# How does increased resistance to flow decrease blood pressure?

I have recently encountered this question:

Waldenström's macroglobulinemia is a condition which causes increased blood viscosity due to high protein content in the blood. How would Waldenström's macroglobulinemia influence blood flow and pressure?

(A) Blood flow would be increased, blood pressure would increase

(B) Blood flow would be increased, blood pressure would decrease

(C) Blood flow would decrease, blood pressure would decrease

(D) Blood flow would decrease, blood pressure would increase

My immediate thought was to consider the relationship between viscosity and resistance. If the viscosity of the blood increases, the resistance (to flow) should also increase. According to the equation for vascular resistance:

$$R=\frac{\Delta P}{Q}$$ Resistance is directly proportional to blood pressure. This lead me to believe that the increased resistance should lead to an increase in blood pressure. But even without the use of equations, intuitively, I suspect that the heart should work harder (thus raise blood pressure) if there is resistance to blood flow.

However, the answer key indicates that choice (C) is correct, and that the pressure decreases. How is this possible? The explanation given in the key is:

Viscosity is directly proportional to resistance.

Blood flow is inversely proportional to resistance.

Blood pressure is directly proportional to flow.

If you have increase viscosity, you'd have increased resistance, resulting in less flow, and consequently lower pressure.

There is not enough information in the question to solve it.

The answer key from the original question makes a logical error:

Viscosity is directly proportional to resistance.

This is true. An increase in viscosity increases resistance. Flow and pressure do not matter for this statement to be true. You are correct to assume an increase in resistance.

Blood flow is inversely proportional to resistance.

This is true, but it's missing a qualifying statement: blood flow is inversely proportional to resistance for a given pressure drop. You can only assume blood flow decreases when resistance increases if you also assume pressure stays the same. Maybe this is a reasonable assumption, though I'll note it is not one that you seem expected to make since all the answers involve changes in pressure.

Blood pressure is directly proportional to flow

Again, this is true, but is missing an even more important qualifying statement than the previous one. Blood pressure is directly proportional to flow for a given resistance. Importantly, you know this does not apply because you know resistance changed. If resistance is different between Situation A and Situation B, like in your problem, you cannot assume that flow and pressure change in the same direction from A to B.

What you do know is that

$$R=\frac{\Delta P}{Q}$$

holds. You know that R increases. So you know that the flow decreases if the pressure drop is constant, and you know that the pressure drop must increase if the flow is to remain the same. More generally, you can say "there will be a greater ratio of pressure to flow rate". You cannot solve the problem prompted by the question, which asks you to know the direction of flow and pressure change, without additional information about one or the other. The only way you would get a decrease in both flow and pressure is if the drop in flow is proportionately greater than the drop in pressure differential; nothing in the question suggests this is an assumption you should make.

I would rewrite the solution as:

If you have increase viscosity, you'd have increased resistance, resulting in a greater ratio of pressure to flow rate.

You can only make statements about the ratio with the information given.

• Perfect explanation! Aug 12, 2021 at 18:35