Answer #1. The minute volume to get 40 torr with the same VD / VT of 0.3 for this patient is 7.5 L/min. The change in minute ventilation is therefore 1.5 L/min in this particular case. If you kept the same tidal volume of 700 ml on the ventilator, the Rate would now need to be 11 breaths/min (BPM) to get a 7.5 L/min minute ventilation. You could change the Rate from 8 to 11 immediately without adverse effects. This assumes the condition is acute which means the pH was about 7.32 at a PaCO2 of 50 torr. The change in pH units in acute respiratory acidosis is estimated as .008 x the change in PaCO2. A change in PaCO2 from 40 to 50 = 10. 10 x .008 = .08 change in pH units or 7.40 - .08 = 7.32 approximately.
Another approach is to use the equation PaCO2 (known) x VE (known) = PaCO2 (desired) x VE (desired). If you know the patient has a minute ventilation of 6.0 L/min and the PaCO2 comes back 50 torr, use this formula to find the desired VE.
#2. 55 = 240 / VA. VA = 4.4 L/min. Estimated VD / VT = .6. 4.4 + .6 VE = VE. VE = 11.0 L/min. 11 / .8 = 14 BPM. You'd set a tidal volume of 800 ml and a rate of 14 BPM. Check for signs of air-trapping when ventilation is initiated.
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