Do changes in Vd have any impact on clinical drug effects?

This will depend entirely on which drug concentration measurements have the greatest impact on drug effects. And here is where our relative ignorance of this particular aspect of drug pharmacology constrains our ability to use PK as a predictor of drug effects.

If for example our understanding of what best predicts drug effects is limited to considerations of 'average' or 'steady-state' drug concentrations, then we are compelled to expect that Vd changes will have little or negligible impact on clinical drug effects. This is because Vd changes do not alter the area-under-the-curve (AUC) of a drug's pharmacokinetics (since AUC is determined primarily by clearance and bioavailability). Remember (F x Dose)/AUC = Clearance?

This line of reasoning has dominated and shaped our thinking for the last few decades as evidenced by the large number of studies looking at clearance or AUC changes as predictors of drug effects. Correspondingly, we have tended to minimize the effect of distributional changes as a predictor.

Is this line of reasoning correct?

Only to a limited extent. We have seen in the previous post, that the immediate and most obvious effect of Vd changes is on the C0. Consequently if a drug's effect is dependent on peak concentrations, Vd changes will have inversely related effects on peak concentrations of the drug profile, and by extension, any clinical effect, be it efficacy or toxicity, associated with the peak.

We see this also with multiple dose regiments.

With a multiple dose regiment, even though changes in Vd are not expected to change the AUC or steady state concentrations, you can see that the fluctuations over the dosage interval are greater if the Vd is smaller (in the above case 115L compared to 230L). With the increased fluctuations, one should note that the peak and trough concentration actually move in different directions, i.e. with a smaller Vd, the peak increases but the trough decreases, while the AUC remains unchanged.

Going back to the original question....do Vd changes have an impact on clinical drug effect? It will depend on whether drug effects relate best to steady-state concentration, the AUC, peak or trough concentrations. And this is poorly understood at the moment.

For the moment however, being over-focused on the AUC therefore limits our ability to see potential causes of variability in drug response.

Even more problematic ideas of distribution.....

The simplest idea of the volume of distribution (Vd) of a drug, is to think of it as the volume that a drug distributes into when that drug is administered into the body, but before any elimination has taken place. The simplest approach therefore is to divide the dose of the drug (intravenously administered) by the observed plasma concentration at zero time, C0, i.e. before any elimination has had a chance to occur.

Vd = Dose/C0

Not all of any drug, however, is uniformly distributed throughout the body; and what is seen in the plasma only represents a fraction of all of the drug molecules distributed throughout the body. If more is distributed outside of the plasma 'compartment', the C0 will be smaller for a given dose of drug, and the Vd will appear correspondingly higher. The converse is also true, that if less is distributed outside of the plasma compartment, the Vd will appear lower.

The original ideas of the process of distribution, was that drug molecules were mostly freely permeable entities, and found a 'distributional equilibrium' across cell and tissue membranes. Binding to proteins or other large molecules prevented their effective permeation across membranes, and therefore 'trapped' these drug molecules into various 'compartments'.

Conceptually therefore, the Vd of a drug may be seen to be 'governed' by an expression relating body volumes (presumably determined by body weight), plasma protein binding and tissue binding:

Vd = Volume of central compartment + Volume of peripheral tissue x (fu/fut),

where central compartment referred to plasma volume, tissue referred to undefined number of tissues outside of plasma, fu is unbound or free fraction of drug in plasma, and fut is the unbound fraction of drug in the tissues.

By this expression one can see that the Vd can be reasonably expected to be related directly to the extent of tissue binding, and inversely related to the extent of plasma protein binding.

The Vd of a drug can also be seen to have direct and immediate effects on the starting concentrations of any drug administered, particularly if administered intravenously. And if the starting concentrations were responsible for efficacy or toxicity, the Vd may be expected to be a major determinant of efficacy or toxicity.

Knowing the Vd also helps us estimate the starting dose of a drug if we have a target drug concentration in mind. For this reason, dosage regiments of drugs with large Vds often incorporate a loading dose regiment before settling into a lower maintenance dose regiment.

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.