A Stochastic Model For Immunological Feedback In Carcinogenesis
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A Stochastic Model For Immunological Feedback In Carcinogenesis Analysis And Approximations
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Author : N. Dubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
A Stochastic Model For Immunological Feedback In Carcinogenesis Analysis And Approximations written by N. Dubin 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 2013-03-13 with Mathematics categories.
Stochastic processes often pose the difficulty that, as soon as a model devi ates from the simplest kinds of assumptions, the differential equations obtained for the density and the generating functions become mathematically formidable. Worse still, one is very often led to equations which have no known solution and don't yield to standard analytical methods for differential equations. In the model considered here, one for tumor growth with an immunological re sponse from the normal tissue, a nonlinear term in the transition probability for the death of a tumor cell leads to the above-mentioned complications. Despite the mathematical disadvantages of this nonlinearity, we are able to consider a more sophisticated model biologically. Ultimately, in order to achieve a more realistic representation of a complicated phenomenon, it is necessary to examine mechanisms which allow the model to deviate from the more mathematically tractable linear format. Thus far, stochastic models for tumor growth have almost exclusively considered linear transition probabilities.
A Stochastic Model For Immunological Feedback In Carcinogenesis
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Author : Neil Dubin
language : en
Publisher: Springer Verlag
Release Date : 1976
A Stochastic Model For Immunological Feedback In Carcinogenesis written by Neil Dubin and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Medical categories.
A Stochastic Model For Immunological Feedback In Carcinogenesis
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Author : Neil Dubin
language : en
Publisher:
Release Date : 1976
A Stochastic Model For Immunological Feedback In Carcinogenesis written by Neil Dubin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
A Stochastic Model For Immunological Feedback In Carcinogenesis
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Author : Neil Bubin
language : de
Publisher:
Release Date : 1976
A Stochastic Model For Immunological Feedback In Carcinogenesis written by Neil Bubin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Approximation theory categories.
Mathematical Models In Cell Biology And Cancer Chemotherapy
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Author : M. Eisen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Mathematical Models In Cell Biology And Cancer Chemotherapy written by M. Eisen 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 2013-03-13 with Mathematics categories.
The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.
Models Of The Stochastic Activity Of Neurones
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Author : A. V. Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Models Of The Stochastic Activity Of Neurones written by A. V. Holden 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 2013-03-13 with Mathematics categories.
These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\/~~';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the final typescript and Mr. Peter Hargreaves for preparing the figures.
Stochastic Models For Spike Trains Of Single Neurons
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Author : S.K. Srinivasan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Stochastic Models For Spike Trains Of Single Neurons written by S.K. Srinivasan 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 2013-03-13 with Mathematics categories.
1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic deletion model 45 5. 1. 2 Higher-order properties of the sequence of r-events 55 5. 1. 3 Extended version of Model 5. 1 - Model 60 5. 2 5. 2 Models with dependent interaction of excitatory and inhibitory sequences - MOdels 5. 3 and 5.
Synergetics
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Author : Hermann Haken
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-12
Synergetics written by Hermann Haken 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 2004-01-12 with Language Arts & Disciplines categories.
This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.
Systems Theory In Immunology
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Author : C. Bruni
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Systems Theory In Immunology written by C. Bruni 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 2013-03-08 with Mathematics categories.
This volume collects the contributions presented at the "Working Conference on System Theory in Immunology", held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under standing of basic immunological facts. Conversely, the complexity of experimental results and of interpretative models should stimulate mathematicians to formulate new problems and to design appropriate procedures of analysis. The multitude of scientific publications in theoretical biology, appeared in recent years, confirms this trend and calls for extensive interaction between mat- matics and immunology. The material of this volume is divided into five sections, along the scheme of the Conference program.
Cell Kinetic Modelling And The Chemotherapy Of Cancer
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Author : Helmut Knolle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Cell Kinetic Modelling And The Chemotherapy Of Cancer written by Helmut Knolle 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 2013-03-08 with Medical categories.
During the last 30 years, many chemical compounds that are active against tumors have been discovered or developed. At the same time, new methods of testing drugs for cancer therapy have evolved. nefore 1964, drug testing on animal tumors was directed to observation of the incfease in life span of the host after a single dose. A new approach, in which the effects of multiple doses on the proliferation kinetics of the tumor in vivo as well as of cell lines in vitro are investigated, has been outlined by Skipper and his co-workers in a series of papers beginning in 1964 (Skipper, Schabel and Wilcox, 1964 and 1965). They also investigated the influence of the time schedule in the treatment of experimental tumors. Since the publication of those studies, cell population kinetics cannot be left out of any discussion of the rational basis of chemotherapy. When clinical oncologists began to apply cell kinetic concepts in practice about 15 years ago, the theoretical basis was still very poor, in spite of Skipper's progress, and the lack of re levant cytokinetic and pharmacologic data was apparent. Subsequently, much theoretical work has been done and many cell kinetic models have been elaborated (for a review see Eisen, 1977).