Ethanol elimination kinetics: a zero- to first order approach

Ethanol is primarily metabolized in the body by alcohol dehydrogenase to acetaldehyde. This is a very low Km reaction, so at most alcohol concentrations achieved after social drinking, it is very often assumed to obey a near zero order type of elimination kinetics.

In reality however, ethanol elimination kinetics, like every other drug follows a zero- to first order type of elimination profile. The above concentration-time curve illustrates the elimination kinetics from very high to very low ethanol concentrations.

During the zero order phase, there is a relatively fixed rate of ethanol elimination (NB. not elimination rate constant), but becomes clearly exponential at much lower concentrations. 

All this might be merely of academic interest if not for the fact that ethanol concentrations are very often back-extrapolated to a prior time (e.g. time of an accident or assault) because of forensic investigations. If the wrong model is used, the back-extrapolation can be quite erroneous.

Most often the back-extrapolations have been simplistically done assuming a zero order model, applying a fixed rate of elimination. We can see from the plot below, that the use of a zero order model, when the measured concentration is relatively low (less than 0.1 mg/mL) can lead to significant over-estimates of a prior concentration.

Effect of Vd change on pharmacokinetic parameters

With the interactive graph provided in the previous post you can vary the body weight by using the slider. Here, simplistically, the body weight directly changes the volume of distribution, so effectively the slider just changes the Vd.

What you will observe is that as you change the body weight, the half-life changes, and correspondingly, the time to reach steady state. The accumulation index also changes, because it is affected by the ratio of half-life/dose interval. The AUC and steady state concentrations remain unchanged because these are affected by Clearance and not Vd. The peaks and troughs changes, and these may affect the efficacy-toxicity balance of the dosage regimen if either efficacy or toxicity is affected by peaks or troughs.

In the display above, the body weight was altered from 70kg to 140kg. The half-life and time to reach steady state both corresponding doubled. While the AUC remained unchanged, the peaks have been lowered while the trough has increased. Whether the dosage regimen needs to be adjusted will depend on the therapeutic ratio of the drug, and the therapeutic objectives.

The issue of clarithromycin and increased cardiac deaths #2 - Pharmacology

Clarithromycin is a macrolide bacteriostatic antimicrobial that came onto the market in 1991. It enjoyed considerable success as an orally administrable macrolide, being relatively lipophilic and having a slightly longer elimination half-life. Came off patent about 10 years ago.

It acts by inhibiting bacterial protein synthesis by blocking the ribosomal RNA. Resistance develops as bacteria acquire various resistance genes, such as the plasmid erm (A) gene that confers an ability to methylate the adenine in the binding site.

Clarithromycin can be administered orally with a bioavailability of about 50%. Its permeability across biological membranes is only due in part to its lipophilicity. A significant part of the process depends on a complex interplay between influx and efflux transporters expressed on various membranes. Consequently intra-cellular, and tissue concentrations do not correlate with circulating unbound drug concentrations. Interestingly, tissue interstitial fluid concentrations are lower than free drug concentrations in plasma, but intra-cellular concentrations are to a variably extent much higher than plasma free concentrations.

The protein binding of clarithromycin is about 60-70%. The Volume of Distribution is about 10 L/kg, which is consistent with significant permeability into tissues. Again this increased permeability results not only from lipophilicity but from the complex interplay of influx and efflux transporters, in this case clearly favouring influx.

Clarithromycin is eliminated by both hepatic metabolism and renal elimination. It is extensively metabolized by CYP3A4 (which it also inhibits), to a principal metabolite 14-(R) hydroxyclarithromycin, which is also pharmacologically (less) active. The pharmacokinetics is not linear, and the elimination half-life increases from 3-5 hours at lower doses, to 5-7 hours at higher doses. Tissue concentrations persist for much longer.

Clarithromycin produces a range of adverse reactions, but the one that concerns us for this discussion is with respect to cardiac death. Like many of the macrolides, clarithromycin has an effect on the myocardial delayed potassium rectifier current, leading a prolongation of the QT interval of the ECG. This prolongation of the QT interval is associated with risk of torsades de pointe and a fatal ventricular arrhythmia.

The usual adult dosage is 250-500 mg 12 hourly for 7-14 days.

Clarithromycin is a drug with very interesting pharmacological properties. Give a thought as to how these properties contribute to variability in the clinical response and the risk-benefit ratio particularly with respect to the problem of cardiac death.

(To be continued)

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.