Abstract A11: Calibration, selection and validation of tumor growth models
Authors: Lima Ernesto A. B. F. , Almeida Regina C. , Hormuth David A. , Yankeelov Thomas E. , Oden J. T. 
Published: March 2017

Abstract
As a result of the highly heterogeneous tumor microenvironment and a series of complex phenomena that occur at different scales, several modeling approaches have emerged. The tumor growth models can be categorized by the behaviors they aim to capture, the hallmarks of cancer that are being considered, and the temporal and biological scales represented. Moreover, these models can also be differentiated according to the mathematical framework that is being employed, being either discrete models, continuum models, or hybrid models. Therefore, with this large set of possible models, and with each model choice having many unknown parameters, it is important to develop an adaptive model selection and validation framework in order to choose the best model for the desired application.
In this work, we employ the Occam Plausibility Algorithm (OPAL) framework [1] for model selection and validation of a large body of tumor growth models. We select several continuum tumor growth models, half of them using the phase-field modeling approach, derived from the models developed in [2], and the other half being reaction-diffusion type models derived from [3]. The OPAL framework brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Firstly, we identify the model classes and compute the sensitivity of the quantity of interest (QoI), here the tumor volume as a function of time. The models with parameters that do not influence the QoI are eliminated. The next step consists in dividing the models into Occam categories according to their number of parameters, where the models with fewer parameters are assembled to category 1. Following the principle of Occam's Razor, one of main goals of OPAL is to select the simplest model among the several models that leads to the same prediction. The models from the first category are calibrated using Bayes' rule for a specific calibration scenario. The next step is to compute the plausibilities for the models in this category and choose the most plausible model. Finally, with the most plausible model known, we solve the problem in the validation scenario. The model is valid depending on the accuracy with which the model predictions of the QoI agree with experimental data. If the model is not valid, we move to the next category; otherwise, we select this model as being the simplest and the most plausible valid model.
We demonstrate that the OPAL is able to assist in the selection of the best tumor growth model from a defined set of models. The model selected is valid for particular scenarios. In this work, we consider avascular tumor growth models to reproduce the data obtained in a murine model of glioma growth. The brain data is generated with diffusion weighted magnetic resonance imaging over a period of ten days.
The methodologies and results confirm that the OPAL strategy provides a powerful framework for model selection, parameters estimation, and model validation in the presence of uncertainties.
References
[1] K. Farrell, J. T. Oden, and D. Faghihi. A bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems. J Comput Phys, 295(0):189 - 208, 2015.
[2] E. A. B. F. Lima, J. T. Oden, and R. C. Almeida. A hybrid ten-species phase-field model of tumor growth. Math Mod Meth Appl S, 24(13):2569-2599, 2014.
[3] J. A. Weis, M. I. Miga, L. R. Arlinghaus, X. Li, A. B. Chakravarthy, V. Abramson, J. Farley, and T. E. Yankeelov. A mechanically coupled reaction-diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy. Phys Med Biol, 58(17):5851-66, 2013.
Citation Format: Ernesto A. B. F. Lima, Regina C. Almeida, David A. Hormuth, Thomas E. Yankeelov, J. T. Oden. Calibration, selection and validation of tumor growth models. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A11.