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Ventricular Pump Function
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Anatomy
Ventricular Pump Function
Resting Myocardial Mechanics
Constitutive equations for passive myocardium
Regional Wall Stress and Strain
Cardiac Anatomy
Mitral
SVC Aorta
Pulmonic
Pulmonary
artery
Tricuspid
valves
LA
RA
LV
RV
Septum
Epicardium
Endocardium
Apex
Base
Ventricular Geometry
Truncated ellipses of
revolution
Prolate Spheroidal
Coordinates
x1
x1 = d cosh cos
x2 = d sinh sin cos
θ
x2
b
d
a


x3 = d sinh sin sin
Ventricular Dimensions
Species
dog (21 kg)
dog
dog
dog
dog
young rats
mature rats
human
human
human
Comments
unloaded diastole (0 mm Hg)
normal diastole (2-12 mm Hg)
dilated diastole (24-40 mm Hg)
normal systole (1-9 mm Hg EDP)
long axis, apex-equator (diastole)
unloaded diastole (0 mm Hg)
unloaded diastole (0 mm Hg)
Normal
Compensated pressure overload
Compensated volume overload
Inner
Radius
(mm)
16
19
22
14
42
1.4
3.2
24
27
32
Outer
Radius
(mm)
26
28
30
26
47
3.5
5.8
32
42
42
Wall
Thickness:
Inner Radius
0.62
0.47
0.36
0.86
0.12
1.50
0.81
0.34
0.56
0.33
Ventricular Scaling
Allometric relation between heart mass MH (g) and body
mass, M (kg)
MH = kM
Combined species:
k = 5.8
 = 0.98 ≈ 1.0
→
MH/M = 5.8 g.kg-1
Mature rabbits and rats:
MH/M = 2 g/kg
Adult humans:
MH/M = 5 g/kg
Horses and dogs:
MH/M = 8 g/kg
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The Cardiac Cycle
1
4b
4a
Systole:
1. Isovolumic
contraction
2. Ejection
3
4a
4b
Diastole:
3. Isovolumic
relaxation
1
4. Filling
a) Early, rapid
b) Late, diastasis
3
2
Conduction System
Coronary
System
3
4a
16
AVC
Pressure (kPa)
14
12
Aorta
AVO
10
8
6
4
Left ventricle
2
MVO
MVC
0
150
Volume (ml)
Pressure
and Volume
2
1
4b
120
90
60
30
0
100
200
300
400
Time (msec)
500
600
700
The Pressure-Volume Diagram
Endsystole
(ES)
20
SV=EDV-ESV
Ejection
AVC
Ejection Fraction
EF=SV/EDV
AVO
Stroke
volume
(SV)
8
Isovolumic
contraction
12
Isovolumic
relaxation
Pressure (kPa)
16
4
MVO
End-diastole
(ED)
Filling
MVC
0
0
50
100
Volume (ml)
150
200
The Pressure-Volume Diagram
20
ESV
 P(t )d V
EDV
AVC
AVO
8
Stroke
(external)
work
Isovolumic
contraction
12
Isovolumic
relaxation
Pressure (kPa)
EW 
Ejection
16
4
MVO
Filling
MVC
0
0
50
100
Volume (ml)
150
200
Preload and Afterload
Pressure (kPa)
20
16
control
12
↑preload
8
↓afterload
4
0
0
50
100
Volume (ml)
150
200
Starling’s Law of the Heart
(The Frank-Starling Mechanism)
Stroke work
increased contractility (e.g.
adrenergic agonist)
decreased contractility
(e.g. heart failure)
“Preload” (EDV or EDP)
Contractility (Inotropic State)
increased contractility (e.g.
adrenergic agonist)
20
decreased contractility
(e.g. heart failure)
Pressure (kPa)
16
12
8
4
0
0
50
100
Volume (ml)
150
200
Time-Varying Elastance
P(t) = E(t){V(t) - V0}
E(200)
= Emax
E(160 msec)
Pressure (kPa)
20
E(120 msec)
16
12
E(80 msec)
8
4
0
0
50
100
150
LV Volume (ml)
200
Physiological Basis of Starling’s
Law
20
Pressure (kPa)
16
12
8
4
0
0
50
100
Volume (ml)
150
200
Ventricular Function: Summary of
Key Points
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Ventricular geometry is 3-D and complex
Ventricular shape is similar across mammalian species
and prolate spheroidal coordinates provide a useful
approximation
Fiber angles vary smoothly across the wall
Systole consists of isovolumic contraction and ejection;
diastole consists of isovolumic relaxation and filling
Area of the pressure-volume loop is ventricular stroke
work which increases with filling (Starling’s Law)
Ventricles behave like time-varying elastances
The slope of the end-systolic pressure volume relation is
a load-independent measure of contractility or inotropic
state.