A Time Dependent Mathematical Model For Concentration Of Therapeutic Agents In Neoplasm
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A Time Dependent Mathematical Model For Concentration Of Therapeutic Agents In Neoplasm
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Author : Malisa Sarntinoranont
language : en
Publisher:
Release Date : 1996
A Time Dependent Mathematical Model For Concentration Of Therapeutic Agents In Neoplasm written by Malisa Sarntinoranont and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Mathematical Modeling Of Drug Cross Resistance In Cancer
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Author : Allen Ali Katouli
language : en
Publisher:
Release Date : 2009
Mathematical Modeling Of Drug Cross Resistance In Cancer written by Allen Ali Katouli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
One of the biggest challenges in treatment of cancer is the emergence of drug-resistant mutants during therapy. Combining several drugs may increase chances of treatment success, by reducing the probability of production of fully-resistant cells. Sometimes, one mutation can confer resistance to more than one drug. For example, there are currently three drugs available for treating Chronic Myeloid Leukemia (CML); however, the mutant T315I confers resistance to all three drugs; this is known as cross-resistance. We develop a stochastic model to study various treatments regimes, such as cyclical and combination treatment in presence and absence of cross-resistance. The microevolution of tumor is described by means of a linear birth-death process with mutations. The first-order linear partial differential equation for the probability generating function can be solved using the method of characteristics. The coefficients in the resulting equations are time-dependent quantities which reflect different treatment strategies. Also, ordinary differential equations for the average numbers of mutants of different types are formulated and analyzed. Our studies are divided into three chapters. (i) In the first chapter, we develop the stochastic model for drug resistance in cancer with the inclusion of cross-resistance and show that there is no advantage in combining more than two cross-resistant drugs. (ii) In the second chapter, we extend Roger Day's work on two-drug cyclic treatment, and in particular, we revisit the famous "worst drug rule", by including cross-resistance and using a more systematic methodology. We find that in most circumstances, it is advantageous to start treatment with the better drug, but use the worse drug for longer durations. (iii) In chapter 3, we apply the theory to existing, in vitro, data on mutant outgrowth in CML cancer cells. We find that combinations of different numbers of drugs with specific concentrations can give similar treatment outcomes. From this, we produce a counting and sorting technique that may be performed on any future inhibitors to find the best treatment options, maximizing the success rate of the treatment while minimizing the number and concentrations of the drugs.
Mathematical Modeling Of Oxygen Transport Cell Killing And Cell Decision Making In Photodynamic Therapy Of Cancer
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Author : Ioannis Gkigkitzis
language : en
Publisher:
Release Date : 2012
Mathematical Modeling Of Oxygen Transport Cell Killing And Cell Decision Making In Photodynamic Therapy Of Cancer written by Ioannis Gkigkitzis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Cancer categories.
In this study we present a model of in vitro cell killing through type II Photodynamic Therapy (PDT) for simulation of the molecular interactions leading to cell death in time domain in the presence of oxygen transport within a spherical cell. By coupling the molecular kinetics to cell killing, we develop a modeling method of PDT cytotoxicity caused by singlet oxygen and obtain the cell survival ratio as a function of light fluence or initial photosensitizer concentration with different photon density or irradiance of incident light and other parameters of oxygen transport. A systems biology model is developed to account for the detailed molecular pathways induced by PDT treatment leading to cell killing. We derive a mathematical model of cell decision making through a binary cell fate decision scheme on cell death or survival, during and after PDT treatment, and we employ a rate distortion theory as the logical design for this decision making proccess to understand the biochemical processing of information by a cell. Rate distortion theory is also used to design a time dependent Blahut-Arimoto algorithm of three variables where the input is a stimulus vector composed of the time dependent concentrations of three PDT induced signaling molecules and the output reflects a cell fate decision. The concentrations of molecules involved in the biochemical processes are determined by a group of rate equations which produce the probability of cell survival or death as the output of cell decision. The modeling of the cell decision strategy allows quantitative assessment of the cell survival probability, as a function of multiple parameters and coefficients used in the model, which can be modified to account for heterogeneous cell response to PDT or other killing or therapeutic agents. The numerical results show that the present model of type II PDT yields a powerful tool to quantify various processes underlying PDT at the molecular and cellular levels and to interpret experimental results of in vitro cell studies. Finally, following an alternative approach, the cell survival probability is modeled as a predator - prey equation where predators are cell death signaling molecules and prey is the cell survival. The two models can be compared to each other as well as directly to the experimental results of measured molecular concentrations and cell survival ratios for optimization of models, to gain insights on in vitro cell studies of PDT.
Cancer Modelling And Simulation
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Author : Luigi Preziosi
language : en
Publisher: CRC Press
Release Date : 2003-06-18
Cancer Modelling And Simulation written by Luigi Preziosi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-18 with Mathematics categories.
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.
Multiscale Cancer Modeling
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Author : Thomas S. Deisboeck
language : en
Publisher: CRC Press
Release Date : 2010-12-08
Multiscale Cancer Modeling written by Thomas S. Deisboeck and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-08 with Mathematics categories.
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
Medical Oncology
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Author : Paul Calabresi
language : en
Publisher:
Release Date : 1993
Medical Oncology written by Paul Calabresi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Medical categories.
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.
Mathematical Modeling And Computational Predictions In Oncoimmunology
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Author : Vladimir A. Kuznetsov
language : en
Publisher: Frontiers Media SA
Release Date : 2024-06-06
Mathematical Modeling And Computational Predictions In Oncoimmunology written by Vladimir A. Kuznetsov and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Medical categories.
Cancer is a complex adaptive dynamic system that causes both local and systemic failures in the patient. Cancer is caused by a number of gain-of-function and loss-of-function events, that lead to cells proliferating without control by the host organism over time. In cancer, the immune system modulates cancer cell population heterogeneity and plays a crucial role in disease outcomes. The immune system itself also generates multiple clones of different cell types, with some clones proliferating quickly and maturing into effector cells. By creating regulatory signals and their networks, and generating effector cells and molecules, the immune system recognizes and kills abnormal cells. Anti-cancer immune mechanisms are realized as multi-layer, nonlinear cellular and molecular interactions. A number of factors determine the outcome of immune system-tumor interactions, including cancer-associated antigens, immune cells, and host organisms.
Mathematical Methods And Models In Biomedicine
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Author : Urszula Ledzewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-21
Mathematical Methods And Models In Biomedicine written by Urszula Ledzewicz 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 2012-10-21 with Mathematics categories.
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.
Optimal Control For Mathematical Models Of Cancer Therapies
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Author : Heinz Schättler
language : en
Publisher: Springer
Release Date : 2015-09-15
Optimal Control For Mathematical Models Of Cancer Therapies written by Heinz Schättler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-15 with Mathematics categories.
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.