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88 The origin of third heart sound - III

In this episode, we will discuss the result of our heart model:
$P_{c} = b_{1}(e^{b_{2}(V_{LV} - V_{0})} - 1)$
$P_{o} = \frac{1}{2}K( 1 - \cos(\frac{2\pi t}{T_{s}}))(V_{LV} - V_{d})$
$\frac{dV_{LV}}{dt} = \frac{P_{v}}{R_{LV}} + C_{LV}\frac{dP_{v}}{dt}$
$P_{LV} = P_{c}+P_{o}+P_{v}$
During the systolic phase, the following equations hold but we will not talk about them in detail:
$P_{LV} = P_{ao} + R_{o}Q_{ao}$
$Q_{ao} = C_{s}\frac{d P_{ao}}{dt}+ \frac{P_{ao}}{R_{s}}$

Did we get our third heart sound?

Since this series is about the the third heart sound, we shall look at the heart sound first and compare the simulation results from a normal heart and a heart with dilated cardiomyopathy (DCM) (i.e., the heart is pathologically dilated and can't normally function anymore).

In the original article, the heart sounds generated in systolic phase were eliminated and therefore more easy to read. Clearly, there is a sound generated in early diastolic phase, after the end of isovolemic relaxation (i.e., the ventricular pressure is decreasing, but since its pressure is not below the pressure of pulmonary veins yet, there will be no venous return and the ventricular volume will hence be a constant.), and this sound is much louder in DCM heart than in normal heart.

Aside from this, we can easily observe some differences between a DCM heart from a normal heart. The viscous pressure contributes more in a DCM heart and cancels out most of its active pressure. This may be the main reason why a DCM heart can't pump out blood efficaciously. During diastolic phase, both hearts reach their pressure plateau in early diastolic phase. However, in normal heart, the viscous pressure is gradually replaced by elastic pressure, which means the viscous effect of ventricular wall dissipates and allows more venous return. In comparison, the viscous pressure is not replaced by elastic pressure, which means the venous return is shutdown early in diastolic phase.

Clearly the DCM heart is failing

A viscous cycle that leads to the failure of a DCM heart is clearly seen. Its viscous pressure is too prominent and dissipates too slowly. This prevents it from effectively pump out blood, so the sympathetic system will stimulate its heart rate. However, as heart rate increases, the duration of diastolic phase decreases, which prevents the viscous pressure from dissipating and the venous return is shutdown early. The heart not only fills ineffectively but also ejects blood not efficaciously. Currently, heart transplant is the most definite way to cure a DCM heart while stem cell therapy also showed promising results. We could look at the changes of ventricular volume to further confirm our explanation.

A physical explanation for the third heart sound

If we look at the change rate of left ventricular pressure:
For DCM, there is a large pressure change peak in early diastolic phase that is relatively minor in normal heart. We could therefore hypothesized that this rapid filling wave and its accompanied rapid pressure changes manifest itself as S3. This is mainly because the viscous pressure of left ventricle becomes very responsive to the changes in active pressure but can only slowly dissipate itself. This pathological viscous pressure response generates a rapid filling wave that increases the sound component of higher frequencies and therefore becomes more audible.

The authors of the original article also performed sensitivity analysis by changing different parameters in our heart model to see its effect on the rapid filling wave.
Figure 7 of the original article (Annals of Biomedical Engineering, Vol. 19, pp. 651-667, 1991.) This figure shows that the amplitude of S3 is most sensitive to changes in duration of contraction, viscoelasticity and heart rate.
Their results clearly showed that the rapid filling wave is sensitive to changes in duration of contraction, viscoelasticity and heart rate, which is consistent with our previous discussion.

So now I could finally answer the question of my friend. S3 is generated by the pathological viscous pressure of left ventricle. This pathological viscous pressure not only renders the systole ineffective, but also generates a rapid filling wave in early diastole and soon shutdown nearly all venous return. This rapid pressure changes increase the sound component of higher frequencies and therefore becomes more audible as S3.