Clearance = UV/P...Lightbulb!

A couple months ago I completed the cardiopulmonary block at school. Basically, our curriculum is organized by systems, and within each system we cover physiology, pathology and pharmacology (of course nothing is ever that neat and tidy so sometimes things are randomly strewn in, but for the most part that's how it is). Anyway, while reviewing past exams for our cumulative final exam (the teachers make these readily available to us since the questions vary somewhat each year), I came across a problem that stumped me. It read something like this:

What is the clearance of a drug X?

a) Clearance = UV/ Pt

b) Clearance = V/UP

c) Clearance = UV/P

d) Clearance = U/PV

Straightforward problem, right? After all, we had learned the concept of clearance (CL) probably in our first pharmacology class. Basically, within the context of pharmacokinetics the clearance of a drug is the volume of plasma from which the drug is completely removed or eliminated per unit time, and the equation is

CL = Rate of elimination/Plasma concentration (unit is volume/time)

You can also relate it to volume of distribution (Vd, which is the total amount of drug in the body relative to the plasma concentration):

CL = Vd x Ke , where Ke is the elimination constant

You can even relate the clearance to the half life:

CL = 0.7 Vd/ (t1/2) where t1/2 is the half life

Since I understood all this, I should have known the answer to the question, right? Maybe, except that I had no clue what any of the variables in the equation in question referred to. Since I didn't recall anything like this being taught, I promptly dismissed this question. Except that as I continued reviewing, I noticed that the same problem had showed up on the 2009, 2008, and 2007 exams. By the time I realized this, I was sort of at my studied out phase (i.e. the phase where I'm like I don't care anymore, just give me the damn test already) so I put it out of my mind. Surprise surprise, guess what showed up on test day? Yep, you guessed right. Afterwards I was discussing it with some classmates to try to figure out the answer; pretty much everyone though it was a) because it had the time variable in it. When we got our scores back, I noticed that almost everyone in the class had a) which was of course wrong.

Fast forward to today. Next quarter, we start off with Renal block. The recommended text is Renal Pathophysiology: The Essentials, and our teachers were nice enough to lend us copies to read over the summer. So anyway, I just read the part on glomerular filtration rate (GFR, which is the volume of fluid filtered from the glomerulus per unit time) ; the equation is:

GFR = UV/P

where U is the urine concentration

V is the urine flow rate (in mL/min or L/day)

P is plasma concentration.

So does this look familiar? It turns out that it's the same equation for clearance!

Clearance = UV/P

Note that there is no "t" in this equation because since V is a rate, time if already factored in. The mnemonic to remember this is to think of UV light shining on pee.

So there you have it; months later, I finally understand that question. Yes I got it wrong on my cardiopulmonary test, but USMLE, I dare you to challenge me with that one!

Note: Things in red are must know stuff according to First Aid for the USMLE Step 1, 2010 (First Aid USMLE), so I just thought I'd highlight them.