A fully coupled space–time multiscale modeling framework for predicting tumor growth

Abstract

Most biological systems encountered in living organisms involve highly complex heterogeneous multi-component structures that exhibit different physical, chemical, and biological behavior at different spatial and temporal scales. The development of predictive mathematical and computational models of multiscale events in such systems is a major challenge in contemporary computational biomechanics, particularly the development of models of growing tumors in humans. The aim of this study is to develop a general framework for tumor growth prediction by considering major biological events at tissue, cellular, and subcellular scales. The key to developing such multiscale models is how to bridge spatial and temporal scales that range from 10−3 to 103 mm in space and from 10−6 to 107 s in time. In this paper, a fully coupled space–time multiscale framework for modeling tumor growth is developed. The framework consists of a tissue scale model, a model of cellular activities, and a subcellular transduction signaling pathway model. The tissue, cellular, and subcellular models in this framework are solved using partial differential equations for tissue growth, agent-based model for cellular events, and ordinary differential equations for signaling transduction pathway as a network at subcellular scale. The model is calibrated using experimental observations. Moreover, this model is biologically-driven from a signaling pathway, volumetrically-consistent between cellular and tissue scale in terms of tumor volume evolution in time, and a biophysically-sound tissue model that satisfies all conservation laws. The results show that the model is capable of predicting major characteristics of tumor growth such as the morphological instability, growth patterns of different cell phenotypes, compact regions of the higher cell density at the tumor region, and the reduction of growth rate due to drug delivery. The predicted treatment outcomes show a reduction in proliferation at different rates in response to different drug dosages. Moreover, the results of several 3D applications to tumor growth and the evolution of cellular and subcellular events are presented.

How Machine Learning Will Transform Biomedicine

“…Multiscale modeling will use large biological datasets to investigate the growth and development of an organism across diverse temporal and spatial domains. Already there are computational models of human-virus interactions (Lasso et al, 2019), cell-cell interplay such as tumor-immune cell interactions, and even whole cells (Metzcar et al, 2019;Rahman et al, 2017;Sakamoto et al, 2018). Eventually, we anticipate that computational models of organs and entire individuals-so-called ''digital twins'' (Bjö rnsson et al, 2019)-will be developed.…”

Coupling tumor growth and bio distribution models

“…Multi-parameter models are based on mixture theory (Cowin and Cardoso 2012) where the relevant balance equations are written directly at the level of interest and the thermodynamic consistency is satisfied at the same level. The evolution of phases and species within multi-parameter models is obtained either by use of phase field approach (Hawkins-Daarud et al 2013; Lima et al 2016; Lima et al 2015; Oden et al 2016; Oden et al 2013; Oden et al 2010; Rahman et al 2017; Rocha et al 2018; Vilanova et al 2018) or of Volterra-Lotta (predator/prey like) equations (Carotenuto et al 2018; Fraldi and Carotenuto 2018). Recent multiphase models (Kremheller et al 2018; Sciumè et al 2014a; Sciumè et al 2013) are based on the Thermodynamically Constrained Averaging Theory (TCAT) (Gray and Miller 2014) where the model derivation proceeds systematically from known microscale relations to mathematically and physically consistent larger scale relations.…”

Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

“…Most current tumor growth simulation models, such as [56][57][58][59][60][61][62][63] use a diffusing growth factor (e.g., oxygen or glucose) as the main negative feedback on tumor cell proliferation by scaling cell cycling with local substrate availability. As the avascular tumor grows, it consumes and depletes the substrate, thus slowing growth in a negative feedback.…”