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Introduction: Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant systemic therapy (NAST). However, the response of TNBC to NAST is varied and a prognostic marker is still lacking. Since angiogenesis plays an important role in cancer progression, the quantification of changes in the tumor vasculature during treatment has the potential to provide useful information for characterizing the treatment response. We have recently developed a method to quantify changes in tumor-associated vasculature through a novel analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). In this study, we investigated its ability to monitor the response of TNBC to NAST. Methods: Dynamic contrast-enhanced (DCE) MRI was acquired in TNBC patients (N = 50; 25 pathological complete response (pCR), 25 non-pCR) before, after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C), as part of the ARTEMIS trial (NCT02276433). Using DCE-MRI, we identified the tumor-associated vessels via a breast vasculature analysis. Specifically, the difference between pre- and post-contrast DCE-MRI images was enhanced by a histogram-based intensity transfer function. The 3D vasculature in the breast was then segmented by applying a Hessian filter. Given the vasculature segmented by the algorithms and the tumor masks segmented by radiologists, a lowest-cost tracking algorithm was used to automatically detect the vessels that are most likely to contact the tumor. These vessels are defined as tumor-associated vessels (TAV). The number of TAVs per patient was tabulated and the Wilcoxon rank sum test compared the TAV values before (V1), after 2 cycles (V2), and after 4 cycles of NAST (V3). Additionally, we compared the percent change of TAV from V1 to V3 between the pCR patients and non-pCR patients. Statistical significance was defined as P < 0.05. Results: A significant decrease in the number of TAVs was observed during the NAST. In particular, the number of TAVs has a median (interquartile range) of 15 (7 - 24), 7 (3 - 14), and 2 (0 - 8) at V1, V2, V3, respectively, which are (pair-wise) significantly different (P < 0.01). Moreover, pCR patients showed a significantly greater decrease in the number of TAVs as compared to non-pCR patients. The percent changes in the number of TAVs from V1 to V3 have a median (range) of -88.89% (-100.00% - -60.00%) and -66.67% (-87.85% - -40.88%) in the pCR and non-pCR patients, respectively (P < 0.05). Conclusion: These preliminary results demonstrate that tumor-associated vasculature may be a valuable imaging biomarker for monitoring the response of TNBC to NAST. Ongoing efforts include additional investigation of the TAVs beyond their number, as well as applying the analysis to more patients. Citation Format: Chengyue Wu, Casey E. Stowers, Zhan Xu, Ernesto A. B. F. Lima, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Quantification of tumor-associated vasculature as an imaging biomarker for monitoring the response of triple-negative breast cancer to neoadjuvant chemotherapy. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5569.

Introduction: We show that the combination of quantitative magnetic resonance imaging (MRI) and mathematical modeling can accurately predict tumor response for individual patients, and we demonstrate the selection of personalized therapeutic regimens using our mathematical model to vary, in silico, a range of clinically feasible treatment plans to achieve the greatest tumor control. Methods: Breast cancer patients (N = 18) were scanned by MRI at three time points during neoadjuvant therapy (NAT): 1) prior to NAT, 2) after one cycle of their initial NAT regimen, and 3) after the completion of their initial NAT regimen. Specifically, diffusion-weighted MRI data characterizing tumor cellularity was collected to estimate tumor cell burden, and dynamic contrast-enhanced MRI data was collected to estimate the local drug delivery using pharmacokinetic analysis and population-derived plasma curves of the administered chemotherapies. To predict tumor response, we calibrated our tissue scale, 3D, biophysical mathematical model to each patient's MRI data set using their first two scans. Using the calibrated, patient-specific parameters, the model was projected forward to the third scan time. The predicted total tumor cellularity, volume, and longest axis were compared to the actual values measured from the patient's third scan. Following evaluation of the model's predictive ability, we then employed the model to identify potentially superior, clinically relevant, alternative dosing regimens for each patient. The alternative regimens were defined using the same total amount of drug each patient received during their standard regimen, while varying dosages and frequency between their second and third scans. Statistical analysis was completed with Pearson correlation and Wilcoxon signed rank test. Results: The model's predictions of tumor response are significantly correlated to the measured tumor burden at the time of scan 3 (r2 > 0.88, p < 0.01) for total cellularity, total volume, and longest axis. For the alternative dosing regimens assessed, the model predicted that individual patients could have achieved, on average, an additional 21% (0-46%) reduction in total cellularity. The optimal dosing regimens chosen by the model were predicted to significantly outperform standard regimens for tumor control (p < 0.001). Conclusions: These results suggest that the mathematical model can be predictive of tumor response by MRI in the clinical setting using data at the earliest times of therapy. With in silico studies, we illustrate how therapeutic regimens can be selected for individual patients for better tumor control, revealing that standard regimens may not be the most effective for every patient. These results represent a first step towards mathematically-based, personalized patient regimens. Future work aims to optimize therapy regimens via established optimal control theory methods. Citation Format: Angela M. Jarrett, Ernesto A. Lima, David A. Hormuth, Chengyue Wu, John Virostko, Anna G. Sorace, Julie C. DiCarlo, Debra Patt, Boone Goodgame, Sarah Avery, Thomas E. Yankeelov. Patient-specific neoadjuvant regimens for breast cancer identified via image-driven mathematical modeling [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 5485.

Like every biological process, tumor development is not purely deterministic, as it is subject to random perturbations from the environment. Moreover, mathematical and computational tumor growth models are subject to uncertainties in the parameters, which may arise from experimental variations or intratumor and intrapatient heterogeneities. Tumor growth models are typically deterministic representations of growth, neglecting the aforementioned uncertainties. However, carcinogenesis must be modeled as a stochastic process to generate more informative predictions of the tumor microenvironment, which is particularly important when describing the action of various therapies. The model developed here aims to reflect the stochastic proliferation and differentiation of tumor cells. We present, for the first time, a methodology for performing a stochastic calibration of an agent-based tumor growth model. The agent-based model reproduces the interactions among different tumor cell phenotypes (e.g., proliferative and dead cells). The cell movement is driven by the balance of a variety of forces (e.g., cell-cell adhesion and repulsion) according to Newton’s second law. Transitions among cell phenotypes are defined by rules that depend on glucose concentration and time spent in each phase of cell cycle. The model captures the phenomena at the cell scale, tracking the velocity, position, and confluence, as well as the glucose concentration in the microenvironment. The experiments were done using a HER2+ breast cancer line (BT-474). Cells were seeded at a density of 3.2×104, 4.0×104 and 4.8×104 cells/well on a 96-well tissue culture plate, with four glucose levels (0, 2, 5 and 10 mM), and four replicates for each combination of initial density and glucose levels. The cells were incubated in the IncuCyte live cell imaging system (Essen BioScience, USA). Multiple images were acquired and stitched together automatically by this system with a 4× objective to obtain whole well images for each well. IncuCyte Cytotox Red Reagents (Essen BioScience, USA), a highly sensitive cyanine nucleic acid dye was added into the medium to estimate cell death. The wells were imaged every 2 hours and cell segmentation was performed in Matlab (The Mathworks, Inc., USA). Segmented images from phase-contrast and fluorescent images were employed to determine the confluence of the live cells. The dead and live cells from our agent-based model were calibrated using a Bayesian framework. The likelihood used during the calibration process considers the stochasticity from our model and the variance in the in vitro experiments. Preliminary efforts indicate the average difference between the calibrated model and the experimental data is below 5.6±4.5%. The results of the proposed model suggest that the computational framework developed can correctly calibrate the agent-based model while considering the stochasticity of the model and data. Citation Format: Ernesto A. Lima, Danial Faghihi, Russel Philley, Jianchen Yang, Jack Virostko, Thomas E. Yankeelov. Stochastic calibration of an agent-based tumor growth model using time-resolved microscopy data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 2446.

As a result of the highly heterogeneous tumor microenvironment and a series of complex phenomena that occur at different scales, several modeling approaches have emerged. The tumor growth models can be categorized by the behaviors they aim to capture, the hallmarks of cancer that are being considered, and the temporal and biological scales represented. Moreover, these models can also be differentiated according to the mathematical framework that is being employed, being either discrete models, continuum models, or hybrid models. Therefore, with this large set of possible models, and with each model choice having many unknown parameters, it is important to develop an adaptive model selection and validation framework in order to choose the best model for the desired application. In this work, we employ the Occam Plausibility Algorithm (OPAL) framework [1] for model selection and validation of a large body of tumor growth models. We select several continuum tumor growth models, half of them using the phase-field modeling approach, derived from the models developed in [2], and the other half being reaction-diffusion type models derived from [3]. The OPAL framework brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Firstly, we identify the model classes and compute the sensitivity of the quantity of interest (QoI), here the tumor volume as a function of time. The models with parameters that do not influence the QoI are eliminated. The next step consists in dividing the models into Occam categories according to their number of parameters, where the models with fewer parameters are assembled to category 1. Following the principle of Occam's Razor, one of main goals of OPAL is to select the simplest model among the several models that leads to the same prediction. The models from the first category are calibrated using Bayes' rule for a specific calibration scenario. The next step is to compute the plausibilities for the models in this category and choose the most plausible model. Finally, with the most plausible model known, we solve the problem in the validation scenario. The model is valid depending on the accuracy with which the model predictions of the QoI agree with experimental data. If the model is not valid, we move to the next category; otherwise, we select this model as being the simplest and the most plausible valid model. We demonstrate that the OPAL is able to assist in the selection of the best tumor growth model from a defined set of models. The model selected is valid for particular scenarios. In this work, we consider avascular tumor growth models to reproduce the data obtained in a murine model of glioma growth. The brain data is generated with diffusion weighted magnetic resonance imaging over a period of ten days. The methodologies and results confirm that the OPAL strategy provides a powerful framework for model selection, parameters estimation, and model validation in the presence of uncertainties. References [1] K. Farrell, J. T. Oden, and D. Faghihi. A bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems. J Comput Phys, 295(0):189 - 208, 2015. [2] E. A. B. F. Lima, J. T. Oden, and R. C. Almeida. A hybrid ten-species phase-field model of tumor growth. Math Mod Meth Appl S, 24(13):2569-2599, 2014. [3] J. A. Weis, M. I. Miga, L. R. Arlinghaus, X. Li, A. B. Chakravarthy, V. Abramson, J. Farley, and T. E. Yankeelov. A mechanically coupled reaction-diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy. Phys Med Biol, 58(17):5851-66, 2013. Citation Format: Ernesto A. B. F. Lima, Regina C. Almeida, David A. Hormuth, Thomas E. Yankeelov, J. T. Oden. Calibration, selection and validation of tumor growth models. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A11.