Characterizing Tumor Cell Movement in Partial Differential Equation Models of Triple-Negative Breast Cancer Receiving Neoadjuvant Therapy
Year: 2026
Type: article
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.
Source: Annals of Biomedical Engineering
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,390
Funders: National Science Foundation, Conquer Cancer Foundation, Cancer Prevention and Research Institute of Texas, University of Texas at Austin, Ministerio de Ciencia, Innovación y Universidades, National Institutes of Health, University of Texas MD Anderson Cancer Center, Agencia Estatal de Investigación, National Cancer Institute, European Social Fund, National Science Foundation Graduate Research Fellowship Program
Awards: G1236882788, Quantitative MRI for Predicting Response of Breast Cancer to Neoadjuvant Therapy, INTEGRATING OMICS AND QUANTITATIVE IMAGING DATA IN CO-CLINICAL TRIALS TO PREDICT TREATMENT RESPONSE IN TRIPLE NEGATIVE BREAST CANCER, G3480869486, G4267969883, Graduate Research Fellowship Program (GRFP), G4843297652, G5580968180, G5635532810, G6601967047, G661330594, Imaging-informed, biophysical computational modeling to forecast tumor progression in gliomas, FDT-BioTech: A digital twin framework for developing and analyzing virtual patient cohorts to enable virtual clinical trials, G882206014, G946978917
OpenAlex ID: W7204950928