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Cardiovascular Mathematics by Luca Formaggia,Alfio Quarteroni,Allesandro Veneziani Pdf
Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Cardiovascular Mathematics by Luca Formaggia,Alfio Quarteroni,Alessandro Veneziani Pdf
Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Mathematical and Numerical Modeling of the Cardiovascular System and Applications by Daniele Boffi,Luca F. Pavarino,Gianluigi Rozza,Simone Scacchi,Christian Vergara Pdf
The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.
Mathematical Cardiac Electrophysiology by Piero Colli Franzone,Luca Franco Pavarino,Simone Scacchi Pdf
This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.
Computational And Mathematical Methods In Cardiovascular Physiology by Liang Zhong,Ru San Tan,Eddie Yin-kwee Ng,Dhanjoo N Ghista Pdf
Cardiovascular diseases (CVD) including heart diseases, peripheral vascular disease and heart failure, account for one-third of deaths throughout the world. CVD risk factors include systolic blood pressure, total cholesterol, high-density lipoprotein cholesterol, and diabetic status. Clinical trials have demonstrated that when modifiable risk factors are treated and corrected, the chances of CVD occurring can be reduced. This illustrates the importance of this book's elaborate coverage of cardiovascular physiology by the application of mathematical and computational methods.This book has literally transformed Cardiovascular Physiology into a STEM discipline, involving (i) quantitative formulations of heart anatomy and physiology, (ii) technologies for imaging the heart and blood vessels, (iii) coronary stenosis hemodynamics measure by means of fractional flow reserve and intervention by grafting and stenting, (iv) fluid mechanics and computational analysis of blood flow in the heart, aorta and coronary arteries, and (v) design of heart valves, percutaneous valve stents, and ventricular assist devices.So how is this mathematically and computationally configured landscape going to impact cardiology and even cardiac surgery? We are now entering a new era of mathematical formulations of anatomy and physiology, leading to technological formulations of medical and surgical procedures towards more precise medicine and surgery. This will entail reformatting of (i) the medical MD curriculum and courses, so as to educate and train a new generation of physicians who are conversant with medical technologies for applying into clinical care, as well as (ii) structuring of MD-PhD (Computational Medicine and Surgery) Program, to train competent medical and surgical specialists in precision medical care and patient-specific surgical care.This book provides a gateway for this new emerging scenario of (i) science and engineering based medical educational curriculum, and (ii) technologically oriented medical and surgical procedures. As such, this book can be usefully employed as a textbook for courses in (i) cardiovascular physiology in both the schools of engineering and medicine of universities, as well as (ii) cardiovascular engineering in biomedical engineering departments worldwide.
Mathematical Modeling and Validation in Physiology by Jerry J. Batzel,Mostafa Bachar,Franz Kappel Pdf
This volume synthesizes theoretical and practical aspects of both the mathematical and life science viewpoints needed for modeling of the cardiovascular-respiratory system specifically and physiological systems generally. Theoretical points include model design, model complexity and validation in the light of available data, as well as control theory approaches to feedback delay and Kalman filter applications to parameter identification. State of the art approaches using parameter sensitivity are discussed for enhancing model identifiability through joint analysis of model structure and data. Practical examples illustrate model development at various levels of complexity based on given physiological information. The sensitivity-based approaches for examining model identifiability are illustrated by means of specific modeling examples. The themes presented address the current problem of patient-specific model adaptation in the clinical setting, where data is typically limited.
Cardiovascular and Respiratory Systems by Jerry J. Batzel,Franz Kappel,Daniel Schneditz,Hien T. Tran Pdf
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted. Researchers and graduate students in mathematical biology and biomedical engineering will find this book useful. It will also appeal to researchers in the physiological and life sciences who are interested in mathematical modeling.
Cardiovascular Mechanics by Michel R. Labrosse Pdf
The objective of this book is to illustrate in specific detail how cardiovascular mechanics stands as a common pillar supporting such different clinical successes as drugs for high blood pressure, prosthetic heart valves and coronary artery bypass grafting, among others. This information is conveyed through a comprehensive treatment of the overarching principles and theories that are behind mechanobiological processes, aortic and arterial mechanics, atherosclerosis, blood and microcirculation, hear valve mechanics, as well as medical devices and drugs. Examines all major theoretical and practical aspects of mechanical forces related to the cardiovascular system. Discusses a unique coverage of mechanical changes related to an aging cardiovascular system. Provides an overview of experimental methods in cardiovascular mechanics. Written by world-class researchers from Canada, the US and EU. Extensive references are provided at the end of each chapter to enhance further study. Michel R. Labrosse is the founder of the Cardiovascular Mechanics Laboratory at the University of Ottawa, where he is a full professor within the Department of Mechanical Engineering. He has been an active researcher in academia along with being heavily associated with the University of Ottawa Heart Institute. He has authored or co-authored over 90 refereed communications, and supervised or co-supervised over 40 graduate students and post-docs.
Mathematical Modelling of Haemodialysis by Leszek Pstras,Jacek Waniewski Pdf
Beginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy. Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes. Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy.
Mathematical Modelling in Medicine by Johnny T. Ottesen,Michael Danielsen Pdf
Title page -- Preface -- Contents -- Part I. Heart -- The Changing View of the HeartThrough the Centuries -- The Left Ventricular Ejection Effect -- Human Circulatory System Model Based On Frank's Mechanism -- Modelling Blood Flow in the Left Side of the Heart -- Part II: Arterial Tree -- Models of the Arterial Tree -- A One-Dimensional Fluid Dynamic Model of the Systemic Arteries -- Measurement of Arterial Compliance In Vivo -- Models of the Venous System -- Part III: Baroreceptor Control -- General Compartmental Models of the Cardiovascular System -- Modelling the Interaction Among Several Mechanisms in the Short-term Arterial Pressure Control -- Short term Autonomic Nervous Control of the Cardiovascular System: A System Theoretic Approach -- A Baroreflex Model of Short Term Blood Pressure and Heart Rate Variability -- Part IV: Applications for Simulators -- Mathematical Models Behind Advanced Simulators in Medicine -- Cognitive Studies of Ethical Reasoning Basedon the KARDIO-simulator -- Index -- Author Index
Progress in Industrial Mathematics at ECMI 2002 by Andris Buikis,Raimondas Ciegis,Alistair D. Fitt Pdf
This volume contains the proceedings of the twelfth conference of the Euro pean Consortium for Mathematics in Industry. ECMI was founded in 1986 in to foster research and education in Mathematics in Industry in Europe order and these biannual conferences are the show case for ECMI's research. It is a pleasure to see that six of the plenary speakers have submitted papers for this volume. Their contributions illustrate the breadth of applica tions and the variety of mathematical and computational techniques that are embraced by ECMI. ECMI is also committed to the education of students and it is encouraging that a number of the papers are given by students. The Wacker Prize, which is offered for a Masters Level thesis on an industrial problem, always attracts excellent entries and this year's winner, Nicole Marheineke, is no exception. This is the first time that an ECMI conference has been held in Eastern Europe and the ECMI Council is very grateful to Professor Andris Buikis and his colleagues in Latvia and Lithuania for the excellent job they have done. Thanks too go to the European Union which supported 30 delegates at this conference via TMR Contract No ERBFMRXCT 97-0117 'Differential Equations in Industry and Commerce'. The final meeting of this network was held during this conference which provided a platform for network members to describe their work to a wider audience.
Vortex Formation in the Cardiovascular System by Arash Kheradvar,Gianni Pedrizzetti Pdf
Vortex Formation in the Cardiovascular System will recapitulate the current knowledge about the vortex formation in the cardiovascular system, from mechanics to cardiology. This can facilitate the interaction between basic scientists and clinicians on the topic of the circulatory system. The book begins with a synopsis of the fundamentals aspects of fluid mechanics to give the reader the essential background to address the proceeding chapters. Then the fundamental elements of vortex dynamics will be discussed, explaining the conditions for their formation and the rules governing their dynamics. The main equations are accompanied by mathematical models. Cardiovascular vortex formation is first analyzed in physiological, healthy conditions in the heart chambers and in the large arterial vessels. The analysis is initially presented with an intuitive appeal grounded on the physical phenomena and a focus on its clinical significance.In the proceeding chapters, the knowledge gained from either clinical or basic science literature will be discussed. The corresponding mathematical elements will finally be presented to ensure the adequate diligence. The proceeding chapters ensue to the analysis of pathological conditions, when the reader may have developed the ability to recognize normal from abnormal vortex formation phenomenon. Pathological vortex formation represents vortices that develop at sites where normally laminar flow should exist, e.g. stenosis and aneurisms. This analysis naturally leads to the interaction of vortices due to the surgical procedures with respect to prediction of changes in vortex formation. The existing techniques, from medical imaging to numerical simulations, to explore vortex flows in the cardiovascular systems will also be described. The presentations are accompanied by the mathematical definitions can that be understandable for reader without the advanced mathematical background, while an interested reader with more advanced knowledge in mathematics can be referred to references for further quantitative analyses. The book pursues the objective to transfer the fundamental vortex formation phenomena with application to the cardiovascular system to the reader. This book will be a valuable support for physicians in the evaluation of vortex influence on diagnosis and therapeutic choices. At the same time, the book will provide the rigorous information for research scientists, either from medicine and mechanics, working on the cardiovascular circulation incurring with the physics of vortex dynamics.
Forging Connections between Computational Mathematics and Computational Geometry by Ke Chen,Anton Ravindran Pdf
This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computation of surfaces. Other sections in the volume cover Pure Mathematics and Statistics ranging from partial differential equations to matrix analysis, finite difference or finite element methods and function approximation. This volume will appeal to advanced students and researchers in these areas.
