Apparatus and process for measuring brain activity

Abstract

1. A computer-implemented process for measuring brain activity of a subject, comprising: receiving electroencephalogram (EEG) data representing EEG measurements of the subject's electrical brain activity; fitting parameters of a neuronal population model to the EEG data to determine an inhibitory postsynaptic potential rate constant (γ i and determining corresponding values ​​of said parameters, including one or more values ​​of γ i represents the state of brain responsiveness, and γ i An increase in γ indicates an increased state of brain responsiveness, and i A decrease in the brain's responsiveness indicates a decrease in the computer-implemented process.

Description

[Technical field]

[0001] The present invention relates to devices and processes for measuring brain activity based on electroencephalography (EEG) signals. [Background technology]

[0002]

[0002] Electrical activity in the brain is the result of electrical charge flows generated by neural activity, and fluctuates in characteristic patterns (such as "waves") across adjacent brain regions in response to stimuli. The global synchronous activity of neurons in the human brain can be recorded using electroencephalography (EEG), which involves using electrodes to measure electrical potentials on the outside of an individual's scalp (thus inferring neural function).

[0003]

[0003] EEG provides a simple, non-invasive way to study brain activity based on specific features that appear in the signal output. EEG signals often contain rhythmic features that occur in specific frequency bands, including those referred to in the art as alpha, beta, theta, and delta bands. Alpha rhythmic features have long been considered to be indicators of brain information processing and function. In particular, the characteristic oscillations of the alpha rhythm at 8-13 Hz have played a central role in the phenomenological description of brain electromagnetic activity during cognition and behavior.

[0004]

[0004] The presence of characteristic features in EEG signals has motivated the use of EEG signal analysis for brain function monitoring applications, including seizure diagnosis and treatment (e.g., distinguishing epileptic seizures from other seizures and identifying the area of ​​the brain where a seizure occurs), as well as determining an individual's depth of anesthesia (e.g., during surgery).

[0005]

[0005] Physiological interpretation of features in EEG signals has often involved the use of ensemble models of neuronal populations, referred to in the art as "neuron population models," which represent a large number of interacting neurons as a macroscopic system. Neurophysiological modeling, which is concerned with modeling the structure of the human brain, has utilized neuronal population models in an attempt to understand and characterize the relationship between features of the EEG signals observed from an individual and activity in the individual's brain.

[0006]

[0006] In particular, neuronal population models include sets of parameters describing excitatory and inhibitory neuronal populations, where the values ​​of these parameters specify the predicted electrical responses of the modeled neurons to particular stimuli and inputs. Predicted EEG signals generated by these neuronal population models can reproduce salient features of the EEG, such as the alpha rhythm.

[0007]

[0007] Despite the convenience of conventional means of making brain activity measurements or monitoring based on neurophysiological modeling techniques, there remains room for improvement. It would be desirable to provide brain activity assessment devices and processes that alleviate one or more of the disadvantages of the prior art, or at least provide a useful alternative. Summary of the Invention

[0008] According to some embodiments of the present invention, there is provided a computer-implemented process for measuring brain activity in a subject, the process comprising receiving electroencephalogram (EEG) data representing EEG measurements of the subject's electrical brain activity, fitting parameters of a neuronal population model to the EEG data to determine an inhibitory postsynaptic potential rate constant (γ i and determining corresponding values ​​of said parameters, including one or more values ​​of γ i represents the state of brain responsiveness, and γ i An increase in γ indicates an increased state of brain responsiveness, and i A decrease in β-aminobutyric acid (β-aminobutyric acid) indicates a decrease in the state of brain responsiveness.

[0009] In some embodiments, the step of the process for measuring the subject's brain activity includes measuring γ for each time point to provide real-time monitoring of the subject's brain responsiveness. i is repeated in real time to determine the value of

[0010] In some embodiments, the EEG signal is measured during sedation of a non-stimulated subject, and the determined value γ i quantifies the depth of sedation in subjects and compares γ i A decrease in β indicates a decrease in brain responsiveness or alertness in unstimulated subjects.

[0011] The unstimulated subject may be under anesthesia or undergoing surgery.

[0012] In some embodiments, the reference value is γ in one or more control subjects. i is a predetermined measurement value.

[0013] In some embodiments, the reference value is determined by fitting a neuronal population model to EEG measurements of a subject in an awake or conscious state. i The value is

[0014] In some embodiments, the baseline value is a γ γ -value representing brain activity in one or more control subjects at a level of sedation selected from the group consisting of minimal sedation (stage I), conscious sedation (stage II), deep sedation (stage III), and medullary depression (stage IV). i is a predetermined value.

[0015] In some embodiments, an anesthetic is administered to the subject, and the process described above further comprises: (i)γ i comparing the value of the (ii) determining whether the subject requires additional anesthesia based on the comparison; and (iii) administering additional anesthesia to the subject only if the subject is determined to require additional anesthesia; and Includes.

[0016]

[0016] The subject may be undergoing surgery.

[0017]

[0017] In some embodiments, the supplemental anesthesia is delivered by an automated anesthetic delivery system.

[0018] In some embodiments, γ i The one or more values ​​of quantify an alpha rhythm characteristic of the subject's brain activity.

[0019] According to some embodiments of the present invention, there is provided a system for measuring brain activity in a subject, the system comprising: at least one network interface configured to receive data from a communications network; at least one computer processor; a memory coupled to the at least one computer processor and storing instructions that, when executed by the at least one computer processor, cause the at least one computer processor to perform any of the brain activity measurement processes described above; Equipped with.

[0020] According to some embodiments of the present invention there is provided an apparatus for measuring brain activity in a subject, the apparatus comprising: (i) receiving EEG data representing EEG measures of electrical brain activity of a subject; (ii) Fitting the parameters of the neuronal population model to the EEG data, we obtain the inhibitory postsynaptic potential rate constant (γ i specifying one or more values ​​of said parameters, including one or more values ​​of at least one computing device having a neural population model fitting component configured to: Gamma i represents the state of brain responsiveness, and γ i An increase in γ indicates an increased state of brain responsiveness, and i A decrease in β-aminobutyric acid (β-aminobutyric acid) indicates a decrease in the state of brain responsiveness.

[0021]

[0021] In some embodiments, the neuronal population model fitting component is configured to perform any of the brain activity measurement processes described above.

[0022] In some embodiments, the apparatus comprises: generating EEG data by processing EEG signals acquired from one or more electrodes; Send the EEG data to the neuronal population model fitting component The device includes an EEG monitoring component configured to:

[0023]

[0023] According to some embodiments of the present invention, one or more computer-readable storage media are provided that store instructions that, when executed by at least one processor of a computing system or device, cause the at least one processor to perform any of the brain activity measurement processes described above.

[0024]

[0024] Also described in the specification is a process for identifying physiological parameters for assessing brain function, the process comprising receiving EEG data representative of electrical brain activity of one or more individuals, accessing neuronal population model data representative of a neuronal population model having one or more model parameters, generating fitted model parameter data representative of estimated parameter values ​​for the one or more model parameters according to a model fitting process that fits the one or more model parameters to the EEG data, processing the fitted model parameter data to generate parameter identifiability data representative of at least an individual identifiability of each model parameter, and processing the parameter identifiability data to generate deterministic parameter data representative of an indication of one or more deterministic parameters characterizing one or more features of the EEG data, whereby values ​​of the deterministic parameters provide an indication of corresponding brain function of the assessed individual.

[0025]

[0025] In some embodiments, generating parameter identifiability data includes, for each parameter, i) estimating the marginal posterior distribution of the parameter, and ii) identifying the difference in variability of the parameter between the prior distribution and the posterior distribution.

[0026] In some embodiments, the Kullback-Leibler divergence is used to measure differences in parameter variability.

[0027] In some embodiments, the parameter identifiability data further represents the collective identifiability of the model parameters.

[0028] In some embodiments, the collective identifiability of the model parameters is determined from an eigenanalysis of a Fisher information matrix derived from the parameters.

[0029]

[0029] In some embodiments, the identifiability of the model parameters is processed to generate an indication of the sloppiness of the model, which represents the sensitivity of predictions of neuronal populations to variations across one or more model parameters.

[0030] In some embodiments, the deterministic parameter data is processed to generate optimized neuronal population model data representing a new neuronal population model with reduced degrees of freedom.

[0031] In some embodiments, the neuronal population model is described by a coupled set of first-order and second-order ordinary differential equations.

[0032]

[0032] In some embodiments, the neuronal population model defines interactions between inhibitory and excitatory neuronal populations based on a set of physiological parameters.

[0033]

[0033] In some embodiments, the physiological parameters include one or more measures of resting membrane potential, membrane potential, mean firing rate, firing threshold, passive membrane decay time constant, excitatory postsynaptic potential rate constant, inhibitory postsynaptic potential rate constant, postsynaptic potential amplitude, the rate of excitatory or inhibitory input to any population, and the total number of connections that an excitatory or inhibitory neuron receives from either nearby excitatory or inhibitory neurons.

[0034]

[0034] In some embodiments, the deterministic parameter set includes a measure of the dynamics of inhibitory synaptic activity of one or more individuals, as represented by at least one postsynaptic inhibitory rate constant parameter, for characterizing the alpha rhythm characteristics of the EEG data.

[0035]

[0035] In some embodiments, the model fitting process involves accessing prior distribution data describing an assumed distribution for each parameter, determining an estimated criterion function for evaluating candidate parameters based at least in part on the EEG data, and generating sample value data representing at least estimated parameter values ​​according to the fitting algorithm and the estimated criterion function.

[0036] In some implementations, the fitting algorithm is a particle swarm optimization (PSO) algorithm, where the estimated parameter values ​​are derived based at least in part on the minimization of a least-squares cost function.

[0037] In some embodiments, the fitting algorithm is a Markov Chain Monte Carlo (MCMC) algorithm, where the estimated parameters are derived by maximizing a likelihood function of the parameters.

[0038] In some embodiments, the EEG data is processed prior to performing the model fitting process to generate at least one EEG spectrum.

[0039] In some embodiments, at least one EEG spectrum is generated by averaging spectra derived by superimposing time series EEG signals of one or more individuals.

[0040]

[0040] In some embodiments, the estimated criterion function includes i) a predicted model spectral function of a neural population model and ii) a corresponding likelihood function of the predicted model spectral function, where the estimated parameter values ​​are derived based on at least one EEG spectrum and the estimated criterion function.

[0041]

[0041] Also described herein is a system configured to perform neurophysiological assessment, comprising: (i) a data handler for receiving EEG data representative of electrical brain activity of one or more individuals and accessing neuronal population model data representative of a neuronal population model having one or more model parameters; (ii) a sampling and estimation unit for generating fitted model parameter data representative of estimated parameter values ​​for one or more model parameters based on a model fitting process that fits the one or more model parameters to the EEG data; and (iii) a parameter analyzer for processing the fitted model parameter data to generate parameter identifiability data representative of at least an individual identifiability of each model parameter, and for processing the parameter identifiability data to generate deterministic parameter data representative of an indication of one or more model parameters characterizing one or more features of the EEG data.

[0042]

[0042] Also described herein is a process for assessing brain function during a surgical procedure being performed on a patient, the assessment of brain function being based on generating values ​​of one or more parameters identified from a neurophysiological model, the parameters being identified according to the physiological parameter identification process described herein.

[0043]

[0043] A process for assessing brain function during administration of anesthesia to a patient is also described, the assessment of brain function being based on generating at least a value of an inhibitory postsynaptic potential rate constant parameter of a neurophysiological model, the inhibitory postsynaptic potential rate constant parameter characterizing alpha rhythm features of electroencephalogram (EEG) data of a human individual.

[0044] Some embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0045] [Figure 1]FIG. 1 is a block diagram of a neurophysiological assessment device according to some embodiments of the present invention. [Diagram 2] FIG. 2 is a block diagram of a computing device of the neurophysiological evaluation apparatus. [Figure 3a] 1 is a flow diagram of a process for parameter identification for neurophysiological assessment according to some embodiments of the present invention. [Figure 3b] 1 is a flow diagram of a process for identifying brain functions for neurophysiological assessment according to some embodiments of the present invention. [Figure 4] FIG. 4 is a flow diagram of a model fitting process for the neurophysiological evaluation process of FIG. 3. [Diagram 5] 1 is a flow diagram of a process for generating parameter identification data for a neurophysiological evaluation process. [Figure 6] FIG. 1 is a schematic block diagram of a feedback system for generating predicted model spectra during model fitting for a neurophysiological assessment process. [Figure 7] 11 is a set of graphs of power spectral density as a function of frequency for six subjects showing the best fit of model parameters using least-squares based estimation for the neurophysiological assessment process. [Figure 8] 11 is a set of graphs of power spectral density as a function of frequency for six subjects showing the best fit of model parameters using maximum likelihood based estimation for the neurophysiological assessment process. [Figure 9] 1 is a set of graphs showing the posterior distribution for each parameter for seven subjects as generated based on particle swarm optimization (PSO) sampling for the neurophysiological assessment process. [Figure 10] 1 is a set of graphs showing the posterior distribution for each parameter for seven subjects as generated based on Markov Chain Monte Carlo (MCMC) sampling for the neurophysiological assessment process. [Figure 11]13 is a plot showing the values ​​and distribution of Kullback-Leibler divergence for each parameter identified from a particle swarm optimization (PSO) sampling based fit for the neurophysiological assessment process. [Figure 12] 13 is a plot showing the values ​​and distribution of Kullback-Leibler divergence for each parameter identified from a Markov Chain Monte Carlo (MCMC) sampling-based fit for the neurophysiological assessment process. [Figure 13] FIG. 13 is a graph showing the Fisher Information Matrix (FIM) eigenspectrum generated based on the best fit of model parameters using least-squares based estimation for the neurophysiological assessment process. [Figure 14] 13 is a graph showing the FIM eigenspectrum generated based on the best fit of the model parameters using maximum likelihood based estimation for the neurophysiological assessment process. [Figure 15] 13 is a graph of the FIM eigenvector components corresponding to the first, second and third eigenvalues ​​based on a best fit of the model parameters using least squares based estimation for the neurophysiological assessment process. [Figure 16] 13 is a graph of the FIM eigenvector components corresponding to the first, second and third eigenvalues ​​based on a best fit of the model parameters using maximum likelihood based estimation for the neurophysiological assessment process. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] (Overview)

[0045] There is an important clinical need to be able to measure brain activity in subjects in real time, especially during medical interventions such as surgery, and to monitor anesthesia levels during surgery. Features of EEG signals from human individuals relate to their brain activity. For example, alpha rhythm is a defining feature of human resting EEG signals and has played a central role in the phenomenological description of brain electromagnetic activity during cognition. A macroscopic approach to the assessment of brain function by characterization of EEG features such as alpha rhythm (herein referred to as "neurophysiological assessment") is based on neuronal population models. Traditionally, neuronal population model parameters are identified by an iterative tuning method, where the best parameters are selected from the tuning set as parameters that cause the model to generate (or "predict") an EEG signal that exhibits a particular feature of the observed EEG signal (e.g., a particular alpha oscillation). It is assumed that the match of features between the predicted EEG signal and the observed EEG signal indicates model parameter values ​​that accurately and therefore meaningfully represent the neural activity.

[0047]

[0046] However, neuronal population models are high-order multi-parameter dynamical systems, and therefore different combinations of model parameters may generate not only similar predictions, but often identical predictions. That is, there is a many-to-one mapping between combinations of neuronal population model parameter values ​​and the resulting features in the predicted EEG signal. This many-to-one mapping between parameter inputs and model observables is referred to in the art as structural non-identifiability when the predictions are strictly identical, and "virtual non-identifiability" when the predictions are nearly identical. As a result, a drawback of conventional neuronal population model parameter adjustment is that it is prone to generate structurally non-identifiable models that, when fitted to data, result in large correlated parameter uncertainties for the variations made to the parameter values.

[0048]

[0047] Parameters that sensitively affect the model predictions are called "stiff", whereas parameters that can be changed with little effect on the predictions are called "sloppy". A further drawback of tuning-based approaches is that the resulting neuronal population model may contain a large number of "sloppy" parameters. As a result, the sensitivity of the neuronal population model's predictions may be undesirably affected, whereby values ​​of different parameters (or combinations of parameters) may be estimated with different confidences and therefore accuracy.

[0049]

[0048] Compared to conventional neural model parameter adjustment, a more desirable approach would be to obtain model parameters directly from observed EEG data for a given individual. The ability to estimate these parameters by direct fitting to EEG data promises to provide a real-time, non-invasive method of inferring neuronal properties in various individuals, such as for the purpose of assessing brain function. Despite this promise, the problem of estimating the complete set of parameters and their uncertainties directly from fitting to EEG data is much more difficult to solve compared to parameter adjustment. However, it has not been previously recognized that determining which parameters (or combinations of parameters) are "stiff" and which are "sloppy" can be beneficial for usefully fitting these nonlinear multi-parameter neural models to real EEG data.

[0050]

[0049] Illustrated embodiments of the present invention include an apparatus and process for measuring brain activity in a subject, where a neuronal population model is fitted to EEG data collected from the subject, and an inhibitory postsynaptic potential rate constant (γ i ) are identified, which constitute a quantitative measure of the subject's brain activity. In the described embodiment, the inhibitory postsynaptic potential rate constant (γ i) were identified by a model fitting process that involves obtaining certain parameters of the model. These parameters can be identified for the neural population model using a fitting process based on group data (i.e., data obtained from a training or validation group). An assessment of the subject's brain function can then be performed based on EEG data obtained in real time from the subject.

[0051]

[0050] In particular, the presented apparatus comprises a neurophysiological assessment component that receives EEG data representative of electrical brain activity of one or more individuals. Neuronal population model data is accessed, where the data represents a neuronal population model having certain parameters. The received EEG data is then processed to identify neuronal population model parameters (e.g., by estimating parameter values ​​for one or more model parameters in light of the data). The resulting model is then processed to generate data representative of the individual identifiability of each model parameter (e.g., based on the variability between a prior distribution and a corresponding posterior distribution). The parameter identifiability data is then used to identify "critical" model parameters. These are parameters that are identifiable and "stiff" in the sense that they characterize one or more features of the EEG data (e.g., alpha rhythm).

[0052]

[0051] Given an indication of the critical parameters, the neurophysiological assessment component identifies brain function (or "activity") of a subject (e.g., a patient undergoing a surgical procedure) based on measured EEG data from the subject. Estimates of the values ​​of the critical parameters are generated by fitting neuronal population models to the measured EEG data (as opposed to conventional approaches that rely on direct analysis of the EEG signal for features of interest).

[0053]

[0052] In some embodiments, the neurophysiological assessment component receives the measured EEG data and fits a neural population model to the data to generate real-time estimates of the deterministic parameter values. Following model fitting, the values ​​of the deterministic parameters can be processed to provide an indication of the subject's corresponding brain activity. While the neurophysiological assessment described herein calculates the deterministic parameters through a model fitting process, in other embodiments, the neurophysiological assessment component may be configured to perform measurements of brain activity based on prior knowledge of the deterministic parameters (i.e., without performing a parameter identification sub-process).

[0054]

[0053] Postsynaptic inhibitory rate constant parameter γ i was identified as crucial to the alpha rhythm characteristic of the EEG signal and the gamma rhythm measured from the subjects. i An application of the presented device is described in which an estimate of α can be used as a functional indication of a subject's brain activity. In this application, a neurophysiological model is fitted to EEG data exhibiting alpha oscillations for resting-state EEG recordings from 82 human subjects. The critical parameters identified using the device form a set with a significantly reduced dimensionality compared to the original model parameter space (as described below). For example, by identifying critical parameters that characterize specific EEG features, the presented device and process enable real-time and non-invasive characterization of the physiological properties that underpin the brain activity of a human individual.

[0055]

[0054] In the described embodiment, the identifiability of each parameter is determined by estimating the marginal posterior distribution of the parameter. The Kullback-Leibler divergence (KLD) is used to separate the information derived from the data (as described below) from the information already present in the prior distribution. A measure of the individual identifiability of a parameter is generated by determining the difference in the variability of the parameter between the prior and posterior distributions. For example, the presence of significantly lower variability in the posterior distribution compared to the prior distribution of an EEG feature (e.g., alpha rhythm) indicates that the parameter is identifiable for that feature (e.g., the rate constant associated with inhibitory synaptic activity as shown herein below).

[0056]

[0055] In the described embodiments, the difference between the marginal posterior and marginal prior distributions is used to infer information about the parameters individually. In some embodiments, the apparatus and process are configured to generate parameter identifiability data that further represents the collective identifiability of the model parameters. In such embodiments, the collective identifiability of the model parameters is determined from an eigenanalysis of a Fisher information matrix derived from the parameters. That is, the apparatus uses indications of second-order behavior of the model to infer interactions between parameters, where these interactions cannot be identified by considering only the marginal posterior distributions of each parameter individually.

[0057]

[0056] Eigenanalysis of the Fisher information matrix has the advantage that it allows correlations between parameters to be evaluated without requiring the estimation of joint posterior distributions, which can be overly computationally intensive, especially in the case of high-dimensional parameter spaces. Using this approach, the device can generate a quantitative measure of identifiability for combinations of multiple model parameters. In some embodiments, the device also generates a measure of the sloppiness of the neuronal population model, which represents the sensitivity of the predictions of the neuronal population model to each of the model parameters.

[0058]

[0057] The identification of parameter identifiability and sloppyness measures can be used to quantify the degree to which a model is over-parameterized. In particular, the presence of correlation between parameter estimates suggests that model complexity can be reduced by grouping together, removing or averaging a subset of model parameters. In this way, the device can be configured to process deterministic parameter data to refine the neuronal population model in order to generate a refined model with reduced degrees of freedom but without compromising predictive ability.

[0059] In the described embodiment, the neurophysiological assessment is performed using EEG signal recordings obtained from one or more different individuals. The EEG signal recordings can be selected to highlight spatial locations of oscillatory brain activity associated with the individual's brain activity function. For example, the device can be configured to receive signals obtained from specific electrodes (e.g., electrodes at Oz, Cz, or Pz locations) to highlight specific features from the resulting recordings, etc. The received time series signal of EEG data, once appropriately segmented, is processed to generate a single EEG frequency spectrum for each of the one or more individuals at one or more spatial scalp locations. However, while using a single spectrum per individual reduces the computational requirements for performing the model fitting operation, such a constraint is not required and does not in any way limit the applicability of the process of the present invention to multiple spatial locations and spectra.

[0060]

[0059] In the described embodiment, the EEG spectral signal representation is fitted to a neuronal population model characterized by a coupled set of first-order and second-order ordinary differential equations. This allows the neuronal population model to define the interactions between inhibitory and excitatory neuronal populations (i.e., neurons that have inhibitory and excitatory influences on postsynaptic targets, respectively) based on a set of physiological parameters. These parameters can include, but are not limited to, for each excitatory and inhibitory population, resting membrane potential, synaptic reversal potential, mean firing rate, firing threshold, passive membrane decay time constant, postsynaptic potential amplitude, and rate of excitatory or inhibitory input to either population. Additional parameters can include excitatory postsynaptic potential rate constant, inhibitory postsynaptic potential rate constant, and the total number of connections that an excitatory or inhibitory neuron receives from either nearby excitatory or inhibitory neurons.

[0061]

[0060] In the described embodiment, the fitted model data is generated through a model fitting process performed by the neurophysiological assessment component on the EEG data. As explained above, a problem with conventional approaches to fitting neural population models is that a wide range of parameter combinations may fit the observed spectrum. A sampling-based approach is implemented by the apparatus and process described herein and involves generating many instances of parameter values ​​based on a prior distribution for each parameter. Sample values ​​are identified for each parameter by the fitting process according to the prior distribution. An estimated criterion function is identified to evaluate candidate parameter values ​​during the fitting process based on at least the EEG data. As a result, the sample value data generated by the fitting algorithm converges towards a parameter value distribution estimate that is the best fit to the observed EEG data.

[0062]

[0061] The apparatus may be configured to utilize a particle swarm optimization (PSO) or Markov chain Monte Carlo (MCMC) fitting algorithm to generate marginal posterior parameter distributions from the sampled parameter values ​​(as described herein below). In other embodiments, alternative fitting algorithms may be implemented to generate the marginal posterior parameter distributions (e.g., by generating a sample set of values ​​for each parameter, filtering or selecting from the sample set, and then estimating the posterior distributions from the reduced set of values).

[0063]

[0062] The device and process described herein provide a platform for neurophysiological assessment that identifies parameter values ​​for a given neuronal population model from EEF data dynamically observed in real time. The platform can be used to provide the clinician with an indication of the specific parameters or combinations of parameters that determine one or more characteristic features of the EEG observations. As a result, by using EEG data that includes a specific feature of interest (or selecting this data as a subset of the EEG data received during processing), insight can be gained into which specific parameters are most likely to take into account the feature of interest. Knowing these critical parameters, the clinician can use the device to monitor the brain function of the subject (e.g., in the context of a surgical procedure), since estimates of these critical parameters obtained in real time from EEG recordings measured from the subject can be used to make inferences regarding brain activity.

[0064] For example, most of the drugs used to induce a state of surgical anesthesia are believed to work by altering the time course of postsynaptic inhibition. By fitting neural models to EEG data (as described herein), the postsynaptic inhibitory rate constant γ iIdentifying EEG features can provide a real-time process for quantifying the functional effects of anesthesia, thus improving upon standard methods of neurophysiological assessment that are not built on underlying theories of brain dynamics. The apparatus and process described herein also advantageously provide a way to reduce the dimensionality of the neuronal population model compared to the original model parameter space based on identifying the most identifiable parameters, thereby increasing the practicality of using the model (i.e., because specified EEG features can be predicted with fewer degrees of freedom without compromising accuracy). (Neurophysiological evaluation device)

[0065]

[0064] Figure 1 is a block diagram of a neurophysiological assessment apparatus 100 according to an embodiment of the present invention. The apparatus comprises an EEG monitoring component 105 and a neurophysiological assessment component 102. The EEG monitoring component 105 is configured to generate EEG signal data representative of EEG signals of electrical brain activity of one or more individuals 131-13M.

[0066] In some embodiments, the EEG monitoring component 105 comprises one or more electrodes for measuring electrical brain activity of one or more individuals, and one or more associated EEG signal processing components (e.g., differential amplifiers, analog-to-digital converters, and anti-aliasing filters) for generating EEG recording data representing a time-domain signal of the recordings. In the described embodiment, the EEG monitoring component 105 outputs a set of EEG recordings for each individual. In some embodiments, the apparatus 100 does not comprise an EEG monitoring component 105, and the EEG signal data is received from an external device (e.g., a third-party EEG system, etc.).

[0067] In the described embodiment of the apparatus 100, the neurophysiological assessment component (NAC) 102 is a computing device configured to execute a software application with modules comprising a user interface (UI) 104, a control unit 106, a data handler 108, a sampling and estimation unit 110, a parameter analyzer 112, and a data store 114. In other embodiments, the aforementioned modules may be implemented by one or more dedicated hardware components of the device 102.

[0068]

[0067] The NAC 102 is operated by a user 103, such as a clinician or other professional seeking to obtain diagnostic information regarding an individual's neurological characteristics. The user 103 interacts with the NAC 102 via a UI 104. The UI 104 is configured to receive user input, generate graphical user interface (GUI) data representing GUI elements, and display corresponding output (e.g., via one or more peripherals and a display of a computing device).

[0069]

[0068] The controller 106 provides logical control and configuration functions to the NAC 102. The controller 106 receives input and configuration data from the UI 104 in relation to corresponding input and configuration instructions provided to the components 102 by the user 103. The controller 106 communicates with the data handler 108, the sampling and estimation unit 110, and the parameter analyzer 112 to control the neurophysiological evaluation processes (such as process 300) described herein according to options specified by the user 103.

[0070]

[0069] The controller 106 is also configured to access EEG data including a time domain representation of EEG recordings obtained from the individuals 131-13M by the EEG monitoring component 105. In a described embodiment, the EEG data is received directly from the EEG monitoring component 105 via data transmission between the component 105 and the modeling component 102. In a described embodiment, the NAC 102 receives the EEG data from the EEG monitoring component 105 via communication over the communication network 120 using a secure communication protocol. In other embodiments, the monitoring component 105 is configured to transfer the data to the component 102 via a direct connection (e.g., Ethernet over a LAN).

[0071]

[0070] The controller 106 may also be configured to retrieve previously stored EEG data for one or more individuals 131-13M from the data store 114. The controller 106 transfers the received EEG data to and from the data store 114 and / or to the data handler 108, the user interface 104, and the sampling and estimation unit 110 to enable the neurophysiological assessment process described herein to be performed.

[0072]

[0071] The data handler 108 performs signal analysis and processing operations on the EEG signals and / or neural model data. In the described embodiment, the data handler 108 receives the EEG data in the form of a time domain representation (e.g., a discrete time series signal, etc.) of the EEG recordings for M individuals 131-13M. The data handler 108 performs operations that may include, but are not necessarily limited to, spectral estimation, time and / or frequency averaging, and pre- or post-filtering.

[0073]

[0072] The sampling and estimation unit 110 is configured to perform a fitting between the processed EEG data and a neuronal population model for certain parameters of the model. The neuronal population model and the corresponding fitting algorithm used by the unit 110 are determined based on control data provided by the control module 106.

[0074]

[0073] Parameter analyzer 112 is configured to generate measures of parameter identifiability and / or model sloppiness from the fitted neuronal population model data. Analyzer 112 is configured to generate data indicative of particular critical parameters and / or parameter combinations based on the generated measures and particular critical parameter criteria. The critical parameter criteria may vary according to configuration options specified by user 103 (as described below).

[0075]

[0074] The data store 114 is configured to store data utilized by the component 102, including configuration data, neural model data, and EEG data. The configuration data specifies options and configuration variables of the component 102 for performing the neural modeling and evaluation process described herein. In some embodiments, the neural model data specifies, for each particular neural population model, the type of model, the structural elements of the model (e.g., an equation describing the model), and the parameters of the model. The neural model data also includes instances of fitted model parameter data and parameter identifiability data generated for the model. In some embodiments, the EEG data includes at least a time domain representation of EEG recordings for the individuals 131-13M received by the NAC 102, and processed EEG data (e.g., averaged and / or spectral representations) resulting from application of analysis and processing operations to the time domain data.

[0076]

[0075] In the described embodiment of the apparatus 100, the NAC 102 is implemented as one or more computer systems 200, such as, for example, Intel architecture computer systems, as shown in Figure 2, and the processes executed by the systems 200 are implemented as programming instructions in one or more software modules 202 stored in non-volatile (e.g., hard disk or solid state drive) storage 204 associated with the computer systems. However, it will be apparent that at least one or more portions of these processes may alternatively be implemented as configuration data in a field programmable gate array (FPGA) and / or as one or more dedicated hardware components, such as, for example, an application specific integrated circuit (ASIC).

[0077]

[0076] The system 200 comprises a random access memory (RAM) 206, at least one processor 208, and external interfaces 210, 212, 214, all interconnected by a bus 216. The external interfaces include a universal serial bus (USB) interface 210, at least one of which is connected to a keyboard 218 and a pointing device such as a mouse 219, a network interface connector (NIC) 212 that connects the system 200 to a communications network 120, which may be a wide area network (such as the Internet), and a display adapter 214 that is connected to a display device such as an LCD or LED panel display 222.

[0078]

[0077] The system 200 also includes a number of standard software modules 226-230 including an operating system 224, such as Linux (registered trademark) or Microsoft Windows (registered trademark), web server software 226, such as Apache available at http: / / www.apache.org, scripting language support 228, such as PHP or Microsoft ASP available at http: / / www.php.net, and Structured Query Language (SQL) support 230, such as MySQL available at http: / / www.mysql.com, which enables data to be stored in and retrieved from an SQL database 232.

[0079] In the described embodiment, component 102 operates as a standalone computing device where database 232 is a local database managed by data store component 114. Database 232 is implemented using SQL and is accessed by a database management system (DBMS) of component 102. In other embodiments, database 232 may be implemented in a separate computing device or across multiple computing devices, according to one or more techniques for distributed processing and storage of data. (Neurophysiological evaluation process)

[0080] 3 shows a neurophysiological assessment process 300 performed by the device 100 to identify physiological parameters for assessing brain function. In step 301, pre-configuration operations are performed on the monitoring component 105 and the modeling component 102 to initialize and / or configure the device 100. The configuration of the monitoring component 105 may include placement of electrodes for collecting electrical activity signals from the individuals 131-13M and setting up a processing device for generating EEG data from electrode readings (i.e., during a clinical EEG recording procedure).

[0081]

[0080] Configuration of the NAC 102 is performed by the user 103. The controller 106 receives user input and configuration data from the UI 104 based on input obtained from the user 103. The NAC configuration can include the user 103 specifying information regarding certain system functions, including selection of EEG data, analysis and processing of the selected EEG data, neural population model and parameter priors and / or fitting process selection, identifiability criteria for generating a critical parameter set, and optional refinement of the initial neural model based on the critical parameters (e.g., reducing the number of parameters in the model).

[0082]

[0081] In some embodiments, the selection of EEG data used for modeling is based on the presence of one or more particular features of interest in the EEG signal represented by the data. In some embodiments, the UI 104 provides functionality (e.g., in the form of visualization or display functionality indicating the presence of EEG features, such as rhythmic components, in the recorded signal) that allows the user 103 to evaluate the suitability of particular received and / or stored EEG data for modeling a behavior. In other embodiments, the device 100 can be configured to automatically perform neurophysiological evaluations based on real-time EEG data received from the monitoring component 105 (or other source) or retrieved from the data store 114.

[0083]

[0082] It should be noted that while configuration is described as a preliminary step for the embodiments discussed herein, in other embodiments, the various functions of the device 100 can be configured at other points during the neurophysiological evaluation process 300. For example, the selection of the EEG data to be used for modeling can be performed following at least some of the processing of the time-domain EEG data (i.e., evaluating the spectral characteristics and then selecting the EEG data according to the presence or other aspects of certain spectral features).

[0084]

[0083] In step 302, EEG data is received by the NAC 102. In the described embodiment, the EEG data includes separate time series records for each electrode of the monitoring component 105 for each individual 131-13M. In step 304, neuronal population model data is retrieved from the data store 114 according to a selected neuronal population model that has been fitted to the EEG data. The selected neuronal population model may be selected by the user 103 (e.g., during the configuration step 301) or may be automatically determined by the controller 106 (e.g., according to a default model setting).

[0085]

[0084] An embodiment of a neuronal population model corresponding to the default model of NAC102 is described below. The default model is the neuronal population model of Liley et al. (Liley DTJ, Cadusch PJ, Dafilis MP. A spatially continuous mean field theory of electrocortical activity. Network 2002;13:67). This well-known model (see Coombes S. Large-scale neural dynamics: Simple and complex. NeuroImage 2010;52:731) is described by a coupled set of first-order and second-order ordinary differential equations given by Eqs. (1)-(6), where the meanings of the variables are given in Table 1 below. This model is implemented as the default model because the semi-analytical and numerical solutions of the above equations reveal a rich repertoire of physiologically plausible activities, including driven noise, limit cycles and chaotic fluctuations in the frequency range of mammalian alpha rhythms.

number

number

[0086] These equations describe the interactions between inhibitory and excitatory neuronal populations. In particular, the excitatory population (h e (t)) and the inhibitory population (h i The temporal dynamics of the average somatic membrane potential for synaptic activity (t) is described in Eqs. (1) and (2). ee (t), I ie (t), I ei (t) and I ii The temporal dynamics of (t) are given in equations (3)-(6). The average population firing rate S j The relationship between the mean somatic membrane potential of each population and the local field potential of the excitatory population h is given in equation (7). Previous studies have shown that the local field potentials measured in the EEG correspond to the mean somatic membrane potential of each population h. e It has been shown to be linearly proportional to the mean somatic membrane potential (t).

[0087]

[0086] The neural cell population model data also includes one or more neural model parameters. Table 1 shows the model parameters for the neural cell population models described above, along with their corresponding physiological ranges. [Table 1] JPEG0007601796000004.jpg225149

[0088]

[0087] In some embodiments, the data handler 108 is configured to process the selected EEG data and / or neuronal population model data prior to generation of the fitted model data (i.e., step 305). For example, in the described embodiment, the data handler 108 is configured to generate a spectral frequency domain representation of each time domain signal in the EEG data. In Welch's averaging method (described in Welch P. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Transactions on audio and electroacoustics. 1967;15(2):70-73), a single spectrum for a particular individual is estimated using spectra derived from multiple overlapping time segments. This approach improves the accuracy of the power spectral density (PSD) estimate by sacrificing some spectral resolution. The data handler 108 performs the spectral estimation using a sampling frequency and window function as selected during configuration. For the described embodiment, model parameter fitting was performed based on a spectral representation of the EEG data, but in other embodiments, fitting is performed using time-domain EEG signals. In some embodiments, the data handler 108 is configured to process the neural model ensemble data, such as to perform a parameter simplification operation prior to model data fitting. For example, by equating one or more of the parameters (as described below), the effective dimensionality of the model is reduced, improving computational efficiency.

[0089]

[0088] In step 306, a model fitting process is performed to generate fitted model parameters representing a set of estimates for the parameters of the neuronal population model. Figure 4 is a flow diagram of the model fitting process of the described embodiment performed by the sampling and estimation unit 110, which involves accessing prior distribution data representing an estimated distribution for each parameter (i.e., step 402). In step 404, the sampling and estimation unit 110 identifies an estimated criterion function to be used in the fitting procedure (i.e., to evaluate candidate values ​​based at least in part on EEG data). In the described embodiment, the estimated criterion function includes i) a predicted model spectral function and ii) a corresponding likelihood function. These functions are used to generate spectral and likelihood values ​​for the candidate model parameters considered during the fitting (i.e., to derive the best parameter estimates based on the EEG spectral data and the estimated criterion function).

[0090]

[0089] The sampling and estimation unit 110 determines the predicted model spectrum and likelihood function based on the neural population model. For the default neural model of the described embodiment, the predicted model spectrum function is calculated from a spatially homogeneous version of the full model equations (i.e., equations (1)-(6) above). In the described embodiment, the predicted model spectrum is calculated under the following assumptions: i) The system is linearly stable in the vicinity of a particular solution (eg, the solution corresponding to the eyes-open and eyes-closed spectra at rest in the evaluation discussed below). ii) Excitability rate constant γ ee and γ ei is equal to the inhibitory rate constant γ ie and γ ii The same applies to. iii) The measured EEG signal is expressed as the excitatory mean somatic membrane potential, h e is proportional to. iv) The linearized system is eeis driven by Gaussian white noise fluctuations in the external excitability to

[0091]

[0090] Under these assumptions, the linear system transfer function T(s) can be shown to be that of a simple feedback system 600 as shown in Figure 6, involving two third-order filters H1(s) and H2(s) according to the following:

number

[0092]

[0091] Polynomial k 11 (s) and k 22 (s) is linear in s and k 33 (s) and k 55 (s) is quadratic in s. Let θ be the vector of model parameters. If the spectrum is assumed to arise from a white noise spectrum filtered by this transfer function, then given θ, the predicted value of the spectral estimate at frequency w has the form

number

[0093]

[0092] where the constant α accounts for the unknown drive amplitude and accounts for volume conduction and other (frequency independent) effects. The value of α is obtained using a least squares fit to the measured spectral estimates. The analytical results are as follows:

number

[0094]

[0093] The sampling and estimation unit 110 determines the likelihood function of the predicted spectral function described above by ignoring the effect of overlapping windows and non-uniform window shapes in the resulting distribution. Furthermore, assuming a sufficiently high sampling rate and negligible measurement noise, each sampling frequency 2πf nthe spectral estimates from the Welch periodograms for n=1, 2,...,N are approximated as independent random variables with known distributions. These simplifications are made to improve the computational requirements of the function determination step 404. However, in other embodiments, the effects mentioned above can be taken into account.

[0095] With these simplifications, the spectral estimate S n The probability distribution function (pdf) for is a gamma distribution.

number

[0096]

[0095] For non-zero frequency, the shape parameter K is obtained from the number of epochs averaged in the periodogram (for zero frequency, replace the variable K with K / 2). The scale parameter is given by:

number

[0097]

[0096] Then, the vector of spectral estimates S=[S1S2...S N ] T The likelihood function of is the product of the distributions of the individual spectral estimates.

number

[0098] The constant α is adjusted to give a maximum likelihood fit of the model spectrum to the target experimental spectrum.

number

[0099]

[0098] Then, the likelihood function based on the model parameters is as follows:

number

[0100]

[0099] In step 406, the sampling and estimation unit 110 generates sample data representing estimated model parameter values ​​according to a fitting process and an estimation criterion function. The fitting process can be selected during configuration or determined by the controller 106 according to a default setting of the NAC 102. In particular, the described components implement two processes for fitting model parameters to the spectral-frequency EEG data: a Particle Swarm Optimization (PSO) based on least-squares minimization and a Markov Chain Monte Carlo (MCMC) method with maximum likelihood estimation.

[0101] As known to those skilled in the art, PSO solves a high-dimensional parameter space

number

number

number

number

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[0102] where ψ is a given inertial weight proposed by Shi and Eberhart (see A modified particle swarm optimizer. In: Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on. IEEE; 1998. p. 69-73),

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[0103] When using the PSO fitting process, the sampling and estimation unit 110 calculates the measured spectrum S and the normalized (predicted) model spectrum S.

number

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[0104]

[0103] An initial sample generation process is performed which involves using 1000 independent instantiations of PSO, resulting in 1000 different parameter estimates. By default, the algorithm uses 80 particles per group. Parameter starting points are selected by random sampling from a uniform distribution over the physiologically relevant range, as given in Table 1. During the parameter search, each parameter is forced to stay within its physiologically relevant range by assigning a high cost to particles with values ​​outside these ranges. This is similar to using a Bayesian prior which is flat over the acceptable parameter range and zero everywhere else. This results in 1000 parameter estimates.

number

[0105]

[0104] The samples generated from the initial sampling process described above are then filtered to remove samples that are not an acceptable fit. The sampling and estimation unit 110 is configured to accept only the 10 percent of the estimates that have the lowest cost function. In other embodiments, alternative filtering strategies can be implemented.

[0106]

[0105]

number

[0107] Alternatively, the sampling and estimation unit 110 can perform the fitting operation using MCMC methods. Under this process, an explicit Bayesian framework is used by treating the parameters as random variables to integrate the parameter estimation and posterior distribution determination steps. PSO involves both sample generation and sample selection steps, while MCMC involves sample generation (with burn-in) of long sequences based on log-likelihood ratios and, if necessary, resampling to generate the mean (for KLD estimation). Given a known prior distribution, p0(θ), it is desirable to obtain the posterior distribution condition on the observed spectrum S by the following formula:

number

[0108]

[0107] In the described embodiment, the computation is simplified by searching for a local maximum in the neighborhood of the MCMC sampled parameters that maximizes the likelihood function (given by equation (17)) evaluated for the observed spectrum. The sampling and estimation unit 110 performs Monte Carlo estimation by randomly drawing values ​​from a known prior distribution. To obtain these values, a Metropolis-Hastings Markov Chain Monte Carlo (MCMC) algorithm is implemented based on the log-likelihood ratios obtained from the likelihood function described above, as follows:

number

[0109] The sampled sets acquired for each target spectrum were 10 with a step size (of normalized parameter values) adjusted during a burn-in phase of length 40000. 6MCMC samples, resulting in an acceptance rate of 0.25 in the neighborhood. Where appropriate, sampled long sequences are resampled, typically to obtain sequences of length 1000, on which the mean is based. For consistency with particle swarm methods, the prior distribution is assumed to be uniform over its support.

[0110]

[0109] The parameter analyzer 112 determines the best-fit model parameters

number

[0111]

[0110] In the described embodiments, an identifiability measure is generated for each model parameter individually (referred to as "individual identifiability"). In some embodiments, identifiability is also evaluated for one or more combinations of specific model parameters, resulting in a "collective" identifiability measure (as described below).

[0112]

[0111] Figure 5 is a flow diagram illustrating the generation of data representing measures of individual parameter identifiability. In step 501, particular model parameters are selected for identifiability assessment. The selected parameters may be specified by the user 103 (such as during configuration) or may be automatically selected by the NAC 102 (such as according to default options).

[0113] In step 502, the parameter analyzer 122 (via the controller 106) retrieves distribution data for each selected parameter. In step 504, distribution variability data is generated that represents the individual identifiability of each selected parameter. In the described embodiment, the Kullback-Leibler divergence (KLD) is calculated to measure the information gained about a single parameter as a result of measuring the spectrum. The parameter analyzer 112 calculates the KLD to measure the change in the marginal posterior distribution of each selected parameter relative to its marginal prior distribution.

number

[0114]

[0113] When KLD is used to measure how different the posterior parameter estimates are from the uniform priors predicated for parameter fitting performed with MCMC samples, the integrals are numerically evaluated using marginal distributions approximated by kernel density estimates using 1000 parameter values ​​resampled from the full MCMC sampled parameter set for a given spectrum. In this embodiment, the prior distributions are assumed to be uniform over their support. For consistency, the posterior kernel estimates are truncated to have the same support. The kernel density estimate for a given parameter is sampled at 100 points over its support and the integrals numerically estimated. For parameter fitting performed with PSO, the integrals are estimated using a 10-bin histogram approximation due to the limited number of independent samples.

[0115]

[0114] In some embodiments, the parameter analyzer 112 is configured to generate parameter identifiability data that also represents the identifiability of the combination of model parameters (i.e., referred to as a "collective" measure of identifiability) and / or sloppiness of the model. In (optional) step 506, the collective parameter identifiability is determined based on the Fisher Information Matrix (FIM) of the model. The eigenvalues ​​of the Fisher Information Matrix for a distribution P(S|θ) are given by:

number

[0116]

[0115] Parameter analyzer 112 evaluates equation (23), resulting in an equation involving only the derivatives of the model spectral estimate at the desired parameter values.

number

[0117]

[0116] In the described embodiment, the parameter analyzer 112 is configured to evaluate equation (24) using a five-point finite difference approximation, where the resulting products are summed over the sampled frequencies. Numerical experiments with surrogate matrices suggest that the calculated eigenvalues ​​can be reliable over several tens of orders of magnitude. In the described embodiment, the parameter analyzer 112 assumes that the FIM is semi-positive definite and less than the maximum rank of the modeled spectrum. Thus, the negative eigenvalues ​​and the 10th of the maximum eigenvalue are summed over the sampled frequencies. -10 Eigenvalues ​​less than x are considered to be zero.

[0118]

[0117] The parameter identifiability data generated by analyzer 112 includes distribution variability data and, if generated, Fisher information matrix data. In some embodiments, the parameter identifiability data also includes parameter accuracy data representing one or more measures of accuracy and / or precision of the best fit values.

[0119]

[0118] Referring to the flow diagram of Figure 3, the parameter identifiability data is processed to generate a set of deterministic model parameters, which are parameters that characterize features of the EEG data. In some embodiments, the deterministic parameter set is generated automatically by the parameter analyzer 112 based on identifiability criteria that can be configured by the user 103 (e.g., N-best selection, which identifies identifiable parameters as those with the N highest KLD values, etc.).

[0120] In other embodiments, the NAC 102 is configured to accept user input for generating the deterministic parameter set. For example, the parameter identifiability data can be displayed to the user 103 and the user 103 can be allowed to select particular parameters (e.g., based on the user's own consideration of the KLD and / or FIM values) to form the deterministic set.

[0121]

[0120] The parameter analyzer 112 can be configured to generate a measure of model sloppiness based on the parameter identifiability data. Model sloppiness is defined by the presence of eigenvalues ​​of the Fisher Information Matrix (FIM) that are approximately uniformly spaced across a logarithmic scale. The eigenvalues ​​of the FIM identify the sloppy and stiff parameter eigenvector directions. Larger FIM eigenvalues ​​define the eigenvector directions that correspond to a particular identifiable parameter combination. To understand which parameters contribute most to each (identifiable) eigenvector, the angular distance between each parameter direction and a given eigenvector is calculated. The closer the angular distance is to 0° or 180°, the more the parameter contributes to the parameter combination, and therefore the more identifiable the parameter is. In some embodiments, analysis of simulated spectral data can also be used to assess the accuracy and / or precision of parameters for the purpose of constructing a definitive parameter set.

[0122]

[0121] The generated deterministic parameter data is accessed by the controller 106 and then made available to the user 103 (i.e., via the UI 104). The user 103 can then review the identified parameters in light of the EEG data and characteristics of interest thereof, and in some embodiments provide instructions to the NAC 102 to simplify the neuronal population model. In response to such instructions, the deterministic parameter data is processed to generate optimized neuronal population model data representing the new neuronal population model with reduced degrees of freedom (relative to the initial model). Operations performed by the parameter analyzer to generate the (new) optimized neuronal population model may include grouping together, removing or averaging subsets of parameters.

[0123]

[0122] In step 310, the NAC 102 is configured to utilize the deterministic parameter data to identify aspects of brain function (or brain state activity) of a particular subject (e.g., one of the individuals 131-13M, or another individual for whom EEG data was not received in step 302 to identify the deterministic parameters). As illustrated by FIG. 3b, the process of assessing the subject's brain function involves receiving EEG data representative of an EEG recording obtained from the subject (i.e., step 312). The subject's EEG data is received in the form of a time domain signal. This signal is processed in step 314 to generate a frequency spectral representation according to the process described herein above (i.e., for step 305). A segmentation is performed on the subject EEG data such that spectral analysis is performed on overlapping time domain data segments of a fixed maximum length (i.e., to verify the signal stationarity assumption).

[0124]

[0123] In step 316, model parameter data is generated by fitting a neuronal population model to each EEG spectrum (generated in step 314). For example, model fitting proceeds according to a fitting process that can be selected as a PSO or MCMC process described above (i.e., in step 306). The fitted model parameter data includes at least, for each critical model parameter, a representation of an estimate (referred to as a "critical parameter estimate").

[0125]

[0124] In some embodiments, the deterministic parameter estimates are processed in step 318 to apply certain adjustments or transformation operations to the values. For example, the values ​​of certain deterministic parameters may be scaled to ensure that each value falls within a scaling range. The scaling range may be identified empirically by applying a neural population model fitting process to data collected from one or more validation individuals. Alternatively, the NAC 102 may be configured by applying a predetermined scaling factor to each parameter value, where the scaling factor may be essentially constant (i.e., "global") or may vary dynamically based on the characteristics of the subject (e.g., as specified by the user 103).

[0126]

[0125] Based on the processed deterministic parameter estimates, an indication of brain activity is determined for the subject. Because the deterministic parameters are characteristic of particular EEG features, the scaled (or otherwise processed) estimates of these parameters provide an indication of the underlying aspects of brain function known to be associated with particular EEG features. The brain activity indications output by the NAC 102 can then be used in clinical applications, such as to determine whether or not to perform a particular action, without requiring direct analysis of the subject's EEG data (i.e., step 322).

[0127]

[0126] The indication of brain activity produced by the NAC 102 can be a measurement in the form of a single value (e.g., obtained from aggregating a fixed number of estimates of each deterministic parameter in the case of separate EEG recordings of the subject). Alternatively, the indication of brain activity can be a sequence of deterministic parameter estimates obtained from successively recorded EEG signals. This provides the clinician with a corresponding time series measure of brain activity that can be utilized to monitor (i.e., measure at successive time points) the subject's brain function in response to the operation of the procedure.

[0128]

[0127] As shown in Figure 3b, the indications of brain activity output by the NAC 102 can be used as part of a closed-loop feedback system. In particular, an assessment of brain function based on deterministic parameter estimates generated by real-time EEG recordings of the subject can be used to determine whether or not to perform a particular clinical action (such as step 322) on the subject. Model Parameter Estimation for Alpha Rhythm EEG Data

[0129]

[0128] The neurophysiological evaluation process described herein above i) generated deterministic parameters for the neuronal population model described above to characterize the alpha rhythm (this step is referred to as "evaluating" the model), and ii) the deterministic parameter estimates were then applied to the EEG data containing the alpha rhythm features for the purpose of providing a measure of brain function (or "activity") during surgery.

[0130]

[0129] The evaluation proceeded with experimental EEG data representing EEG signals collected from 82 individuals in a resting state. The experimental EEG data received by NAC102 to perform the evaluation is a subset of a larger EEG evaluation dataset, where the evaluation dataset consists of data acquired across 14 experimental tasks performed by 109 subjects. EEG recordings were acquired using 64 electrodes according to the international 10-10 system. The complete EEG evaluation dataset collected and contributed by Schalk et al. (i.e., Schalk G, McFarland DJ, Hinterberger T, Birbaumer N, Wolpaw JR. BCI2000: a general-purpose brain-computer interface (BCI) system. IEEE Transactions on biomedical engineering. 2004;51(6):1034-1043) using the BCI2000 measurement system is available for public access on PhysioNet (https: / / www.physionet.org / pn4 / eegmmidb / ). The EEG recordings used for the evaluation included the Oz electrode and signals from individuals whose EEG spectra exhibited alpha rhythm characteristics (i.e., in the form of a distinct alpha peak as obtained during the relevant eyes-closed task). It is noted that alpha band activity obtained from a single electrode (such as from the Oz electrode in the evaluation above) represents a superposition of multiple independent, spatially distributed alpha rhythm generators. By fitting models to signals from multiple electrodes simultaneously, it may be possible to differentiate between these different sources.

[0131]

[0130] The NAC 102 was configured to use the default neuronal population model described herein above. The model specifies 26 physiological parameters for evaluation purposes (see Table 1), while the data handler 108 selects p ie and p ii is set as a fixed constant and the postsynaptic potential velocity is set as γ ee =γei ≡γ e and γ ie =γ ii ≡γ i A simplification of the model was configured by setting: The resulting neural model has 22 effective parameters, where the values ​​were calculated by applying a fitting process to the experimental EEG data.

[0132]

[0131] Processing of the EEG data involved generating a 1-minute EEG signal associated with a particular individual, sampled at 160 Hz, divided into multiple segments using a 4-second Hamming window with 50% overlap. The data handler 108 was configured to assume stationarity over the 1-minute EEG signal, where stationarity means that this is a constant parameter, whereas the states are allowed to fluctuate around a stable fixed point. The deviation of the states from the fixed point was assumed to be small enough to allow linearization of the model.

[0133]

[0132] The parameters were assumed to be constant within a given EEG signal, but they may of course vary between different recordings (and therefore individuals). Due to well-known nonlinearities and nonstationarities in EEG recordings, linearized models were used in the estimation procedure only for frequencies between 2 Hz and 20 Hz. It can be assumed that well over 95% of the spectral power in the resting M / EEF falls below 30 Hz. In fact, a common measurement of the resting M / EEG spectral edge frequency (SEF95) (i.e., the 139 frequency with 95% of the spectral power below 139 frequencies) is in the range of 24-26 Hz.

[0134] To demonstrate the accuracy of the estimation method, parameters can be estimated using simulated spectra, where the underlying parameter set is known (called ground truth). A reasonable parameter set for this study was selected using maximum likelihood estimates obtained for subject 77. The simulated spectra were calculated by sampling each frequency channel from the gamma distribution model predictions.

[0135] A parameter fitting process based on Particle Swarm Optimization (PSO) and Markov Chain Monte Carlo (MCMC) was applied as described above. Estimation of 22 posterior distributions was performed using both algorithms for each of the 82 different EEG spectra (i.e., for each unknown model parameter).

[0136]

[0135] Figure 7 is a set of graphs of power spectral density as a function of frequency for six subjects showing the use of PSO to obtain the best parameter fit using least squares (LS). Each graph shows a comparison of the model spectrum (blue dotted line) fit to the experimental spectrum (red thick line) by least squares (LS) minimization using particle swarm optimization for a selected set of subjects. The 16% and 84% quantiles for the gamma distribution of the fitted spectra are also shown (black thin line). Subjects were selected that represented the range of spectra included in the complete data set.

[0137]

[0136] Figure 8 is a set of graphs of power spectral density as a function of frequency for six subjects, showing the use of an MCMC method to obtain the best parameter fit, sampling the solution based on maximum likelihood (ML) estimation. The figure shows a comparison of the model spectrum (blue dotted line) fit to the experimental spectrum (red thick line) by maximum likelihood (ML) estimation using MCMC. The 16% and 84% quantiles are also shown (black thin line). The subjects are the same as in Figure 7. Note that the LS and MS fits are expected to be different in this case, because the LS fit is more sensitive to deviations in the unweighted spectral power (usually in regions with larger power), whereas the ML fit is more sensitive to deviations in regions with smaller spectral power variations (usually in regions of lower spectral power).

[0138]

[0137] Although the fits shown in Figures 7 and 8 have similarities, slight differences can be observed. For example, in subject 72, the ML fit performs better in regions with lower power, but not in regions with higher power. This difference is expected because LS is calculated over the unweighted power spectrum, whereas ML favors frequencies with lower variability, which are usually frequencies with lower power spectra.

[0139] 9 and 10 show a set of graphs showing a comparison of the posterior (colored solid lines) and a priori (green lines) marginal distributions for selected subjects for PSO and MCMC sampling, respectively. The top row, which corresponds to the analysis of the simulated spectra, also shows the ground truth values ​​(red). Each parameter is plotted in normalized coordinates, where -1 corresponds to the lower limit and +1 corresponds to the upper limit of the plausible parameter interval (see Table 1).

[0140] When using PSO, the distribution is based on kernel density estimates from the best 100 of 1000 random seed particle swarm optimizations per subject. The seeds are uniformly distributed over the allowed parameter range. Over the complete set of 82 subjects, the parameter γ i It is observed that only σ is significantly constrained. All other parameters have approximately the same uncertainty as the prior distribution.

[0141] When using MCMC, each distribution is 6 Based on kernel density estimates from 1000 samples (subsampled from 1 MCMC samples). Consistent with the observations from using PSO sampling, when viewed across all subjects, the parameter γ i Only is consistently constrained.

[0142]

[0141] The posterior distributions obtained using PSO sampling are usually broader than those obtained using MCMC sampling. This behavior is expected from the differences between the sampling methods, where MCMC sampling is able to preserve correlations between samples even with large subsampling, while different PSO samples are independent of each other. This demonstrates that the PSO approach is superior, at least under the sampling conditions used here. Nevertheless, the only distribution that both methods are consistently constrained by data across different subjects is the inhibitory ensemble postsynaptic potential rate constant γ i This indicates that.

[0143]

[0142] To assess the extent to which the actual data reduces the uncertainty in the estimation of each parameter, Kullback-Leibler Divergence (KLD) values ​​from all 82 subjects for each parameter are calculated as shown in Figure 11 (for PSO) and Figure 12 (for MCMC). In particular, Figure 5 shows the KLD of the marginal posterior parameter distributions calculated for a uniform prior distribution. The posterior distributions are based on the best 100 of 1000 random seed runs of particle swarm optimization (see Figure 9). The boxes represent the 25% and 75% quantiles, the whiskers represent the 5% and 95% quantiles, the red line shows the median KLD, and the circle represents the mean KLD of the distribution of KLD over the complete set of 82 subjects.

[0144] The result is that the parameter γ i We confirm that γ is best constrained by the data. Most other posterior distributions are only slightly narrower than their priors. Table 2 shows the analysis of simulated spectra performed to evaluate the accuracy and precision of the parameter estimates. Shown in the table is the average deviation of the estimates from the ground truth values ​​normalized to the prior distributions of the parameters. The accuracy given by the standard deviation of the sample estimates is also shown. The values ​​in bold are the top three lowest values ​​per category. For both PSO and MCMC sampling, γ i The estimate of always has the highest precision and also has one of the highest accuracy rates. [Table 2]

[0145]

[0144] Figure 13 shows the eigenvalues ​​of the Fisher Information Matrix (FIM) on the logarithmic scale for selected subjects. The FIM is calculated using dimensionless increments in parameters corresponding to a least-squares fit to the experimental spectra. Of the 22 possible eigenvalues, roughly 7 correspond to zero, at least to the numerical accuracy of the eigenvalue estimation routine. Of the remaining 15, usually 7 are too small (relative to the largest eigenvalue) to be calculated reliably. The roughly uniform distribution of eigenvalues ​​on the logarithmic scale is a characteristic of sloppy models. The blue dotted line depicts the separation of the identifiable regime (above the dotted line) from the unidentifiable regime (below the dotted line). Thus, about 5 parameter combinations are usually identifiable, suggesting that the 22-parameter model can be described using 5 or 6 effective parameters.

[0146]

[0145] Figure 14 shows the corresponding analysis for the MCMC method, where the FIM eigenspectra are calculated around the best fit obtained from maximum likelihood optimization for each subject's spectrum.

[0147]

[0146] In the examples shown in Figures 13 and 14, the eigenvalues ​​are roughly uniformly spaced across the logarithmic scale and spread over many decades, indicating that the neuronal population model is sloppy. Comparing these eigenspectra across different subjects suggests that there are typically about five identifiable parameter combinations per subject.

[0148]

[0147] The larger the FIM eigenvalue, the more the eigenvector direction corresponds to the identifiable parameter combination. To understand which parameters contribute most to each (identifiable) eigenvector, the angular distance between each parameter direction and a given eigenvector is calculated. The closer the angular distance is to 0° or 180°, the more the parameter contributes to the parameter combination, and therefore the more identifiable the parameter is.

[0149]

[0148] Figure 15 shows the components of the eigenvectors corresponding to the first, second and third eigenvalues ​​based on the LS best fit. Alignment of the leading eigenvector for each parameter. Values ​​of 0° and 180° represent perfect alignment (maximum contribution), whereas 90° represents orthogonality (no contribution). To compare the 82 subjects, the results are presented as angle distributions (red lines). The first row is for the largest eigenvalue, the second row for the second largest eigenvalue, etc. The blue line shows the predicted angle distribution of randomly oriented vectors in the 22-dimensional parameter space, showing how these are most likely to be orthogonal to any parameter direction. The angle is the inverse cosine of the vector's direction cosine. The distribution is scaled by the parameter γ i and (to a lesser extent) γ e We show that,can play a significant role in identifying the spectral morphology by itself.,The remaining parameters mostly appear in complex combinations.,Figure 16 shows the corresponding distribution of,eigenvectors based on the ML best fit.

[0150] The results shown in Figures 15 and 16 again show that γ i parameter is large. This has the largest contribution to the stiffest parameter direction, which indicates that it can be identified. Interestingly, the postsynaptic potential rate constant for the excitatory population, γ e dominates the third stiffest parameter combination, which is γ e But, γ i We show that eigenvalues ​​can also play an identifiable role in driving system dynamics, albeit to a lesser extent than

[0151] In the evaluation described above, the device 100 generated a deterministic parameter set consisting of five identifiable model parameter combinations that characterize the alpha peak characteristics of the input experimental EEG data. Among these parameters, the postsynaptic potential rate constant γ iis determined to be largest (i.e., identifiable). This supports the quantitative analysis presented above, where there are only about five identifiable eigenvalues ​​in the FIM spectrum (indicating that the number of effective parameters in our model is only about five).

[0152] Some insight into the role of the critical parameters can be gained by further inspecting the modeled spectrum, such as by considering its derivative in the direction of the leading eigenvector of the Fisher information matrix. In a broad sense, for most subjects, the leading eigenvector (effectively the rate parameter γ i ) appears to be related to the variation in the position of the alpha peak, the second eigenvector to (somewhat more loosely) the height of the alpha peak compared to the overall background level, and the third to the width of the alpha peak. The remaining combinations do not appear to be related to easily identifiable features of the spectrum. Importantly, although each eigenvalue may have contributions from all 22 original parameters, the main three eigenvectors appear to be influenced by only a few of these. This is due to the fact that γ i is the only clearly identifiable parameter, a subset of other parameters is also constrained. This shows that the important parameters of the alpha peak, i.e., its position, height and width, are constrained by only a few original parameters, especially γ i This suggests that the term is identified by

[0153]

[0152] Postsynaptic inhibitory rate constant γ i The identification of γ as a critical parameter for indicating brain function has clinical importance in the context of surgical anesthesia. In particular, the majority of drugs used to induce a state of surgical anesthesia are thought to act by altering the time course of postsynaptic inhibition. i By fitting model parameters to EEG data, it is possible to determine the postsynaptic inhibitory rate constants, providing real-time physiological insight into the functional effects of anesthesia, i.e., γ iBy monitoring EEG, aspects of an individual's brain function (e.g., state of surgical anesthesia) can be inferred that would otherwise have to be derived from an individual's directly observed EEG signal (and subsequent analysis of alpha rhythm features), which may not be possible (e.g., in a surgical setting).

[0154] In view of the above, the apparatus 100 uses γ to quantify the effect that an anesthetic agent has on structural aspects of brain function. i That is, from the EEG data of a given subject, i By estimating the value of , the subject's brain activity can be measured or monitored for clinical purposes.

[0155] In some embodiments, the device 100 is configured to receive EEG data representing EEG measures of electrical brain activity in the subject, and measure brain activity in the subject by fitting parameters of a neuronal population model to the EEG data to identify corresponding values ​​of said parameters. This value is the inhibitory postsynaptic potential rate constant (γ i ) and the value of γ i An increase in γ indicates an improved state of brain responsiveness, and i A decrease in β-aminobutyric acid (β-aminobutyric acid) indicates a decreased state of brain responsiveness.

[0156]

[0155] Continuous real-time monitoring of brain activity in a subject is performed based on received EEG data obtained from the subject, using γ i This can be achieved by iteratively identifying multiple values ​​(i.e., estimates) for θ and applying a fitting process (described above) to fit a neuronal population model to the EEG data.

[0157]

[0156] The reference value can be determined in various ways according to the particular configuration of the NAC 102. In some configurations, the reference value is a single numerical value determined according to application of a brain activity state measurement process. The reference value can be a constant or can vary according to the type of sedation or anesthetic drug treatment administered to the subject. γ i The determination that the value of γ is above or below the reference value can be interpreted differently depending on the application. For example, for the purpose of monitoring the depth of unstimulated sedation, the γ i A decrease in can indicate decreased brain activity or alertness in the subject.

[0158] In some configurations, the reference values ​​are predefined values ​​representative of brain activity in one or more control subjects. The set of control subjects may be identified based on application of a brain function monitoring or measurement process (e.g., to take into account certain characteristics of the surgical procedure, such as sedation level, and / or the subject of the surgery). In other configurations, the reference values ​​are identified by classification and / or mathematical analysis. For example, a neuronal population model may be fitted to EEG data obtained from an awake or conscious subject to identify relevant reference values ​​for measuring brain activity states during a subsequent surgery.

[0159]

[0158] In some configurations, the reference value is taken from a range of values. For example, a reference interval can be specified by a minimum reference value and a maximum reference value, where the estimated γ i is compared to one or both of a minimum and a maximum baseline value to identify a corresponding indication of the subject's measured brain activity. i There may be multiple reference values ​​for the purpose of indicating whether or not the sedation level is within a particular reference interval (e.g., separate intervals for stages I-IV sedation levels, as described below).

[0160]

[0159] The device 100 can be applied to measure brain activity to monitor the depth of sedation in unstimulated subjects, and γ i A decrease in is indicative of decreased responsiveness or alertness in the subject. The baseline value may be determined as described above according to the configuration of the device. In some configurations, the baseline value represents brain activity of one or more control subjects at a sedation level selected from the group consisting of minimal sedation (stage I), conscious sedation (stage II); deep sedation (stage III); and medullary depression (stage IV).

[0161]

[0160] Sedation levels are typically used to quantify the responsiveness of a subject and the state of one or more vital functions (airway reflexes, spontaneous ventilation, and cardiovascular function) in response to administration of a sedative-type drug. Under minimal sedation (stage I), the subject typically responds to verbal commands, and airway reflexes, as well as ventilation and cardiovascular function, are unaffected. Moderate sedation (stage II, or "conscious sedation") is a reduction in consciousness during which the subject responds purposefully to verbal commands alone or with slight tactile stimulation. Deep sedation (stage III) is a reduction in consciousness during which the subject cannot be easily awakened, but can respond purposefully following repeated or painful stimulation, and usually maintains cardiovascular function, although he or she may have difficulty maintaining ventilatory function independently. Medullary depression (stage IV) is a loss of consciousness during which the subject cannot be aroused by painful stimuli, may have difficulty maintaining respiratory function independently (whereby positive pressure ventilation of the airways may be required due to reduced spontaneous ventilation or drug-induced depression of neuromuscular function), and cardiovascular function may be impaired.

[0162]

[0161] The device 100 can be configured to monitor the depth of sedation while a resting subject is undergoing a surgical procedure and / or when the subject is under anesthesia. In some applications, the device 100 is used to administer an initial dose of anesthesia to the subject, measure brain activity in the subject by receiving EEG data from the subject, and measure γ by fitting the EEG data to a neuronal population model. i Determine the measured value of γ i If decreases relative to the baseline value, it is determined that the subject requires additional anesthesia, and anesthesia can be administered to the subject by administering additional anesthesia to the subject in need of additional anesthesia.

[0163] For example, with reference to the sedation levels discussed above, it may be desirable to maintain a subject in a state of deep sedation during a surgical procedure. i An increase in γ can indicate that the subject is awake. In this case, additional anesthesia is administered to maintain the desired sedation. However, if too much anesthesia is administered, the subject will experience a decrease in γ relative to baseline. i Thus, brain function of a subject while under anesthesia can be monitored in real time, where the measured γ i The value is used to control administration of anaesthetic over a period of time (eg, for the duration of a surgical procedure) according to the feedback delivery process of FIG. 3b.

[0164]

[0163] Many modifications will become apparent to those skilled in the art without departing from the scope of the invention.

[0165]

[0164] Throughout this specification, unless the context otherwise requires, the words "comprise" and its variations "comprise" or "comprising" etc. are understood to mean the inclusion of a stated whole or step, or group of whole or steps, but not the exclusion of any other whole or step, or group of whole or steps.

[0166]

[0165] Reference in this specification to any prior publication (or information derived therefrom) or any known thing is not, and should not be construed as, an acknowledgement or acceptance, or any form of suggestion, that that prior publication (or information derived therefrom) or known thing forms part of the common general knowledge in the art to which this specification pertains.

Claims

1. 1. A computer-implemented process for measuring brain activity of a subject, comprising: (i) receiving electroencephalogram (EEG) data representative of electroencephalogram (EEG) measurements of electrical brain activity of the subject; (ii) Fitting the parameters of the neuronal population model to the electroencephalogram data, the inhibitory postsynaptic potential rate constant (γ ｉ determining corresponding values ​​of said parameters, including one or more values ​​of Including, According to the neuronal population model, γ ｉ represents the state of brain responsiveness of the subject, and γ ｉ An increase in γ indicates an enhanced state of brain responsiveness, and ｉ A decrease in the level of responsiveness of the brain indicates a decrease in the state of responsiveness of the brain. fitting parameters of the neuronal population model to the electroencephalogram data; estimating parameter values ​​for said parameters based on said electroencephalogram data; processing the neural population model to generate data representative of individual identifiability of each of the parameters; and Identifying γ i as a critical model parameter; Computer-implemented processes.

2. (iii) Step (i) and step (ii) are repeated in real time to obtain γ ｉ 2. The computer-implemented process of claim 1, further comprising determining a value of , and providing real-time monitoring of responsiveness of the brain of the subject.

3. The electroencephalogram signal was measured during sedation in unstimulated subjects, and γ ｉ The identified value of γ quantifies the depth of sedation of the subject, and ｉ3. The computer-implemented process of claim 2, wherein a decrease in indicates a decrease in brain responsiveness or alertness of the unstimulated subject.

4. The computer-implemented process of claim 3 , wherein the unstimulated subject is anesthetized.

5. The computer-implemented process of claim 3 , wherein the unstimulated subject is undergoing surgery.

6. The reference value is γ ｉ The computer-implemented process of any one of claims 1 to 5, wherein the predetermined measure of

7. The reference value is determined by fitting a neuronal population model to electroencephalogram measurements of the subject in an awake or conscious state. ｉ The computer-implemented process of any one of claims 1 to 5, wherein the value of

8. The baseline values ​​are γ γ -γ ... ｉ 4. The computer-implemented process of claim 3, wherein the predetermined value is:

9. The computer-implemented process of claim 8 , wherein the subject is undergoing surgery.

10. The baseline value is a γ ｉ 10. The computer-implemented process of claim 9, wherein the predetermined value is

11. The reference value is determined by fitting a neuronal population model to electroencephalogram measurements of the subject in an awake or conscious state. ｉ 10. The computer-implemented process of claim 9, wherein the value of

12. The baseline values ​​are γ γ -γ ... ｉ 10. The computer-implemented process of claim 9, wherein the predetermined value is

13. Gamma ｉ 6. The computer-implemented process of claim 1, wherein the one or more values ​​of quantifies an alpha rhythm characteristic of the brain activity of the subject.

14. 1. A system for measuring brain activity in a subject, comprising: at least one network interface configured to receive data from a communications network; at least one computer processor; a memory coupled to said at least one computer processor and storing instructions which, when executed by said at least one computer processor, cause said at least one computer processor to perform a process according to any one of claims 1 to 13; A system comprising:

15. 1. An apparatus for measuring brain activity in a subject, comprising: (i) receiving electroencephalogram data representative of electroencephalogram measurements of electrical brain activity of the subject; (ii) Fitting the parameters of the neuronal population model to the electroencephalogram data, the inhibitory postsynaptic potential rate constant (γ ｉ ) one or more values ​​of said parameters, at least one computing device having a neural population model fitting component configured to: According to the neuronal population model, γ ｉ represents the state of brain responsiveness of the subject, and γ ｉ An increase in γ indicates an enhanced state of brain responsiveness, and ｉ A decrease in the level of responsiveness of the brain indicates a decrease in the state of responsiveness of the brain. fitting parameters of the neuronal population model to the electroencephalogram data; estimating parameter values ​​for said parameters based on said electroencephalogram data; processing the neural population model to generate data representative of individual identifiability of each of the parameters; and Identifying γ i as critical model parameters; Device.

16. The apparatus of claim 15, wherein the neural population model fitting component is configured to perform the process of any one of claims 2 to 13.

17. generating said electroencephalogram data by processing electroencephalogram signals obtained from one or more electrodes; Sending the electroencephalogram data to the neural population model fitting component 17. Apparatus according to claim 15 or 16, comprising an electroencephalogram monitoring component configured to:

18. One or more computer-readable storage media storing instructions which, when executed by at least one processor of a computing system or device, cause the at least one processor to perform a process according to any one of claims 1 to 13.

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