The Evolution Of The Use Of Mathematics In Cancer Research
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The Evolution Of The Use Of Mathematics In Cancer Research
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Author : Pedro Jose Gutiérrez Diez
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-17
The Evolution Of The Use Of Mathematics In Cancer Research written by Pedro Jose Gutiérrez Diez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-17 with Medical categories.
The book will provide an exhaustive and clear explanation of how Statistics, Mathematics and Informatics have been used in cancer research, and seeks to help cancer researchers in achieving their objectives. To do so, state-of-the-art Biostatistics, Biomathematics and Bioinformatics methods will be described and discussed in detail through illustrative and capital examples taken from cancer research work already published. The book will provide a guide for cancer researchers in using Statistics, Mathematics and Informatics, clarifying the contribution of these logical sciences to the study of cancer, thoroughly explaining their procedures and methods, and providing criteria to their appropriate use.
Mathematical Models Of Cancer And Different Therapies
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Author : Regina Padmanabhan
language : en
Publisher: Springer Nature
Release Date : 2020-10-31
Mathematical Models Of Cancer And Different Therapies written by Regina Padmanabhan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Technology & Engineering categories.
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
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Author : Lalitha R
language : en
Publisher: Independent Author
Release Date : 2023-03-31
A Study On Mathematical Models For The Effect Of Different Therapies And Combination Of Therapies In Cancer Treatments written by Lalitha R and has been published by Independent Author this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-31 with categories.
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.
Methods Of Mathematical Oncology
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Author : Takashi Suzuki
language : en
Publisher: Springer Nature
Release Date : 2021-08-21
Methods Of Mathematical Oncology written by Takashi Suzuki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-21 with Mathematics categories.
This book presents original papers reflecting topics featured at the international symposium entitled “Fusion of Mathematics and Biology” and organized by the editor of the book. The symposium, held in October 2020 at Osaka University in Japan, was the core event for the final year of the research project entitled “Establishing International Research Networks of Mathematical Oncology.” The project had been carried out since April 2015 as part of the Core-to-Core Program of Japan Society for the Promotion of Science (JSPS). In this book, the editor presents collaborative research from prestigious organizations in France, the UK, and the USA. By utilizing their individual strengths and realizing the fusion of life science and mathematical science, the project achieved a combination of mathematical analysis, verification by biomedical experiments, and statistical analysis of chemical databases. Mathematics is sometimes regarded as a universal language. It is a valuable property that everyone can understand beyond the boundaries of culture, religion, and language. This unifying force of mathematics also applies to the various fields of science. Mathematical oncology has two aspects, i.e., data science and mathematical modeling, and definitely helps in the prediction and control of biological phenomena observed in cancer evolution. The topics addressed in this book represent several methods of applying mathematical modeling to scientific problems in the natural sciences. Furthermore, novel reviews are included that may motivate many mathematicians to become interested in biological research.
Mathematical Methods For Cancer Evolution
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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2017-06-13
Mathematical Methods For Cancer Evolution written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-13 with Mathematics categories.
The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
The Exact Mathematical Solutions Of Cancer
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Author : Samson Taiwo Babatunde
language : en
Publisher: Independently Published
Release Date : 2019-05-15
The Exact Mathematical Solutions Of Cancer written by Samson Taiwo Babatunde and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-15 with categories.
About The BookWhile compiling this book, I have developed chapter 1 on 'Partial Differential Equations, Stochastic Generalization and Coordinate Systems Orthogonality for Modeling Cancer', Chapter 2 on 'Hilbert Space and Orthogonal Basis for Precise Understanding of Cancer Prognosis and Treatments via orthogonal Therapies, ' Chapter 3 on 'Adomian Decomposition, Laguerre Polynomials and Series Solution for Cancer Modeling, ' Chapter 4 on 'Partial Fraction Decomposition: Decomposing Cancer Anomalies via Nonlinear Fractional PDEs, ' Chapter 5 on 'The Harmonics: Cancer Prognosis and Treatments Using Resonant Frequencies and Harmonic Generation Imaging, ' Chapter 6 on 'The Laplace Transforms: Applications of CNT's In Cancer Prognosis and Treatments, ' Chapter 7 on 'Applications of Random Initial Values Generation in Cancer Initiation and Progression, ', Chapter 8 on 'Mathematical Models and Cancer Research, ' Chapter 9 on 'Genetic Algorithms in Cancer Research, ' Chapter 10 on 'Somatic Evolution: Harnessing Evolution in Therapeutics, ' Chapter 11 'Power Law Applications in Modeling Cancer Tumor and Metastatic Growth, ' Chapter 12 on 'Models Integration in Cancer Systems Biology and Fuzzy Imaging', Chapter 13 on 'Evolutionary Dynamics for Precise Understanding of Tumor Growth via Exponential Growth Model, ' Chapter 14 on 'Quantitative Computer Simulation for Modeling Cancer Anomalous Behavior via Nonlinear Fractional PDEs, ' Chapter 15 on 'Statistical Testing of Hypotheses in Cancer Research, ' Chapter 16 on 'Optimal Control Problems in clinical trials and Cancer Prognosis and Treatments', ' Chapter 17 on Applications of Boundary-Value Analysis of Non Fractional PDEs in Modeling Anomalous Behavior in Cancer' and Chapter 18 on 'Spectral Clustering Applications in Cancer Prognosis and Treatments via Nonlinear Stochastic PDEs'. Partial differential equation is known to be the basis of all physical problems and real world problems like CANCER can be formulated as initial-boundary value partial differential equation. It was in the year 2016, that I wrote a book entitled "Exact Solutions for Partial Differential Equations," Published in Germany. The book presents a novel and robust initial-boundary value analysis framework for partial differential equations. The EXACT analytical solutions are generated from the initial conditions and satisfied the boundary conditions of the fractional nonlinear partial differential equations.In this book, which has been written completely new, I have explored the evolutionary dynamics of cancer and the use of evolutionary and genetic PDEs equations with random initial values in cancer development and response to therapies. Cancer emerges due to an evolutionary process in the SOMATIC tissue. The fundamental laws of evolution can best be formulated as EXACT mathematical equations. Therefore, the process of cancer initiation, progression and treatment is amenable to mathematical investigation. Thus, cancer as a random biodynamical system with anomalous behavior can be modeled with exact mathematical formulation.The subject matter has been so arranged that even a layman can understand how to apply the "exact mathematical solutions" to the problems of CANCER! This book is strongly and widely recommended for in-depth references in all matter of cancer research.
Introduction To Mathematical Oncology
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Author : Yang Kuang
language : en
Publisher: CRC Press
Release Date : 2016-04-05
Introduction To Mathematical Oncology written by Yang Kuang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-05 with Mathematics categories.
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 Mathematical Foundations Of Oncology
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Author : Dominik Wodarz
language : en
Publisher: World Scientific
Release Date : 2014-04-24
Dynamics Of Cancer Mathematical Foundations Of Oncology written by Dominik Wodarz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-24 with Mathematics categories.
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.
Mathematical Oncology 2013
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Author : Alberto d'Onofrio
language : en
Publisher: Springer
Release Date : 2014-10-16
Mathematical Oncology 2013 written by Alberto d'Onofrio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Mathematics categories.
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.
Mathematical Models Of Tumor Immune System Dynamics
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Author : Amina Eladdadi
language : en
Publisher: Springer
Release Date : 2014-11-06
Mathematical Models Of Tumor Immune System Dynamics written by Amina Eladdadi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Mathematics categories.
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.
