Muutke küpsiste eelistusi

Applied Mathematical Models in Human Physiology illustrated edition [Pehme köide]

5.00/5 (2 hinnangut Goodreads-ist)
, ,
  • Formaat: Paperback, 311 pages, kõrgus x laius x paksus: 229x152x16 mm, kaal: 588 g, Illustrations (some col.)
  • Sari: Mathematical Modeling and Computation No. 9
  • Ilmumisaeg: 01-Feb-2004
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898715393
  • ISBN-13: 9780898715392
Teised raamatud teemal:
Applied Mathematical Models in Human Physiology illustrated editionSuurem pilt
  • Formaat: Paperback, 311 pages, kõrgus x laius x paksus: 229x152x16 mm, kaal: 588 g, Illustrations (some col.)
  • Sari: Mathematical Modeling and Computation No. 9
  • Ilmumisaeg: 01-Feb-2004
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898715393
  • ISBN-13: 9780898715392
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780898715392.html
Märksõnad:
Ottesen (Roskilde University), Olufsen (North Carolina State) and Larsen (Math-Tech, Denmark) explore the mathematical modeling of human cardiovascular and respiratory physiology at the systems level, and develop comprehensive models that adequately describe the physiology in a detailed way but cannot run in real time and simple models that utilize the understanding obtained from the comprehensive models but are modified to run in real time. Separate chapters present a two-dimensional model of the pumping heart based on Navier-Stokes equations, a one-dimensional model for predicting blood flow and pressure at any location along the large systemic arteries, and two zero-dimension models that provide flow and pressure at a number of discrete locations in the cardiovascular system. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors discuss models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation. This is the only book available that analyzes up-to-date models of the physiological system at several levels of detail; both simple 'real-time' models that can be directly used in larger systems, and more detailed 'reference' models that show the underlying physiological mechanisms and provide parameters for and validation of simpler models. The book also covers two-dimensional modeling of the fluid dynamics in the heart and its ability to pump, and includes a discussion of modeling wave-propagation throughout the systemic arteries.
Preface xi
Introduction
1(6)
Background
1(2)
Mathematical Modeling
3(4)
Cardiovascular and Pulmonary Physiology and Anatomy
7(28)
Introduction
7(1)
Cardiovascular Physiology
7(1)
The Heart
8(9)
The Cardiac Cycle
10(1)
Internal Anatomy
11(3)
Conduction System of the Heart
14(1)
Muscle Physiology
15(2)
Systemic Arteries
17(10)
Arterial Wall
20(5)
Blood
25(2)
Cardiovascular Regulation
27(1)
Pulmonary Physiology
28(7)
Ventilation
29(2)
Gas Exchange between Lungs and Blood
31(4)
Blood Flow in the Heart
35(38)
Introduction
35(2)
Continuous Formulation
37(5)
Discrete Formulation
42(11)
Discretization of Equations of Motion
42(3)
Discrete Windkessel Model for the Aortic Sink
45(2)
Boundary Forces
47(3)
Activation Function
50(1)
Topology and Initial Geometry of the Heart
51(2)
Evaluation of the Windkessel Model
53(4)
MR Data
57(1)
Comparison between Simulation and MR Data
58(12)
Velocity Fields
58(6)
Velocity Profiles
64(3)
Vortex Data
67(3)
Conclusions
70(3)
The Ejection Effect of the Pumping Heart
73(18)
Introduction
73(1)
Model of the Isovolumic Ventricle
74(4)
The Ejection Effect
78(3)
Formulation of the Ejection Effect
81(4)
Summary and Discussion
85(6)
Modeling Flow and Pressure in the Systemic Arteries
91(46)
Introduction
91(5)
Structure of the Large Arteries
96(4)
Geometric Properties of the Large Arteries
96(2)
Structural Properties of the Vessel Walls
98(2)
Structure of the Small Arteries
100(5)
Radius and Asymmetry Relations
102(2)
Order of the Structured Tree
104(1)
Length of Segments
104(1)
Wall Thickness and Young's Modulus
104(1)
Fluid Dynamic Model of a Large Artery
105(7)
Momentum and Continuity Equations
105(6)
State Equation
111(1)
Flow and Pressure in the Tree of Large Arteries
112(4)
Inflow Condition
113(1)
Bifurcation Conditions
113(1)
Outflow Condition
114(2)
Fluid Dynamic Model of a Small Artery
116(4)
Momentum Equation
117(1)
Continuity and State Equations
118(1)
Solution to the Linear Model
119(1)
Impedance at the Root of the Structured Tree
120(3)
Bifurcation Condition
120(1)
Outflow Condition
120(1)
Root Impedance of the Structured Tree
121(2)
Results
123(9)
Model Problem
124(3)
Structured Tree Model, Windkessel Model, Pure Resistance Model, and Measured Data
127(5)
Conclusion
132(5)
Perspectives
135(1)
Pathological Conditions
136(1)
A Cardiovascular Model
137(20)
Introduction
137(1)
Architecture of Cardiovascular Models
138(1)
Cardiovascular Model
139(8)
Heart
142(1)
The Vasculature
143(1)
Determination of Parameter Values
144(1)
Computed Results
144(3)
The Cardiovascular Model in Equations
147(6)
Parameter Values
153(4)
A Baroreceptor Model
157(40)
Control Mechanisms in the Human Circulatory System
159(1)
Baroreceptor Mechanism
159(1)
Afferent Part
160(5)
Models of the Firing Rates
162(1)
The Unified Models
162(3)
CNS and the Efferent Part
165(1)
Open Loop Descriptions of the Baroreceptor Mechanism
166(2)
Estimation of the Distributed Time Delay
167(1)
The First Baroreceptor Model
168(2)
Modelling the Sympathetic and Parasympathetic Activities Using a Steady State Description
168(1)
Formulation of the Efferent Responses
169(1)
The Baroreceptor Model and the Cardiovascular System
170(2)
Control of the Two Ventricles
170(2)
Control of the Vasculature
172(1)
Determination of Parameter Values
172(1)
Results
173(2)
Acute Hemorrhage
175(4)
Sensitivity Results during a Hemorrhage
175(4)
Heart Pacing
179(4)
Responses to Pulsatile Carotid Sinus Pressure Using the First Model
183(6)
Unified Baroreceptor Model
189(1)
Model of the Afferent Part
189(1)
Generation of the Sympathetic and Parasympathetic Activities
189(1)
Efferent Responses
190(1)
Parameter Values
190(1)
Acute Hemorrhage Using the Unified Baroreceptor Model
190(2)
Summary and Discussion
192(5)
Respiration
197(52)
Introduction
197(4)
Lung Modeling
198(2)
Blood Gas Transport
200(1)
Modeling the Lung
201(12)
Pressure Model
202(5)
Gas Model
207(5)
Parameters in the Lung Model
212(1)
Models of the Blood Transport System
213(19)
Mass Balance Equations
216(5)
Metabolism
221(1)
Gas Dissociation and pH Value
222(3)
Models of Gas Dissociation and pH Value
225(5)
Control of Respiration
230(2)
Results
232(17)
Lung Model
232(4)
Dissociation Curves
236(6)
Blood Transport Model
242(7)
A The SIMA Simulator
249(6)
Introduction
249(1)
Anesthesia Simulation
249(2)
The Models of SIMA
251(4)
B Momentum Equation for a Small Artery
255(20)
Introduction
255(1)
Motion of the Fluid
255(1)
Motion of the Vessel Wall
256(6)
Internal Forces
256(1)
External Forces
257(3)
Balancing Internal and External Forces
260(2)
Elasticity Relations
262(1)
Balancing Fluid and Wall Motions
263(1)
Linearization
263(3)
Terms of Zeroth Order Approximations
264(1)
Terms of First Order Approximations
264(2)
Solution of the Linearized Equations
266(9)
Bibliography 275(18)
Index 293


Johnny T. Ottesen is a Professor of Mathematics and Physics at Roskilde University, Denmark. His main research interests include mathematical modeling of biological systems, biofluids, optimal control, scientific computing, and dynamical systems. He is a leading researcher in the area of modeling of physiological systems, especially in modeling the cardiovascular system and its control mechanisms. He has also contributed to research in the teaching of mathematical modeling at all university levels. He has been a Visiting Researcher at the University of California, Santa Barbara and at RIMS, Kyoto, Japan. Mette S. Olufsen is a Professor of Mathematics at North Carolina State University. Her research is in the fields of biofluid dynamics, computational neuroscience, scientific computation, and interdisciplinary research in mathematical biology. In particular she is interested in multiscale modeling including models from detailed fluid dynamics models to lumped compartmental models. Jesper K. Larsen is Director of Math-Tech and an applied mathematics educator at the department of Mathematics and Physics at Roskilde University, Denmark. His research areas include applied mathematical modeling, and he was one of the founders of the simulation project SIMA (SIMulation in Anesthesia), which was the project that brought together all the contributions documented in this book.