Fast model calibration for predicting the response of breast cancer to chemotherapy using proper orthogonal decomposition

Abstract

Constructing digital twins for predictive tumor treatment response models can have a high computational demand that presents a practical barrier for their clinical adoption. In this work, we demonstrate that proper orthogonal decomposition, by which a low-dimensional representation of the full model is constructed, can be used to dramatically reduce the computational time required to calibrate a partial differential equation model to magnetic resonance imaging (MRI) data for rapid predictions of tumor growth and response to chemotherapy. In the proposed formulation, the reduction basis is based on each patient’s own MRI data and controls the overall size of the “reduced order model”. Using the full model as the reference, we validate that the reduced order mathematical model can accurately predict response in 50 triple negative breast cancer patients receiving standard of care neoadjuvant chemotherapy. The concordance correlation coefficient between the full and reduced order models was 0.986 ± 0.012 (mean ± standard deviation) for predicting changes in both tumor volume and cellularity across the entire model family, with a corresponding median local error (inter-quartile range) of 4.36 % (1.22 %, 15.04 %). The total time to estimate parameters and to predict response dramatically improves with the reduced framework. Specifically, the reduced order model accelerates our calibration by a factor of (mean ± standard deviation) 378.4 ± 279.8 when compared to the full order model for a non-mechanically coupled model. This enormous reduction in computational time can directly help realize the practical construction of digital twins when the access to computational resources is limited.