Using Dynamic Active Subspaces to Construct Surrogate Models for Calibrating Tumor Growth Models to Data

Abstract

While the use of complex ODE models describing tumor growth and tumor-immune interactions may be desirable for accurately representing the biological mechanisms that govern tumor growth, the high-dimensionality of the parameter space can make it difficult to uniquely identify optimal parameter estimates during model calibration. Construction of a surrogate model that can accurately approximate the quantity of interest with fewer parameters may enable us to fit this alternate model to the data in place of the original ODE system. In this investigation, we consider how active subspaces may be used to construct time-dependent surrogate models with reduced parameter dimension, and analyze the trade-offs in parameter identifiability, model fit error, and computational run-time to provide a roadmap for ensuring an identifiable parameter set during model calibration.