236
5 Contraction
In theory, the instantaneous PVR can be determined by letting the unloaded
ventricle contract to a specified time during systole; then, with the contraction
level fixed, pressure is applied gradually while recording cavity volume. Repeating
this process with contraction frozen at various time points during the cardiac cycle
(various values of K) would generate pressure-volume curves analogous to the timedependent stress-stretch curves for a CF (see Fig. 5.10). Of course, this procedure is
not possible for heart muscle, but PVRs can be constructed by connecting points on
a set of PV loops at equal times during systole (dashed curve in Fig. 5.15a).
5.5.3 Energetics
Pressure-volume analysis is an important clinical tool. For example, the slope of
the ESPVR provides a quantitative measure of cardiac contractility, or the intrinsic
contractile strength of the myocardium. If contractility is increased by administering
epinephrine (adrenaline), the slope increases (Sagawa et al. 1988).
Pressure-volume loops also can be used to estimate the mechanical efficiency of
the heart as a pump. Efficiency of the LV is defined as the ratio of the energy used
to pump blood to the total energy consumed by the myocardium. Recall that the
strain energy density stored during uniaxial stretching of a passive bar is equal to
the area under the stress-strain curve (see Fig. 3.23d, page 130). Analogously, the
strain energy stored while blowing up a rubber (elastic) balloon is equal to the area
under the pressure-volume curve, i.e., the work of inflation is given by
p dV .
The repeatability of the PV loop for a given LV over many cycles suggests that
viscous losses are relatively small, and myocardium can be treated as approximately
pseudoelastic in the beating heart. Thus, the energy stored during passive filling,
given by the area under the EDPVR, is recovered upon unloading and does not
enter the calculation of mechanical efficiency.
Consider now isovolumic contraction. Suppose the unloaded passive LV fills
with blood to reach end diastole, then contracts with the valves staying closed so
the cavity volume remains constant. During contraction, the pressure would rise
vertically from the EDPVR to the ESPVR (isovolumic contraction). In pressurevolume space, this path follows from point A to B to C as shown in Fig. 5.16a. As in
Fig. 5.8c, we also consider an alternate path from A to C, whereby the unloaded
LV first undergoes contraction to point D, then filling the ventricle takes us up
the ESPVR to point C. Under the assumption of elasticity, the work done is the
same for both paths. Hence, the total strain energy at point C consists of passive
potential energy (area under the EDPVR) and active potential energy (area between
the EDPVR and ESPVR) (Fig. 5.16a). The active energy is metabolic energy used
by the cross-bridges to generate tension.
More generally, the total energy per beat consists of three parts (Fig. 5.16b): (1)
passive end-diastolic potential energy (area A 1 ); (2) active end-systolic potential
energy (area A 2 ); and (3) stroke work (area A 3 ). Passive end-diastolic potential
energy is recovered, active end-systolic potential energy is wasted energy dissipated
5 Contraction
In theory, the instantaneous PVR can be determined by letting the unloaded
ventricle contract to a specified time during systole; then, with the contraction
level fixed, pressure is applied gradually while recording cavity volume. Repeating
this process with contraction frozen at various time points during the cardiac cycle
(various values of K) would generate pressure-volume curves analogous to the timedependent stress-stretch curves for a CF (see Fig. 5.10). Of course, this procedure is
not possible for heart muscle, but PVRs can be constructed by connecting points on
a set of PV loops at equal times during systole (dashed curve in Fig. 5.15a).
5.5.3 Energetics
Pressure-volume analysis is an important clinical tool. For example, the slope of
the ESPVR provides a quantitative measure of cardiac contractility, or the intrinsic
contractile strength of the myocardium. If contractility is increased by administering
epinephrine (adrenaline), the slope increases (Sagawa et al. 1988).
Pressure-volume loops also can be used to estimate the mechanical efficiency of
the heart as a pump. Efficiency of the LV is defined as the ratio of the energy used
to pump blood to the total energy consumed by the myocardium. Recall that the
strain energy density stored during uniaxial stretching of a passive bar is equal to
the area under the stress-strain curve (see Fig. 3.23d, page 130). Analogously, the
strain energy stored while blowing up a rubber (elastic) balloon is equal to the area
under the pressure-volume curve, i.e., the work of inflation is given by
p dV .
The repeatability of the PV loop for a given LV over many cycles suggests that
viscous losses are relatively small, and myocardium can be treated as approximately
pseudoelastic in the beating heart. Thus, the energy stored during passive filling,
given by the area under the EDPVR, is recovered upon unloading and does not
enter the calculation of mechanical efficiency.
Consider now isovolumic contraction. Suppose the unloaded passive LV fills
with blood to reach end diastole, then contracts with the valves staying closed so
the cavity volume remains constant. During contraction, the pressure would rise
vertically from the EDPVR to the ESPVR (isovolumic contraction). In pressurevolume space, this path follows from point A to B to C as shown in Fig. 5.16a. As in
Fig. 5.8c, we also consider an alternate path from A to C, whereby the unloaded
LV first undergoes contraction to point D, then filling the ventricle takes us up
the ESPVR to point C. Under the assumption of elasticity, the work done is the
same for both paths. Hence, the total strain energy at point C consists of passive
potential energy (area under the EDPVR) and active potential energy (area between
the EDPVR and ESPVR) (Fig. 5.16a). The active energy is metabolic energy used
by the cross-bridges to generate tension.
More generally, the total energy per beat consists of three parts (Fig. 5.16b): (1)
passive end-diastolic potential energy (area A 1 ); (2) active end-systolic potential
energy (area A 2 ); and (3) stroke work (area A 3 ). Passive end-diastolic potential
energy is recovered, active end-systolic potential energy is wasted energy dissipated