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I found this sentence from my notes which I cannot understand

PR < CO, CO $\uparrow$, PR > CO $\downarrow$

where

\item CO = AP / PR, Cardiac Output = Arterial P / Peripheral Resistance

I cannot understand the first sentence. I cannot understand how you can deduce by Ohm's law the relationship.

What is the point of the first sentence?

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1 Answer 1

up vote 2 down vote accepted

I don't get the first sentence either, since PR and CO in your notation are in fundamentally different units. It's like saying '4 Celsius < 5 meters.' You will have to think about what you are implicitly holding constant and ignoring in that relationship to make it meaningful. I suspect the first sentence is just emphasizing the inverse relationship between CO and PR (PR goes up, CO goes down, etc).

As for Ohm's law, absolutely! You have it written right there. I assume Cardiac output is the flow rate of fluid in a blood vessel, and AP is arterial pressure, and PR is peripheral resistance. Stated another way,

$\textrm{Flow} = \frac{\textrm{Pressure}}{\textrm{Resistance}}$,

which is exactly Ohm's law. Frequently electrical current is described with a Hydraulic analogy, with pressure$\rightarrow$voltage, fluid flow$\rightarrow$current, and flow resistance$\rightarrow$electrical resistance. It makes a lot of sense, since electric current is literally flow of electrons. Poiseuille's Law that makes this analogy rigorous, deriving an Ohmic relationship between those variables. Interestingly enough, Poiseuille derived the law in the context of blood flow, making it particularly applicable.

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