Some More of Fluid Mechanics to understand Blood Flow
In my last blog, I wrote about the blood coming out of LV and how to estimate its velocity if there is stenosis at the AoV level. It can be on account of several reasons one of them being the calcification of valves. When the LVOT and AoV are of normal size, the velocity of the blood entering the Aorta is ~ 30 cm/sec and by the time it reaches the capillary beds in a human body the velocity reduces to 0.026 cm/sec. It means there is a 1000 times slowdown in the flow velocity of the blood. Also please remember the average length of the thoracic aorta is 33.2 cm! In other words, the blood flowing through the thoracic aorta is at a very high speed. Blood flowing towards the abdomen and in lower extremities also gets help from gravity but what about when the blood has to move to the head, say when the human being is in a standing position. At that time blood movement has to be against the force of gravity. How does it happen naturally?
Further, it is required that the blood flow velocity at a capillary level should be extremely low as at that level; the nutrients being carried in the oxygen-rich blood are to be exchanged with a “single-cell wall thickness” across capillaries and exchange O2 across the tissue cells of the body while collecting the CO2. If the speed is at which blood enters the Aorta from LVOT, then this exchange may not be able to take place across with cell walls and ensure the human body remains healthy for its functioning. So the fluid dynamics ensure to slow down the speed of flow naturally.
Now the Physics principle used to estimate the pressure exerted by a flowing fluid is by Bernoulli’s theorem which can be reduced to say the pressure exerted by a flowing fluid is directly proportional to the square of the velocity viz., V² where V is the measured velocity of blood flow in this case. We also know the normal blood pressure during systole is 120/80 mm Hg. The normal cross-section of the AoV is 2.5–4.5 cm².
While as per the Poiseuille’s law the Pressure difference is inversely proportional to the fourth power of the radius (R) of the pipe or artery through which fluid is flowing i.e., R⁴. Hence it can be seen as the stenosis reduces the cross sectional area of the AoV or of the arteries, there will be instant increase in the pressure gradient.
The obvious question for a common person that crops up is then how does the blood moves during diastole when the AoV shuts down and the blood has to move against gravity in the Asc-Ao portion, in the arteries branching out towards the head as well as till the Abd-Ao, though once descending aorta starts; gravity plays a positive role unlike during the Asc-Ao part. Now the major arteries are made up of three concentric layers viz., intima, media, and adventitia.
In the image above there are two elastic-lamina shown, one internal and the other external. So, during systole the inherent elasticity of these muscles by stretching stores energy. And during diastole when the AoV is closed, the elastic energy stored in the lamina makes it return to its normal position, thereby pushing the blood forward in the aortic arch portion and that continues in the descending aorta part making sure the blood crosses the aortic arch hump. The same action helps in pushing the blood in the three major arteries which branch out of the aortic arch towards the head viz., Brachiocephalic, Left Common Carotid, and Left Subclavian arteries. In these three major arteries, the blood has to move against the gravity away from the heart during each diastole phase to maintain a continuous flow of blood coming out from LV as synchronized with the heart rate. For that additional force is required to push. This is carried out by the elastic-lamina storing the elastic energy (analogous to streching of a rubber band) formed in the aorta and plays a major role in blood’s fluid dynamics.
There is one more fluid mechanic’s phenomenon that takes place because of the stenosis, it reduces the cross-section of AoV and blood velocity increases as stated above. Then no more it is a laminar flow of blood once it crosses the reduced orifice resulting in turbulence giving rise to vortex creation in the separation zone as shown.
This can be experienced as an analogy at a macro level not in a visual manner but more by the hearing of “sound”. Recall the watering of the backyard through a flexible pipe mentioned in PHDM-5. There, no sooner the cross-section of the pipe is reduced, the velocity of the water coming out increases. But also, one can hear a “hissing sound” of the water coming out. This sound is on account of the “turbulence” generation.
The “size of the vena contracta” shown getting created, plays a very vital role in assessing the pathology of blood regurgitation when the valves’ leaflets become insufficient in stopping the backflow of blood into atriums during diastole. We will deal with it in another blog. Let us stop here.
Cameron Ahmad
Code: PHDM-6
April 28, 2021
Brampton ON
Canada
