### #86 The origin of third heart sound - I

It is really nice to see you guys again after a long update withhold. This post came from a question from one of my friends. He asked me "what is the origin of the third and fourth heart sound?" As a sixth year medical student, it is not a difficult question at first glance.
"The third and fourth heart sounds occur in diastolic phase of a cardiac cycle. While they could both imply a heart failure, the third heart sound is sometimes normal in children, young adults and pregnant women."
However, he is clearly not satisfied with this answer. He persisted with his questioning. "But how could a failing heart generate an audible sound?"

At that point, I could only come up with some plausible explanations that you could easily found in Wikipedia or medical textbooks, but I can't give any concrete details about how the stiffness of wall affect the blood flow and why that generates a sound. Therefore, I decided to do some research and build a simplified model for it.

### Wait! What do you mean by "the third and fourth heart sound"?

That's a good question. In a cardiac cycle, there are normally 2 audible heart sounds -- the first and the second ones. Let's see the figure below showing a cardiac cycle from Guyton Physiology.
Figure 1. A normal cardiac cycle. Figure source: Guyton and Hall Textbook of Medical Physiology, 13ed. Note that this figure is not totally correct. The ventricular pressure should intersect with the aortic pressure when the aortic valve closes. This figure does not show the fourth heart sound since it is always pathological. If it is present, since it is caused by the blood flow from atrial kicking into a stiff ventricle, it should be right after the P wave on electrocardiogram (ECG).

The first and second heart sounds are caused by the retrograde blood flow hitting on the mitral valve and the aortic valve, respectively (we will just talk about the left heart, anyway). Sometimes during the ventricular filling phase, or the diastolic phase of a cardiac cycle, some audible sounds are generated. Since they occur after the second heart sound, they are just sequentially named. The third heart sound occurs in the mid-diastolic phase and the fourth heart sound in the late-diastolic phase.

### Hmm ... So what happens during the diastolic phase? Could this be the basis of our model?

Now let's see a schematic diagram of our left heart during diastolic phase.
Figure 2. Schematic diagram of a left heart in diastolic phase. Blood flows from pulmonary vein, through the left atrium and open mitral valves to the left ventricle. The pressure of pulmonary veins are $P_{PV}$, which reflects preload and is set to be a constant. The blood flow passes through an resistance of $R_{PV}$ and enters left ventricle with a volume flow rate of $Q_{MV}$. The blood flow would increase the pressure and volume of left ventricle. Through out the whole diastolic phase, the aortic valves are closed since the diastolic blood pressure (~80mmHg) is much higher than the pressure of left ventricle throughout the diastolic phase (<20mmHg).

Figure 2 shows our schematic left heart, with pulmonary vein, left atrium, mitral valves, left ventricle and aortic valves. Blood flows from pulmonary veins with a relatively constant pressure $P_{PV}$, which represents the preload, through the left atrium and mitral valve, overcoming a resistance of $R_{PV}$, to the left ventricle. This could be easily formulated as below.
$P_{PV}=P_{LV}+Q_{MV}R_{PV}$
The real problem is, how could we relate $P_{LV}$ and $V_{LV}$ ? There are different hypotheses, but not all are suitable to explain the phenomenon of the third heart sound. We can put the conclusion here before we discuss it in more detail in our next episode involving some simulation. A pure elastic response of ventricle that follows Laplace’s law (i.e., $\Delta P = \sigma(\frac{1}{R_1}+\frac{1}{R_2})$) will not generate a third heart sound because there will be no pressure fluctuation of audible frequencies generated. A viscous response of ventricular wall is required, and we will see why later.