Maths Questions

Question 1

You are transferring an intubated patient from your hospital’s ICU to that of a hospital forty-five miles away due to bed pressures. The pressure gauge on the size E oxygen cylinder reads 7500 kPa. The patient has a minute ventilation of 9 litres per minute, and has an inspired oxygen fraction of 0.4. The ventilator uses 500ml oxygen per minute.

Answer 1

90 minutes

680L in cylinder, full at 13700
(7500/13700)x680 = 372 litres
O2 consumption: 0.9 x 9 = 3.6l/min
3.6 + 0.5 =4.1 (total consumption)
372/ 4.1 =90.732

Question 2

A 50kg patient has a plasma concentration of 5mg/litre of a mystery drug. You wish to increase this to 20mg/litre with a single loading dose.

The drug has a volume of distribution of 0.6L/kg and a clearance of 0.7ml/min/kg

Answer 2

450mg

5mg/litre = x mg / (0.6 x 50kg) litres
5 = x / 30 litres
x = 150 mg
20 = x / 30
x = 600 mg
But he’s already had 150mg so 600 - 150 = 450mg.