Appendix 1: Physical Quantities for Selected Arteries
6.4 Control of Cardiac Output .1 Frank – Starling Mechanism
inner and outer walls differ by±60° from the circumferential direction, producing a longitudinal component to the wall stress that results in twisting of the ventricle as it contracts.
6.4 Control of Cardiac Output
In Fig.6.13a, the left-hand graph shows the relationship between pressure and volume, in which the total pressure (green line) arises from passive tension (blue line) and active tension (red line). If the volume of the left ventricle is held constant, as in the experiments of Otto Frank, then at rest the left ventricular pressure will be produced by the passive tension. When stimulated, the left ventricular pressure will increase up to a value given by the sum of pressure due to active and passive tension. This increase is shown for two volumes in the figure. A higher volume results in a higher tension, and hence, a higher pressure is generated. The right-hand graph shows pressure plotted against time for small and large volumes.
In Fig.6.13b, the idea is extended to the ejecting heart, as investigated by Ernest Starling and colleagues. Note that the volume axis in Fig.6.13b is stroke volume, which is the volume ejected during each beat. The effect of increased filling pressure is to increase preload, and this results in an increased stroke volume. The curve is shifted upwards and downwards by decreased and increased afterload, respectively.
6.4.2 Work in the Heart
During the cardiac cycle, energy is expended to generate tension. Some of this energy is expended as heat, and some of this energy performs work to eject blood from the chambers.
The change in pressure and volume in the heart during the cardiac cycle has already been illustrated in Fig.6.2. An alternative way to depict these changes is to plot pressure against volume for the left and right ventricles. In this type of plot, the
Volume
Pressure
Time Stroke volume
Filling pressure
Active tension
Passive tension Total tension
In the isovolumic heart, increasing volume produces a higher total tension, which results in a higher systolic pressure.
In the ejecting heart, a higher filling pressure increases stroke volume
Increased afterload or decreased contractility
Decreased afterload or increased contractility
(a) (b)
Fig. 6.13 Illustration of the Frank–Starling law, showing the relationship between pressure and volume under isovolumic conditions (a) and during ejection (b)
pressure and volume follows an anticlockwise loop trajectory, once for each cycle.
Figure6.14 illustrates a typical pressure-volume loop for the left ventricle. The initial (isovolumetric) contraction starts on the lower bound (A), which is deter- mined by the end diastolic (passive) pressure-volume relationship in the left ven- tricle (blue line). Pressure increases until the aortic valve opens (B). The volume then decreases until the loop reaches the upper bound, set by the end systolic (both active and passive) pressure-volume relationship (green line). At this point the aortic valve closes, and the left ventricle relaxes while maintaining a constant volume (C). On opening of the mitral valve, the ventricle fills along the passive pressure-volume curve (D), and then the cycle repeats.
As the pressure-volume loop is traversed, the myocardium converts metabolic energy into mechanical work. During each cardiac cycle, the mechanical work performed, or stroke work, is given by the change in pressure multiplied by the change in volume. Stroke work is often approximated as mean arterial pressure during ejection multiplied by the stroke volume. A more accurate approach is to integrate the change in pressure over the change in volume throughout the cycle, and so stroke work can also be calculated as the area of the pressure-volume loop.
The pressure-volume loop is influenced by changes in preload, afterload and contractility. These changes are illustrated in Fig.6.15. An increase in preload increases end diastolic volume, and so this is reflected as a rightward shift of the isovolumic contraction phase of the pressure volume loop. An increased afterload (higher systolic arterial pressure) results in earlier closure of the aortic valve, and so the isolvolumic relaxation phase of the pressure volume loop is shifted rightwards.
Increased contractility shifts the end systolic pressure-volume curve upwards, and so the isovolumic relaxation phase of the pressure-volume loop is shifted leftwards.
LV volume
LV pressure
A C B
D
AorƟc valve opens AorƟc
valve closes
Mitral valve opens
Mitral valve closes
End diastolic pressure-volume curve End systolic pressure-volume curve
Fig. 6.14 Relationship between LV pressure and LV volume during a single cardiac cycle
6.4.3 Regulation of the Heart
The Frank–Starling mechanism is an important component of the control of the heart, because any change in end diastolic volume (point A on Fig.6.14) results in a change in cardiac output. This effect is seen very clearly in the way that left ventricular output is balance with right ventricular output. It is crucial that the output from each ventricle is balanced. If there is any sustained difference, then congestion of either pulmonary or systemic circulation follows very quickly.
If there is a transient increase in the output of the right ventricle so that it exceeds the output of the left ventricle, then the volume of blood in the pulmonary circu- lation increases. This increase results in a rise in pulmonary venous pressure, which in turn acts to increase the preload of the left ventricle. The increase in left ven- tricular preload then results, through the Frank–Starling mechanism, in a stronger contraction of the left ventricle, and hence an increase in the left ventricular output.