Characterizing Tumor Cell Movement in Partial Differential Equation Models of Triple-Negative Breast Cancer Receiving Neoadjuvant Therapy

Abstract

[Abstract] Purpose: Approximately half of triple-negative breast cancer (TNBC) patients attain a complete response to neoadjuvant therapy (NAT). Thus, methods to predict and optimize NAT response are essential to improving patient outcomes. Methods: Previously, mathematical models with a reaction term describing cell growth and death and a diffusion term describing cell invasion have accurately forecasted NAT response but have had limited flexibly in capturing cell movement. We investigate the relative contributions of reaction, diffusion, and advection terms in predicting TNBC response to NAT. We compare a reaction-only model to three models capturing cell movement using advection and diffusion terms that can be coupled to tissue mechanics. Results: When compared to a reaction-only model, the reaction–diffusion model did not improve calibration or prediction accuracy for tumor volume or cell count. For example, the median absolute difference between the predicted and measured percent change in tumor volume across the cohort was 9.1% for both models. While computationally burdensome, the reaction–diffusion–advection model provided significantly (p < 0.05) more accurate calibrations and offered a small (e.g., 4-5% reduction in tumor volume error), but not significant, improvement in predictive accuracy for non-responding patients. Conclusion: These results suggest (i) a reaction-only model can provide fast predictions with equivalent accuracy to a reaction–diffusion model but cannot characterize an expanding tumor and (ii) the reaction–diffusion–advection model is the most accurate but is computationally burdensome. These insights could inform computational methods balancing the efficiency of the reaction-only model with the accuracy of the reaction–diffusion–advection model to guide clinical NAT decisions.