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Mathematical Modeling and
Simulation of the Cardiovascular
System
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Electrical Analog Model of the Cardiovascular System
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Electrical Analog Model of the Cardiovascular System
Right Heart Pulmonary Left Heart LV-Aorta
WedgeMV Coronary
Pericardial
Pleural Septal LVAD
Venous
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Intra-Aortic Balloon Pump (IABP)
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Electrical Equivalence for Fluid Dynamic Components
Resistance – Viscous resistance against flowsInductance – Inertance, inertia of flows (storing kinetic energy)Capacitance – Compliance, elastic walls (storing static energy)
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Optimization of IABP Parameters
BalloonConfigurations
Timing
Sun Y. Modeling the dynamic interaction between left ventricle and intraaortic balloon pump. American Journal of Physiology 261(4) (Heart Circulatory Physiology 30): H1300-H1311, 1991.
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Sun Y, Beshara M, Lucariello RJ, Chiaramida SA. A comprehensive model for right-left heart interaction under the influence of pericardium and intrathoracic pressure. American J. Physiology 272 (3 Pt 2; Heart Circ Physiol 41): H1499-H1515, Mar. 1997.
Coupling Between Right and Left Ventricles
Hemodynamic Transseptal Pericardial
Which one is more important?
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Electrical Analog Model of the Cardiovascular System
Right Heart Pulmonary Left Heart LV-Aorta
WedgeMV Coronary
Pericardial
Pleural Septal LVAD
Venous
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Sun, Chiaramida et al., American J of Physiology 1997
Validation – Cath Lab Data (Pressures)
a
x y
v
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Validation – Doppler Echocardiographic Data
Sun, Chiaramida et al., American J of Physiology 1997
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Validation – Valsalva Maneuver.
160
140
120
100
80
60
40
20
0
-20
Pre
ssur
e (m
mH
g)Valsalva Maneuver
0 5 10 15 20 25
Time (s)
pit
1
2
3
4
5 10 15 20 25
Time (s)
200
150
100
50
00
Pre
ssur
e (m
mH
g)
Model Representation Measured Arterial Pressure
AorticPressure
IntrathoracicPressure
Sun, Chiaramida et al., American J of Physiology 1997
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Coupling Between Right and Left Ventricles
Hemodynamic Transseptal ~2% Pericardial ~20%
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Left Ventricular Assist Device(LVAD)
LV
LA
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3D Model of the Left Ventricle with Infarction
A finite element model of the left ventricle interacts dynamically with the circulatory model at a 5-ms time step.
US Patent No. US 8,295,907 B2, October 23, 2012
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3D LV Model and Hemodynamic Waveforms
For an infarct size of 20% of the total left ventricular mass, the LV ejection fraction reduces from 59% to 41%.
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Validation
The integrated model predicts the decrease of LV ejection fraction and the increase of LV volumes as infarct size increases in consistence with clinical data (Sciagra et al. European J Nuclear Medicine & Molecular Imaging 31: 969-974, 2004).
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To remove infarction and to restore a remodeled left ventricle to its optimal size and shape for a patient with congestive heart failure
Surgical Ventricular Restoration
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Model Predictions of LV pressure and volume waveforms for a 40% infarction under various preoperative LV geometries
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Optimal Infarct Removal for Various LV Geometries with a 40%
Preoperative Infarction
LV E DVLV Mass 150 ml 225 ml 300 ml
150 g 50% 76% 100%
225 g 40% 75% 100%
300 g 39% 76% 88%
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Summary
Mathematical models and simulations can be useful for biomedical research for the following purposes:
• Data regression 數據內插 • Mechanism explanation 解釋機制 • Hypothesis formulation 創造假設 • Outcome prediction 預測結果