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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.Simplicial complexes are generated from the Kety-Tofts model pharmacokinetic parameters KThe 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.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 KIt 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.

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 < 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.

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 < 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.

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

The early assessment of neoadjuvant therapy (NAT) response in triple-negative breast cancer (TNBC) would enable a treating oncologist to adjust a therapeutic plan of a non-responding patient, and thereby enhance outcomes while preventing unnecessary toxicities. To address this challenge, we propose leveraging personalized, in silico forecasts of tumor response to therapeutic regimens via a mechanistic mathematical model calibrated with patient-specific longitudinal magnetic resonance imaging (MRI) data acquired early during NAT. Here, we focus on identifying the driving mechanisms involved in the model formulation through a global sensitivity analysis. Our model describes the dynamics of TNBC cell density as a combination of mobility, which is formulated as a diffusion process constrained by local tumor-induced mechanical stress, and net proliferation, which is represented with a logistic term. To model TNBC response to NAT drug combinations, we adjust the tumor cell proliferation rate with a recent pharmacodynamic model, MuSyC, which also accounts for synergy of potency and efficacy. Tumor cell density is estimated from diffusion-weighted MRI data, while tissue mechanical properties are defined from segmented contrast-enhanced T1-weighted MRI data. To model the heterogeneous intratumoral delivery of drugs, we use perfusion maps estimated from dynamic contrast-enhanced MRI data. NAT drug pharmacokinetics are approximated with a linear model, which reasonably represents their temporal decay during NAT. Sobol’s method is used for the global sensitivity analysis of the NAT response of two different tumors (one well-perfused and one poorly-perfused) on a 3D, tissue-scale domain. This allows us to assess the total effect (ST) of each model parameter on tumor volume and global cellularity. Here, we focus on two standard NAT regimens: doxorubicin plus cyclophosphamide, and paclitaxel plus carboplatin. The parameter space is constructed by integrating three approaches. First, we use prior patient-specific in silico estimates of tumor cell mobility and proliferation. Second, we experimentally constrain the parameters accounting for potential synergistic drug activity by using time-resolved, high-throughput, automated microscopy assays that capture drug-induced changes in proliferation rates of various TNBC lines (HCC1143, SUM149, MDAMB231, and MDAMB468; perfosfamide was used in lieu of the pro-drug cyclophosphamide). Third, we scale the resulting in vitro parameter ranges to be clinically-relevant through an in silico study with our mechanistic model. Our results show that out of the 15 model parameters considered in the sensitivity analysis only a minority exhibited a driving role (ST > 0.1) in representing the dynamics of TNBC response to NAT, namely: the baseline tumor cell proliferation rate along with the effect and ratio of peak concentration to EC50 of doxorubicin, paclitaxel, and carboplatin. The other parameters have a marginal effect and can thus be fixed to any value within the parameter space. We select these constant parameters such that they contribute to simplifying the model formulation, leading to a surrogate reduced model. We further show that the reduced and the original model produce distributions of tumor volume and global cellularity that are in remarkable agreement both qualitatively (Dice similarity coefficient > 0.90 and > 0.94, respectively) and parameter-wise (concordance correlation coefficient > 0.85 and > 0.89, respectively). Thus, we conclude that our reduced model constitutes a feasible surrogate for future clinical calibration-forecasting studies, thereby facilitating personalized NAT response forecasting with patient-specific imaging datasets acquired in vivo. Citation Format: Guillermo Lorenzo, Angela M. Jarrett, Christian T. Meyer, Darren R. Tyson, Vito Quaranta, Thomas E. Yankeelov. In silico analysis of a novel mathematical model integrating in vitro and in vivo imaging data reveals driving mechanisms of breast cancer response to NAT for personalized tumor forecasting [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P1-08-20.

Introduction:. Patients with locally advanced triple-negative breast cancer (TNBC) typically receive neoadjuvant therapy (NAT) to downstage the tumor and to improve the outcome of the subsequent breast conservation surgery. A critical unmet need is the lack of a method to accurately predict how a patient with TNBC will respond to NAT before surgery. In this work, we applied a clinical-computational framework to predict response of TNBC early in the course of NAT, by integrating quantitative MRI with mechanism-based mathematical modeling. Methods:. Patients and Data. Multiparametric quantitative MRI was acquired in patients (n = 46) before, and after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C) regimen as part of the MD Anderson Cancer Center TNBC Moonshot Program. Within each imaging session, dynamic contrast-enhanced (DCE-), diffusion-weighted imaging (DWI), and a pre-contrast T1-map were acquired. Image processing. The processing pipeline consisted of three components. First, the images within each visit were registered to account for patient motion, and the parametric maps from the DCE and DWI images were computed. Second, inter-visit image registration was achieved by a non-rigid registration applied on breast, with a rigid penalty applied on the tumor region to preserve its size and shape. Third, post-processing was performed for preparation of modeling, including segmentation of the breast contour and tissues, and calculation of voxel-wise cellularity within tumors. Mathematical modeling. A predictive model was developed based on a reaction-diffusion equation (Eq. 1). The mobility of tumor cells is represented by diffusion coupled to mechanical properties of the tissue (Eq. 2), and the proliferation of the tumor is described with logistic growth. The injection and decay of administered therapies, inducing tumor cell death, is also represented in the model (Eq. 3). The variables and parameters used are listed in Table 1. Eq. 1: ∂N(x,t)/∂t = ∇⋅(D(x,t) ∇N(x,t)) + k(x) (1 - N(x,t)/θ)N(x,t) - (λ1(x,t) + λ2(x,t))N(x,t). Eq. 2: D(x,t) = D0 e-γσ(x,t). Eq. 3: λn(x,t) = αne-βn t C(x,t), n = 1, 2. For each patient, the domain and initial condition were generated from the pre-treatment images, and the images acquired during NAT were used for patient-specific calibration of parameters. The calibrated model was then used to predict the response to be observed at the end of NAT. We evaluated the model by comparing its predictions of tumor volume, longest axis, voxel-wise cellularity, and total tumor cellularity to the imaging measurements at the end of A/C. Results:. Our model predicted the tumor volume, total cellularity, and longest axis with a Pearson correlation coefficient (PCC) of 0.85, 0.80, and 0.60, respectively. The accuracy of voxel-wise cellularity achieved a PCC with the median (range) of 0.89 (0.77 - 0.93) between the prediction and the actual measurement. Moreover, we set criteria of 70% shrinkage of tumor volume to define response versus non-response cases, with which our model achieved a differentiation sensitivity/specificity of 0.90/0.73. Discussion:. Preliminary results of our study demonstrate the potential of the clinical-computational framework as a powerful tool for predicting response to NAT. Once validated, the method could also assist in optimizing treatment plans on a patient specific basis, or guiding patient selection in trials for novel NAT regimens. Table 1. Summary of the variables and parameters in the modelQuantitiesDefinition AssignmentDomainsΩbreast tissue domainGenerated from pre-treatment MRITEnd time point of NAT procedureDetermined from NAT schedulexCoordinate in breast tissueAssociated with spatial domain, ΩttimeAssociated with temporal domain, [0, T]VariablesN(x,t)Tumor cell numberInitialized from pre-treatment ADC, computed via Eq. 1D(x,t)Diffusive mobility of tumor cellsComputed via Eq. 2λn(x,t)Death rate induced by nth type of drugComputed via Eq. 3, n = 1 and 2 for A/Cσ(x,t)Von Mises stressComputed from gradient of N(x,t), based on Hormuth et al., 2018C(x,t)Spatiotemporal distribution of drugsAssigned based on NAT schedule and DCE imagesParametersk(x)Proliferation rate of tumor cellsLocally calibratedθTumor cells carry capacityGlobally calibratedαnEfficacy rate of nth type of drugGlobally calibratedβnDecay rate of of nth type of drugGlobally calibratedD0Diffusion coefficient of tumor cells in the absence of mechanical restrictionsGlobally calibratedγStress-tumor cell diffusion coupling constantAssigned based on Hormuth et al., 2018 Citation Format: Chengyue Wu, Angela M. Jarrett, Zijian Zhou, Nabil Elshafeey, Beatriz E. Adrada, Rosalind P. Candelaria, Rania M. Mohamed, Medine Boge, Lei Huo, Jason White, Debu Tripathy, Vicente Valero, Jennifer Litton, Stacy Moulder, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Forecasting treatment response to neoadjuvant systemic therapy in triple negative breast cancer viamathematical modeling and quantitative MRI [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P1-08-08.

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 early determination of response to neoadjuvant therapy (NAT) in triple-negative breast cancer would enable the treating oncologist to adapt the therapeutic regimen of a non-responding patient (e.g., by changing dosage, dose schedule, prescribed drugs), and thereby improve treatment outcomes while avoiding unnecessary toxicities. To address this challenge, we propose to use personalized, in silico forecasts of tumor response to therapeutic regimens via a mechanistic mathematical model calibrated with patient-specific longitudinal multi-parametric magnetic resonance imaging (MRI) data acquired early in the course of NAT. Here, we extend our mechanistic model to include a new term describing the synergistic effects of NAT drug combinations and identify the driving parameters involved in its formulation by means of a sensitivity analysis. Our model describes tumor cell dynamics as a combination of proliferation, which is regulated by a logistic term, and mobility, which is described as a diffusion process constrained by the local tumor-induced mechanical stress. Tumor cell density is extracted from diffusion-weighted MRI data, while tissue mechanical properties are defined from segmented T1-weighted MRI data. We adjust the tumor proliferation rate in response to NAT drug combinations with a recent model of drug synergy, MuSyC, which accounts for distinct types of synergistic drug effects (synergy of potency vs. synergy of efficacy). We also consider the heterogeneous intratumoral delivery of drugs by means of perfusion maps estimated from dynamic contrast-enhanced MRI data. We use Sobol’s method for the sensitivity analysis of two different tumors - one well-perfused and one poorly-perfused. We simulate a four-cycle NAT protocol in which NAT drugs are delivered every 14 days, and assess the total effect (ST) of each parameter on the mean relative difference of tumor cell density with respect to a control simulation of tumor growth without NAT. Sensitivity analysis results directly depend on the definition of the parameter space, which we construct by combining two approaches. First, we experimentally constrain parameter ranges using time-resolved, high-throughput, automated microscopy assays to capture the changes in proliferation rates of various breast cancer lines (HCC1143, SUM149, MDAMB231, and MDAMB468) caused by two standard drug combinations: paclitaxel with carboplatin and doxorubicin with perfosfamide (metabolic derivative of the pro-drug cyclophosphamide), and fitting the MuSyC model to these data. Second, we scale the resulting in vitro parameter ranges to clinically-relevant in vivo ranges by running an in silico study with our mechanistic model of breast cancer growth and NAT response. Our results show that, out of the ten parameters involved in the synergy term, three have a dominant role in the dynamics of breast cancer during NAT (ST > 0.1): synergistic potency, the maximal change in tumor cell proliferation by the slowest decaying drug, and its concentration producing half of maximal effects. The other parameters have marginal (0.02 < ST < 0.1) to negligible effect (ST < 0.02). Ongoing studies are assessing the ability of our mechanistic model to forecast NAT response over a small patient cohort after patient-specific calibration of the driving parameters identified in the present study. Citation Format: Guillermo Lorenzo, Angela M. Jarrett, Christian T. Meyer, Darren R. Tyson, Vito Quaranta, Thomas E. Yankeelov. Identifying relevant parameters that characterize the early response to NAT in breast cancer patients using a novel personalized mechanistic model integrating in vitro and in vivo imaging data [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 PS13-44.

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.

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-1β, 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.

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.

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.

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 Ktrans, ADC, cellularity, and bulk tumor flow from baseline (pre-treatment) were all significantly greater (p 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.

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 expression 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. To the best of our knowledge, this represents the first study to integrate well-controlled, experimental data into a mechanism-based, multiscale, mathematical model of angiogenic sprouting to make specific, testable predictions.

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.

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.

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.

Introduction: We have previously established a tissue scale mathematical model with 5 coupled, ordinary differential equations (ODEs) describing the longitudinal relationship of vasculature, hypoxia, necrosis, immune infiltration, and tumor growth in a preclinical model of human epidermal growth factor receptor 2 positive (HER2+) breast cancer undergoing trastuzumab treatment. The purpose of this study is to expand this model to multiple scales (tissue and cellular) and to explicitly include the effects of combination trastuzumab-paclitaxel therapy as measured by time-resolved microscopy of in vitro HER2+ breast cancer cells. This requires interlacing experimental data and additional ODEs at the cellular scale to incorporate drug dynamics within the tissue scale model for overall tumor growth. An integrated multi-scale mathematical-experimental approachbridging in vivo and in vitro experimental data has potential to elucidate the optimal strategies for combination therapy for HER2+ breast cancer. Experimental: In vitro data was collected to longitudinally evaluate BT474 HER2+ human cancer cells growth when treated with trastuzumab (25-50 ug/ml) and/or paclitaxel (10-250 nmol/L) measured by time-resolved microscopy. Changes in confluence before and after treatment are recorded every 3 hours over the course of 7 days. Ongoing studies are quantifying the change in confluence for these cells with alternating dosing and timing of the two therapies. Modeling: Thein vivo, tissue-scale model parameters were calibrated using mean and 95% confidence intervals of tumor volume from caliper measurements, vasculature and hypoxia from imaging data, and necrosis from histology. The in vitro scale of the model is calibrated with confluence data for controls to define intervals for growth rates and carrying capacities. Experimental results for single drug applications are used to estimate cell death, and data from combinations of both the targeted anti-HER2 therapy and cytotoxic therapies provide estimates of synergistic drug effects. After calibration of parameters, the two scales of the model are coupled via the tumor volume and vasculature components to simulate the effects of combination therapy in vivo. Results and Discussion: The confluence data shows that trastuzumab dosing in combination with paclitaxel results in the greatest reduction in tumor cells than either drug alone (p < 0.05), and there are distinct differences in alternating the order and timing of these drugs. Further, preliminary results show that the model's in vitro scale equations can be calibrated with the available longitudinal data. As dosing of combination therapy in vitro provides the opportunity to quantify the effects of combination therapy that would not be feasible to collect in an in vivo setting, our aim is to generate experimentally testable predictions for improved combination therapy in vivo with our multiscale model. This is an important step for future clinical translation to provide temporal guidance of standard-of-care, combination therapies, potentially leading to significantly improved anticancer response in HER2+ breast cancer. We acknowledge the support of NCI U01CA174706, NCI R01CA186193, CPRIT RR160005, and ACS RSG-18-006-01-CCE. Citation Format: Jarrett AM, Shah A, Bloom MJ, Yankeelov TE, Sorace AG. A multi-scale mathematical model of combination targeted and cytotoxic therapy to evaluate treatment response in HER2+ breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P6-17-33.

Introduction: Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant therapy (NAT) to downstage the tumor and to improve the outcome of subsequent breast conservation surgery. There are currently no methods to accurately predict how a TNBC patient will respond to NAT before surgery. In this work, we applied a digital twin framework to address this unmet clinical need, by integrating quantitative magnetic resonance imaging (MRI) data with mechanism-based mathematical modeling. Methods: Multiparametric MRI was acquired in patients (N = 50) before, after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C), and again after 12 cycles of Paclitaxel as part of the ARTEMIS (NCT02276433) trial. Within each imaging session, dynamic contrast-enhanced (DCE) MRI, diffusion-weighted imaging (DWI), and a pre-contrast T1-map were acquired. The images were processed by a pipeline consisting of motion correction, multiparametric image alignment, inter-visit image registration to align the tumor and surrounding breast tissue, tissue segmentation, and estimation of tumor cellularity from DWI. A mechanism-based mathematical model, a reaction-diffusion equation, is used to characterize the mobility of tumor cells via diffusion damped by mechanical tissue properties, tumor proliferation via logistic growth, and treatment-induced cell death via the delivery and decay of therapies. For each patient, pre-treatment images were used for model initialization. The model calibration and prediction were implemented with two strategies: 1) using images acquired during the A/C for calibration and predicting up to the end of A/C, and 2) using images acquired during and after the A/C for calibration and predicting up to the end of NAT. For strategy 1), we evaluated the model by comparing its predicted tumor volume and total tumor cellularity to the imaging measurements at the end of A/C. For strategy 2), we evaluated the model by comparing its predicted final response to the post-surgical pathological findings. Results: For strategy 1), our framework predicted the change of tumor volume and total tumor cellularity with Pearson correlation coefficients of 0.91 and 0.89, respectively. Regarding strategy 2), our framework achieved an area under the receiver operator characteristic curve of 0.88 for distinguishing pCR from non-pCR. As a comparison, imaging measurement of tumor volume at the end of A/C achieved an AUC of 0.79. Conclusion: Our approach successfully captures the patient-specific dynamics of TNBC response to NAT and provides an improved prediction of final response, which demonstrates the potential of a digital twin framework to be a powerful tool for predicting response to NAT. Once validated, the method will provide a unique opportunity for optimizing treatment plans on a patient-specific basis. Citation Format: Chengyue Wu, Angela M. Jarrett, Zijian Zhou, Nabil Elshafeey, Beatriz E. Adrada, Rosalind P. Candelaria, Rania Mohamed, Medine Boge, Lei Huo, Jason White, Debu Tripathy, Vicente Valero, Jennifer Litton, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Forecasting treatment response to neoadjuvant therapy in triple-negative breast cancer via an image-guided digital twin [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 2736.

INTRODUCTION: A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways, to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. AREAS COVERED: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. EXPERT COMMENTARY: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

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.

Background: Early and accurate prediction of response to neoadjuvant therapy (NAT) would empower personalization of breast cancer treatment regimens based on expected response. Noninvasive, quantitative dynamic contrast-enhanced (DCE-MRI) and diffusion-weighted magnetic resonance imaging (DW-MRI), when performed during the course of NAT, can accurately predict the ultimate pathological response. While these techniques have been incorporated into clinical trials in the academic setting, they have not yet been translated to the community setting, where most cancer patients receive their care. Implementation of quantitative MRI in the community setting widely expands the potential impact it can provide by 1) allowing community settings to participate in clinical trials that require quantitative MRI, and 2) advancing quantitative MRI towards standard-of-care for prediction of response in breast cancer. Methods: Women with locally advanced breast cancer (N = 28) were imaged four times during the course of NAT: 1) prior to the start of NAT, 2) after 1 cycle of NAT, 3) after 2-4 cycles of NAT, and 4) 1 cycle after MRI #3. Imaging data was acquired on 3T Siemens Skyra scanners equipped with breast coils and sited in a community hospital and radiology clinic, respectively. DW-MRI and DCE-MRI were acquired over 10 slices of 5 mm thickness. DW-MRI was acquired with diagonal monopolar diffusion-encoding gradients with b-values of 0, 200, and 800 s/mm2 in a total scan time of 1 minute 39 seconds. Voxel wise tumor cellularity was quantified using the apparent diffusion coefficient (ADC). For DCE-MRI, a gadolinium-based contrast agent was administered intravenously at 2 mL/sec after the acquisition of baseline scans. DCE-MRI data was acquired dynamically with a temporal resolution of 7.27 seconds for a total acquisition time of 8 minutes. The volume transfer constant Ktrans was calculated using Patlak analysis of DCE-MRI data to characterize the tumor vasculature. The tumor was semi-automatically segmented using a manually drawn region of interest followed by fuzzy c-means clustering of DCE-MRI data to identify a functional tumor volume. Measurements of tumor volume were combined with both ADC and Ktrans to yield metrics of tumor cellularity and bulk tumor flow, respectively. Results: Women who achieved pathological complete response at the time of surgery (pCR; n=8) displayed significantly different treatment-induced changes in MRI-derived tumor parameters versus women who did not achieve pCR (non-pCR, n=20). After 1 cycle of NAT, women who achieved pCR had smaller functional tumor volume and lower cellularity (p < 0.05) than non-pCR study participants. At the third and fourth MRI, tumor volume, ADC, Ktrans, cellularity, and bulk tumor flow were all significantly different between the pCR and non-pCR cohorts (p < 0.05). Of note, longest tumor diameter was not predictive of pCR at any time point in this study. Conclusions: This study demonstrates that quantitative DCE- and DW-MRI can be implemented successfully in community care facilities within standard-of-care settings for imaging locally advanced breast cancer. Metrics extracted from the change in DW-MRI (ADC) and DCE-MRI (Ktrans) can accurately predict pathological complete response to neoadjuvant therapy and may be more sensitive to tumor response than the RECIST criteria. Furthermore, incorporating quantitative metrics with tumor volume further increases the ability to predict pathological response to NAT in locally advanced breast cancer. While there are still challenges to address to effectively implement these quantitative metrics into the clinical workflow, this study is first in its kind to transition a decade’s worth of quantitative MRI advancements from academic settings into standard-of-care. Citation Format: John Virostko, Anna G Sorace, Kalina P Slavkova, Anum S Kazerouni, Angela M Jarrett, Julie C DiCarlo, Stefanie Woodard, Sarah Avery, Boone W Goodgame, Debra Patt, Thomas E Yankeelov. Quantitative multiparametric MRI predicts response to neoadjuvant therapy in the community setting [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P3-03-03.

Background: Standard of care (SOC) breast MRI exams typically acquire 4-7 frames of dynamic contrast-enhanced MRI (DCE-MRI) for cancer screening and staging. Post-contrast images depict lesion spiculations and boundaries to identify and characterize tumors. Pharmacokinetic (PK) analysis of DCE-MRI involves modeling blood flow to the lesion and surrounding tissue and has shown promise in diagnosis and prediction of therapeutic response. Currently, SOC DCE-MRI requires ~60-90 seconds per volume for images with sufficient quality and spatial resolution. However, PK analysis of DCE-MRI requires faster time course sampling. For this reason, PK modeling is limited to research scans with lower spatial resolution and higher temporal resolution. PK modeling would improve feedback of treatment response, and implementation in the SOC exam would increase imaging trial participation. In this study, we tested the estimation of Ktrans, a mixed perfusion and permeability PK parameter, from three images at optimal time points after contrast agent (CA) injection, and compared it to the Ktrans estimation from analysis of the full-length time course.. Methods: Women (N=23) with newly diagnosed invasive breast cancers who were eligible for neoadjuvant therapy (NAT) were scanned with a research MRI protocol as part of a treatment-monitoring study. Images acquired prior to the start of NAT were used. MRI was performed on 3.0T Siemens Skyra scanners at two sites with bilateral breast coils. The research protocol included ten sagittal slices centered about the primary tumor. The DCE-MRI images came from a fast sequence with 1.3 × 1.3 × 5.0 mm resolution acquired at 7.3 seconds per frame (66 frames total,) with a gadolinium-based CA injected one minute into the scan. A population arterial input function was used to implement a mathematical graph-based search of possible tissue CA concentration curves from the expected range of PK parameters. The search results gave a set of three optimized sub-sampled timepoints, Topt, from the full set of sample times, Tfull, at which to best sample the CA concentration curves to optimally estimate PK values. The imaging data was analyzed to find one parameter map from image times Tfull, and another from the subset of images at times Topt. The difference in Ktrans was computed at each parameter map voxel, and the concordance correlation coefficient (CCC) was computed per patient to determine agreement. The median Ktrans values were also compared for each patient. Results: The graph-based search of CA concentration curves found optimal times Topt of 37, 66, and 153 seconds after injection. The averaged values over all patients for median and maximum Ktrans from the original Tfull image set were 0.07 and 0.5 (min)-1. The average difference in Ktrans values between the Topt and Tfull sets was 0.02 (min)-1. When the median Ktrans values for each patient were compared, the average difference in median Ktrans values was 15% +/- 9%. The concordance correlation coefficients comparing the Topt and Tfull -sampled parameter maps for each patient were 0.89 +/- 0.12, showing high agreement. Discussion: This retrospective analysis suggests that it is possible to estimate PK parameters from a few properly selected post-contrast images inserted into a SOC DCE-MRI exam. The combination of optimal timing with fast acquisition techniques for high-resolution imaging could be used to provide quantitative data while preserving post-contrast images with the necessary spatial resolution for clinical reading. Importantly, the test images were acquired in the community setting with widely available MRI hardware, further indicating the potential for integration with SOC exams. Funding: NCI U24 CA226110, NCI U01 CA174706, NCI U01 CA142565, CPRIT RR160005 Citation Format: Julie C DiCarlo, Angela M Jarrett, Anum S Kazerouni, John Virostko, Anna G Sorace, Kalina P Slavkova, Debra Patt, Boone W Goodgame, Sarah Avery, Thomas E Yankeelov. Three timepoint pharmacokinetic modeling to incorporate within standard of care MRI breast exams [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr P3-02-09.

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.

SummaryA 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 data types. 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 mechanistic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal population-size data. We demonstrate that the explicit inclusion of the transcriptomic information in the parameter estimation is critical for identification of the model parameters and enables accurate prediction of new treatment regimens. Inclusion of the transcriptomic data improves predictive accuracy in new treatment response dynamics with a concordance correlation coefficient (CCC) of 0.89 compared to a prediction accuracy of CCC = 0.79 without integration of the single cell RNA sequencing (scRNA-seq) data directly into the model calibration. To the best our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with longitudinal treatment response data into a mechanistic mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multimodal data sets into identifiable mathematical models to develop optimized treatment regimens from data.

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.

Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model’s behaviour were made including interacting effects of the bacteria’s growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.

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.

Introduction: The purpose of this study is to identify temporal changes in the identity and cellularity of myeloid cells infiltrating human epidermal growth factor receptor type 2 positive (HER2+) breast cancer following trastuzumab therapy. Trastuzumab is a targeted therapy used in combination with cytotoxic therapies to treat HER2+ breast cancer. Previous data shows that in HER2+ tumors, trastuzumab increases vascular maturation and decreases hypoxia, both of which can sensitize tumors to cytotoxic therapies. Preliminary immunofluorescent data reveals a significant increase in the amount of myeloid cell infiltrates in trastuzumab treated tumors during the same temporal window as vascular and hypoxia alterations. The balance of myeloid cells in the tumor microenvironment (TME) can impact neovascularization, hypoxia, and tumor progression. Thus, we hypothesize that quantifying immune modulation following trastuzumab treatment will identify mechanistic properties of trastuzumab induced vascular alterations in the TME. We present results identifying an increase in various myeloid infiltrates between control and trastuzumab treated tumors in HER2+ breast cancer. Experimental Design: BT474 HER2+ breast cancer cells were implanted subcutaneously into athymic nude mice. After reaching 250 mm3, tumors were treated with trastuzumab (10 mg/kg) or saline for one week and were excised for analysis on days 0, 4, and 7. Each tumor was cut at the largest cross-section; half was fixed in 10% neutral buffered formalin for immunohistochemistry staining of TME markers (pimonidazole, CD11c, F4/80, CD31, and alpha-SMA), and half was digested for single cell analysis using flow cytometry. Data was analyzed with FlowJo software. Distinct populations of myeloid cells have been quantified in day 4 control (n = 6) and trastuzumab treated (n = 4) tumors. A non-parametric Wilcoxon rank sum test was used to determine statistical differences. Results and Discussion: Flow analysis revealed a significant (p < 0.05) increase of macrophages in tumors treated with trastuzumab for 4 days compared to control tumors. Spatial immunofluorescent data confirms these findings showing a significant increase in macrophage populations, indicated with increased CD11c+ and F4/80+ co-staining in day 4 treated tumors compared to control (p < 0.01). Additionally, flow cytometry results show a significant (p < 0.05) increase in neutrophils in day 4 trastuzumab treated tumors compared to control tumors. Ongoing studies are evaluating spatial variations in myeloid infiltration (CD11c, F4/80), hypoxia (pimonidazole), and vascular maturation index (ratio of alpha-smooth muscle actin to total CD31 stained vessel count) through immunohistochemistry as well as comparing myeloid infiltration in trastuzumab-treated and control mice on day 7. Conclusion: Quantifying trastuzumab induced immune-modulation will provide mechanistic insight into how trastuzumab alters the TME and improves tumor sensitivity to treatment. This information will be of great importance to identifying optimal windows to administer combination therapies as well as in the development of novel immunotherapies in breast cancer. We acknowledge the support of CPRIT RR160005, NCI R01CA186193, and ACS RSG-18-006-01-CCE. Citation Format: Bloom MJ, Jarrett AM, Triplett TA, Syed AK, Yankeelov TE, Sorace AG. Investigating trastuzumab-induced myeloid cell alterations for improving combination therapy in HER2+ breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P4-06-17.

Upon recognition of auto-antigens, thymocytes are negatively selected or diverted to a regulatory T cell (Treg) fate. CCR7 is required for negative selection of auto-reactive thymocytes in the thymic medulla. Here, we describe an unanticipated contribution of CCR7 to intrathymic Treg generation. Ccr7(-/-) mice have increased Treg cellularity because of a hematopoietic but non-T cell autonomous CCR7 function. CCR7 expression by thymic dendritic cells (DCs) promotes survival of mature Sirpα(-) DCs. Thus, CCR7 deficiency results in apoptosis of Sirpα(-) DCs, which is counterbalanced by expansion of immature Sirpα(+) DCs that efficiently induce Treg generation. CCR7 deficiency results in enhanced intrathymic generation of Tregs at the neonatal stage and in lymphopenic adults, when Treg differentiation is critical for establishing self-tolerance. Together, these results reveal a complex function for CCR7 in thymic tolerance induction, where CCR7 not only promotes negative selection but also governs intrathymic Treg generation via non-thymocyte intrinsic mechanisms. ispartof: Cell Reports vol:21 issue:1 pages:168-180 ispartof: location:United States status: published

Introduction: Trastuzumab is a targeted antibody to the human epidermal growth factor receptor 2 (HER2) that induces cell cycle arrest and is used in the treatment of HER2+ positive breast cancer. We have recently presented in vivo evidence in a murine model that trastuzumab also improves vascular delivery of subsequent cytotoxic therapies. The mechanism by which trastuzumab and the immune system interact to regulate tumor-associated angiogenesis is not well characterized. Therefore, we offer a preliminary report on a mathematical framework to systematically investigate the potential interactions among the immune response, tumor cells, vasculature, and other environmental factors based on experimental data for the BT474 murine model of HER2+ breast cancer. Experimental: BT474 breast cancer cells were implanted subcutaneously into athymic nude mice. After tumors reached 250 mm3, mice were treated with trastuzumab or saline, tumor volumes were recorded, and tumors were extracted at various times over seven days. Immunohistochemistry for treated and control tumors were evaluated for 0, 1, 3, 4, and 7 days post trastuzumab treatment. Histology data includes: percent hypoxia (pimonidazole), percent necrosis, and vascular maturation index (VMI, ratio of alpha-smooth muscle actin to total vessel counts as stained with CD31). Ongoing studies are quantifying immune cell infiltration through immunofluorescent imaging of F4/80 and CD11c expression. Modeling: We developed a system of five coupled, ordinary differential equations that accounts for the temporal variation in tumor growth, vasculature, hypoxia, necrosis, and immune response. The general immune response component corresponds to the mouse's pro-inflammatory responses, as T cell driven responses are absent in this murine model. Uncertainty analysis was performed to verify plausible overlap between the model's predictions and the experimental data—where local and global samplings of all parameters were used to generate potential model results to be compared to the data for both control and treated mouse sets. Sensitivity analysis was performed using Sobol' Indices to determine the driving parameters of the system to identify target parameters for experimental estimation. The model parameters were calibrated using mean and standard deviations for the available data (tumor volume, VMI, percentage of hypoxia, and percentage of necrosis) for each experimental time point to predict the differences of the immune component between the treated and control tumors. Results and Discussion: The model is well behaved and can be calibrated with the available data. The model predicts distinct differences for the immune response between the control and treated groups—showing increasing versus decreasing immune component values over time for treated versus control results, respectively. Preliminary results from the immunofluorescent imaging data support the immunological predictions of the model; in particular, the amount of immune infiltration (i.e., more immune cells) in necrotic areas is greater in the treated than the untreated tumors (p We acknowledge the support of CPRIT RR160005 and NCI R01CA186193. Citation Format: Jarrett AM, Yankeelov TE, Ehrlich LI, Godfrey W, Sorace AG. A mathematical model for predicting immune response in a trastuzumab treated HER2+ breast cancer animal model: Preliminary efforts [abstract]. In: Proceedings of the 2017 San Antonio Breast Cancer Symposium; 2017 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2018;78(4 Suppl):Abstract nr P3-05-16.

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., Graphical Abstract ‘Two Beasts’ (2017) Artist: Ben Day Todd. Acrylic, gouache on canvas ’Two Beasts’ is an exploration of form and colour. By adding and subtracting paint, pushing and pulling colour, new information is found and previously unknown dialogues are recorded.