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.

Implications of the Effect-Time relationship

The relationship as plotted in the earlier post assumes the concentration move from an initial position when it associated with maximum pharmacological effect.

In the first phase, even when concentrations are declining at an exponential rate, effect hardly changes. Not until the effect reaches about 85% of Emax does the rate of decrease in the effect assumes some linearity with respect to time. Between 85% and 15% of Emax, the rate of change of effect is linear when the concentrations are expected to be falling exponentially. Only when the effect is less than 15% of Emax is the rate of decrease exponential. Only then is the rate of change of effect parallel to the change in concentrations.

Implications:

a] When using plasma concentrations as a surrogate for pharmacological effect, a linear relationship between plasma concentration and effect is only seen at low effect levels (less than 15% Emax)

b] At toxicological levels (>85% Emax) as might occur in poisonings, concentrations may fall exponentially with any improve in patient's condition. Some drugs are actually dosed under Emax or near Emax conditions. In such situations one should expect that fluctuations in concentrations, or small adjustments to doses will not be associated with any significant effect changes.

c] For most drugs, presumably the concentrations operate somewhere between 85-15% of Emax. Under such conditions, the effect falls linearly with time, but it is important to note that the effects fall linearly even though concentrations are falling exponentially.

d] Few drugs operate throughout the entire range of concentration-effect curve, hence the effect time relationship is entirely dependent on the concentrations ranges the drug exhibits under a certain dosing regiment. It is important to know where any drug is operating to appreciate how changes of concentrations over time will determine effect variability.

Generating an Effect-Time plot

First step is to generate a Concentration - Time plot. We know that in its simplest form, an IV dose of a drug will be eliminated by a mono-exponential process. The plamsa concentration at any time, C, can be described by an equation using the starting concentration C0, elimination rate constant, k, and the time, t.

C = C0exp-kt

Secondly, we know that the effect at any concentration can be described by an 'Emax model', which is similar to a Michaelis Menten equation, using Emax (max effect), ED50 (concentration producing 50%) effect, and E0 (residual effect when there is no drug).

Effect = E0 + Emax. C/(ED50+ C)

It is then a simple matter to link those the above two relationships in an EXCEL spreadsheet and generate a plot of Effect vs Time. You can arbitrarily use the following constants: C0=100, k=0.015, E0=10, Emax=100, ED50=5

Here is the output using the above method. This plot assumes the concentrations begin at a point associated with Emax and reduces down to zero.

Temporal considerations in understanding efficacy

This is one of the overlook areas for lab-based pharmacologists.

It is easy enough to think of a concentration-response relationship based on static concentrations of active drug in an incubation medium but drug concentrations in clinical practice are almost never static (unless administered as a fixed infusion regiment). Concentrations fluctuate over a dosage interval, and even in a pseudo-steady state situation simulated through multiple dosing, concentrations continue to fluctuate. Even 'average' concentration are seldom stable because patient's compliance vary dose to dose and over days and weeks. It is therefore almost never possible to identify drug effects with any drug concentration. For convenience, we refer to average (randomly obtained) concentrations, peak concentrations, trough concentrations or even areas-under-the-curve (AUC) if multiple sampling has been done over a dosage interval, but in reality we seldom know which concentration measurements best reflect the observed drug effects.

Different aspects of the drug effects may in fact to different types of concentration measurements. Toxicity effects may in fact relate more to peak concentrations while therapeutic effects may related better to trough concentrations. In some situations the converse may even be true. In various other situations drug efficacy may better relate to an index of exposure such as the AUC, or even the amount of time exposed to concentrations above a certain threshold concentration value.

Another aspect of the temporality of drug effects may be related to the involvement of down-stream effects of any drug action. Significant delays in drug effects 'coming on' and 'going off' will make the association between drug effects and concentrations less obvious.

Here's an interesting exercise for you:

We know that there is a sigmoidal log concentration-effect relationship. There is also a log decline of concentrations (assume simplest one compartmental IV model) over time. How would the Effect - Time relationship look like? Email me your answer.

Mechanisms of drug action - we need to rethink our models

When we think about the mechanism of drug action we almost always look to the traditional sigmoidal log dose or log concentration response relationship.

Students are almost always befuddled by the fact that once you go into the clinics, hardly anyone ever refers to this fundamentally important relationship. It seems to be important only at lab benches and do not seem to apply in the clinical context. Part of the reason for this is few drugs exhibit a range of actions that span the entire range of that sigmoidal curve. Many drugs either just operate close to the Emax or are limited in getting close to Emax because of toxicity, or compensatory mechanisms. One other constraint is that the estimates of concentrations are poorly representative of the actual concentrations at the effector site. So often we are reduced to just looking at circulating (fluctuating) plasma concentrations (which are very distant from the effector site) or a very crude estimate of the administered dose.

One other problem is that our ideas of drug response mechanisms are heavily influenced by receptor binding models shaped by earlier studies of G-protein type membrane receptors. The simplistic model assumes easily reversible competitive binding to a receptor with almost immediate effects. More and more drugs nowadays do not operate that way.

Here is a list of the top 50 prescribed drugs (as listed by IMS in 2007).

Of these only a minority can be regarded as operating according to that model of drug action. If you consider that many clinically useful drugs (antiinfectives, anticancer, etc) work through mechanisms more related to irreversible cell kill type models, I think you can readily appreciate the inadequacy of that simplistic traditional concentration-response model of drug action.

Measures of efficacy

In the previous posts we had considered the optimization of warfarin dosages. The genotyping offers an added dimension to the optimization process, but may not be really cost effective. The warfarin problem is probably not a good example for predictive genotyping. This is because it already has a very good biomarker of clinical response - the INR (International Normalized Ratio). Most other drugs do not have good measures of clinical response. The absence of such measures of efficacy makes the optimization much more challenging.

Some drugs like warfarin allow direct measurement of the therapeutic efficacy. So for warfarin, it is the INR. For antihypertensive drugs, it could be the blood pressure response. For an antiasthmatic bronchodilator, it could be the airway relaxation, FEV1 for example. For an antidiabetic drug, it could easily be the blood glucose response. There are many other examples.

But for many therapeutic areas, the clinical response is much less directly quantifiable. For example, in the use of an antiepileptic drug, without a good surrogate measure of response, one is never really sure whether appropriate amounts of drug have been used. Likewise, for an antibiotic or a chemotherapeutic agent, the inappropriateness of the dosing regiment may not be recognized until it is too late.

For such situations, the availability of a 'surrogate' measure of response may be critical in patient care. One such surrogate measure is the measurement of circulating drug concentrations. Crude though it may be, getting the patient into a 'therapeutic range' may provide some guidance as to whether or not appropriate dosages have been used. Such an approach is sometimes referred to as the 'target concentration strategy'. There are however limitations to this method and it is not always applicable.

For the target concentration strategy to work, there must be evidence that circulating concentrations bear a good relationship to therapeutic outcome.

CYP4F2

The CYP4F2 is involved in the synthesis of a number of sterols and lipids. Because it was involved in the production of 20-hydroxyeicosatetraenoic acid (20-HETE), it was postulated to be involved in the pathophysiology of hypertension. It is now thought to be also involved in the breakdown of Vit K1. Correspondingly, the V433M variant is thought to result in decreased breakdown of VitK1 and an leading an excess of VitK1, leading to relative warfarin resistance. Recent studies have suggested that the polymorphism contributes 1-2% of the variability in warfarin dosage requirements.

The frequency of the polymorphism in Caucasians and 'Asians' is approximately 30%. There isn't any more specific population frequencies than these, and I have no breakdown of Chinese, Malay and Indian frequncies.