Sensitivity analysis applied to Coburn-Forster-Kane models of carboxyhemoglobin formation

When mathematical model predictions disagree with the behavior of the physiological system modeled, blame is generally placed on the inadequacy of the model. It was shown using the Coburn-Forster-Kane (CFK) models of carboxyhemoglobin (COHb) formation as illustrations, that a sensitivity analysis of the model can provide estimates of the effects of data variability and inaccuracy on model predictions. Sensitivity functions were derived for each variable in the model, and families of them were plotted as functions of time with work level as a parameter. The sensitivity plots identify the variables which can contribute the most to disparities between model and system behavior and illustrate how the relative importance of the error in each variable changes with both time and work level. For example, with exposure to a constant concentration of carbon monoxide (CO) at a constant level of exercise, errors in blood volume determination, initial [COHb], and total hemoglobin concentration do not affect the calculated equilibrium value of blood [COHb]; neither inspired concentration of carbon monoxide nor endogenous production rate affect the rate at which equilibrium is achieved; and all other variables affect both the equilibrium value of blood [COHb] and the rate at which it is achieved. The sensitivity analysis provides a link between model output variability and input or data variability which can be used to assess the value of efforts to reduce data error and to estimate the overall uncertainty of model predictions.