Mathematical Models Of Cancer And Different Therapies

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Mathematical Models of Cancer and Different Therapies

Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa
Mathematical Models of Cancer and Different Therapies Book PDF

Author : Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa
Publisher : Springer Nature
Page : 256 pages
File Size : 52,9 Mb
Release : 2020-10-31
Category : Technology & Engineering
ISBN : 9789811586408

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Mathematical Models of Cancer and Different Therapies by Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa Pdf

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.

Mathematical Models of Cancer and Different Therapies

Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa
Mathematical Models of Cancer and Different Therapies Book PDF

Author : Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa
Publisher : Unknown
Page : 0 pages
File Size : 44,8 Mb
Release : 2021
Category : Electronic
ISBN : 9811586411

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Mathematical Models of Cancer and Different Therapies by Regina Padmanabhan,Nader Meskin,Ala-Eddin Al Moustafa Pdf

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.

A Study On Mathematical Models For The Effect Of Different Therapies And Combination Of Therapies In Cancer Treatments

Lalitha R
A Study On Mathematical Models For The Effect Of Different Therapies And Combination Of Therapies In Cancer Treatments Book PDF

Author : Lalitha R
Publisher : Independent Author
Page : 0 pages
File Size : 42,9 Mb
Release : 2023-03-31
Category : Electronic
ISBN : 1805251961

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A Study On Mathematical Models For The Effect Of Different Therapies And Combination Of Therapies In Cancer Treatments by Lalitha R Pdf

Mathematical modeling is a great tool in the medical field. Mathematical models help to simulate the dynamics of complex systems. Dynamic models typically are represented by differential equations. Mathematical models are used everywhere in cancer research. The number of cancer cells in a tumor is not easy to calculate due to continuous changes in time. So may have to calculate with the help of differential equations easily. Challenge of mathematical modeling is to produce simplest possible model. Many of the researchers developed mathematical models that identify the most effective chemotherapeutic administration regimens using optimization and control techniques. In 1962 L.S. Pontryagin, etal. was developed the model for optimal control. A. Lotka and R. Fisher has been developed the mathematical theory life history evolution in 1970s. Panetta was developed an effective model for heterogeneous tumor and chemotherapeutic drug action in 1996. A.J.Coldman and J.M.Murray was developed the stochastic model of cancer treatment in 2000. L.G. de Pillis, etal. developed the system of ODE for variety of cancers and different treatments in between 2000 to 2013. In recent years so many authors developed them new models based on the above author's research. In recent years most of the people were affected by different types of cancer. Some type of cancer is the curable disease when we detect in early stage. Rare type of cancer is the not fully curable disease but to controls the tumor growth and gives assumption of survival for some years. There are different types of treatments are available according to their stage of the disease. Stages were defined from their tumor size and disease spreading position of their disease. Main treatments of cancers are Surgery, Chemotherapy, Radiation therapy, Immunotherapy, Gene therapy and Hormone therapy. Mathematical modeling of tumor dynamics and treatment responses can be applied to identify better drug administration regimes. Using mathematical model for tumor growth and cancer treatments we can reduce the tumor size. Now everyone must know about types of cancer and correct treatments for that. So select this area and developed the mathematical models for tumor dynamics and combinations of treatments. Collected the breast and colorectal cancer patient's details and fitted to our model then reduced the tumor burden. Also have find that which type of drug combinations are used for colorectal cancer and breast cancer treatments. Here we used Mathematical Tools are Differential Equation, Ordinary Differential Equation (ODE), Formulation of differential equation, Growth model, optimal control, Equilibrium and Stability Analysis in ODE.

Optimal Control for Mathematical Models of Cancer Therapies

Heinz Schättler,Urszula Ledzewicz
Optimal Control for Mathematical Models of Cancer Therapies Book PDF

Author : Heinz Schättler,Urszula Ledzewicz
Publisher : Springer
Page : 496 pages
File Size : 43,6 Mb
Release : 2015-09-15
Category : Mathematics
ISBN : 9781493929726

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Optimal Control for Mathematical Models of Cancer Therapies by Heinz Schättler,Urszula Ledzewicz Pdf

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

An Introduction to Physical Oncology

Vittorio Cristini,Eugene Koay,Zhihui Wang
An Introduction to Physical Oncology Book PDF

Author : Vittorio Cristini,Eugene Koay,Zhihui Wang
Publisher : CRC Press
Page : 204 pages
File Size : 49,8 Mb
Release : 2017-06-26
Category : Mathematics
ISBN : 9781466551367

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An Introduction to Physical Oncology by Vittorio Cristini,Eugene Koay,Zhihui Wang Pdf

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.

Mathematical Models in Cancer Research,

T. E. Wheldon
Mathematical Models in Cancer Research Book PDF

Author : T. E. Wheldon
Publisher : CRC Press
Page : 272 pages
File Size : 43,5 Mb
Release : 1988
Category : Art
ISBN : UOM:39015014464666

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Mathematical Models in Cancer Research, by T. E. Wheldon Pdf

Cancer research deals with all aspects of malignant transformation, tumour growth and the effects of treatment. Mathematical models enable quantitative representations of the changes affecting cell state and cell number. This book provides a review of the scope of mathematical modelling in cancer research, bringing together for the first time a group of related mathematical topics including multistage carcinogenesis, tumour growth kinetics, growth control, radiotherapy, chemotherapy and biological targeting in cancer treatment. Physicists and mathematicians interested in medical research, biomathematicians, biostatisticians, radiation and medical oncologists and experimental and theoretical biologists will welcome this critical review of mathematical modelling in cancer research. This book will also be of interest to clinicians, basic cancer scientists and physicists working in radiotherapy departments, and to postgraduate students on courses in oncology and subjects.

Optimal Control for Mathematical Models of Cancer Therapies

Heinz M. Schättler,Urszula Ledzewicz
Optimal Control for Mathematical Models of Cancer Therapies Book PDF

Author : Heinz M. Schättler,Urszula Ledzewicz
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 2015
Category : Cancer
ISBN : 1493929739

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Optimal Control for Mathematical Models of Cancer Therapies by Heinz M. Schättler,Urszula Ledzewicz Pdf

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Selected Topics in Cancer Modeling

Nicola Bellomo,Elena de Angelis
Selected Topics in Cancer Modeling Book PDF

Author : Nicola Bellomo,Elena de Angelis
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 53,7 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780817647131

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Selected Topics in Cancer Modeling by Nicola Bellomo,Elena de Angelis Pdf

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.

System Engineering Approach to Planning Anticancer Therapies

Andrzej Świerniak,Marek Kimmel,Jaroslaw Smieja,Krzysztof Puszynski,Krzysztof Psiuk-Maksymowicz
System Engineering Approach to Planning Anticancer Therapies Book PDF

Author : Andrzej Świerniak,Marek Kimmel,Jaroslaw Smieja,Krzysztof Puszynski,Krzysztof Psiuk-Maksymowicz
Publisher : Springer
Page : 235 pages
File Size : 51,6 Mb
Release : 2016-05-19
Category : Mathematics
ISBN : 9783319280950

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System Engineering Approach to Planning Anticancer Therapies by Andrzej Świerniak,Marek Kimmel,Jaroslaw Smieja,Krzysztof Puszynski,Krzysztof Psiuk-Maksymowicz Pdf

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.

Mathematical Models of Tumor-Immune System Dynamics

Amina Eladdadi,Peter Kim,Dann Mallet
Mathematical Models of Tumor Immune System Dynamics Book PDF

Author : Amina Eladdadi,Peter Kim,Dann Mallet
Publisher : Springer
Page : 282 pages
File Size : 44,6 Mb
Release : 2014-11-06
Category : Mathematics
ISBN : 9781493917938

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Mathematical Models of Tumor-Immune System Dynamics by Amina Eladdadi,Peter Kim,Dann Mallet Pdf

This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences.

Mathematical Oncology 2013

Alberto d'Onofrio,Alberto Gandolfi
Mathematical Oncology 2013 Book PDF

Author : Alberto d'Onofrio,Alberto Gandolfi
Publisher : Springer
Page : 336 pages
File Size : 52,9 Mb
Release : 2014-10-16
Category : Mathematics
ISBN : 9781493904587

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Mathematical Oncology 2013 by Alberto d'Onofrio,Alberto Gandolfi Pdf

With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways. Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways. Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.

Introduction to Mathematical Oncology

Yang Kuang,John D. Nagy,Steffen E. Eikenberry
Introduction to Mathematical Oncology Book PDF

Author : Yang Kuang,John D. Nagy,Steffen E. Eikenberry
Publisher : CRC Press
Page : 472 pages
File Size : 42,8 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315361987

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Introduction to Mathematical Oncology by Yang Kuang,John D. Nagy,Steffen E. Eikenberry Pdf

Introduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.

Dynamics of Cancer

Dominik Wodarz,Natalia L Komarova
Dynamics of Cancer Book PDF

Author : Dominik Wodarz,Natalia L Komarova
Publisher : World Scientific
Page : 532 pages
File Size : 45,6 Mb
Release : 2014-04-24
Category : Medical
ISBN : 9789814566384

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Dynamics of Cancer by Dominik Wodarz,Natalia L Komarova Pdf

The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells. Contents:Teaching GuideCancer and Somatic EvolutionMathematical Modeling of TumorigenesisBasic Growth Dynamics and Deterministic Models:Single Species GrowthTwo-Species Competition DynamicsCompetition Between Genetically Stable and Unstable CellsChromosomal Instability and Tumor GrowthAngiogenesis Inhibitors, Promoters, and Spatial GrowthEvolutionary Dynamics and Stochastic Models:Evolutionary Dynamics of Tumor Initiation Through Oncogenes: The Gain-of-Function ModelEvolutionary Dynamics of Tumor Initiation Through Tumor-Suppressor Genes: The Loss-of-Function Model and Stochastic TunnelingMicrosatellite and Chromosomal Instability in Sporadic and Familial Colorectal CancersEvolutionary Dynamics in Hierarchical PopulationsSpatial Evolutionary Dynamics of Tumor InitiationComplex Tumor Dynamics in SpaceStochastic Modeling of Cellular Growth, Treatment, and Resistance GenerationEvolutionary Dynamics of Drug Resistance in Chronic Myeloid LeukemiaAdvanced Topics:Evolutionary Dynamics of Stem-Cell Driven Tumor GrowthTumor Growth Kinetics and Disease ProgressionEpigenetic Changes and the Rate of DNA MethylationTelomeres and Cancer ProtectionGene Therapy and Oncolytic Virus TherapyImmune Responses, Tumor Growth, and TherapiesTowards Higher Complexities: Social Interactions Readership: Researchers in mathematical biology, mathematical modeling, biology, mathematical oncology. Keywords:Mathematical Oncology;Dynamics;Evolution;Evolutionary Dynamics;Cancer;Mathematical Models;Somatic Evolution;TeachingKey Features:Both a reference book for the topic, and provides material for undergraduate and graduate coursesTries to bridge the divide between mathematicians and biologists, which is also reflected in the backgrounds of the two authorsShows how mathematical concepts can be translated into experimentally and clinically useful insightsRooted in evolutionary biology, the book handles this very complex phenomenon in an intuitive and mathematically elegant wayContains problems and research projects for each topic10 pages of figures in color

Mathematical and Computational Studies on Progress, Prognosis, Prevention and Panacea of Breast Cancer

Suhrit Dey,Charlie Dey
Mathematical and Computational Studies on Progress Prognosis Prevention and Panacea of Breast Cancer Book PDF

Author : Suhrit Dey,Charlie Dey
Publisher : Springer Nature
Page : 377 pages
File Size : 50,5 Mb
Release : 2022-03-25
Category : Computers
ISBN : 9789811660771

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Mathematical and Computational Studies on Progress, Prognosis, Prevention and Panacea of Breast Cancer by Suhrit Dey,Charlie Dey Pdf

This book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.

Tutorials in Mathematical Biosciences III

Avner Friedman
Tutorials in Mathematical Biosciences III Book PDF

Author : Avner Friedman
Publisher : Springer
Page : 246 pages
File Size : 52,9 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9783540324157

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Tutorials in Mathematical Biosciences III by Avner Friedman Pdf

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.