Understanding how cancer tumours develop and spread is vital for finding treatments and cures. Cancer Modelling and Simulation demonstrates how mathematical modelling and computer simulation techniques are used to discover and gain insight into the dynamics of tumour development and growth. It highlights the benefits of tumour modelling, such as discovering optimal tumour therapy schedules, identifying the most promising candidates for further clinical investigation, and reducing the number of animal experiments. By examining the analytical, mathematical, and biological aspects of tumour growth and modelling, the book provides a common language and knowledge for professionals in several disciplines.

Understanding how cancer tumours develop and spread is vital for finding treatments and cures. Cancer Modelling and Simulation demonstrates how mathematical modelling and computer simulation techniques are used to discover and gain insight into the dynamics of tumour development and growth. It highlights the benefits of tumour modelling, such as discovering optimal tumour therapy schedules, identifying the most promising candidates for further clinical investigation, and reducing the number of animal experiments. By examining the analytical, mathematical, and biological aspects of tumour growth and modelling, the book provides a common language and knowledge for professionals in several disciplines.

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

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.

This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that direction.

Mathematical Modeling and Immunology An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest pos sible cooperation among scientists working in different fields: biology, im munology, medicine, physics and, we believe, mathematics. Certainly, bi ologists and immunologists will make the greatest contribution to the re search. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such prob lems. We cannot expect mathematicians alone to solve fundamental prob lems in immunology and (in particular) cancer research, but valuable sup port, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field.

- Provides an introduction to computational methods in cancer biology - Follows a multi-disciplinary approach

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.

Countless medical researchers over the past century have been occupied by the search for a cure of cancer. So far, they have developed and implemented a wide range of treatment techniques, including surgery, chemo- and radiotherapy, antiangiogenic drugs, small molecule inhibitors, and oncolytic viruses. However, patterns of these treatments' effectiveness remain largely unclear, and a better understanding of how cancer therapies work has become a key research goal. Cancer Treatment in Silico provides the first in-depth study of approaching this understanding by modeling cancer treatments, both mathematically and through computer simulations. The main goal of this book is to help expose students and researchers to in silico methods of studying cancer. It is intended for both the applied mathematics and experimental oncology communities, as mathematical models are playing an increasingly important role to supplement laboratory biology in the fight against cancer. Written at a level that generally requires little technical background, the work will be a valuable resource for scientists and students alike.

This book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind. In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.