This book addresses the analysis, in the continuum regime, of biological systems at various scales, from the cellular level to the industrial one. It presents both fundamental conservation principles (mass, charge, momentum and energy) and relevant fluxes resulting from appropriate driving forces, which are important for the analysis, design and operation of biological systems. It includes the concept of charge conservation, an important principle for biological systems that is not explicitly covered in any other book of this kind. The book is organized in five parts: mass conservation; charge conservation; momentum conservation; energy conservation and multiple conservations simultaneously applied. All mathematical aspects are presented step by step, allowing any reader with a basic mathematical background (calculus, differential equations, linear algebra, etc.) to follow the text with ease. The book promotes an intuitive understanding of all the relevant principles and in so doing facilitates their application to practical issues related to design and operation of biological systems. Intended as a self-contained textbook for students in biotechnology and in industrial, chemical and biomedical engineering, this book will also represent a useful reference guide for professionals working in the above-mentioned fields.
This book is devoted to the question: What fundamental ideas and concepts can phys ics contribute to the analysis of complex systems like those in biology and ecolo gy? The book originated from two lectures which I gave during the winter term 1974/75 and the summer term 1976 at the Rheinisch-Westfalische Technische Hoch schule in Aachen. The wish for a lecture with this kind of subject was brought forward by students of physics as well as by those from other disciplines like biology, physiology, and engineering sciences. The students of physics were look ing for ways which might lead them from their monodisciplinary studies into the interdisciplinary field between physics and life sciences. The students from the other disciplines suspected that there might be helpful physical concepts and ideas for the analysis of complex systems they ought to become acquainted with. It is clear that a lecture or a book which tries to realize the expectations of both these groups will meet with difficulties arising from the different train ings and background knowledge of physicists and nonphysicists. For the physicists, I have tried to give a brief description of the biological aspect and significance of a problem wherever it seems necessary and appropriate and as far as a physicist like me feels authorized to do so.
This book serves as an introduction to the continuum mechanics and mathematical modeling of complex fluids in living systems. The form and function of living systems are intimately tied to the nature of surrounding fluid environments, which commonly exhibit nonlinear and history dependent responses to forces and displacements. With ever-increasing capabilities in the visualization and manipulation of biological systems, research on the fundamental phenomena, models, measurements, and analysis of complex fluids has taken a number of exciting directions. In this book, many of the world’s foremost experts explore key topics such as: Macro- and micro-rheological techniques for measuring the material properties of complex biofluids and the subtleties of data interpretation Experimental observations and rheology of complex biological materials, including mucus, cell membranes, the cytoskeleton, and blood The motility of microorganisms in complex fluids and the dynamics of active suspensions Challenges and solutions in the numerical simulation of biologically relevant complex fluid flows This volume will be accessible to advanced undergraduate and beginning graduate students in engineering, mathematics, biology, and the physical sciences, but will appeal to anyone interested in the intricate and beautiful nature of complex fluids in the context of living systems.
This book is concerned with the study of continuum mechanics applied to biological systems, i.e., continuum biomechanics. This vast and exciting subject allows description of when a bone may fracture due to excessive loading, how blood behaves as both a solid and fluid, down to how cells respond to mechanical forces that lead to changes in their behavior, a process known as mechanotransduction. We have written for senior undergraduate students and first year graduate students in mechanical or biomedical engineering, but individuals working at biotechnology companies that deal in biomaterials or biomechanics should also find the information presented relevant and easily accessible. Table of Contents: Tensor Calculus / Kinematics of a Continuum / Stress / Elasticity / Fluids / Blood and Circulation / Viscoelasticity / Poroelasticity and Thermoelasticity / Biphasic Theory
This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.
An appealing and engaging introduction to Continuum Mechanics in Biosciences This book presents the elements of Continuum Mechanics to people interested in applications to biological systems. It is divided into two parts, the first of which introduces the basic concepts within a strictly one-dimensional spatial context. This policy has been adopted so as to allow the newcomer to Continuum Mechanics to appreciate how the theory can be applied to important issues in Biomechanics from the very beginning. These include mechanical and thermodynamical balance, materials with fading memory and chemically reacting mixtures. In the second part of the book, the fully fledged three-dimensional theory is presented and applied to hyperelasticity of soft tissue, and to theories of remodeling, aging and growth. The book closes with a chapter devoted to Finite Element analysis. These and other topics are illustrated with case studies motivated by biomedical applications, such as vibration of air in the air canal, hyperthermia treatment of tumours, striated muscle memory, biphasic model of cartilage and adaptive elasticity of bone. The book offers a challenging and appealing introduction to Continuum Mechanics for students and researchers of biomechanics, and other engineering and scientific disciplines. Key features: Explains continuum mechanics using examples from biomechanics for a uniquely accessible introduction to the topic Moves from foundation topics, such as kinematics and balance laws, to more advanced areas such as theories of growth and the finite element method.. Transition from a one-dimensional approach to the general theory gives the book broad coverage, providing a clear introduction for beginners new to the topic, as well as an excellent foundation for those considering moving to more advanced application
Microprobe Analysis of Biological Systems covers the proceedings of the 1980 Microprobe Analysis of Biological Systems conference held at Battelle Conference Center in Seattle, Washington. Most of the major laboratories in the field of biological microanalysis in the United States, England, Scotland, France, and Germany are represented. The conference presents the findings, theories, techniques, and procedures of the laboratory represented, no matter how tentative and exploratory. This book is divided into four parts encompassing 22 chapters that focus on biological applications of microprobe analysis. The introductory part describes the application of electron microprobe and X-ray microanalyses in studies of epithelial transport, avian salt gland, electrolyte transport, and acrosome reaction. The subsequent part covers the application of microprobe techniques in the analysis of cardiac, skeletal, vascular smooth, and freeze-dried muscles. It also describes a method for obtaining erythrocyte preparations for validating biological microprobe methods and the continuum-fluorescence effect on thick biological tissue. The method using freeze-substitution to localize calcium in quick-frozen tissue for X-ray microanalysis is also explained. The third part of the book tackles the principles, basic features, and applications of electron energy-loss spectroscopy. Discussions on the use of inner-shell signals for a quantitative local microanalysis technique; theoretical study of the energy resolution; and collection efficiency of a magnetic spectrometer are also included. The final part covers the elemental distribution in single erythrocytes using X-ray microanalysis. It also discusses the fundamentals of cryosectioning process for X-ray microanalysis of diffusible elements and the freezing behavior of a number of chemically different gels chosen for their partial resemblance to biological structures. Considerable chapters contain materials and methods, results, discussions, conclusions, and references. This book will be of value to scientists interested in elemental and ion transport within cells and between cells and extracellular compartments.
For one-semester, advanced undergraduate/graduate courses in Biotransport Engineering. Presenting engineering fundamentals and biological applications in a unified way, this text provides students with the skills necessary to develop and critically analyze models of biological transport and reaction processes. It covers topics in fluid mechanics, mass transport, and biochemical interactions, with engineering concepts motivated by specific biological problems.
This dissertation, "Applications of Continuum Mechanics: Computational Studies in Biological and Discrete Systems" by Yik-sau, Tang, 鄧亦修, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: This thesis is divided into two parts: part A and part B. Part A mainly focused on the biological systems while part B emphasized on discrete systems. Both studies can be applied readily in the scientific world. Part A: Computational Fluid Dynamics Study of Biological Systems Cerebrovascular and cardiovascular diseases are life threatening diseases, and are leading causes of death and disability in the civilized world. Thoracic aortic dissection (TAD), a form of cardiovascular disease, occurs when blood infiltrates into the layers of vascular aortic wall, creating a new artificial channel (the false lumen) alongside with the original channel (the true lumen). The weakened false lumen wall may expand due to the blood pressure, and high mortality rate is resulted upon imminent rupture. A clinical question is to determine the timing of the surgical procedure. By employing computational fluid dynamics techniques, several biomechanical factors including aneurysm size, blood pressure and tear distance were investigated. Generally speaking, a greater dissecting aneurysm, a higher blood pressure and a partially thrombosed false lumen might lead to undesirable hemodynamics consequences. This analysis may improve the healthcare of patients in the future as it can provide useful information for clinicians to access the risk of aneurysm rupture. On the other hand, intracranial aneurysm, a dangerous cerebrovascular disorder, occurs when a cerebral artery dilates. Such aneurysm is usually located near the arterial bifurcation in the Circle of Willis, and can lead to massive internal bleeding in the subarachnoid space upon rupture. An endovascular treatment is the implantation of a flow diverting stent which covers the aneurysm orifice. This metallic stent, namely the Pipeline Embolization Device (PED), can restrict the blood flow into the aneurysm, and thus reduces the rupture risk. The clinical question is to determine the factors affecting the stent efficiency. Computational fluid dynamics (CFD) analysis was performed to investigate the flow properties before and after stenting. Several factors including side branch diameter, aneurysm aspect ratio and the stent porosity were tested. Generally speaking, a larger side branch diameter or a higher aspect ratio might provide an undesirable hemodynamic condition, e.g. lower shear stress. In addition, two patient-specific bifurcation aneurysms reconstructed from Computed Tomography (CT) imaging data were tested, and the results showed good agreements with the idealized geometries. This study can definitely provide physicians with valuable information for treatment planning, therapeutic decision making and for future stent design. Part B: Discrete Systems In nonlinear optics and plasmonics, the dissipative spatial solitons are of fundamental importance. Here a discrete dissipative model was introduced, with hot spots (HSs) embedded into it. Symmetric solutions were determined in an implicit analytical form In addition, a two-dimensional discrete dynamical system based on bulk linear lossy lattice was also tested. The analysis of localized modes pinned to the HSs was performed semi-analytically using truncated lattices. These systems can be applied in photonics and plasmonics readily. Subjects: Solitons - Mathematical models Fluid dynamics - Mathematical models Continuum mech
The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.
