🟨 Area Under the Moment Curve

The area under the moment curve (AUMC) is a measure of the total area under the first moment curve. The Moment Curve is a paired set of values (x,y) where x is the time and y is the time multiplied by the concentration from the concentration-time curve. Just as AUC is calculated using partial areas, the AUMC is calculated using partial areas for the moment curve ($pAUMC$). The $pAUMCs$ can be calculated using the linear method or linear up logarithmic down method.

The linear method is the most commonly used calculation of AUMC because there is no assumption of exponential decline in the first moment curve (contrary to the concentration-time curve which normally exhibits exponential decline). However, both methods are performed in Aplos NCA for the user.

Linear Method

The following equation is used to calculate the $pAUMC$ between any two data points with concentration values:

$pAUMC=\frac{1}{2}\ast (C2\ast T2+C1\ast T1)\ast (T2-T1)$

Linear Up Logarithmic Down method

The following equation is used to calculate the $pAUMC$ for any two data points with concentration values which are increasing, or when either concentration value is 0:

$pAUMC=\frac{1}{2}\ast (C2\ast T2+C1\ast T1)\ast (T2-T1)$

When the concentrations are declining, and neither concentration value is 0, the following equation is used to calculate the $pAUMC$:

$pAUMC=[\frac{C1\ast T1-C2\ast T2}{ln(\frac{C1}{C2})}]\ast (T2-T1)-\frac{C2-C1}{ln(\frac{C2}{C1})}\ast {(T2-T1)}^2$