# How does vasoconstriction/vasodilation change blood pressure?

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.

2. 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?
• How do say pressure drop is fixed by heart? Jan 20, 2015 at 17:10
• Its engineering lingo..I apologize. It essentially means that the only energy in the system is provided by the heart. Jan 20, 2015 at 17:15
• I mean, if you increase a single resistance in a series circuit, will there be no change in the potential drop across the entire circuit? Jan 20, 2015 at 17:19
• correct by conservation of energy Jan 20, 2015 at 17:22

## 3 Answers

The circulatory system is a dynamic system which cannot be adequately explained by your example (at least not by me). You need to understand it, not seek to make it fit your (especially) electrical circuits with resistors. Blood isn't electricity. At least try a fluid dynamics model.

Let's take this very simple model: Blow up a balloon four-fifths of the way, and put a wide inflatable cuff around its middle. Inflate the cuff so that the balloon bulges just a tiny bit at the ends, then stuff it all into a plexiglass box so that the balloon has no room to expand. The plexiglass box represents our body. Lets call the pressure inside the balloon now normal blood pressure. The air in the balloon represents your total blood volume. It can't change from moment to moment; it's fixed. The box can't change it's volume moment to moment either. It's fixed.

The cuff represents arterial smooth muscle. Vasoconstriction can be represented by inflating the cuff further. Constriction (inflation of the cuff) will increase the pressure throughout inside the balloon, because the same amount of gas now has to exist in a smaller space. Vasodilation (deflating the cuff) decreases the pressure inside the balloon, because the gas can now inhabit a larger amount of space.

That's it, really. If the same volume must inhabit a smaller, constricted space, the pressure exerted by blood in that space will be higher. If the blood vessles dilate, the pressure in the blood vessels falls.

Now add about 20 layers of complexity to that simple model, and you have a working model of the circulatory system.

Sparknote answers:

1. Arterial and arteriolar smooth muscle "injects energy into the system", resulting in systemic increases in the pressure existing in the vascular "circuit" (meaning somewhat elastic tubing) if resistance requires energy. (So I have misunderstood: see @Raoul's answer.)

2. Sorry, I didn't read this properly the first time around. Yes, the heart supplies the energy. The contribution of the elastic walls of the arteries is not active, but passive.

3. Absolutely. The more elastic/compliant the arteries are, the less work the heart must exert to pump the blood through the circuits. The stiffer and narrower the arteries are, the harder the heart must work to pump blood through the circuits. The result of that increased work is a thickening of the muscular walls of the heart, called ventricular hypertrophy, which is a sign of elevated pressure in the system.

4. I'm not sure I want to commit here to your lingo, but the answer should be inferable from numbers 1-3. Elastic vessels help (by rebound compression) to propel the blood through the circuits. Stiff vessels hinder it, making the heart do more of the work.

I am not an engineer, so I may be misusing some of the terms.

Edited to add: Please see @Raoul's answer for a better explanation.

I'll try a brief answer myself.

1. No, the heart is not the only energy provider, as others have stated above. Does vasoconstriction inject energy into the system? Not really. Arteriolar constriction will increase the resistance of the system. Therefore, more energy will be required to keep flow at a constant level when vasocontriction occurs. Arteriolar vasoconstriction forces the system to function at a higher energy level, yet it does not inject energy targeted at facilitating flow.

2. Yes, your assumption is correct.

3. @anongoodnurse answered correctly.

4. There is no direct relationship between compliance and flow. They are independent factors. The important point is the following: during diastole, the heart is isolated from the vessels. The higher the vessel compliance is, the more potential elastic energy will be transferred from the heart to the vessels during systole, to then ensure good flow during diastole. In elderly persons for example, arteries are usually stiff, systolic pressure is high, and diastolic pressure is low (as is flow).

To conclude, I would say that the most important lesson that is to be learned here is that although a higher blood pressure means a higher energy state and more work for the heart, it is incorrect to assume that blood flow is physiologically adequate because pressure is high! This is a common mistake made in the emergency room.

• +1 - glad to read your answer. You understand fluid dynamics better than I do. Because of your different answer, I had to rethink my own, and see my errors. I do find myself sometimes wishing you were around more. Care to weigh in on the cardiac output question? ') Jan 21, 2015 at 15:37
• @anongoodnurse Thanks! I'll have a look at that one. I spend a lot of time on stackoverflow, but I like it here as well. I'll definitely stick around. BTW, your answers are usually very good! Jan 21, 2015 at 16:36

I just want to add a few points to the above answer:

Heart is not the only organ which helps blood flow. The following structures also help:

• The action of muscles on deep veins acts as a pump - Soleus is called peripheral heart for that matter
• The compliance itself adds to the flow - Infact the compliance of the blood vessels is what makes the blood flow continuous instead of pulsatile like a system with stiff tubes would be expected to act when the pump is pulsatile in nature

Some Critical Points to keep in mind:

1. The circulatory system is made in such a way that the total sum of cross sections of all the vessels at a particular level is as follows:

• The sumtotal of cross-sections of all capillaries is the largest cross section ~ 11308 cm2, (approximately only 1/4 are open under normal pressure, so effective cross section is ~ 2827 cm2)
• The sumtotal of cross-sections of venules followed by arterioles (~141 cm2) (venules more than arterioles as arterioles normally are under a tonal contraction)
• Sumtotal of cross-sections of veins followed by arteries (~63 cm2)
• Cross-section of Vena Cava ~ 1.38 cm2 followed by Aorta ~ 1.13 cm2

So if the cross sections are added up: Capillaries > Venules > Arterioles > Veins > Arteries

2. The Pressure Blood Pressure we measure is not exactly the flow pressure aka the pressure gradient. We measure the radial pressure not the pressure gradient. Special equipment is needed to measure pressure gradient.

3. The volume of fluid inside a parallel circuit (artery to capillary to vein) is not constant as plasma diffuses out at the small arterioles and capillary levels and diffuses back in at the venous side.

4. The pressure flow curve is not linear due to the compliance of the blood vessels.

5. The heart contributes very little to the blood flow in the veins. (To re emphasize that heart is not the only organ driving circulation). It is mainly through postural drainage and muscle action.

Coming to your question I like to point out one thing:

If there is a need to increase perfusion, the vasoconstriction occurs at the venular side. The capillary pressure is responsible for perfusion.

$$P_c = \frac{(R_{post}/R_{pre}).P_a + P_v}{1 + (R_{post}/R_{pre})}$$ Where P - pressure and the characters a, v and c denotes artery, vein and capillary resistance

Rpost - Post-capillary resistance

Rpre - Pre-capillary resistance

The equation and picture are taken from Boron and Boulpaep textbook of Medical Physiology, 2nd Edition, Chapter 19: Arteries and Viens.

When there is a need to increase the perfusion to an organ the post capillary pressure is raised by venoconstiction (or in the case of glomeruli of kidney constriction of efferent arterioles). As you can see from the above equation, such a rise will cause rise in the capillary pressure and increase the perfusion.

Otherwise vasoconstriction occurs to do exactly what you assumed would happen: to redirect blood flow. In fact this happens at several levels:

1. Vasoconstriction of periphery (limbs) occur in cold conditions which causes cyanosis (meaning the flow is so reduced that most oxygen is used up)
2. Vasoconstriction of Splanchnic vessels occur when muscles need more blood (during exercise, flight, fight, etc...)

If you can read this chapter you will understand the equation much better. This book explains the physics behind physiology in a beautiful manner.