Calculating Pharmacokinetic Areas

Although it is recognized that pharmacokinetic processes follow exponential processes, area under the curve ( AUC ) estimations are frequently carried out using linear trapezoidal methods. This is justified based on the fact that most human studies are carried out following oral dosing, and it is believed that a logarithmic trapezoidal method will markedly underpredict the areas for increasing drug concentrations. Here we show that increasing concentrations can be estimated more accurately using a new simple logarithmic method for increasing concentrations. Further, no previous discussion of linear versus logarithmic calculation has been published for area under the moment curve ( AUMC ) calculations. Thus, the derivation of a new methodology for calculating area values for logarithmic processes exhibiting increasing values of concentrations and moments is shown. Use of the methodology is presented and compared with the presently utilized linear approach. Pharmacokinetic absorption and elimination processes are primarily assumed to follow an exponential process, so that measurements of concentrations over time exhibit exponential versus linear relationships with time. Therefore, calculations of AUC should be more accurate using logarithmic methods than with linear methods. It is recognized that for decreasing concentrations with time, more accurate calculations of AUC will be estimated using the logarithmic trapezoidal rather than the linear trapezoidal rule. However, it was believed that logarithmic AUC calculations would be more inaccurate for increasing concentrations and moment values. Therefore, there is no generally recommended rule as to how AUC s should be estimated. We show here that a simple logarithmic methodology can be utilized for all increasing values except to the first measurement after time zero. It appears that for concentration-time curves, AUC will be best estimated using logarithmic methods for both increasing and decreasing concentrations. However, it appears that for well-designed sampling schedules, the increased accuracy of using logarithmic trapezoidal methods versus using linear trapezoidal methods is not sufficient to give significant errors in clearance calculations. In contrast, here we show that using linear area calculations for AUMC is probably more accurate than using any combination of linear and logarithmic methods.