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All macroscopic systems experience some form of damping, be it friction or viscosity, so it is not possible to have steady oscillations without some form of forcing of the system. Forced oscillations are divided into two categories, under-damped oscillations which are characterised by a slow decay of the oscillations when the forcing is stopped, and over-damped oscillations which cease oscillating immediately when the forcing is stopped. The boundary between these two conditions is termed critically-damped oscillation which is an important concept in engineering because critically-damped systems exhibit the fastest possible transient between the forced and stationary state when the forcing is stopped and most measuring instruments are designed to exhibit this behaviour to increase their temporal resolution. A critically-damped system will decay to the stationary, stable state within approximately one period of its natural oscillation when the forcing is stopped.
As long as a periodic forcing is applied to the system it is impossible to tell whether the system is under- or over-damped because it will continue to oscillate in response to the forcing. If the forcing is stopped, however, it is very easy to differentiate between the two conditions: an under-damped system will continue to oscillate with ever decreasing amplitude until it finally decays to the new steady state while an over-damped system will stop oscillating immediately and decrease smoothly to the new steady state at a rate dependent upon the degree of over-damping.
Missing or ectopic beats are commonly observed, even in healthy subjects, when some irregularity in the pacing of the heart occurs which interrupts the regular contraction of the heart for a single beat. This 'natural' stopping of the periodic forcing of the arterial system by the heart provides a convenient way to assess the level of damping in the cardiovascular system. A typical 'missing' beat measured in the left main stem coronary artery of a patient undergoing routine catheterisation is shown in the figure below.
Pressure response measured in the left main stem coronary artery during a missing beat. The top trace shows the pressure in kPa and the bottom trace shows the simultaneously measured ECG. Just before 26 s the ECG shows a premature QRS complex resulting in a contraction of the left ventricle that was barely able to create enough pressure to open the aortic valve. The small notch on the pressure signal indicates that the valve was opened very briefly but that there was negligible blood ejected during that cardiac cycle. The response to this missing beat is a smooth continuation of the exponential fall-off of pressure that is normally observed during diastole. Following the missing beat, the ECG is normal and the pressure is close to normal. The pulse pressure of the beat immediately following the missing beat has a slightly increased pulse pressure consistent with the potentiation of the ventricular contracted produced by the increased filling due to the preceding missing beat (the Frank-Starling mechanism). There is also a decrease in mean pressure which persists for about 4-5 beats before the oscillation returns to its state prior to the missing beat.
During the missing beat we see a smooth continuation of the exponential fall-off of pressure that is normally observed during diastole. This is typical of an over-damped system. There is no hint of a slightly damped oscillation at the normal heart frequency that would be characteristic of an under-damped system. This behaviour indicates that the cardiovascular system is over-damped and, by definition, over-damped systems cannot exhibit steady-state oscillation.
The origin of the belief that the cardiovascular system is in steady-state oscillation in the face of this simple and frequently observed behaviour during missing beats is difficult to ascertain, most discussions reducing to proof by assertion. The section titled Regularity of the heart-beat is one of its most characteristic features, and in terms of the length of an individual pulse this regularity is normally maintained for a very long time. This is indeed a condition of steady-state oscillation.
and then seem to imply that steady-state oscillation is necessary for the application of Fourier methods. This is not true since Fourier analysis can be applied to any period process whether it is in steady-state oscillation or not. Milnor [Hemodynamics, 1989] simply states in Chapter 12
... under constant conditions the circulation behaves like a system in steady-state oscillation. Even the transient disturbances introduced by an extrasystole die away within about 0.5 sec, as McDonald (1974) showed in peripheral canine arteries.
Interestingly, the last observation is actually evidence that the circulation is not in steady-state oscillation; 0.5 s is approximately the period of the dog heart beat and this behaviour would indicate that the circulation is close to critically-damped.
We must conclude, therefore, that the cardiovascular system is not in steady-state oscillation. It is probably better to think of each heart beat as an isolated event that just happens to occur periodically because of the regularity of the normal heart beat under constant conditions.