Patient-Specific, Mechanistic Models of Tumor Growth Incorporating Artificial Intelligence and Big Data.

Despite the remarkable advances in cancer diagnosis, treatment, and management over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires the integration of patient-specific information with an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous yet practical mathematical theory of tumor initiation, development, invasion, and response to therapy. We begin this review with an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on big data and artificial intelligence. We then present illustrative examples of mathematical models manifesting their utility and discuss the limitations of stand-alone mechanistic and data-driven models. We then discuss the potential of mechanistic models for not only predicting but also optimizing response to therapy on a patient-specific basis. We describe current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models.

The ISMRM Open Science Initiative for Perfusion Imaging (OSIPI): Results from the OSIPI-Dynamic Contrast-Enhanced challenge.

PURPOSE: K trans $$ {K}^{\mathrm{trans}} $$ has often been proposed as a quantitative imaging biomarker for diagnosis, prognosis, and treatment response assessment for various tumors. None of the many software tools for K trans $$ {K}^{\mathrm{trans}} $$ quantification are standardized. The ISMRM Open Science Initiative for Perfusion Imaging-Dynamic Contrast-Enhanced (OSIPI-DCE) challenge was designed to benchmark methods to better help the efforts to standardize K trans $$ {K}^{\mathrm{trans}} $$ measurement. METHODS: A framework was created to evaluate K trans $$ {K}^{\mathrm{trans}} $$ values produced by DCE-MRI analysis pipelines to enable benchmarking. The perfusion MRI community was invited to apply their pipelines for K trans $$ {K}^{\mathrm{trans}} $$ quantification in glioblastoma from clinical and synthetic patients. Submissions were required to include the entrants' K trans $$ {K}^{\mathrm{trans}} $$ values, the applied software, and a standard operating procedure. These were evaluated using the proposed OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score defined with accuracy, repeatability, and reproducibility components. RESULTS: Across the 10 received submissions, the OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score ranged from 28% to 78% with a 59% median. The accuracy, repeatability, and reproducibility scores ranged from 0.54 to 0.92, 0.64 to 0.86, and 0.65 to 1.00, respectively (0-1 = lowest-highest). Manual arterial input function selection markedly affected the reproducibility and showed greater variability in K trans $$ {K}^{\mathrm{trans}} $$ analysis than automated methods. Furthermore, provision of a detailed standard operating procedure was critical for higher reproducibility. CONCLUSIONS: This study reports results from the OSIPI-DCE challenge and highlights the high inter-software variability within K trans $$ {K}^{\mathrm{trans}} $$ estimation, providing a framework for ongoing benchmarking against the scores presented. Through this challenge, the participating teams were ranked based on the performance of their software tools in the particular setting of this challenge. In a real-world clinical setting, many of these tools may perform differently with different benchmarking methodology.

Multi-Site Concordance of Diffusion-Weighted Imaging Quantification for Assessing Prostate Cancer Aggressiveness.

BACKGROUND: Diffusion-weighted imaging (DWI) is commonly used to detect prostate cancer, and a major clinical challenge is differentiating aggressive from indolent disease. PURPOSE: To compare 14 site-specific parametric fitting implementations applied to the same dataset of whole-mount pathologically validated DWI to test the hypothesis that cancer differentiation varies with different fitting algorithms. STUDY TYPE: Prospective. POPULATION: Thirty-three patients prospectively imaged prior to prostatectomy. FIELD STRENGTH/SEQUENCE: 3 T, field-of-view optimized and constrained undistorted single-shot DWI sequence. ASSESSMENT: Datasets, including a noise-free digital reference object (DRO), were distributed to the 14 teams, where locally implemented DWI parameter maps were calculated, including mono-exponential apparent diffusion coefficient (MEADC), kurtosis (K), diffusion kurtosis (DK), bi-exponential diffusion (BID), pseudo-diffusion (BID*), and perfusion fraction (F). The resulting parametric maps were centrally analyzed, where differentiation of benign from cancerous tissue was compared between DWI parameters and the fitting algorithms with a receiver operating characteristic area under the curve (ROC AUC). STATISTICAL TEST: Levene's test, P < 0.05 corrected for multiple comparisons was considered statistically significant. RESULTS: The DRO results indicated minimal discordance between sites. Comparison across sites indicated that K, DK, and MEADC had significantly higher prostate cancer detection capability (AUC range = 0.72-0.76, 0.76-0.81, and 0.76-0.80 respectively) as compared to bi-exponential parameters (BID, BID*, F) which had lower AUC and greater between site variation (AUC range = 0.53-0.80, 0.51-0.81, and 0.52-0.80 respectively). Post-processing parameters also affected the resulting AUC, moving from, for example, 0.75 to 0.87 for MEADC varying cluster size. DATA CONCLUSION: We found that conventional diffusion models had consistent performance at differentiating prostate cancer from benign tissue. Our results also indicated that post-processing decisions on DWI data can affect sensitivity and specificity when applied to radiological-pathological studies in prostate cancer. LEVEL OF EVIDENCE: 1 TECHNICAL EFFICACY: Stage 3.

Quantitative analysis of vascular properties derived from ultrafast DCE-MRI to discriminate malignant and benign breast tumors.

PURPOSE: We propose a novel methodology to integrate morphological and functional information of tumor-associated vessels to assist in the diagnosis of suspicious breast lesions. THEORY AND METHODS: Ultrafast, fast, and high spatial resolution DCE-MRI data were acquired on 15 patients with suspicious breast lesions. Segmentation of the vasculature from the surrounding tissue was performed by applying a Hessian filter to the enhanced image to generate a map of the probability for each voxel to belong to a vessel. Summary measures were generated for vascular morphology, as well as the inputs and outputs of vessels physically connected to the tumor. The ultrafast DCE-MRI data was analyzed by a modified Tofts model to estimate the bolus arrival time, Ktrans (volume transfer coefficient), and vp (plasma volume fraction). The measures were compared between malignant and benign lesions via the Wilcoxon test, and then incorporated into a logistic ridge regression model to assess their combined diagnostic ability. RESULTS: A total of 24 lesions were included in the study (13 malignant and 11 benign). The vessel count, Ktrans , and vp showed significant difference between malignant and benign lesions (P = 0.009, 0.034, and 0.010, area under curve [AUC] = 0.76, 0.63, and 0.70, respectively). The best multivariate logistic regression model for differentiation included the vessel count and bolus arrival time (AUC = 0.91). CONCLUSION: This study provides preliminary evidence that combining quantitative characterization of morphological and functional features of breast vasculature may provide an accurate means to diagnose breast cancer.

The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Translating preclinical MRI methods to clinical oncology.

The complexity of modern in vivo magnetic resonance imaging (MRI) methods in oncology has dramatically changed in the last 10 years. The field has long since moved passed its (unparalleled) ability to form images with exquisite soft-tissue contrast and morphology, allowing for the enhanced identification of primary tumors and metastatic disease. Currently, it is not uncommon to acquire images related to blood flow, cellularity, and macromolecular content in the clinical setting. The acquisition of images related to metabolism, hypoxia, pH, and tissue stiffness are also becoming common. All of these techniques have had some component of their invention, development, refinement, validation, and initial applications in the preclinical setting using in vivo animal models of cancer. In this review, we discuss the genesis of quantitative MRI methods that have been successfully translated from preclinical research and developed into clinical applications. These include methods that interrogate perfusion, diffusion, pH, hypoxia, macromolecular content, and tissue mechanical properties for improving detection, staging, and response monitoring of cancer. For each of these techniques, we summarize the 1) underlying biological mechanism(s); 2) preclinical applications; 3) available repeatability and reproducibility data; 4) clinical applications; and 5) limitations of the technique. We conclude with a discussion of lessons learned from translating MRI methods from the preclinical to clinical setting, and a presentation of four fundamental problems in cancer imaging that, if solved, would result in a profound improvement in the lives of oncology patients. Level of Evidence: 5 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2019;50:1377-1392.

The effects of intravoxel contrast agent diffusion on the analysis of DCE-MRI data in realistic tissue domains.

PURPOSE: Quantitative evaluation of dynamic contrast enhanced MRI (DCE-MRI) allows for estimating perfusion, vessel permeability, and tissue volume fractions by fitting signal intensity curves to pharmacokinetic models. These compart mental models assume rapid equilibration of contrast agent within each voxel. However, there is increasing evidence that this assumption is violated for small molecular weight gadolinium chelates. To evaluate the error introduced by this invalid assumption, we simulated DCE-MRI experiments with volume fractions computed from entire histological tumor cross-sections obtained from murine studies. METHODS: A 2D finite element model of a diffusion-compensated Tofts-Kety model was developed to simulate dynamic T1 signal intensity data. Digitized histology slices were segmented into vascular (vp ), cellular and extravascular extracellular (ve ) volume fractions. Within this domain, Ktrans (the volume transfer constant) was assigned values from 0 to 0.5 min-1 . A representative signal enhancement curve was then calculated for each imaging voxel and the resulting simulated DCE-MRI data analyzed by the extended Tofts-Kety model. RESULTS: Results indicated parameterization errors of -19.1% ± 10.6% in Ktrans , -4.92% ± 3.86% in ve , and 79.5% ± 16.8% in vp for use of Gd-DTPA over 4 tumor domains. CONCLUSION: These results indicate a need for revising the standard model of DCE-MRI to incorporate a correction for slow diffusion of contrast agent. Magn Reson Med 80:330-340, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data.

Reaction-diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction-diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor 'grown' for ten days as dictated by the reaction-diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model's accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction-diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions.

Impact of donor age on survival after heart transplantation: an analysis of the United Network for Organ Sharing (UNOS) registry.

BACKGROUND: Data are limited regarding the influence of donor age on outcomes after heart transplantation. We sought to determine if advanced donor age is associated with differences in survival after heart transplantation and how this compares to waitlist survival. METHODS: All adult heart transplants from 2000 to 2012 were identified using the United Network for Organ Sharing database. Donors were stratified into four age groups: 18-39 (reference group), 40-49, 50-54, and 55 and above. Propensity scoring was used to compare status IA waitlist patients who did not undergo transplantation with IA recipients who received hearts from advanced age donors. The primary outcome of interest was recipient survival and this was analyzed with multivariate Cox regression analysis and the Kaplan-Meier method. RESULTS: A total of 22,960 adult heart transplant recipients were identified. Recipients of hearts from all three older donor groups had significantly increased risk of mortality (HR, 1.187-1.426, all p < 0.001) compared to recipients from donors age 18 to 39. Additionally, propensity-matched status IA patients managed medically without transplantation had significantly worse adjusted survival than status IA recipients who received hearts from older donors age ≥55 (HR, 1.362, p < 0.001). CONCLUSIONS: Compared to donors aged 18-39, age 40 and above is associated with worse adjusted recipient survival in heart transplantation. This survival difference becomes more pronounced as age increases to above 55. However, the survival rate among status IA patients who receive hearts from advanced age donors (≥55) is significantly better compared to similar status IA patients who are managed without transplantation.

Systematic evaluation of MRI-based characterization of tumor-associated vascular morphology and hemodynamics via a dynamic digital phantom.

Purpose: Validation of quantitative imaging biomarkers is a challenging task, due to the difficulty in measuring the ground truth of the target biological process. A digital phantom-based framework is established to systematically validate the quantitative characterization of tumor-associated vascular morphology and hemodynamics based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Approach: A digital phantom is employed to provide a ground-truth vascular system within which 45 synthetic tumors are simulated. Morphological analysis is performed on high-spatial resolution DCE-MRI data (spatial/temporal resolution = 30 to 300 µm/60 s) to determine the accuracy of locating the arterial inputs of tumor-associated vessels (TAVs). Hemodynamic analysis is then performed on the combination of high-spatial resolution and high-temporal resolution (spatial/temporal resolution = 60 to 300 µm/1 to 10 s) DCE-MRI data, determining the accuracy of estimating tumor-associated blood pressure, vascular extraction rate, interstitial pressure, and interstitial flow velocity. Results: The observed effects of acquisition settings demonstrate that, when optimizing the DCE-MRI protocol for the morphological analysis, increasing the spatial resolution is helpful but not necessary, as the location and arterial input of TAVs can be recovered with high accuracy even with the lowest investigated spatial resolution. When optimizing the DCE-MRI protocol for hemodynamic analysis, increasing the spatial resolution of the images used for vessel segmentation is essential, and the spatial and temporal resolutions of the images used for the kinetic parameter fitting require simultaneous optimization. Conclusion: An in silico validation framework was generated to systematically quantify the effects of image acquisition settings on the ability to accurately estimate tumor-associated characteristics.

A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin.

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.

Designing clinical trials for patients who are not average.

The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.

Image-guided patient-specific optimization of catheter placement for convection-enhanced nanoparticle delivery in recurrent glioblastoma.

BACKGROUND: Proper catheter placement for convection-enhanced delivery (CED) is required to maximize tumor coverage and minimize exposure to healthy tissue. We developed an image-based model to patient-specifically optimize the catheter placement for rhenium-186 (186Re)-nanoliposomes (RNL) delivery to treat recurrent glioblastoma (rGBM). METHODS: The model consists of the 1) fluid fields generated via catheter infusion, 2) dynamic transport of RNL, and 3) transforming RNL concentration to the SPECT signal. Patient-specific tissue geometries were assigned from pre-delivery MRIs. Model parameters were personalized with either 1) individual-based calibration with longitudinal SPECT images, or 2) population-based assignment via leave-one-out cross-validation. The concordance correlation coefficient (CCC) was used to quantify the agreement between the predicted and measured SPECT signals. The model was then used to simulate RNL distributions from a range of catheter placements, resulting in a ratio of the cumulative RNL dose outside versus inside the tumor, the "off-target ratio" (OTR). Optimal catheter placement) was identified by minimizing OTR. RESULTS: Fifteen patients with rGBM from a Phase I/II clinical trial (NCT01906385) were recruited to the study. Our model, with either individual-calibrated or population-assigned parameters, achieved high accuracy (CCC > 0.80) for predicting RNL distributions up to 24 h after delivery. The optimal catheter placements identified using this model achieved a median (range) of 34.56 % (14.70 %-61.12 %) reduction on OTR at the 24 h post-delivery in comparison to the original placements. CONCLUSIONS: Our image-guided model achieved high accuracy for predicting patient-specific RNL distributions and indicates value for optimizing catheter placement for CED of radiolabeled liposomes.

Comparing mechanism-based and machine learning models for predicting the effects of glucose accessibility on tumor cell proliferation.

Glucose plays a central role in tumor metabolism and development and is a target for novel therapeutics. To characterize the response of cancer cells to blockade of glucose uptake, we collected time-resolved microscopy data to track the growth of MDA-MB-231 breast cancer cells. We then developed a mechanism-based, mathematical model to predict how a glucose transporter (GLUT1) inhibitor (Cytochalasin B) influences the growth of the MDA-MB-231 cells by limiting access to glucose. The model includes a parameter describing dose dependent inhibition to quantify both the total glucose level in the system and the glucose level accessible to the tumor cells. Four common machine learning models were also used to predict tumor cell growth. Both the mechanism-based and machine learning models were trained and validated, and the prediction error was evaluated by the coefficient of determination (R2). The random forest model provided the highest accuracy predicting cell dynamics (R2 = 0.92), followed by the decision tree (R2 = 0.89), k-nearest-neighbor regression (R2 = 0.84), mechanism-based (R2 = 0.77), and linear regression model (R2 = 0.69). Thus, the mechanism-based model has a predictive capability comparable to machine learning models with the added benefit of elucidating biological mechanisms.

PhysiCOOL: A generalized framework for model Calibration and Optimization Of modeLing projects.

In silico models of biological systems are usually very complex and rely on a large number of parameters describing physical and biological properties that require validation. As such, parameter space exploration is an essential component of computational model development to fully characterize and validate simulation results. Experimental data may also be used to constrain parameter space (or enable model calibration) to enhance the biological relevance of model parameters. One widely used computational platform in the mathematical biology community is PhysiCell, which provides a standardized approach to agent-based models of biological phenomena at different time and spatial scales. Nonetheless, one limitation of PhysiCell is the lack of a generalized approach for parameter space exploration and calibration that can be run without high-performance computing access. Here, we present PhysiCOOL, an open-source Python library tailored to create standardized calibration and optimization routines for PhysiCell models.

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth.

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

Predicting the spatio-temporal response of recurrent glioblastoma treated with rhenium-186 labelled nanoliposomes.

Rhenium-186 (186Re) labeled nanoliposome (RNL) therapy for recurrent glioblastoma patients has shown promise to improve outcomes by locally delivering radiation to affected areas. To optimize the delivery of RNL, we have developed a framework to predict patient-specific response to RNL using image-guided mathematical models. Methods: We calibrated a family of reaction-diffusion type models with multi-modality imaging data from ten patients (NCR01906385) to predict the spatio-temporal dynamics of each patient's tumor. The data consisted of longitudinal magnetic resonance imaging (MRI) and single photon emission computed tomography (SPECT) to estimate tumor burden and local RNL activity, respectively. The optimal model from the family was selected and used to predict future growth. A simplified version of the model was used in a leave-one-out analysis to predict the development of an individual patient's tumor, based on cohort parameters. Results: Across the cohort, predictions using patient-specific parameters with the selected model were able to achieve Spearman correlation coefficients (SCC) of 0.98 and 0.93 for tumor volume and total cell number, respectively, when compared to the measured data. Predictions utilizing the leave-one-out method achieved SCCs of 0.89 and 0.88 for volume and total cell number across the population, respectively. Conclusion: We have shown that patient-specific calibrations of a biology-based mathematical model can be used to make early predictions of response to RNL therapy. Furthermore, the leave-one-out framework indicates that radiation doses determined by SPECT can be used to assign model parameters to make predictions directly following the conclusion of RNL treatment. Statement of Significance: This manuscript explores the application of computational models to predict response to radionuclide therapy in glioblastoma. There are few, to our knowledge, examples of mathematical models used in clinical radionuclide therapy. We have tested a family of models to determine the applicability of different radiation coupling terms for response to the localized radiation delivery. We show that with patient-specific parameter estimation, we can make accurate predictions of future glioblastoma response to the treatment. As a comparison, we have shown that population trends in response can be used to forecast growth from the moment the treatment has been delivered.In addition to the high simulation and prediction accuracy our modeling methods have achieved, the evaluation of a family of models has given insight into the response dynamics of radionuclide therapy. These dynamics, while different than we had initially hypothesized, should encourage future imaging studies involving high dosage radiation treatments, with specific emphasis on the local immune and vascular response.

Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma.

Tumors exhibit high molecular, phenotypic, and physiological heterogeneity. In this effort, we employ quantitative magnetic resonance imaging (MRI) data to capture this heterogeneity through imaging-based subregions or "habitats" in a murine model of glioma. We then demonstrate the ability to model and predict the growth of the habitats using coupled ordinary differential equations (ODEs) in the presence and absence of radiotherapy. Female Wistar rats (N = 21) were inoculated intracranially with 106 C6 glioma cells, a subset of which received 20 Gy (N = 5) or 40 Gy (N = 8) of radiation. All rats underwent diffusion-weighted and dynamic contrast-enhanced MRI at up to seven time points. All MRI data at each visit were subsequently clustered using k-means to identify physiological tumor habitats. A family of four models consisting of three coupled ODEs were developed and calibrated to the habitat time series of control and treated rats and evaluated for predictive capability. The Akaike Information Criterion was used for model selection, and the normalized sum-of-square-error (SSE) was used to evaluate goodness-of-fit in model calibration and prediction. Three tumor habitats with significantly different imaging data characteristics (p < 0.05) were identified: high-vascularity high-cellularity, low-vascularity high-cellularity, and low-vascularity low-cellularity. Model selection resulted in a five-parameter model whose predictions of habitat dynamics yielded SSEs that were similar to the SSEs from the calibrated model. It is thus feasible to mathematically describe habitat dynamics in a preclinical model of glioma using biology-based ODEs, showing promise for forecasting heterogeneous tumor behavior.

Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas.

We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data. The calibrated digital twin is used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.

Toward Practical Integration of Omic and Imaging Data in Co-Clinical Trials.

Co-clinical trials are the concurrent or sequential evaluation of therapeutics in both patients clinically and patient-derived xenografts (PDX) pre-clinically, in a manner designed to match the pharmacokinetics and pharmacodynamics of the agent(s) used. The primary goal is to determine the degree to which PDX cohort responses recapitulate patient cohort responses at the phenotypic and molecular levels, such that pre-clinical and clinical trials can inform one another. A major issue is how to manage, integrate, and analyze the abundance of data generated across both spatial and temporal scales, as well as across species. To address this issue, we are developing MIRACCL (molecular and imaging response analysis of co-clinical trials), a web-based analytical tool. For prototyping, we simulated data for a co-clinical trial in "triple-negative" breast cancer (TNBC) by pairing pre- (T0) and on-treatment (T1) magnetic resonance imaging (MRI) from the I-SPY2 trial, as well as PDX-based T0 and T1 MRI. Baseline (T0) and on-treatment (T1) RNA expression data were also simulated for TNBC and PDX. Image features derived from both datasets were cross-referenced to omic data to evaluate MIRACCL functionality for correlating and displaying MRI-based changes in tumor size, vascularity, and cellularity with changes in mRNA expression as a function of treatment.