Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data

• Published in: Computer methods in applied mechanics and engineering Vol. 327; no. C; pp. 277 - 305
• Main Authors: Lima, E.A.B.F., Oden, J.T., Wohlmuth, B., Shahmoradi, A., Hormuth, D.A., Yankeelov, T.E., Scarabosio, L., Horger, T.
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.12.2017; Elsevier BV; Elsevier
• Subjects: Bayesian analysis; Bayesian inference; Calibration and Validation of Phenomenological models; Cancer; Computer simulation; Deformation effects; Finite element method; Markov chains; Mathematical models; Model plausibilities; Monte Carlo methods; Monte Carlo simulation; MRI imaging; Nonlinear differential equations; Nonlinear equations; Numerical analysis; Parameter uncertainty; Partial differential equations; Prediction models; Radiation effects; Radiation therapy; Studies; Tumors; Vascular tissue; Model plausibilities; Monte Carlo methods; Calibration and Validation of Phenomenological models; MRI imaging; Bayesian inference; Cancer; statistical sampling; phenomenological models; radiotherapy; model plausibilities; calibration; validation
• DOI: 10.1016/j.cma.2017.08.009
• ISSN: 0045-7825

The use of mathematical and computational models for reliable predictions of tumor growth and decline in living organisms is one of the foremost challenges in modern predictive science, as it must cope with uncertainties in observational data, model selection, model parameters, and model inadequacy, all for very complex physical and biological systems. In this paper, large classes of parametric models of tumor growth in vascular tissue are discussed including models for radiation therapy. Observational data is obtained from MRI of a murine model of glioma and observed over a period of about three weeks, with X-ray radiation administered 14.5 days into the experimental program. Parametric models of tumor proliferation and decline are presented based on the balance laws of continuum mixture theory, particularly mass balance, and from accepted biological hypotheses on tumor growth. Among these are new model classes that include characterizations of effects of radiation and simple models of mechanical deformation of tumors. The Occam Plausibility Algorithm (OPAL) is implemented to provide a Bayesian statistical calibration of the model classes, 39 models in all, as well as the determination of the most plausible models in these classes relative to the observational data, and to assess model inadequacy through statistical validation processes. Discussions of the numerical analysis of finite element approximations of the system of stochastic, nonlinear partial differential equations characterizing the model classes, as well as the sampling algorithms for Monte Carlo and Markov chain Monte Carlo (MCMC) methods employed in solving the forward stochastic problem, and in computing posterior distributions of parameters and model plausibilities are provided. The results of the analyses described suggest that the general framework developed can provide a useful approach for predicting tumor growth and the effects of radiation. •This paper presents a comprehensive approach to predict the growth of tumors in laboratory animals accounting for uncertainties in data, model selection, model inadequacy, and in model outputs.•Systems of stochastic partial differential equations are derived that characterize models of volume fractions of cell species, mechanical effects, and chemical potentials that depict the evolution of tumor masses.•Non-invasive MRI data on the growth of glioma in the brains of rat subjects are collected to provide a basis for model calibration, validation, and prediction using Bayesian methods.•The Occam Plausibility Algorithm is implemented to determine plausible models and valid models of tumor growth that include the effects of X-ray therapy on tumor viability.•Applications to tumor predictions in two dimensions, corresponding to MRI-tomographic slices, are discussed as well as three-dimensional simulations performed with a model proven valid in the 2D calculations.