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## Main Question or Discussion Point

Hello, I'm a physician with special interest in cardiovascular physiology. I'm trying to comprehend the basic physics of the cardiovascular system. Here's my thought process -

Simply stated - the heart muscle contracts, thereby causing a reduction in the cardiac chamber volume and release of blood out of the chanber in the process. Consider an ideal situation where cardiac contraction produces X units of force, which then pumps 70 mL of blood out in to the arteries. If the heart beats 70 times a minute, this would add up to around 5L/min - aka the cardiac output (Q). Total resistance of the arterial network against which the blood is pumped (R) = 20 mm Hg/L/min. When blood is pumped against this resistance, it produces an arterial pressure (P) of 100 mm Hg.

The relationship between cardiac output (flow), mean arterial pressure (P), and total peripheral resistance (R) has been described as -

Q = P/R (some sources call it Ohm's law of fluid flow). I understand it is actually "delta P" that drives blood flow, but pressure on the venous end is considered negligible and not considered here. This formula is intuitive in the sense that if R is increased (referred to as increase in afterload in physiology texts), Q should decrease as the heart is pumping blood against higher resistance. Also, if P increases, the "delta P" increases, i.e. the pressure gradient between the arterial side and venous side increases, and blood flow should increase.

However, my biggest conundrum is, that P itself is dependent on R (as widely noted in literature). When R increases, blood is pumped against a larger resistance and that causes a larger outward push on the walls of the arteries - thereby increasing the P. Hence, this relation can be written as P = Q.R. Based on my current understanding, R is the only exclusive physical property here that is not influenced by other properties of the equation.

Quoting a thought experiment from a physiology textbook -

Experiment 1 - Imagine an instantaneous increase in total periperhal resistance (R) from 20 to 40. They cite "P = Q.R" and say P would jump from 100 to 200 mm Hg. Now Q = P/R --> both P and R doubled so Q would remain constant (5 L/min).

Experiment 2 - The alternate thought process in my head is - R doubles to 40 --> causing reduction in cardiac output to 2.5 from 5 L/min (because Q = P/R). Now, P = Q.R --> Q halved but R doubled so P would remain same (100).

I would guess the reality lies somewhere in between these two extreme outcomes (but perhaps more inclined towards the outcomes of experiment 1). Based purely on clinical experience, we often see a significant increase in P while increasing R but it has been experimentally established that increasing R does cause SOME (if not a huge) reduction in Q. I'm sure there has to be a more precise physical/mathematical explanation for this. I feel like I'm missing something obvious here. Any direction would be greaatly appreciated. Sorry for the long thread.

Simply stated - the heart muscle contracts, thereby causing a reduction in the cardiac chamber volume and release of blood out of the chanber in the process. Consider an ideal situation where cardiac contraction produces X units of force, which then pumps 70 mL of blood out in to the arteries. If the heart beats 70 times a minute, this would add up to around 5L/min - aka the cardiac output (Q). Total resistance of the arterial network against which the blood is pumped (R) = 20 mm Hg/L/min. When blood is pumped against this resistance, it produces an arterial pressure (P) of 100 mm Hg.

The relationship between cardiac output (flow), mean arterial pressure (P), and total peripheral resistance (R) has been described as -

Q = P/R (some sources call it Ohm's law of fluid flow). I understand it is actually "delta P" that drives blood flow, but pressure on the venous end is considered negligible and not considered here. This formula is intuitive in the sense that if R is increased (referred to as increase in afterload in physiology texts), Q should decrease as the heart is pumping blood against higher resistance. Also, if P increases, the "delta P" increases, i.e. the pressure gradient between the arterial side and venous side increases, and blood flow should increase.

However, my biggest conundrum is, that P itself is dependent on R (as widely noted in literature). When R increases, blood is pumped against a larger resistance and that causes a larger outward push on the walls of the arteries - thereby increasing the P. Hence, this relation can be written as P = Q.R. Based on my current understanding, R is the only exclusive physical property here that is not influenced by other properties of the equation.

Quoting a thought experiment from a physiology textbook -

Experiment 1 - Imagine an instantaneous increase in total periperhal resistance (R) from 20 to 40. They cite "P = Q.R" and say P would jump from 100 to 200 mm Hg. Now Q = P/R --> both P and R doubled so Q would remain constant (5 L/min).

Experiment 2 - The alternate thought process in my head is - R doubles to 40 --> causing reduction in cardiac output to 2.5 from 5 L/min (because Q = P/R). Now, P = Q.R --> Q halved but R doubled so P would remain same (100).

I would guess the reality lies somewhere in between these two extreme outcomes (but perhaps more inclined towards the outcomes of experiment 1). Based purely on clinical experience, we often see a significant increase in P while increasing R but it has been experimentally established that increasing R does cause SOME (if not a huge) reduction in Q. I'm sure there has to be a more precise physical/mathematical explanation for this. I feel like I'm missing something obvious here. Any direction would be greaatly appreciated. Sorry for the long thread.