Blood flow, Bernoulli's equation and Poiseuille's equation

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Discussion Overview

The discussion revolves around the relationship between blood flow, Bernoulli's equation, and Poiseuille's equation, particularly in the context of arterial constriction due to cholesterol buildup and arteriosclerosis. Participants explore the implications of these equations on blood pressure and flow rate, considering both theoretical and physiological aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes the continuity of flow equation, Bernoulli's equation, and Poiseuille's equation, questioning their application to blood flow in arteries affected by arteriosclerosis.
  • The same participant argues that a decrease in arterial area due to cholesterol buildup should lead to an increase in blood velocity and a decrease in pressure at that area, as per Bernoulli's principle.
  • The participant also states that according to Poiseuille's equation, a decrease in radius would increase the pressure gradient needed to maintain flow rate, suggesting that the heart would need to exert more pressure.
  • Another participant challenges the relevance of the equations to cardiovascular disease, noting that plaques do not create uniform constrictions and that blood flow is highly variable and non-Newtonian.
  • This participant emphasizes that blood pressure is influenced by systemic physiological features rather than solely by localized obstructions.
  • A later reply asserts that the introduction of an obstruction alters the system dynamics, implying that the continuity equation may not apply in the same way.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of fluid dynamics equations to biological systems, with some supporting the theoretical framework and others questioning its relevance in the context of cardiovascular physiology. The discussion remains unresolved regarding the implications of these equations for understanding blood flow in diseased arteries.

Contextual Notes

Participants note limitations in applying theoretical fluid dynamics to biological systems, including the non-uniform nature of arterial plaques and the complex behavior of blood as a non-Newtonian fluid. There is also mention of the variability in blood flow and pressure dynamics that may not align with simplified models.

gkangelexa
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Blood flow...
Relating the Continuity of flow equation (A1v1 = A2v2) with Bernoulli's equation, with Poiseuille's equation.

Continuity of flow equation tells us this: when the area decreases, the velocity increases in order to maintain a constant flow rate.
Bernoulli's equation tells us that when velocity increases, the pressure (that the fluid exerts on its walls) decreases.

Poiseuille's equation says that the flow rate Q is directly proportional to the pressure gradient (P1 - P2).

So, knowing all this, where am I thinking wrong in the following situation involving blood? (I'm assuming blood has laminar flow like my physics book does).

When you have cholesterol buildup and arterosclerosis, then the arteries decrease in area since the radius is smaller. From the continuity of flow equation, the velocity of the blood must increase to maintain the same flow rate Q. This increase in velocity results in a lower pressure at that area.

However, based on Poiseuille's equation, the arterosclerosis would cause a decrease in R in the equation, and consequently cause an increase in the pressure gradient in order to maintain the same flow rate. This means that the heart should increase the pressure (high blood pressure as is observed)
How can this be though? If P2 is decreased (as was established in the previous paragraph), then P1 should decrease, not increase. or It shouldn't have to increase since P2 decreased, and this already created a greater pressure gradient.
 
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gkangelexa said:
Blood flow...
Relating the Continuity of flow equation (A1v1 = A2v2) with Bernoulli's equation, with Poiseuille's equation.

Continuity of flow equation tells us this: when the area decreases, the velocity increases in order to maintain a constant flow rate.
Bernoulli's equation tells us that when velocity increases, the pressure (that the fluid exerts on its walls) decreases.

Poiseuille's equation says that the flow rate Q is directly proportional to the pressure gradient (P1 - P2).

So, knowing all this, where am I thinking wrong in the following situation involving blood? (I'm assuming blood has laminar flow like my physics book does).

When you have cholesterol buildup and arterosclerosis, then the arteries decrease in area since the radius is smaller. From the continuity of flow equation, the velocity of the blood must increase to maintain the same flow rate Q. This increase in velocity results in a lower pressure at that area.

However, based on Poiseuille's equation, the arterosclerosis would cause a decrease in R in the equation, and consequently cause an increase in the pressure gradient in order to maintain the same flow rate. This means that the heart should increase the pressure (high blood pressure as is observed)
How can this be though? If P2 is decreased (as was established in the previous paragraph), then P1 should decrease, not increase. or It shouldn't have to increase since P2 decreased, and this already created a greater pressure gradient.

This is a good example of 'biology without biology'. In terms of fluid dynamics, the thread Studiot linked to is a reasonable discussion about the relevant mechanics, including the difference between pressure and pressure drop.

In terms of cardiovascular disease, however, the question is completely irrelevant. Plaques do not form a uniform constriction of an artery, for example. Blood flow is not steady, but highly variable in time. Blood is a nonNewtonian fluid. Blood pressure (systole and diastole) are systemic physiological features and are not driven by a single plaque- in fact, the main loss of driving pressure occurs in the arterioles. I could go on...

To be sure, there is good work being done:
http://www.cism.it/courses/c0204/
http://www.ncbi.nlm.nih.gov/pubmed/8302047
http://www.sciencedirect.com/science/article/pii/0021929096845441
http://www.google.com/url?sa=t&sour...sg=AFQjCNEMQOAbrdkMP81kgLBrqDJnXEB2DA&cad=rja
 
In addition, when you add an obstruction, you're no longer talking about the same system, so continuity doesn't apply!
 

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