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.

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

Multiscale Modelling in Biomedical Engineering Discover how multiscale modeling can enhance patient treatment and outcomes In Multiscale Modelling in Biomedical Engineering, an accomplished team of biomedical professionals delivers a robust treatment of the foundation and background of a general computational methodology for multi-scale modeling. The authors demonstrate how this methodology can be applied to various fields of biomedicine, with a particular focus on orthopedics and cardiovascular medicine. The book begins with a description of the relationship between multiscale modeling and systems biology before moving on to proceed systematically upwards in hierarchical levels from the molecular to the cellular, tissue, and organ level. It then examines multiscale modeling applications in specific functional areas, like mechanotransduction, musculoskeletal, and cardiovascular systems. Multiscale Modelling in Biomedical Engineering offers readers experiments and exercises to illustrate and implement the concepts contained within. Readers will also benefit from the inclusion of: A thorough introduction to systems biology and multi-scale modeling, including a survey of various multi-scale methods and approaches and analyses of their application in systems biology Comprehensive explorations of biomedical imaging and nanoscale modeling at the molecular, cell, tissue, and organ levels Practical discussions of the mechanotransduction perspective, including recent progress and likely future challenges In-depth examinations of risk prediction in patients using big data analytics and data mining Perfect for undergraduate and graduate students of bioengineering, biomechanics, biomedical engineering, and medicine, Multiscale Modelling in Biomedical Engineering will also earn a place in the libraries of industry professional and researchers seeking a one-stop reference to the basic engineering principles of biological systems.

This book presents a theoretical multiscale modeling framework for the integration of processes spanning from molecular signaling to individual and collective cellular behavior to complex spatiotemporal dynamics at the tissue and organ levels. It then gives a detailed discussion on how to incorporate experimental and patient data into the modeling framework. The book also illustrates multiscale modeling approaches through several applications, including breast cancer and mammary gland development, lymphoma and leukemia growth, the investigation of biobarriers to chemotherapeutic drugs, and nanoparticle-based delivering strategies.

Cancer development and progression is the result of biological phenomena that occur across multiple temporal and spatial scales. Recent years have seen a flurry of multi-scale mathematical models developed to generate and test new biological hypotheses related to cancer development, progression, and various treatment approaches. This led to the development of new computational and analytical approaches aimed at investigating these multiscale models.This review volume summarises some of the current state of the art related to the modelling, experimental investigation and data assimilation for multiscale phenomena during cancer development, evolution and treatment, as well as computational and analytical investigation of the multi-scale models developed to reproduce the biological phenomena. The book also identifies the experimental and theoretical open problems that will have to be addressed in the near future in order to advance this field. Modelling and Computational Approaches for Multi-scale Phenomena in Cancer Research is an excellent resource for both early career and advanced researchers.