n Transit compartment single distribution compartment PK absorption model in simbiology

I have built a n-transit compartment with single distibutional pharmacokinetic absorption model using SimBiology. This model is based on the TRANSIT model descibed in the following publication: Savic, R.M., Jonker, D.M., Kerbusch, T. et al. J Pharmacokinet Pharmacodyn (2007) 34: 711. https://doi.org/10.1007/s10928-007-9066-0

I chose to start by loading a one compartment absorption model with Clearance parmaeterization (macro parameters) and then modified the absorption reaction equation as n transit compartment that is based on an analytical solution to determine the transit compartment number as a continuous variable (not an interger).

analytical solution for number of compartments:

Single distribution compartment ODE:

transform of ODE for numerical stability when n is large:

Attache is a report summarizing how I defined the model in simbiology.

I am not sure if I have used the wrong syntax but I am seeing negative cincentrations at the first simulated timepoints as shown by this simulation plot:

The simulation should be a gradual absorption phase in contrast to typical tlag absorption models that are in the simbiology PK model library.

Cheers,

Dan

[Arthur Goldsipe]

I have two comments/questions:

1) What question are you asking use? I'm hoping you can formulate something fairly specific.

2) If you want us to debug your model, could you could attach the actual model, either as a MAT file or an SBPROJ file?

[Daniel Hines]

I am trying to recreat the n transit PK absorption model that ius described in the aforementioned publication.

In comparison to typical lag time absortion models, this transit model considers the delay to absorption as the transport through multiple tansit compartments prior to absorption.

Also, the number of transit compartments are typically defined as a positive integer value. But in this case, and anlytical solution to the number of transit compartments is included so that n may defined as a non-integer value.

That solution is defined by:

where Aa is the mass of drug at the absorption site

Dose*F is the available dose for absorption,

ktr is the transit rate constant

n is the number of transit compartments

ka is the absorption rate constant into the central compartment

ktr can be defined by the parameters n and MTT (mean transit time)

I attempted to define this transit model by first loading a one compartment absorption model from the simbiology PK model library and then modifying the absorption flux equation as the absorption site drug ODE above.

However after simulating a 400mg dose I am seeing a PK response that isnt making sense (negative concentration at early timepoints) which tells me something is wrong with how I defined the model. Here's the response I am seeing

Here's the response I want to see (solid bacl curve) in comparison toa lag time absorption model (dotted black curve):

Apparently I can't upload the simbiology project file here so if there is another way you would like me to share the model with me just let m e know.

This model would be very useful in contrast to conventional PK absorption models for drugs that exhibit slow or delayed absorption. A simple model structure in between lag time response models and large PBPK models.

I greatly appreciate the help!

Cheers

Dan

Answer 1

[Wojciech Krzyzanski]

Dear Dan,

For a positive input to the Aa compartment and 0 initial value (Aa(0)=0), your solultion Aa(t) should be always positive. Your simulated absorption curve implies that you have ODE solver issues. Since you mentioned that the number of transit compartments is large, I think this is a stiffness problem, and your ODE solver is not suited for stiff equations. Did you get negative Aa for smaller n? Stiffness can occur for large ka as well.

Regards,

Wojciech

[Daniel Hines]

Hi Wojciech,

Thanks for the reply. I restructured the simbiology model to define the input of drug from the nth transit compartment as a reaction where null -> Aa. And the reaction rate equation is expressed as the exponential term included in absorbed drug mass balance ODE:

However, in this solution the fraction of dose available, "Dose*F" is defined as a parameter value. So there will have to be another modification to this model to allow for repeat dosing schedules.

I have included a zip file of the current model to this reply and pasted a screenshot of the model schematic and a acute dose simulation below:

[Jeremy Huard]

Hi Daniel,

the equation defining the transit compartment is only valid for a single bolus.

But you can modify it for repeated dosing by replacing 'time' in the equation by the time from dosing as suggested here: https://dx.doi.org/10.1128%2FAAC.00461-07

In SimBiology you would need to add an event that stores the time of dosing. If your dose amount is constant, this is all you would need to do. If your dose amount depends on a model parameter, you can modify Dose in this event.

I have implemented this in your model (see attached file).

Edit: This was the wrong URL. I have corrected it.