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The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well as solutions to selected exercises, so as to lead readers to discover interesting extensions of that material. Throughout, illustrations depict physiological processes, population biology phenomena, corresponding models, and the results of computer simulations. Topics covered range from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models.
The aim of this book is to introduce the subject of mathematical modeling in the life sciences. It is intended for students of mathematics, the physical sciences, and engineering who are curious about biology. Additionally, it will be useful to students of the life sciences and medicine who are unsatisfied with mere description and who seek an understanding of biological mechanism and dynamics through the use of mathematics. The book will be particularly useful to premedical students, because it will introduce them not only to a collection of mathematical methods but also to an assortment of phenomena involving genetics, epidemics, and the physiology of the heart, lung, and kidney. Because of its introductory character, mathematical prerequisites are kept to a minimum; they involve only what is usually covered in the first semester of a calculus sequence. The authors have drawn on their extensive experience as modelers to select examples which are simple enough to be understood at this elementary level and yet realistic enough to capture the essence of significant biological phenomena drawn from the areas of population dynamics and physiology. Because the models presented are realistic, the book can serve not only as an introduction to mathematical methods but also as a mathematical introduction to the biological material itself. For the student, who enjoys mathematics, such an introduction will be far more stimulating and satisfying than the purely descriptive approach that is traditional in the biological sciences.
I have long had an interest in the life sciences, but have had few opportunities to indulge that interest in my professional activities. It has only been through simulation that those opportunities have arisen. Some of my most enjoyable classes were those I taught to students in the life sciences, where I attempted to show them the value of simulation to their discipline. That there is such a value cannot be questioned. Whether you are interested in population ecology, phar macokinetics, the cardiovascular system, or cell interaction, simulation can play a vital role in explaining the underlying processes and in enhancing our understanding of these processes. This book comprises an excellent collection of contributions, and clearly demonstrates the value of simulation in the particular areas of physiology and bioengineering. My main frustration when teaching these classes to people with little or no computer background was the lack of suitable simulation software. This di rectly inspired my own attempts at producing software usable by the computer novice. It is especially nice that software is available that enables readers to experience the examples in this book for themselves. I would like to congratulate and thank the editors, Rogier P. van Wijk van Brievingh and Dietmar P. P. Moller, for all of their excellent efforts. They should be proud of their achievement. This is the sixth volume in the Advances in Simulation series, and other volumes are in preparation.
A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical engineering and the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book employs computational models as synthesized tools for the investigation, quantification, verification, and comparison of different conjectures or scenarios of the behavior of a given compartment of the human body under physiological and pathological conditions. - Presents theoretical (modeling), biological (experimental), and computational (simulation) perspectives - Features examples, exercises, and MATLAB codes for further reader involvement - Covers basic and advanced functional and computational techniques throughout the book
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
This book provides readers with a detailed orientation to healthcare simulation research, aiming to provide descriptive and illustrative accounts of healthcare simulation research (HSR). Written by leaders in the field, chapter discussions draw on the experiences of the editors and their international network of research colleagues. This seven-section practical guide begins with an introduction to the field by relaying the key components of HSR. Sections two, three, four, and five then cover various topics relating to research literature, methods for data integration, and qualitative and quantitative approaches. Finally, the book closes with discussions of professional practices in HSR, as well as helpful tips and case studies.Healthcare Simulation Research: A Practical Guide is an indispensable reference for scholars, medical professionals and anyone interested in undertaking HSR.
Digital Human Modeling and Medicine: The Digital Twin explores the body of knowledge and state-of-the-art in Digital Human Modeling (DHM) and its applications in medicine. DHM is the science of representing humans with their physical properties, characteristics and behaviors in computerized, virtual models. These models can be used standalone or integrated with other computerized object design systems to both design or study designs of medical devices or medical device products and their relationship with humans. They serve as fast and cost-efficient computer-based tools for the assessment of human functional systems and human-system interaction. This book provides an industry first introductory and practitioner focused overview of human simulation tools, with detailed chapters describing body functional elements and organs, organ interactions and fields of application. Thus, DHM tools and a specific scientific/practical problem - functional study of the human body - are linked in a coherent framework. Eventually the book shows how DHM interfaces with common physical devices in medical practice, answering to a gap in literature and a common practitioner question. Case studies provide the applied knowledge for practitioners to make informed decisions. A non-specialist level, up-to-date overview and introduction to all medically relevant DHM systems to inform trialing, procurement decisions and initial application Includes user-level examples and case studies of DHM applications in various medical fields Clearly structured and focused compendium that is easy to access, read and understand
Over two thirds of magnet hospitals in the United States use simulation in staff education programs, and many educators have introduced simulation into their nursing and healthcare curricula. This highly practical volume meets a growing need for guidelines on planning, organizing, and implementing a health care education simulation center, using the collaborative and cost effective consortium model.
Mixture Modelling for Medical and Health Sciences provides a direct connection between theoretical developments in mixture modelling and their applications in real world problems. The book describes the development of the most important concepts through comprehensive analyses of real and practical examples taken from real-life research problems in