Rapamycin pharmacokinetics model

I’m still waiting for my 4 rapamycin blood tests to come back so that I can make my personal pharmacokinetics model so in the mean time I used the data from this paper: The Effect of a High-Fat Meal on the Oral Bioavailability of the Immunosuppressant Sirolimus (Rapamycin)

I’m implementing a 3 compartments pharmacokinetics model.
The compartments are :

  • The intestine that absorbs the rapamycin and send it into the blood
  • The blood is the central compartment that gets the rapamycin from the intestine and has bidirectional exchanges with the organs as well as some elimination (by metabolization)
  • The organs which exchange Rapamycin with the blood (both ways)

Here is that model with the differential equations fitted to the paper data for rapamycin + fat (dots)

As you can see the fit is very good which shows that the 3 compartment model is good enough.
As this model is based on differential equations I can (and will!) use it to simulate some popular dosage scenarios.
BTW in addition to the blood concentration this model gives the concentrations in the organs too, which if probably even more interesting, though there are some caveats here.

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Here is a first simulation for the popular 6mg/week dose. In fact it reaches a steady state after the third week:

And here is a 1 mg daily simulation which is a similar total dose of rapamycin but with a totally different result:

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The same plots in linear scale.


Scaled:

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What is the F (fraction of dose absorbed) in your model?

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Very nice, I am working on a product to do something very similar! https://rapatrack.com

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Can you do a simulation of 1 mg EOD (every other day)? As this is similar to the level in the 2014 Mannick paper at 0.5 mg everolimus a day and was as effective as 5 mg one time a week.

What about 10 mg every other week, and 20 mg one time a month?

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@Stijn this service looks very interesting. Will it be available to US customers? When will it be live?

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@cl-user Here is the argument for Rapa holidays. This is interesting. Thanks.

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Few more months, yes, should ship to US, but not meant for US, because you can already do a Labcorp Rapamycin test, in Europe you can’t anywhere.

Working with lab to get testing blood originating from finger to be validated, we still have a few more months of blood draws to go. Relevant: Dutch Volunteers Wanted: Make Rapamycin Blood Testing a Reality Across Europe - #4 by Stijn only 1 person is helping.

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Is it dried blood like an omega 3 test? If valid would be much easier than sitting at Lab Corp all day getting draw after draw. I’d do it.

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It uses a finger lancet system, you prick your finger and drip blood in a little tube and ship it.

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1mg every other day looks very low:



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@cl-user Rapa doesn’t go to zero after 30 days? Is that just an artifact of your model or do you think that is really what is happening?

I do a 14 day cycle with an extra week off every 5th week. The point is to get to zero. Maybe I need to take a month off every few months.

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It’s not an artifact. When the concentration is very low the elimination is also very low because the probability that a rapa molecule encounters an enzyme that will metabolize it is very low.
On the other hand the probability that this rapa molecule binds to mTOR is also very low.
That’s why some residual concentration will remain for a very long time but it will have no biological effects.

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Here is the same 6mg/week average dose but with different schedules.

Blood log scale:

Blood linear scale:

Organs log scale:

Organs linear scale:

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@cl-user where does the 10x dilution in organs come from?

I cannot find anything on people (who might not like having their organs assayed) but I found this paper on rat blood vs organs after 24 hours that was interesting. The rat clears its blood very fast but the organs retain the rapa longer, and of course the organs are fairly different in this function. I was surprised to see that muscle was low…would you think that is because it cleared faster or didn’t get in well like the brain (BBB effect)

https://www.researchgate.net/publication/6417356_Pharmacometrics_and_delivery_of_novel_nanoformulated_PEG-b-poly-_caprolactone_micelles_of_rapamycin

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Interpretation of the above needs to take into account the blood-to-plasma ratio (Rb)which is defined as Cb (blood concentration of compound) / Cp (plasma concentration of compound). Rapamycin exhibits a preferential distribution into red blood cells (94.5%) compared to plasma (3.1%), lymphocytes (1.01%) and granulocytes (1.0%) [30, 48]. Noted that Labcorp does whole blood level so edited.

For PK modeling after oral dosing, the frequency of sampling is critical, answering the question of what sampling times provide the most information to estimate the pharmacokinetic parameters. This requires some fancy schmancy math but greatly simplifying the issue: a) get enough time points around the a priori estimated Cmax/Tmax and b) the sampling frequency along the curve should be proportional to the magnitude of the absolute value of the second derivative of the log concentration time curve. This is an iterative process that requires several dosing experiments to gain familiarity with the pharmacokinetic behavior of a particular drug in a population of individuals with adjustment in sampling times based on the population variance results.

An finally, this is pretty good online PK analytical software.

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The volume of the body (all organs) is roughly 10 times the volume of blood + blood saturated organs so when N molecules of rapa go from blood to the organs they are diluted into a 10x greater volume.
The issue is that as shown in the paper you cite that distribution can be very different from one organ to another. The organs diluted by 10 is just the average concentration on all organs and there will be a lot of variations between different organs like brain vs liver for instance.

Unfortunately there is not enough data from just the blood concentration to calculate anything more meaningful than the average for all the organs.

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@cl-user Thanks. I am learning today. One more big thing I do not understand about the model curves is related to blood vs organ rapa. What delay do you assume for human organs in clearing the rapa? The rat chart indicated that rat organs retained rapa after rat blood rapa was essentially (but not totally) gone after 24 hours. Would human organs retain rapa longer than a rat just as we seem to have longer half-lives of rapa in human blood?

No idea, it’s not a parameter of the model. Basically I use an optimizer to fit the parameters of the differential PK equations to fit the model to the measurements.
Maybe I can modify the model to estimate F though some data is missing like the volume of the blood compartment. I’ve seen estimates of 6l to 8l for that. A rough estimation for F here would be around 11%.

I’m open to any suggestions to improve the model.

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