Book Description

Cancer is a major life threatening disease in the world. With the advancement of computational mathematics, big data science and unprecedented computational power, it becomes possible to investigate the complex multiscale growth phenomenon of the tumor for cancer prognosis to provide pre-operative treatment planning and predict treatment outcome using mathematical modeling and computer simulation. The growth of biological tissue is a complex process because it involves various biophysically- and biochemically-induced events at different spatial and temporal scales. Multiscale modeling techniques allow us to incorporate important features at multiple scales to examine the tissue growth mechanism and determine the major factors affecting the growth process. The primary objective of this doctoral research is to develop a multiscale modeling framework for the growth of biological tissue and apply to tumor growth and cancer prognosis. Another objective of this study is to understand the effect of anticancer drugs on cancer cell growth, cell proliferation, and overall tumor size. The multiscale framework consists of a tissue scale model, a cellular activity and growth model and a subcellular signaling pathway model. To predict the tissue growth in the macroscopic (tissue) scale, a continuum model is constructed where the biological tissue is represented as a mixture of multiple constituents. Each of such constituents, in their solid, liquid or gas phase, are represented by either a volume fraction or concentration. The constituents interact with each other through mass and momentum exchange. The governing equations are developed based on both mass and momentum conservation laws. The constitutive equations account for tissue anisotropy, nonlinear behavior, and thermodynamic consistency. The system of partial differential equations are solved using finite element techniques. To bridge the spatial scales, each finite element is further discretized into finer cell clusters of different kinds to represent various biological cellular states at the microscopic scale to model cellular growth and proliferation by using an agent-based model to determine various activities at the cellular scale such as the cell division, cell death, phenotypical alteration, etc. The cellular scale events are also broken down and discretized temporally to model the effects of a subcellular signaling pathway (e.g. PI3K/AKT/mTOR pathway, also known as mTOR pathway) on the cellular and tissue scales. In many cancers, mTOR pathway becomes hyperactive and promotes abnormal cell proliferation. The mechanism and effects of an mTOR inhibiting drug known as rapamycin (e.g., eRapa) are tested using in silico methods. These subcellular activities are modeled using a set of ordinary differential equations. A statistical inverse algorithm is used for model calibration and validation. The Bayesian inference method accounts for the uncertainties of the model parameters, which are calibrated with the experimental observations. Generally speaking, the multiscale modeling framework presented in this dissertation may provide better understanding of the tissue growth process by providing insight on the effects of various factors at different spatiotemporal scales. It can also be potentially used to construct patient-specific tissue growth models for in silico drug testing, treatment planning, and prognosis.