Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

Hof, F.; Bridge, L. J.

Abstract

Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.

• Journal Article Type: Article
• Acceptance Date: Sep 17, 2020
• Online Publication Date: Oct 10, 2020
• Publication Date: 2021-02
• Deposit Date: Oct 12, 2020
• Publicly Available Date: Oct 14, 2020
• Journal: Journal of Pharmacokinetics and Pharmacodynamics
• Print ISSN: 1567-567X
• Electronic ISSN: 1573-8744
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 48
• Pages: 99-131
• DOI: https://doi.org/10.1007/s10928-020-09719-8
• Keywords: Pharmacology Mathematical pharmacology Pharmacokinetics Compartment models Differential equations Transit compartments Regimen design
• Public URL: https://uwe-repository.worktribe.com/output/6771286