## The best way to approach simple PK calculations.

Aron Van De Pol

## Overview

As you can imagine, pharmacokinetics (PK) plays a huge role in drug absorption, distribution, metabolism, and excretion (ADME). However, do you really need to know every single detail as a practicing pharmacist? Absolutely not. If anything, you may have to do antibiotic dosing (I?m referring to vancomycin, gentamicin, etc) as a hospital pharmacist but for most other practices, you probably won?t be dealing with this subject matter

That?s is why I am not focusing to heavily on PK because you are better off focusing on other material to better prepare for the exam. You may or not get a question or two regarding PK but it won?t make or break you exam.

To make things easier for you, I decided to break down some of the most common questions I get about PK and walk you guys through them. They aren?t necessarily difficult, just a bit unique especially if you didn?t have too much of a background in PK or just simply looking for a brief refresher. Let?s get started.

## Volume of Distribution, Clearance, and KE

This is probably the simplest and most important equation you should know. It?s really not that difficult. Just a proportion, but is the foundation of most PK questions. If you can remember this equation, you can pretty much extrapolate all the others.

Formula | Volume of Distribution = Total Dose / Concentration

Say that a question asks you to determine the volume of distribution (VD) of a drug with a total dose of 2,000 mg and a concentration of 600 mg/L. You simply do this:

VD = 2,000 / 600 = 3.33 L

VD is typically in liters and is the total amount of drug distributed in the body with regards to the dose and concentration of the a given drug.

However, another note to keep mind of is that VD also relates to clearance (CL) and elimination rate constant (KE).

Formula | VD = CL / KE

So you may get a question about finding the KE. They will likely give it in parts and expect you to put two and two together. So it will be given like this:

A 2,000 mg dose with a concentration of 600 mg/L has a clearance of 0.05 L/hr. What is the elimination rate constant (KE)?

See how they expect you to utilize both variations of the VD formula this time. This is how it would look like:

VD = 0.05 / KE

(2,000 / 600) = 0.05/ KE = 0.015 hr (-)

Which means that this is the amount of time it will take to remove the drug from the body and is given as a negative in hours since it is being ?eliminated?.

## But wait? the fun is just beginning.

Now you are asked to find the half life of the drug. This is actually the easiest formula to remember but you have to remember it.

Formula | Half Life = 0.693 / KE

Half Life = 0.693 / 0.015 = 46.2 hours

So this means that the drug will take 46.2 hours to remove roughly half of the drug?s concentration in the body. A very common assumption is that it takes about 5.5 half lives to completely clear a drug from the body. Absolutely remember this because it is common knowledge in PK and is highly testable.

## AUC & Bioavailability

As you can tell, all the formulas thus far have been related to the foundational VD = CL / KE. In a way, the last two I will be talking about also relates this formula but also expands it. I?m talking about clearance with regards to area under curve (AUC) and the bioavailability (F) formula.

Let?s start with bioavailability first. The concept here is that drugs may or may not behave similarly when taking PO vs. IV. This is because when taken IV, you can assume a drug will have 100% bioavailability since it is directly introduced into distribution (AKA bloodstream). But with PO drugs, you must first be absorbed through GI tract before being distributed. Then add on the the potential for liver elimination (it?s more commonly referred to as the first pass liver screening which actually reduces a drug?s concentration) and all of a sudden, that initial dose is significantly reduced.

Bioavailability (F) = 100% x [(PO AUC / IV AUC)] x [(IV Dose/ PO Dose)]

So when tasked with finding (F), you will always be given everything in the formula. In fact, they have to, or else you won?t be able to find F.

It is usually given like this: Find the bioavailability of X drug if the IV dose is 100 mg with an AUC of 100 vs. a PO dose of 200 mg with an AUC of 75.

It is literally this simple. The hardest part is memorizing the actual formula. You always start with the AUC then multiply by Dose. Do not mix up the proportion. PO is on top of AUC and IV is on top of Dose.

F = 100% x [75 / 100 ] x [ 100 / 200] = 37.5%

As you can tell, this drug has a terrible bioavailability of only 37.5%. Yikes! This patient is getting just 1/3 of actual dose.

Now? let?s relate this to our final formula.

Clearance = (F x Dose) / AUC

In this case, we want to find the IV dose with regards to a specific clearance. Remember up top, we had a clearance of 0.05 L/hr. Now let?s find the corresponding dose with the determine AUC and bioavailability (F)

0.05 = (37.5 x Dose) / 100

Dose = 7.5 mg

This means that with this corresponding AUC, bioavailability, and clearance, the initial dose given was 7.5 mg.

## Conclusion

That?s it folks! Simple and straight to the point. I hope that this minimalist overview of pharmacokinetic basics can help someone utilize this information to better prepare for the NAPLEX.

Best,

M/P

## Excellent Resources

- Pharmaceutical Calculations
- NAPLEX Nuggets
- NAPLEX Practice Question Bank
- Medcharts
- PASS-NAPLEX
- Goodnight Pharmacology
- Dipiro
- Letters to a Young Pharmacist
- Kaplan NAPLEX
- NAPLEX Workbook
- NAPLEX Comprehensive Review

## MPJE Resource

- Federal Guide (Reiss & Hall)

## Pharmacy Management Resource

- Pharmacy Management (Essentials For All Practice Settings)

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