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.
Highlights
Mathematical models for the absorption, distribution and elimination of drugs are common in the pharmacokinetics (PK) literature
The generalised model allows for simulation of realistic repeated dosing regimens that have traditionally been analysed in detail for simpler one- and two-compartment models [10, 43, 45]
Further complexity may be added as a future modelling extension by considering the ‘‘body’’ as a two-compartment schematic including central and peripheral compartments
Summary
Mathematical models for the absorption, distribution and elimination of drugs are common in the pharmacokinetics (PK) literature. We further consider the case of equi-infusion dosing, whereby for model (M1), the input is periodic constant infusions of drug to the central compartment, over fixed ‘‘on’’ time intervals, separated by fixed ‘‘off’’ intervals (Fig. 2, regimen (Ieq)). Beyond these relatively simple models, our analysis extends to the n-transit compartment model with input into the first transit compartment (model (Mt)).
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