How does Matlab Simbiology calculate pharmacokinetic (PK) non-compartmental (NCA) area under the curve (AUC)?

I can't seem to find the answer to my question in SimBiology's documentation.

Does anyone know how Matlab calculates the non-compartmental AUC? Does it use the linear / log-linear trapezoidal rule? How many points does it use to extrapolate the curve to infinity? Does it use log or linear extension?

Many thanks!

Answer 1

[Arthur Goldsipe]

Hi,

Some of the details of SimBiology's non-compartmental analysis (NCA) depend on the type of data and type of dose. However, the conceptual approach is similar, so I will explain below how SimBiology calculates the AUC for a single dose with an IV bolus dose.

First, SimBiology uses the linear trapezoidal rule to estimate the area under the time-concentration curve until the last concentration measurement. This is denoted as AUC_0_tz in the SimBiology desktop. If time is denoted as t and concentration as y, then the following formula is used:

AUC_0_tz = trapz(t,y);

Next, the final two concentration measurements are used to estimate the terminal rate constant, denoted as Lambda_z in the SimBiology desktop. This is calculated in log-space as follows:

Lambda_z = -((log(y(end)) - log(y(end-1)))/(t(end) - t(end-1)));

The extrapolated area under the curve (from t(end) to infinity) is calculated analytically by assuming exponential decay as y(end)/Lambda_z.

Combining all of these, you can see that the AUC is calculated as

AUC = trapz(t,y) - y(end)*(t(end) - t(end-1))/(log(y(end)) - log(y(end-1)))