A Population-Based (Super-Child) Approach for Predicting Vitamin A Total Body Stores and Retinol Kinetics in Children Is Validated by the Application of Model-Based Compartmental Analysis to Theoretical Data

Abstract

Background: Public health nutritionists need accurate and feasible methods to assess vitamin A status and to evaluate efficacy of interventions, especially in children. The application of population-based designs to tracer kinetic data is an effective approach that reduces sample burden for each child.

Objectives: Objectives of the study were to use theoretical data to validate a population-based (super-child) approach for estimating group mean vitamin A total body stores (TBS) and retinol kinetics in children and to use population-based data to improve individual TBS predictions using retinol isotope dilution (RID).

Methods: We generated plasma retinol kinetic data from 6 h to 56 d for 50 theoretical children with high vitamin A intakes, assigning values within physiologically reasonable ranges for state variables and kinetic parameters ("known values"). Mean data sets for all subjects at extensive (n = 36) and reduced (n = 11) sampling times, plus 5 data sets for reduced numbers (5/time, except all at 4 d) and times, were analyzed using Simulation, Analysis and Modeling software. Results were compared with known values; population RID coefficients were used to calculate TBS for individuals.

Results: For extensive and reduced data sets including all subjects, population TBS predictions were within 1% of the known value. For 5 data sets reflecting numbers and times being used in ongoing super-child studies, predictions were within 1-17% of the known group value. Using RID equation coefficients from population modeling, TBS predictions at 4 d were within 25% of the known value for 66-80% of subjects and reflected the range of assigned values; when ranked, predicted and assigned values were significantly correlated (R_s = 0.93, P < 0.0001). Results indicate that 7 d may be better than 4 d for applying RID in children. For all data sets, predictions for kinetic parameters reflected the range of known values.

Conclusion: The population-based (super-child) approach provides a feasible experimental design for quantifying retinol kinetics, accurately estimating group mean TBS, and predicting TBS for individuals reasonably well.

Keywords: WinSAAM; high vitamin A intake; humans; nutrition assessment; retinol isotope dilution; theoretical children; vitamin A kinetics; vitamin A status.

FIGURE 1

Flow chart of the theoretical analysis used to evaluate the super-child approach. A database for 50 theoretical children with known values for vitamin A TBS and other variables was used to generate population (mean) data sets for 3 sampling protocols. For each data set, model-based compartmental analysis was applied to estimate vitamin A TBS and retinol kinetics for the group. Population estimates for RID equation coefficients were calculated from the model and used to predict vitamin A TBS at 4 d for individual subjects. Predictions of TBS were compared with known values using the specified evaluation criteria. Circled numbers correspond to the following objectives: 1) use model-based compartmental analysis to generate a database of known values for theoretical subjects that was needed to test the population-based approach, 2) establish proof-of-concept that population-based modeling of a detailed data set provides accurate estimates for the variables of interest, 3) validate the approach using reduced sampling times, and 4) validate the super-child design being implemented in ongoing super-child studies. RID, retinol isotope dilution; TBS, total body stores.

FIGURE 2

Working compartmental model for retinol kinetics in children. Circles represent compartments; the rectangle is a delay component and DT(3) is the delay time retinol spent in component 3; and interconnectivities between compartments (arrows) are fractional transfer coefficients [L(I,J)s, or the fraction of retinol in compartment J transferred to compartment I each day]. For example, L(6,5) is the fraction of retinol in compartment 5 transferred to compartment 6 each day and L(5,6) is the fraction in compartment 6 transferred to compartment 5 each day. Compartment 1 is the site of input of orally ingested tracer (*) and dietary vitamin A [U(1)]; fractional absorption efficiency was fixed at 0.80. Components 1–4 represent the processing of preformed dietary vitamin A, chylomicron production and metabolism, hepatic uptake of chylomicron remnant retinyl esters, and processing of retinol (compartment 4); delay component 3 is the site of loss of unabsorbed tracer. Retinol is secreted from the liver bound to retinol-binding protein into plasma compartment 5, the site of sampling (triangles). Retinol in the plasma pool can exchange with vitamin A in 2 extravascular compartments: a faster turning-over pool (compartment 7) and a slower turning-over storage pool (compartment 6), which is also the site of irreversible loss from the system. The inset shows the simplified model used to analyze the reduced data sets (protocols 2 and 3). In the simplified model, delay component 3 is the site of input for tracer (*) and dietary vitamin A [U(3)]. TBS, total body stores.

FIGURE 3

Model-simulated plasma retinol response data vs. time after ingestion of labeled retinyl acetate for 2 theoretical subjects. Shown are data for the fraction of dose simulated at all sampling times (n = 36) from 6 h to 56 d using parameters listed in Supplemental Table 1. For subject 39, we used the model (Figure 2) with both extravascular compartments (compartments 6 and 7); for subject 10, we used the model with only one compartment (compartment 6). The inset shows simulations for the same subjects using the reduced (super-child) sampling schedule (n = 11 samples collected from 6 h to 28 d).

FIGURE 4

Model-simulated composite plasma retinol response data vs. time after ingestion of labeled retinyl acetate for 50 theoretical subjects generated using the super-child protocol. Shown are “observed” FD_p for individual subjects (50 subjects at 4 d and 5 randomly assigned children at each remaining time), the geometric mean FD_p at each time, and the model-calculated fit to the mean data for 1 of the 5 super-child data sets (protocol 3/scenario 5). FD_p, fraction of dose in plasma.

FIGURE 5

Assigned compared with predicted values for vitamin A TBS for 50 theoretical subjects (A) and rank-order of values (B). TBS was predicted using retinol isotope dilution (Equation 2) at 4 d for 1 of the 5 super-child data sets (protocol 3/scenario 5); least-squares regression lines were y = 0.95x − 4.1 (R² = 0.86, P < 0.0001) (A) and y = 0.93x + 1.7 (R_s = 0.93, P < 0.0001) (B). TBS, total body stores.