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Mathematical Models Of Cancer And Different Therapies
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Book Synopsis Optimal Control for Mathematical Models of Cancer Therapies by : Heinz Schättler
Download or read book Optimal Control for Mathematical Models of Cancer Therapies written by Heinz Schättler and published by Springer. This book was released on 2015-09-15 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Physical Oncology by : Vittorio Cristini
Download or read book An Introduction to Physical Oncology written by Vittorio Cristini and published by CRC Press. This book was released on 2017-06-26 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Cancer Models with Applications by : W. Y. Tan
Download or read book Handbook of Cancer Models with Applications written by W. Y. Tan and published by World Scientific. This book was released on 2008 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composed of contributions from an international team of leading researchers, this book pulls together the most recent research results in the field of cancer modeling to provide readers with the most advanced mathematical models of cancer and their applications.Topics included in the book cover oncogenetic trees, stochastic multistage models of carcinogenesis, effects of ionizing radiation on cell cycle and genomic instability, induction of DNA damage by ionizing radiation and its repair, epigenetic cancer models, bystander effects of radiation, multiple pathway models of human colon cancer, and stochastic models of metastasis. The book also provides some important applications of cancer models to the assessment of cancer risk associated with various hazardous environmental agents, to cancer screening by MRI, and to drug resistance in cancer chemotherapy. An updated statistical design and analysis of xenograft experiments as well as a statistical analysis of cancer occult clinical data are also provided.The book will serve as a useful source of reference for researchers in biomathematics, biostatistics and bioinformatics; for clinical investigators and medical doctors employing quantitative methods to develop procedures for cancer diagnosis, prevention, control and treatment; and for graduate students.
Book Synopsis Geometric Optimal Control by : Heinz Schättler
Download or read book Geometric Optimal Control written by Heinz Schättler and published by Springer Science & Business Media. This book was released on 2012-06-26 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
Book Synopsis Mathematical Models of Cancer and Different Therapies by : Regina Padmanabhan
Download or read book Mathematical Models of Cancer and Different Therapies written by Regina Padmanabhan and published by Springer Nature. This book was released on 2020-10-31 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Mathematical Oncology by : Yang Kuang
Download or read book Introduction to Mathematical Oncology written by Yang Kuang and published by CRC Press. This book was released on 2016-04-05 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamics Of Cancer: Mathematical Foundations Of Oncology by : Dominik Wodarz
Download or read book Dynamics Of Cancer: Mathematical Foundations Of Oncology written by Dominik Wodarz and published by World Scientific. This book was released on 2014-04-24 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Oncology 2013 by : Alberto d'Onofrio
Download or read book Mathematical Oncology 2013 written by Alberto d'Onofrio and published by Springer. This book was released on 2014-10-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Methods and Models in Biomedicine by : Urszula Ledzewicz
Download or read book Mathematical Methods and Models in Biomedicine written by Urszula Ledzewicz and published by Springer Science & Business Media. This book was released on 2012-10-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
Book Synopsis Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling by : Dominik Wodarz
Download or read book Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling written by Dominik Wodarz and published by World Scientific. This book was released on 2005-01-24 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how mathematical and computational models can be used to study cancer biology. It introduces the concept of mathematical modeling and then applies it to a variety of topics in cancer biology. These include aspects of cancer initiation and progression, such as the somatic evolution of cells, genetic instability, and angiogenesis. The book also discusses the use of mathematical models for the analysis of therapeutic approaches such as chemotherapy, immunotherapy, and the use of oncolytic viruses.
Book Synopsis Cancer Modelling and Simulation by : Luigi Preziosi
Download or read book Cancer Modelling and Simulation written by Luigi Preziosi and published by CRC Press. This book was released on 2003-06-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Multiscale Cancer Modeling by : Thomas S. Deisboeck
Download or read book Multiscale Cancer Modeling written by Thomas S. Deisboeck and published by CRC Press. This book was released on 2010-12-08 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Irreversible Electroporation by : Boris Rubinsky
Download or read book Irreversible Electroporation written by Boris Rubinsky and published by Springer Science & Business Media. This book was released on 2009-11-25 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-thermal irreversible electroporation is a new minimally invasive surgical p- cedure with unique molecular selectivity attributes – in fact it may be considered the first clinical molecular surgery procedure. Non-thermal irreversible electro- ration is a molecular selective mode of cell ablation that employs brief electrical fields to produce nanoscale defects in the cell membrane, which can lead to cell death, without an effect on any of the other tissue molecules. The electrical fields can be produced through contact by insertion of electrode needles around the undesirable tissue and non-invasively by electromagnetic induction. This new - dition to the medical armamentarium requires the active involvement and is of interest to clinical physicians, medical researchers, mechanical engineers, che- cal engineers, electrical engineers, instrumentation designers, medical companies and many other fields and disciplines that were never exposed in their training to irreversible electroporation or to a similar concept. This edited book is designed to be a comprehensive introduction to the field of irreversible electroporation to those that were not exposed or trained in the field before and can also serve as a reference manual. Irreversible electroporation is broad and interdisciplinary. Therefore, we have made an attempt to cover every one of the various aspects of the field from an introductory basic level to state of the art.
Book Synopsis Adaptive Radiation Therapy by : X. Allen Li
Download or read book Adaptive Radiation Therapy written by X. Allen Li and published by CRC Press. This book was released on 2011-01-27 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern medical imaging and radiation therapy technologies are so complex and computer driven that it is difficult for physicians and technologists to know exactly what is happening at the point-of-care. Medical physicists responsible for filling this gap in knowledge must stay abreast of the latest advances at the intersection of medical imaging an
Book Synopsis Selected Topics in Cancer Modeling by : Nicola Bellomo
Download or read book Selected Topics in Cancer Modeling written by Nicola Bellomo and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by : Rebecca Sanft
Download or read book Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities written by Rebecca Sanft and published by Academic Press. This book was released on 2020-04-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected.
Book Synopsis Stochastic Models Of Tumor Latency And Their Biostatistical Applications by : Alexander D Tsodikov
Download or read book Stochastic Models Of Tumor Latency And Their Biostatistical Applications written by Alexander D Tsodikov and published by World Scientific. This book was released on 1996-03-20 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph discusses newly developed mathematical models and methods that provide biologically meaningful inferences from data on cancer latency produced by follow-up and discrete surveillance studies. Methods for designing optimal strategies of cancer surveillance are systematically presented for the first time in this book. It offers new approaches to the stochastic description of tumor latency, employs biologically-based models for making statistical inference from data on tumor recurrence and also discusses methods of statistical analysis of data resulting from discrete surveillance strategies. It also offers insight into the role of prognostic factors based on the interpretation of their effects in terms of parameters endowed with biological meaning, as well as methods for designing optimal schedules of cancer screening and surveillance. Last but not least, it discusses survival models allowing for cure rates and the choice of optimal treatment based on covariate information, and presents numerous examples of real data analysis.
