Parameter identifiability and Extended Multiple Studies Analysis of a compartmental model for human vitamin A kinetics: fixing fractional transfer coefficients for the initial steps in the absorptive process

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Metabolism and Metabolic Studies

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Present address: ICAN Nutrition Education and Research, Seoul, Korea.

Abbreviations: DT, delay time; EMSA, Extended Multiple Studies Analysis; FSD, fractional standard deviation; WinSAAM, Windows version of the Simulation, Analysis and Modeling software

Over the past 30 years, mathematical modelling (specifically model-based compartmental analysis) of vitamin A kinetic data has generated important information about the whole-body metabolism of this essential nutrient. In model-based compartmental analysis, temporal data on plasma (and sometimes organ) retinol response following administration of labelled vitamin A are analysed mathematically in light of a postulated compartmental model that describes the vitamin A system. The simplest model that provides a good fit to the data generates both quantitative and predictive information about the system⁽¹⁾.

In the 1980s and 1990s, Green and colleagues used model-based compartmental analysis to study vitamin A metabolism in rodent models following IV administration of [³H]retinol in its physiological transport complex. In addition to an active recycling of retinol between the plasma and tissues, these researchers found correlations between plasma vitamin A concentrations and both vitamin A disposal rates⁽²⁾and storage pool size⁽³⁾. Later, Cifelli et al.⁽⁴⁾developed a compartmental model for vitamin A kinetics in humans following oral administration of a labelled dose and confirmed that vitamin A disposal rate is positively correlated with vitamin A stores in well-nourished American and Chinese subjects (n 26).

In human subjects, one challenge in advancing models for vitamin A metabolism is the between-subject variability in absorption of the orally administered isotopic dose. In a previous report⁽⁴⁾, the standard deviations for the fractional transfer coefficients related to vitamin A absorption were over half (0·5-2 times) the estimates. A fractional standard deviation (FSD) less than 0·5 is significant, because it indicates 95 % confidence that the parameter value is different from zero⁽⁵⁾. Thus, models for which the FSD for the parameter estimates are less than 0·5 can be considered to have adequate numerical identifiability. Using these criteria, the fractional transfer coefficients related to vitamin A absorption calculated for the Cifelli et al.⁽⁴⁾model have...