Methods and related aspects for identifying tumor subtypes

Abstract

Examples may provide a method of identifying tumor subtypes. The method includes using a variational autoencoder (VAE) and a radiomic feature space comprising a set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features and identifying relationships between tumor subtypes in a set of predicted tumor segmentations using trajectory inference. The methods also include generating predicted risk scores for each tumor in the set of predicted tumor segmentations, discovering radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes, and producing a set of identified tumor subtypes at least partially based on comparisons of a distribution of PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes. Related methods, systems, and computer readable media are also provided.

Description

METHODS AND RELATED ASPECTS FOR IDENTIFYING TUMOR SUBTYPESCross-Reference to Related Applications

[0001] This application claims priority to U.S. Provisional Patent Application Ser. Nos. 63 / 852,099, filed July 28, 2025, and 63 / 710,921 , filed October 23, 2024, the disclosure of which is incorporated herein by reference.Government Funding

[0002] This invention was made with government support under grant CA287045 awarded by the National Institutes of Health. The government has certain rights in the invention.Field

[0003] This disclosure relates generally to machine learning, e.g., in the context of medical applications, such as diagnostics.Background

[0004] Positron emission tomography (PET) is a molecular imaging modality that offers rich functional insights into the metabolism of normal and cancerous tissues. Increased glucose uptake and glycolysis in tumor cells, the Warburg Effect, can be measured by 2-deoxy-2-[18F]fluoro-D-glucose (18F-FDG) PET imaging.18F-FDG PET is widely used in oncology to visualize increased glucose transport in actively proliferating tumor cells and plays a major clinical role in the staging and monitoring of many cancers. However, some tumors may rely on substrates other than glucose to support cell growth and may consequently have a different metabolism profile.

[0005] Prostate cancer often does not undergo glycolytic metabolism and is heavily dependent on glutamine for cell proliferation and survival.18F-FDG PET is generally not useful for the initial staging of prostate cancer and has limited utility in the clinical setting of biochemical failure after definitive therapy. Prostate-specific membrane antigen (PSMA), also termed glutamate carboxypeptidase II, is highly expressed in prostate cancer and is a biomarker for aggressive tumor phenotypes and poor prognosis. PSMA-targeted PET has a high detection rate and superior diagnostic accuracy for prostate cancer compared with conventional imaging modalities,including bone scintigraphy, computed tomography (CT), and magnetic resonance imaging (MRI). PSMA PET / CT is useful in prostate cancer throughout the course of the disease, from initial staging to metastatic castration-resistant prostate cancer. PSMA PET can detect small-volume disease that is difficult to target via conventional imaging and may be an alternative to histopathology for characterizing indeterminant lesions.

[0006] Androgen deprivation therapy is an effective systemic treatment for prostate cancer that inhibits the androgen receptor and suppresses glutamine utilization necessary for tumor cell survival. However, castration-resistant disease is inevitable as hormonally treated prostate cancer always recurs as adenocarcinoma or extremely aggressive small-cell neuroendocrine carcinoma. The development of advanced prostate cancer and therapeutic resistance is driven, in part, by a glutaminase isoform switch that leads to hyperproliferation and aggressive tumor phenotypes. Heterogenous metabolic phenotypes exist in prostate cancer as PSMA expression is decreased in castration-resistant prostate cancer compared to castration-sensitive disease.

[0007] 177Lu-PSMA radioligand therapy is a treatment option for patients with end-stage prostate cancer after failure of androgen deprivation therapy and chemotherapy. Although177Lu-PSMA therapy has been shown to extend survival in patients with metastatic castration-resistant prostate cancer, biochemical response is achieved in approximately half of patients. Identifying biomarkers to predict response to therapy and outcome is an important clinical need that would enable early treatment management changes. PSMA PET / CT can predict response to systemic therapies including, chemotherapy and177Lu-PSMA therapy. High maximum standardized uptake values (SUVmax) and mean whole-body PSMA expression on PSMA PET were predictors of biochemical response and overall survival, respectively, in patients receiving177Lu-PSMA therapy. Quantification of molecular parameters heavily depends on the segmentation method. Thus, the development of automated tools for tumor quantification and subtype characterization on PSMA PET / CT are important clinical needs to optimize the early treatment of patients with prostate cancer, especially for those with advanced disease.Summary

[0008] The present disclosure provides, in certain aspects, an artificial intelligence (Al) method, system, and computer readable media capable of segmenting and / or classifying image data sets that comprise positron emission tomography (PET) images and / or computed tomography (CT) images of use in identifying tumor subtypes, among other applications. As exemplified in the present disclosure, retrospective data, including18F-DCFPyL PSMA PET / CT scans from patients with prostate cancer, were randomly partitioned into discovery and validation cohorts using a 70% / 30% split. PSMA reporting and data system (PSMA-RADS) scores of 1-5 were assigned to segmented lesions, with higher scores having a greater likelihood of prostate cancer. Tumors on PSMA PET / CT scans were automatically detected and segmented using a nnll-net, and radiomic features were extracted. Molecular tumor phenotypes were identified using k-means clustering on latent features learned by a variational autoencoder optimized on the radiomic feature space. Predicted risk scores were derived for each tumor via trajectory inference with minimum spanning trees. The nnll-net yielded a true positive rate of 0.75 and a Dice similarity coefficient of 0.73 on the tumor segmentation task. Three tumor subtypes were discovered. Subtype 1 was associated with PSMA-RADS-1 / 2 / 3, indicating a low probability of prostate cancer. Subtype 2 was associated with PSMA-RADS-4. Subtype 3 was most closely associated with PSMA-RADS-5, indicating a high probability of prostate cancer. Distance zone matrix features had the highest discriminatory ability and yielded an overall accuracy of 0.90 for the subtype classification task on both the discovery and validation cohorts. Increasingly aggressive tumor subtypes were associated with higher predicted risk scores and higher PSMA-RADS scores. The developed unsupervised learning approach elucidated three distinct molecular subtypes of prostate cancer with varying levels of tumor aggressiveness on PSMA PET / CT. These and other aspects will be apparent upon a complete review of the present disclosure, including the accompanying figures.

[0009] According to various embodiments, a computer-implemented method of identifying tumor subtypes, the method comprising: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or morePSMA reporting and data system (PSMA-RADS) scores of 1, 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans and / or to lesions on the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes, thereby identifying the tumor subtypes.

[0010] Various optional features of the above embodiments include the following. The identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another. The identified tumor subtypes comprise at least three distinct tumor subtypes, wherein: a tumor subtype 1 (S1) is associated with PSMA-RADS-1, PSMA-RADS-2, and / or PSMA-RADS-3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer. The method comprises quantifying one or more molecular parameters on the PSMA PET / CT scans. The method comprises identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique. The method comprises identifying the relationships between the tumor subtypes in the set of predicted tumor segmentationsusing trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees. The method further comprises determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task. The method further comprises validating one or more of the method steps and / or products thereof. The radiomic signatures corresponding to the distinct molecular subtypes are identified using a hierarchical agglomerative clustering technique. The PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

[0011] Various additional optional features of the above embodiments include the following. The detecting step comprises removing false-positive VOIs. The radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs. The radiomic features comprise one or more three-dimensional (3D) distance zone matrix features. The radiomic features comprise between about 300 and about 500 radiomic features. The method further comprises identifying one or more molecular tumor phenotypes using a clustering technique. The extracting and detecting steps comprise one or more of a median true positive rate of about 0.75, a median positive predictive value of about 0.76, a median Dice similarity coefficient of about 0.73, a median false discovery rate of about 0.24, a true negative rate of about 1.00, or a negative predictive value of about 1.00. The trained radiomics classifier detects true positive-positive VOIs with an overall accuracy of about 0.93 and / or an area under the receiver-operating-characteristic (AUC) curve of about 0.87. The method comprises using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject. The method further comprises administering one or more therapies to the test subject to treat the characterized tumors in the test subject.

[0012] According to various embodiments, a computer-implemented method of detecting a tumor subtype in a test subject, the method comprising: segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET) / computed tomography (CT) scan obtained from the test subject toproduce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject, thereby detecting the tumor subtype in the test subject. In some embodiments, the method further comprises administering one or more therapies to the test subject to treat the characterized tumor in the test subject.

[0013] According to various embodiments, a system, comprising: a processor; and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or morecomparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes.

[0014] Various optional features of the above embodiments include the following. The identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another. The identified tumor subtypes comprise at least three distinct tumor subtypes, wherein: a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer. The instructions which, when executed on the processor, further perform operations comprising: quantifying one or more molecular parameters on the PSMA PET / CT scans. The instructions which, when executed on the processor, further perform operations comprising: identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique. The instructions which, when executed on the processor, perform operations comprising: identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees. The instructions which, when executed on the processor, further perform operations comprising: determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task. The instructions which, when executed on the processor, further perform operations comprising: using a hierarchical agglomerative clustering technique to identify the radiomic signatures corresponding to the distinct molecular subtypes. The PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

[0015] Various additional optional features of the above embodiments include the following. The instructions which, when executed on the processor, perform operations comprising: removing false-positive VOIs from the set of predicted tumor segmentations. The radiomic features comprise a set of quantitative features thatdescribe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs. The radiomic features comprise one or more three-dimensional (3D) distance zone matrix features. The radiomic features comprise between about 300 and about 500 radiomic features. The instructions which, when executed on the processor, perform operations comprising: identifying one or more molecular tumor phenotypes using a clustering technique. The instructions which, when executed on the processor, perform operations comprising: using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject.

[0016] According to various embodiments, a system, comprising: a processor; and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject. In some embodiments, the instructions which, when executed on the processor, perform operations comprising: outputting one or more therapy recommendations to treat the characterized tumor in the test subject.

[0017] According to various embodiments, a computer readable media is presented. The computer readable media comprises non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to eachof the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes.

[0018] According to various embodiments, a computer readable media is presented. The computer readable media comprises non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least: segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject.Drawings

[0019] The above and / or other aspects and advantages will become more apparent and more readily appreciated from the following detailed description of examples, taken in conjunction with the accompanying drawings, in which:

[0020] Fig. 1 A is a flow chart that schematically shows exemplary method steps of identifying tumor subtypes using a computer according to some aspects disclosed herein;

[0021] Fig. 1 B is a flow chart that schematically shows exemplary method steps of detecting a tumor subtype in a test subject using a computer according to some aspects disclosed herein;

[0022] Fig. 2 is a schematic diagram of an exemplary system suitable for use with certain aspects disclosed herein;

[0023] Fig. 3 shows incomplete manual tumor segmentations compared to automatically predicted segmentations on PSMA PET scans of six patients with prostate cancer;

[0024] Figs. 4A and 4B show Kaplan-Meier overall survival curves of patients with head and neck cancer (A) and receiver-operating-characteristic curve of a prognostic risk stratification model for prostate cancer (B);

[0025] Fig. 5 show predicted segmentations on PSMA PET scans of twelve patients with prostate cancer. MTV, PSA doubling times (DT), and follow-up PSA levels were measured in cm3, months, and ng / mL, respectively;

[0026] Figs. 6A and 6B show receiver-operating-characteristic curves for prostate cancer diagnosis (A) and patient-level PSMA-RADS classification (B) on the test set;

[0027] Figs. 7A and 7B show simulation-based training improves deep learning performance on the tumor segmentation (A) and localization (B) tasks for varying dataset sizes;

[0028] Fig. 8 shows a workflow for automatic tumor segmentation on PSMA PET / CT scans of prostate cancer, radiomic feature extraction, trajectory inference for subtype discovery and tumor progression, and validation and prognosis;

[0029] Figs. 9A and 9B show evaluating the optimal size of VAE latent dimensions and the number of clusters to use for trajectory inference and subtype classification;

[0030] Fig. 10 shows topologies of learned trajectory paths in the VAE latent space (top row) and radiomic features space (bottom row) using 2 to 6 clusters (left to right). Black dots denote the cluster centers, and the black lines denote trajectory paths;

[0031] Fig. 11 shows a visualization of the VAE latent encodings of the clustered tumor subtypes by trajectory inference;

[0032] Figs. 12A-12D show boxplots of predicted risk scores by PSMA-RADS scores (A-B) and distribution plots of PSMA-RADS scores by tumor subtype (C-D);

[0033] Fig. 13 shows a dendrogram resulting from the hierarchical clustering procedure. Rows represent radiomic features and columns represent tumor profiles sampled along the trajectory path;

[0034] Fig. 14 shows boxplots of the radiomic feature distribution according to tumor subtype on the validation set;

[0035] Fig. 15 show scatter plots of the predicted trajectory scores and radiomic features on the validation set;

[0036] Figs. 16A-16D show log-log plots of TLA, SDHGE, and LDLGE (A-C). Principal component analysis (D). Black arrows represent the basis vector directions for each feature;

[0037] Figs. 17A-17H show that the superlinear scaling law governs PSMA expression and proliferation in prostate cancer. MTV-TLA log-log plots of tumor subtypes (A-D) and PSMA-RADS categories (E-G). Scaling exponents, (3 (H);

[0038] Figs. 18A-18D show the distribution of patient scores (A), tumor subtype distribution (B), Kaplan-Meier overall survival curves (C), and waterfall plot of PSA response (D); and

[0039] Fig. 19 schematically show GAN architecture (A), CycleGAN (B), and PET image simulation process (C).

[0040] Fig. 20. Kaplan-Meier overall survival (top row) and progression-free survival (bottom row) curves of patients stratified by whole-body PSMA PET imaging measures.

[0041] Figs. 21 A and 21 B. Kaplan-Meier overall survival and progression-free survival curves of patients stratified by the predicted imaging-based risk score (A). Bar plots of the clinical PSA measures and imaging measures based on the predicted riskscore (B). The units of PSA levels, PSA doubling time, MTV, and TLA were ng / mL, months, cm3, and SUV cm3, respectively.

[0042] Figs. 22A-22D. Scatter plots of the predicted risk probabilities of experiencing death (A) or disease progression (B) within 1 , 3, and 5 years after PSMA PET imaging versus the observed overall survival and progression-free survival times. Calibration plots of the observed risk probabilities versus the predicted risk probabilities for overall survival (C) and progression-free survival (D).

[0043] Fig. 23. Illustrative examples of automated tumor segmentations on PSMA PET and the predicted 5-year overall survival probabilities. OS: overall survival. Cens: censored.

[0044] Figs. 24A and 24B. The observed Kaplan-Meier survival curves compared to the predicted survival probabilities for patients stratified by the predicted risk groups (A) and imaging-based risk score (B). Shaded regions indicate 95% confidence intervals.

[0045] Fig. 25. The observed Kaplan-Meier survival curves compared to the predicted survival probabilities of patients stratified by the predicted risk groups according to post-PSMA PET therapy status. Shaded regions indicate 95% confidence intervals.

[0046] Figs. 26A-26F. Superlinear scaling laws govern PSMA expression and proliferation in prostate cancer. Linear regressions of the log (MTV) versus log (TLA) are plotted for Datasets 1 and 2 (A-C) and PSMA-RADS scores (D-F).

[0047] Fig. 27. Quantified scaling exponents of patient cohorts.

[0048] Fig. 28. Quantified scaling exponents of tumors based on PSMA-RADS scores.

[0049] Fig. 29. Quantified scaling exponents of tumors under different therapy modalities.

[0050] Fig. 30. Quantified scaling exponents across all patient cohorts and subgroups. Error bars denote 95% confidence intervals.

[0051] Fig. 31. Growth trajectories for sublinear and superlinear scaling laws.

[0052] Fig. 32. Workflow of trajectory inference approach.

[0053] Fig. 33. Dendrogram of hierarchical clustering of radiomic signatures revealing tumor subtypes.

[0054] Fig. 34. Overall survival and progression-free survival curves according to patient-level trajectory scores.

[0055] Fig. 35. Quantified scaling exponents of tumor subtypes.Definitions

[0056] In order for the present disclosure to be more readily understood, certain terms are first defined below. Additional definitions for the following terms and other terms may be set forth throughout the specification. If a definition of a term set forth below is inconsistent with a definition in an application or patent that is incorporated by reference, the definition set forth in this application should be used to understand the meaning of the term.

[0057] As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Thus, for example, a reference to “a method” includes one or more methods, and / or steps of the type described herein and / or which will become apparent to those persons skilled in the art upon reading this disclosure and so forth.

[0058] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. Further, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. In describing and claiming the methods, systems, and computer readable media, the following terminology, and grammatical variants thereof, will be used in accordance with the definitions set forth below.

[0059] Classifier. As used herein, “classifier” generally refers to algorithm computer code that receives, as input, test data and produces, as output, a classification of the input data as belonging to one or another class.

[0060] Data set: As used herein, “data set” refers to a group or collection of information, values, or data points related to or associated with one or more objects, records, and / or variables. In some embodiments, a given data set is organized as, or included as part of, a matrix or tabular data structure. In some embodiments, a data set is encoded as a feature vector corresponding to a given object, record, and / or variable, such as a given test or reference subject. For example, a medical data setfor a given subject can include one or more observed values of one or more variables associated with that subject.

[0061] Electronic neural network: As used herein, “electronic neural network” refers to a machine learning algorithm or model that includes layers of at least partially interconnected artificial neurons (e.g., perceptrons or nodes) organized as input and output layers with one or more intervening hidden layers that together form a network that is or can be trained to classify data, such as test subject medical data sets (e.g., medical images or the like).

[0062] Labeled: As used herein, “labeled” or “assigned” in the context of data sets or points refers to data that is classified as, or otherwise associated with, having or lacking a given characteristic or property.

[0063] Machine Learning Algorithm: As used herein, "machine learning algorithm" generally refers to an algorithm, executed by computer, that automates analytical model building, e.g., for clustering, classification or pattern recognition. Machine learning algorithms may be supervised or unsupervised. Learning algorithms include, for example, artificial neural networks (e.g., back propagation networks), discriminant analyses (e.g., Bayesian classifier or Fisher’s analysis), multiple-instance learning (MIL), support vector machines, decision trees (e.g., recursive partitioning processes such as CART (classification and regression trees, or random forests), linear classifiers (e.g., multiple linear regression (MLR), partial least squares (PLS) regression, and principal components regression), hierarchical clustering, and cluster analysis. A dataset on which a machine learning algorithm learns can be referred to as "training data." A model produced using a machine learning algorithm is generally referred to herein as a “machine learning model.”

[0064] Subject: As used herein, “subject” or “test subject” refers to an animal, such as a mammalian species (e.g., human) or avian (e.g., bird) species. More specifically, a subject can be a vertebrate, e.g., a mammal such as a mouse, a primate, a simian ora human. Animals include farm animals (e.g., production cattle, dairy cattle, poultry, horses, pigs, and the like), sport animals, and companion animals (e.g., pets or support animals). A subject can be a healthy individual, an individual that has or is suspected of having a disease or pathology or a predisposition to the disease or pathology, or an individual that is in need of therapy or suspected of needing therapy. The terms “individual” or “patient” are intended to be interchangeable with “subject.” A“reference subject” refers to a subject known to have or lack specific properties (e.g., a known pathology, such as melanoma and / or the like).

[0065] System: As used herein, "system" in the context of analytical instrumentation refers a group of objects and / or devices that form a network for performing a desired objective.

[0066] Treat: As used herein the terms “treat”, “treated”, or “treating” refer to both therapeutic treatment and prophylactic or preventative measures, wherein the object is to protect against (partially or wholly) or slow down (e.g., lessen or postpone the onset of) an undesired physiological condition, disorder or disease, or to obtain beneficial or desired clinical results such as partial or total restoration or inhibition in decline of a parameter, value, function or result that had or would become abnormal. For the purposes of this application, beneficial or desired clinical results include, but are not limited to, alleviation of symptoms; diminishment of the extent or vigor or rate of development of the condition, disorder or disease; stabilization (i.e., not worsening) of the state of the condition, disorder or disease; delay in onset or slowing of the progression of the condition, disorder or disease; amelioration of the condition, disorder or disease state; and remission (whether partial or total), whether or not it translates to immediate lessening of actual clinical symptoms, or enhancement or improvement of the condition, disorder or disease. Treatment seeks to elicit a clinically significant response without excessive levels of side effects.

[0067] Value: As used herein, “value” generally refers to an entry in a dataset that can be anything that characterizes the feature to which the value refers. This includes, without limitation, numbers, words or phrases, symbols (e.g., + or -) or degrees.Description of the Embodiments

[0068] Reference will now be made in detail to example implementations. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the invention. The following description is, therefore, merely exemplary.

[0069] Description of Example Embodiments

[0070] In some aspects, the present disclosure provides computer-implemented methods of identifying tumor subtypes. To illustrate, Fig. 1A is a flow chart that schematically shows certain of these exemplary method steps. As shown, method 100 includes extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans (e.g., whole-body PSMA PET / CT scans) obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects (step 102). Method 100 also includes detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs (step 104) and using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes (step 106). As shown, method 100 also includes identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features (step 108) and generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space (step 110). In addition, method 100 also includes discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes (step 112), producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes (step 114), and outputting the set of identified tumor subtypes (step 116).

[0071] Typically, the identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another. In some embodiments, the identified tumor subtypes comprise at least three distinct tumor subtypes, for example, a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a lowprobability of being prostate cancer, a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer. In some embodiments, method 100 includes quantifying one or more molecular parameters on the PSMA PET / CT scans. In some embodiments, method 100 includes identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique. In some embodiments, method 100 includes identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees.

[0072] In some embodiments, method 100 also includes determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task. In some embodiments, method 100 also includes validating one or more of the method steps and / or products thereof. In some embodiments, the radiomic signatures corresponding to the distinct molecular subtypes are identified using a hierarchical agglomerative clustering technique. In some embodiments, the detecting step of method 100 comprises removing falsepositive VOIs.

[0073] In some embodiments, the radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs. In some embodiments, the radiomic features comprise one or more three-dimensional (3D) distance zone matrix features. In some embodiments, the radiomic features comprise between about 300 and about 500 radiomic features.

[0074] In some embodiments, method 100 also includes identifying one or more molecular tumor phenotypes using a clustering technique. In some embodiments, the extracting and detecting steps of method 100 comprise one or more of a median true positive rate of about 0.75, a median positive predictive value of about 0.76, a median Dice similarity coefficient of about 0.73, a median false discovery rate of about 0.24, atrue negative rate of about 1.00, or a negative predictive value of about 1.00. In some embodiments, the trained radiomics classifier detects true positive VOIs with an overall accuracy of about 0.93 and / or an area under the receiver-operating-characteristic (AUC) curve of about 0.87.

[0075] In some embodiments, method 100 includes using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject. In some embodiments, method 100 also includes administering one or more therapies to the test subject to treat the characterized tumors in the test subject.

[0076] To further illustrate, Fig. 1B is a flow chart that schematically shows exemplary method steps of detecting a tumor subtype in a test subject using a computer. As shown, method 120 includes segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET) / computed tomography (CT) scan obtained from the test subject to produce a segmented test subject tumor (step 122). Method 102 also includes characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1 ) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject (step 124). In some embodiments, method 120 also includes administering one or more therapies to the test subject to treat the characterized tumor in the test subject.

[0077] Fig. 2 is a schematic diagram of a hardware computer system 200 suitable for implementing various embodiments. For example, Fig. 2 illustrates various hardware, software, and other resources that can be used in implementations of any of methods disclosed herein, including, e.g., method 100 and / or one or more instances of an electronic neural network. System 200 includes training corpus source 202 and computer 201. Training corpus source 202 and computer 201 may be communicatively coupled by way of one or more networks 204, e.g., the internet.

[0078] Training corpus source 202 may include an electronic clinical records system, such as an LIS, a database, a compendium of clinical data, or any other source of images suitable for use as a training corpus as disclosed herein. Due tohardware volatile memory storage limitations, constituent parts of an image may be broken down into a number of tiles, which may be, e.g., 128 pixels by 128 pixels or the like. Such tiles are examples of “components” as that term is sometimes used herein. According to some embodiments, each component is implemented as a vector, such as a feature vector, that represents a respective tile. Thus, the term “component” refers to both a tile and a feature vector representing a tile in some contexts.

[0079] Computer 201 may be implemented as any of a desktop computer, a laptop computer, can be incorporated in one or more servers, clusters, or other computers or hardware resources, or can be implemented using cloud-based resources. Computer 201 includes volatile memory 214 and persistent memory 212, the latter of which can store computer-readable instructions, that, when executed by electronic processor 210, configure computer 201 to perform any of the methods disclosed herein, including method 100, 110, or 120, and / or form or store any electronic neural network, and / or perform any classification other technique as described herein. Computer 201 further includes network interface 208, which communicatively couples computer 201 to training corpus source 202 via network 204. Other configurations of system 200, associated network connections, and other hardware, software, and service resources are possible.

[0080] Certain embodiments can be performed using a computer program or set of programs. The computer programs can exist in a variety of forms both active and inactive. For example, the computer programs can exist as software program(s) comprised of program instructions in source code, object code, executable code or other formats; firmware program(s), or hardware description language (HDL) files. Any of the above can be embodied on a transitory or non-transitory computer readable medium, which include storage devices and signals, in compressed or uncompressed form. Exemplary computer readable storage devices include conventional computer system RAM (random access memory), ROM (read-only memory), EPROM (erasable, programmable ROM), EEPROM (electrically erasable, programmable ROM), and magnetic or optical disks or tapes.

[0081] II. Examples

[0082] Example 1

[0083] We have developed a number of artificial intelligence approaches for a range of image analysis tasks to automatically characterize disease on nuclear medicine images in several prior works and the present disclosure. Such works included approaches for generalizable tumor segmentation and prognosis on18F-FDG PET / CT scans of patients with lung cancer, melanoma, lymphoma, head and neck cancer, and breast cancer and PSMA PET / CT scans of patients with prostate cancer, automated diagnosis and classification on PSMA PET images of prostate cancer, and simulation-based transfer learning on18F-FDG PET images of lung cancer. We have also conducted work that develops an unsupervised learning framework on PSMA PET / CT radiomics data to model tumor progression and characterize distinct subtypes of prostate cancer. These studies offer support, provide a foundation, and demonstrate the feasibility of the approaches disclosed herein.

[0084] Tumor Segmentation and Quantification. In a prior study, we developed a deep semi-supervised transfer learning (DeepSSTL) approach for fully automated whole-body tumor segmentation and prognosis on ^®F-FDG and ^®F-DCFPyL PSMA PET / CT scans. The DeepSSTL approach was developed to address the challenge of learning the generalized tumor segmentation task across different PET / CT radiotracers with a limited amount of physician-defined tumor annotations. This study consisted of 611 ^®F-FDG PET / CT scans of patients with lung cancer, melanoma, lymphoma, head and neck cancer, and breast cancer with complete tumor annotations and 408 PSMA PET / CT scans of patients with prostate cancer with incomplete or partially labeled annotations (Fig. 3). The DeepSSTL approach yielded median true positive rates of 0.75, 0.85, 0.87, and 0.75 and median Dice similarity coefficients of 0.81, 0.76, 0.83, and 0.73 for patients with lung cancer, melanoma, lymphoma, and prostate cancer, respectively, on the tumor segmentation task, demonstrating accurate and generalizable tumor delineation and quantification.

[0085] Survival Estimation and Response Prediction. PET / CT whole-body imaging measures, including MTV, TLA, number of lesions, mean standardized uptake value (SUVmean), and SUVmax, were quantified from segmentations predicted by the DeepSSTL approach and used to build prognostic models for survival estimation, prediction of treatment response, and risk stratification. Patients with head and neck cancer were stratified based on the imaging measures and plotted using Kaplan-Meier estimators. Patients predicted as high-risk had asignificantly shorter median overall survival compared to low- and intermediate-risk patients (Fig. 4A). Imaging measures were extracted from pre- and post-therapy PET / CT scans of 36 patients with breast cancer undergoing neoadjuvant chemotherapy and were used to predict pathological complete response with an overall accuracy of 0.84 and an area under the receiver-operating- characteristic (AUC) curve of 0.76. This demonstrated the feasibility of using whole-body PET / CT measures to predict response to neoadjuvant therapy prior to definitive treatment using a small patient cohort.

[0086] Risk Stratification. A prognostic risk model used whole-body imaging measures extracted from PSMA PET / CT scans to perform risk stratification of prostate cancer. The risk model stratified patients with prostate cancer into low-to-intermediate-versus high-risk groups based on PSA levels. The risk model yielded an overall accuracy of 0.83 and an AUC of 0.86 on the risk stratification task (Fig. 4B). A risk score was derived from the prognostic risk model and was significantly correlated with PSMA reporting and data system (PSMA-RADS) scores (r = 0.44, P < 0.001) and post-PSMA PET therapies and systemic treatments (r = 0.37, P < 0.001). PSMA-RADS scores are on a 5-point scale where a higher score reflects a greater likelihood of prostate cancer. Illustrative examples of predicted tumor segmentations and risk scores on PSMA PET / CT scans of patients with prostate cancer by the DeepSSTL approach are shown in Fig. 5. Patients classified as having high-risk by the risk model had higher follow-up PSA levels and shorter PSA doubling times. Low-, intermediate-, and high- risk patients classified by the risk model had mean follow-up PSA levels of 9.18, 26.92, and 727.46 ng / mL and mean PSA doubling times of 8.67, 8.18, and 4.81 months, respectively.

[0087] Diagnosis and Classification. In a prior study, a framework that incorporated deep learning and radiomics was developed to perform the diagnosis and classification of prostate cancer on 267 ^®F-DCFPyL PSMA PET images. The framework classified regions of uptake as benign or malignant prostate cancer lesions and yielded an AUC of 0.92 and an overall accuracy of 0.85 on 732 lesions in the test set (Fig. 6A). The framework also categorized each PSMA PET scan into one of nine PSMA- RADS categories and subcategories. The framework yielded an AUC of 0.90 and an overall accuracy of 0.77 on the test set for the patient-level PSMA-RADS classification task (Fig. 6B).

[0088] Physics-guided Transfer Learning. In a prior study, a physics-guided deep learning framework was developed for tumor segmentation on ^®F-FDG PET images of patients with lung cancer. The framework developed a stochastic and physics- based approach to generate highly realistic tumors on simulated PET images with known ground truth. The framework pre-trained a modified ll-net (mil-net) on 10,000 realistic simulated images. The mU-net was then fine-tuned on a small-sized dataset of clinical PET images with manually annotated ground truth. The network that was first pre-trained on simulated and then fine- tuned on clinical data showed improved accuracy levels compared to the network that was only trained on clinical data for both the tumor segmentation and localization tasks across a range of clinical dataset sizes (Fig. 7). This study demonstrated the feasibility of utilizing realistic simulated data to train and improve the performance of deep learning approaches when training data is limited.

[0089] Tumor Progression and Subtype Characterization. In a study, an unsupervised learning framework was developed to computationally model tumor progression dynamics and cluster molecular subtypes of prostate cancer using radiomic data extracted from PSMA PET / CT scans. The developed workflow consists of several modules (Fig. 8). First, tumors on whole-body PSMA PET / CT images were automatically detected and segmented while using limited manual tumor annotations for training. Second, a number of radiomic features were extracted from segmented volumes of interest (VOIs) to yield radiomic signatures for all detected tumors. Third, a trajectory inference approach was developed to learn a latent representation of the radiomic signatures. Fourth, a score reflecting disease progression was derived from the predicted position along the learned trajectory path. Lastly, the characterization, biological validation, and clinical significance of the discovered tumor subtypes were assessed.

[0090] The automated PET / CT tumor segmentation task was learned with a DeepSSTL approach using limited tumor annotations manually delineated by nuclear medicine physician readers. Data from 408 ^F-DCFPyL PSMA PET / CT scans of patients with prostate cancer with incomplete manual tumor annotations were used to learn the tumor segmentation task. Data from 167 and 241 patients had partially labeled manual tumor annotations and no available tumor annotations, respectively. A subset of patients with prostate cancer had clinical information on PSMA-RADSscores of 1-5 assigned to segmented tumors indicating the likelihood of prostate cancer, initial and follow-up PSA levels, and overall survival. A 5-fold cross-validation was used to cross-val idate the segmentation task on the PSMA PET / CT scans, respectively, and yielded test predictions on hold-out sets. PET / CT VOIs were derived from the predicted tumor segmentations on 408 PSMA PET / CT scans of patients with prostate cancer and used for further analysis. Radiomic signatures were calculated from the PET / CTVOIs using the Image Biomarker Standardization Initiative guidelines for reproducible feature extraction. A total of 397 first-order statistical and high-order textural features, including morphology, intensity, intensity histogram, intensity volume histogram, co-occurrence matrix, run length matrix, size zone matrix, distance zone matrix, and neighborhood gray tone difference matrix, were extracted. Classifiers were trained on the radiomic signatures to identify and discard false-positives VOIs. The PET / CTVOIs were randomly partitioned into discovery and validation sets on a patient basis using a 70% / 30% split. The discovery and validation sets had 2,744 and 1,464 VOIs, respectively.

[0091] A trajectory inference approach was developed to learn a continuous latent representation of prostate cancer tumors and metastases that captures important factors of variation in the PSMA PET / CT radiomic feature space. A variational autoencoder (VAE) was trained in an unsupervised fashion on radiomic signatures to learn tumor encodings in a low-dimensional latent space. To learn the appropriate trajectory paths, the data were clustered using a k-means algorithm. The piecewise linear path through the cluster centers defined by a minimum spanning tree algorithm was taken as the trajectory path. The optimal VAE latent dimension size and number of clusters used for trajectory inference were evaluated by assessing the Davies-Bouldin index, a commonly used metric to evaluate clustering algorithms, as these parameters are not known a priori. Although lower values of the Davies-Bouldin index may indicate higher clustering quality with increased separation between clusters and decreased intra-cluster variation, lower index values do not necessarily denote optimal information retrieval. The VAE was trained on radiomic signatures using 2 to 10 latent dimensions on the discovery set. The VAE with a latent dimensionality size of 3 had the lowest Davies-Bouldin index on the discovery set (Fig. 9A). The VAE latent features and radiomic signatures were then clustered using 2 to 6 clusters on the discovery set. Although the Davies-Bouldin index was minimizedwhen using a fewer number of clusters on the VAE latent features, this may have been due to imposing less structure on the data when fewer clusters were used (Fig. 9B). The Davies-Bouldin index converged when 3 or more clusters were used on the radiomic features, indicating that higher cluster numbers may not degrade cluster quality. However, using a higher cluster number may result in spurious findings. Thus, a cluster number of 3 was selected to reduce unnecessary complexity while maximizing information gain.

[0092] We hypothesized that the VAE latent features would correspond to smoothly varying tumor characteristics associated with the biological processes underlying tumor progression. To test this hypothesis, trajectory inference was performed in both the low-dimensional space VAE latent space and the highdimensional radiomic feature space. The topologies of the learned trajectories were assessed (Fig. 10). The learned trajectory paths in the VAE latent space have linear topologies even with an increasing number of clusters. In contrast, the learned trajectory paths in the radiomic feature space become increasingly non-linear and branched as the cluster number increases. This observation agrees with our initial hypothesis that performing trajectory inference on the VAE latent encodings would encourage learning continuous trajectory paths that smoothly transition between the clustered tumor subtypes.

[0093] A VAE with a latent dimensionality of 3 was trained on the radiomic signatures from the discovery set, and a cluster number of 3 was used to perform trajectory inference on the VAE latent encodings. Three distinct tumor subtypes were identified by clustering analysis using the learned VAE latent features. Fig. 11 shows a visualization by principal component (PC) analysis of the tumor subtypes in the VAE latent space. A predicted trajectory score representing the progression between tumor subtypes was derived by projecting the latent encoding of each tumor onto the learned trajectory path. The predicted trajectory score was normalized from 0 to 1 to represent the beginning and end stages of tumor progression. The distribution of PSMA-RADS scores was assessed for the predicted scores and the discovered tumor subtypes to characterize the direction of tumor progression. Fig. 12 shows boxplot distributions of predicted scores compared to PSMA-RADS scores and distribution plots of PSMA-RADS scores compared to tumor subtype on the discovery and validation sets. The predicted trajectory scores were significantly correlated to thePSMA-RADS scores on the discovery (r= 0.57, P< 0.001) and validation (r = 0.56, P < 0.001) sets (Fig. 12A-B). The predicted trajectory scores of tumors categorized as PSMA-RADS-5 were significantly higher than those categorized as PSMA-RADS-1 / 2 / 3 and PSMA-RADS-4 on the discovery and validation sets (P < 0.001). Tumor subtype 1 (S1) was most associated with PSMA-RADS-1 / 2 / 3 with approximately half the tumors in the S1 group belonging to PSMA-RADS-1, -2, or -3 categories on the discovery and validation sets (Fig. 12C- D). PSMA-RADS-1 and -2 are defined as definitively or likely benign findings, and PSMA-RADS-3 is defined as equivocal uptake. This indicates a relatively low probability of prostate cancer for S1. Tumor subtype 2 (S2) was more evenly distributed across the PSMA-RADS-1 / 2 / 3, PSMA-RADS-4, and PSMA-RADS-5 categories. This indicates that S2 may be a transitionary tumor subtype representing progression between tumor subtypes 1 and 3. Tumor subtype 3 (S3) was predominantly associated with PSMA-RADS-5, which is defined as definitively or almost certainly representative of prostate cancer. These findings suggest that the progression of benign tumors into malignant metastases may be represented by a tumor subtype transition from S1 to S2 to S3, where S2 may represent an intermediate state in the malignant transformation.

[0094] Biomarker Identification. Radiomic signatures corresponding to locations along the learned trajectory path were sampled. The sampled radiomic signatures were characterized using a hierarchical agglomerative clustering algorithm to identify patterns in radiomic feature expression levels that correspond to tumor progression. Fig. 13 shows a dendrogram that illustrates the normalized expression of radiomic features for the clustered tumor profiles. The radiomic features were clustered into two main clusters, referred to as Group 1 and Group 2. Radiomic features in Group 1 had higher levels of expression for S1 profiles and lower levels of expression for S3 profiles. In contrast, radiomic features in Group 2 had lower levels of expression for S1 and higher levels of expression for S3. Radiomic features in Groups 1 and 2 had decreasing and increasing levels of expression for S2, respectively, as the sampled tumor profiles traversed the trajectory path from S1 to S2 to S3 (Fig. 13). These observations support the notion that S2 is an intermediate transitionary tumor state in the benign to malignant transformation. To identify features as potential biomarkers of tumor progression, pairs of radiomic features from Groups 1 and 2 were evaluated on the tumor subtype classification task on the discovery set.A simple classifier was devised. Feature pairs with the Group 1 feature in the upper quartile and the Group 2 feature in the lower quartile were classified as S1. Feature pairs with the Group 1 feature in the lower quartile and the Group 2 feature in the upper quartile were classified as S3. Other feature pairs were classified as S2. The top features from Groups 1 and 2 with the highest performance on the tumor classification task were distance zone matrix features with small distance high gray-level emphasis (SDHGE) and large distance low gray- level emphasis (LDLGE), respectively. Graylevel distance zone matrix is a textural feature that counts the number of connected regions or zones at a constant gray-level value that are at the same distance from the ROI edge. Higher values of SDHGE indicate more zones at smaller distances and higher gray levels whereas higher values of LDLGE indicate more zones at larger distances and lower gray levels. This feature pair yielded an overall accuracy on the tumor subtype classification task of 0.90 on both the discovery and validation sets, indicating a high discriminatory ability.

[0095] The distribution of commonly used PET / CT metrics with prognostic value, including MTV, TLA, SUVmean, and SUVmax, and distance zone matrix features with SDHGE and LDLGE were assessed on the validation set according to tumor subtypes and trajectory progression scores. MTV, TLA, SUVmean, SUVmax, and LDLGE had higher values for tumor subtypes associated with higher probabilities of prostate cancer, whereas SDHGE had lower values for tumor subtypes with higher disease likelihoods (Fig. 14). The relationships of the radiomic features as a function of the predicted trajectory scores were visualized in Fig. 15. Similarly, MTV, TLA, SUVmean, SUVmax, and LDLGE had higher values with higher predicted trajectory scores, and SDHGE had lower values with higher predicted trajectory scores. MTV, TLA, SDHGE, and LDLGE had coefficient of determination (adjusted R2) values of 0.77, 0.81, 0.88, and 0.90 on the validation set, respectively, indicating a large association with the predicted trajectory scores. SUVmean and SUVmax had R2values of 0.43 and 0.67 on the validation set, respectively, indicating a moderate association with the predicted trajectory scores.

[0096] We further investigated the relationships between TLA, SDHGE, and LDLGE, which had the highest levels of association with the predicted trajectory scores (Fig. 16A-C). SDHGE had inverse relationships with TLA and LDLGE. LDLGE had a positive relationship with TLA. SDHGE and LDLGE were highly associated withan R value of 0.98. A principal component analysis performed on all three features revealed that the basis directions for SDHGE and LDLGE were aligned along the same axis (in opposing directions) and the basis direction for TLA was orthogonal to the SDHGE-LDLGE axis (Fig. 16D). This indicates that TLA together with SDHGE and LDLGE may provide complementary information to inform tumor progression status.

[0097] Biological Validation. It was observed by Kleiber that the metabolic rates for a variety of species scale to 3 / 4 the power of an organism’s body mass. Allometric scaling laws take the form Y = aMP, where Y is an observable quantity, M is a measure of the size or mass, a is a rate constant, and (3 denotes the scaling exponent. The observation that the metabolism of many organisms obeys sublinear scaling laws with exponent (3 = 3 / 4 may be a consequence of the energy minimization principle. However, it was recently shown that many human cancers obey superlinear (i.e., / ? > 1) universal metabolic scaling laws that lead to explosive tumor growth. The metabolic scaling law of the form TLA = a MT VP was observed in measurements obtained from18F-FDG PET / CT scans of patients with breast cancer, head and neck cancer, non-small cell lung cancer, and rectal cancer. The scaling exponents of those cancers were clustered around (3 = 5 / 4. We hypothesized that prostate cancer may also exhibit superlinear scaling in tumor measurements obtained by PSMA PET / CT and that the metabolic scaling exponents of prostate cancer subtypes are higher for aggressive tumor subtypes with higher metastatic potential. Fig. 17 shows log-log plots of MTV versus TLA for the discovered prostate cancer subtypes and tumors categorized according to PSMA-RADS. In agreement with our hypothesis, we observed that the S1, S2, and S3 had sublinear ((3 = 0.8), linear ((3 = 1.00), and superlinear ((3 = 1.21) scaling exponents, respectively, indicating increasingly aggressive tumor growth dynamics along the S1-S2-S3 trajectory path. We observed a / ? = 1.25 across all prostate cancer subtypes, which agreed with the previously observed scaling of / ? = 5 / 4 in other cancers. PSMA-RADS-1 / 2 / 3, PSMA-RADS-4, and PSMA-RADS-5 tumors had superlinear scaling exponents of / ? = 1.14, / ? = 1.20, and ft = 1.30, respectively, indicating that higher PSMA-RADS scores denote more explosive growth.

[0098] Clinical Significance. The predicted trajectory scores were integrated into a patient-level score that reflected an individual patient’s progression status (Fig.18A). Patients with progression scores in the fourth quartile (Q4) had a higherdistribution of S3 tumors, lower distributions of S1 and S2 tumors, and significantly shorter overall survival (P < 0.01 ) compared to patients with scores in first, second, and third quartiles (Fig. 18B-C). A waterfall plot of PSA response showed that 16 / 34 (47%) of patients with predicted scores in Q4 failed to achieve a 50% decline in PSA from baseline (Fig. 18D).

[0099] Databases. The approach is developed and validated with retrospective, deidentified data from 772 ^8F- DCFPyL PSMA PET / CT scans across three independent cohorts consisting of 270, 140, and 362 patients with prostate cancer, respectively. Additional retrospective data is extracted from openly available sources, including The Cancer Imaging Archive (TCIA). Retrospective, deidentified datasets from available databases at the Johns Hopkins University (JHU) and the National Cancer Institute (NCI) is also processed. Demographic and clinical outcomes data, such as age, sex, overall survival, progression-free survival, grade, stage, recurrence, pathological biomarkers, treatment response, and physician-defined manual annotations and segmentations are collected. Clinical, genetic, and pathological data are also be extracted from The Cancer Genome Atlas (TCGA) for each of the relevant TCGA datasets. To this end, we have collected 32 datasets from TCIA, JHU, and NCI databases that have a combined 10,757 studies of 5,654 subjects representing a wide range of cancers, including bladder, brain, breast, endometrial, head and neck, kidney, liver, lung, lymphoma, melanoma, neuroendocrine, prostate, soft-tissue sarcoma, and thyroid cancer. Across all 32 datasets, there are 4,068 subjects with a PET, 5,424 with a CT, and 416 with an MRI. PET scans were imaged with radiotracers, including ^8F-FDG, ^8F-FLT, ^F-FMISO, ^8F-NaF,88Ga aerosol,68Ga-DOTA-TATE, and18F-DCFPyL.

[0100] Example 2

[0101] Artificial intelligence studies use large amounts of annotated data to achieve acceptable levels of performance and generalizability for clinical utility. We address the challenge of the limited availability of annotated clinical datasets to develop tools for large-scale, whole-body tumor quantification of prostate cancer on PSMA PET / CT using two general strategies. The first strategy creates a large database of clinical PET / CT scans with physician-defined manual annotations of patients with a range of cancers, including prostate cancer, imaged with different radiotracers. Semisupervised transfer learning is then used on the large clinical database of PET / CTimages to train deep learning methods to learn the generalized whole-body tumor quantification task on PSMA PET / CT scans of patients with prostate cancer. Since physician-defined manual annotations are difficult to obtain, the second strategy generates a large dataset of simulated PET / CT images with known ground truth. A generative modeling approach that incorporates PET imaging physics is used to create realistic simulated PET / CT images that reflect population-level biological variations in anatomy and radiotracer uptake.

[0102] Methods

[0103] Semi-supervised transfer learning. A deep semi-supervised transfer learning is developed to perform domain adaptation across source and target domains of clinical PET / CT datasets imaged with different radiotracers using limited manual tumor annotations. The approach jointly optimizes a deep learning model (e.g., convolutional neural network (CNN) or Transformer architectures) to perform the transfer learning task while iteratively improving tumor quantification performance. The source domain consists of PET / CT scans of patients with a range of cancers imaged primarily with18F-FDG and complete tumor annotations. The target domain consists of PSMA PET / CT scans of patients with prostate cancer imaged with18F-DCFPyL. Available physician-defined manual segmentations annotated on the clinical datasets serve as ground truth to evaluate performance.

[0104] Generative modeling. Generative adversarial networks (GANs) are used to generate synthetic activity distributions and attenuation maps for realistic simulations. GANs are trained to generate activity PSMA distributions of normal patient background and synthetic lesions (Fig. 19A). Synthetic lesions serve as known ground truth for tumor 746 delineations. A CycleGAN generates the corresponding CT image (Fig. 19B) for CT-based attenuation correction.

[0105] PET image simulation process. The synthetic patient backgrounds and lesions are forward projected by a system matrix simulating a PET system (Fig. 19C). Simulated background images and lesions are summed in the projection space and reconstructed to incorporate the effect on tumor appearance and noise texture due to iterative reconstruction. Images are reconstructed via an ordered subsets expectation maximization (OSEM) algorithm with varying subsets and iterations. The quality and structural similarity of the simulated and clinical images are assessed with the FrechetInception Distance (FID) and multi-scale structural similarity index measure (MS-SSIM).

[0106] Three-dimensional (3D) PET simulation and reconstruction software. 3D PET simulations are performed to capture the full anatomy. A fast analytic PET simulator provided by the ASIM (Analytical PET Simulator) package is used to perform 3D PET simulations while modeling aspects of PET imaging physics, including noise, scatter, randoms, and attenuation correction. The STIR (Software for Tomographic Image Reconstruction) software package is used to perform iterative reconstruction of the simulated images.

[0107] Physics-based transfer learning. Simulated PSMA PET / CT images of patients with prostate cancer are generated to augment the clinical datasets while also providing known ground truth labels for training. A physics-based transfer learning approach is developed to train a deep learning architecture to learn the tumor quantification task by performing domain adaptation across the simulated and clinical PSMA PET / CT datasets.

[0108] Task-based training. Multiple deep learning-based approaches are used for the tumor quantification task. For the tumor detection task, approaches include both single-stage and multi-stage object detectors, such as SSD, YOLO, Faster R-CNN, Mask R-CNN, Cascade Mask R-CNN, and nnDetection. Voxel-wise segmentation approaches, including ll-net, nnll-net, Swin-UNET, and nnFormer, are trained. The performance is evaluated on the basis of Dice similarity coefficient, Jaccard index, Hausdorff distance, true positive rate, false discovery rate, true negative rate, and receiver-operating-characteristic analysis.

[0109] Evaluating generalizability. The generalizability of the developed transfer learning approaches is evaluated with a per-dataset 5-fold cross-validation. The clinical and simulated PET / CT datasets is randomly partitioned on a per-dataset basis into 5 folds. Four folds are used for semi-supervised or simulation-based training, and the hold-out validation fold is used for generalizability evaluation on tumor quantification.

[0110] The datasets consisting of ^®F-DCFPyL PSMA PET / CT images of patients with prostate cancer may be underrepresented across the entire clinical database as most of the TCIA datasets consist of ^®F-FDG PET / CT data. This imbalance may encourage the detection of non-prostate malignancies on PSMAPET / CT scans and may affect the generalizability assessment of the semi-supervised and simulation-based transfer learning approaches. An alternative approach is to perform transfer learning using a per-patient 5-fold cross-validation for individual datasets separately and then to evaluate performance on an external test dataset of PSMA PET / CT images of prostate cancer. Another challenge is ensuring sufficient diversity across the prostate cancer patient cohorts such that demographic attributes, including age, race, ethnicity, and socioeconomic status, are evenly represented. Evaluation may also be performed on stratified patient cohorts to account for disparities in the overall population. It may be difficult to generate full 3D volumes for activity distribution phantoms using GANs due to adversarial training dynamics. Alternative approaches are to train progressively growing GANs to generate phantoms with increasing levels of resolution or to use VAEs or diffusion models. While the ASIM analytic simulator can perform fast PET simulations, we can use the GATE software to perform advanced Monte Carlo-based PET simulations to more accurately model the imaging physics. When the CT is not available, a GAN can be trained on MRI to generate attenuation maps.

[0111] Example 3

[0112] The biological heterogeneity of cell populations that underlies cancer progression can be characterized by genomics, transcriptom ics, and proteomics data derived from single cells. Trajectory inference methods can computationally model cancer progression dynamics using single-cell omics data. However, there is a paucity of trajectory inference methods developed to computationally track tumor changes as the disease progresses using radiomics data derived from medical images. Radiomic features that capture textural properties on PET / CT images can quantify intratumoral heterogeneity and are correlated with patient prognosis. We develop an unsupervised manifold learning approach that uses trajectory inference to model tumor progression trajectories on radiomic signatures derived from PSMA PET / CT data and characterize molecular subtypes of prostate cancer.

[0113] Methods

[0114] Tumor quantification. Prostate cancer tumors and metastases are automatically detected and segmented on whole-body PSMA PET / CT scans by deep learning models that were trained by the transfer learning approaches described above. False-positive VOIs are detected and removed from the tumorsegmentations by radiomics classifiers using the random forest algorithm. The truepositive VOIs are used for radiomic analysis.

[0115] Radiomic analysis. Radiomic features, including morphology, intensity, and textural features, are extracted from VOIs following the Image Biomarker Standardization Initiative guidelines to yield radiomic signatures. Such radiomic features include local intensity, intensity-based statistics, intensity histogram, intensity-volume histogram, grey-level co-occurrence matrix, grey-level distance-zone matrix, grey-level run-length matrix, grey-level size-zone matrix, neighboring grey-level dependence matrix, and neighborhood grey tone difference matrix.

[0116] Manifold learning for tumor progression. A manifold learning approach is developed to learn a low- dimensional latent tumor encoding from the highdimensional radiomic signatures using a VAE. Trajectory paths are determined by first clustering the latent encodings using a k-means algorithm and then finding the path through the cluster centers defined by a minimum spanning tree. Tumor latent encodings are projected onto the nearest location on the trajectory path and ordered to characterize tumor progression along the trajectory path. A normalized score is derived to yield a continuous predicted value reflecting the stage of tumor progression.

[0117] Subtype characterization. The disease risk of the tumor subtypes of prostate cancer discovered by the manifold learning approach is characterized by comparison to clinically determined PSMA-RADS scores. Radiomic signatures of distinct molecular subtypes are characterized via a hierarchical agglomerative clustering procedure to identify patterns of differential expression levels of radiomic features across tumor subtypes.

[0118] Biomarker identification. Features with a high discriminatory ability in detecting high-risk tumor subtypes are identified as potential biomarkers of tumor aggressiveness. The correlation and association of the potential biomarkers with the predicted trajectory scores denoting tumor progression is assessed. Independent component analysis of MTV, TLA, SUV, and textural radiomic measures of heterogeneity is performed to identify biologically interpretable features and potential synergies in quantifying tumor progression.

[0119] Benchmarking Evaluation. The performance of the developed manifold learning approach is evaluated and benchmarked against existing trajectory inferencemethods developed for single-cell analysis, such as Slingshot, Monocle, Wishbone, and TSCAN, to assess trajectory quality with alternative topology inference methods.

[0120] Determining trajectory paths using the piecewise linear path defined by a minimum spanning tree procedure may result in discontinuous paths with sharp transitions between clustered subtypes. An alternative approach is to use simultaneous principal curves to learn smooth trajectory paths. Using a VAE to learn latent tumor encodings may introduce stochasticity when sampling the latent features. Averaging predictions over Monte Carlo samples of the latent features can be used to generate more stable predictions while also providing a measure of uncertainty in the predictions. Although identifying radiomic biomarkers for tumor aggressiveness and progression on a retrospect retrospective dataset consisting of many features may lead to false-positive findings, evaluation of such biomarkers on independent external test data may enable prognostic validation.

[0121] Example 4

[0122] The elucidated molecular subtypes of prostate cancer are characterized by PSMA PET / CT metrics and radiomic features. The biological properties of each subtype are assessed by quantifying tumor proliferation dynamics using allometric scaling laws. The clinical significance of a patient score that integrates whole-body tumor subtype findings is assessed by evaluating clinical outcomes, including PSA response and survival, and prognostic tasks, including risk stratification and prediction of treatment response.

[0123] Methods

[0124] Subtype classification. The discovered molecular subtypes of prostate cancer is characterized by PSMA PET / CT metrics, such as MTV, TLA, SUVmean, SUVmax, and textural features, such as distance zone matrix features SDHGE and LDLGE. The optimal threshold values of such metrics to characterize tumor subtypes will be identified by receiver-operating-characteristic curve analysis. The diagnostic accuracy of the molecular subtype classification task is assessed. Metrics with high discriminatory ability are integrated into a machine learning classifier (e.g., random forest, logistic regression, etc.) to perform tumor subtype classification.

[0125] Biological validation. The tumor proliferation dynamics of the prostate cancer subtypes are quantified using universal metabolic scaling laws that rule explosive tumor growth. Scaling exponents, (3, for each subtype are be quantified fromtumor measurements on PSMA PET / CT scans under the scaling law TLA = aMTVP. Values of / ? < 1, / ? = 1, / ? > 1 denote sublinear, linear, and superlinear dynamics, respectively, where higher values indicate higher levels of tumor aggression and proliferation. We hypothesize that tumor subtypes with higher (3 values indicate worse prognostic outcomes. Biological validation of the tumor subtypes will be adjudicated by clinical assessment, comparison to clinical PSMA-RADS scores, and radiologist visual evaluation.

[0126] Clinical significance and prognosis. A patient-level score that reflects disease progression status is constructed by integrating the predicted trajectory scores across all detected tumors on PSMA PET / CT. The patient-level score will be quantified by taking the weighted average by tumor volume of the predicted trajectory score across all tumors. The prognostic significance of the patient-level score is evaluated by overall survival analysis via the Kaplan-Meier method, Cox regression analysis, and concordance index. PSA response according to patient-level scores is assessed. The patient score is evaluated on prognostic tasks, including risk stratification, survival estimation, and treatment response prediction to optimize personalized treatment selection.

[0127] Although the use of scaling exponents according to metabolic scaling laws has been validated in several human cancers using tumor measurements quantified by ^®F-FDG PET / CT, the clinical utility of this measure has not been previously established and validated in prostate cancer using PSMA PET / CT. In addition to visual assessment and clinical evaluation on imaging, histopathological evaluation may be needed to further correlate and validate the use of scaling exponents in assessing the biological properties of tumor subtypes. Further prognostic assessment of the predicted patient scores on independent, external datasets may be needed to validate and establish clinical significance for response prediction and treatment selection optimization.

[0128] Example s

[0129] Data is randomly partitioned into training, validation, and test sets for algorithm assessment across all datasets. At least 30% of the data is allocated for independent external testing and the remaining will be used for training and cross-validation. The normality of PET / CT measures and radiomic features is assessed by the Shapiro-Wilk test. Feature reproducibility is quantified by using the coefficient ofvariation (COV) and Bland-Altman analysis across all image reconstruction settings, voxel samplings, and tumor segmentation methods. A COV <5% is considered robust and COV > 20% is considered non-robust. The Standardized Environment for Radiomics Analysis, an Image Biomarker Standardization Initiative-compliant radiomics processor with high reproducibility, is used to extract radiomic features. Statistical significance is assessed using the Wilcoxon signed-rank test, Wilcoxon rank-sum test, and McNemar test when comparing paired, unpaired, and binary observations, respectively. A P value of less than 0.05 is used to infer significant differences. The Benjamini-Hochberg method is used for multiple comparisons. Spearman rank correlation coefficients (r) and coefficients of determination (R ) are quantified to assess associations between imaging-based biomarkers and clinical measures. Receiver-operating-characteristic curves with 95% confidence intervals are computed with 1,000 bootstrap samples. Optimal thresholds for the tumor subtype discrimination task are determined by receiver-operating-characteristic analysis using the Youden index.

[0130] Example 6

[0131] Introduction

[0132] Prostate cancer was estimated to be the leading cause of new cancer cases and the second leading cause of cancer deaths for men in 2025. The annual number of new cases of prostate cancer is expected to rise from 1.4 million in 2020 to 2.9 million in 2040 globally. Despite the wide range of available treatment options, most patients with metastatic prostate cancer eventually die of their disease with the most deaths occurring two years after diagnosis. Moreover, treatment delays beyond 6 to 12 months may adversely impact outcomes for patients with high-risk prostate cancer.

[0133] Prostate-specific membrane antigen (PSMA)-targeted PET / computed tomography (CT) is highly sensitive and specific for the detection of prostate cancer tumors and metastases and is a useful tool for the assessment of treatment response and outcome prediction. As the presence of metastases drives mortality, accurate quantification of whole-body tumor burden is relevant for survival estimation and individualized treatment monitoring and planning. Proposed approaches for the prediction of overall survival using PSMA PET metrics often employ semi-automated or thresholding-based methods to perform volumes of interest (VOI) delineation.However, such approaches are susceptible to noise and partial volume effects and subject to scalability issues. Thus, fully automated tumor quantification PSMA PET is an important clinical need for survival prediction and prognosis of prostate cancer.

[0134] We developed a fully automated workflow that quantified whole-body tumor burden on PSMA PET / CT scans and predicted the survival of patients with prostate cancer. PSMA PET biomarkers were extracted and incorporated into an imaging-based risk score. Imaging and clinical measures were combined in Cox proportional hazards models to yield a prognostic index that predicted the probability of overall survival and progression-free survival on an individual basis. The approach demonstrated prognostic value and may further inform personalized treatment plans.

[0135] Materials and Methods

[0136] This retrospective study was approved by the Johns Hopkins Institutional Review Board. Deidentified data from 106 patients with prostate cancer, including 18F-DCFPyL PSMA PET / CT scans, treatment status before and after the PSMA PET scan, prostate-specific antigen (PSA) levels, overall staging by the American Joint Committee on Cancer (AJCC) tumor-node-metastasis staging system, Gleason scores, overall survival, and progression-free survival, were used in this example (Table 1). Overall survival was defined as the time between the PSMA PET scan and death from any cause. Progression-free survival was defined as the time between the PSMA PET scan and disease progression based on PSA values or imaging.Table 1. Summary of patient demographics.Characteristics ValuesAge (mean ± std. dev.) 66.75 ± 7.64 yearsRaceAsian 3Black 25White 78Overall AJCC stagingUnknown 13Stage I 3Stage II 19Stage III 37Stage IV 34Gleason scoreUnknown 26 97 328 219 3310 9Pre- PSMA PET therapyNone 13Local* 53Systemic androgen-targetedt 25Systemic cytotoxic? 15Post-PSMA PET therapyUnknown 11Opted for no treatment 5Local* 3Systemic androgen-targeted^ 46Systemic cytotoxic? 41PSA PSMA PET scan 81.58 ± 493.44 ng / mLFollow-up PSA 122.81 ± 771.17 ng / mLPSA doubling time 8.20 ± 9.90 monthsOverall survival (median) Not reachedProgression-free survival (median) 44.98 months*Local and focal therapies included prostatectomy, radiation, brachytherapy, high- intensity focused ultrasound, and cryoablation. ^Systemic androgen-targeted therapies included androgen deprivation therapy, abiraterone, and enzalutamide. Patients in this group may have previously received local or focal therapies but not systemic cytotoxic therapy. ^Systemic cytotoxic therapies included taxane-based chemotherapy (docetaxel) and177Lu-PSMA radioligand therapy (Pluvicto).

[0137] Fully Automated Tumor Quantification

[0138] We employed a fully automated workflow using a deep learning-based approach to perform tumor quantification on PSMA PET / CT scans and predict the survival of patients with prostate cancer. A deep semi-supervised transfer learning approach with a nnll-net backbone was trained and validated to perform automated tumor segmentation on PSMA PET / CT as previously described. The predicted tumorsegmentations were used to automatically extract whole-body imaging metrics, including molecular tumor volume (MTV), total lesion activity (TLA), mean standardized uptake value (SUVmean), maximum standardized uptake value (SUVmax), and number of lesions, from the PSMA PET / CT scans.

[0139] Risk Stratification and Survival Prediction

[0140] An imaging-based risk score that incorporated the extracted whole-body imaging measures was constructed. Imaging measures in the first, second, third, and fourth quartiles were assigned 0, 1 , 2, and 3 points, respectively. The points were summed to yield a predicted risk score ranging from 0 to 15. The risk score was combined with patient-specific covariates known at the time of the PSMA PET scan, including pre-PSMA PET treatment status and MTV, to yield a prognostic index that was used for risk stratification and survival prediction.

[0141] Cox proportional hazards regression models were trained and evaluated on the overall survival and progression-free survival prediction tasks using a 10-fold cross-validation. The survival probabilities were predicted by estimating the baseline survival function and the (3 coefficients of the covariates by Cox regression for both overall survival and progression-free survival. The prognostic index was defined as the weighted sum of the patient covariates and the (3 coefficients. The predicted risk probability of a patient experiencing an event was computed as the complement of the predicted survival probability.

[0142] Evaluation of Predicted Survival Probabilities

[0143] Based on the approach, we calculated the 1-year, 3-year, and 5-year overall survival and progression-free survival. The Brier score and time-dependent area under the receiver-operating-characteristic curve (AUC) were evaluated to assess the accuracy of the predicted survival probabilities. The Brier score ranges from 0 to 1 where a lower score indicates higher prediction accuracy. Scatter plots were generated to visualize the predicted risk probabilities of experiencing death or progression within 1, 3, and 5 years compared to the observed survival times. Calibration plots were used to compare the observed and predicted risk probabilities of experiencing an event within 1, 3, and 5 years. The observed survival curves were compared to the predicted survival probabilities of patients stratified by the predicted risk groups and post-PSMA PET treatment status.

[0144] Statistical Assessment

[0145] The observed survival curves were estimated by the Kaplan-Meier method. The inverse probability of censoring weights was applied to account for censored data. The Akaike information criterion was used to inform model and covariate selection. The observed survival of different groups was compared by the log-rank test. The Wilcoxon rank-sum test was used to compare unpaired observations. A P < 0.05 was used to infer significant differences. The Benjamini-Hochberg method was applied for multiple comparisons. Optimal thresholds were determined by receiver-operating-characteristic curve analysis using Youden’s index. Univariable and multivariable Cox regression models were assessed. Covariates that were insignificant by univariable analysis were excluded in the multivariable analysis. The Harrell's concordance index (C-index) was evaluated. The analyses were conducted with MATLAB (2024b) and R (4.5.0). The deep learning-based approach was implemented with Python (3.10.5) and PyTorch (1.12.0) using an NVIDIA A6000 GPU.

[0146] Results

[0147] Quantification of Tumor Burden and Imaging Biomarkers

[0148] The predicted tumor segmentations yielded mean values of 158.99 ± 573.65 cm3, 1301.04 ± 3637.24 SUV cm3, 7.96 ± 5.13, 39.93 ± 35.52, and 17.77 ± 29.20 for MTV, TLA, SUVmean, SUVmax, and lesion number, respectively. The observed survival curves of patients in each quartile of the extracted whole-body imaging measures were plotted using Kaplan-Meier estimators (Fig. 20). Patients with MTV and TLA values in the fourth quartile (Q4) had a shorter median overall survival and progression-free survival than of those in the first (Q1 ), second (Q2), and third quartiles (Q3), respectively (P < 0.001). Patients with SUVmean and SUVmax values in Q1 had a longer median overall survival and progression-free survival than those in Q3 and Q4, respectively (P < 0.01). Patients with SUVmean values in Q1 had a longer median overall survival than patients in Q2 (P < 0.01 ). Patients with lesion numbers in Q4 had a shorter median overall survival than patients in Q1 , Q2, and Q3 (P < 0.01 ). Patients with lesion numbers in Q4 had a shorter median progression-free survival than patients in Q1 (P < 0.001 ).

[0149] Imaging-based Risk Score

[0150] Patients were stratified by the predicted risk score and the observed survival curves of patients in each tertile were plotted (Fig. 21 A). Patients in the thirdtertile (T3, risk scores ranged from 11 to 15) compared to those in the first tertile (T1 , risk scores ranged from 0 to 5) had a shorter median overall survival (30.58 months vs. median not reached, P < 0.001) and a shorter median progression-free survival (20.81 months vs. median not reached, P < 0.001). Patients in T3 compared to those in the second tertile (T2, risk scores ranged from 6 to 10) had a shorter median overall survival (30.58 months vs. median not reached, P < 0.01) and a shorter median progression-free survival (20.81 months vs. 63.75, P < 0.01). Patients in T2 had a shorter median overall survival compared to patients in T1 (medians not reached, P < 0.01).

[0151] The distribution of mean values of clinical measures, including PSA at PSMA PET scan, follow-up PSA, and PSA doubling time, as well as imaging measures, including MTV, TLA, SUVmean, SUVmax, and number of lesions, based on the predicted imaging-based risk score are shown in Fig. 21 B. Patients with predicted risk scores in T3 had significantly higher PSA values at PSMA PET imaging and followup compared to those in T1 and T2, respectively (P < 0.05). Patients in T2 had significantly higher PSA values at PSMA PET imaging compared to patients in T1 (P < 0.001). All comparisons of MTV, TLA, SUVmean, SUVmax, and lesion number for patients with predicted risk scores in T1 , T2, and T3 were significant (P < 0.001 ).

[0152] Cox Regression Analysis

[0153] The extracted whole-body imaging measures and clinical PSA measures were used as continuous values in the Cox regression analysis. AJCC staging, Gleason score, pre-PSMA PET therapy, post-PSMA PET therapy, PSA at PSMA PET, follow-up PSA, PSA doubling time, MTV, TLA, SUVmax, lesion number, and the predicted risk score were significantly associated with overall survival by univariable Cox regression analysis (Table 2). Gleason score, pre-PSMA PET therapy, post-PSMA PET therapy, PSA at PSMA PET, follow-up PSA, MTV, TLA, SUVmean, SUVmax, lesion number, and the predicted risk score were significantly associated with progression-free survival by univariable analysis (Table 3). The predicted risk score was an independent prognosticator of overall survival and progression-free survival by multivariable Cox regression analysis (P < 0.05) and yielded C-index values of 0.81 and 0.75, respectively.Table 2. Cox regression analysis of overall survival.Univariable Cox Regression Multivariable Cox Regression Hazard Hazard C Param eter 95% Cl PValue 95% Cl PValue Ratio Ratio Index Age 1.03 0.98, 1.09 0.23 — — — 0.53 Race 1.06 0.49, 2.29 0.88 — — — 0.52 AJCC staging 1.23 1.03, 1.47 0.03 0.69 0.20, 2.34 0.55 0.62 Gleason score 1.61 1.13, 2.28 <0.01 2.27 0.32, 16.17 0.41 0.67 Pre- PSMA PET3.20 1.99, 5.14 <0.001 1.51 0.60, 3.81 0.38 0.74 therapyPost-PSMA PET3.19 1.76, 5.76 <0.001 0.56 0.07, 4.50 0.59 0.69 therapyPSA at PSMA PET 1.00 1.00, 1.00 <0.001 1.00 0.99, 1.00 0.74 0.73 Follow-up PSA 1.00 1.00, 1.00 <0.001 1.00 1.00, 1.01 0.30 0.81 PSA doubling time 0.89 0.81, 0.98 0.02 0.52 0.31, 0.90 0.02 0.70 MTV 1.00 1.00, 1.00 <0.001 1.00 0.99, 1.00 0.64 0.87 TLA 1.00 1.00, 1.00 <0.001 1.00 1.00, 1.00 0.43 0.85 SUVmean 1.03 0.98, 1.08 0.23 — — — 0.65 SUVmax 1.01 1.00, 1.02 0.04 1.00 0.96, 1.03 0.83 0.69 Number of lesions 1.02 1.01, 1.03 <0.001 1.00 0.97, 1.04 0.79 0.81 Predicted risk1.42 1.22, 1.65 <0.001 1.58 1.04, 2.38 0.03 0.81scoreCl: confidence intervals.Table 3. Cox regression analysis of progression-free survival.Univariable Cox Regression Multivariable Cox Regression Hazard Hazard C Parameter 95% Cl PValue 95% Cl PValue Ratio Ratio Index Age 1.02 0.98, 1.07 0.33 — — — 0.53 Race 1.20 0.65, 2.20 0.56 — — — 0.50 AJCC staging 1.04 0.91, 1.18 0.57 — — — 0.53 Gleason score 1.36 1.02, 1.81 0.04 0.98 0.69, 1.39 0.91 0.60 Pre-PSMA PET1.77 1.24, 2.53 <0.01 1.02 0.62, 1.66 0.95 0.64 therapyPost-PSMA PET2.75 1.71, 4.44 <0.001 2.13 0.95, 4.74 0.07 0.67 therapyPSA PSMA PET 1.00 1.00, 1.00 <0.001 1.00 1.00, 1.01 0.38 0.67 Follow-up PSA 1.00 1.00, 1.00 <0.001 1.00 1.00, 1.00 0.62 0.78 PSA doubling time 0.95 0.90, 1.01 0.08 — — — 0.65 MTV 1.00 1.00, 1.00 <0.001 1.00 0.99, 1.00 0.61 0.78 TLA 1.00 1.00, 1.00 <0.001 1.00 1.00, 1.00 0.41 0.77 SUV mean 1.05 1.01, 1.09 0.03 1.02 0.89, 1.17 0.77 0.62 SUV max 1.01 1.00, 1.01 <0.01 0.99 0.97, 1.01 0.36 0.68 Number of lesions 1.02 1.01, 1.03 <0.001 1.01 0.98, 1.04 0.45 0.73 Predicted risk1.24 1.13, 1.35 <0.001 1.20 1.02, 1.41 0.02 0.75scoreCl: confidence intervals.

[0154] Prediction of Survival and Risk Probabilities

[0155] The approach predicted the likelihood of overall survival and progression-free survival at 1 , 3, and 5 years after the PSMA PET scan. The approachyielded Brier scores of 0.09, 0.15, and 0.10 and AUC values of 0.85, 0.88, and 0.93 on the 1-year, 3-year, and 5-year overall survival prediction tasks, respectively. For the 1-year, 3-year, and 5-year progression-free survival prediction tasks, the approach yielded Brier scores of 0.10, 0.21 , and 0.19 and AUC values of 0.80, 0.76, and 0.80, respectively. The prognostic index yielded C-index values of 0.87 and 0.76 for overall survival and progression-free survival, respectively.

[0156] Patients were stratified into low- and high-risk groups by the prognostic index. Scatter plots visualized the predicted risk probabilities of experiencing an event at 1 , 3, and 5 years after the PSMA PET scan versus the observed overall survival and progression-free survival times (Fig. 22A-B). Calibration plots showed that the predicted risk probabilities were well-aligned with the observed risk probabilities (Fig.22C-D). Illustrative examples of the predicted 5-year overall survival probabilities for low- and high-risk patients are shown in Fig. 23.

[0157] The observed Kaplan-Meier survival curves were in close agreement with the predicted overall survival and progression-free survival probabilities for patients stratified by the predicted risk groups and imaging-based risk scores (Fig. 24). High-risk patients had a significantly shorter observed median overall survival (30.58 months vs. median not reached, P < 0.001) and median progression-free survival (22.85 months vs. median not reached, P < 0.001) compared to low-risk patients. The predicted median overall survival and progression-free survival times were 38.00 and 25.50 months for high-risk patients, respectively, and were unreached for low-risk patients (Fig. 24A).

[0158] Patients with an imaging-based risk score in T3 had observed and predicted median overall survival times of 30.58 and 31.00 months, respectively, and observed and predicted median progression-free survival times of 20.81 and 23.00 months, respectively (Fig. 24B). Patients with risk scores in T2 had observed and predicted median progression-free survival times of 63.75 and 57.50 months, respectively. The observed and predicted median overall survival times for patients with risk scores in T1 and T2 were unreached. The observed and predicted median progression-free survival times for patients with risk scores in T1 were unreached.

[0159] The observed and predicted survival curves were compared for low- and high-risk patients based on their post-PSMA PET therapy status (Fig. 25). All patients that received local post-PSMA PET therapy were predicted as low risk. For thesystemic androgen-targeted post-PSMA PET therapy group, high-risk patients had a shorter observed median overall survival (medians not reached, P < 0.05) and median progression-free survival (medians not reached, P < 0.01) compared to low-risk patients. For the systemic cytotoxic post-PSMA PET therapy group, high-risk patients had a shorter observed median overall survival (25.35 months vs. median not reached, P < 0.001) and median progression-free survival (20.81 months vs. median not reached, P < 0.001) compared to low-risk patients. High-risk patients who received systemic androgen-targeted and systemic cytotoxic post-PSMA PET therapies had predicted median overall survival times of 44.50 and 31.00 months, respectively, and predicted median progression-free survival times of 29.50 and 23.00 months, respectively.

[0160] Discussion

[0161] PSMA PET / CT is a valuable tool for the early detection and localization of prostate cancer tumors and metastatic lesions and plays an important role in therapy management. Quantitative parameters measured from baseline PSMA PET imaging are predictive of overall survival and treatment response for patients with metastatic castration-resistant prostate cancer. However, such quantitative approaches have been slow to adopt in clinical workflows, in part, due to the need for additional computation time and manual corrections. Accordingly, we developed a fully automated approach for tumor quantification on PSMA PET / CT scans and prediction of overall survival and progression-free survival of patients with prostate cancer (Fig.23).

[0162] Our approach performed automated tumor segmentation on PSMA PET / CT and extracted whole-body imaging measures, including MTV, TLA, SUVmean, SUVmax, and lesion number (Fig. 20). The extracted biomarkers were integrated into an imaging-based risk score using a straightforward point-based system (Fig. 21 A). In the univariable Cox regression analysis, MTV, TLA, SUVmax, and lesion number were significantly associated with overall survival, and all imaging biomarkers were significantly associated with progression-free survival (Tables 2 - 3). Patients with higher predicted risk scores had higher PSA values at PSMA PET and follow-up than patients with lower risk scores (Fig. 21 B). The predicted imaging-based risk score was an independent, negative prognosticator of overall survival and progression-free survival and yielded hazard ratios of 1.58 and 1.20, respectively, bymultivariable analysis, even while accounting for prognostic clinical factors, including AJCC staging, Gleason score, pre- and post-PSMA PET therapy status, PSA at PSMA PET, follow-up PSA, and PSA doubling time.

[0163] Patient covariates known at PSMA PET imaging, including pre-PSMA PET therapy status, MTV, and the imaging-based risk score, were combined and used as inputs to Cox proportional hazards models that yielded a prognostic index for survival prediction and risk stratification. The predicted 1-year, 3-year, and 5-year overall survival and progression-free survival probabilities agreed with the observed survival times and probabilities (Fig. 22), indicating accurate and well-calibrated survival predictions. The observed Kaplan-Meier survival curves of low- and high-risk patients closely matched the predicted survival probabilities (Fig. 24). The observed and predicted median survival times for high-risk patients were 30.58 and 38.00 months for overall survival and 22.85 and 25.50 months for progression-free survival, respectively, and were unreached for low-risk patients. The observed Kaplan-Meier survival curves were well-aligned with the predicted survival probabilities for patients who received different post-PSMA PET therapies (Fig. 25), highlighting the potential utility of our approach for the prediction of treatment response and prognosis.

[0164] Prior works have developed approaches that predict overall survival using quantitative measures on PSMA PET. However, such studies often utilize semiautomated or threshold-based segmentation methods, which may suffer from a lack of reliability or require manual intervention. Other groups have used a semi-automated software for quantitative tumor burden assessment with RECIP and reported that manual corrections were required in approximately 85% of cases due to nonspecific PSMA uptake and that clinical implementation was not expected soon. Other groups have also reported that, while total tumor volume on PSMA PET was the best independent prognostic marker for overall survival, the maximum distance between lesions may be a simpler alternative for settings where automated segmentation software is not readily available. Similarly, others have developed a visually calculated SUVmean HIT Score as the software required to derive quantitative SUVmean is not clinically available. This emphasizes the critical need for fully automated approaches to enable the clinical adoption of quantitative methods for the prognostication of prostate cancer.

[0165] In contrast to prior works, our approach employed a fully automated deep learning approach to perform tumor segmentation and biomarker quantification on PSMA PET / CT for the survival prediction task. Another group developed prognostic nomograms using PSMA PET staging by PROMISE criteria for the prediction of overall survival in all stages of prostate cancer. Additionally, we and others have developed automated deep learning-based approaches for prostate cancer classification and staging based on the PROMISE and PSMA-RADS frameworks. Our developed approach may be extended to incorporate such frameworks to further improve prognosis.

[0166] A limitation of this study was the availability of a limited dataset that consisted of patients with prostate cancer at different stages of disease progression. Despite this limitation, our approach yields robust predictions of overall survival and progression-free survival at different time points for patients with diverse pre- and post-PSMA PET therapy status. Although quantitative SUVmean is predictive of treatment response to177Lu-PSMA therapy and associated with survival outcomes, the association of SUVmean with overall survival did not reach statistical significance by univariable Cox analysis in the present example. This may be, in part, due to the limited dataset of patients with heterogenous therapy status as certain treatments, such as androgen deprivation therapy, may alter PSMA expression. This underscores the need for further validation of the developed approach in the context of patient outcomes, treatment response, and other PSMA-targeted radiotracers, such as68Ga-PSMA-11,18F-PSMA-1007, and18F-rhPSMA-7.3, to support clinical implementation.

[0167] Conclusion

[0168] Our approach performed fully automated tumor quantification on PSMA PET / CT scans and integrated whole-body imaging biomarkers into an imaging-based risk score. A prognostic index that incorporated the imaging-based risk score, MTV, and pre-PSMA PET therapy status was developed and demonstrated accurate risk stratification and survival prediction in patients with prostate cancer.

[0169] Example 7

[0170] Introduction

[0171] It was observed by Kleiber that the metabolic rates for a variety of species scale to 3 / 4 the power of an organism’s body mass. Allometric scaling laws take the formK - aMe, (1)where Y is an observable quantity, M is a measure of the size or mass, a is a rate constant, and (3 denotes the scaling exponent. The observation that the metabolism of many organisms obeys sublinear scaling laws with exponent (3 = 3 / 4 may be a consequence of the energy minimization principle.

[0172] Many cancers have high metabolic requirements and have increased uptake of nutrients, such as glucose and glutamine, to facilitate increased tumor growth and proliferation. It was shown by others that many human cancers obey superlinear (i.e., ? > 1) universal metabolic scaling laws that lead to explosive tumor growth. This contradicted the hypothesis of metabolic scaling being sublinear in cancer.

[0173] The metabolic scaling law of the formTLA = aMTV^, (2)where TLA is the total lesion activity and MTV is the molecular tumor volume, was observed in measurements obtained from 2- deoxy-2-[18F]fluoro-D-glucose (18F-FDG) positron emission tomography (PET) / computed tomography (CT) scans of patients with cancer. The scaling exponents of patients with breast cancer, head and neck cancer, non-small cell lung cancer, and rectal cancer were clustered around the rational number (3 = 5 / 4. The observed superlinear glucose uptake was likely due to an increasing rate of proliferation with tumor size. These findings were also confirmed in patients with glioma and breast cancer imaged with18F-fluorocholine and18F-fluorothymidine PET, respectively, which supported the hypothesis that the observed superlinear glucose uptake was to satisfy the increased tumor proliferation demands.

[0174] While many cancers may exhibit increased glucose uptake and glycolysis due to the Warburg Effect, prostate cancer often does not undergo glycolytic metabolism and is heavily dependent on glutamine through glutaminolysis for tumor cell proliferation and survival. Glutamine is metabolized into glutamate in the first step of the glutaminolysis pathway and is subsequently used as a substrate for the tricarboxylic acid cycle.

[0175] Prostate-specific membrane antigen (PSMA) is highly expressed in prostate cancer and is a biomarker for aggressive tumor phenotypes and poor prognosis. As such, PSMA-targeted PET / CT has a high detection rate and superiordiagnostic accuracy for prostate cancer compared with conventional imaging modalities, including bone scintigraphy, CT, and magnetic resonance imaging (MRI).

[0176] PSMA, also termed glutamate carboxypeptidase II, has been implicated in the generation of glutamate through its enzymatic activity on the glutamate moieties of polyglutamated folates, laminin peptides, and N-acetyl-aspartyl-glutamate (NAAG). PSMA has been shown to generate a localized reservoir of glutamate from tumor-derived NAAG to fuel tumor growth in other cancers, including glioma and ovarian cancer, although this phenomenon has not yet been shown in prostate cancer [4], While the role of PSMA in glutaminolysis and prostate cancer progression is not well understood, the increasing metabolic demand for glutamate in high-risk prostate cancer may increase tumor cell vulnerability to PSMA targeting.

[0177] Given the implication of PSMA in glutamate metabolism and tumor proliferation in prostate cancer, we hypothesized that prostate cancer tumors may exhibit superlinear metabolic scaling as measured by PSMA PET / CT. Accordingly, we developed an automated tumor segmentation workflow to estimate MTV and TLA values of prostate cancer tumors on PSMA PET / CT scans. We quantified the scaling exponents of prostate cancer tumors on two datasets of PSMA PET / CT scans and validated the quantified scaling exponents based on the PSMA reporting and data system (PSMA-RADS).

[0178] Methods

[0179] A. Datasets

[0180] 18F-DCFPyL PSMA PET / CT scans of patients with prostate cancer were used for analysis in this study. Datasets 1 and 2 consisted of 292 and 139 PSMA PET / CT scans, respectively. Dataset 1 had a limited set of manual segmentations, and Dataset 2 had no tumor annotations. A subset of the segmented tumors was assigned PSMA-RADS scores of 1 to 5. PSMA-RADS scores are on a 5-point scale where a higher score reflects a greater likelihood of prostate cancer.

[0181] B. Automated workflow for tumor segmentation on PET / CT

[0182] We developed a fully automated workflow to perform tumor segmentation on PSMA PET / CT images using a deep semi-supervised transfer learning (DeepSSTL) approach. A 5-fold cross-validation was used to cross-validate the segmentation task on the PSMA PET / CT scans with available manual tumor annotations and yielded test predictions on the hold-out sets. The DeepSSTLapproach yielded predicted segmentations on the remaining test set of PSMA PET / CT scans with no available tumor annotations. The predicted tumor segmentations yielded volumes of interest (VOIs) that were used for further analysis.

[0183] C. Metabolic scaling laws in prostate cancer

[0184] MTV and TLA values were quantified from the automatically predicted tumor VOIs on PSMA PET / CT scans from Datasets 1 and 2. Linear regressions of the log (MTV) versus log (TLA) were performed to estimate the metabolic scaling law p exponents following equation (2). The scaling exponents were estimated for Dataset 1 , Dataset 2, and All Datasets. The scaling exponents were also estimated for tumor VOIs that were assigned PSMA-RADS-3, PSMA-RADS-4, and PSMA-RAD-5 scores. Tumor VOIs that were assigned PSMA-RADS-1 or PSMA-RADS-2 scores were discarded from the analysis since those scores indicate certainly or almost certainly benign findings, respectively.

[0185] Results and Discussion

[0186] A. Automated tumor segmentation on PSMA PET / CT

[0187] The DeepSSTL approach detected 2,354 and 2,121 tumor VOIs on PSMA PET / CT scans from Datasets 1 and 2, respectively. For tumor VOIs with known PSMA-RADS scores, 119, 214, and 457 tumor VOIs were assigned as PSMA-RADS-3, PSMA-RADS-4, and PSMA-RADS-5, respectively. The approach yielded a median true positive rate of 0.75, a median Dice similarity coefficient of 0.73, and a true negative rate of 1.00 on the tumor segmentation task when compared to the manual tumor annotations.

[0188] B. Quantification of metabolic scaling laws on PSMA PET

[0189] The metabolic scaling law p exponents were estimated from MTV and TLA values extracted from PSMA PET using the automatically segmented tumor VOIs. The quantified scaling exponents for Dataset 1 , Dataset 2, and All Datasets were p = 1.28 ± 0.01 (R2= 0.90), p = 1.22 ± 0.01 (R2= 0.94), and p = 1.26 ± 0.01 (R2= 0.91 ), respectively (Fig. 26A-C). The obtained scaling exponents were superlinear (p > 1) and clustered around the rational number p = 5 / 4 across both datasets of PSMA PET scans of patients with prostate cancer. The tumor VOIs that were assigned PSMA-RADS-3, PSMA-RADS- 4, and PSMA-RADS-5 scores had scaling exponents of p = 1.09 ± 0.03 (R2= 0.90), p = 1.19 ± 0.03 (R2 = 0.89), and p = 1.31 ± 0.02 (R2= 0.93), respectively (Fig. 26D-F). This indicates that tumors with higher PSMA-RADS scoreshad greater rates of PSMA expression. These findings show that tumor PSMA expression scales superlinearly with tumor size.

[0190] Conclusion

[0191] PSMA is an important marker of tumor aggression that is highly expressed in prostate cancer. Prostate cancer cells exhibit a strong reliance on glutamine metabolism for tumor cell proliferation and survival. However, the role of PSMA in glutamine metabolism and tumor growth has not been fully elucidated. We developed an automated workflow that extracted MTV and TLA values from prostate cancer tumor segmentations on PSMA PET / CT and quantified allometric scaling laws. The obtained scaling exponents denoted a superlinear relationship between PSMA expression and tumor size, highlighting a potential metabolic link between PSMA and increasing rates of tumor proliferation in prostate cancer.

[0192] Example s

[0193] Metabolic rates of biological systems play a central role in determining the dynamics of the survival, growth, and propagation of a species. All organisms perform metabolic processes that transform nutrients into biochemical energy and biomass, which are essential for their growth and maintenance. It was first observed by Klieber that the metabolic rates of a variety of animals were proportional the 3 / 4 power of body size. The classic allometric scaling law that describes the power-law relationship between metabolic rate and body size is of the following formM = M0Va(1)where M is the total metabolic rate, Mo is a normalization constant, V is the size of the biological system (which can be measured by volume or mass), and a is the scaling exponent. The observed a = 3 / 4 scaling exponent was proposed to be a consequence of energy minimizing principles that constrain nutrient and oxygen transport in vascular systems modeled as fractal networks. The 3 / 4 power scaling law, also known as Klieber’s law, was confirmed in a wide range of organisms across 27 orders of magnitude of biological hierarchical organization, ranging from the largest to smallest mammals and from single mammalian cells to the molecules of the respiratory complexes of the mitochondrion.

[0194] Despite its broad scope, Klieber’s law does not universally apply across all organisms. Unicellular prokaryotes and eukaryotes exhibit scaling exponents of a > 1 and a = 1, respectively, whereas multicellular metazoans exhibit a scalingexponent of a < 1 closer to that of Klieber’s law. The superlinear scaling of metabolic rate in prokaryotes is thought to be possible due to an increasing number of genes with larger genome sizes allowing for more complex metabolic networks and greater efficiency in adenosine triphosphate (ATP) production. As the respiratory complexes are localized on the cell surface in prokaryotes, their metabolic rates are eventually limited by cell surface area with increasing cell size. Unicellular eukaryotes overcome this limitation by compartmentalizing the respiratory enzymes in the ancestral organelle of mitochondria which leads to a linear metabolic scaling as the volume of respiratory complexes scale linearly with size. The development of multicellular organisms gives rise to more complex body plans, including digestive and vascular systems required to process and distribute metabolic substrates and oxygen. This further decreases the efficiency of biomass production as an increasing fraction of metabolic power must be devoted towards maintenance. Thus, the shift from a highly superlinear scaling of metabolic rate towards a sublinear scaling across the major evolutionary transitions of unicellular to multicellular life forms reflect the differences in constraints of different body sizes and organizational architectures.

[0195] Another notable exception to Klieber’s law is the metabolic activity of malignant tumors. Some prior evidence from xenograft data suggests that tumors may follow linear to sublinear scaling. However, a superlinear scaling exponent of a = 5 / 4 was observed in vivo using18F-fluorodeoxyglucose (18F-FDG) positron emission tomography (PET) images of patients with different cancers, including breast cancer, head and neck cancer, non-small cell lung cancer, and rectal cancer7. Many cancers have high metabolic requirements and have increased uptake of nutrients, predominately glucose and glutamine, to facilitate increased tumor growth and proliferation. Accordingly, the observed superlinear glucose uptake was likely to satisfy the increasing demands of proliferation with increasing tumor size. This finding was further supported by measurements of choline and thymidine metabolism in patients with glioma and breast cancer imaged with18F-fluorocholine and18F-fluorothymidine PET. As higher levels of multicellular organization lead to increasingly sublinear scaling exponents tending towards Kleiber’s law, the decreased efficiency of the local vascular network of tumors may disrupt the organizational structures of the tumor microenvironment and contribute to superlinear scaling dynamics.

[0196] Another essential factor that may contribute to the increasing of metabolic scaling exponents of tumors is the Warburg effect. In normal mammalian cells, approximately 89% of the total ATP produced by the complete respiration of glucose is from oxidative phosphorylation in mitochondria. Cancer cells exhibiting the Warburg phenotype favor high rates of glycolysis, even in the presence of oxygen, for rapid fermentation of glucose producing up to 50-60% of total ATP, whereas the normal cells of the liver and kidney derive less than 1% of their cellular energy from glycolysis. The increased rate of glycolysis allows cancer cells to rapidly generate ATP and pools of glycolytic intermediates that are shunted into alternative pathways to synthesize nucleotides, lipids, and amino acids.

[0197] Another essential factor that may contribute to the increasing of metabolic scaling exponents of tumors is the Warburg effect. In normal mammalian cells, approximately 89% of the total ATP produced by the complete respiration of glucose is from oxidative phosphorylation in mitochondria. Cancer cells exhibiting the Warburg phenotype favor high rates of glycolysis, even in the presence of oxygen, for rapid fermentation of glucose producing up to 50-60% of total ATP, whereas the normal cells of the liver and kidney derive less than 1% of their cellular energy from glycolysis. The increased rate of glycolysis allows cancer cells to rapidly generate ATP and pools of glycolytic intermediates that are shunted into alternative pathways to synthesize nucleotides, lipids, and amino acids.

[0198] While aerobic glycolysis is a metabolic hallmark of cancer, the Warburg effect is not a universal feature of all cancers as there is significant heterogeneity across tumor types. Some cancers, including many early-stage prostate cancers, are not highly glycolytic but are heavily dependent on glutamine for tumor proliferation and survival. Many cancers exhibit glutamine addition, including prostate cancer, pancreatic cancer, breast cancer, and ovarian cancers. Glutamine is the most abundant amino acid in circulation, and the rate of glutamine uptake in HeLa cells is one to two orders of magnitude greater than those of other amino acids. Glutamine is first metabolized to glutamate in the glutaminolysis pathway by the glutaminase enzyme located primarily in the mitochondria. Glutamate is then converted to oc-ketoglutarate by the oxidative deamination or transamination pathways catalyzed by the glutamate dehydrogenase and transaminase enzymes. Subsequently, oc-ketoglutarate enters the tricarboxylic acid (TCA) cycle and provides anapleroticintermediates to fuel nucleotide, lipid, and amino acid biosynthesis, the production of reducing equivalents of NADH and FADH2, and ATP generation.

[0199] Glutamine is a conditionally essential amino acid for survival and growth for both normal and cancer cells. However, in the absence of glutamine, high levels of glutamate at concentrations 10 to 20 times the maximally effective concentration of glutamine can enable cell growth in HeLa cells but not normal cells. The requirement of such high concentrations of exogenous glutamate may be in part due to the lower permeability of glutamate to cell membranes relative to glutamine. The addition of glutamate to respiring tumor mitochondria while in the presence of glutamine also enhances oxygen consumption, which may be due to the saturation of the transamination and glutamate dehydrogenase pathways by each respective substrate. Exogenous glutamate can also be metabolized through transaminase enzymes present in the cytosol whereas glutamine metabolism through the glutamate dehydrogenase pathway occurs primarily in the mitochondria.

[0200] Glutamate carboxypeptidase II, also termed prostate-specific membrane antigen (PSMA), has been implicated in the generation of glutamate through its enzymatic action on glutamate moieties present in the tumor microenvironment, such as those of polyglutamated folates, laminin peptides, and N-acetyl-aspartyl-glutamate. PSMA generates a localized reservoir of glutamate from N-acetyl-aspartyl-glutamate to fuel tumor growth in high-grade cancers. PSMA is also highly expressed in prostate cancer and is a biomarker for aggressive tumor phenotypes and poor prognosis. While the role of PSMA in glutaminolysis and prostate cancer progression is not fully understood, the increasing metabolic demand for glutamate in high-risk prostate cancer may increase tumor cell vulnerability to PSMA targeting.

[0201] Given the role of PSMA in glutamate metabolism in high-grade cancers, we hypothesized that PSMA expression in prostate cancer contributes to tumor progression by driving the uptake of exogenous sources of glutamate and replenishing anaplerotic intermediates to fuel the production of energy and biomass. To test this hypothesis, we investigated the allometric scaling relationship between PSMA expression and tumor size in two independent cohorts of patients with prostate cancer imaged with18F-DCFPyL PSMA PET. If PSMA is driving glutamate metabolism and tumor proliferation in prostate cancer, then the observed scaling exponent of tumorsexpressing PSMA should be close to the a = 5 / 4 scaling exponent of other cancers exhibiting the Warburg phenotype.

[0202] Data from patient cohorts 1 and 2 consisted of 292 and 13918F-DCFPyL PSMA PET / CT scans, respectively. Tumor segmentation was performed on the PSMA PET / CT images using a fully automated deep learning-based approach. Tumors from a subset of patients from cohort 1 were assigned PSMA reporting and data systems (PSMA-RADS) scores of 1 to 5, where a higher score reflects a greater probability of prostate cancer. Clinical information, including overall survival, progression-free survival, and treatment status were available for a subset of patients from cohort 2. Molecular tumor volume (MTV) and total lesion activity (TLA) were quantified from the automatically predicted segmentations of tumors on the PSMA PET / CT scans. TLA was computed as the product of the mean standardized uptake value (SUVmean) of the tumor and the MTV. We evaluated the allometric scaling relationship TLA = Mo* MTVa. Linear regressions were performed of the linearized allometric scaling equation log(TM) = log(M0) + c log MTV) to estimate the scaling exponents a.

[0203] The quantified scaling exponent for all patients across cohorts 1 and 2 were a = 1.26 ± 0.01 (R2= 0.91). The estimated scaling exponents for cohorts 1 and 2 were a = 1.28 ± 0.01 (R2= 0.90) and a = 1.22 ± 0.01 (R2= 0.94), respectively (Figure 27). The estimated scaling exponents were all significantly greater than one by a onesided t-test (P < 0.001), indicating superlinear scaling dynamics across all cohorts. The estimated scaling exponents across both patient cohorts were approximately 5 / 4 supporting our hypothesis that PSMA expression is driving tumor proliferation through superlinear exogenous glutamate uptake.

[0204] Tumors that were assigned higher PSMA-RADS scores had larger scaling exponents (Figure 28). Tumors that were assigned PSMA-RADS-1 or PSMA-RADS-2 were excluded from the analysis as those scores indicate benign findings. Tumors with an intermediate risk (PSMA-RADS-3) had the smallest scaling exponent of a = 1.09 ± 0.03 (R2= 0.90). Tumors with a high likelihood of prostate cancer (PSMA-RADS-4) had a scaling exponent of a = 1.19 ± 0.03 (R2= 0.89). Tumors with a very high likelihood of clinically significant prostate cancer (PSMA-RADS-5) had the largest scaling exponent of a = 1.31 ± 0.02 (R2= 0.93), indicating decidedly superlinear scaling dynamics for tumors that were almost certainly malignant. The scaling exponent for PSMA-RADS-5 tumors were significantly higher than those of PSMA-RADS-3 and PSMA-RADS-4 by a one-way analysis of covariance (ANCOVA) test (P < 0.001).

[0205] The treatment status of patients may also affect the quantification of the metabolic scaling exponents as many systemic therapies can alter PSMA expression. Systemic androgen-targeted therapies, such as androgen deprivation therapy (ADT), abiraterone, and enzalutamide, initially upregulate PSMA causing a transient shortterm rise in PSMA expression known as the flare phenomenon. Prolonged long-term ADT leads to the downregulation of PSMA leading to decreased PSMA expression per cell. Systemic cytotoxic therapies, such as docetaxel and177Lu-PSMA radioligand therapy result in decreased PSMA expression by reducing tumor burden rather than downregulating expression. We evaluated the scaling exponents in the context of systemic androgen-targeted and cytotoxic therapies (Figure 29). Patients that were treatment naive or that had received local or focal therapy prior to imaging had a scaling exponent of a = 1.26 ± 0.01 (R2= 0.95), which was indistinguishable from the scaling exponent estimated for patients across all cohorts. Patients that received systemic therapy prior to PSMA PET imaging had a significantly lower scaling exponent of a = 1.20 ± 0.01 (R2= 0.95) compared to that of patients that had not received any systemic therapy prior to imaging by a one-way ANCOVA test (P < 0.001). Those observations confirm that systemic androgen-targeting and cytotoxic therapies decrease PSMA expression and result in slightly less aggressive, albeit superlinear, metabolic scaling dynamics compared to baseline.

[0206] The quantified scaling exponents for all patient cohorts were clustered around a = 5 / 4 (Figure 30). Tumors that had a lower likelihood for malignancy (lower PSMA-RADS scores) or exposure to systemic therapies that can reduce PSMA expression had scaling exponents lower than 5 / 4, in line with our expectations. To further understand how the scaling exponents impact tumor growth dynamics, we describe the growth equations and relate them to the quantified metabolic scaling laws. By the conservation of energy, the total metabolic rate of a system is equivalent to metabolic expenditure required for maintenance and growth. The following differential equation can be derived that describes the growth trajectories of biological systems— = AVa- LlV (2)^4-rwhere X and p are rate constants. In the special case of a = 1 , the solution to the differential equation is a pure exponential function. The growth trajectories of sublinear and superlinear scaling laws in the more general caseof a 1 are shown in Figure 31. For a < 1 , the size of the system will undergo stable bounded growth or decay tending towards a threshold size. For a > 1 and an initial size above a threshold size, the size of the system will undergo unbounded growth where the solution explodes in finite time. For an initial size below a threshold size, the solution will decay to zero. Thus, the observed allometric scaling law of a = 5 / 4 for PSMA expression and tumor size indicates that tumors above a certain threshold size will tend towards explosive growth leading to a blow-up in size at the critical time.

[0207] The process of tumorigenesis involves the gradual transformation of a normal cell to a precancerous cell which will eventually transform into a malignant neoplasia. We reasoned that because the process of carcinogenesis is continuous that there should be a gradual shift in the metabolic scaling exponents starting from the sublinear dynamics of Kleiber’s law to the eventual superlinear scaling observed in tumors with a high degree of malignancy. Radiomic features on PSMA PET imaging capture important characteristics of tumors that indicate their metabolic state. We hypothesized the existence of a continuous low-dimensional manifold in the space of radiomic features that corresponds to tumor progression. To investigate this hypothesis, radiomic signatures from the segmented tumors were extracted from PSMA PET scans. A trajectory inference approach using a variational autoencoder was developed to learn a low-dimensional latent space from the radiomic signatures of tumors. Trajectory inference was applied in the low-dimensional latent space using minimum spanning trees. The learned low-dimensional manifold was projected back into the high-dimensional space of radiomic features to learn a path that corresponded to important variations along the tumor progression (Figure 32).

[0208] Radiomic features of tumors along the learned trajectory path were sampled and then used to perform hierarchical clustering. A dendrogram is shown in Figure 33 that visualizes the hierarchical clustering. Three main clusters of tumors emerged referred to as subtypes 1, 2, and 3 (S1, S2, and S3). Two main clusters of features emerge referred to as groups 1 and 2. In general, the expression of features from group 1 were high for S1 and low for S3 whereas the opposite pattern was observed for group 2 features. As seen from the dendrogram, S2 appears to be atransitionary subtype from S1 to S3. A trajectory score for each tumor was computed by projecting their radiomic signatures onto the learned trajectory path and normalizing their position on the path to a score ranging from 0 to 1. A patient-level score was constructed that averaged trajectory scores from all tumors for a given patient. The overall survival and progression-free survival curves were computed for each quartile of the patient-level trajectory scores (Figure 34). Patients with higher scores in the upper quartile were associated with S3 and had shorter overall-survival and progression-free survival times. Patients with lower scores in the lower quartile were associated with S1 and had longer survival times. Patients with intermediate scores within the interquartile range were associated with S2 and had intermediate survival times.

[0209] The metabolic scaling exponents were estimated for each the tumor subtypes (Figure 35). The quantified scaling exponents were a = 0.79 ± 0.04, 0.98 ± 0.02, and a = 1.22 ± 0.01 denoting sublinear, linear, and superlinear scaling dynamics for S1, S2, and S3, respectively. Those findings confirmed the hypothesis that there was a smooth transition from sublinear dynamics characterized by stable bounded growth to superlinear dynamics characterized by unstable explosive growth during the transformation of a benign to malignant neoplasia. Tumor subtypes with more aggressive scaling dynamics had worse prognosis in terms of overall survival and progression-free survival.

[0210] In summary, we discovered for the first time a superlinear metabolic scaling law of PSMA expression in prostate cancer with an allometric scaling exponent of a = 1.26 ± 0.01. This finding supports the hypothesis that PSMA expression drives tumor growth and proliferation by facilitating uptake of exogenous glutamate from the tumor microenvironment to provide anaplerotic intermediates for increased rates of biosynthesis. Metabolic subtypes were characterized that revealed a gradual transformation from normal to malignant growth dynamics. Tumor subtypes with higher scaling exponents had a higher likelihood of malignancy and worse survival outcomes. The observed superlinear scaling law predicts a metabolic phenotype that is characterized by explosive, unbounded tumor growth. Our findings have important implications for developing rational personalized therapies for a patient based on findings on their PSMA PET scan. Simultaneously targeting glutamine and glutamate metabolism through a combination therapy may improve the efficacy and effectivenessof PSMA-targeted radioligand therapy and may help to overcome therapeutic resistance.

[0211] Some further aspects are also defined in the following clauses:

[0212] Clause 1: A computer-implemented method of identifying tumor subtypes, the method comprising: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes, thereby identifying the tumor subtypes.

[0213] Clause 2: The method of Clause 1 , wherein the identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another.

[0214] Clause 3: The method of Clause 1 or Clause 2, wherein the identified tumor subtypes comprise at least three distinct tumor subtypes, wherein: a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a lowprobability of being prostate cancer, a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer.

[0215] Clause 4: The method of any of Clauses 1-3, comprising quantifying one or more molecular parameters on the PSMA PET / CT scans.

[0216] Clause 5: The method of any of Clauses 1-4, comprising identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique.

[0217] Clause 6: The method of any of Clauses 1-5, comprising identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees.

[0218] Clause 7: The method of any of Clauses 1-6, further comprising determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task.

[0219] Clause 8: The method of any of Clauses 1-7, further comprising validating one or more of the method steps and / or products thereof.

[0220] Clause 9: The method of any of Clauses 1-8, wherein the radiomic signatures corresponding to the distinct molecular subtypes are identified using a hierarchical agglomerative clustering technique.

[0221] Clause 10: The method of any of Clauses 1-9, wherein the PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

[0222] Clause 11: The method of any of Clauses 1-10, wherein the detecting step comprises removing false-positive VOIs.

[0223] Clause 12: The method of any of Clauses 1-11 , wherein the radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs.

[0224] Clause 13: The method of any of Clauses 1-12, wherein the radiomic features comprise one or more three-dimensional (3D) distance zone matrix features.

[0225] Clause 14: The method of any of Clauses 1-13, wherein the radiomic features comprise between about 300 and about 500 radiomic features.

[0226] Clause 15: The method of any of Clauses 1-14, further comprising identifying one or more molecular tumor phenotypes using a clustering technique.

[0227] Clause 16: The method of any of Clauses 1-15, wherein the extracting and detecting steps comprise one or more of a median true positive rate of about 0.75, a median positive predictive value of about 0.76, a median Dice similarity coefficient of about 0.73, a median false discovery rate of about 0.24, a true negative rate of about 1.00, or a negative predictive value of about 1.00.

[0228] Clause 17: The method of any of Clauses 1-16, wherein the trained radiomics classifier detects true positive VOIs with an overall accuracy of about 0.93 and / or an area under the receiver-operating-characteristic (AUC) curve of about 0.87.

[0229] Clause 18: The method of any of Clauses 1 -17, comprising using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject.

[0230] Clause 19: The method of any of Clauses 1-18, further comprising administering one or more therapies to the test subject to treat the characterized tumors in the test subject.

[0231] Clause 20: A computer-implemented method of detecting a tumor subtype in a test subject, the method comprising: segmenting a tumor on a prostatespecific membrane antigen (PSMA) positron emission tomography (PET) / computed tomography (CT) scan obtained from the test subject to produce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1 ) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject, thereby detecting the tumor subtype in the test subject.

[0232] Clause 21: The method of Clause 20, further comprising administering one or more therapies to the test subject to treat the characterized tumor in the test subject.

[0233] Clause 22: A system, comprising: a processor; and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes.

[0234] Clause 23: The system of Clause 22, wherein the identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another.

[0235] Clause 24: The system of Clause 22 or Clause 23, wherein the identified tumor subtypes comprise at least three distinct tumor subtypes, wherein: a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer.

[0236] Clause 25: The system of any of Clauses 20-24, wherein the instructions which, when executed on the processor, further perform operations comprising: quantifying one or more molecular parameters on the PSMA PET / CT scans.

[0237] Clause 26: The system of any of Clauses 20-25, wherein the instructions which, when executed on the processor, further perform operations comprising: identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique.

[0238] Clause 27: The system of any of Clauses 20-26, wherein the instructions which, when executed on the processor, perform operations comprising: identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees.

[0239] Clause 28: The system of any of Clauses 20-27, wherein the instructions which, when executed on the processor, further perform operations comprising: determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task.

[0240] Clause 29: The system of any of Clauses 20-28, wherein the instructions which, when executed on the processor, perform operations comprising: using a hierarchical agglomerative clustering technique to identify the radiomic signatures corresponding to the distinct molecular subtypes.

[0241] Clause 30: The system of any of Clauses 20-29, wherein the PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

[0242] Clause 31 : The system of any of Clauses 20-30, wherein the instructions which, when executed on the processor, perform operations comprising: removing false-positive VOIs from the set of predicted tumor segmentations.

[0243] Clause 32: The system of any of Clauses 20-31, wherein the radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs.

[0244] Clause 33: The system of any of Clauses 20-32, wherein the radiomic features comprise one or more three-dimensional (3D) distance zone matrix features.

[0245] Clause 34: The system of any of Clauses 20-33, wherein the radiomic features comprise between about 300 and about 500 radiomic features.

[0246] Clause 35: The system of any of Clauses 20-34, wherein the instructions which, when executed on the processor, perform operations comprising: identifying one or more molecular tumor phenotypes using a clustering technique.

[0247] Clause 36: The system of any of Clauses 20-35, wherein the instructions which, when executed on the processor, perform operations comprising: using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject.

[0248] Clause 37: A system, comprising: a processor; and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject.

[0249] Clause 38: The system of Clause 37, wherein the instructions which, when executed on the processor, perform operations comprising: outputting one or more therapy recommendations to treat the characterized tumor in the test subject.

[0250] Clause 39: A computer readable media comprising non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least: extracting radiomic features from volumes of interest (VOIs) on prostate-specific membrane antigen (PSMA) positron emission tomography(PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects; detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes; identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features; generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space; discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes; producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes.

[0251] Clause 40: A computer readable media comprising non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least: segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and, characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject.

[0252] While the invention has been described with reference to the exemplary embodiments thereof, those skilled in the art will be able to make various modifications to the described embodiments without departing from the true spirit and scope. The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. In particular, although the method has been described by examples, the steps of the method can be performed in a different order than illustrated or simultaneously. Those skilled in the art will recognize that these and other variations are possible within the spirit and scope as defined in the following claims and their equivalents. All patents, patent applications, other publications or documents, and the like cited herein are incorporated by reference in their entirety for all purposes to the same extent as if each individual item were specifically and individually indicated to be so incorporated by reference.

Claims

1. What is claimed is:

1. A computer-implemented method of identifying tumor subtypes, the method comprising:3.extracting radiomic features from volumes of interest (VOIs) on prostatespecific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1 , 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects;4.detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs;5.using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes;6.identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features;7.generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space;8.discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes;9.producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and, outputting the set of identified tumor subtypes, thereby identifying the tumor subtypes.

2. The method of claim 1 , wherein the identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another.

3. The method of claim 1 , wherein the identified tumor subtypes comprise at least three distinct tumor subtypes, wherein:12.a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer,13.a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and14.a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer.

4. The method of claim 1 , comprising quantifying one or more molecular parameters on the PSMA PET / CT scans.

5. The method of claim 1, comprising identifying one or more imagingbased tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique.

6. The method of claim 1 , comprising identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees.

7. The method of claim 1, further comprising determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task.

8. The method of claim 1, further comprising validating one or more of the method steps and / or products thereof.

9. The method of claim 1, wherein the radiomic signatures corresponding to the distinct molecular subtypes are identified using a hierarchical agglomerative clustering technique.

10. The method of claim 1, wherein the PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

11. The method of claim 1 , wherein the detecting step comprises removing false-positive VOIs.

12. The method of claim 1 , wherein the radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs.

13. The method of claim 1, wherein the radiomic features comprise one or more three-dimensional (3D) distance zone matrix features.

14. The method of claim 1 , wherein the radiomic features comprise between about 300 and about 500 radiomic features.

15. The method of claim 1, further comprising identifying one or more molecular tumor phenotypes using a clustering technique.

16. The method of claim 1, wherein the extracting and detecting steps comprise one or more of a median true positive rate of about 0.75, a median positive predictive value of about 0.76, a median Dice similarity coefficient of about 0.73, a median false discovery rate of about 0.24, a true negative rate of about 1.00, or a negative predictive value of about 1.00.

17. The method of claim 1, wherein the trained radiomics classifier detects true positive VOIs with an overall accuracy of about 0.93 and / or an area under the receiver-operating-characteristic (AUC) curve of about 0.87.

18. The method of claim 1, comprising using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject.

19. The method of claim 1, further comprising administering one or more therapies to the test subject to treat the characterized tumors in the test subject.

20. A computer-implemented method of detecting a tumor subtype in a test subject, the method comprising:30.segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET) / computed tomography (CT) scan obtained from the test subject to produce a segmented test subject tumor; and,31.characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject, thereby detecting the tumor subtype in the test subject.

21. The method of claim 20, further comprising administering one or more therapies to the test subject to treat the characterized tumor in the test subject.

22. A system, comprising:34.a processor; and35.a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: extracting radiomic features from volumes of interest (VOIs) on prostatespecific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1, 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects;36.detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs;37.using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes;38.identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features;39.generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space;40.discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes;41.producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and,42.outputting the set of identified tumor subtypes.

23. The system of claim 22, wherein the identified tumor subtypes comprise levels of tumor aggressiveness that differ from one another.

24. The system of claim 22, wherein the identified tumor subtypes comprise at least three distinct tumor subtypes, wherein:a tumor subtype 1 (S1) is associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer,45.a tumor subtype 2 (S2) is associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, and46.a tumor subtype 3 (S3) is associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer.

25. The system of claim 22, wherein the instructions which, when executed on the processor, further perform operations comprising:48.quantifying one or more molecular parameters on the PSMA PET / CT scans.

26. The system of claim 22, wherein the instructions which, when executed on the processor, further perform operations comprising:50.identifying one or more imaging-based tumor subtypes of tumors on the PSMA PET / CT scans using an unsupervised learning technique.

27. The system of claim 22, wherein the instructions which, when executed on the processor, perform operations comprising:52.identifying the relationships between the tumor subtypes in the set of predicted tumor segmentations using trajectory inference with minimum spanning trees on the set of learned continuous latent features, and generating the predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto the axis in the continuous latent space determined by the minimum spanning trees.

28. The system of claim 22, wherein the instructions which, when executed on the processor, further perform operations comprising:54.determining one or more importance estimates by finding an optimal threshold of each latent feature as part of a tumor subtype classification task.

29. The system of claim 22, wherein the instructions which, when executed on the processor, perform operations comprising:using a hierarchical agglomerative clustering technique to identify the radiomic signatures corresponding to the distinct molecular subtypes.

30. The system of claim 22, wherein the PSMA PET / CT scans comprise whole-body PSMA PET / CT scans.

31. The system of claim 22, wherein the instructions which, when executed on the processor, perform operations comprising:58.removing false-positive VOIs from the set of predicted tumor segmentations.

32. The system of claim 22, wherein the radiomic features comprise a set of quantitative features that describe a distribution of intensity values, shape characteristics, and textural patterns within the VOIs.

33. The system of claim 22, wherein the radiomic features comprise one or more three-dimensional (3D) distance zone matrix features.

34. The system of claim 22, wherein the radiomic features comprise between about 300 and about 500 radiomic features.

35. The system of claim 22, wherein the instructions which, when executed on the processor, perform operations comprising:63.identifying one or more molecular tumor phenotypes using a clustering technique.

36. The system of claim 22, wherein the instructions which, when executed on the processor, perform operations comprising:65.using the set of identified tumor subtypes to characterize one or more tumors in a test subject to produce one or more characterized tumors in the test subject.

37. A system, comprising:67.a processor; and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising:68.segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and,69.characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject.

38. The system of claim 37, wherein the instructions which, when executed on the processor, perform operations comprising:71.outputting one or more therapy recommendations to treat the characterized tumor in the test subject.

39. A computer readable media comprising non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least:73.extracting radiomic features from volumes of interest (VOIs) on prostatespecific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scans obtained from a population of reference subjects to produce a set of radiomic features, wherein the VOIs comprise putative tumors in the reference subjects and wherein one or more PSMA reporting and data system (PSMA-RADS) scores of 1, 2, 3, 4, or 5 are independently assigned to each of the PSMA PET / CT scans obtained from at least a sub-population of the reference subjects;74.detecting true-positive VOIs on the PSMA PET / CT scans using a trained radiomics classifier generated from the set of radiomic features to produce a set of predicted tumor segmentations that comprise substantially only the true-positive VOIs; using a variational autoencoder (VAE) and a radiomic feature space comprising at least a portion of the set of radiomic features to produce a continuous latent space comprising a set of learned continuous latent features that comprise one or more variations among tumor subtypes;75.identifying one or more relationships between tumor subtypes in the set of predicted tumor segmentations using trajectory inference on the set of learned continuous latent features;76.generating predicted risk scores for each tumor in the set of predicted tumor segmentations by projecting the learned continuous latent features onto an axis in the continuous latent space;77.discovering one or more radiomic signatures corresponding to distinct molecular subtypes in the set of predicted tumor segmentations to produce a set of discovered tumor subtypes;78.producing a set of identified tumor subtypes at least partially based on one or more comparisons of a distribution of the PSMA-RADS scores to the predicted risk scores and the set of discovered tumor subtypes; and,79.outputting the set of identified tumor subtypes.

40. A computer readable media comprising non-transitory computer executable instructions which, when executed by at least one electronic processor, perform at least:81.segmenting a tumor on a prostate-specific membrane antigen (PSMA) positron emission tomography (PET)Zcomputed tomography (CT) scan obtained from a test subject to produce a segmented test subject tumor; and,82.characterizing whether the segmented test subject tumor is a tumor subtype 1 (S1) associated with PSMA-RADS-1 / 2 / 3, indicating that S1 has a low probability of being prostate cancer, a tumor subtype 2 (S2) associated with PSMA-RADS-4, indicating that S2 has an intermediate probability of being prostate cancer, or a tumor subtype 3 (S3) associated with PSMA-RADS-5, indicating that S3 has a high probability of being prostate cancer to produce a characterized tumor in the test subject.

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