(F-232) Introducing mechanical stress into a reduced order model for breast cancer response to chemotherapy

Introduction:: Mechanical stresses that develop in the tumor microenvironment as breast tumors grow or shrink have previously been found to significantly alter the growth patterns of these cancers. The mechanical balance of developing force and stress and its effect on tumor development can be included in a spatial tumor model. Our lab has shown that a mechanically-coupled mathematical model can successfully be calibrated to predict the response of locally advanced breast cancer to neoadjuvant therapy. However, this process is computationally expensive and difficult to solve without access to parallelized high-performance computing resources. To address this practical issue, we aim to develop a reduced order method that can evaluate this equation faster and be included in a patient-specific calibration to estimate parameters.


Materials and Methods:: We will use imaging data from 50 patients, consisting of pre-treatment magnetic resonance imaging (MRI), and two follow-up MRI scans. The imaging protocol includes diffusion weighted MRI, to inform tumor cellularity, and dynamic contrast enhanced MRI, to inform drug concentrations. The mathematical model is based on a reaction diffusion equation which describes tumor invasion, cell proliferation, and treatment effects [1]. The local stress tensors are solved under a linear elastic assumption, utilizing the cell gradients as the body force, and then converted to a von Mises stress. The stress estimates are then used to reduce tumor invasion locally based on their magnitude.



We use a projection-based method to build the reduced order model (ROM) , with data derived from patient-specific images serving as the snapshot matrix. For the calibration framework, we need three different bases to project different portions of the coupled equations. The first basis is used to reduce the state, forward evaluation, and spatially varying proliferation maps, the second reduces the mechanical stress solve, and the third reduces the spatially varying diffusivity maps. The reduced model is then calibrated to patient-specific images and used to predict (and ultimately optimize) future response. A calibrated full order model (FOM) is also utilized to validate the performance of the reduced framework.


Results, Conclusions, and Discussions:: Results: Working under the linear-elastic assumption allows for high accuracy of the reduced stress solver. Stress maps from reduced method achieved a concordance correlation coefficient (CCC) of 1.00 compared to the full order solve, with the total time being 15× faster in 2D, and 30× faster in 3D. The fast stress calculation led to an overall speed increase of 35× for the mechanically coupled model in 2D, and 40× in 3D. This speed increase is directly incorporated into the patient-specific calibration but adds an additional offline-stage for initializing the ROM.

For the 50-patient dataset, calibrations yielded a CCC of 0.99 between the FOM and ROM results for both change in tumor volume and change in cellularity estimates from all patients. At the local level, the percent difference between the FOM and ROM calibrated maps from all patients achieved a mean absolute percent difference (25%, 75% IQR) of 3.1% (1.7%, 5.2%). Predicting forward in time resulted in a slight drop in accuracy between the two methods, where CCC = 0.94 for change in tumor volume and CCC = 0.93 for change in tumor cellularity. The mean absolute percent difference in the predictions is 3.2% (1.6%, 6.8%). The overall calibration time decreased by over 10× for 2D, and 5× for 3D, when utilizing the ROM. The offline stage consists of 80% of the ROM calibration time.

Discussion: This method requires data from a pre-treatment imaging session, and just a single post-treatment session, allowing for rapid predictions of response for guiding future therapeutic interventions. Future work includes the development of an optimal control framework utilizing the estimated parameters to optimize follow-up interventions for each patient.

Conclusions: We have shown that reduced order modeling can be applied to a mechanically-coupled model describing breast tumor growth to reduce the overall time for completion of a model simulation. This method was then used to calibrate patient specific parameters with a significant reduction in the total time required. This framework has minimal loss in prediction accuracy compared to the full order method, and results in similar parameters for future use and analysis.


Acknowledgements (Optional): : We thank the NCI for funding through U01CA142565, U01CA174706, and U24CA226110. We thank the Cancer Prevention and Research Institute of Texas for support through CPRIT RR160005. T.E. Yankeelov is a CPRIT Scholar in Cancer Research

References (Optional): : [1] Wu, Chengyue, et al. "MRI-based digital models forecast patient-specific treatment responses to neoadjuvant chemotherapy in triple-negative breast cancer." Cancer Research 82.18 (2022): 3394-3404.