condition in which one compartment does not affect the mass balance

Hi, I'm following the instruction of bacterial PK-PD model based on the previous model

(Nielsen, E. I. et al. Semimechanistic pharmacokinetic/pharmacodynamic model for assessment of activity of antibacterial agents from time-kill curve experiments. Antimicrobial Agents and Chemotherapy. 51:128-136.) https://www.mathworks.com/help/simbio/ug/model-views.html

In this instruction, there are two compartments named to Central and Biophase compartment and are assumed that the presence of the Biophase compartment does not affect the mass balance.

When should I meet this condition "some compartment doesn't affect the mass balance" ?

I would be appreciate if you could share some examples.

Thanks

Answer 1

[Sietse Braakman]

Hi Kazutaka,

In the example you are following along with (https://www.mathworks.com/help/simbio/ug/model-views.html), the PK part of the model is determined by a one compartment model with linear clearance (the compartment Central, with species Drug_Central and elimination reaction reaction_1). The biophase of the drug is modeled in a separate compartment: Biophase, with species Drug_Biophase, and creation reaction reaction_3 and elimination reaction reaction_2. The assumption in this model is that the drug concentration in the biophase does not affect the drug concentration in the central compartment and thereby the mass balance. This concept is implemented through reaction_3 : the stoichiometry of the reaction (Drug_Central -> Drug_Central + Drug_Biophase) has Drug_Central on both sides of the arrow, ensuring that Drug_Central is not being 'consumed' by the reaction. In other words: the concentration of Drug_Central is not affected by reaction_3 and reaction_3 doesn't show up in the ODEs for Drug_Central. In the diagram, this is illustrated by the dashed line between Drug_Central and reaction_3.

The assumption that the Biophase compartment does or doesn't affect the mass balance is a modeling decision made by the authors of the paper referenced at the bottom of the example page. As such, there is no condition that I can say your model should comply with in order to say that the compartment doesn't affect mass balance. The example merely states how to implement this.

I hope that helps. Let me know if you have further questions.

Best,

Sietse

[Kazutaka Sekiguchi]

Hi Sietse

Thank you for your kind answer.

I can understand the meaning and figure out how should be considered in the model well.