# How do I graph pharmacokinetics?

September 30, 2009 9:42 AM Subscribe

How can I visualize the pharmacokinetics of a drug? Is there a way to create a graph of the blood plasma levels of a drug including the fluctuations caused by time of administration?

To make a long story short, my doctor changed one of my prescriptions and I'm curious how it will affect the plasma level of the drug.

I can find the half life and some other pharmacokinetic info on the drug through the FDA web site and the prescribing information, but I'm having trouble understanding the steady state level of the drug and fluctuations in blood plasma levels due to different time release formulations and times of dosage. I haven't been able to find any blood plasma curves drawn out. Basically, I wanna SEE what's going on.

How can I create a graph of this information using Excel or some other software? Is there some magic software or website designed to do precisely this? Ideally I'd like to be able to input different doses and times of administration to see how they affect blood plasma levels over time. I have access to MatLab if that helps (but no idea how to use it), Excel, SPSS. I haven't done calculus in about a decade but consider myself competent at basic algebra and number crunching. I'd be up for some calc review if it ill help me wrap my head around all this.

To make a long story short, my doctor changed one of my prescriptions and I'm curious how it will affect the plasma level of the drug.

I can find the half life and some other pharmacokinetic info on the drug through the FDA web site and the prescribing information, but I'm having trouble understanding the steady state level of the drug and fluctuations in blood plasma levels due to different time release formulations and times of dosage. I haven't been able to find any blood plasma curves drawn out. Basically, I wanna SEE what's going on.

How can I create a graph of this information using Excel or some other software? Is there some magic software or website designed to do precisely this? Ideally I'd like to be able to input different doses and times of administration to see how they affect blood plasma levels over time. I have access to MatLab if that helps (but no idea how to use it), Excel, SPSS. I haven't done calculus in about a decade but consider myself competent at basic algebra and number crunching. I'd be up for some calc review if it ill help me wrap my head around all this.

If the only inputs you have are the drug, the dosage, and the times of administration, I'm afraid you're going to get pretty meaningless results. Many drugs, especially orally administered drugs, are absorbed and metabolized differently for different people, and regular blood tests are really the only way to get good information for a particular patient (i.e., you). I doubt you want to have you blood sampled hourly for a few days just to see some graphs of serum levels.

Also, it depends on what drug you're talking about, but many so-called time-release formulations don't actually work all that well. 8 hour acetaminophen is a good example: there's not much evidence that it does a good job of maintaining a steady, effective dose over 8 hours. A lot of time-release formulations are just an attempt by the manufacturer to wring some more money out of the drug by patenting the time-release version and then convincing doctors and patients that it's worth it over just, you know, taking 2 of the regular generic kind.

In short: getting good numbers would be difficult, time consuming, expensive, and quite possibly disappointing.

posted by jedicus at 9:57 AM on September 30, 2009

Also, it depends on what drug you're talking about, but many so-called time-release formulations don't actually work all that well. 8 hour acetaminophen is a good example: there's not much evidence that it does a good job of maintaining a steady, effective dose over 8 hours. A lot of time-release formulations are just an attempt by the manufacturer to wring some more money out of the drug by patenting the time-release version and then convincing doctors and patients that it's worth it over just, you know, taking 2 of the regular generic kind.

In short: getting good numbers would be difficult, time consuming, expensive, and quite possibly disappointing.

posted by jedicus at 9:57 AM on September 30, 2009

Thanks you James Scott-Brown! That provided some helpful single dose curves (which I had been driving myself crazy trying to find). I'm still having trouble wrapping my head around around the cumulative effect of daily dosing or twice daily dosing.

posted by ladypants at 9:57 AM on September 30, 2009

posted by ladypants at 9:57 AM on September 30, 2009

Which is not to say that you couldn't get a good picture of the average or typical serum levels, just that it won't necessarily be an accurate picture of what's going on in your own body.

posted by jedicus at 10:00 AM on September 30, 2009

posted by jedicus at 10:00 AM on September 30, 2009

jedicus, I'll settle for a quick and dirty approximation. I realize that everyone's metabolism is different and I'll take a crude approximation based on other people's data. I can also approximate my blood volume if that helps. Basically, I'm not going to use this information to

posted by ladypants at 10:01 AM on September 30, 2009

*change*my dosage (that's something to discuss with my doctor), but rather to just generally get a grasp of how things should look in some kind of abstract, idealized (if non existent) patient/system.posted by ladypants at 10:01 AM on September 30, 2009

Ooh! Fun! My favorite class in pharmacy school was kinetics. If you want a clear, readable explanation, this book is awesome.

Here is my cheap and quick oversimplification. Imagine that I've drawn this on a handy napkin.

When you take a single dose of an oral drug, the curve generally looks like a hill - plasma levels rise as the drug is absorbed, peak, then fall as the drug is eliminated (usually via the kidneys as you pee it out). If you just take 1 dose, eventually your plasma levels return to 0.

If you take a 2nd dose, though, you still have drug in your body from dose #1. The second peak is higher than the first.

If you take a 3rd dose, the 3rd peak is higher than the first 2. This continues until the amount of drug coming in (via regular doses) equals the amount going out (via metabolism & the kidneys). This is called steady state.

Fun fact: It takes about 4 half-lives of a drug to reach steady state. So if I'm taking a drug with a t1/2 (half life) of 10 hrs, then I am at steady state about 2 days into taking the drug.

Notice the 2 factors of importance: Dose and Interval. Taking 80mg once a day is going to produce the same average plasma level as taking 20mg 4 times a day - but the hills and valleys are going to be a lot less extreme with the 4x/day dosing.

Time-release capsules are an attempt to give you the convenience of once a day dosing without the big ups and downs.

So if your doctor gave you the same total amount of the drug per day, just divided into more frequent doses, then your average plasma level will be the same - but you will have smaller ups and downs.

posted by selfmedicating at 10:40 AM on September 30, 2009

Here is my cheap and quick oversimplification. Imagine that I've drawn this on a handy napkin.

When you take a single dose of an oral drug, the curve generally looks like a hill - plasma levels rise as the drug is absorbed, peak, then fall as the drug is eliminated (usually via the kidneys as you pee it out). If you just take 1 dose, eventually your plasma levels return to 0.

If you take a 2nd dose, though, you still have drug in your body from dose #1. The second peak is higher than the first.

If you take a 3rd dose, the 3rd peak is higher than the first 2. This continues until the amount of drug coming in (via regular doses) equals the amount going out (via metabolism & the kidneys). This is called steady state.

Fun fact: It takes about 4 half-lives of a drug to reach steady state. So if I'm taking a drug with a t1/2 (half life) of 10 hrs, then I am at steady state about 2 days into taking the drug.

Notice the 2 factors of importance: Dose and Interval. Taking 80mg once a day is going to produce the same average plasma level as taking 20mg 4 times a day - but the hills and valleys are going to be a lot less extreme with the 4x/day dosing.

Time-release capsules are an attempt to give you the convenience of once a day dosing without the big ups and downs.

So if your doctor gave you the same total amount of the drug per day, just divided into more frequent doses, then your average plasma level will be the same - but you will have smaller ups and downs.

posted by selfmedicating at 10:40 AM on September 30, 2009

If you any proficiency in Excel, you can graph this fairly easily. I have done so on numerous occasions in order to approximate bloodlevels.

To start out with, assume instant absorption. In one column, have time in intervals of the half-life. So if the half-life is 8 hours, start at 0 and for each row down add 8. In the second column have dose (the amount of drug taken in mg), and with each row down, divide by 2. Now you've got a simplified curve showing bloodlevels as a function of time for 1 administration. Then make another column identical to the last, but staggered forward in time by the interval between administrations (presumably 24 hours). Add this bloodlevel to the last one, and you've got the cumulative bloodlevels from 2 administrations over time. You'll need at least a few such additive columns before the individual doses add up to a reasonably steady bloodlevel.

Factoring in absorption would be a bit trickier. I think you'd have to model it as a negative exponential, but precisely what form that should take is beyond me.

posted by dephlogisticated at 12:55 PM on September 30, 2009

To start out with, assume instant absorption. In one column, have time in intervals of the half-life. So if the half-life is 8 hours, start at 0 and for each row down add 8. In the second column have dose (the amount of drug taken in mg), and with each row down, divide by 2. Now you've got a simplified curve showing bloodlevels as a function of time for 1 administration. Then make another column identical to the last, but staggered forward in time by the interval between administrations (presumably 24 hours). Add this bloodlevel to the last one, and you've got the cumulative bloodlevels from 2 administrations over time. You'll need at least a few such additive columns before the individual doses add up to a reasonably steady bloodlevel.

Factoring in absorption would be a bit trickier. I think you'd have to model it as a negative exponential, but precisely what form that should take is beyond me.

posted by dephlogisticated at 12:55 PM on September 30, 2009

Here's about as close as I'm going to get with my very rudimentary math skills. I think an absorption curve could be approximated with: y = D (1 -

posted by dephlogisticated at 2:15 PM on September 30, 2009

*e*^{-kt}), where D would be the dose, t would be time, and k would be a constant representing the absorption rate of the drug. You probably won't be able to find an exact value for this constant on the internet, but you can find an approximate value by adjusting it until y is about equal to D when t is equal to the amount of time it takes for the max plasma concentration to be reached (this number is usually not hard to find for a given drug).posted by dephlogisticated at 2:15 PM on September 30, 2009

Ah, here's the equation I was looking for. It factors in interval doses, absorption, and elimination. Probably overkill for what you're looking for, but functionally elegant nonetheless.

posted by dephlogisticated at 6:19 PM on September 30, 2009

posted by dephlogisticated at 6:19 PM on September 30, 2009

Thanks selfmedicating and dephlogisticated! These are some excellent tools!

posted by ladypants at 9:49 AM on October 1, 2009

posted by ladypants at 9:49 AM on October 1, 2009

This thread is closed to new comments.

posted by James Scott-Brown at 9:54 AM on September 30, 2009