated based on the matrix-pattern graph. As shown in FIG. 4A, a darker red color represents a greater positive association between the global atrophy and the FC scores. It means the more atrophy a subject has, the stronger the coupling between the two regions. The matrix-pattern graph may also be used to show that global atrophy causes region synchronization.

[0164] Taking the matrix-pattern graph as a whole, these clusters of regions in blue are brain regions that have weaker connection with atrophy, and then clusters of regions in red are brain regions that have stronger connection with atrophy. The matrix-pattern graph of a subject may be used to dynamically supervise a development of cognitive impairment of a subject.

[0165] The matrix-pattern graph may be used to generate or validate the measure of cognitive impairment. A trained graph-based machine learning model may be used to perform the generation or validation. 2. Oscillator Models and Eigenmode Analysis

[0166] The oscillator models may be used to explain patterns in the matrix-pattern graph. In various embodiments, coupled oscillators are used in generating a model to explain the patterns. In some embodiments, a system of multiple coupled oscillators is used in the model and the model is trained using a machine learning approach. In some embodiments, only fMRI data are necessary to generate the model to explain the patterns.

[0167] In a healthy brain (e.g., no cognitive impairment), there is a temporal separation between different regions in the brain and some regions do not need to be correlated with each other. Too much correlation may result in electrical activities that are hyper- synchronized. Too little correlation is still problematic because the brain may malfunction. An optimal point for the healthy brain is to have synchronization activities that are not too much and not too little. Using oscillator models, it can be found the optimal point and models can thus explain the patterns in the matrix-pattern graph.

[0168] In some embodiments, a dynamic systems model is used to simulate gradient dynamic activities in different groups of subjects using gradient timeseries simulations based on gradients from a given subject or group of subjects. For each gradient timeseries, a first and second derivatives can be calculated by finite differencing. A linear regression may be run for each gradient to estimate its second derivative (G'') as a function of all six gradients (G) and first derivatives (G') along with an intercept. Coupling parameters from each regression are then used to define a system of coupled second-order ordinary differential equations. A system with six gradients can be defined as shown in Equation 1. G1''= ^1,0+ ^G1,1G1 + ^G1’,1G1' + ^G2,1G2 + ^G2’,1G2' + … + ^G6,1G6 + ^G6’,1G6' G2''= ^2,0+ ^G1,2G1 + ^G1’,2G1' + ^G2,2G2 + ^G2’,2G2' + … + ^G6,2G9 + ^G6’,2G6' Equation 1

[0169] The system may be trained using training data and the coupling parameters may be determined based on the training. Eigen decomposition may be performed to analyze the system. A second order system can be represented as a set of two first order equations. This linear system can be represented as shown in Equation 2.Equation 2

[0170] Here Y is the gradient timeseries and A is a coupling parameter matrix. The eigendecomposition of the coupling parameter matrix is shown in Equation 3.AV ൌ ^V Equation 3

[0171] Here ^ and V are eigenvalues and eigenvectors for the m eigenmodes. Each eigenmode represents a signal oscillating at a specific frequency. Eigen decomposition of a harmonic oscillator system with damping typically yields complex eigenvalues, with the real and imaginary parts (Į+iȕ) describing the damping (exponential growth or decay) andfrequency of each eigenmode, respectively. The solution to the differential equation with complex eigenvalues is shown in Equation 4. Equation 4

[0172] The positive or negative values of ^ represent the damping of each eigenmode over time. The eigenvector components are also complex, with the real and imaginary parts describing the amplitude and phase angle of each gradient on that eigenmode. When solving the equation for a given set of initial conditions, the real and imaginary parts of each eigenmode are each scaled by constants k to satisfy the initial conditions. An example equation is shown in Equation 5. Equation 5

[0173] For a given gradient G, the overall solution for its timeseries on an eigenmode can be solved by Equation 6, where a and b are the real and imaginary parts of the gradient's eigenvector component on eigenmode m. Equation 5

[0174] Subjects may be sorted based on their FC scores on a given structure-function component and binned them into groups of five. Coupling parameters for each group are estimated and eigenmodes are derived by the model. The eigenmodes for a given group of subjects formed the constitutive elements that are then used to measure the cumulative amplitude of each gradient and / or the cumulative phase angle between each pair of gradients. A gradient’s cumulative amplitude can be computed as shown in Equation 6.Equation 6

[0175] The phase angle difference between a pair of gradients on a given mode can be calculated by subtracting the angles for^ ^^^and ^ଶ^ ^^ଶ. The cumulative phase angle difference between a pair of gradients across modes may then be measured as a circular average of angle differences, weighted by the product of the gradient amplitudes on the respective eigenmodes. Gradient amplitudes and gradient-pair angles for each group of subjects are then compared to external quantities like the FC scores on each SF component, averaged across the set of subjects in each group.

[0176] The patterns and / or the matrices can be explained by percentage by each of the eigenmode. A higher percentage stands for a better explanation. The patterns and / or the matrices can be validated. In some embodiments, if the pattern in the matrix is X but driven by mode Y, it shows invalidity of a prediction. IV. EXAMPLES

[0177] The systems and methods implemented in various embodiments may be better understood by referring to the following examples. A. Introduction

[0178] Cognitive deficits in Alzheimer’s disease dementia (AD) and frontotemporal dementia (FTD) depend on gray matter atrophy in specific brain regions. Brain functional connectivity alterations are also common in AD and FTD, involving both decreases and increases in connectivity when compared to cognitively unimpaired individuals. It is unclear how structural and functional alterations are related in AD and FTD and what overlapping or unique contributions they make to cognitive impairment. Making progress on this question requires datasets and methods that can unravel the subtypes and stages of atrophy and map these two distinct patterns of functional hypo and hyper-connectivity.

[0179] While brain structure-function mapping in health and disease is a major challenge, one recent advance in functional brain activity modeling may make structure-function mapping in dementia more tractable. Brain activity states appear to have a low-dimensional basis, with a limited number of dimensions explaining the majority of functional variance. No study has an answer to a central question that whether different atrophy patterns in FTD and AD relate to specific perturbations of the low-dimensional brain activity manifold.

[0180] This problem was addressed using a diverse dataset of structural and functional MRI from 221 patients with Alzheimer’s disease amnestic dementia (AD), behavioral variant FTD (bvFTD), corticobasal syndrome (CBS), nonfluent and semantic variants of primary progressive aphasia (nfvPPA / svPPA), and 100 age-matched cognitively normal (CN) controls subjects. Three principal structure-function components linking different atrophy patterns to specific brain-wide functional connectivity alterations were identified. These structural and functional components made independent contributions to cognitive deficits. The present analysis revealed that functional connectivity decreases and increases were attributable to alterations in a low-dimensional set of activity gradients. Evidence was found that atrophycauses gradients to collapse away from their healthy brain configuration. This process underlies both the convergent and divergent patterns of connectivity alteration found in individual patients with different atrophy subtypes and stages. B. Results Functional Connectivity Decreases and Increases Across the Atrophy Spectrum

[0181] Structure-function relationships were assessed in 221 patients across the FTD-AD spectrum and 100 healthy control subjects matched for age, sex, scanner, and head motion collectively comprising the study’s primary cohort (see Table 1). Gray matter atrophy was measured in 246 cortical and subcortical regions using regional W-scores (see Methods). Task-free functional connectivity (FC) was measured for each pair of the 246 regions (30135 unique edges).97% of regions had significant gray matter atrophy (W > 1.5) in at least five subjects, demonstrating that this set of syndromes collectively involved nearly the entire brain. Partial least squares regression (PLSR) was used to identify the primary structure- function components in this cohort. Split-half analysis showed that the first three structure components had high reproducibility (see Methods and FIG.4B) and were the focus of this study. Table 1 Patient demographic and clinical information

[0182] FIG.4B is a violin plot showing PLSR structure component reliability using split- half analysis.1000 trials of independent PLSR were run on the first and second halves of the subjects, randomly split with balanced classes for each trial. The structure component loadingvectors were correlated between split halves for the 1000 trials for the first five PLSR components. The median correlations were S1: r=0.93±0.03, S2: r=0.88±0.14, S3: r=0.77±0.20, S4: r=0.34±0.23, S5: r=0.39±0.24. The most substantial drop in reliability was between components 3 and 4.

[0183] FIGS.5A-5B illustrate correlations using three structure-function components across the AD-FTD spectrum. The correlation between partial least squares regression- derived atrophy and functional connectivity (FC) scores for components 1-3 is shown in FIG. 5A. Beneath each correlation plot are the associated atrophy patterns reflecting a negative or positive atrophy score. For component 1, three example patients with different patterns but equivalent mean global atrophy is shown. FIG.5B are matrix-pattern graphs showing the partial least squares FC weights for each component, along with the network membership for each brain region. Negative and positive weights indicate decrease or increase in FC with an increase in the positive atrophy pattern (and vice versa). Matrix-pattern graphs and brains show 14 brain FC modules for reference. (VIS: visual; SM: sensory-motor; DA: dorsal attention network; AUD: auditory; HIP: hippocampal; PHC: parahippocampal; AMY: amygdala; CO: cingulo-opercular; SAL: salience; AT: anterior temporal; FPl: left fronto- parietal; DMN: default mode network; FPr: right fronto-parietal; SUB: subcortical.)

[0184] FIGS.6A-6C are boxplots showing statistics regarding FC edge weights for the bottom / top 1% of edges on each function component. Mean FC edge weights are shown for each component for groups of 30 subjects with the lowest / intermediate / highest atrophy scores. All boxplots throughout the paper show the median, lower and upper quartile range, and the non-outlier minimum / maximum.

[0185] For the first three structure-function components, subjects were sorted based on their structural score for that component and binned into groups of 30. For a given component, FC edges were sorted based on their PLSR weight. The bottom / top 1% of edges (300 edges) were kept and the mean FC weight for these two sets were computed for each subject. These mean edge weights were statistically compared for the groups of 30 subjects with low / middle / high atrophy on that component, both for the bottom and top FC edges. The edge weights were always statistically significant between low and high subjects (all p < 0.001, see table below) and were nearly always significant in other tests except for a two marginal cases (p=0.07 and p=0.049). This indicated that the partial FC variance captured bythe FC scores was substantial enough to capture significant differences in overall FC edge weights between groups of subjects. Table 2 is a summary of the statistics.

[0186] The first structure-function component (SF1) captured the relationship between global atrophy and a distributed FC pattern of decreases and increases, explaining 51.2% of the brain atrophy variance. This component represented the cumulative global atrophy level, correlating perfectly with subject mean atrophy (r=0.994). The correlation of the atrophy and FC scores was significant (r=0.56, p < 0.001; FIG.5A, left). The FC pattern associated with greater global atrophy included prominent reductions between primary visual, somatomotor, and auditory regions (FIG.5B, left). Contrasting these reductions was elevated subcortical- cortical FC, most strongly between the striatum, thalamus, and motor regions, along with more subtle fronto-parietal association cortex increases to widespread cortical and subcortical regions. This pattern captured statistically significant differences in FC edge strength for subjects at the bottom, middle, and top of the atrophy spectrum (FIGS.6A-6C).

[0187] The second and third components captured syndrome-specific atrophy patterns that explained 9.1% and 6.5% of the atrophy variance. Atrophy and FC scores were significantly correlated on Component 2 (r=0.49, p < 0.001; FIG.5A middle). Patients on the positive end of the spectrum for Component 2 had an svPPA-like phenotype with pronounced left anterior temporal atrophy. This accompanied weakened functional connectivity (lower than controls) from anterior and medial temporal regions, both locally and globally to the entire brain (FIG. 5B middle). These patients showed strengthened functional connectivity most prominently incontralateral right dorsal parietal areas. In contrast, patients at the negative end of this spectrum had diagnoses of AD or CBS and the mirror image pattern of atrophy and functional connectivity: atrophy in the right dorsal parietal cortex, sensory-motor cortex, and thalamic areas; peri-atrophy connectivity deficits; and FC enhancements in the left anterior temporal lobe. Healthy control subjects appeared in the middle of the spectrum, with minimal brain atrophy and balanced functional connectivity in these two systems. Atrophy and FC scores were also significantly correlated on Component 3 (r=0.68, p < 0.001; FIG.5A right). Components 2 and 3 both also captured statistically significant differences in edge connectivity strength for subjects at the bottom and top of the atrophy spectrum (FIGS.6A- 6C).

[0188] FIG.7 shows the atrophy and functional connectivity patterns for each clinical syndrome. The central scatter plot represents the atrophy similarity of individual subjects in two dimensions, derived from multidimensional scaling of structural components 1-3, with large dots indicating the mean position for each syndrome. For each syndrome, the mean atrophy pattern and functional connectivity matrix are presented for the subset of “typical” patients accurately classified based on their individual atrophy patterns. Additionally, the mean functional connectivity difference matrix for these typical patients, compared to cognitively normal subjects, is shown in the upper triangles, while the reconstructed matrix based on functional components 1-3 is displayed in the lower triangles.

[0189] The three structural components were utilized to assess syndrome differences in atrophy and functional connectivity. Initially, the three atrophy components were reduced to two dimensions using multidimensional scaling to visualize the AD-FTD atrophy spectrum (FIG.7). Subsequently, the subset of patients for each syndrome expressing the “typical” atrophy pattern and the corresponding functional connectivity alterations were identified. AD patients exhibited atrophy in the posterior temporal and parietal lobes; bvFTD in the insula, rostral / orbital frontal lobe, and anterior cingulate; CBS in the primary sensory / motor cortex and superior frontal lobe; nfvPPA in the inferior frontal lobe, insula, and premotor cortex; and svPPA in the anterior temporal lobe. The associated functional connectivity alterations are displayed in FIG.7. The next step involved testing how well those FC patterns could be explained in terms of the three functional components. For each syndrome, the best match to the true FC difference matrix (FIG.7, upper triangles) was the corresponding reconstructed FC matrix (FIG.7, lower triangles) (AD, actual versus reconstructed r=0.81; bvFTD r=0.82;CBS r=0.41; nfvPPA r=0.50; svPPA r=0.82). This confirmed that three structure-function components captured the predominant syndrome-associated patterns.

[0190] FIG.8A is a violin plot showing out-of-sample correlation coefficients between atrophy component scores and ridge regression-derived functional connectivity scores. Each dot represents a single fold out of four folds per 1000 trials. FIG.8B are three violin plots showing correlation coefficients between ridge regression functional connectivity edge weights (a [30135 x 1] vector) derived separately for each cross-validation fold versus partial least square regression-derived weights. The median correlations between corresponding ridge regression and PLSR components were 1-1: r=0.68, 2-2: r=0.75, 3-3: r=0.78.

[0191] The reliability of the structure-function relationships was evaluated using ridge regression with cross-validation (see Methods). The three primary components were found that each had significant structure-function correlation in the out-of-sample data (SF1: median r=0.49, median p < 0.001; SF2: r=0.32, p=0.003; SF3: r=0.39, p < 0.001; FIG.8A). Importantly, the FC edge weights associated with each atrophy component in cross-validated subsamples best matched the FC edge weights derived for the full sample using PLSR (FIG. 8B). Collectively, the three main structure-function components in AD and FTD reflected convergent and divergent patterns of hypo and hyper-FC. Neuropsychological Correlations with Structural and Functional Components

[0192] FIGS.9A-9B illustrate the neuropsychological correlation of brain structure- function components. FIG.9A shows results from the generalized additive model estimating each cognitive test score based on brain structure-function components and covariates. The F- statistic for the structure and function terms in each model are shown when significant (p < 0.05, FDR-corrected) or trending (p < 0.05, uncorrected). The overall variance explained for each cognitive test is also shown. Brains show the positive / negative weight of each region for structure components and the positive / negative sum of region FC edge weights for each region for function components. FIG.9B shows the correlation between actual and estimated test scores for clinical health (CDR-SB), global cognition (MMSE), executive functioning (Stroop Interference), and episodic memory (California Verbal Learning Test, CVLT total). Test scores are presented with higher values representing worse performance and converted to Z-scores for Stroop and CVLT. Partial effect plots are shown for three predictors of interest for each test. Higher values on the X-axis represent positive correspondence with the given structure / function pattern, while lower values show the reverse. Shaded bands show ± 2x standard errors of the fit (95% confidence interval) (BNT: Boston Naming Test; PPVT: Peabody Picture Vocabulary Test; VOSP: Visual Object and Space Perception).

[0193] The relationship between the brain structure-function components and cognitive performance was examined next. The focus was on two tests of global functioning, the CDR®+NACC-FTLD sum of boxes (Miyagawa et al., Utility of the global CDR® plus NACC FTLD rating and development of scoring rules: Data from the ARTFL / LEFFTDS Consortium, Alzheimer’s & Dementia 16, 106–117; henceforth referred to as CDR-SB) and MMSE. A generalized additive model was used to estimate cognitive scores based on the first three structure and function scores, either as linear or non-linear terms, and covariates (see Methods). The model for CDR-SB explained 50% of the variance. The strongest predictors were S1 (F=22.88, p < 0.001; FIGS.9A-9B), F1 (F=17.16, p < 0.001), and S3 (F=10.74, p < 0.001). This indicated that patients with the most severe clinical impairment had high global atrophy (S1), most pronounced in the frontal lobe (S3), along with subcortical hyperconnectivity and primary sensory cortical hypoconnectivity (F1). For MMSE, the model explained 40% of the variance with the strongest predictions from S1 (F=22.31, p < 0.001), F3 (F=13.94, p < 0.001), and S3 (F=7.22, p=0.001). S3 had significant nonlinearity (FIG. 9B), such that subjects with either the positive atrophy pattern (frontal) or the negative atrophy pattern (temporal) had equivalently poor MMSE scores. Subjects with worse MMSE scores also had anterior connectivity deficits and posterior connectivity enhancements when holding other terms at their mean levels. Thus, the CDR-SB and MMSE both had expected correlations with atrophy amount, atrophy pattern, and critically, correlations with functional components capturing systems-level imbalances.

[0194] The relationship between brain structure-function component scores and neuropsychological test scores for episodic memory, working memory, processing speed, executive function, visuospatial processing, speech and language was assessed. Across domains, the models explained an average of 34% of the variance (FIG.9A; mean r2=0.34±0.09; range=0.17-0.50). The brain-behavior relationships clustered into two groups. The first group represented dysfunctions in clinical / global functioning, language, and episodic memory, most strongly influenced by S1, F1, and S3. This pattern was most strongly exhibited by patients with AD or svPPA, with high mean atrophy, most prominent in the temporal lobe, along with global dysfunction. The second group included dysfunctions in executive function, processing speed, language production, and visuospatial processing, driven by S1 and S2. The patients most strongly representing this group had CBS, nfvPPA, orAD, also with high mean atrophy but focused on the parietal lobe. Overall, brain-behavior relationships were strongest for structural components, though key functional relationships predicted global cognition and memory performance.

[0195] FIG.10 are longitudinal relationship effect plots showing the partial relationship of CDR-SB with structure component 1 (S1) mean (between-subject), function component 1 (F1) mean (between-subject), S1 change (within-subject), and F1 change (within-subject).

[0196] The longitudinal relationship was evaluated between S1, F1, and CDR-SB in a targeted analysis using baseline and follow-up data from a subset of 47 patients and 6 cognitively normal subjects (mean visit interval=1.1±0.5 years, range=0.4-2.6 years). Using a mixed effect generalized additive model, within-subject CDR-SB change was found to be significantly correlated with F1 change (t=2.05, p=0.04; FIG.10) and S1 change (t=2.15, p=0.04). Between-subject CDR-SB mean was significantly related to S1 mean (F=6.06, p=0.02) and F1 mean (F=3.34, p=0.03) as expected from the cross-sectional model. A brain- only model showed that overall F1 correlated with both S1 mean (F=21.42, p < 0.001) and S1 change (F=6.21, p=0.02). Thus within-subject changes in structure and function component 1 were related, and both tracked a patient’s change in clinical dementia severity. Low-Dimensional Functional Connectivity Changes Associate with Different Atrophy Components

[0197] FIGS.11A-11F illustrate low-dimensional gradient activity correlates with structure-function components. FIG.11A is a gradient spatial weight maps from the independent cognitively normal cohort. FIG.11B shows variance explained in each PLSR functional component by individual gradient variances (e.g.1-1, 2-2) and paired gradient covariances (e.g.1-2, 2-3). Insets show PLSR component functional connectivity (FC) edge weight matrices. C-F. Select gradient timeseries and associated FC differences for the gradients that explained the most variance in each PLSR functional component. FIG.11C and FIG.11D illustrates Gradient 1 variance, Gradient 1-4 covariance, and FC differences for two subjects at the negative and high ends PLSR component 1. FIG.11E illustrates Gradient 1-2 covariance and FC differences for two subjects at the negative and high ends PLSR component 2. FIG.11F illustrates Gradient 2 variance and FC differences for two subjects at the negative and high ends PLSR component 3.

[0198] FIG.12 is a matrix-pattern graph showing spatial correlations between the PCA spatial components (gradients; n=246 regions per component) derived from the independent cognitively normal cohort (n=321, rows) and the main combined patient and control cohort (n=321, columns). The spatial gradient patterns were highly consistent in the independent cognitively normal cohort and the primary cohort. The median spatial correlation was r=0.98 for gradients 1-6 (max=0.99, min=0.95) and r=0.97 for gradients 1-12 (max=0.99, min=0.83).

[0199] Each of the three primary structure-function components involved both hypo and hyper-FC that collectively contributed to cognitive impairments. The recurring presence of paired FC decreases and increases suggested a possible common origin. Specific alterations in low-dimensional brain activity were hypothesized to underlie the hypo / hyper-FC patterns for each functional component. This was tested by performing PCA dimensionality reduction on the fMRI timeseries data to derive spatial components, henceforth referred to as gradients, (FIG.11A) and their associated temporal fluctuations (see Methods). Specifically, the PCA space was derived from an independent cohort of age-matched cognitively normal subjects (n=321) and projected all primary cohort patient and control fMRI data into this space. This approach was based on the expectation that spatial gradient patterns are stable across individuals, regardless of disease presence or absence, and that atrophy perturbs gradient temporal dynamics.

[0200] The spatial patterns reflected gradients established in the literature including the unipolar sensory-to-association (Gradient 1), sensory-to-cognitive (Gradient 2), visual-to- sensorimotor (Gradient 3), task-negative-to-task-positive (Gradient 4), and left-right asymmetric (Gradient 6). The gradient spatial maps derived from the independent cohort were confirmed to be highly similar to those obtained from the primary cohort (FIG.12). The relationship between functional connectivity component F1-F3 scores and specific across- subject differences in the gradient amplitudes (variance) and gradient pair coupling (covariance) was then assessed. Each function component was found to have a strong and specific relationship with the six primary gradients, in each case explaining the majority of the across-subject FC variance.

[0201] For F1, the first six gradients explained 82.0% of the functional connectivity variance, with the biggest contributions from Gradient 1 amplitude (26.4% of F1 variance, t=- 17.08; p < 0.001 for all reported terms; FIGS.11B-11C), Gradient 1 / 4 coupling (15.1% of F1 variance, t=+10.32; FIGS.11B & 11D), and Gradient 1 / 5 coupling (10.8% of F1 variance,t=+10.11). Subjects with higher global atrophy had lower Gradient 1 variance, which because of its unipolar nature (with all regions having positive weights), resulted in lower global BOLD signal amplitude. Indeed, the relationship between Gradient 1 variance and global signal amplitude was very strong (r=0.91, p < 0.001). This explained the weakened global functional connectivity, most extremely in sensory-motor regions with the largest Gradient 1 weights. These high global atrophy subjects also had stronger Gradient 1-4 coupling than low atrophy subjects. This resulted in more positive functional connectivity between regions with positive weights on Gradient 4 (dorsal attention, cingulo-opercular) and positive weights on Gradient 1 (every brain region). In contrast, regions with negative weights on Gradient 4 (default mode) had negative correlation with Gradient 1 and therefore with the whole brain. Thus, the atrophy-driven shift in coupling of a bipolar gradient with global Gradient 1 caused specific networks to increase or decrease their integration with the rest of the brain.

[0202] Function components 2 and 3 also both had strong relationships with gradient activity. Gradient activity explained 86.2% of the F2 variance, with the strongest influence by Gradient 1 variance (58.3% of variance, t=+31.02), Gradient 1 / 2 covariance (10.8% of variance, t=+10.82; FIGS.11B&11E), and Gradient 1 / 6 covariance (5.3% of variance, t=- 8.93). F3 had 55.2% of its variance explained by Gradient 1 / 2 covariance (14.0% of variance, t=-8.20; FIGS.11B&11F), Gradient 2 variance (10.2% of variance, t=-6.97), and Gradient 2 / 3 covariance (6.8% of variance, t=-5.21). Here, subjects with greater frontal atrophy had lower Gradient 2 variance, resulting in reduced within-network connectivity for regions on either pole of the gradient, and also less anticorrelation (i.e. stronger FC) between regions at opposite gradient poles. Thus, the majority of the atrophy-associated FC variance was explained by six gradients and their interactions, indicating a low-dimensional basis for the observed FC alterations. Gradient Collapse Drives Hypo and Hyper-Connectivity Patterns

[0203] The clear association between atrophy, gradient activity, and FC, but a central question of whether different atrophy patterns cause specific perturbations in brain-wide activity flow that give rise to observed FC patterns and if so, whether a dynamical systems model could generate the convergent and divergent FC alterations remains unsolved.

[0204] To provide a solution to the above questions and limitations, model gradient interactions were chosen as a system of linear coupled harmonic oscillators (see Methods).

[0205] FIGS.13A-13C illustrate eigenmode derivation and properties in low and high atrophy subjects. FIG.13A shows the procedure for deriving gradient coupling parameters and eigenmodes. FIG.13B shows the six eigenmodes for two example subgroups (n=5) with the lowest or highest total atrophy. Circle plots show the phase angle and amplitude of each gradient on a given eigenmode. Timeseries plots show the resultant gradient oscillations, occurring with the eigenmode-specific frequency and damping. FIG.13C shows eigenmode- based FC matrices for low and high atrophy subjects and the FC difference matrix.

[0206] FIG.14 illustrates correlations between each subject’s actual [246 x 246] FC matrix (rows) and the simulated FC matrix (columns).

[0207] In a coupled oscillator system, eigen decomposition of the coupling parameters yields a set of eigenmodes that completely describe the system dynamics (FIG.13A). Each eigenmode represents one spatio-temporal component of the system, oscillating at a single fixed frequency. On a given eigenmode, each gradient has a specific phase angle and amplitude. Overall brain activity at each timepoint is then represented by the summed activity of the gradients across eigenmodes. Here, the gradient coupling parameters for each subject and derived eigenmodes was computed. The accuracy of this modeling approach was validated by simulating gradient timeseries based on subject-specific eigenmodes and comparing simulated to actual FC patterns. Each subject's simulated and actual FC was found to be significantly more similar than to simulated FC from the remaining subjects (self actual- self simulated, median r=0.96; self actual-other simulated, median r=0.72; t=31.46, p < 0.001; FIG.14).

[0208] As an illustration of how the eigenmodes captured different FC patterns, the eigenmodes for the group of n=5 subjects were computed with the lowest or highest global atrophy captured by structure-function component 1 (FIG.13B). These eigenmodes was then used to simulate regional timeseries and FC matrices for each group (FIG.13C). The FC difference matrix revealed the same pattern of atrophy-associated FC changes represented on SF1 – reduced primary sensory FC, elevated subcortical-cortical FC, and elevated fronto- parietal association FC. This indicated that the eigenmodes contained sufficient information to explain observed hypo / hyper-FC patterns.

[0209] FIG.15 illustrates correlations between observed gradient variance / covariance and coupling parameter-derived gradient amplitude / angles.

[0210] Based on the demonstrated relationship between eigenmodes and atrophy-associated FC patterns, two eigenmode-derived quantities were hypothesized to describe the atrophy- associated gradient alterations: 1) the cumulative amplitude of each gradient across all six eigenmodes and 2) the average angle (phase difference) between each pair of gradients across all modes. The correlation between eigenmode gradient amplitude / angles and gradient variance / covariance was tested and the strongest relationship was always found for the expected association (FIG.15; corresponding: mean r=0.75, non-corresponding: mean r=0.10). This demonstrated that atrophy-related shifts in brain-wide FC correspond to decreasing gradient amplitudes and alterations in the typical phase angle between pairs of gradients.

[0211] The gradient amplitude and phase angles were evaluated for four examples most strongly associated with the structure-function components and assessed the gradient amplitude and angles in individuals with specific atrophy-associated FC patterns.

[0212] FIGS.16A-16D illustrate eigenmode relationships with gradient activity and different structure-function components. On SF1, subjects with higher total atrophy had progressively lower Gradient 1 amplitude (FIG.16A), which resulted in globally reduced functional connectivity strength because of Gradient 1's unipolarity. These subjects also had a progressively smaller angle between Gradients 1 and 4, decreasing from nearly orthogonal (101°) to a smaller angle that reflected more positive temporal correlation (FIG.16B). A shift away from 90° was interpreted as a “collapse,” given that the gradients were identified as temporally orthogonal (i.e. uncorrelated) components in cognitively normal control subjects. Gradient 1-4 collapse resulted in hypersynchrony of these two systems with respect to controls subjects, driving hyperconnectivity in regions with the same sign (+ / + or - / -) on Gradients 1 and 4 and hypoconnectivity of opposite-signed (+ / -) regions. On SF2, subjects with greater left temporal atrophy had a Gradient 1-2 collapse to 57° (FIG.16C, bottom), while subjects with greater right parietal atrophy showed the opposite effect, a collapse in the opposite direction to 109° (i.e. a collapse to 71° if the Gradient 2 sign was flipped). Finally, subjects with posterior temporal atrophy (SF3) had greater Gradient 2 amplitude than those with frontal atrophy (FIG.16D). In general, any atrophy-associated functional connectivity alteration could be linked to a specific gradient amplitude or phase angle change.C. Discussion

[0213] Herea dataset of structural and functional MRI from patients across the AD-FTD spectrum were used to identify a set of structure-function components. A primary component was found relating global atrophy to hypo-connectivity in primary cortical regions and hyper- connectivity between subcortical and cortical regions. The second and third components linked focal syndrome-specific atrophy patterns to peri-lesional hypo-connectivity and distal hyper-connectivity. These structure-function relationships were robust and explained independent variance in cognition on both global and domain-specific neuropsychological measures. The brain-wide functional connectivity patterns were largely explained by variance in six spatial activity gradients, suggesting a low-dimensional basis for the connectivity alterations. Analysis of the gradient coupling parameters revealed diminished amplitude of specific gradients and collapsed phase angles between gradients, collectively yielding the observed alterations in brain-wide functional connectivity.

[0214] Principal component analysis identified three brain atrophy components that explained 66.3% of the variance in cortical and subcortical regions. The first atrophy component captured mean global atrophy and served as a proxy for disease stage. The second and third components described opposing focal atrophy patterns in the left-predominant temporal pole versus right-predominant dorsal parietal cortex (component 2) and left- predominant temporal-occipital lobe versus prefrontal-insula-cingulate areas (component 3). These components stratified patients with different syndromes in the expected ways, separating atrophy patterns along ventral-dorsal, anterior-posterior, and left-right axes. Partial least squares regression was used to derive atrophy components and continuous scores so that progressive atrophy patterns across stages could be linked to corresponding functional connectivity alterations.

[0215] Distinct functional hypo / hyper-connectivity patterns were associated with each atrophy component. The first structure-function component was a specific functional pattern of primary sensorimotor reduction and subcortical / association enhancements, regardless of where the atrophy occurred.

[0216] Here widespread FC alterations were assessed by deriving summary scores capturing different FC patterns and then linked these scores to underlying low-dimensional gradient activity levels. The principal FC pattern was found to be based on reduced Gradient 1 variance and increased Gradient 1-4 coupling. A critical question is how atrophy indisparate locations can cause the same alterations in these brain-wide functional systems. Structural damage may cause specific gradients to collapse away from orthogonality, resulting in hypo- and hypersynchrony between different networks as two sides of the same coin. This may occur in a convergent or divergent fashion, as observed here with SF1 and SF2 / 3, respectively.

[0217] The identified structure-function components explained unique variance in cognitive deficits. These deficits largely clustered into two groups: clinical / global functioning, language, and episodic memory, most strongly influenced by S1, F1, and S3; and executive function, processing speed, language production, and visuospatial processing, driven by S1 and S2. The structural components explained significantly more variance in cognitive deficits across this diverse cohort. Nonetheless, functional components did explain significant variance in cognitive deficits. Most strikingly, F1 was a significant predictor of CDR-SB over and above the amount of global atrophy (i.e., S1 score). F1 may represent a neural substrate for cognitive reserve that compensates for structural degeneration. Reduced global modularity (i.e., less segregation between networks) was found to be negatively impacts cognition across dementia syndromes. Considering the low-dimensional framework in the study, specific gradient alterations change modularity in specific ways. Diminished Gradient 1 amplitude will increase global modularity because of its unipolar (all-positive) nature, reducing positive correlation between all regions. In contrast, diminished amplitude of the other bipolar gradients will decrease modularity by decreasing the anti-correlation of regions at opposing ends. Altered coupling between specific gradient pairs will change the segregation and integration of specific networks. Here the correlation of functional scores from the structure-function components and the modularity Q value were r=0.19, r=-0.76, and r=0.55, reflecting the combined alterations in low-dimensional gradient activity. This implies that changes in modularity and cognition across disease stages will depend on both the total amount of atrophy and the spatial pattern.

[0218] Here a functional biomarker is described that correlates with clinical impairment equally well in FTD and AD. The functional imbalance pattern (F1) has several desirable biomarker properties including: 1) surrogacy with CDR, the standard primary endpoint in dementia clinical trials; 2) longitudinal within-subject correlation with clinical worsening and progressive atrophy; and 3) reliability with cross-validation, replicating across two different scanners using single and multiband sequences. In this study, structural and functional components explained independent variance in CDR. This indicates that patients mayclinically benefit from treatments that slow neurodegeneration, rebalance function, or both, and that it will be advantageous to monitor both structural and functional biomarkers in a clinical trial. D. Methods Subject Selection

[0219] Patients and control subjects were recruited through ongoing studies at the University of California San Francisco (UCSF) Memory and Aging Center (MAC). All subjects or their surrogates provided informed consent according to the Declaration of Helsinki and the procedures were approved by the UCSF Institutional Review Board. All subjects underwent a clinical history, physical examination, neuroimaging, and comprehensive neuropsychological assessment within 90 days of scanning. Healthy control subjects were recruited from the Hillblom Healthy Aging Study with ages between 45-85, minor or no memory problems, and no diagnosis of a neurodegenerative disease or other major health condition. A large initial control dataset (n=568) was subsequently divided for multiple purposes.

[0220] None of the patients had significant history of other neurological diseases or structural brain abnormalities inconsistent with their primary clinical syndrome. The initial patient group consisted of patients (n=309) who received a primary clinical diagnosis of either Alzheimer’s disease, behavioral variant frontotemporal dementia, semantic variant or nonfluent variant primary progressive aphasia, or corticobasal syndrome. All diagnoses were made within 90 days of the patients’ MRI scan.

[0221] Each patient was assigned to a high, intermediate, or low confidence diagnosis group. High confidence subjects had a single clinical diagnosis of one of the five syndromes of interest at one or more clinical visits. Intermediate confidence subjects had a best estimate clinical diagnosis of the syndrome of interest, but additionally either: 1) an alternative possible diagnosis including AD, bvFTD, CBS, nfvPPA, svPPA, progressive supranuclear palsy (PSP), amyotrophic lateral sclerosis (ALS), posterior cortical atrophy (PCA), or logopenic variant PPA (lvPPA) or 2) a best estimate clinical diagnosis that was stable for multiple visits before shifting away from the syndrome of interest in a later visit. These subjects were assigned to the intermediate confidence group if they had three or more clinic visits with a stable primary diagnosis of the syndrome of interest. Low confidence subjectshad multiple diagnoses as best estimates, including the syndrome of interest, or a diagnosis for the syndrome of interest that shifted away at the next visit. The primary analysis targeted 221 high and intermediate confidence patients with dementia, excluding low confidence patients and MRI quality control failures (see below).100 cognitively normal subjects were selected who passed image quality control and were matched to the overall patient group for age, sex, MRI scanner distribution, and fMRI head motion. The number of subjects with each diagnosis are shown in Table 1. The self-reported race / ethnicity for the 321 subjects included 25 Asian, 5 Black, 5 Hispanic, 263 White, and 23 unreported. Neuroimaging Acquisition

[0222] All subjects were scanned at the UCSF Neuroscience Imaging Center, on either Siemens Trio or Siemens Prisma Fit 3T MRI scanners. Subjects were scanned between one and eight times over the course of their clinic visits. The main analysis targeted the baseline scan for each subject. The number of patients with each diagnosis scanned on either the Trio or Prisma are shown in Table 1. Subjects received T1-weighted magnetization-prepared rapid gradient echo structural MRI (MPRAGE) scans with similar acquisition parameters on the Trio or Prisma: acquisition time: 8:53; sagittal slice orientation; thickness: 1.0 mm; field of view: 160x240x256 mm; isotropic voxel resolution: 1mm3; TR: 2300 ms; TE: 2.98 ms for Trio, 2.9 ms for Prisma; TI: 900 ms, flip angle: 9°.

[0223] Task-free fMRI scans were run using a T2*-weighted echoplanar scan with subjects instructed to remain awake with their eyes closed. The parameters on the Trio were: acquisition time: 8:06; axial orientation with interleaved ordering; field of view: 230x230x129 mm; matrix size: 92x92, effective voxel resolution: 2.5x2.5x3.0 mm; TR: 2000 ms, for a total of 240 volumes; TE: 27 ms. For the Prisma, the fMRI parameters were: acquisition time: 8:05; axial orientation with interleaved multi-slice mode and multiband acceleration=6; field of view: 211x211x145 mm; matrix size: 92x92, effective voxel resolution: 2.2x2.2x2.2 mm; TR: 850 ms, for a total of 560 volumes; TE: 33 ms. Structural Image Processing

[0224] MPRAGE scans were visually assessed by trained technicians and scans with excessive motion artifact (ringing or blurring) were excluded. MPRAGE scans for all time points for a given subject that passed quality control were registered using the serial longitudinal registration in SPM12 (Ashburner and Ridgway, 2012). Default parameters were used for warping regularization and bias regularization. Jacobian determinant and divergencemaps were produced that represent the amount of longitudinal brain contraction and expansion. Unified normalization / segmentation was then applied to register the midpoint average T1 images to standard space (Ashburner and Friston, 2005) with light regularization, a 60 mm bias FWHM cutoff, and Gaussians per tissue type of [2,2,2,3,4,2]. The gray matter tissue segmentation for the midpoint average was multiplied by the deformation fields for each time point to obtain time point-specific gray matter maps. These images were then warped to standard space using the deformation fields from the unified normalization / segmentation procedure. The resulting normalized gray matter maps were smoothed with an 8 mm FWHM Gaussian kernel.

[0225] Voxel wise gray matter tissue probability maps were derived from an independent set of healthy controls (n=397) using the same structural image processing methods. These subjects had the following characteristics: mean age=69.3±8.8; 239 female / 158 male; 345 right-handed / 43 left-handed; 1.5T / 3T Trio / 3T Prisma / 4T=58 / 144 / 140 / 52). Multiple regression was run for each voxel to estimate gray matter volume as a function of age, sex, handedness, total intracranial volume, and MRI scanner. For the 321 subjects in the primary analysis, their demographic values were entered into this regression model to estimate their gray matter volume in each voxel. The voxel W-score was calculated as the difference between actual gray matter volume and the estimated gray matter volume, divided by the standard deviation of the model fit in controls. W-scores were used as the measurement of gray matter atrophy throughout the study. Functional Image Processing

[0226] Functional MRI scans were processed using fMRIPrep (Esteban et al., fMRIPrep: a robust preprocessing pipeline for functional MRI, Nature Methods, 16, 111-116 (2019)) (RRID:SCR_016216). For anatomical image processing, the MPRAGE images were corrected for intensity non-uniformity with N4BiasFieldCorrection in ANTs (Avants et al., 2008) (RRID:SCR_004757), and used as T1-weighted (T1w) reference throughout the workflow. The T1w reference was skull-stripped with a Nipype (Gorgolewski et al., Nipype: a flexible, lightweight and extensible neuroimaging data processing framework in python. Front Neuroinform 5, 13 (2011)) (RRID:SCR_002502) implementation of the antsBrainExtraction.sh workflow using OASIS30ANTs as target template. Brain tissue segmentation of cerebrospinal fluid (CSF), white-matter (WM) and gray-matter (GM) was performed on the brain-extracted T1w using FSL fast. Volume-based spatial normalization tothe MNI152NLin6Asym standard space was performed through nonlinear registration with antsRegistration, using brain-extracted versions of both T1w reference and the T1w template.

[0227] For functional image processing, the first five volumes were removed to allow for scanner equilibration. A reference volume and its skull-stripped version were generated by fMRIPrep. The BOLD reference was then co-registered to the T1w reference using FSL flirt with 6-degrees-of-freedom affine registration. Co-registration was configured with nine degrees of freedom to account for distortions remaining in the BOLD reference. Head-motion parameters with respect to the BOLD reference (transformation matrices, and six corresponding rotation and translation parameters) were estimated using FSL mcflirt and were used to compute the framewise displacement (FD). BOLD runs were slice-time corrected using AFNI 3dTshift. The BOLD images were realigned from native to MNI152NLin6Asym standard space using antsApplyTransforms, configured with Lanczos interpolation, with a single interpolation step by composing transformations for head-motion and co-registrations to anatomical and output spaces.

[0228] Images were spatially smoothed with a 6mm FWHM (full-width half-maximum) kernel using FSL susan. Confounding CSF and WM timeseries were calculated based on the preprocessed BOLD images, deriving average signals using the subject-specific anatomically derived tissue masks after erosion. The confound timeseries for head motion estimates, CSF, and WM were expanded with the inclusion of temporal derivatives and quadratic terms for each. Bandpass filtering in the frequency range 0.008-0.08 Hz was performed on the confound timeseries and BOLD images using fslmaths and AFNI 3dBandpass respectively.

[0229] Global signal variance was assessed as a disease-relevant variable of interest. The global signal was computed as the mean BOLD signal across the 246 regions (see below) at each timepoint. Confound timeseries were then regressed out of the BOLD images using fslglm. Scans were standardized voxel wise to have mean=0 and standard deviation=1 across time. Subjects with greater than 0.55 mm mean FD were excluded from subsequent analysis. From the pool of all fMRI scans for all available control and patient subjects (n=1591), this resulted in the exclusion of 194 scans (12.2%).

[0230] A subsequent data-driven denoising procedure was performed using PCA to remove scans with implausible functional connectivity patterns likely due to noise from the scanner hardware (field instabilities) and the subject (head motion, heartbeat, respiration). PCA has previously been applied for outlier detection in fMRI data . Here, all subject’s functionalconnectivity matrices (see below) were flattened and combined into one single matrix ([1591 scans x 30135 edges]). PCA was run on this matrix and subjects with an outlying score on the first component (> 1 standard deviation above the mean) were flagged. This excluded 288 scans and left an available pool of 1108 scans. Scanner Harmonization

[0231] Structural and functional MRI data from the two different MRI scanners was harmonized using ComBat. Gray matter mean W-score values were estimated for 246 regions of interest (210 cortical, 36 subcortical including the caudate, putatmen, globus pallidus, and thalamus) from the Brainnetome atlas. A design matrix was constructed including MRI scanner as the main batch variable and covariates for patient / control status, age, and sex. ComBat was then used to harmonize the W-score values for each region. For functional MRI, mean BOLD timeseries for each scan were obtained for each region and entered into a temporal PCA (see next section). Using the 246 temporal component timeseries, the covariance matrix was computed. The upper triangle from each [246 x 246] covariance matrix was extracted, including the diagonal, flattened into a [30381 x 1] vector, and stacked for all subjects. The [321 x 30381] matrix was run through ComBat with the same design matrix. The harmonized covariance values were then used to derive harmonized FC matrices. Gradient Derivation and Functional Connectivity Analysis

[0232] The low-dimensional basis of functional connectivity patterns in this cohort was studied by performing dimensionality reduction on fMRI BOLD timeseries data. Here an independent cohort of cognitively normal subjects (n=321) were obtained that were age, sex, and scanner-matched to the primary cohort of 221 patients and 100 cognitively normal subjects. The 246 regional mean BOLD timeseries for the independent cohort subjects were temporally concatenated into a [122795 x 246] matrix and PCA was performed. This yielded a brain activity latent space in which region-wise component loadings (eigenvectors scaled by their corresponding eigenvalues) represented each region’s weight on that component. The spatial maps for each component are referred to as gradients and the component scores as the gradient timeseries.

[0233] The main analysis targeted the first six dimensions with additional consideration of 12 dimensions. The fMRI data matrix for the primary cohort ([119915 x 246]) was projected into this latent space to obtain the gradient timeseries. For each subject, the [246 x 246] gradient covariance matrix was computed. These matrices were then used to derive functionalconnectivity matrices by obtaining each region’s variance (summing on-diagonal values across all components), each region pair’s covariance (summing off-diagonal values across all component pairs), and using these quantities to compute the region pairwise Pearson correlation coefficients. An independent PCA was run on the primary cohort [119915 x 246] matrix to validate the spatial gradient pattern reliability. Brain Structure-Function Statistical Analysis

[0234] The relationship between atrophy and brain-wide functional connectivity was assessed in two stages. In the first stage, each subject’s FC matrix upper triangle was vectorized into a [30135 x 1] vector and stacked to obtain the ([321 subject x 30135 edge] group FC matrix. Partial least squares regression was performed on the brain atrophy W- scores ([321 subjects x 246 regions]) and the functional connectivity ([321 subject x 30135 edges]). PLSR is asymmetric, designed to completely decompose the ‘X’ variable into components that maximally covary with ‘Y’ variable. Atrophy was chosen as the ‘X’, i.e. the “grounding” variable, based on two factors: 1) a stronger hypothesis about the spatial patterns of the atrophy components, and 2) lower noise in structural MRI than functional MRI. PLSR was performed to derive five components and used split-half analysis to determine which components had sufficient reliability.

[0235] The focus was on the structural component reliability, with the procedure for functional component reliability in the next section. To achieve this, 1000 random splits of the 321 subjects into two equally sized groups was generated, each time balancing the number of subjects from each diagnostic class. Independent PLSR was conducted on the first and second halves of the subjects across 1000 trials, with random splits and balanced classes for each trial. The structure component loading correlations were computed across the 1000 trials for the first five PLSR components. Analysis revealed that the first three components had acceptable reliability. Atrophy and FC scores for each subject were then obtained for these three components and correlated these scores to measure the strength of each independent structure-function relationship.

[0236] In the second stage, the reliability of the structure-function relationships was validated by performing ridge regression with cross-validation. For this analysis, atrophy component scores from the PLSR model could not be used because these were derived based on their covariance with FC and would contaminate cross-validation. Instead, atrophy component scores were derived using PCA on the atrophy data alone. The spatial patterns ofthe first three PCA-derived atrophy components were essentially identical to the first three PLSR atrophy components (Component 1, r=0.999; Component 2, r=0.98, Component 3, r=0.97). Ridge regression was chosen for cross-validating atrophy-associated FC scores based on the hypothesis that a low-dimensional set of activity gradients explained the brain-wide FC patterns. Because of this, a summary FC score that treats each FC edge independently would be at risk of inflating redundant information. Ridge regression avoids this problem by shrinking coefficient weights, thereby reducing the variance coming from redundant predictor variables. This property makes ridge regression preferable in this use case to other shrinkage methods like partial least squares regression or principal components regression. Ridge regression was run using scikit-learn. Models of the relationship between each atrophy component (one score per subject per component) and brain-wide FC weights (30135 features per subject) were evaluated. Stratified cross-validation was run to measure model out-of- sample accuracy with four folds with 240 train subjects and 81 test subjects per fold, balanced for the number of subjects with each syndrome.1000 trials with an empirically selected alpha value of 1000 were performed, which produced optimal cross-validation accuracy. Ridge coefficients for each component were averaged across 1000 trials and 4 folds to obtain the average coefficients. Individual subject functional scores for each component were derived by taking each subject's score from their left-out fold for each trial and averaging across the 1000 trials. Deriving these out-of-sample ridge FC scores also served to decorrelate structure and function scores sufficiently to use them as independent predictors of neuropsychological scores.

[0237] Structure-function relationships for each component were visualized as matrices of PLSR FC edge weights. The 246 regions were grouped into 14 previously defined functional connectivity modules, based on a modular partitioning of a group-averaged task-free functional connectivity matrix from 75 healthy older control subjects. These modules included in this partition are: visual, sensory-motor, dorsal attention network, auditory, hippocampal, parahippocampal, amygdala, cingulo-opercular, salience, anterior temporal, left fronto-parietal, default mode network, right fronto-parietal, and subcortical. To create spatial maps summarizing the most prominent FC patterns for each component, region-wise sums of the PLSR FC edge weight matrices were computed.Neuropsychological Testing

[0238] Each subject completed a neuropsychological battery. This included assessments for global cognition and function with the Clinical Dementia Rating CDR®+NACC-FTLD and the Mini-mental status exam (MMSE). The battery also tested the following domains: episodic memory with the short form California Verbal Learning Test (CVLT) and the Benson figure delayed recall from the uniform data set; working memory with the forward and backward digit span length tests; processing speed with the trail making test (Trails A) and Stroop naming tests; executive function with the Stroop interference test, Delis–Kaplan Executive Function System (DKEFS) Design Fluency, and the modified trail making test (Trails B); visuospatial processing with the Benson figure copy test and Number Location subtest of the Visual Object and Space Perception battery (VOSP) ; and speech and language with the Boston Naming Test (BNT), the Peabody Picture Vocabulary Test (PPVT), the animal and vegetable naming tests, the D-letter naming test, syntax comprehension, and verbal articulatory agility. Brain-Behavior Statistical Analysis

[0239] Brain-behavior relationships were estimated with generalized additive models using the ‘mgcv’ package in R. Tests were selected where 120 or more subjects had scores. For each test, a model was set up with the following predictors: atrophy scores for the first three atrophy components, functional scores associated with the first three atrophy components (from ridge regression), and the structure-function score interactions for each component. Each of these terms was restricted to have a maximal non-linear basis of 3 by setting k=3 in the model formula. Explicit structure-by-function interaction terms were not included because non-linear terms estimated by a GAM implicitly capture differences in slope across the range of each variable. Each model included linear covariates for age, sex, years of education, scanner type (Trio vs Prisma), and fMRI head motion (mean framewise displacement). Models were fit for 24 cognitive tests and predictors were deemed significant when their F-statistic associated p-values survived global FDR correction (24 tests x 6 brain- based predictors = 148 terms) with q=0.05.

[0240] A targeted longitudinal model was used to estimate the relationship between F1, S1, and CDR.53 subjects (47 patients, 6 cognitively normal subjects) had longitudinal data (mean visit interval=1.1±0.5 years, range=0.4-2.6 years) that passed all quality control tests. S1 and F1 scores were measured for follow-up scans using the linear weights from atrophyPLSR component S1 for structure and from ridge regression for function. A mixed effects model using ‘mgcv’ with CDR-SB score from each scan-associated visit (106 total) was specified as the outcome variable. The model estimated both between-subject and within- subject variation by including S1 subject mean (averaged across timepoints; non-linear basis k=3 to match the cross-sectional model), S1 longitudinal change (difference from the subject's mean, varying within-subject across timepoints; k=1 to limit model degrees of freedom), F1 mean (k=3), F1 longitudinal change (k=1), age, sex, years of education, and random intercepts for each subject. In a complementary model, F1 was estimated as a function of S1 baseline (k=3), S1 change (k=3), age, sex, years of education, visit interval, and random intercepts for each subject. V. ADDITIONAL CONSIDERATIONS

[0241] Although specific examples have been described, various modifications, alterations, alternative constructions, and equivalents are possible. Examples are not restricted to operation within certain specific data processing environments but are free to operate within a plurality of data processing environments. Additionally, although certain examples have been described using a particular series of transactions and steps, it should be apparent to those skilled in the art that this is not intended to be limiting. Although some flowcharts describe operations as a sequential process, many of the operations may be performed in parallel or concurrently. In addition, the order of the operations may be rearranged. A process may have additional steps not included in the figure. Various features and aspects of the above-described examples may be used individually or jointly.

[0242] Further, while certain examples have been described using a particular combination of hardware and software, it should be recognized that other combinations of hardware and software are also possible. Certain examples may be implemented only in hardware, or only in software, or using combinations thereof. The various processes described herein may be implemented on the same processor or different processors in any combination.

[0243] Where devices, systems, components or modules are described as being configured to perform certain operations or functions, such configuration may be accomplished, for example, by designing electronic circuits to perform the operation, by programming programmable electronic circuits (such as microprocessors) to perform the operation such as by executing computer instructions or code, or processors or cores programmed to execute code or instructions stored on a non-transitory memory medium, or any combination thereof.Processes may communicate using a variety of techniques including but not limited to conventional techniques for inter-process communications, and different pairs of processes may use different techniques, or the same pair of processes may use different techniques at different times.

[0244] Specific details are given in this disclosure to provide a thorough understanding of the examples. However, examples may be practiced without these specific details. For example, well-known circuits, processes, algorithms, structures, and techniques have been shown without unnecessary detail in order to avoid obscuring the examples. This description provides example examples only, and is not intended to limit the scope, applicability, or configuration of other examples. Rather, the preceding description of the examples will provide those skilled in the art with an enabling description for implementing various examples. Various changes may be made in the function and arrangement of elements.

[0245] The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that additions, subtractions, deletions, and other modifications and changes may be made thereunto without departing from the broader spirit and scope as set forth in the claims. Thus, although specific examples have been described, these are not intended to be limiting. Various modifications and equivalents are within the scope of the following claims.

[0246] In the foregoing specification, aspects of the disclosure are described with reference to specific examples thereof, but those skilled in the art will recognize that the disclosure is not limited thereto. Various features and aspects of the above-described disclosure may be used individually or jointly. Further, examples may be utilized in any number of environments and applications beyond those described herein without departing from the broader spirit and scope of the specification. The specification and drawings are, accordingly, to be regarded as illustrative rather than restrictive.

[0247] In the foregoing description, for the purposes of illustration, methods were described in a particular order. It should be appreciated that in alternate examples, the methods may be performed in a different order than that described. It should also be appreciated that the methods described above may be performed by hardware components or may be embodied in sequences of machine-executable instructions, which may be used to cause a machine, such as a general- purpose or special-purpose processor or logic circuits programmed with the instructions to perform the methods. These machine-executable instructions may be stored on one or moremachine readable mediums, such as CD-ROMs or other type of optical disks, floppy diskettes, ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, flash memory, or other types of machine-readable mediums suitable for storing electronic instructions. Alternatively, the methods may be performed by a combination of hardware and software.

[0248] Where components are described as being configured to perform certain operations, such configuration may be accomplished, for example, by designing electronic circuits or other hardware to perform the operation, by programming programmable electronic circuits (e.g., microprocessors, or other suitable electronic circuits) to perform the operation, or any combination thereof.

[0249] While illustrative examples of the application have been described in detail herein, it is to be understood that the inventive concepts may be otherwise variously embodied and employed, and that the appended claims are intended to be construed to include such variations, except as limited by the prior art.

Claims

WHAT IS CLAIMED IS:

1. A computer-implemented method comprising: accessing structural neuroimaging signals and functional neuroimaging signals for a brain of a subject; inputting the structural neuroimaging signals and the functional neuroimaging signals into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; and generating, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and cognitive performance.

2. The computer-implemented method of claim 1, further comprising outputting, a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment.

3. The computer-implemented method of claim 1 or 2, wherein the structural neuroimaging signals are structural magnetic resonance imaging (sMRI) data generated using a Magnetic Resonance Imaging (MRI) scanner, and the functional neuroimaging signals are functional magnetic resonance imaging (fMRI) data generated using the same MRI scanner or a different MRI scanner, wherein the subject is instructed to perform different tasks during sMRI and fMRI data acquisition.

4. The computer-implemented method of claim 1 or 2, wherein the structural neuroimaging signals and / or the functional neuroimaging signals are obtained using one or more of the following techniques: Computed Tomography (CT), Magnetic Resonance Imaging (MRI), diffusion-based MRI, Positron Emission Tomography (PET), Magnetoencephalography (MEG), Transcranial Electrical Stimulation (TES), Photoacoustic Imaging, and Molecular Imaging.

5. The computer-implemented method of any one of claims 1-4, further comprises preprocessing the structural neuroimaging signals and the functional neuroimaging signals to generate structural neuroimaging data and functional neuroimaging data, wherein the structural neuroimaging data and the functional neuroimaging data are input into the structure-function model, and wherein the structural neuroimaging data comprises W-scores as a measurement of gray matter atrophy within the brain, and the functional neuroimaging data comprises functional connectivity patterns across multiple regions of the brain.

6. A computer-implemented method comprising: accessing structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject; inputting the sMRI data and the fMRI data into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; predicting, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and cognitive performance; and generating a treatment or clinical trial protocol for the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment.

7. The computer-implemented method of claim 6, wherein the sMRI data comprises W- scores as a measurement of gray matter atrophy within the brain, and the fMRI data comprises functional connectivity patterns across multiple regions of the brain.

8. The computer-implemented method of any one of claims 1-7, wherein the predetermined number is 3.

9. The computer-implemented method of claim 8, wherein a first principal structure- function component of the three principal structure-function components captures arelationship between global atrophy and a distributed functional connectivity pattern of decreases and increases.

10. The computer-implemented method of claim 8 or 9, wherein a second principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in a left-predominant temporal pole versus right-predominant dorsal parietal cortex.

11. The computer-implemented method of claim 8, 9, or 10, wherein a third principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in left-predominant temporal-occipital lobe versus prefrontal- insula-cingulate areas.

12. The computer-implemented method of claim 6, wherein the generating the treatment or clinical trial protocol comprises stratifying the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and the measure of cognitive impairment, wherein the stratifying is a pattern recognition process based on a two-dimensional matrix and comprises generating a matrix-pattern graph corresponding to weights associated with the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components.

13. The computer-implemented method of claim 12, further comprising rendering the treatment or clinical trial protocol and the matrix-pattern graph in a graphical user interface.

14. The computer-implemented method of claim 13, wherein the graphical user interface comprises the atrophy score and the functional connectivity score for the subject within a correlation plot, an atrophy pattern reflecting the atrophy score, and relationships between the treatment or clinical trial protocol and the matrix-pattern graph based on the stratifying.

15. The computer-implemented method of claim 12, further comprising determining an expected response of the subject to a therapeutic agent based on (i) the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components, (ii) the measure of cognitive impairment, (iii) the matrix-pattern graph, or (iv) a combination thereof.

16. The computer-implemented method of claim 12, further comprising comparing the matrix-pattern graph of the subject with a matrix-pattern graph of the subject prior to a treatment with a therapeutic agent and updating the treatment or clinical trial protocol for the subject based on the comparing.

17. The computer-implemented method of any one of claims 6-16, further comprising: inputting the fMRI data into a dynamic systems model; determining, using the dynamic systems model, a set of eigenmodes for the subject based on the fMRI data and simulated gradient dynamic activity for the subject, wherein each eigenmode of the set of eigenmodes represents one spatio-temporal component of a system, oscillating at a single fixed frequency, and wherein on a given eigenmode, each gradient has a specific amplitude and phase angle; measuring a cumulative amplitude of each gradient and an average phase angle between each pair of the gradients based on the set of eigenmodes for the subject; comparing the cumulative amplitude of each gradient and the average phase angle between each pair of the gradients to the functional connectivity score for each of the predetermined number of principal structure-function components; and validating or explaining the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment based on the comparing.

18. The computer-implemented method of claim 17, wherein the validating or explaining comprises determining an accuracy of the structure-function model, determining the accuracy is greater than a predetermined threshold, and in response to determining the accuracy is greater than the predetermined threshold, generating the treatment or clinical trial protocol for the subject.

19. The computer-implemented method of any one of claims 6-18, wherein the treatment or clinical trial protocol comprises monitoring the subject or administering a monitor of the subject regarding a progress of the cognitive impairment.

20. A system comprising: one or more data processors; anda non-transitory computer readable storage medium containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising: accessing structural neuroimaging signals and functional neuroimaging signals for a brain of a subject; inputting the structural neuroimaging signals and the functional neuroimaging signals into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure- function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; and generating, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and cognitive performance.

21. The system of claim 20, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising outputting, a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment.

22. The system of claim 20 or 21, wherein the structural neuroimaging signals are structural magnetic resonance imaging (sMRI) data generated using a Magnetic Resonance Imaging (MRI) scanner, and the functional neuroimaging signals are functional magnetic resonance imaging (fMRI) data generated using the same MRI scanner or a different MRI scanner, wherein the subject is instructed to perform different tasks during sMRI and fMRI data acquisition.

23. The system of claim 20 or 21, wherein the structural neuroimaging signals and / or the functional neuroimaging signals are obtained using one or more of the following techniques: Computed Tomography (CT), Magnetic Resonance Imaging (MRI), diffusion-based MRI,Positron Emission Tomography (PET), Magnetoencephalography (MEG), Transcranial Electrical Stimulation (TES), Photoacoustic Imaging, and Molecular Imaging.

24. The system of any one of claims 20-23, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising preprocessing the structural neuroimaging signals and the functional neuroimaging signals to generate structural neuroimaging data and functional neuroimaging data, wherein the structural neuroimaging data and the functional neuroimaging data are input into the structure-function model, and wherein the structural neuroimaging data comprises W-scores as a measurement of gray matter atrophy within the brain, and the functional neuroimaging data comprises functional connectivity patterns across multiple regions of the brain.

25. A system comprising: one or more data processors; and a non-transitory computer readable storage medium containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising: accessing structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject; inputting the sMRI data and the fMRI data into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure- function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; predicting, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and cognitive performance; andgenerating a treatment or clinical trial protocol for the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment.

26. The system of claim 25, wherein the sMRI data comprises W-scores as a measurement of gray matter atrophy within the brain, and the fMRI data comprises functional connectivity patterns across multiple regions of the brain.

27. The system of any one of claims 20-26, wherein the predetermined number is 3.

28. The system of claim 27, wherein a first principal structure-function component of the three principal structure-function components captures a relationship between global atrophy and a distributed functional connectivity pattern of decreases and increases.

29. The system of claim 27 or 28, wherein a second principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in a left-predominant temporal pole versus right-predominant dorsal parietal cortex.

30. The system of claim 27, 28, or 29, wherein a third principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in left-predominant temporal-occipital lobe versus prefrontal-insula- cingulate areas.

31. The system of claim 25, wherein the generating the treatment or clinical trial protocol comprises stratifying the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment, wherein the stratifying is a pattern recognition process based on a two-dimensional matrix and comprises generating a matrix-pattern graph corresponding to weights associated with the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components.

32. The system of claim 31, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising rendering the treatment or clinical trial protocol and the matrix-pattern graph in a graphical user interface.

33. The system of claim 32, wherein the graphical user interface comprises the atrophy score and the functional connectivity score for the subject within a correlation plot, an atrophy pattern reflecting the atrophy score, and relationships between the treatment or clinical trial protocol and the matrix-pattern graph based on the stratifying.

34. The system of claim 31, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising determining an expected response of the subject to a therapeutic agent based on (i) the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components, (ii) the measure of cognitive impairment, (iii) the matrix-pattern graph, or (iv) a combination thereof.

35. The system of claim 31, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising comparing the matrix-pattern graph of the subject with a matrix-pattern graph of the subject prior to a treatment with a therapeutic agent and updating the treatment or clinical trial protocol for the subject based on the comparing.

36. The system of any one of claims 25-35, wherein the non-transitory computer readable storage medium further containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform operations comprising: inputting the fMRI data into a dynamic systems model; determining, using the dynamic systems model, a set of eigenmodes for the subject based on the fMRI data and simulated gradient dynamic activity for the subject, wherein each eigenmode of the set of eigenmodes represents one spatio-temporal component of a system, oscillating at a single fixed frequency, and wherein on a given eigenmode, each gradient has a specific amplitude and phase angle; measuring a cumulative amplitude of each gradient and an average phase angle between each pair of the gradients based on the set of eigenmodes for the subject;comparing the cumulative amplitude of each gradient and the average phase angle between each pair of the gradients to the functional connectivity score for each of the predetermined number of principal structure-function components; and validating or explaining the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment based on the comparing.

37. The system of claim 36, wherein the validating or explaining comprises determining an accuracy of the structure-function model, determining the accuracy is greater than a predetermined threshold, and in response to determining the accuracy is greater than the predetermined threshold, generating the treatment or clinical trial protocol for the subject.

38. The system of any one of claims 25-37, wherein the treatment or clinical trial protocol comprises monitoring the subject or administering a monitor of the subject regarding a progress of the cognitive impairment.

39. A non-transitory computer readable storage medium storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations comprising: accessing structural neuroimaging signals and functional neuroimaging signals for a brain of a subject; inputting the structural neuroimaging signals and the functional neuroimaging signals into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; and generating, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and cognitive performance.

40. The non-transitory computer readable storage medium of claim 39, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising outputting, a report summarizing a cognitive impairment status of the subject based on the measure of cognitive impairment.

41. The non-transitory computer readable storage medium of claim 39 or 40, wherein the structural neuroimaging signals are structural magnetic resonance imaging (sMRI) data generated using a Magnetic Resonance Imaging (MRI) scanner, and the functional neuroimaging signals are functional magnetic resonance imaging (fMRI) data generated using the same MRI scanner or a different MRI scanner, wherein the subject is instructed to perform different tasks during sMRI and fMRI data acquisition.

42. The non-transitory computer readable storage medium of claim 39 or 40, wherein the structural neuroimaging signals and / or the functional neuroimaging signals are obtained using one or more of the following techniques: Computed Tomography (CT), Magnetic Resonance Imaging (MRI), diffusion-based MRI, Positron Emission Tomography (PET), Magnetoencephalography (MEG), Transcranial Electrical Stimulation (TES), Photoacoustic Imaging, and Molecular Imaging.

43. The non-transitory computer readable storage medium of any one of claims 39-42, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising preprocessing the structural neuroimaging signals and the functional neuroimaging signals to generate structural neuroimaging data and functional neuroimaging data, wherein the structural neuroimaging data and the functional neuroimaging data are input into the structure-function model, and wherein the structural neuroimaging data comprises W-scores as a measurement of gray matter atrophy within the brain, and the functional neuroimaging data comprises functional connectivity patterns across multiple regions of the brain.

44. A non-transitory computer readable storage medium storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations comprising: accessing structural magnetic resonance imaging (sMRI) data and functional magnetic resonance imaging (fMRI) data for a brain of a subject;inputting the sMRI data and the fMRI data into a structure-function model; determining, using the structure-function model, an atrophy score and a functional connectivity score for each of a predetermined number of principal structure-function components of the structure-function model, which map different atrophy patterns to specific brain-wide functional connectivity alterations; inputting the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components into a cognitive impairment model; predicting, using the cognitive impairment model, a measure of cognitive impairment for the subject based on an estimation of relationships between the atrophy score and the functional connectivity score for each of the predetermined number of principal structure- function components and cognitive performance; and generating a treatment or clinical trial protocol for the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment.

45. The non-transitory computer readable storage medium of claim 44, wherein the sMRI data comprises W-scores as a measurement of gray matter atrophy within the brain, and the fMRI data comprises functional connectivity patterns across multiple regions of the brain.

46. The non-transitory computer readable storage medium of any one of claims 39-45, wherein the predetermined number is 3.

47. The non-transitory computer readable storage medium of claim 46, wherein a first principal structure-function component of the three principal structure-function components captures a relationship between global atrophy and a distributed functional connectivity pattern of decreases and increases.

48. The non-transitory computer readable storage medium of claim 46 or 47, wherein a second principal structure-function component of the three principal structure-function components describes opposing focal atrophy patterns in a left-predominant temporal pole versus right-predominant dorsal parietal cortex.

49. The non-transitory computer readable storage medium of claim 46, 47, or 48, wherein a third principal structure-function component of the three principal structure-functioncomponents describes opposing focal atrophy patterns in left-predominant temporal-occipital lobe versus prefrontal-insula-cingulate areas.

50. The non-transitory computer readable storage medium of claim 44, wherein the generating the treatment or clinical trial protocol comprises stratifying the subject based on the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment, wherein the stratifying is a pattern recognition process based on a two-dimensional matrix and comprises generating a matrix-pattern graph corresponding to weights associated with the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components.

51. The non-transitory computer readable storage medium of claim 50, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising rendering the treatment or clinical trial protocol and the matrix-pattern graph in a graphical user interface.

52. The non-transitory computer readable storage medium of claim 51, wherein the graphical user interface comprises the atrophy score and the functional connectivity score for the subject within a correlation plot, an atrophy pattern reflecting the atrophy score, and relationships between the treatment or clinical trial protocol and the matrix-pattern graph based on the stratifying.

53. The non-transitory computer readable storage medium of claim 50, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising determining an expected response of the subject to a therapeutic agent based on (i) the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components, (ii) the measure of cognitive impairment, (iii) the matrix-pattern graph, or (iv) a combination thereof.

54. The non-transitory computer readable storage medium of claim 50, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising comparing the matrix-pattern graph of the subject with a matrix-pattern graph of the subject prior to a treatment with atherapeutic agent and updating the treatment or clinical trial protocol for the subject based on the comparing.

55. The non-transitory computer readable storage medium of any one of claims 44-54, further storing instructions that, when executed by the one or more processors of the computing system, cause the computing system to perform operations comprising: inputting the fMRI data into a dynamic systems model; determining, using the dynamic systems model, a set of eigenmodes for the subject based on the fMRI data and simulated gradient dynamic activity for the subject, wherein each eigenmode of the set of eigenmodes represents one spatio-temporal component of a system, oscillating at a single fixed frequency, and wherein on a given eigenmode, each gradient has a specific amplitude and phase angle; measuring a cumulative amplitude of each gradient and an average phase angle between each pair of the gradients based on the set of eigenmodes for the subject; comparing the cumulative amplitude of each gradient and the average phase angle between each pair of the gradients to the functional connectivity score for each of the predetermined number of principal structure-function components; and validating or explaining the atrophy score and the functional connectivity score for each of the predetermined number of principal structure-function components and the measure of cognitive impairment based on the comparing.

56. The non-transitory computer readable storage medium of claim 55, wherein the validating or explaining comprises determining an accuracy of the structure-function model, determining the accuracy is greater than a predetermined threshold, and in response to determining the accuracy is greater than the predetermined threshold, generating the treatment or clinical trial protocol for the subject.

57. The non-transitory computer readable storage medium of any one of claims 44-56, wherein the treatment or clinical trial protocol comprises monitoring the subject or administering a monitor of the subject regarding a progress of the cognitive impairment.

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