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It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called “mass effect”). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained $\boldsymbol{{\it T}_2}$ -weighted and contrast-enhanced $\boldsymbol{{\it T}_1}$ -weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and the volume fraction of tumor cells, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 × 10 $\boldsymbol{^{-3}}$ mm $\boldsymbol{^2\cdot }$ d $\boldsymbol{^{-1}}$ ) is significantly less than those for the RD and RDM models (17.46 × 10 $\boldsymbol{^{-3}}$ mm $\boldsymbol{^2\cdot }$ d $\boldsymbol{^{-1}}$ and 19.38 × 10 $\boldsymbol{^{-3}}$ mm $\boldsymbol{^2\cdot }$ d $\boldsymbol{^{-1}}$ , respectively). The error in the tumor volume fraction for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

This protocol describes a complete data acquisition, analysis and computational forecasting pipeline for employing quantitative MRI data to predict the response of locally advanced breast cancer to neoadjuvant therapy in a community-based care setting. The methodology has previously been successfully applied to a heterogeneous patient population. The protocol details how to acquire the necessary images followed by registration, segmentation, quantitative perfusion and diffusion analysis, model calibration, and prediction. The data collection portion of the protocol requires ~25 min of scanning, postprocessing requires 2–3 h, and the model calibration and prediction components require ~10 h per patient depending on tumor size. The response of individual breast cancer patients to neoadjuvant therapy is forecast by application of a biophysical, reaction–diffusion mathematical model to these data. Successful application of the protocol results in coregistered MRI data from at least two scan visits that quantifies an individual tumor’s size, cellularity and vascular properties. This enables a spatially resolved prediction of how a particular patient’s tumor will respond to therapy. Expertise in image acquisition and analysis, as well as the numerical solution of partial differential equations, is required to carry out this protocol.

Background: This study evaluates the ability to predict the response of locally advanced breast cancers to neoadjuvant therapy (NAT) using patient-specific magnetic resonance imaging (MRI) data and a biophysical mathematical model. The 3D mathematical model consists of three parts: tumor cell proliferation, tumor spread (diffusion), and treatment. In particular, the tumor cells proliferate according to logistic growth, and the diffusion term is coupled to the mechanical properties of the surrounding fibroglandular and adipose tissues to inform individual tumor growth patterns (specific to each patient’s anatomy). The model’s treatment term accounts for tumor cell reduction according to approximate local drug delivery for each patient. Methods: Patients (N = 21) with intermediate to high grade invasive breast cancers with varying receptor status, who were eligible for NAT as a component of their clinical care, were recruited. Each patient was treated with standard-of-care consisting of one or two NAT regimens in sequence followed by surgical resection of any residual tumor. MRI data are acquired at four time points: 1) prior to initiation of NAT, 2) after 1 cycle of NAT, 3) after 2-4 cycles of NAT, and 4) 1 cycle after scan 3. The MRI data is processed and evaluated using our semi-automated pipeline. Specifically, diffusion-weighted MRI data is utilized to characterize the cellularity throughout the tumor tissue, and dynamic contrast-enhanced (DCE-) MRI data is used to segment the breast tissue and analyze the local drug delivery using pharmacokinetic analysis and population-derived plasma curves of drug concentrations. The model’s predictive ability is assessed using three different strategies. First, the model is calibrated using each patient’s first two scans to enable predictions of the total tumor cellularity, volume, and longest axis that are directly compared to the values measured from their third scan. Second, the model’s predictions for tumor response are compared to the corresponding response evaluation criteria in solid tumors (RECIST) results. Third, the model is re-calibrated using scans 3 and 4 and simulated to the time of surgery to compare the model’s predictions to each patient’s response status determined by surgical pathology. Results: Calibrating the model with MRI data for one cycle of therapy yields predictions strongly correlated with tumor response measured from each patient’s third scan, concordance correlation coefficients of 0.91, 0.90, and 0.86 for total cellularity, volume, and longest axis, respectively (p < 0.01, N = 18). The model’s predictions are significantly (p < 0.01) correlated with tumor response as designated by RECIST for the cohort. Specifically, the model predicts greater percent reduction in the longest axis for the RECIST designated responder group (i.e., complete response and partial response) compared to non-responders. At the time of surgery, the model predicts changes in total tumor cellularity from baseline that are significantly (p < 0.01) correlated with pathological response status—an area under the receiver operator characteristic curve of 0.92 and a sensitivity and specificity of 1.0 and 0.74, respectively. Discussion: These preliminary results suggest that this clinical-mathematical approach can be predictive of tumor response very early in the course of NAT on a patient-specific basis. Moreover, the study was performed in the community-care setting across a heterogenous group of patients, indicating the approach may be practical for wide-spread application. NCI U01 CA174706, NCI U01 CA154602, CPRIT RR160005, ACS-RSG-18-006-01-CCE, R01CA240589, NCI-U24CA226110, CPRIT RR160093 Citation Format: Angela M Jarrett, David A. Hormuth, II, Anum K Syed, Chengyue Wu, John Virostko, Anna G Sorace, Julie C DiCarlo, Jeanne Kowalski, Debra Patt, Boone Goodgame, Sarah Avery, Thomas E Yankeelov. Predicting breast cancer response to neoadjuvant therapies using a mathematical model individualized with patient-specific magnetic resonance imaging data: Preliminary Results [abstract]. In: Proceedings of the 2020 San Antonio Breast Cancer Virtual Symposium; 2020 Dec 8-11; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2021;81(4 Suppl):Abstract nr PS13-18.

The ability to accurately predict response and then rigorously optimize a therapeutic regimen on a patient-specific basis, would transform oncology. Toward this end, we have developed an experimental-mathematical framework that integrates quantitative magnetic resonance imaging (MRI) data into a biophysical model to predict patient-specific treatment response of locally advanced breast cancer to neoadjuvant therapy. Diffusion-weighted and dynamic contrast-enhanced MRI data is collected prior to therapy, after 1 cycle of therapy, and at the completion of the first therapeutic regimen. The model is initialized and calibrated with the first 2 patient-specific MRI data sets to predict response at the third, which is then compared to patient outcomes (N = 18). The model's predictions for total cellularity, total volume, and the longest axis at the completion of the regimen are significant within expected measurement precision (P< 0.05) and strongly correlated with measured response (P < 0.01). Further, we use the model to investigate, in silico, a range of (practical) alternative treatment plans to achieve the greatest possible tumor control for each individual in a subgroup of patients (N = 13). The model identifies alternative dosing strategies predicted to achieve greater tumor control compared to the standard of care for 12 of 13 patients (P < 0.01). In summary, a predictive, mechanism-based mathematical model has demonstrated the ability to identify alternative treatment regimens that are forecasted to outperform the therapeutic regimens the patients clinically. This has important implications for clinical trial design with the opportunity to alter oncology care in the future.

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

The overall goal of this study is to employ quantitative magnetic resonance imaging (MRI) data to constrain a patient-specific, computational fluid dynamics (CFD) model of blood flow and interstitial transport in breast cancer. We develop image processing methodologies to generate tumor-related vasculature-interstitium geometry and realistic material properties, using dynamic contrast enhanced MRI (DCE-MRI) and diffusion weighted MRI (DW-MRI) data. These data are used to constrain CFD simulations for determining the tumor-associated blood supply and interstitial transport characteristics unique to each patient. We then perform a proof-of-principle statistical comparison between these hemodynamic characteristics in 11 malignant and 5 benign lesions from 12 patients. Significant differences between groups (i.e., malignant versus benign) were observed for the median of tumor-associated interstitial flow velocity ( ${P} =0.028$ ), and the ranges of tumor-associated blood pressure ( P = 0.016) and vascular extraction rate ( P = 0.040). The implication is that malignant lesions tend to have larger magnitude of interstitial flow velocity, and higher heterogeneity in blood pressure and vascular extraction rate. Multivariable logistic models based on combinations of these hemodynamic data achieved excellent differentiation between malignant and benign lesions with an area under the receiver operator characteristic curve of 1.0, sensitivity of 1.0, and specificity of 1.0. This image-based model system is a fundamentally new way to map flow and pressure fields related to breast tumors using only non-invasive, clinically available imaging data and established laws of fluid mechanics. Furthermore, the results provide preliminary evidence for this methodology’s utility for the quantitative characterization of breast cancer.

Introduction: Tumor forecasting methods for predicting treatment response of individual breast cancer patients to neoadjuvant therapy (NAT) have shown promise in clinical application. Our framework for predicting tumor response integrates quantitative magnetic resonance imaging (MRI) data acquired early in the course of NAT into a mechanism-based, biophysical model that predicts the eventual treatment response of breast tumors. Being able to predict which patient will respond effectively to NAT would have a fundamental and lasting impact on healthcare. However, the ultimate goal is to optimize therapy given the unique characteristics of each patient. Here we show that the detailed combination of advanced image analysis and rigorous mathematical modeling can accurately predict response for the individual patient. Further, we use the model to demonstrate the potential selection of personalized therapeutic regimens. This is accomplished by initializing the mathematical model with patient-specific characteristics and then varying, in silico, a range of treatment plans to achieve the greatest tumor control. Methods: Quantitative MRI was acquired from breast cancer patients (N = 11) at three time points during the course of NAT: 1) prior to NAT, 2) after 1 cycle of their initial chemotherapy, and 3) after the completion of the initial chemotherapy regimen. With these data, we implemented our recently established mechanically coupled, reaction-diffusion model at the tissue scale for predicting breast tumor response to therapy. The 3D model is initialized with patient-specific, diffusion-weighted MRI data characterizing tumor cellularity. Additionally, the model includes a tumor cell reduction term for local drug delivery as estimated from pharmacokinetic analysis of dynamic contrast-enhanced MRI data and population-derived plasma curves of therapeutic concentrations. The model’s predictive ability was assessed using three different measures. Using the first two scans, the model is calibrated and simulated forward to the third scan time to compare the predicted total tumor cellularity, volume, and longest axis to the actual values measured from the patient’s third scan. We then simulate alternate regimens using the same total dose each patient received during their standard regimen, while varying dosages and frequency between their second and third scans. Results: After calibrating the model using the first two imaging time points, the model’s predictions are significantly correlated to the measured tumor burden at scan three with Pearson Correlation Coefficients of 0.93, 0.89, 0.96 (p < 0.01) for total cellularity, total volume, and longest axis, respectively. The model predicts that for the alternative dosing regimens assessed, individual patients could have achieved an additional 0-43% reduction in total cellularity compared to the therapeutic regimens patients actually received. This indicates that standard regimens may not be the most effective for every patient. Discussion and future directions: These results demonstrate that the mathematical model can be predictive of tumor response using data at the earliest times of therapy regimens. The in silico results illustrate how for individual patients (depending on their unique tumor characteristics and vasculature—captured by the calibrated parameters of the model), therapy regimens can be tailored and even optimized (via established optimal control theory methods) to each patient using a mathematical model and simulation studies. The present investigation represents a significant first step towards personalizing patient regimens through quantitative imaging and mathematical modeling. NCI U01 CA174706, NCI U01 CA154602, CPRIT RR160005, ACS-RSG-18-006-01-CCE Citation Format: Angela M Jarrett, David A Hormuth II, Chengyue Wu, John Virostko, Anna G Sorace, Julie C DiCarlo, Debra Patt, Boone Goodgame, Sarah Avery, Thomas E Yankeelov. Optimizing neoadjuvant regimens for individual breast cancer patients generated by a mathematical model utilizing quantitative magnetic resonance imaging data: Preliminary results [abstract]. In: Proceedings of the 2019 San Antonio Breast Cancer Symposium; 2019 Dec 10-14; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2020;80(4 Suppl):Abstract nr P2-16-17.

This study identifies physiological habitats using quantitative magnetic resonance imaging (MRI) to elucidate intertumoral differences and characterize microenvironmental response to targeted and cytotoxic therapy. BT-474 human epidermal growth factor receptor 2 (HER2+) breast tumors were imaged before and during treatment (trastuzumab, paclitaxel) with diffusion-weighted MRI and dynamic contrast-enhanced MRI to measure tumor cellularity and vascularity, respectively. Tumors were stained for anti-CD31, anti-ɑSMA, anti-CD45, anti-F4/80, anti-pimonidazole, and H&E. MRI data was clustered to identify and label each habitat in terms of vascularity and cellularity. Pre-treatment habitat composition was used stratify tumors into two “tumor imaging phenotypes” (Type 1, Type 2). Type 1 tumors showed significantly higher percent tumor volume of the high-vascularity high-cellularity (HV-HC) habitat compared to Type 2 tumors, and significantly lower volume of low-vascularity high-cellularity (LV-HC) and low-vascularity low-cellularity (LV-LC) habitats. Tumor phenotypes showed significant differences in treatment response, in both changes in tumor volume and physiological composition. Significant positive correlations were found between histological stains and tumor habitats. These findings suggest that the differential baseline imaging phenotypes can predict response to therapy. Specifically, the Type 1 phenotype indicates increased sensitivity to targeted or cytotoxic therapy compared to Type 2 tumors.

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.

Convection-enhanced delivery (CED) of Rhenium-186 nanoliposomes (RNL) is a promising approach to provide precise delivery of large, localized doses of radiation with the goal of extending overall survival for patients with recurrent GBM. A central component of successful CED, is achieving optimal catheter placement for delivery of the therapy. While surgical planning software exists for this purpose, current approaches are designed for small molecules and therefore are not appropriate for larger particles like RNL. To address this concern, we have developed a mathematical model to predict the distribution of RNL via CED on a patient-specific basis. The model is defined on the 3D brain domain which consists of 1) pressure and flow fields generated by accounting for catheter infusion, flow through brain, and fluid loss into capillaries, and 2) the transport of RNL governed by an advection-diffusion equation. We utilize pre-operative MRI to assign patient-specific tissue geometry and properties (e.g., diffusivity, conductivity), and calibrate the model with SPECT measurements within 24 h post the RNL delivery. This model is implemented on one patient enrolled in NCT01906385. The accuracy of model calibration and prediction is evaluated by the Dice score and concordance correlation coefficient (CCC) between modeled and measured distributions of RNL. Our model calibration achieves Dice scores of 0.80, 0.81, 0.69 and CCC of 0.92, 0.93, 0.73 for RNL distributions at the mid-delivery, end of delivery, and 24 h after the delivery, respectively. Long-term model prediction achieves Dice scores of 0.69 and 0.52 at 144 h and 196 h after the delivery, respectively, and CCC of 0.57 and 0.31. Preliminary results demonstrate a proof-of-concept for a patient-specific model to predict the spatiotemporally-resolved distribution of nanoparticles. Ongoing efforts focus on improving our model by accounting backflow and angle of catheter placement, and applying to more patients. Funding: NIH R01CA235800, CPRIT RR160005.

Conventional radiobiology models, including the linear-quadratic model, do not explicitly account for the temporal effects of radiation, thereby making it difficult to make time-resolved predictions of tumor response to fractionated radiation. To overcome this limitation, we propose and validate an experimental-computational approach that predicts the changes in cell number over time in response to fractionated radiation.We irradiated 9L and C6 glioma cells with six different fractionation schemes yielding a total dose of either 16 Gy or 20 Gy, and then observed their responseFor the 9L cells, we observed PCCs and CCCs between the model predictions and validation data of (mean ± standard error) 0.96 ± 0.007 and 0.88 ± 0.013, respectively, across all fractionation schemes. For the C6 cells, we observed PCCs and CCCs between model predictions and the validation data were 0.89 ± 0.008 and 0.75 ± 0.017, respectively, across all fractionation schemes.By proposing a time-resolved mathematical model of fractionated radiation response that can be experimentally verified

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

Simple Summary The recruitment of new vasculature via angiogenesis is a critical component of tumor development, which fundamentally influences tumor growth and response to treatment. The characterization of tumor-induced angiogenesis via mathematical models could enable approaches to forecast tumor response and improve patient care. In this review, we discuss how time-resolved imaging data integrated with mathematical modeling can be used to systematically investigate angiogenesis from the cell to tissue scale and ultimately forecast response to therapy. Abstract Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2–3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

The spatiotemporal variations in tumor vasculature inevitably alters cell proliferation and treatment efficacy. Thus, rigorous characterization of tumor dynamics must include a description of this phenomenon. We have developed a family of biophysical models of tumor growth and angiogenesis that are calibrated with diffusion-weighted magnetic resonance imaging (DW-MRI) and dynamic contrast-enhanced (DCE-) MRI data to provide individualized tumor growth forecasts. Tumor and blood volume fractions were evolved using two, coupled partial differential equations consisting of proliferation, diffusion, and death terms. To evaluate these models, rats (n = 8) with C6 gliomas were imaged seven times. The tumor volume fraction was estimated using DW-MRI, while DCE-MRI provided estimates of the blood volume fraction. The first three time points were used to calibrate model parameters, which were then used to predict growth at the remaining four time points and compared directly to the measurements. The best performing model predicted tumor growth with less than 10.3% error in tumor volume and with less than 9.4% error at the voxel-level at all prediction time points. The best performing model resulted in less than 9.3% error in blood volume at the voxel-level. This pre-clinical study demonstrates the potential for image-based, mechanistic modeling of tumor growth and angiogenesis.

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.

Introduction: 186Re-nanoliposomes (RNL) are a theranostic that emits a therapeutic payload of ionizing beta radiation, and a gamma photon to be measured with SPECT. The RNL is delivered via convection-enhanced delivery, resulting in a highly localized distribution around the glioma that produces up to a 30-fold increase in maximum tolerable dose. RNL provides a continuous source of low dose rate irradiation, until the particles are cleared biologically or decay. The goal of this study is to evaluate the accuracy of a patient calibrated reaction-diffusion equation for predicting the growth and response of recurrent glioblastoma multiforme (GBM) following treatment with RNL. Methods: Multi-parametric images were collected from patients (n=10) receiving RNL treatment, consisting of pre-treatment and follow-up MRIs (Day 0, 28*, 56, 112*) and SPECT/CTs acquired at the middle and end of infusion, and 24-, 112-, and 192-hours post-infusion. For each time point, tumor segmentations and cell count maps are computed using contrast enhanced and diffusion weighted MRI, respectively. The spatio-temporal response to RNL is modeled using a biology-informed reaction-diffusion model describing tumor cell proliferation, invasion, and radiation induced death. Key model parameters related to the RNL activity are populated through a quantification of the SPECT time course. The remaining model parameters related to diffusivity, proliferation, and death rate are calibrated via the Levenberg-Marquardt algorithm for each individual patient, and then used to forecast growth. Calibrations are performed in two different scenarios, first to all imaging time points to assess the model capabilities (Scenario 1), and then without the last acquired MRI, which is set aside to evaluate prediction accuracy (Scenario 2). Error will be assessed at the global (Dice similarity coefficient and percent error in total cell number) and local (concordance correlation coefficient or CCC) levels for both scenarios. *Patients are scanned on day 28 or day 112 at a minimum, potentially both (n=5) Results: Scenario 1 calibrations produced on average, Dice=0.92, CCC=0.69, and total cell percent error = 10.2%, validating usage of the current model formulation. Scenario 2 calibrations show high prediction success on a global scale, mean Dice=0.78, mean total cell percent error =23%, but resulted in poor local accuracy, mean CCC=0.21. Discussion & conclusion: The mathematical model and processing framework can predict the spatiotemporal evolution of recurrent GBM after treatment with RNL. Ongoing efforts include validating the methodology on a larger cohort and further model selection to improve predictive capabilities. Citation Format: Chase Christenson, Chengyue Wu, David A. Hormuth, Shiliang Huang, Andrew Brenner, Thomas E. Yankeelov. A biology-based, mathematical model to predict the response of recurrent glioblastoma to treatment with 186Re-labeled nanoliposomes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2742.

Simple Summary Using medical imaging data and computational models, we develop a modeling framework to provide personalized treatment response forecasts to fractionated radiation therapy for individual tumors. We evaluate this approach in an animal model of brain cancer and forecast changes in tumor cellularity and vasculature. Abstract Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy. Importantly, these models can be personalized for individual tumors via quantitative imaging measurements. To evaluate this family of models, rats (n = 7) with U-87 glioblastomas were imaged with magnetic resonance imaging (MRI) before, during, and after treatment with fractionated radiotherapy (with doses of either 2 Gy/day or 4 Gy/day for up to 10 days). Estimates of tumor and blood volume fractions, provided by diffusion-weighted MRI and dynamic contrast-enhanced MRI, respectively, were used to calibrate tumor-specific model parameters. The Akaike Information Criterion was employed to select the most parsimonious model and determine an ensemble averaged model, and the resulting forecasts were evaluated at the global and local level. At the global level, the selected model’s forecast resulted in less than 16.2% error in tumor volume estimates. At the local (voxel) level, the median Pearson correlation coefficient across all prediction time points ranged from 0.57 to 0.87 for all animals. While the ensemble average forecast resulted in increased error (ranging from 4.0% to 1063%) in tumor volume predictions over the selected model, it increased the voxel wise correlation (by greater than 12.3%) for three of the animals. This study demonstrates the feasibility of calibrating a model of response by serial quantitative MRI data collected during fractionated radiotherapy to predict response at the conclusion of treatment.

High-grade gliomas are an aggressive and invasive malignancy which are susceptible to treatment resistance due to heterogeneity in intratumoral properties such as cell proliferation and density and perfusion. Non-invasive imaging approaches can measure these properties, which can then be used to calibrate patient-specific mathematical models of tumor growth and response. We employed multiparametric magnetic resonance imaging (MRI) to identify tumor extent (via contrast-enhanced T1-weighted, and T2-FLAIR) and capture intratumoral heterogeneity in cell density (via diffusion-weighted imaging) to calibrate a family of mathematical models of chemoradiation response in nine patients with unresected or partially resected disease. The calibrated model parameters were used to forecast spatially-mapped individual tumor response at future imaging visits. We then employed the Akaike information criteria to select the most parsimonious member from the family, a novel two-species model describing the enhancing and non-enhancing components of the tumor. Using this model, we achieved low error in predictions of the enhancing volume (median: − 2.5%, interquartile range: 10.0%) and a strong correlation in total cell count (Kendall correlation coefficient 0.79) at 3-months post-treatment. These preliminary results demonstrate the plausibility of using multiparametric MRI data to inform spatially-informative, biologically-based predictive models of tumor response in the setting of clinical high-grade gliomas.

We present the development and validation of a mathematical model that predicts how glucose dynamics influence metabolism and therefore tumor cell growth. Glucose, the starting material for glycolysis, has a fundamental influence on tumor cell growth. We employed time-resolved microscopy to track the temporal change of the number of live and dead tumor cells under different initial glucose concentrations and seeding densities. We then constructed a family of mathematical models (where cell death was accounted for differently in each member of the family) to describe overall tumor cell growth in response to the initial glucose and confluence conditions. The Akaikie Information Criteria was then employed to identify the most parsimonious model. The selected model was then trained on 75% of the data to calibrate the system and identify trends in model parameters as a function of initial glucose concentration and confluence. The calibrated parameters were applied to the remaining 25% of the data to predict the temporal dynamics given the known initial glucose concentration and confluence, and tested against the corresponding experimental measurements. With the selected model, we achieved an accuracy (defined as the fraction of measured data that fell within the 95% confidence intervals of the predicted growth curves) of 77.2 ± 6.3% and 87.2 ± 5.1% for live BT-474 and MDA-MB-231 cells, respectively.

Quantitative evaluation of an image processing method to perform as designed is central to both its utility and its ability to guide the data acquisition process. Unfortunately, these tasks can be quite challenging due to the difficulty of experimentally obtaining the “ground truth” data to which the output of a given processing method must be compared. One way to address this issue is via “digital phantoms”, which are numerical models that provide known biophysical properties of a particular object of interest. In this contribution, we propose an in silico validation framework for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) acquisition and analysis methods that employs a novel dynamic digital phantom. The phantom provides a spatiotemporally-resolved representation of blood-interstitial flow and contrast agent delivery, where the former is solved by a 1D-3D coupled computational fluid dynamic system, and the latter described by an advection-diffusion equation. Furthermore, we establish a virtual simulator which takes as input the digital phantom, and produces realistic DCE-MRI data with controllable acquisition parameters. We assess the performance of a simulated standard-of-care acquisition (Protocol A) by its ability to generate contrast-enhanced MR images that separate vasculature from surrounding tissue, as measured by the contrast-to-noise ratio (CNR). We find that the CNR significantly decreases as the spatial resolution (SR(A), where the subscript indicates Protocol A) or signal-to-noise ratio (SNR(A)) decreases. Specifically, with an SNR(A) / SR(A) = 75 dB / 30 μm, the median CNR is 77.30, whereas an SNR(A) / SR(A) = 5 dB / 300 μm reduces the CNR to 6.40. Additionally, we assess the performance of simulated ultra-fast acquisition (Protocol B) by its ability to generate DCE-MR images that capture contrast agent pharmacokinetics, as measured by error in the signal-enhancement ratio (SER) compared to ground truth (PE(SER)). We find that PE(SER) significantly decreases the as temporal resolution (TR(B)) increases. Similar results are reported for the effects of spatial resolution and signal-to-noise ratio on PE(SER). For example, with an SNR(B) / SR(B) / TR(B) = 5 dB / 300 μm / 10 s, the median PE(SER) is 21.00 %, whereas an SNR(B) / SR(B) / TR(B) = 75 dB / 60 μm / 1 s, yields a median PE(SER) of 0.90 %. These results indicate that our in silico framework can generate virtual MR images that capture effects of acquisition parameters on the ability of generated images to capture morphological or pharmacokinetic features. This validation framework is not only useful for investigations of perfusion-based MRI techniques, but also for the systematic evaluation and optimization new MRI acquisition, reconstruction, and image processing techniques.

While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2+) breast cancer, HER2+ patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2+ breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and 64Cu-DOTA-Trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient. MRI and PET data are collected prior to therapy, and follow-up MRI scans are acquired at a midpoint in therapy. Given these data types, we align the data sets to a common image space to enable model calibration. Once the model is parameterized with these data, we forecast treatment response with and without HER2-targeted therapy. By incorporating targeted therapy into the model, the resulting predictions are able to distinguish between the two different patient responses, increasing the difference in tumor volume change between the two patients by >40%. This work provides a proof-of-concept strategy for processing and integrating PET and MRI modalities into a predictive, clinical-mathematical framework to provide patient-specific predictions of HER2+ treatment response.

While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2 +) breast cancer, HER2 + patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2 + breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and 64Cu-DOTA-trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient. MRI and PET data are collected prior to therapy, and follow-up MRI scans are acquired at a midpoint in therapy. Given these data types, we align the data sets to a common image space to enable model calibration. Once the model is parameterized with these data, we forecast treatment response with and without HER2-targeted therapy. By incorporating targeted therapy into the model, the resulting predictions are able to distinguish between the two different patient responses, increasing the difference in tumor volume change between the two patients by > 40%. This work provides a proof-of-concept strategy for processing and integrating PET and MRI modalities into a predictive, clinical-mathematical framework to provide patient-specific predictions of HER2 + treatment response.