Cardiovascular Physiology

Confusion #1 - Resistance vs Impedance

We are usually taught that blood flow = blood pressure / resistance

And that resistance is 8*length*blood viscosity/(pi*r^4)

But this is a drastic oversimplification. It assumes that the heart is like a direct current battery - a VAD with nonpulsatile flow. But the heart is pulsatile, ejecting blood during systole, yet there is also blood flow in diastole. So one cannot simply say that the cardiovascular system is like a direct current battery that is turned on and off at a certain frequency.

The pulsatile heart is in reality much more akin to alternating current batteries where there is rhythmic swings in pressure (aka voltage) leading to continuous blood flow.

With alternating current, flow = blood pressure / impedance.

Resistance and impedance seem similar but are fundamentally different. They both oppose flow. But the resulting loss of energy from resistance is changed into heat. Whereas the resultant loss of energy in impedance is NOT lost but converted into potential energy and is converted back into kinetic energy (flow) during a different period of the cardiac cycle.

In electrical engineering, capacitors and inductors oppose current by without a loss of energy. In the cardiovascular system, energy is stored as compliance (capacitor is the electrical analogue) and inertance (inductor is the electrical analogue).

Compliance. Systolic blood flow distends the arteries. This opposes blood flow by converting the kinetic energy into potential energy. During diastole, this potential energy is converted back into kinetic energy producing diastolic blood flow. The formula for compliance is [3*pi*length*radius^3]/[2*Elasticity Modulus*Thickness]. The formula for the opposition of flow imposed by compliance (aka capacitor reactance) is (1/[2*pi*f]) * (1/compliance)

Faster HR leads to lower impedance from compliance; slower HR leads to higher impedance

More compliant arteries lead to lower impedance; stiff arteries lead to higher impedance

Inertance is the property of the circulation that opposes a change in flow rate. Once blood has been accelerated to a certain velocity during systole, it will stay at this velocity until acted upon by other forces which also produces flow during diastole. The formula for inertance of a parabolic shape (because flow is faster in the center of the vessel) is (9 * length * blood density) / (4 * Area). The formula for opposition of flow imposed by inertance is 2*pi*f*Inertance.

Faster HR leads to higher impedance from inertance (opposite to compliance)

Impedance is the summation of Resistance, Capacitor Reactance, and Inductor Reactance. But you can't just add them because they have different phases (their peaks and troughs are different). Capacitor Reactance is directly opposite of Inductor Reactance so they subtract. And Resistance is 90deg off both of them. Therefore we have to use pythagoras.

Impedance = sqrt (Resistance^2 + [Capacitor Reactance - Inductor Reactance]^2)


I'm impressed you've read this far. Now for the most important question: does distinguishing resistance from impedance matter? - It does a lot.

The table below demonstrates that the opposition to flow in the arteries is mainly driven by compliance and resistance is minimal.

This more accurate schema also explains how how peripherally inserted VA-ECMO produces different pressure volume loops than centrally inserted VA-ECMO. Peripheral VA ECMO leads to retrograde flow up the aorta, dramatically adding to the inertance.


On the other hand, opposition to flow in the arterioles is mainly resistance. And veins have such high compliance than they are almost entirely inertance.

Arteries.xlsx

Confusion #2 - SVR vs Blood Pressure


Confusion #3 - MAP

We are classically taught that MAP = DBP + 1/3 (SBP - DBP). This assumes that 1/3 of the cardiac cycle is spent in diastole. This was originally described by Gauer who meticulously documented the blood pressure of a young healthy male at rest.

Obviously this assumption is dramatically flawed. The percentage of time spent in systole completely depends on the heart rate. At a HR of 50, the time spent in systole is indeed close to 1/3. But at a HR of 150, the time is closer to 1/2. When the traditional formula was used, the MAP was consistently underestimated by ~7pts with the error ranging ~13pts.

A better formula for estimating MAP is DP + [0.33 + (HR x 0.0012)] x PP. This formula was derived in a series of 450 patients in the cath lab and then verified in another cohort of patients paced at different rates.