Question

The cardiac output of a person at rest is 5 litres per minute and the mean aortic pressure is 100 mmHg.
During exercise, if the cardiac output doubles and mean aortic pressure rises to 110 mmHg, then the peripheral resistance in the systemic circulation will decrease by _______%.
(rounded off to the nearest integer). Assume venous pressure in systemic circulation to be negligible.

Hint:

In cardiovascular physiology, the cardiac output is inversely related to the peripheral resistance for a given mean aortic pressure. A rise in cardiac output leads to a decrease in peripheral resistance if the pressure increase is not proportional.

Answer 1

The relationship between cardiac output (\( Q \)), mean aortic pressure (\( P \)), and peripheral resistance (\( R \)) is given by Ohm’s law: \[ Q = \frac{P}{R} \] Where:
\( Q \) is the cardiac output,
\( P \) is the mean aortic pressure,
\( R \) is the peripheral resistance.
At rest: \[ Q_{{rest}} = 5 \, {L/min}, \quad P_{{rest}} = 100 \, {mmHg} \] During exercise: \[ Q_{{exercise}} = 2 \times Q_{{rest}} = 10 \, {L/min}, \quad P_{{exercise}} = 110 \, {mmHg} \] We can calculate the peripheral resistance at rest and during exercise using the formula for cardiac output: 1. At rest: \[ R_{{rest}} = \frac{P_{{rest}}}{Q_{{rest}}} = \frac{100 \, {mmHg}}{5 \, {L/min}} = 20 \, {mmHg} \cdot {min/L} \] 2. During exercise: \[ R_{{exercise}} = \frac{P_{{exercise}}}{Q_{{exercise}}} = \frac{110 \, {mmHg}}{10 \, {L/min}} = 11 \, {mmHg} \cdot {min/L} \] Now, we can calculate the percentage decrease in peripheral resistance: \[ {Percentage decrease} = \frac{R_{{rest}} - R_{{exercise}}}{R_{{rest}}} \times 100 = \frac{20 - 11}{20} \times 100 = 45% \] Thus, the peripheral resistance decreases by approximately \( 45% \).