Cancer is a complex and devastating disease, responsible for millions of deaths worldwide each year. While traditional oncology focuses on diagnosis and treatment through medical, surgical, radiation and clinical techniques, mathematical oncology has emerged as a powerful discipline that applies mathematical modelling to understand cancer growth, spread, and response to treatment.
This volume provides a comprehensive exploration of mathematical approaches in oncology, offering a deep dive into differential equation models and biomechanical models. From reaction-diffusion equations that capture tumour growth and spread, to mechanical models that examine cellular interactions within tissues and vessels, this book presents both analytical techniques and computational modelling approaches that enhance our understanding of cancer dynamics.
This book serves as both a reference for researchers and a foundation for integrating mathematical oncology into university curricula. By bridging the gap between mathematics, biology, and clinical research, it highlights the crucial role of mathematical modelling in advancing cancer treatment strategies and improving patient outcomes.
Preface.- Biology/Pathology of Cancer.- Modeling the Immune Response to
Cancer.- Simple Models of Tumor Growth.- Modeling Avascular, Multicellular
Spheroid Growth.- Pre-pattern Models of Tumor Growth.- Modeling Tumor-induced
Angiogenesis.- Modeling Invasion and Metastasis.- Mechanical Models of
Growth.- Index.
Mark Chaplain holds the Gregory Chair of Applied Mathematics in the School of Mathematics and Statistics, University of St Andrews. He is a pioneer in the field of mathematical oncology, his main area of research for over 35 years, and during this time has developed a number of innovative, predictive models for the growth, spread and treatment of cancer.
Luigi Preziosi is a Full Professor of Mathematical Physics at the Politecnico di Torino and member of the Accademia dei Lincei. He has been working in the field of mathematical oncology for 30 years, mainly focussing on the mechanical aspects of tumour growth, tissue remodelling, cell migration, and vasculogenesis.
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