Question

A patient has a breathing rate of 18 breaths per minute, with a tidal volume of 500 mL, having an anatomical dead space of 150 mL. If the person has a heart rate of 120 beats per minute and a stroke volume of 50 mL, the alveolar ventilation to perfusion ratio is ________ (accurate to two decimal places).

Hint:

Alveolar ventilation is calculated by subtracting the anatomical dead space from tidal volume and multiplying by the breathing rate. The ventilation to perfusion ratio is the ratio of alveolar ventilation to the perfusion rate.

Answer 1

Correct Answer: 1.05

Alveolar ventilation \(V_A\) is the volume of air that reaches the alveoli and participates in gas exchange, calculated as: \[ V_A = (V_T - V_D) \times f \] Where:
- \(V_T = 500 \, \text{mL}\) (tidal volume)
- \(V_D = 150 \, \text{mL}\) (dead space)
- \(f = 18 \, \text{breaths/min}\) (breathing rate)
Substituting values: \[ V_A = (500 - 150) \times 18 = 350 \times 18 = 6300 \, \text{mL/min} = 6.3 \, \text{L/min} \] Perfusion \(Q\) is given by: \[ Q = \text{Heart rate} \times \text{Stroke volume} \] \[ Q = 120 \times 50 = 6000 \, \text{mL/min} = 6 \, \text{L/min} \] The alveolar ventilation to perfusion ratio \(V_A/Q\) is: \[ \frac{V_A}{Q} = \frac{6.3}{6} = 1.05 \] Thus, the alveolar ventilation to perfusion ratio is: \[ \boxed{1.05} \] Final Answer: 1.05