Looking at PK data #2

Here is a parallel set of data comparing young healthy adults and patients with cirrhosis. Again, this set of data is not meant to prove changes which happen in cirrhosis but more as an exercise to explore and understand PK effects.

As in the previous post, the first thing that strikes you is the massive changes in AUC seen in cirrhotics. The AUC for cirrhotics is 1.85 times that of the young. By the same logic as in the previous post this AUC increase is inversely related to a decrease in clearance and/or bioavailability. Since there is no way to assess bioavailability in this set of data, we shall leave it out of the discussion for the time being. It is not that the cirrhosis did not result in a change of bioavailability, it is just that the experimental design does not allow us to examine bioavailability effects.

Unlike the situation with the elderly, the reduction in clearance in cirrhotics is not accompanied by a fall in the unbound fraction. Instead, the unbound fraction is elevated from 3.5 to 5.3%. Changes in protein binding is not uncommon in liver cirrhosis. Often serum albumin is reduced. Here the protein binding is decreased with a corresponding increase in the free fraction. In fact the increase in free fraction has the effect of actually increasing metabolic clearance.The reduction in clearance is therefore not a result of a decrease free fraction, but primarily due to loss of enzyme activity. One can in addition, expect that the extent of degradation of enzyme activity is even greater than indicated by the extent of decrease of clearance because part of this effect is mitigated by an increased clearance caused by the increase in free fraction.

The increase in elimination halflife and corresponding fall in Kel is related to the reduction in clearance. The magnitude of the change in halflife is however larger than the fall in clearance and suggests that perhaps the Vd may have increased as well. This is expected because of the increase in free fraction.

Looking at PK data #1

Here is a set of data, adapted from published information comparing pk data of orally administered Drug X between young subjects and elderly subjects. The data here just provides an opportunity to qualitatively discuss PK effects, and it is not the intention here to 'prove' any PK changes in the elderly.

In this case the most apparent difference is rather large and significant difference in AUC between young and elderly. The AUC in elderly is about 1.84 times greater than that for the young. This is not an unexpected finding. The question is what is the cause of the reduced AUC?

We know from theory that AUC is determined primarily by bioavailability and clearance. However, since we have no way to assess bioavailability here, we shall concentrate on clearance effects instead. The increase in AUC is consistent with a reduction in clearance in the elderly. Again from theory, assuming this is primarily metabolic clearance, we expect that metabolic clearance of an orally administered drug is dependent on protein binding and enzyme activity.

When we inspect the protein binding data we find that the protein binding in elderly is actually increased with the unbound fraction falling from 4.3 to 3.4%. But this magnitude of change is relatively small compared to the estimated change in clearance. Hence it is possible the the total change in clearance reflects both a reduction in unbound fraction as well as a degradation of enzyme activity.

The fall in the unbound fraction potentially also affects the Vd. We have no direct way of assessing the Vd changes here but the Cmax provides indirect (though inaccurate) look at possible Vd changes. The Cmax for the elderly is higher than in the young but marginally less (probably insignificantly less) than the magnitude of change for AUC, so the Vd effect is uncertain.

The halflife changes in the elderly are consistent with the reduction in metabolic clearance.

The uncertainty in this case study is how much any bioavailability changes play in affecting the PK data. The magnitude of halflife change is quite comparable to the magnitude of AUC and clearance changes. This suggests that if there are bioavailability effects it is probably minimal.

The enigmatic AUC (area-under-the-curve)

The area under the plasma concentration-time curve (AUC) is an easily measurable pharmacokinetic parameter. It is used extensively in clinical pharmacokinetic studies, but students very often have a poor idea of what to make of the AUC.

Mathematically, the AUC is obtained by integrating the mathematical function that describes the plasma concentration-time profile. Practically however, it is estimated by summing all the small trapezoids that can be constructed under the concentration-time plot, using what is well known as the "trapezoidal rule".

Since it is mathematically the sum of all the plasma concentrations over the dose interval, it is often taken to represent clinical drug 'exposure'.

Pharmacokinetically however, the AUC is used to estimate drug clearance,

Clearance = Dose/AUC ...................(1)

After an oral dose, the equation is,

Clearance = (Bioavailability x Dose)/AUC ................(2)

A corollary of the above statements is that, since AUC is assumed to represent clinical drug exposure, and since AUC is determined principally by Bioavailability and Clearance, clinical drug exposure can be assumed to be determined primarily by clearance and bioavailability.

This concept has shaped our thinking for many decades, and it has closed our minds to distribution being perhaps an equal if not more important determinant of drug effects (more about this later!).

One particular area of confusion for students is that they too readily associate the AUC with bioavailability. When asked why the AUC changes for a particular drug, their first response is often that the bioavailability has changed. This is only half right.....since the AUC is determined by both clearance and bioavailability. In a situation where there are no bioavailability issues, AUC is determined primarily by clearance. AUC is only reflective of bioavailability when the clearance remains stable.

Experimentally, bioavailability is determined by measuring the AUC under oral and intravenous administrations. The clearance of the drug, measured under intravenous administration allows calculation of the clearance, which can then be used to estimate the bioavailability from the oral experiment.