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Ottesen J.T. — Applied Mathematical Models in Human Physiology
Ottesen J.T. — Applied Mathematical Models in Human Physiology

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Название: Applied Mathematical Models in Human Physiology

Автор: Ottesen J.T.

Аннотация:

This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors focus on 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.

Applied Mathematical Models in Human Physiology is the only book available that analyzes up-to-date models of the physiological system at several levels of detail. Some are simple "real-time" models that can be directly used in larger systems, while others are 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.

The models presented can be used as case studies in courses on mathematical modeling or as an inspiration for the study and development of physiological models. The first two chapters of the book provide an excellent introduction to the physiologic concepts necessary for understanding the modeling assumptions and methodologies. The remaining chapters describe six different models of the cardiovascular and pulmonary system. Each model is introduced by a case study and can be studied individually.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 298

Добавлена в каталог: 26.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E_{max}$      142 149 173
$\delta$ function      38
$\delta$ function, approximation      43
2D model      35
Actin      17
Activation function      38 50—51
Active muscle tissue      38
Acute hemorrhage      175 190
Afferent part      160
Afferent part, model      189
Alveoli      8 28
Angiotensin II      27
Annulus fibrosus      11
Aorta      8
Aorta, flow, $q(x_{fixed},t)$      124
Aorta, flow, q(x,t)      125
Aorta, pressure, $p(x_{fixed}, t)$      124
Aorta, pressure, p(x,t)      125
Aortic valve      10 13
Area ratio, structured tree      102
Arterial load      76 77
Arterial pulse, characteristics      93 123 133
Arterial pulse, diagnostic significance      95
Arterial pulse, pathological conditions      136
Arterial pulse, reflections      93 114 124 131
Arterial pulse, shape      93
Arterial tree      20 93 96 97
Arteries, bifurcation      19
Arteries, cross-sectional area      17 19
Arteries, elasticity      19
Arteries, muscles      19
Arteries, systemic      8 17
Arteries, wall properties      19
Arteries, wall thickness      23
Assumptions, large arteries      95 105
Assumptions, small arteries      117
Asymmetry ratio, structured tree      102
Atrioventricular, opening      13
Atrioventricular, valves      12
Atrium, left      10 35
Atrium, right      10
Automatism      14
Autoregulation      28 195
Baroreceptor      28
Baroreceptor mechanism      158 159
Baroreceptor mechanism, distributed time delay      167
Baroreceptor mechanism, model      168 171
Baroreceptor mechanism, open loop descriptions      166
Baroreceptor model      157
Baroreceptor model, parameter values      172
Baroreceptor, efferent part      165
Baroreceptor, firing rates      162
Baroreceptor, nonlinear phenomena      161
Baroreceptor, open loop response      166
Baroreceptor, unified model      162
Bessel equations, small arteries      117 266
Bicuspid valve      see "Mitral valve"
Bifurcation condition, large arteries      113
Bifurcation condition, small arteries      120
Biochemical energy      17
Blood      25
Blood flow, heart      35
Blood flow, inertial effects      94
Blood flow, large arteries      105
Blood flow, small arteries      255
Blood flow, viscous effects      94
Blood gas transport      200
Blood transport      213 242
Blood, density      37 38
Blood, deoxygenated      8
Blood, regulation      19
Blood, reoxygenated      8
Blood, viscosity      37 38 45
Bode plot, brachiocephalic artery      131 133
Bohr effect      244
Brachialis, flow, $q(x_{fixed},t)$      124
Brachialis, flow, q(x,t)      126
Brachialis, pressure, $p(x_{fixed}, t)$      124
Brachialis, pressure, p(x,t)      126
Brachiocephalic artery, Bode plot      131 133
Bundle, atrioventricular      see "Bundle of His"
Bundle, of His      14
Carbon dioxide      28
Carbon dioxide, dissociation      227
Carbon dioxide, transport      223
Cardiac, contractility      173
Cardiac, cycle      35
Cardiac, output      11
Cardiovascular, model      138—140 147 170
Cardiovascular, regulation      27
Cardiovascular, system      7
Carotid sinus pressure, pulsatile      183
Central nervous system      28
Characteristic systemic resistance      141
Chemoreceptor      28
Chordae tendineae      13
Chronotropic effect      170
CNS      28 see
Compartment equations      211
Compartment model      197
Compliance      30 98 138
Compliance, venous      173
Conclusion      132
Conduction zone      30
Conservation form, Navier — Stokes equations      111
Continuity equation      38
Continuity equation, discretization      44
Continuity equation, large arteries      106
Continuity equation, small arteries      118
Contraction isovolumic      74
Control mechanisms      159
Control of respiration      230
Control, peripheral resistance      172
Control, unstressed volume      172
Control, venous compliance      172
Convolution theorem      116
Cross-sectional area      101
Crossbridge bonds      17
Cycling of bonds      17
Deactivation      79 80 82 88
Dead space      31
Diastole      10 37
Dicrotic wave      93 95 114 124
Diffusion      210
Dissociation curves      236
Distributed model      138
Distributed time delay, baroreceptor mechanism      167
Efferent part, baroreceptor      165
Efferent responses      190
Ejection effect      74 78
Ejection effect, model      81 88
Ejection fraction      10
Elastance      30
Elastance function      141 142 149
Elasticity, large arteries      111
Elasticity, small arteries      262
Erythrocytes      25
External forces, small arteries      257
External forces, small arteries, total      259
Fibril      15
Filling resistance      141
Firing rates, baroreceptors      162
Flow, aorta, $q(x_{fixed},t)$      124
Flow, aorta, measured      128
Flow, aorta, q(x,t)      125
Flow, subclavia and brachialis, $q(x_{fixed},t)$      124
Flow, subclavia and brachialis, q(x,t)      126
Fluid dynamic model, large arteries      105
Fluid dynamic model, small arteries      116
Force density      38
Fourier expansion      116
Frank mechanism      74 77
Gas, dissociation      222 225
Gas, exchange      31
Gas, model      207 234
Geometry, large arteries      96
Geometry, small arteries      100
Harmonic waves, small arteries      266
Heart model      142
Heart model, $\gamma$ factor      45
Heart model, activation function      50 51 54
Heart model, active muscle tissue      48
Heart model, cross links      52
Heart model, initial geometry      51 54
Heart model, link formalism      47
Heart model, papillary muscle      52
Heart model, passive tissue      48
Heart model, pressure      54
Heart model, sink      37 39
Heart model, source      37 39
Heart model, tethering      53
Heart model, velocity field      58
Heart model, velocity profiles      64
Heart model, vortex data      67
Heart pacing      179
Heart, active muscle      35
Heart, apex of      11 35
Heart, base of      11
Heart, blood flow      35
Heart, blood flow, velocity field      37
Heart, mitral valve      35
Heart, passive tissue      35
Hematocrit      25
Hemoglobin      33
Hill’s force-velocity relation      79
Hill’s three-element model      49
Human circulation model      140
Hyperactivation      79 80 82 88
Immersed boundary method      36
Immersed boundary method, stability analysis      36
Impedance      116
Impedance, structured tree      120 121
Impedance, structured tree, algorithm      122
Impedance, structured tree, terminal      123
Inductance      138
Inertial effects of blood      80
Inertial force, small arteries      258
Inflow condition      113
Inotropic effect      170
Inspiration      28
Internal and external forces, small arteries, normal part      261
Internal and external forces, small arteries, tangential part      260
Internal and external forces, small arteries, total      260
Internal forces, small arteries      256
Interpleural fluid      30
Interstitial space      30
Isovolumic contraction      74
Isovolumic pressure model      76
Laminar flow      208
Large arteries, arterial tree      97
Large arteries, assumptions      95 105
Large arteries, blood flow      105
Large arteries, continuity equation      106
Large arteries, fluid dynamic model      105
Large arteries, geometry      96
Large arteries, momentum equation      107
Large arteries, Navier — Stokes equations      105
Large arteries, state equation      111
Large arteries, tapering factor      96
Large arteries, vessel      106
Leucocytes      25
Linear resistance model      40
Linearized equations, small arteries, definitions      263
Linearized equations, small arteries, first order      264
Linearized equations, small arteries, solution      266
Linearized equations, small arteries, zeroth order      264
Long axis plane      35 57
Lumped model      138
Lung model      198 201 232
Lung simulation      232
Mass balance      216
Mechanoreceptor      28 195
Metabolism      29 221
Mitral valve      10 13
Model, afferent part      189
Model, baroreceptor mechanism      168 171
Model, ejection effect      81 88
Model, firing rates      162
Model, isovolumic      76
Model, isovolumic pressure      76
Modified Windkessel model      138
Moens — Korteweg wave propagation      118 267 272
Momentum equation, large arteries      107
Momentum equation, small arteries      117
Motion, small arteries, fluid      255
Motion, small arteries, fluid and vessel wall      263
Motion, small arteries, vessel wall      256
MR data      52 56—58
MR data, modulus image      58
MR data, velocity profile      58
Muscle fiber      15
Myocardium      12
Myocytes      15
myosin      17
Navier — Stokes equation      38 94
Navier — Stokes equation, conservation form      111
Navier — Stokes equation, discretization      44
Navier — Stokes equation, large arteries      105
Navier — Stokes equation, small arteries      256
Negative effects of ejection      88
Newton’s Second Law      37
Nodes, atrioventricular      14
Nodes, sinoatrial      14
Nonlinear phenomena, baroreceptor      161
Nonpulsatile models      139
Numerical scheme      36
One-dimensional model      93 105
Open loop descriptions, baroreceptor mechanism      166
Open loop response, baroreceptor      166
Order, structured tree      135
Organ compartments      216
Outflow condition      93 114 120
Outflow condition, pure resistance condition      94 114 127 134
Outflow condition, Windkessel condition      94 115 127
Oxygen carriage      225
Oxygen dissociation      228
Papillary muscle      13
Papillary muscle, heart model      52
Parameter values      144
Parameter values, baroreceptor model      172
Parasympathetic activity      166 189
Passive tissue      38
Peripheral resistance      19 134
Peripheral resistance, control      172
PH model      225
pH value      28 33 222 225
Phase lag, flow and pressure      133
plasma      25
Plasma, viscosity      27
Poiseuille flow      271
Positive effects of ejection      88
Pressure model      202 232
Pressure, aorta $p(x_{fixed}, t)$      124
Pressure, aorta $p(x_{fixed}, t)$, measured      128
Pressure, aorta p(x,t)      125
Pressure, pulmonary circulation      8
Pressure, subclavia and brachialis, $p(x_{fixed}, t)$      124
Pressure, subclavia and brachialis, p(x,t)      126
Pressure, systemic circulation      8
Pressure, three boundary conditions      130 131
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