Stochastic Methods in Cancer Research. Applications to Genomics and Angiogenesis
Stochastic Methods in Cancer Research. Applications to Genomics and Angiogenesis

Author: Paola M. V. Rancoita

Publisher: Ledizioni

Published: 2011

Total Pages: 301

ISBN-13: 8895994582

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In this thesis, I study three stochastic methods that can be applied for the analysis of data in cancer research and, in particular, to cancer genomic data and to images of angiogenic processes. Cancer is a multistep process where the accumulation of genomic lesions alters cell biology. The latter is under control of several pathways and thus, cancer can arise via different mechanisms affecting different pathways. Due to the general complexity of this disease and the different types of tumors, the efforts of cancer research cover several research areas such as, for example, immunology, genetics, cell biology, angiogenesis.

Stochastic Models Of Tumor Latency And Their Biostatistical Applications
Stochastic Models Of Tumor Latency And Their Biostatistical Applications

Author: Alexander D Tsodikov

Publisher: World Scientific

Published: 1996-03-20

Total Pages: 287

ISBN-13: 9814501840

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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.

Stochastic Modelling of Reaction–Diffusion Processes
Stochastic Modelling of Reaction–Diffusion Processes

Author: Radek Erban

Publisher: Cambridge University Press

Published: 2020-01-30

Total Pages: 322

ISBN-13: 1108572995

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This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems
Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems

Author: W. Y. Tan

Publisher: World Scientific

Published: 2002

Total Pages: 464

ISBN-13: 9789810248697

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This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems.

Stochastic Models for Carcinogenesis
Stochastic Models for Carcinogenesis

Author: Wai-Yuan Tan

Publisher: CRC Press

Published: 2020-01-31

Total Pages: 268

ISBN-13: 1000715647

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An up-to-date survey of mathematical models of carcinogenesis, providing the most recent findings of cancer biology as evidence of the models, as well as extensive bibliographies of cancer biology and in-depth mathematical analyses for each of the models. May be used as a reference for biostaticians, biometricians, mathematical and molecular biologists, applied mathematicians, oncologists, cancer and toxicology researchers, environmental scientists, and graduate students in these fields.

Applied Probability and Stochastic Processes
Applied Probability and Stochastic Processes

Author: Richard M. Feldman

Publisher: Springer Science & Business Media

Published: 2009-11-27

Total Pages: 400

ISBN-13: 3642051588

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This book is a result of teaching stochastic processes to junior and senior undergr- uates and beginning graduate students over many years. In teaching such a course, we have realized a need to furnish students with material that gives a mathematical presentation while at the same time providing proper foundations to allow students to build an intuitive feel for probabilistic reasoning. We have tried to maintain a b- ance in presenting advanced but understandable material that sparks an interest and challenges students, without the discouragement that often comes as a consequence of not understanding the material. Our intent in this text is to develop stochastic p- cesses in an elementary but mathematically precise style and to provide suf?cient examples and homework exercises that will permit students to understand the range of application areas for stochastic processes. We also practice active learning in the classroom. In other words, we believe that the traditional practice of lecturing continuously for 50 to 75 minutes is not a very effective method for teaching. Students should somehow engage in the subject m- ter during the teaching session. One effective method for active learning is, after at most 20 minutes of lecture, to assign a small example problem for the students to work and one important tool that the instructor can utilize is the computer. So- times we are fortunate to lecture students in a classroom containing computers with a spreadsheet program, usually Microsoft’s Excel.

Dynamics Of Cancer: Mathematical Foundations Of Oncology
Dynamics Of Cancer: Mathematical Foundations Of Oncology

Author: Dominik Wodarz

Publisher: World Scientific

Published: 2014-04-24

Total Pages: 533

ISBN-13: 9814566381

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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.

Debating Cancer: The Paradox In Cancer Research
Debating Cancer: The Paradox In Cancer Research

Author: Henry H Q Heng

Publisher: World Scientific

Published: 2015-10-08

Total Pages: 463

ISBN-13: 9814520861

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Cancer research is at a crossroads. Traditionally, cancer has been thought of as a disease of gene mutation, where the stepwise accumulation of cancer gene mutations is the key, and the identification of common gene mutations has been considered to be essential for diagnosis and treatment. Despite extensive research efforts and accumulated knowledge on cancer genes and pathways, the clinical benefits of this traditional approach have been limited. Recently, cancer genome sequencing has revealed an extensive amount of genetic heterogeneity where the long-expected common mutation drivers have been difficult, if not impossible, to identify. These realities ultimately challenge the conceptual framework of current cancer biology.This book introduces a new concept of genome theory of cancer evolution, in an attempt to unify the field. Many important and representative, but often confusing, questions and paradoxes are critically analyzed. By comparing gene- and genome-based theories, the hidden flaws of many popular viewpoints are addressed. This discussion is intended to initiate a much-needed critical re-evaluation of current cancer research.

Handbook of Cancer Models with Applications
Handbook of Cancer Models with Applications

Author: W. Y. Tan

Publisher: World Scientific

Published: 2008

Total Pages: 592

ISBN-13: 9812779485

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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.

Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment
Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment

Author: Lutz Edler

Publisher: John Wiley & Sons

Published: 2005-12-13

Total Pages: 502

ISBN-13: 0470857668

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Human health risk assessment involves the measuring of risk of exposure to disease, with a view to improving disease prevention. Mathematical, biological, statistical, and computational methods play a key role in exposure assessment, hazard assessment and identification, and dose-response modelling. Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment is a comprehensive text that accounts for the wealth of new biological data as well as new biological, toxicological, and medical approaches adopted in risk assessment. It provides an authoritative compendium of state-of-the-art methods proposed and used, featuring contributions from eminent authors with varied experience from academia, government, and industry. Provides a comprehensive summary of currently available quantitative methods for risk assessment of both cancer and non-cancer problems. Describes the applications and the limitations of current mathematical modelling and statistical analysis methods (classical and Bayesian). Includes an extensive introduction and discussion to each chapter. Features detailed studies of risk assessments using biologically-based modelling approaches. Discusses the varying computational aspects of the methods proposed. Provides a global perspective on human health risk assessment by featuring case studies from a wide range of countries. Features an extensive bibliography with links to relevant background information within each chapter. Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment will appeal to researchers and practitioners in public health & epidemiology, and postgraduate students alike. It will also be of interest to professionals working in risk assessment agencies.