Structural identifiability analysis of pharmacokinetic models using DAISY: semi-mechanistic gastric emptying models for 13C-octanoic acid

Abstract

Structural identifiability analysis is necessary for efficient parameter estimation and it is concerned with determination of whether the parameters in a model can be identified from specified experiments with perfect input-output data. Structural identifiability analysis is very important in mathematical modelling of biological and biomedical experiments and should be considered at the design stage of these experiments. There are three possible outcomes from a structural identifiability analysis; globally/uniquely identifiable, locally/non-uniquely identifiable or non-identifiable/unidentifiable. An ideal outcome is a globally/uniquely identifiable model, however a locally/non-uniquely identifiable outcome can help to identify areas of the model or experiment that need improvement. Despite the importance of structural identifiability analysis, it is still not widely used due to the heavy computational burden involved and the lack of software. A new software package, DAISY, that implemented differential algebra for identifiability analysis was recently released. DAISY is freely available, easy to use and does not require any high-level programming skill. The (13)C-octanoic acid breath test is now widely used for assessing the rate of gastric emptying in patients. Unlike scintigraphy, which is the gold standard and is a direct measure of the rate of gastric emptying, the (13)C-octanoic acid breath test is an indirect method for assessing the rate of gastric emptying. However the (13)C-octanoic acid breath test is cheaper, safer and easy to perform. Because the rate of excretion of (13)CO(2) in breath does not only reflect the rate of gastric emptying but other processes involved between the ingestion of (13)C-octanoic acid and elimination of (13)CO(2) in breath, the parameters commonly derived from the excretion data are not direct measures of gastric emptying. The aim of this paper was to propose a new semi-mechanistic model for the analysis of (13)C-octanoic acid breath excretion data and demonstrate the use of DAISY to assess the identifiability of the model. One- and two-compartment disposition models were linked to a model which has separate compartments for the stomach, intestine and breath. To obtain a globally identifiable model, a repeated (13)C-octanoic breath test in the same individual experimental design was also investigated and this adds a separate stomach compartment to the model. Finally the gastric emptying rate constant from the first (13)C-octanoic breath test was constrained to be the same as the absorption rate constant from the intestine. From the structural identifiability analysis carried out in DAISY, the model based on two experiments (baseline and treatment) and a constraint is globally identifiable. In summary, the present work describes a new semi-mechanistic model that will allow efficient and reliable assessment of the rate of gastric emptying from the (13)C-octanoic breath test.