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Background: I am coming at this question from an electrical engineering background, and I feel like I am missing certain assumptions that are going into the statement found in my physiology textbook, "vasoconstriction increases blood pressure"."

Consider a simple series circuit and a parallel circuit run by a battery/heart *[you will find the parallel and series circuit in any physiology book description of the vasculature, yet I can't find any exploration of the assumptions made when applying these circuit models]:*****

  1. In the series circuit, if I have an increase in resistance across one of my resistors, this will basically redistribute the pressure drops across the resistors, but it will not alter the total pressure drop across all the resistors [fixed by the heart].

  2. In the parallel circuit, if I have an increase in resistance across one of my resistors, this will redistribute the flow to different branches, but the pressure drop will not change as again this is fixed by the heart.

This analysis seems to suggest that if the resistance across an organ [branch of parallel circuit] changes, the flow changes, not the pressure. The heart, I would assume, then responds by increasing the pressure to increase flow ie actually injecting energy into the system.

Here is the problem with the circuit model though:

  1. it assumes that the battery/heart is the only source of energy in the system, and the resistors are passive re distributors of that energy.

-the controllers of vascular resistance are smooth muscle which must actively put energy into the system to vasoconstrict. This could be a source of pressure increase as the smooth muscle would be actively constricting against an incompressible fluid, but I am really not sure.

  1. it does not account for the compliance of the vasculature.

-the tubing the heart is hooked up to modifies the blood pressure the heart has to generate to inject fluid into that tube. If the tubing was stiff, the heart would have to generate very high systolic pressures that would then rapidly decrease during the diastolic phase. The more compliant the tubing, the less pressure the heart has to generate to inject fluid into the tube. Intuitively though, there would seem to some relationship between the ability of a fluid to flow and vessel compliance. A highly compliant vessel with a fluid injection will simply expand and hold the fluid while a less compliant vessel will maintain a pressure necessary to push the fluid along.

Sparknotes in the form of questions:

*1.Is the only source of energy in the cardiac circuit the heart? Or
does artiole smooth muscle actually inject energy into the system,
and result in systemic increases in the pressure available in the
closed circuit? 
 2. I don't think vascular compliance ie expansion of the artery walls due to volume filling results in any active injections of
energy into the system..it should simply transfer the energy
available to push fluid to elastic energy in the connective tissue
of the artery walls. Is this correct?
 3. Does vessel compliance partly determine the pressure the heart has to inject into the system?
 4. What is the relationship between compliance and flow if there is one?*
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  • $\begingroup$ I think this may be off-topic because it is about biology. $\endgroup$ – ACuriousMind Jan 20 '15 at 17:00
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    $\begingroup$ Seems to be a straight-forward application of Bernoulli's principle. I also don't see a relationship with circuits as anything valid. $\endgroup$ – Kyle Kanos Jan 20 '15 at 17:08
  • $\begingroup$ Regarding 1), yes, of course a muscle compressing fluid adds energy to the system. But the vascular musculature is not there to push the blood around, it's there to regulate local blood-pressure in the body (like the brain) and to regulate the amount of blood required in different body parts depending on the need (accumulated metabolites, heat transfer etc.). As a sidenote, do note that stiff vascularity leads to congestive heart failure sooner or later, it's really important to have the vascular compliance, the EE analogue is bypass capacitors on a power-net :) $\endgroup$ – BjornW Jan 20 '15 at 17:13
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    $\begingroup$ Bernoulli's principle only applies to inviscid flow, blood has viscosity. Bernoulli's principle would suggest that during vasoconstriction, blood pressure drops..instead it rises. $\endgroup$ – Zachary Miller Jan 20 '15 at 17:20
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    $\begingroup$ @ZacharyMiller: We apply Bernoulli to water, which is slightly less viscous than blood ($9\times10^{-4}$ Pa$\cdot$s for water versus $3\times10^{-3}$ Pa$\cdot$s for blood). And your analysis is wrong: in order to make up for the pressure decrease at the restriction, the heart must increase the pressure elsewhere. $\endgroup$ – Kyle Kanos Jan 20 '15 at 17:46
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Seems to me the electrical analogy is a good one. The heart system is trying to maintain a certain current I (to ensure adequate O2 flow). Raising any resistance, serial or parallel, increases R, thus raising V. There is vascular smooth-muscle compliance, but that just complicates the analogy.

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1.The heart is the only appreciable source of energy used to pump blood through the circulatory system. The low-pressure venous system might somewhat be aided by movements of the body's skeletal muscles since the larger veins contain 'check valves' that inhibit reverse flow. But none of the systems vessels I'm aware of provide fluid movement by peristaltic action from smooth muscle contractions. But vaso constriction/dilation do increase/decrease resistance against the heart and so are part of a system for regulating blood pressure. 2. That's right, the compliance of the vessel walls, like a capacitor in an electrical circuit only store the energy 3.Yes - however only the transient response. For any element or local branch of the system, the compliance of the vessels together with the resistance result in a 'time constant' for transmitting the fluid over a distance. 4. The larger the compliance, the longer the time constant, and so the longer it takes to move a volume of fluid.

A very good book that takes into account details in the physiology,physics and mathematics of the cardiovascular system is Cardiovascular and Respiratory Systems Modeling Analysis and Control By Batzel, et. al. SIAM Frontiers in Applied Mathematics, 2007. It contains models that can be directly simulated.

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This topic is clearly about physics as well as biology so don't let anybody tell you otherwise.

Bernoulli's Equation for incompressible fluid flow is applicable here:

$ {v^2 \over 2g}+z+{p\over\gamma}=\text{constant}$ where $v=\frac{Q}{A}$

Forget about the elevation Z for this analysis then:

$ {p\over\gamma}=\text{constant}-{Q^2 \over 2gA^2}$

"A" would be the cross sectional area of a blood vessel. "Q" is the blood flow rate. "P" equals pressure.

This is a starting point for deeper analysis. Try looking here as well:

http://forums.studentdoctor.net/threads/blood-pressure-velocity-in-capillaries.643725/

Also, the Hardy-Cross method for a network of fluid pipes could be very helpful. I'm imagining the system of equations to be incredibly dynamic and complex.

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