Plan B and Pharmacokinetics

On my way to work this morning, I heard a story on NPR about Plan B emergency contraception (Levonorgestrel), and how the efficacy at preventing pregnancy is reduced in women who are overweight or obese. The story reported that levonorgestrel, the active ingredient in Plan B…

starts losing its effectiveness in women weighing as little as 165 pounds and loses it completely in women who weigh more than about 175 pounds.

A later airing of the same segment I heard on my way home stated that this effect was independent of BMI – so a tall woman who is not even overweight might also experience a reduced efficacy. This text doesn’t appear in the linked story, and I haven’t read the primary study the story references – I didn’t have time today.

Because I was busy making a quick PBPK model to illustrate the impact of differences in weight on levonorgestrel pharmacokinetics.

*record scratch*

All but approximately three of my readers just got really confused, so here are some key terms and a very fast primer. Pharmacokinetics is the fate of a substance of interest once it is introduced to a living organism. For example, when you take medicine, say a pill that you swallow, how that drug is absorbed through your GI tract, distributed through out your body, metabolized, and eventually eliminated in your pee or various other routes. PBPK models: physiologically based pharmacokinetic models are mathematical descriptions of all the physiology and biochemistry that influence pharmacokinetics. So to make a model, I describe physiological aspects of the body like the volume and composition of organs of interest, and rates of blood flow to those organs. Then I add biochemical details, like how water or fat soluble the substance of interest is, how quickly it is metabolized and in what tissues, how quickly the substance is absorbed or eliminated in various tissues, and so forth. I incorporate all of that information into differential equations (calculus! fun!) that allow me to simulate exposure scenarios I am interested in.

For levonorgestrel, I was interested in what the blood concentration might look like based on changes in body weight (and associated organ volumes, blood flows, etc.). I focused on three scenarios for a 5’4″ tall woman: a normal BMI, overweight BMI, and obese BMI. I used the low end for each (18.5, 25, and 30, yielding body weights of approximately 109 lbs, 147 lbs, and 176 lbs).

I built a model with explicitly described liver and fat tissues, as well as arterial and venous blood, and the rest of the body lumped together into tissues that are slowly perfused (bone, skin, muscle) and rapidly perfused (brain, visceral organs, etc.). I incorporated chemical specific information for levonorgestrel from the wikipedia page (protein binding, bioavailability) and from the literature (rates of metabolism, Kuhnz & Gieschen 1998).

I made a pile of assumptions that, given enough free time, I could vet against the available literature (i.e. actual data). For one, I assumed that in a 5’4″ woman, as weight increased, some tissue volumes increased and others did not – for example, I assumed that the liver size would be similar in a woman with a BMI of 18.5 or 30.0, but that fat, muscle, and blood volumes would be greater in a woman with a BMI of 30 than a BMI of 18.5. I would need to revisit and expand on these assumptions, especially if I get a look at the original study and it DOES say the observed (lack of) effect was independent of height. I also had to estimate rates of absorption, which I did by visually fitting them to data on blood concentrations in the drug pamphlet (you know, that thing that comes with your prescription drugs that is covered in teeny tiny writing that you immediately throw away). I can provide a lot more detail here, but I think I’ve already provided more than all but three of you care about.

SO ANYWAY. I did a couple of simulations to illustrate my point. Did I ever say what my point is? It’s this: I WAS NOT SHOCKED BY THE NEWS STORY. If you give the same amount of a drug to people of different sizes, without accounting for the size difference in the dose given, you will sometimes see a change in efficacy. That is: if you give a 1.5 mg of levonorgestrel to a 109 lb woman, a 147 lb woman, and 176 lb woman, they will have different blood concentrations of the drug. THE DOSE IS NOT WEIGHT ADJUSTED. Thus, if there is a threshold below which the drug ceases to be effective (LIKELY), it is possible that this might be breached, resulting in some effect (or lack thereof), like…. pregnancy, here. Look, some pictures.

First, here is some evidence that the model I whipped up isn’t complete crap. Predicted blood concentrations of levonorgestrel following a 1.5 mg oral exposure. This is where I visually fitted the oral absorption parameters. If I have time, I can find more pharmacokinetic data to better optimize these parameters, but this is sufficient to support my point.

Model fit (109 lb woman) to reported data on maximum blood concentrations of levonoregstrel in 30 women (mean +/- standard deviation).
Model fit (109 lb woman) to reported data on maximum blood concentrations (nmol/mL) of levonoregstrel in 30 women (mean +/- standard deviation) over time (min) after 1.5 mg oral bolus.

Next, the point: here you can see model predictions of blood concentration of levonorgestrel after a 1.5 mg oral dose in women with three different BMIs (18.5, 25, and 30).

Predicted effect of BMI on blood concentrations (nmol/mL) of levonorgestrel following 1.5 mg oral bolus exposure in 5’4″ women weighing 109 (red), 147 (blue), or 176 (green) lbs.

So there is definitely more fiddling I can do to make the model a hell of a lot better – for instance, if I can get my hands on the weight info for the women represented by the data in the first graph, as it is pretty unlikely that they had an average BMI of 18.5 (109 lbs! That was me in 9th grade! Haaaa!). But, my point is that body weight exerts a SIGNIFICANT impact on maximum blood concentration – it is almost 50% higher in the BMI 18.5 woman compared to the BMI 30.0 woman. That’s potentially a big deal, depending on what the therapeutic index is, and what the outcome is.

Now, as I said, I haven’t read the original study, which is kind of a big oversight. I will. I do think that the pharma company that makes this drug should have addressed this issue before the drug made it to market, but you need a large population exposed before some of these effects come to light – human variability is a big deal, and it’s not like you can do clinical trials for a drug like this on zillions of people.

BUT. Think about all the medicine you take. SO MUCH of it never takes weight into consideration – it’s just “for adults, take two pills” or whatever. Kid medicine does – you choose the dose based on which weight range they fall into – but not grown up medicine!  For most stuff, it’s ok – the therapeutic index is wide enough that it doesn’t matter. But it ticks me off. Imprecision BUGS THE SHIT OUT OF ME. Dose matters! Look at the graph! Yes, it is impossible (at this point) to account for all of human variability, but that doesn’t mean we shouldn’t at least TRY to account for something as simple as BODY WEIGHT, does it? Maybe my friend Robin can swoop in here and tell me why I shouldn’t care this much. I hope he does. As it stands, I have had way too much coffee and spent way too much of my day on this mess.

Also, I accidentally saw some of the comments on the article on, and now I think humanity is a lost cause, someone please get me some cake.

This entry was posted in Grumpy Toxicologist, Science!, soapbox, times when people annoyed me. Bookmark the permalink.

14 Responses to Plan B and Pharmacokinetics

  1. peacelovemath says:

    Well this just made my day. DiffEqs! In a blog I read! Applied to a story that I, too heard on NPR! This is amazing. Also I want to have skills like this, where do I acquire them? I.e. what degrees do you even have? I have a math degree, and I loved my math modeling class, but I sure can’t whip up a crazy differential equation modeling the processing of a drug in the human body over time. Amazing.

    • admin says:

      I acquired the skills in grad school, where I studied toxicology. But it is a niche area within that field (also within pharmacology), and I happened across it almost accidentally, when I switched to a new graduate mentor specializing in biological modeling. Happily I had taken a fair amount of math for funsies in undergrad, but also the modeling program we use has an ODE solver, so it’s not like I’m over here solving them by hand.

  2. Roberta says:

    The lack of weight & sex based dosages for adults has long really bothered me. Why does my 175 lb husband get the exact same dose as 125 lb me? Women also metabolize things differently. A lot of heart attack/heart disease research was long done on men, and only in the last 10 years or so has medicine been like, oh duh, women are different! Great post, even if I only understood every 3rd word in part of it. :-)

  3. Erica says:

    Oh the comments on news stories. I think about the effect you discuss when uri and I split a bottle of wine because I weigh 100 lbs less than him so I should give him more of the bottle but I don’t because 2 kids. All day.

  4. Adah says:

    Sweet. I’m not one of the ones in your audience that you knew would get this, but I think I’m picking up what you’re putting down pretty well. I’m using an (as-of-yet) unpublished textbook to teach AP Biology this year, and the premise of the book is interpreting the research and models behind the basic biology concepts that everyone learns in AP Bio. The text also has some models that are presented as Excel files so that we can manipulate numbers and change the models. It’s all a work in progress, and the math is mostly algebra, but it’s fun because it’s different. Your modeling makes me want to get up with our Calculus teacher and put together a project for the AP Bio/AP Calculus kids that might get somewhere close to asking them to produce something like this (or play with an established model). Plus, Plan B! They would love talking about something so grown up! Your kids are so lucky to have such a talented mother!!

  5. I love you. This post made me do a happy dance. That is all.

  6. Jesabes says:

    So fascinating. And so simple (body weight! of course!) yet…not simple. You’re awesome.

  7. Sarah in Ottawa says:

    This post is awesome! I should also note that I am 5ft4 and I weighed just above 109 when I was an disordered eater as a teen. Needless to say I am a huge proponent of adjusting dosage based on reasonable parameters like weight.

  8. Carmen says:

    I love that you sit around and do this for fun, based on a story you heard on NPR. You are a better science geek than I am, I’ll tell you that. I do rail at the inaccuracies of news reports (“Do they never actually ASK a scientist before they publish shit? No, that skier cannot test negative for hemoglobin!”) but I have never sat down to actually model or test stuff from the media. This was fun to read, thought so perhaps I should start doing that as well.

  9. HereWeGoAJen says:

    I love these posts.

    Also, I have always been astounded that my 280 pound husband takes the same dose of medication that I do. It doesn’t make sense. I get that there are other things at play there besides weight, but seriously?

  10. Carla says:

    Does it warm your heart to know that I read and LOVED the SHIT out of this whole thing even though I could technically only understand about 40% of it? You are the very, very best.

  11. RA says:

    Waaay late to the commenting game, but I thoroughly enjoyed reading this during the drive to Thanksgiving festivities. I am a small adult, and I almost always reduce doses when I can. A full 2 Nyquil will leave me groggy for like 18 hours. It makes sense, since I am about the size of, oh, a 12-year-old.

  12. Jenny says:

    I am in awe of your smarts. Holy COW.

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