Selection, calibration, and validation of models of tumor growth

Abstract

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as “model agnostic” in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology (in vivo). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction–diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory animals while demonstrating successful implementations of OPAL.

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

“…The present investigation extends the work in [29] to the prediction of effects of X-ray radiation applied to a murine model of brain cancer. New models of the decline in tumor cell proliferation due to radiation are presented and calibrated against dynamic contrast-enhanced MRI (DCE-MRI) data.…”

“…To lay down notation and preliminaries to the analysis and developments described in later sections, we provide here a brief account of a framework for predictive modeling based on Bayesian inference and statistical inverse analysis that is drawn from earlier work (e.g., [35, 29, 16, 33, 21, 32, 34]). As noted in the introduction, the goal is to develop tools and algorithms for predictive modeling in the presence of uncertainties, including uncertainties in the observational data, in the selection of plausible models from a set $ℳ$ of proposed models (large families of various reaction-diffusion and phase-field models with different characterizations of the effects of radiotherapy), model parameters, which are generally represented by probability distributions, and target quantities of interest (QoIs).…”

“…Examples of the use of imaging data to ascertain the predictivity of tumor growth models can be found in [2, 1, 29, 45, 46, 43, 42, 41]. In this study, we make use of contrast-enhanced MRI to identify the boundaries of the tumor.…”

“…In Lima et al [29], a general framework and process for selecting and validating predictive phenomenological models of tumor growth in living tissue was put forth in the form of an adaptive algorithm referred to as OPAL: the Occam Plausibility Algorithm, described in [16, 33]. The algorithm attempts to address and quantify uncertainties in model selection, observational data, and model parameters and to address model inadequacy and parameter sensitivity, while also quantifying uncertainties in outputs – the quantities of interest.…”

Calibração de um Modelo de Crescimento Tumoral Avascular

“…Dentre os estudos realizados, alguns têm como enfoque o desafio da construção de modelos matemáticos preditivos, como em [3][4][5]. Para que um modelo seja preditivo, istoé, capaz de predizer o fenômeno que se propõe a representar,é necessário considerar três etapas:…”