Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models.

Mathematical modelling applied to preclinical, clinical, and public health research is critical for our understanding of a multitude of biological principles. Biology is fundamentally heterogeneous, and mathematical modelling must meet the challenge of variability head on to ensure the principles of diversity, equity, and inclusion (DEI) are integrated into quantitative analyses. Here we provide a follow-up perspective on the DEI plenary session held at the 2023 Society for Mathematical Biology Annual Meeting to discuss key issues for the increased integration of DEI in mathematical modelling in biology.

Sex-specific impact of patterns of imageable tumor growth on survival of primary glioblastoma patients.

BACKGROUND: Sex is recognized as a significant determinant of outcome among glioblastoma patients, but the relative prognostic importance of glioblastoma features has not been thoroughly explored for sex differences. METHODS: Combining multi-modal MR images, biomathematical models, and patient clinical information, this investigation assesses which pretreatment variables have a sex-specific impact on the survival of glioblastoma patients (299 males and 195 females). RESULTS: Among males, tumor (T1Gd) radius was a predictor of overall survival (HR = 1.027, p = 0.044). Among females, higher tumor cell net invasion rate was a significant detriment to overall survival (HR = 1.011, p < 0.001). Female extreme survivors had significantly smaller tumors (T1Gd) (p = 0.010 t-test), but tumor size was not correlated with female overall survival (p = 0.955 CPH). Both male and female extreme survivors had significantly lower tumor cell net proliferation rates than other patients (M p = 0.004, F p = 0.001, t-test). CONCLUSION: Despite similar distributions of the MR imaging parameters between males and females, there was a sex-specific difference in how these parameters related to outcomes.

Speed Switch in Glioblastoma Growth Rate due to Enhanced Hypoxia-Induced Migration.

We analyze the wave speed of the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model that was previously created and applied to simulate the growth and spread of glioblastoma (GBM), a particularly aggressive primary brain tumor. We extend the PIHNA model by allowing for different hypoxic and normoxic cell migration rates and study the impact of these differences on the wave-speed dynamics. Through this analysis, we find key variables that drive the outward growth of the simulated GBM. We find a minimum tumor wave-speed for the model; this depends on the migration and proliferation rates of the normoxic cells and is achieved under certain conditions on the migration rates of the normoxic and hypoxic cells. If the hypoxic cell migration rate is greater than the normoxic cell migration rate above a threshold, the wave speed increases above the predicted minimum. This increase in wave speed is explored through an eigenvalue and eigenvector analysis of the linearized PIHNA model, which yields an expression for this threshold. The PIHNA model suggests that an inherently faster-diffusing hypoxic cell population can drive the outward growth of a GBM as a whole, and that this effect is more prominent for faster-proliferating tumors that recover relatively slowly from a hypoxic phenotype. The findings presented here act as a first step in enabling patient-specific calibration of the PIHNA model.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma.

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.

Learning Equations from Biological Data with Limited Time Samples.

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.

Fractal-Based Morphometrics of Glioblastoma.

Morphometrics have been able to distinguish important features of glioblastoma from magnetic resonance imaging (MRI). Using morphometrics computed on segmentations of various imaging abnormalities, we show that the average and range of lacunarity and fractal dimension values across MRI slices can be prognostic for survival. We look at the repeatability of these metrics to multiple segmentations and how they are impacted by image resolution. We speak to the challenges to overcome before these metrics are included in clinical care, and the insight that they may provide.

Androgen loss weakens anti-tumor immunity and accelerates brain tumor growth.

Many cancers, including glioblastoma (GBM), have a male-biased sex difference in incidence and outcome. The underlying reasons for this sex bias are unclear but likely involve differences in tumor cell state and immune response. This effect is further amplified by sex hormones, including androgens, which have been shown to inhibit anti-tumor T cell immunity. Here, we show that androgens drive anti-tumor immunity in brain tumors, in contrast to its effect in other tumor types. Upon castration, tumor growth was accelerated with attenuated T cell function in GBM and brain tumor models, but the opposite was observed when tumors were located outside the brain. Activity of the hypothalamus-pituitary-adrenal gland (HPA) axis was increased in castrated mice, particularly in those with brain tumors. Blockade of glucocorticoid receptors reversed the accelerated tumor growth in castrated mice, indicating that the effect of castration was mediated by elevated glucocorticoid signaling. Furthermore, this mechanism was not GBM specific, but brain specific, as hyperactivation of the HPA axis was observed with intracranial implantation of non-GBM tumors in the brain. Together, our findings establish that brain tumors drive distinct endocrine-mediated mechanisms in the androgen-deprived setting and highlight the importance of organ-specific effects on anti-tumor immunity.

Quantifying intra-tumoral genetic heterogeneity of glioblastoma toward precision medicine using MRI and a data-inclusive machine learning algorithm.

BACKGROUND AND OBJECTIVE: Glioblastoma (GBM) is one of the most aggressive and lethal human cancers. Intra-tumoral genetic heterogeneity poses a significant challenge for treatment. Biopsy is invasive, which motivates the development of non-invasive, MRI-based machine learning (ML) models to quantify intra-tumoral genetic heterogeneity for each patient. This capability holds great promise for enabling better therapeutic selection to improve patient outcome. METHODS: We proposed a novel Weakly Supervised Ordinal Support Vector Machine (WSO-SVM) to predict regional genetic alteration status within each GBM tumor using MRI. WSO-SVM was applied to a unique dataset of 318 image-localized biopsies with spatially matched multiparametric MRI from 74 GBM patients. The model was trained to predict the regional genetic alteration of three GBM driver genes (EGFR, PDGFRA and PTEN) based on features extracted from the corresponding region of five MRI contrast images. For comparison, a variety of existing ML algorithms were also applied. Classification accuracy of each gene were compared between the different algorithms. The SHapley Additive exPlanations (SHAP) method was further applied to compute contribution scores of different contrast images. Finally, the trained WSO-SVM was used to generate prediction maps within the tumoral area of each patient to help visualize the intra-tumoral genetic heterogeneity. RESULTS: WSO-SVM achieved 0.80 accuracy, 0.79 sensitivity, and 0.81 specificity for classifying EGFR; 0.71 accuracy, 0.70 sensitivity, and 0.72 specificity for classifying PDGFRA; 0.80 accuracy, 0.78 sensitivity, and 0.83 specificity for classifying PTEN; these results significantly outperformed the existing ML algorithms. Using SHAP, we found that the relative contributions of the five contrast images differ between genes, which are consistent with findings in the literature. The prediction maps revealed extensive intra-tumoral region-to-region heterogeneity within each individual tumor in terms of the alteration status of the three genes. CONCLUSIONS: This study demonstrated the feasibility of using MRI and WSO-SVM to enable non-invasive prediction of intra-tumoral regional genetic alteration for each GBM patient, which can inform future adaptive therapies for individualized oncology.

An image-based modeling framework for predicting spatiotemporal brain cancer biology within individual patients.

Imaging is central to the clinical surveillance of brain tumors yet it provides limited insight into a tumor's underlying biology. Machine learning and other mathematical modeling approaches can leverage paired magnetic resonance images and image-localized tissue samples to predict almost any characteristic of a tumor. Image-based modeling takes advantage of the spatial resolution of routine clinical scans and can be applied to measure biological differences within a tumor, changes over time, as well as the variance between patients. This approach is non-invasive and circumvents the intrinsic challenges of inter- and intratumoral heterogeneity that have historically hindered the complete assessment of tumor biology and treatment responsiveness. It can also reveal tumor characteristics that may guide both surgical and medical decision-making in real-time. Here we describe a general framework for the acquisition of image-localized biopsies and the construction of spatiotemporal radiomics models, as well as case examples of how this approach may be used to address clinically relevant questions.

Towards Longitudinal Glioma Segmentation: Evaluating combined pre- and post-treatment MRI training data for automated tumor segmentation using nnU-Net.

Identification of key phenotypic regions such as necrosis, contrast enhancement, and edema on magnetic resonance imaging (MRI) is important for understanding disease evolution and treatment response in patients with glioma. Manual delineation is time intensive and not feasible for a clinical workflow. Automating phenotypic region segmentation overcomes many issues with manual segmentation, however, current glioma segmentation datasets focus on pre-treatment, diagnostic scans, where treatment effects and surgical cavities are not present. Thus, existing automatic segmentation models are not applicable to post-treatment imaging that is used for longitudinal evaluation of care. Here, we present a comparison of three-dimensional convolutional neural networks (nnU-Net architecture) trained on large temporally defined pre-treatment, post-treatment, and mixed cohorts. We used a total of 1563 imaging timepoints from 854 patients curated from 13 different institutions as well as diverse public data sets to understand the capabilities and limitations of automatic segmentation on glioma images with different phenotypic and treatment appearance. We assessed the performance of models using Dice coefficients on test cases from each group comparing predictions with manual segmentations generated by trained technicians. We demonstrate that training a combined model can be as effective as models trained on just one temporal group. The results highlight the importance of a diverse training set, that includes images from the course of disease and with effects from treatment, in the creation of a model that can accurately segment glioma MRIs at multiple treatment time points.

Image-based models of T-cell distribution identify a clinically meaningful response to a dendritic cell vaccine in patients with glioblastoma.

BACKGROUND: Glioblastoma is an extraordinarily heterogeneous tumor, yet the current treatment paradigm is a "one size fits all" approach. Hundreds of glioblastoma clinical trials have been deemed failures because they did not extend median survival, but these cohorts are comprised of patients with diverse tumors. Current methods of assessing treatment efficacy fail to fully account for this heterogeneity. METHODS: Using an image-based modeling approach, we predicted T-cell abundance from serial MRIs of patients enrolled in the dendritic cell (DC) vaccine clinical trial. T-cell predictions were quantified in both the contrast-enhancing and non-enhancing regions of the imageable tumor, and changes over time were assessed. RESULTS: A subset of patients in a DC vaccine clinical trial, who had previously gone undetected, were identified as treatment responsive and benefited from prolonged survival. A mere two months after initial vaccine administration, responsive patients had a decrease in model-predicted T-cells within the contrast-enhancing region, with a simultaneous increase in the T2/FLAIR region. CONCLUSIONS: In a field that has yet to see breakthrough therapies, these results highlight the value of machine learning in enhancing clinical trial assessment, improving our ability to prospectively prognosticate patient outcomes, and advancing the pursuit towards individualized medicine.

Integrated molecular and multiparametric MRI mapping of high-grade glioma identifies regional biologic signatures.

Sampling restrictions have hindered the comprehensive study of invasive non-enhancing (NE) high-grade glioma (HGG) cell populations driving tumor progression. Here, we present an integrated multi-omic analysis of spatially matched molecular and multi-parametric magnetic resonance imaging (MRI) profiling across 313 multi-regional tumor biopsies, including 111 from the NE, across 68 HGG patients. Whole exome and RNA sequencing uncover unique genomic alterations to unresectable invasive NE tumor, including subclonal events, which inform genomic models predictive of geographic evolution. Infiltrative NE tumor is alternatively enriched with tumor cells exhibiting neuronal or glycolytic/plurimetabolic cellular states, two principal transcriptomic pathway-based glioma subtypes, which respectively demonstrate abundant private mutations or enrichment in immune cell signatures. These NE phenotypes are non-invasively identified through normalized K2 imaging signatures, which discern cell size heterogeneity on dynamic susceptibility contrast (DSC)-MRI. NE tumor populations predicted to display increased cellular proliferation by mean diffusivity (MD) MRI metrics are uniquely associated with EGFR amplification and CDKN2A homozygous deletion. The biophysical mapping of infiltrative HGG potentially enables the clinical recognition of tumor subpopulations with aggressive molecular signatures driving tumor progression, thereby informing precision medicine targeting.

Image-localized biopsy mapping of brain tumor heterogeneity: A single-center study protocol.

Brain cancers pose a novel set of difficulties due to the limited accessibility of human brain tumor tissue. For this reason, clinical decision-making relies heavily on MR imaging interpretation, yet the mapping between MRI features and underlying biology remains ambiguous. Standard (clinical) tissue sampling fails to capture the full heterogeneity of the disease. Biopsies are required to obtain a pathological diagnosis and are predominantly taken from the tumor core, which often has different traits to the surrounding invasive tumor that typically leads to recurrent disease. One approach to solving this issue is to characterize the spatial heterogeneity of molecular, genetic, and cellular features of glioma through the intraoperative collection of multiple image-localized biopsy samples paired with multi-parametric MRIs. We have adopted this approach and are currently actively enrolling patients for our 'Image-Based Mapping of Brain Tumors' study. Patients are eligible for this research study (IRB #16-002424) if they are 18 years or older and undergoing surgical intervention for a brain lesion. Once identified, candidate patients receive dynamic susceptibility contrast (DSC) perfusion MRI and diffusion tensor imaging (DTI), in addition to standard sequences (T1, T1Gd, T2, T2-FLAIR) at their presurgical scan. During surgery, sample anatomical locations are tracked using neuronavigation. The collected specimens from this research study are used to capture the intra-tumoral heterogeneity across brain tumors including quantification of genetic aberrations through whole-exome and RNA sequencing as well as other tissue analysis techniques. To date, these data (made available through a public portal) have been used to generate, test, and validate predictive regional maps of the spatial distribution of tumor cell density and/or treatment-related key genetic marker status to identify biopsy and/or treatment targets based on insight from the entire tumor makeup. This type of methodology, when delivered within clinically feasible time frames, has the potential to further inform medical decision-making by improving surgical intervention, radiation, and targeted drug therapy for patients with glioma.

Weakly Supervised Skull Stripping of Magnetic Resonance Imaging of Brain Tumor Patients.

Automatic brain tumor segmentation is particularly challenging on magnetic resonance imaging (MRI) with marked pathologies, such as brain tumors, which usually cause large displacement, abnormal appearance, and deformation of brain tissue. Despite an abundance of previous literature on learning-based methodologies for MRI segmentation, few works have focused on tackling MRI skull stripping of brain tumor patient data. This gap in literature can be associated with the lack of publicly available data (due to concerns about patient identification) and the labor-intensive nature of generating ground truth labels for model training. In this retrospective study, we assessed the performance of Dense-Vnet in skull stripping brain tumor patient MRI trained on our large multi-institutional brain tumor patient dataset. Our data included pretreatment MRI of 668 patients from our in-house institutional review board-approved multi-institutional brain tumor repository. Because of the absence of ground truth, we used imperfect automatically generated training labels using SPM12 software. We trained the network using common MRI sequences in oncology: T1-weighted with gadolinium contrast, T2-weighted fluid-attenuated inversion recovery, or both. We measured model performance against 30 independent brain tumor test cases with available manual brain masks. All images were harmonized for voxel spacing and volumetric dimensions before model training. Model training was performed using the modularly structured deep learning platform NiftyNet that is tailored toward simplifying medical image analysis. Our proposed approach showed the success of a weakly supervised deep learning approach in MRI brain extraction even in the presence of pathology. Our best model achieved an average Dice score, sensitivity, and specificity of, respectively, 94.5, 96.4, and 98.5% on the multi-institutional independent brain tumor test set. To further contextualize our results within existing literature on healthy brain segmentation, we tested the model against healthy subjects from the benchmark LBPA40 dataset. For this dataset, the model achieved an average Dice score, sensitivity, and specificity of 96.2, 96.6, and 99.2%, which are, although comparable to other publications, slightly lower than the performance of models trained on healthy patients. We associate this drop in performance with the use of brain tumor data for model training and its influence on brain appearance.

Shape matters: morphological metrics of glioblastoma imaging abnormalities as biomarkers of prognosis.

Lacunarity, a quantitative morphological measure of how shapes fill space, and fractal dimension, a morphological measure of the complexity of pixel arrangement, have shown relationships with outcome across a variety of cancers. However, the application of these metrics to glioblastoma (GBM), a very aggressive primary brain tumor, has not been fully explored. In this project, we computed lacunarity and fractal dimension values for GBM-induced abnormalities on clinically standard magnetic resonance imaging (MRI). In our patient cohort (n = 402), we connect these morphological metrics calculated on pretreatment MRI with the survival of patients with GBM. We calculated lacunarity and fractal dimension on necrotic regions (n = 390), all abnormalities present on T1Gd MRI (n = 402), and abnormalities present on T2/FLAIR MRI (n = 257). We also explored the relationship between these metrics and age at diagnosis, as well as abnormality volume. We found statistically significant relationships to outcome for all three imaging regions that we tested, with the shape of T2/FLAIR abnormalities that are typically associated with edema showing the strongest relationship with overall survival. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location or microenvironmental factors that should be further explored.

Assessment of Prognostic Value of Cystic Features in Glioblastoma Relative to Sex and Treatment With Standard-of-Care.

Glioblastoma (GBM) is the most aggressive primary brain tumor and can have cystic components, identifiable through magnetic resonance imaging (MRI). Previous studies suggest that cysts occur in 7-23% of GBMs and report mixed results regarding their prognostic impact. Using our retrospective cohort of 493 patients with first-diagnosis GBM, we carried out an exploratory analysis on this potential link between cystic GBM and survival. Using pretreatment MRIs, we manually identified 88 patients with GBM that had a significant cystic component at presentation and 405 patients that did not. Patients with cystic GBM had significantly longer overall survival and were significantly younger at presentation. Within patients who received the current standard of care (SOC) (N = 184, 40 cystic), we did not observe a survival benefit of cystic GBM. Unexpectedly, we did not observe a significant survival benefit between this SOC cystic cohort and patients with cystic GBM diagnosed before the standard was established (N = 40 with SOC, N = 19 without SOC); this significant SOC benefit was clearly observed in patients with noncystic GBM (N = 144 with SOC, N = 111 without SOC). When stratified by sex, the survival benefit of cystic GBM was only preserved in male patients (N = 303, 47 cystic). We report differences in the absolute and relative sizes of imaging abnormalities on MRI and the prognostic implication of cysts based on sex. We discuss hypotheses for these differences, including the possibility that the presence of a cyst could indicate a less aggressive tumor.

Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations.

Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute to disappointing clinical trial results. Image-localized biopsy techniques allow multiple biopsies to be taken during surgery and provide information that identifies regions where particular sub-populations occur within an individual GBM, thus providing insight into their regional genetic variability. These sub-populations may also interact with one another in a competitive or cooperative manner; it is important to ascertain the nature of these interactions, as they may have implications for responses to targeted therapies. We combine genetic information from biopsies with a mechanistic model of interacting GBM sub-populations to characterise the nature of interactions between two commonly occurring GBM sub-populations, those with EGFR and PDGFRA genes amplified. We study population levels found across image-localized biopsy data from a cohort of 25 patients and compare this to model outputs under competitive, cooperative and neutral interaction assumptions. We explore other factors affecting the observed simulated sub-populations, such as selection advantages and phylogenetic ordering of mutations, which may also contribute to the levels of EGFR and PDGFRA amplified populations observed in biopsy data.