1. Pressure-Volume Models of Cardiac Pump Function
Questions:
What is the significance of stroke work? How does it relate to myocardial energetics?
How well does the time-varying elastance approximation work?
How do we account for ventricular-vascular coupling?
Are there P-V models of diastolic function?
4-Mar-1999:
outline
Models: HMT and graphs therein (?)
Resting Myocardial Mechanics
-nonlinearity (Vaplon)
-hysteresis (Emery)
-relaxation (Emery)
-strain softening (Emery)
-anisotropy (Guccione)
-biaxial testing (Yin)
-biaxial active contraction (barium contracture) Lin and Yin
-Constitutive equations (strain energy functions)
Anatomy and Fiber Architecture (incl sheets)
Netter pictures
Prolate sphroidal coordinates
include Tables of geometry from CRC
allometric relations
fibers/sheets from CRC and Vetter and Costa
Functional Anatomy (from Netter, LifeArt and Lilly book and Opie)
Blood flow and valves
Conduction system
Coronary system
Ventricular Pump Function
My 252A lecture and Sagawa
CRC chapter including time varying elastance
Time varying elastance and ventricular-vascular coupling
Regional Stress and Strain
Determinants Table
Factors affected Table
Lame solution
- compatibility
- biharmonic equation
- polar coordinates
Residual stress
Torsion (252a and ODell)

2. Stroke Work 2
Ejection 1 6
accounting for kinetic energy of blood flow associated with pressure gradient:
Pi − Po
AVC
AVO 1 2
Pressure (kPa)
Stroke
(external)
work
Isovolumic relaxation
Isovolumic contraction 8 4
Filling
MVO
MVC 5 1 1 5 2
Volume (ml)

3. Myocardial Oxygen Consumption
Since 95% of ATP in myocytes is normal produced by aerobic metabolism (oxidative phosphorylation), myocardial oxygen consumption (MVO2) is often used to determine cardiac energy utilization by multiplying coronary blood flow by the arterio-venous O2 difference.
While the energy generated by the oxidation of 1 mole of substrate varies with substrate, the energy generated per unit oxygen is fairly constant and similar to that for glucose and lactate ~20 J/ml O2
External work should be related to regional work done by the myocardium:

4. MVO2 Increases with External Work
Dog heart-lung preparation, Evans and Matsuoka, 1915
Efficiency in dotted lines
Steeper relationship when work is increased by increasing preload than when it is increased by increasing afterload
Indices that correlate somewhat better include the rate-pressure product, tension-time index and contractility

5. Pressure-Volume Area (PVA)
Suga (1979) used the time-varying elastance concept (Suga & Sagawa, 1974) and considered the elastic potential energy generated during an isovolumic contraction, and realized that this pressure development required metabolic energy though it did no external work. Rather it must be dissipated as heat.
Hence Suga defined the pressure-volume area (PVA) as the sum:
PVA=PE+EW

6. Potential Energy
1 mm.Hg.ml = 1.33 × 10-4 J

7. Measuring Steady-State Myocardial Oxygen Consumption in Isolated Cross-Circulated Heart

8. MVO2 increases linearly with PVA

9. No effect of heart rate after measuring VO2 per heart beat

10. Fenn Effect
Fenn (1923) found that the total amount of external work done plus heat released by a skeletal muscle contracting from a constant initial increases and then decreases with the amount of shortening
This suggests an additional energy cost of ejection even though the total energy of a contracting beat is less than that of an isovolumic beat at the same end-diastolic volume.
This can be explained by the PVA-MVO2 relationship

11. Fenn Effect
Here time-varying elastance is used to predict oxygen cost of ejecting vs isovolumic beats (C) and compared with experiments vby Gibbs (1998) in isolated papillary muscles.

12. Effect of Inotropy
Increased Emax due to Ca, epinephrine shifts MVO2-PVA curve up
Beta blocker or Ca channel blocker shifts it down
Hence slope of the MVO2-PVA relation is independent of contractility too.

13. Basal and activation energy
Basal energy is oxygen consumption when heart is not beating
Activation energy increases with contractility and is mainly the energy of calcium cycling

14. Efficiency Conversion efficiency varies from 10-30%
Myofibrillar efficiency varies from 30-40%

15. How Well Does Time-Varying Elastance Work?
P(t) = E(t){V(t) - V0}
200
150
100 50 4 8 1 2 6
Pressure (kPa)
LV Volume (ml)
EDPV R
ESP VR
E(8
0 m
sec )
E(1 20 ms
ec) 60 E( 0)
= E
max

16. Ejecting vs Isovolumic Beats
There are both positive and negative effects of shortening on pressure development though they are small.

17. Effects of preload and afterload on ESPVR
Larger ejecting beats decreased end-systolic pressure by up tp 15-20% from isovolumic

18. Revised Models
Time-varying elastance model has been modified to include:
Inertial effects
Viscous resistance
Force deactivation terms

19. Ventricular-Vascular Coupling
Guyton’s equilibrium diagram for RA pressure, venous return and cardiac output. Normal cardiac output is determined by the intersection of the venous return curve and the cardiac output curve.

20. Ventricular-Vascular Coupling

21. Ventricular-Vascular Coupling
Both the ventricular system and the arterial systems are characterized by the relationship of end-systolic pressure to stroke volume. The intersection between these two relations gives the stroke volume of the coupled system.