Toward Predictive Multiscale Modeling of Vascular Tumor Growth

Abstract

New directions in medical and biomedical sciences have gradually emerged over recent years that will change the way diseases are diagnosed and treated and are leading to the redirection of medicine toward patientspecific treatments. We refer to these new approaches for studying biomedical systems as predictive medicine, a new version of medical science that involves the use of advanced computer models of biomedical phenomena, high-performance computing, new experimental methods for model data calibration, modern imaging technologies, cutting-edge numerical algorithms for treating large stochastic systems, modern methods for model selection, calibration, validation, verification, and uncertainty quantification, and new approaches for drug design and delivery, all based on predictive models. The methodologies are designed to study events at multiple scales, from genetic data, to sub-cellular signaling mechanisms, to cell interactions, to tissue physics and chemistry, to organs in living human subjects. The present document surveys work on the development and implementation of predictive models of vascular tumor growth, covering aspects of what might be called modeling-and-experimentally based computational oncology. The work described is that of a multi-institutional team, centered at ICES with strong participation by members at M. D. Anderson Cancer Center and University of Texas at San Antonio. This exposition covers topics on signaling models, cell and cell-interaction models, tissue models based on multi-species mixture theories, models of angiogenesis, and beginning work of drug effects. A number of new parallel computer codes for implementing finite-element methods, multi-level Markov Chain Monte Carlo sampling methods, data classification methods, stochastic PDE solvers, statistical inverse algorithms for model calibration and validation, models of events at different spatial and temporal scales is presented. Importantly, new methods for model selection in the presence of uncertainties fundamental to predictive medical science, are described which are based on the notion of Bayesian model plausibilities. Also, as part of this general approach, new codes for determining the sensitivity of model outputs to variations in model parameters are described that provide a basis for assessing the importance of model parameters and controlling and reducing the number of relevant model parameters. Model specific data is to be accessible through careful and model-specific platforms in the Tumor Engineering Laboratory. We describe parallel computer platforms on which large-scale calculations are run as well as specific time-marching algorithms needed to treat stiff systems encountered in some phase-field mixture models. We also cover new non-invasive imaging and data classification methods that provide in vivo data for model validation. The study concludes with a brief discussion of future work and open challenges.

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

“…To achieve this, Statistics (namely Bayesian inference) and Machine Learning methods [42][43][44][45][46][47] have been leveraged for a few years. The Bayesian paradigm, in particular, enables the enrichment of prior (expert) knowledge about the system with new data, as it is being acquired.…”

“…In this field, it is necessary to infer the best possible model for a patient from a priori knowledge obtained from other patients. Successful approaches have been recently published [19,47] which enable predictive science in Medicine, for example for lasertreatment of tumours [42]. The reader is referred to [47] for a recent discussion of the emerging field known as "ComputerGuided Predictive Medicine", to [52] for applications to brain tumour model personalisation and to [53] for sparse Bayesian image registration.…”

Computational Phase‐Field Modeling

“…In particular, we consider avascular tumor growth, which is the growth of cancerous tumors without blood vessels. Phase-field tumor growth models have recently been proposed; see, e.g., (Cristini et al, 2009), (Lowengrub et al, 2010) and (Oden et al, 2015). Thermomechanical derivations of such models have been considered in (Wise et al, 2008), (Oden et al, 2010) and (Hawkins-Daarud et al, 2012).…”

A monolithic multiphase porous medium framework for (a-)vascular tumor growth

“…Two very prominent and often re-used methods are the ones developed by [30], where a continuum approach has been compared to a continuum-discrete approach based on a random walk formulation including migration, proliferation, branching and anastomosis. While earlier attempts did not include a dynamic coupling between angiogenesis and tumor growth, more advanced vascular tumor growth models such as [31][32][33] have evolved.…”