Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis.

The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.

Analysis of simplicial complexes to determine when to sample for quantitative DCE MRI of the breast.

PURPOSE: A method is presented to select the optimal time points at which to measure DCE-MRI signal intensities, leaving time in the MR exam for high-spatial resolution image acquisition. THEORY: Simplicial complexes are generated from the Kety-Tofts model pharmacokinetic parameters Ktrans and ve . A geometric search selects optimal time points for accurate estimation of perfusion parameters. METHODS: The DCE-MRI data acquired in women with invasive breast cancer (N = 27) were used to retrospectively compare parameter maps fit to full and subsampled time courses. Simplicial complexes were generated for a fixed range of Kety-Tofts model parameters and for the parameter ranges weighted by estimates from the fully sampled data. The largest-area manifolds determined the optimal three time points for each case. Simulations were performed along with retrospectively subsampled data fits. The agreement was computed between the model parameters fit to three points and those fit to all points. RESULTS: The optimal three-point sample times were from the data-informed simplicial complex analysis and determined to be 65, 204, and 393 s after arrival of the contrast agent to breast tissue. In the patient data, tumor-median parameter values fit using all points and the three selected time points agreed with concordance correlation coefficients of 0.97 for Ktrans and 0.67 for ve . CONCLUSION: It is possible to accurately estimate pharmacokinetic parameters from three properly selected time points inserted into a clinical DCE-MRI breast exam. This technique can provide guidance on when to capture images for quantitative data between high-spatial-resolution DCE-MRI images.

Quantitative multiparametric MRI predicts response to neoadjuvant therapy in the community setting.

BACKGROUND: The purpose of this study was to determine whether advanced quantitative magnetic resonance imaging (MRI) can be deployed outside of large, research-oriented academic hospitals and into community care settings to predict eventual pathological complete response (pCR) to neoadjuvant therapy (NAT) in patients with locally advanced breast cancer. METHODS: Patients with stage II/III breast cancer (N = 28) were enrolled in a multicenter study performed in community radiology settings. Dynamic contrast-enhanced (DCE) and diffusion-weighted (DW)-MRI data were acquired at four time points during the course of NAT. Estimates of the vascular perfusion and permeability, as assessed by the volume transfer rate (Ktrans) using the Patlak model, were generated from the DCE-MRI data while estimates of cell density, as assessed by the apparent diffusion coefficient (ADC), were calculated from DW-MRI data. Tumor volume was calculated using semi-automatic segmentation and combined with Ktrans and ADC to yield bulk tumor blood flow and cellularity, respectively. The percent change in quantitative parameters at each MRI scan was calculated and compared to pathological response at the time of surgery. The predictive accuracy of each MRI parameter at different time points was quantified using receiver operating characteristic curves. RESULTS: Tumor size and quantitative MRI parameters were similar at baseline between groups that achieved pCR (n = 8) and those that did not (n = 20). Patients achieving a pCR had a larger decline in volume and cellularity than those who did not achieve pCR after one cycle of NAT (p < 0.05). At the third and fourth MRI, changes in tumor volume, Ktrans, ADC, cellularity, and bulk tumor flow from baseline (pre-treatment) were all significantly greater (p < 0.05) in the cohort who achieved pCR compared to those patients with non-pCR. CONCLUSIONS: Quantitative analysis of DCE-MRI and DW-MRI can be implemented in the community care setting to accurately predict the response of breast cancer to NAT. Dissemination of quantitative MRI into the community setting allows for the incorporation of these parameters into the standard of care and increases the number of clinical community sites able to participate in novel drug trials that require quantitative MRI.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

Anti-HER2 induced myeloid cell alterations correspond with increasing vascular maturation in a murine model of HER2+ breast cancer.

BACKGROUND: Therapy targeted to the human epidermal growth factor receptor type 2 (HER2) is used in combination with cytotoxic therapy in treatment of HER2+ breast cancer. Trastuzumab, a monoclonal antibody that targets HER2, has been shown pre-clinically to induce vascular changes that can increase delivery of chemotherapy. To quantify the role of immune modulation in treatment-induced vascular changes, this study identifies temporal changes in myeloid cell infiltration with corresponding vascular alterations in a preclinical model of HER2+ breast cancer following trastuzumab treatment. METHODS: HER2+ tumor-bearing mice (N = 46) were treated with trastuzumab or saline. After extraction, half of each tumor was analyzed by immunophenotyping using flow cytometry. The other half was quantified by immunohistochemistry to characterize macrophage infiltration (F4/80), vascularity (CD31 and α-SMA), proliferation (Ki67) and cellularity (H&E). Additional mice (N = 10) were used to quantify differences in tumor cytokines between control and treated groups. RESULTS: Immunophenotyping showed an increase in macrophage infiltration 24 h after trastuzumab treatment (P ≤ 0.05). With continued trastuzumab treatment, the M1 macrophage population increased (P = 0.02). Increases in vessel maturation index (i.e., the ratio of α-SMA to CD31) positively correlated with increases in tumor infiltrating M1 macrophages (R = 0.33, P = 0.04). Decreases in VEGF-A and increases in inflammatory cytokines (TNF-α, IL-1ß, CCL21, CCL7, and CXCL10) were observed with continued trastuzumab treatment (P ≤ 0.05). CONCLUSIONS: Preliminary results from this study in a murine model of HER2+ breast cancer show correlations between immune modulation and vascular changes, and reveals the potential for anti-HER2 therapy to reprogram immunosuppressive components of the tumor microenvironment. The quantification of immune modulation in HER2+ breast cancer, as well as the mechanistic insight of vascular alterations after anti-HER2 treatment, represent novel contributions and warrant further assessment for potential clinical translation.

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.

Repeatability, reproducibility, and accuracy of quantitative mri of the breast in the community radiology setting.

BACKGROUND: Quantitative diffusion-weighted MRI (DW-MRI) and dynamic contrast-enhanced MRI (DCE-MRI) have the potential to impact patient care by providing noninvasive biological information in breast cancer. PURPOSE/HYPOTHESIS: To quantify the repeatability, reproducibility, and accuracy of apparent diffusion coefficient (ADC) and T1 -mapping of the breast in community radiology practices. STUDY TYPE: Prospective. SUBJECTS/PHANTOM: Ice-water DW-MRI and T1 gel phantoms were used to assess accuracy. Normal subjects (n = 3) and phantoms across three sites (one academic, two community) were used to assess reproducibility. Test-retest analysis at one site in normal subjects (n = 12) was used to assess repeatability. FIELD STRENGTH/SEQUENCE: 3T Siemens Skyra MRI quantitative DW-MRI and T1 -mapping. ASSESSMENT: Quantitative DW-MRI and T1 -mapping parametric maps of phantoms and fibroglandular and adipose tissue of the breast. STATISTICAL TESTS: Average values of breast tissue were quantified and Bland-Altman analysis was performed to assess the repeatability of the MRI techniques, while the Friedman test assessed reproducibility. RESULTS: ADC measurements were reproducible across sites, with an average difference of 1.6% in an ice-water phantom and 7.0% in breast fibroglandular tissue. T1 measurements in gel phantoms had an average difference of 2.8% across three sites, whereas breast fibroglandular and adipose tissue had 8.4% and 7.5% average differences, respectively. In the repeatability study, we found no bias between first and second scanning sessions (P = 0.1). The difference between repeated measurements was independent of the mean for each MRI metric (P = 0.156, P = 0.862, P = 0.197 for ADC, T1 of fibroglandular tissue, and T1 of adipose tissue, respectively). DATA CONCLUSION: Community radiology practices can perform repeatable, reproducible, and accurate quantitative T1 -mapping and DW-MRI. This has the potential to dramatically expand the number of sites that can participate in multisite clinical trials and increase clinical translation of quantitative MRI techniques for cancer response assessment. LEVEL OF EVIDENCE: 1 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018.

Combining Two Methods of Global Sensitivity Analysis to Investigate MRSA Nasal Carriage Model.

We apply two different sensitivity techniques to a model of bacterial colonization of the anterior nares to better understand the dynamics of Staphylococcus aureus nasal carriage. Specifically, we use partial rank correlation coefficients to investigate sensitivity as a function of time and identify a reduced model with fewer than half of the parameters of the full model. The reduced model is used for the calculation of Sobol' indices to identify interacting parameters by their additional effects indices. Additionally, we found that the model captures an interesting characteristic of the biological phenomenon related to the initial population size of the infection; only two parameters had any significant additional effects, and these parameters have biological evidence suggesting they are connected but not yet completely understood. Sensitivity is often applied to elucidate model robustness, but we show that combining sensitivity measures can lead to synergistic insight into both model and biological structures.

Short-Term Antiretroviral Treatment Recommendations Based on Sensitivity Analysis of a Mathematical Model for HIV Infection of CD4âºΤ Cells.

HIV infection is one of the most difficult infections to control and manage. The most recent recommendations to control this infection vary according to the guidelines used (US, European, WHO) and are not patient-specific. Unfortunately, no two individuals respond to infection and treatment quite the same way. The purpose of this paper is to make use of the uncertainty and sensitivity analysis to investigate possible short-term treatment options that are patient-specific. We are able to identify the most significant parameters that are responsible for ART outcome and to formulate some insights into the ART success.

Mathematical Model for MRSA Nasal Carriage.

An interesting biological phenomenon that is a factor for the spread of antibiotic-resistant strains, such as MRSA, is human nasal carriage. Here, we evaluate several biological hypotheses for this problem in an effort to better understand and narrow the scope of the dominant factors that allow these bacteria to persist in otherwise healthy individuals. First, we set up and analyze a simple PDE model created to generally mimic the interactions of the microbes and nasal immune response. This includes looking at different types of diffusion and chemotaxis terms as well as different boundary conditions. Then, using sensitivity analysis, we walk through several biological hypotheses and compare to the model's results looking for persistent infection scenarios indicated by the model's bacteria component surviving over time.

Global sensitivity analysis used to interpret biological experimental results.

Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are 'frozen' to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.

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.

Investigating tumor-host response dynamics in preclinical immunotherapy experiments using a stepwise mathematical modeling strategy.

Immunotherapies such as checkpoint blockade to PD1 and CTLA4 can have varied effects on individual tumors. To quantify the successes and failures of these therapeutics, we developed a stepwise mathematical modeling strategy and applied it to mouse models of colorectal and breast cancer that displayed a range of therapeutic responses. Using longitudinal tumor volume data, an exponential growth model was utilized to designate response groups for each tumor type. The exponential growth model was then extended to describe the dynamics of the quality of vasculature in the tumors via [18F] fluoromisonidazole (FMISO)-positron emission tomography (PET) data estimating tumor hypoxia over time. By calibrating the mathematical system to the PET data, several biological drivers of the observed deterioration of the vasculature were quantified. The mathematical model was then further expanded to explicitly include both the immune response and drug dosing, so that model simulations are able to systematically investigate biological hypotheses about immunotherapy failure and to generate experimentally testable predictions of immune response. The modeling results suggest elevated immune response fractions (> 30 %) in tumors unresponsive to immunotherapy is due to a functional immune response that wanes over time. This experimental-mathematical approach provides a means to evaluate dynamics of the system that could not have been explored using the data alone, including tumor aggressiveness, immune exhaustion, and immune cell functionality.

Towards Patient-Specific Optimization of Neoadjuvant Treatment Protocols for Breast Cancer Based on Image-Guided Fluid Dynamics.

OBJECTIVE: This study establishes a fluid dynamics model personalized with patient-specific imaging data to optimize neoadjuvant therapy (i.e., doxorubicin) protocols for breast cancers. METHODS: Ten patients recruited at the University of Chicago were included in this study. Quantitative dynamic contrast-enhanced and diffusion weighted magnetic resonance imaging data are leveraged to estimate patient-specific hemodynamic properties, which are then used to constrain the mechanism-based drug delivery model. Then, computer simulations of this model yield the subsequent drug distribution throughout the breast. By systematically varying the dosing schedule, we identify an optimized regimen for each patient using the maximum safe therapeutic duration (MSTD), which is a metric balancing treatment efficacy and toxicity. RESULTS: With an individually optimized dose (range = 12.11-15.11 mg/m2 per injection), a 3-week regimen consisting of a uniform daily injection significantly outperforms all other scheduling strategies (P < 0.001). In particular, the optimal protocol is predicted to significantly outperform the standard protocol (P < 0.001), improving the MSTD by an average factor of 9.93 (range = 6.63 to 14.17). CONCLUSION: A clinical-mathematical framework was developed by integrating quantitative MRI data, advanced image processing, and computational fluid dynamics to predict the efficacy and toxicity of neoadjuvant therapy protocols, thus enabling the rational identification of an optimal therapeutic regimen on a patient-specific basis. SIGNIFICANCE: Our clinical-computational approach has the potential to enable optimization of therapeutic regimens on a patient-specific basis and provide guidance for prospective clinical trials aimed at refining neoadjuvant therapy protocols for breast cancers.

MRI-Based Digital Models Forecast Patient-Specific Treatment Responses to Neoadjuvant Chemotherapy in Triple-Negative Breast Cancer.

Triple-negative breast cancer (TNBC) is persistently refractory to therapy, and methods to improve targeting and evaluation of responses to therapy in this disease are needed. Here, we integrate quantitative MRI data with biologically based mathematical modeling to accurately predict the response of TNBC to neoadjuvant systemic therapy (NAST) on an individual basis. Specifically, 56 patients with TNBC enrolled in the ARTEMIS trial (NCT02276443) underwent standard-of-care doxorubicin/cyclophosphamide (A/C) and then paclitaxel for NAST, where dynamic contrast-enhanced MRI and diffusion-weighted MRI were acquired before treatment and after two and four cycles of A/C. A biologically based model was established to characterize tumor cell movement, proliferation, and treatment-induced cell death. Two evaluation frameworks were investigated using: (i) images acquired before and after two cycles of A/C for calibration and predicting tumor status after A/C, and (ii) images acquired before, after two cycles, and after four cycles of A/C for calibration and predicting response following NAST. For Framework 1, the concordance correlation coefficients between the predicted and measured patient-specific, post-A/C changes in tumor cellularity and volume were 0.95 and 0.94, respectively. For Framework 2, the biologically based model achieved an area under the receiver operator characteristic curve of 0.89 (sensitivity/specificity = 0.72/0.95) for differentiating pathological complete response (pCR) from non-pCR, which is statistically superior (P &lt; 0.05) to the value of 0.78 (sensitivity/specificity = 0.72/0.79) achieved by tumor volume measured after four cycles of A/C. Overall, this model successfully captured patient-specific, spatiotemporal dynamics of TNBC response to NAST, providing highly accurate predictions of NAST response. SIGNIFICANCE: Integrating MRI data with biologically based mathematical modeling successfully predicts breast cancer response to chemotherapy, suggesting digital twins could facilitate a paradigm shift from simply assessing response to predicting and optimizing therapeutic efficacy.

Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy.

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.

A time-resolved experimental-mathematical model for predicting the response of glioma cells to single-dose radiation therapy.

PURPOSE: To develop and validate a mechanism-based, mathematical model that characterizes 9L and C6 glioma cells' temporal response to single-dose radiation therapy in vitro by explicitly incorporating time-dependent biological interactions with radiation. METHODS: We employed time-resolved microscopy to track the confluence of 9L and C6 glioma cells receiving radiation doses of 0, 2, 4, 6, 8, 10, 12, 14 or 16 Gy. DNA repair kinetics are measured by γH2AX expression via flow cytometry. The microscopy data (814 replicates for 9L, 540 replicates for C6 at various seeding densities receiving doses above) were divided into training (75%) and validation (25%) sets. A mechanistic model was developed, and model parameters were calibrated to the training data. The model was then used to predict the temporal dynamics of the validation set given the known initial confluences and doses. The predictions were compared to the corresponding dynamic microscopy data. RESULTS: For 9L, we obtained an average (± standard deviation, SD) Pearson correlation coefficient between the predicted and measured confluence of 0.87 ± 0.16, and an average (±SD) concordance correlation coefficient of 0.72 ± 0.28. For C6, we obtained an average (±SD) Pearson correlation coefficient of 0.90 ± 0.17, and an average (±SD) concordance correlation coefficient of 0.71 ± 0.24. CONCLUSION: The proposed model can effectively predict the temporal development of 9L and C6 glioma cells in response to a range of single-fraction radiation doses. By developing a mechanism-based, mathematical model that can be populated with time-resolved data, we provide an experimental-mathematical framework that allows for quantitative investigation of cells' temporal response to radiation. Our approach provides two key advances: (i) a time-resolved, dynamic death rate with a clear biological interpretation, and (ii) accurate predictions over a wide range of cell seeding densities and radiation doses.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data.

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.

Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting.

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.

Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling.

BACKGROUND: Intra-and inter-tumoral heterogeneity in growth dynamics and vascularity influence tumor response to radiation therapy. Quantitative imaging techniques capture these dynamics non-invasively, and these data can initialize and constrain predictive models of response on an individual basis. METHODS: We have developed a family of 10 biologically-based mathematical models describing the spatiotemporal dynamics of tumor volume fraction, blood volume fraction, and response to radiation therapy. To evaluate this family of models, rats (n = 13) with C6 gliomas were imaged with magnetic resonance imaging (MRI) three times before, and four times following a single fraction of 20 Gy or 40 Gy whole brain irradiation. The first five 3D time series data of tumor volume fraction, estimated from diffusion-weighted (DW-) MRI, and blood volume fraction, estimated from dynamic contrast-enhanced (DCE-) MRI, were used to calibrate tumor-specific model parameters. The most parsimonious and well calibrated of the 10 models, selected using the Akaike information criterion, was then utilized to predict future growth and response at the final two imaging time points. Model predictions were compared at the global level (percent error in tumor volume, and Dice coefficient) as well as at the local or voxel level (concordance correlation coefficient). RESULT: The selected model resulted in < 12% error in tumor volume predictions, strong spatial agreement between predicted and observed tumor volumes (Dice coefficient > 0.74), and high level of agreement at the voxel level between the predicted and observed tumor volume fraction and blood volume fraction (concordance correlation coefficient > 0.77 and > 0.65, respectively). CONCLUSIONS: This study demonstrates that serial quantitative MRI data collected before and following radiation therapy can be used to accurately predict tumor and vasculature response with a biologically-based mathematical model that is calibrated on an individual basis. To the best of our knowledge, this is the first effort to characterize the tumor and vasculature response to radiation therapy temporally and spatially using imaging-driven mathematical models.