Understanding Bernoulli's Pressure Equation and its Impact on Blood Pressure

[Art]

Bernoulli's hydrodynamic pressure equations show that when a fluid flows from a large bore to a smaller bore the velocity of the fluid increases and the pressure decreases so why is it that when people suffer from arterio sclerosis (a hardening and narrowing of the arteries) they suffer from high blood pressure rather than low blood pressure?

 

[Moonbear]

I'm not a cardiovascular physiologist, so I'll give it my best shot and then point you to a reference that has more nitty-gritty details than you probably ever wanted to know (and shows that biologists don't get away without knowing some math ).

The Bernoulli equation only refers to non-viscous, ideal fluids in a closed system. Pressure exerted by a viscous fluid, such as blood, can arise from other sources other than those accounted for by the Bernoulli equation, including turbulence at the site of artery blockages.

And here's the article I mentioned; ask the physicists if you need help understanding the equations.

http://advan.physiology.org/cgi/content/full/25/1/44
Badeer, H.S., Hemodynamics for medical students. Advan. Physiol. Edu. 25: 44-52, 2001.

 

[honestrosewater]

Are you also trying to fit the same amount of blood into a smaller container? That is, does the total volume of blood (and whatever else) stay constant while the total capacity of the circulatory system decreases? My intuition might be wrong, of course, but it seems that that would result in an increase in blood pressure (and change the interpretation).

 

[Astronuc]

Bernoulli's hydrodynamic pressure equations show that when a fluid flows from a large bore to a smaller bore the velocity of the fluid increases and the pressure decreases so why is it that when people suffer from arterio sclerosis (a hardening and narrowing of the arteries) they suffer from high blood pressure rather than low blood pressure?

Due to the continuity, a fluid must increase its velocity when moving from a larger cross section to a small cross section.

The other hydrodynamic effect is that the resistance to flow increases as the diameter (or flow area) decreases and as the 'roughness' of the pipe surface increases (as in the case of plaque buildup). So with flow restrictions, the pump or heart has to work harder to maintain a given flow, so the high pressure level must increase.

 

[Orefa]

Bernoulli's hydrodynamic pressure equations show that when a fluid flows from a large bore to a smaller bore the velocity of the fluid increases and the pressure decreases so why is it that when people suffer from arterio sclerosis (a hardening and narrowing of the arteries) they suffer from high blood pressure rather than low blood pressure?

I can think of at least a couple of important factors that have little to do with the Bernoulli behaviour.

First, you have to consider where blood pressure readings are taken: at the main arteries, not at the arteriolar level. As peripheral resistance to the flow of blood increases then the pressure within the main arteries increases as well since the same volume of blood must still circulate throughout the body.

Also, healty arteries are elastic and respond to pressure by dilating, as you can feel when you take a pulse. Each heart contraction causes the aorta to expand as blood rushes in, and this elasticity helps to regulate blood flow: elastic arteries prevent excessive pressure fluctuations between systole and diastole. If these vessels harden then the heart has to work harder to force blood through rigid tubes that do not compensate so pressure increases accordingly.

 

[Art]

Due to the continuity, a fluid must increase its velocity when moving from a larger cross section to a small cross section.

The other hydrodynamic effect is that the resistance to flow increases as the diameter (or flow area) decreases and as the 'roughness' of the pipe surface increases (as in the case of plaque buildup). So with flow restrictions, the pump or heart has to work harder to maintain a given flow, so the high pressure level must increase.

I read the article Moonbear referenced and I follow what you say above i.e. flow velocity increases and viscous fluids are susceptible to drag from the roughness of the pipe but these are both conditions that result in lower fluid pressure, not higher. It also is logical that the heart increases it's work rate to maintain a given flow but I still don't see how this leads to higher blood pressure for a given body of fluid in a closed system. The faster the blood flows (as a result of increased heart activity) the lower the pressure should be

Also, healty arteries are elastic and respond to pressure by dilating, as you can feel when you take a pulse. Each heart contraction causes the aorta to expand as blood rushes in, and this elasticity helps to regulate blood flow: elastic arteries prevent excessive pressure fluctuations between systole and diastole. If these vessels harden then the heart has to work harder to force blood through rigid tubes that do not compensate so pressure increases accordingly.

Yes, but when arteries dilate the increased diameter results in a higher pressure per Bernoulli's equations and as I mentioned above why doesn't faster moving blood from a faster beating heart cause reduced blood pressure?

 

[Orefa]

It also is logical that the heart increases it's work rate to maintain a given flow but I still don't see how this leads to higher blood pressure for a given body of fluid in a closed system. The faster the blood flows (as a result of increased heart activity) the lower the pressure should be

Take a bucket or water connected to a hose with a valve at the end. Change the height of the bucket to change the pressure at the valve, adjust the valve opening to change the resistance to flow. If you open the valve all the way then water will flow at a certain rate. If you close the valve half way then the flow rate will be cut by half. In order to restore the original flow you will need to raise the bucket to twice the height, which doubles the pressure and restores the flow.

When your arteries become clogged up, resistance to flow increases as if you were shutting the valve. This is not just in the main arteries but all over, and resistance to flow probably increases a lot more in smaller arteries (due to blood viscosity). The heart compensates as well as it can by beating harder in order to generate enough pressure to circulate all blood through the body as it should. This rise in pressure is highest in the aorta and the main arteries and it is easily measurable in the brachial artery commonly used for that.

 

[Orefa]

Yes, but when arteries dilate the increased diameter results in a higher pressure per Bernoulli's equations and as I mentioned above why doesn't faster moving blood from a faster beating heart cause reduced blood pressure?

You are comparing flexible arteries that respond to pressure change and hard pipes that do not respond the same way. An artery dilates somewhat like a balloon in response to increased pressure. Compare a baloon and a hard metal cartridge. If you inject the same amount of helium in a balloon as in a metal cartridge then the balloon will inflate but not the cartridge. As a result, pressure inside the cartridge will be much greater than inside the balloon. The same effect applies to arteries. As they receive pressurised blood they respond by dilating in order to absorb some of this pressure. This alows a smoother flow of blood. At the capilary level, blood flows at an almost fixed rate. It does not accelerate and decelerate with each heart beat since elastic arteries have all contributed to even out the flow.

 

[Schrodinger's Dog]

http://en.wikipedia.org/wiki/Blood_pressure

This is actually one of the more credible wiki links and should tell you everything you need to know.

Factors influencing blood pressure

The physics of the circulatory system, as of any fluid system, are very complex. That said, there are many physical factors that influence blood pressure. Each of these may in turn be influenced by physiological factors, such as diet, exercise, disease, drugs, etc.

Some physical factors are:

* Rate of pumping. In the circulatory system, this rate is called heart rate, the rate at which blood (the fluid) is pumped by the heart. The higher the heart rate, the higher (potentially, assuming no change in stroke volume) the blood pressure.
* Volume of fluid. In the case of the circulatory system, this is blood volume, the amount of blood present in the body. The more blood present in the body, the higher the rate of blood return to the heart and the resulting cardiac output. There is some relationship between dietary salt intake and increased blood volume, potentially resulting in higher blood pressure, though this varies with the individual and is highly dependent on autonomic nervous system response.
* In cardiac physiology, the rate and volume of flow are accounted for in a combined fashion by cardiac output. Cardiac output is the product of the heart rate, or the rate of contraction, multiplied by the stroke volume, the amount of blood pumped out from the heart with each contraction. Basically, it represents the efficiency with which the heart circulates the blood throughout the body.
* Resistance. In the circulatory system, this is the resistance of the blood vessels. The higher the resistance, the higher the blood pressure. Resistance is related to size (The larger the blood vessel, the lower the resistance), as well as the smoothness of the blood vessel walls. Smoothness is reduced by the buildup of fatty deposits on the arterial walls. Substances called vasoconstrictors can reduce the size of blood vessels, thereby increasing blood pressure. Vasodilators (such as nitroglycerin) increase the size of blood vessels, thereby decreasing blood pressure.
* Viscosity, or thickness of the fluid. If the blood gets thicker, the result is an increase in blood pressure. Certain medical conditions can change the viscosity of the blood. For instance, low red blood cell concentration, anemia, reduces viscosity, whereas increased red blood cell conentration increases viscosity. (The effect of so-called blood thinners are not on viscosity but on ability of the blood to clot, thus a misnomer.)

In practice, each individual's autonomic nervous system responds to and regulates all these interacting factors so that, although the above issues are important, the actual blood pressure response of a given individual varies widely because of both split-second and slow-moving responses of the nervous system and end organs. These responses are very effective in changing the variables and resulting blood pressure from moment to moment.