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© 2021, The Association for Women in Mathematics and the Author(s). Recent technological advances make it possible to collect detailed information about tumors, and yet clinical assessments about treatment responses are typically based on sparse datasets. In this work, we propose a workflow for choosing an appropriate model, verifying parameter identifiability, and assessing the amount of data necessary to accurately calibrate model parameters. As a proof-of-concept, we compare tumor growth models of varying complexity in an effort to determine the level of model complexity needed to accurately predict tumor growth dynamics and response to radiotherapy. We consider a simple, one-compartment ordinary differential equation model which tracks tumor volume and a two-compartment model that accounts for tumor volume and the fraction of necrotic cells contained within the tumor. We investigate the structural and practical identifiability of these models, and the impact of noise on identifiability. We also generate synthetic data from a more complex, spatially-resolved, cellular automaton model (CA) that simulates tumor growth and response to radiotherapy. We investigate the fit of the ODE models to tumor volume data generated by the CA in various parameter regimes, and we use sequential model calibration to determine how many data points are required to accurately infer model parameters. Our results suggest that if data on tumor volumes alone is provided, then a tumor with a large necrotic volume is the most challenging case to fit. However, supplementing data on total tumor volume with additional information on the necrotic volume enables the two compartment ODE model to perform significantly better than the one compartment model in terms of parameter convergence and predictive power.

Original publication





Book title

Association for Women in Mathematics Series

Publication Date





179 - 216