Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.

Cancer is a complex disease process that spans multiple scales in space and time. Driven by cutting-edge mathematical and computational techniques, in silico biology provides powerful tools to investigate the mechanistic relationships of genes, cells, and tissues. It enables the creation of experimentally testable hypotheses, the integration of dat

Physical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome. This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient’s clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.

This work shows how the cellular Potts model can be used as a framework for model building and how extended models can achieve even better biological practicality, accuracy, and predictive power. It focuses on ways to integrate and interface the basic cellular Potts model at the mesoscopic scale with approaches that accurately model microscopic dynamics. These extensions are designed to create a nested and hybrid environment, where the evolution of a biological system is realistically driven by the constant interplay and flux of information between the different levels of 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.