Applied mathematical models in human physiology:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM
2004
|
| Schriftenreihe: | SIAM monographs on mathematical modeling and computation
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 298 S. graph. Darst. |
| ISBN: | 0898715393 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV024507041 | ||
| 003 | DE-604 | ||
| 005 | 20120710 | ||
| 007 | t | ||
| 008 | 090924s2004 d||| |||| 00||| eng d | ||
| 020 | |a 0898715393 |9 0-89871-539-3 | ||
| 035 | |a (OCoLC)802338952 | ||
| 035 | |a (DE-599)BVBBV024507041 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-739 | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a 92C30 |2 msc | ||
| 100 | 1 | |a Ottesen, Johnny T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied mathematical models in human physiology |c Johnny T. Ottesen ; Mette S. Olufsen ; Jesper K. Larsen |
| 264 | 1 | |a Philadelphia |b SIAM |c 2004 | |
| 300 | |a XIII, 298 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a SIAM monographs on mathematical modeling and computation | |
| 700 | 1 | |a Olufsen, Mette S. |e Verfasser |4 aut | |
| 700 | 1 | |a Larsen, Jesper K. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018481508&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018481508 | ||
Datensatz im Suchindex
| _version_ | 1804140505223659520 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
Background
............................... 1
1.2
Mathematical Modeling
......................... 3
2
Cardiovascular and Pulmonary Physiology and Anatomy
7
2.1
Introduction
............................... 7
2.2
Cardiovascular Physiology
....................... 7
2.3
The Heart
................................ 8
2.3.1
The Cardiac Cycle
..................... 10
2.3.2
Internal Anatomy
..................... 11
2.3.3
Conduction System of the Heart
.............. 14
2.3.4
Muscle Physiology
..................... 15
2.4
Systemic Arteries
............................ 17
2.4.1
Arterial Wall
........................ 20
2.4.2
Blood
............................ 25
2.5
Cardiovascular Regulation
........................ 27
2.6
Pulmonary Physiology
.......................... 28
2.6.1
Ventilation
......................... 29
2.6.2
Gas Exchange between Lungs and Blood
......... 31
3
Blood Flow in the Heart
35
3.1
Introduction
............................... 35
3.2
Continuous Formulation
......................... 37
3.3
Discrete Formulation
.......................... 42
3.3.1
Discretization of Equations of Motion
........... 42
3.3.2
Discrete
Windkessel
Model for the Aortic Sink
...... 45
3.3.3
Boundary Forces
...................... 47
3.3.4
Activation Function
.................... 50
3.3.5
Topology and Initial Geometry of the Heart
........ 51
3.4
Evaluation of the
Windkessel
Model
.................. 53
3.5
MR Data
................................. 57
3.6
Comparison between Simulation and MR Data
............. 58
vii
3.6.1
Velocity Fields
....................... 58
3.6.2
Velocity Profiles
...................... 64
3.6.3 .
Vortex Data
........................ 67
3.7
Conclusions
............................... 70
The Ejection Effect of the Pumping Heart
73
4.1
Introduction
............................... 73
4.2
Model of the Isovolumic Ventricle
................... 74
4.3
The Ejection Effect
........................... 78
4.4
Formulation of the Ejection Effect
................... 81
4.5
Summary and Discussion
........................ 85
Modeling Flow and Pressure in the Systemic Arteries
91
5.1
Introduction
............................... 91
5.2
Structure of the Large Arteries
..................... 96
5.2.1
Geometric Properties of the Large Arteries
........ 96
5.2.2
Structural Properties of the Vessel Walls
......... 98
5.3
Structure of the Small Arteries
..................... 100
5.3.1
Radius and Asymmetry Relations
............. 102
5.3.2
Order of the Structured Tree
................ 104
5.3.3
Length of Segments
.................... 104
5.3.4
Wall Thickness and Young s Modulus
........... 104
5.4
Fluid Dynamic Model of a Large Artery
................ 105
5.4.1
Momentum and Continuity Equations
........... 105
5.4.2
State Equation
.......................
Ill
5.5
Flow and Pressure in the Tree of Large Arteries
............ 112
5.5.1
Inflow Condition
...................... 113
5.5.2
Bifurcation Conditions
................... 113
5.5.3
Outflow Condition
..................... 114
5.6
Fluid Dynamic Model of a Small Artery
................ 116
5.6.1
Momentum Equation
................... 117
5.6.2
Continuity and State Equations
.............. 118
5.6.3
Solution to the Linear Model
............... 119
5.7
Impedance at the Root of the Structured Tree
.............. 120
5.7.1
Bifurcation Condition
................... 120
5.7.2
Outflow Condition
..................... 120
5.7.3
Root Impedance of the Structured Tree
.......... 121
5.8
Results
.................................. 123
5.8.1
Model Problem
...................... 124
5.8.2
Structured Tree Model,
Windkessel
Model, Pure
Resistance Model, and Measured Data
.......... 127
5.9
Conclusion
................................ 132
5.9.1
Perspectives
........................ 135
5.9.2
Pathological Conditions
.................. 136
A Cardiovascular Model
137
6.1
Introduction
............................... 137
6.2
Architecture of Cardiovascular Models
................. 138
6.3
Cardiovascular Model
.......................... 139
6.3.1
Heart
............................ 142
6.3.2
The Vasculature
...................... 143
6.3.3
Determination of Parameter Values
............ 144
6.3.4
Computed Results
..................... 144
6.4
The Cardiovascular Model in Equations
................ 147
6.5
Parameter Values
............................ 153
A Baroreceptor Model
157
7.1
Control Mechanisms in the Human Circulatory System
........ 159
7.2
Baroreceptor Mechanism
........................ 159
7.3
Afferent Part
............................... 160
7.3.1
Models of the Firing Rates
................. 162
7.3.2
The Unified Models
.................... 162
7.4
CNS and the Efferent Part
........................ 165
7.5
Open Loop Descriptions of the Baroreceptor Mechanism
....... 166
7.5.1
Estimation of the Distributed Time Delay
......... 167
7.6
The First Baroreceptor Model
...................... 168
7.6.1
Modelling the Sympathetic and Parasympathetic
Activities Using a Steady State Description
........ 168
7.6.2
Formulation of the Efferent Responses
.......... 169
7.7
The Baroreceptor Model and the Cardiovascular System
........ 170
7.7.1
Control of the Two Ventricles
............... 170
7.7.2
Control of the Vasculature
................. 172
7.8
Determination of Parameter Values
................... 172
7.9
Results
.................................. 173
7.10
Acute Hemorrhage
............................ 175
7.10.1
Sensitivity Results during a Hemorrhage
......... 175
7.11
Heart Pacing
............................... 179
7.12
Responses to Pulsatile Carotid Sinus Pressure Using the First
Model
.................................. 183
7.13
Unified Baroreceptor Model
....................... 189
7.13.1
Model of the Afferent Part
.................189
7.13.2
Generation of the Sympathetic and Parasympathetic
Activities
.......................... 189
7.13.3
Efferent Responses
..................... 190
7.13.4
Parameter Values
...................... 190
7.14
Acute Hemorrhage Using the Unified Baroreceptor Model
....... 190
7.15
Summary and Discussion
........................ 192
Respiration
197
8.1
Introduction
............................... 197
8.1.1
Lung Modeling
...................... 198
8.1.2
Blood
Gas Transport
....................200
8.2
Modeling the Lung
...........................201
8.2.1
Pressure Model
.......................202
8.2.2
Gas Model
.........................207
8.2.3
Parameters in the Lung Model
...............212
8.3
Models of the Blood Transport System
.................213
8.3.1
Mass Balance Equations
..................216
8.3.2
Metabolism
........................221
8.3.3
Gas Dissociation and
pH
Value
..............222
8.3.4
Models of Gas Dissociation and
pH
Value
........225
8.3.5
Control of Respiration
...................230
8.4
Results
..................................232
8.4.1
Lung Model
........................232
8.4.2
Dissociation Curves
....................236
8.4.3
Blood Transport Model
..................242
A The
SIMA
Simulator
249
A.I Introduction
...............................249
A.2 Anesthesia Simulation
..........................249
A.3 The Models of
SIMA
..........................251
В
Momentum Equation for a Small Artery
255
B.I Introduction
...............................255
B.2 Motion of the Fluid
...........................255
B.3 Motion of the Vessel Wall
........................ 256
B.3.1 Internal Forces
.......................256
B.3.2 External Forces
......................257
B.3.3 Balancing Internal and External Forces
..........260
B.4 Elasticity Relations
..................,........262
B.5 Balancing Fluid and Wall Motions
...................263
B.6 Linearization
...............................263
B.6.1 Terms of Zeroth Order Approximations
..........264
B.6.2 Terms of First Order Approximations
...........264
B.7 Solution of the Linearized Equations
..................266
Bibliography
275
Index
293
|
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| ctrlnum | (OCoLC)802338952 (DE-599)BVBBV024507041 |
| discipline | Mathematik |
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| id | DE-604.BV024507041 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:01:02Z |
| institution | BVB |
| isbn | 0898715393 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018481508 |
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| physical | XIII, 298 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | SIAM |
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| series2 | SIAM monographs on mathematical modeling and computation |
| spelling | Ottesen, Johnny T. Verfasser aut Applied mathematical models in human physiology Johnny T. Ottesen ; Mette S. Olufsen ; Jesper K. Larsen Philadelphia SIAM 2004 XIII, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier SIAM monographs on mathematical modeling and computation Olufsen, Mette S. Verfasser aut Larsen, Jesper K. Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018481508&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ottesen, Johnny T. Olufsen, Mette S. Larsen, Jesper K. Applied mathematical models in human physiology |
| title | Applied mathematical models in human physiology |
| title_auth | Applied mathematical models in human physiology |
| title_exact_search | Applied mathematical models in human physiology |
| title_full | Applied mathematical models in human physiology Johnny T. Ottesen ; Mette S. Olufsen ; Jesper K. Larsen |
| title_fullStr | Applied mathematical models in human physiology Johnny T. Ottesen ; Mette S. Olufsen ; Jesper K. Larsen |
| title_full_unstemmed | Applied mathematical models in human physiology Johnny T. Ottesen ; Mette S. Olufsen ; Jesper K. Larsen |
| title_short | Applied mathematical models in human physiology |
| title_sort | applied mathematical models in human physiology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018481508&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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