Basic Principles of Pharmacokinetics

(I notice that my overall page views seem to have dropped off quite a bit since the test yesterday. Good job, guys.)

(EDIT 17/6/16: I noticed that there were some errors with regards to the half-life equations. I have fixed them up, and hopefully they should be correct now.)

1) Show awareness of how plasma drug concentration versus time curves provide valuable insight into the pharmacokinetic properties of any drug

Plasma drug concentration versus time curves are a great way to show trends in plasma concentrations of drugs (well, that's pretty much what they're meant to do, by definition). Also, if you calculate the area under the curve, by integration or otherwise, you can find out the patient's total exposure to a drug over a given time. A larger area under a curve would suggest that the drug is better absorbed. As well as this, you can also use the area under a curve to calculate other pharmacokinetic parameters, such as clearance: more on this in a bit.

2) Show an understanding of the concept of “clearance” and how it is determined for a given drug

Clearance is the volume of blood cleared of the drug per unit of time (and is hence measured in units such as L/hr or mL/min). It is also the constant that relates the plasma drug concentration with the rate of elimination. "Total body clearance" refers to the overall clearance, whereas "renal clearance" and "hepatic clearance" refer to clearance by the kidneys and liver, respectively. To determine the clearance, you first need to give the patient a single IV dose of the drug. (Oral won't work, because there are too many confounding factors surrounding the absorption of oral drugs.) After that, you need to take blood samples at various time points and work out the plasma drug concentration at each time point. These points can then be plotted onto a curve and the area under the curve calculated. Finally, to work out the clearance, simply divide the dose by the area under the curve.

Clearance is important in determining drug concentration at "steady state." Steady state is the state in which the rate of drug administration is equal to the rate of drug elimination.

Now, as I've mentioned before, clearance is the constant that relates the plasma drug concentration with the rate of elimination. Hence:

Clearance * Plasma drug concentration = elimination rate

However, when the plasma drug concentration = steady state drug concentration, elimination rate = rate of drug administration. Hence:

Clearance * Steady state drug concentration = Rate of drug administration

Again, this gets a bit more complicated during oral dosing. There isn't really a "steady state drug concentration" in oral dosing as the drug isn't being constantly infused- rather, it is taken over several intervals. However, to my understanding, this equation is still somewhat applicable, but you have to replace "steady state drug concentration" with "average drug plasma concentration between dosing intervals," which is a bit of a mouthful.

3) Show an appreciation of the “volume of distribution” and how it is estimated together with an awareness of how this value reveals the behaviour of drugs within the human body

I feel like I've already spoken about this before. Oh wait, I have, on an earlier post: Drug Absorption and Distribution.

Now I'm going to go a bit further and talk about how the volume of distribution is estimated. It's best estimated using the plasma drug concentration at zero time, as you know that no drug could have been metabolised by that point. Once again, IV dosing is used so as to avoid the confounding variables of absorption by the gut and so forth. Blood samples are collected at various intervals, and then the curve is extrapolated back to find the plasma drug concentration at t = 0. The original dose is then divided by this plasma drug concentration to give the volume of distribution.

Why is the volume of distribution important? Volume of distribution can be useful for helping us determine how to achieve a therapeutic drug concentration in a short period of time. As the volume of distribution = (dose)/(plasma drug concentration), then the dose required to reach a particular plasma concentration can be calculated by dose = (volume of distribution)*(plasma drug concentration).

4) Be able to provide a simple sketch to show an appreciation of the concept of drug “half-life” together with an awareness of how it is estimated in human subjects.

Okay well screw the "simple sketch" part because I'm too lazy to draw a diagram. Half-life is probably a concept that you've encountered before, though: it's simply the time that it takes for the plasma concentration of a drug to drop by 50%. Half-life is not considered to be a fundamental pharmacokinetic parameter (as opposed to clearance and volume of distribution) as it is determined by clearance and volume of distribution.

Plasma drug concentrations can also be described using a nice little exponential equation:

C_t = C₀ e^(-kt)
where C_t = concentration at time t, C₀ = concentration at time 0, k = the elimination rate constant (which is the proportion of drug removed in an hour, or whatever time units you're using) and t = time.

This can then be used to determine half-life. You see, after the first half life, C_t = 0.5C₀. Hence the equation can be rearranged to directly link k and t:

0.5C₀ = C₀ e^(-kt)
0.5 = e^(-kt)
ln 0.5 = -kt
-k = (ln 0.5)/t
-k = (ln 2^(-1))/t
-k = (-ln 2)/t
k = (ln 2)/t

You may also see this equation written as k = 0.693/t. It's the same thing really: 0.693 is the natural log of 2.

As I mentioned before, half-life is determined by clearance and volume of distribution. Naturally, there's an equation linking these three variables:

t = (0.693*V)/CL (where t = time at the first half-life).

Hence, half-life is increased by an increased volume of distribution, but decreased with an increased clearance. This makes sense: the more of the drug that's "filling up" your body, the more time you'll need to get rid of it. Also, if clearance (which is constant for a particular drug and a particular patient) is high, then it'll be cleared pretty quickly and so half-life will be low.

5) Define the concept of “oral bioavailability,” showing a basic awareness of the factors that influence it together with how it is determined experimentally.

Bioavailability, sometimes denoted by the letter F (presumably B was already taken up, or "bioavailability" starts with the letter F in some weird language), is essentially the proportion of drug that reaches the systemic circulation. IV drugs pretty much all have a bioavailability of 1 as they are taken directly into the bloodstream. Oral drugs are a bit different, however: they must first be absorbed by the gut, and then passed through the liver. Not all of a drug will make it through the liver, as some of it will be metabolised there. The overall bioavailability for an oral drug can be calculated by multiplying the percentage that was absorbed via the gut by the percentage that makes it through the liver in its original form.

There are other ways of calculating bioavailability, again using the area under a curve. Bioavailability can be calculated by dividing the area under a curve for the oral dose by the area under a curve for the IV dose. If the oral and IV doses are different, just use this nifty formula:

F = (AUC(oral)*DOSE(IV))/(AUC(IV)*DOSE(oral))
where F = bioavailability and AUC = area under the curve

Aaaaaaaaaaand I think that's pretty much it for this lecture! (At some point I need to revise my Research and Communications Exercise, though. I wrote a helluva lot of bullshit on steady state concentrations and stuff in there, and it's probably not very accurate. This unit coordinator is pretty merciless- and he's going to be the one marking the assignment. Ah well, I still have over a month to fix it up :) )