This book focuses on the analysis of cancer dynamics and the mathematically based synthesis of anticancer therapy. It summarizes the current state-of-the-art in this field and clarifies common misconceptions about mathematical modeling in cancer. Additionally, it encourages closer cooperation between engineers, physicians and mathematicians by showing the clear benefits of this without stating unrealistic goals. Development of therapy protocols is realized from an engineering point of view, such as the search for a solution to a specific control-optimization problem. Since in the case of cancer patients, consecutive measurements providing information about the current state of the disease are not available, the control laws are derived for an open loop structure. Different forms of therapy are incorporated into the models, from chemotherapy and antiangiogenic therapy to immunotherapy and gene therapy, but the class of models introduced is broad enough to incorporate other forms of therapy as well. The book begins with an analysis of cell cycle control, moving on to control effects on cell population and structured models and finally the signaling pathways involved in carcinogenesis and their influence on therapy outcome. It also discusses the incorporation of intracellular processes using signaling pathway models, since the successful treatment of cancer based on analysis of intracellular processes, might soon be a reality. It brings together various aspects of modeling anticancer therapies, which until now have been distributed over a wide range of literature. Written for researchers and graduate students interested in the use of mathematical and engineering tools in biomedicine with special emphasis on applications in cancer diagnosis and treatment, this self-contained book can be easily understood with only a minimal basic knowledge of control and system engineering methods as well as the biology of cancer. Its interdisciplinary character and the authors' extensive experience in cooperating with clinicians and biologists make it interesting reading for researchers from control and system engineering looking for applications of their knowledge. Systems and molecular biologists as well as clinicians will also find new inspiration for their research.

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) "This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences." (Short Book Reviews of the ISI, Vol. 23 (2), 2003)

The blood system is multi-scale, from the organism to the organs to cells to intracellular signaling pathways to macromolecule interactions. Blood consists of circulating cells, cellular fragments (platelets and microparticles), and plasma macromolecules. Blood cells and their fragments result from a highly-ordered process, hematopoiesis. Definitive hematopoiesis occurs in the bone marrow, where pluripotential stem cells give rise to multiple lineages of highly specialized cells. Highly-productive and continuously regenerative, hematopoiesis requires a microenvironment of mesenchymal cells and blood vessels. A Systems Biology Approach to Blood is divided into three main sections: basic components, physiological processes, and clinical applications. Using blood as a window, one can study health and disease through this unique tool box with reactive biological fluids that mirrors the prevailing hemodynamics of the vessel walls and the various blood cell types. Many blood diseases, rare and common can and have been exploited using systems biology approaches with successful results and therefore ideal models for systems medicine. More importantly, hematopoiesis offers one of the best studied systems with insight into stem cell biology, cellular interaction, development; linage programing and reprograming that are every day influenced by the most mature and understood regulatory networks.

This book focuses on the analysis of cancer dynamics and the mathematically based synthesis of anticancer therapy. It summarizes the current state-of-the-art in this field and clarifies common misconceptions about mathematical modeling in cancer. Additionally, it encourages closer cooperation between engineers, physicians and mathematicians by showing the clear benefits of this without stating unrealistic goals. Development of therapy protocols is realized from an engineering point of view, such as the search for a solution to a specific control-optimization problem. Since in the case of cancer patients, consecutive measurements providing information about the current state of the disease are not available, the control laws are derived for an open loop structure. Different forms of therapy are incorporated into the models, from chemotherapy and antiangiogenic therapy to immunotherapy and gene therapy, but the class of models introduced is broad enough to incorporate other forms of therapy as well. The book begins with an analysis of cell cycle control, moving on to control effects on cell population and structured models and finally the signaling pathways involved in carcinogenesis and their influence on therapy outcome. It also discusses the incorporation of intracellular processes using signaling pathway models, since the successful treatment of cancer based on analysis of intracellular processes, might soon be a reality. It brings together various aspects of modeling anticancer therapies, which until now have been distributed over a wide range of literature. Written for researchers and graduate students interested in the use of mathematical and engineering tools in biomedicine with special emphasis on applications in cancer diagnosis and treatment, this self-contained book can be easily understood with only a minimal basic knowledge of control and system engineering methods as well as the biology of cancer. Its interdisciplinary character and the authors' extensive experience in cooperating with clinicians and biologists make it interesting reading for researchers from control and system engineering looking for applications of their knowledge. Systems and molecular biologists as well as clinicians will also find new inspiration for their research.

The blood system is multi-scale, from the organism to the organs to cells to intracellular signaling pathways to macromolecule interactions. Blood consists of circulating cells, cellular fragments (platelets and microparticles), and plasma macromolecules. Blood cells and their fragments result from a highly-ordered process, hematopoiesis. Definitive hematopoiesis occurs in the bone marrow, where pluripotential stem cells give rise to multiple lineages of highly specialized cells. Highly-productive and continuously regenerative, hematopoiesis requires a microenvironment of mesenchymal cells and blood vessels. A Systems Biology Approach to Blood is divided into three main sections: basic components, physiological processes, and clinical applications. Using blood as a window, one can study health and disease through this unique tool box with reactive biological fluids that mirrors the prevailing hemodynamics of the vessel walls and the various blood cell types. Many blood diseases, rare and common can and have been exploited using systems biology approaches with successful results and therefore ideal models for systems medicine. More importantly, hematopoiesis offers one of the best studied systems with insight into stem cell biology, cellular interaction, development; linage programing and reprograming that are every day influenced by the most mature and understood regulatory networks.

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) "This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences." (Short Book Reviews of the ISI, Vol. 23 (2), 2003)

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellularbiology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians.The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology.

This textbook presents mathematical models in bioinformatics and describes biological problems that inspire the computer science tools used to manage the enormous data sets involved. The first part of the book covers mathematical and computational methods, with practical applications presented in the second part. The mathematical presentation avoids unnecessary formalism, while remaining clear and precise. The book closes with a thorough bibliography, reaching from classic research results to very recent findings. This volume is suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on mathematical and computer science background.

This textbook presents mathematical models in bioinformatics and describes biological problems that inspire the computer science tools used to manage the enormous data sets involved. The first part of the book covers mathematical and computational methods, with practical applications presented in the second part. The mathematical presentation avoids unnecessary formalism, while remaining clear and precise. The book closes with a thorough bibliography, reaching from classic research results to very recent findings. This volume is suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on mathematical and computer science background.

This authored monograph presents a mathematical description of the time evolution of neutral genomic regions in terms of the differential Lyapunov equation. The qualitative behavior of its solutions, with respect to different mutation models and demographic patterns, can be characterized using operator semi group theory. Mutation and drift are two of the main genetic forces, which act on genes of individuals in populations. Their effects are influenced by population dynamics. This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions. The effects of demographic change to the asymptotic of the distribution are also covered. The target audience primarily covers researchers and experts in the field but the book may also be beneficial for graduate students.