# Contractility, MAP, and Kinetic energy of blood

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#### Wannabedoctah

##### New Member

Hi everyone,
It would seem to me that blood pressure would be due to the amount of blood in a vessel as well as the force that blood was ejected from the left ventricle with since blood ejected with a greater force could exert a greater force on the wall of an artery. However, the equation for MAP: MAP=CO x TPR only seems to take into account blood volume. Where am i going wrong?

#### backside_attack

##### MS2
Hi everyone,
It would seem to me that blood pressure would be due to the amount of blood in a vessel as well as the force that blood was ejected from the left ventricle with since blood ejected with a greater force could exert a greater force on the wall of an artery. However, the equation for MAP: MAP=CO x TPR only seems to take into account blood volume. Where am i going wrong?
I think either I'm misunderstanding you or you don't quite grasp what TPR is. "only takes into account blood volume" is not the same thing as TPR, as the resistance in the vessels "pushes back" on the blood (for lack of a better way to explain this) and increases blood pressure.

Think about good ol' physics and electrical circuits. How does resistance affect flow through a circuit? You can also think of this in term's of Ohm's Law for fluid flow where...
TPR = MAP/CO (assuming CVP = 0...)
Q = deltaP/R

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#### Psai

##### This space for lease
Removed
5+ Year Member Don't just memorize the equation, learn what the letters actually mean

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D

#### deleted763299

Ok... let's go way back to physics! Recall Poiseuille's equation: So, how does this help you at all? In a human being, the flow rate (Q) comes from cardiac output (CO), which is in turn related to heart rate and stroke volume. Radius (r) in the above equation is related to total peripheral resistance (TPR), which is related to how vasodilated or vasoconstricted the various vascular beds are in the patient (the arterioles are the most important contributors to TPR). The viscosity of blood (mu) is not often clinically relevant, and we never really give the path length (L) any consideration in terms of blood vessels.

So to circle all the way back to your question, the equation MAP = CO x TPR does not only account for blood volume. It accounts for much more, as discussed above.

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#### Wannabedoctah

##### New Member
Thanks for the replies guys. Very helpful. I worded my question poorly though. What I was trying to get at is: Does the kinetic energy of blood contribute to blood pressure? If so, where does our equation take that into account?

#### NotaCop

##### Full Member
5+ Year Member
It's not a simple black and white answer, but my understanding is that the force aspect is layered into CO. Go back and look at the CO output formula and review the variables that can change it. Stroke volume and heart rate. If you're asking about force specifically, and increased force will lead to a higher stroke volume if nothing else changes. Ways to raise this specifically are with higher contractility (sympathetics, positive inotropes, epinephrine,etc.).

That's simplified and boiled down but hope it helps. And disclaimer is that I only recently learned this too so can't guarantee it's 100% accurate

#### Wannabedoctah

##### New Member
Ok... let's go way back to physics! Recall Poiseuille's equation:

View attachment 214541

So, how does this help you at all? In a human being, the flow rate (Q) comes from cardiac output (CO), which is in turn related to heart rate and stroke volume. Radius (r) in the above equation is related to total peripheral resistance (TPR), which is related to how vasodilated or vasoconstricted the various vascular beds are in the patient (the arterioles are the most important contributors to TPR). The viscosity of blood (mu) is not often clinically relevant, and we never really give the path length (L) any consideration in terms of blood vessels.

So to circle all the way back to your question, the equation MAP = CO x TPR does not only account for blood volume. It accounts for much more, as discussed above.

Thanks for the detailed reply! Unfortunately I still have some confusion.

I would think that if contractility increases, blood will be ejected at a higher velocity. Thus, it will have more kinetic energy that can be converted into pressure energy. Does this higher kinetic energy not contribute to MAP?

D

#### deleted763299

I would think that if contractility increases, blood will be ejected at a higher velocity. Thus, it will have more kinetic energy that can be converted into pressure energy. Does this higher kinetic energy not contribute to MAP?

So if contractility increases (in a healthy heart) what does that mean? An increase in stroke volume, which (since CO = HR x SV) means an increase in CO assuming that HR doesn't decrease proportionately. An increase in CO at a constant TPR means an increase in MAP.

Generally, thinking about blood velocity is not useful. Neither is blood's kinetic energy. I think you also may have an incorrect idea in your head that pressure is a representation of energy... it is NOT! Pressure is defined as Force divided by area, and will have units of pressure such as: mmHg, cmH2O, Pascals, psi, etc. Energy is measured in units of work such as: Joules, Calories, BTU, etc.

Does the kinetic energy of blood contribute to blood pressure?

Strictly speaking, that answer to this question is yes. Algebra can get you to the relationship that will show you exactly how... but I don't have an easy way to show that on SDN.

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#### Wannabedoctah

##### New Member
So if contractility increases (in a healthy heart) what does that mean? An increase in stroke volume, which (since CO = HR x SV) means an increase in CO assuming that HR doesn't decrease proportionately. An increase in CO at a constant TPR means an increase in MAP.

Generally, thinking about blood velocity is not useful. Neither is blood's kinetic energy. I think you also may have an incorrect idea in your head that pressure is a representation of energy... it is NOT! Pressure is defined as Force divided by area, and will have units of pressure such as: mmHg, cmH2O, Pascals, psi, etc. Energy is measured in units of work such as: Joules, Calories, BTU, etc.

Strictly speaking, that answer to this question is yes. Algebra can get you to the relationship that will show you exactly how... but I don't have an easy way to show that on SDN.

Ok sounds good. Thank you!

#### Wannabedoctah

##### New Member
So if contractility increases (in a healthy heart) what does that mean? An increase in stroke volume, which (since CO = HR x SV) means an increase in CO assuming that HR doesn't decrease proportionately. An increase in CO at a constant TPR means an increase in MAP.

Generally, thinking about blood velocity is not useful. Neither is blood's kinetic energy. I think you also may have an incorrect idea in your head that pressure is a representation of energy... it is NOT! Pressure is defined as Force divided by area, and will have units of pressure such as: mmHg, cmH2O, Pascals, psi, etc. Energy is measured in units of work such as: Joules, Calories, BTU, etc.

Strictly speaking, that answer to this question is yes. Algebra can get you to the relationship that will show you exactly how... but I don't have an easy way to show that on SDN.

Im really sorry, last question. I am looking at a pressure volume loop. If we increase contractility, the intraventricular pressure for a given volume increases. Since aortic pressure essentially mirrors intraventircular pressure once the aortic valve opens, we can call the highest point in the pressure volume loop systolic pressure. I understand that when contractility increases it will increase blood pressure bc of the increase in stroke volume, but since an increase contractility increases the pressure for a given volume won't there be an increase in blood pressure independent of the stroke volume if the contractility is increased? If so, how does the equation for MAP take this into account?

D

#### deleted763299

I am looking at a pressure volume loop.

A physiology classic...

If we increase contractility, the intraventricular pressure for a given volume increases

I assume the volume you're talking about is the left ventricular end-diastolic volume (LVEDV). I'm with you so far.

Since aortic pressure essentially mirrors intraventircular pressure once the aortic valve opens, we can call the highest point in the pressure volume loop systolic pressure.

I'll accept this for the purposes of our discussion, since we're talking about normal physiology, and normal healthy hearts. Don't get too attached to this assumption going forward. But sure, we'll call the highest point the SBP.

I understand that when contractility increases it will increase blood pressure bc of the increase in stroke volume,

Perfect...

but since an increase contractility increases the pressure for a given volume won't there be an increase in blood pressure independent of the stroke volume if the contractility is increased?

Found the problem! Stroke volume and contractility are not independent. You've already correctly pointed out that on you're pressure volume loop demonstrating an increase in contractility, the LVEDV for both loops is the same (stated another way, there's no change in preload). What's different about the loops? You've correctly observed that the pressure appears higher after contractility increased. The other thing that's different is that the left ventricular end-systolic volume (LVESV) is lower after contractility is increased. And the equation for stroke volume is: SV = LVEDV - LVESV. Therefore as LVESV gets smaller, SV gets larger.

If so, how does the equation for MAP take this into account?

You can't get an increase in contractility without getting a decrease in LVESV (in a healthy heart), which intimately connects these two quantities. Therefore, the equation for MAP does account for contractility.

#### Wannabedoctah

##### New Member
A physiology classic...

I assume the volume you're talking about is the left ventricular end-diastolic volume (LVEDV). I'm with you so far.

I'll accept this for the purposes of our discussion, since we're talking about normal physiology, and normal healthy hearts. Don't get too attached to this assumption going forward. But sure, we'll call the highest point the SBP.

Perfect...

Found the problem! Stroke volume and contractility are not independent. You've already correctly pointed out that on you're pressure volume loop demonstrating an increase in contractility, the LVEDV for both loops is the same (stated another way, there's no change in preload). What's different about the loops? You've correctly observed that the pressure appears higher after contractility increased. The other thing that's different is that the left ventricular end-systolic volume (LVESV) is lower after contractility is increased. And the equation for stroke volume is: SV = LVEDV - LVESV. Therefore as LVESV gets smaller, SV gets larger.

You can't get an increase in contractility without getting a decrease in LVESV (in a healthy heart), which intimately connects these two quantities. Therefore, the equation for MAP does account for contractility.

Thank you very much for your help and time! i greatly appreciate it!