carbon cost = CO2 x time (area under the curve )

for e.g: i change the ventilatory setting from Control mode (PC/VC) to Synchronised mode; Intuitively the work of breathing is increased to the extent that the patient has begun to trigger own breaths which are then supported by the ventilator. How is this work of breathing defined in terms of the "CO2" produced cumulatively. So is the case of an intravenous cannulation!