Duration of Retinol Isotope Dilution Studies with Compartmental Modeling Affects Model Complexity, Kinetic Parameters, and Calculated Vitamin A Stores in US Women

Abstract

Background: Retinol isotope dilution (RID) indirectly estimates vitamin A (VA) status. Multicompartment modeling of RID data is used to refine study designs and equations to calculate VA stores. Previous studies suggest that VA in slowly turning over pools is not traced if follow-up is not long enough; however, shorter RID studies are being investigated. Few long-term models have been published.

Objective: We determined the effect of time on mathematical models of VA kinetics, model parameters, and outcomes.

Methods: In this longitudinal study, women (mean ± SD age: 22 ± 3 y; n = 7) were given 2.0 µmol [14,15]-13C2-retinyl acetate. Blood samples were staggered from 4 h to 152 d; the fraction of dose in serum was modeled with compartmental models. Four model-time categories were created: full models that used all data (median: 137 d; range 97-152 d) and truncated shorter studies of 14, 27, and 52 d (range: 42-62 d). Outcomes included number of compartments to adequately model serum data, kinetic parameters, total traced VA mass, and time-to-dose equilibration. To gain insight into longer follow-up, an additional participant was given 17.5 µmol 13C4-VA, and data were modeled as long as enrichment was above baseline (5 y).

Results: Longer follow-up times affected kinetic parameters and outcomes. Compared with the 14-d models, long-term full models required an additional compartment for adequate fit (14.3% compared with 100%; P = 0.0056) and had longer [median (quartile 1, quartile 3)] whole-body half-life [15.0 d (10.5, 72.6 d) compared with 135 d (115, 199 d); P = 0.0006], time-to-dose equilibration [3.40 d (3.14, 6.75 d) compared with 18.9 d (11.2, 25.7 d); P < 0.0001], and total traced mass [166 µmol VA (162, 252 µmol VA) compared with 476 µmol VA (290, 752 µmol VA); P = 0.0031].

Conclusions: Extended RID sampling alters numerous mathematically modeled, time-dependent outcomes in women. Length of study should be considered when using mathematical models for calculating total-body VA stores or kinetic parameters related to VA turnover. This study is registered at www.clinicaltrials.gov as NCT03248700.

Figures

FIGURE 1

One- (A) and 2- (B) extravascular-pool compartment models of VA kinetics in US women given 13C-retinyl acetate. Circles represent compartments, arrows represent fractional transfer coefficients [denoted L(I,J), the fraction of compartment J transferred to compartment I per day], and the square represents a delay element. Compartments 1–4 (with delay element 3) represent the absorption, chylomicron delivery, and liver processing of VA. Compartment 5 refers to the serum, compartments 6 and 7 represent extravascular VA pools, and compartment 0 (not pictured) represents irreversible loss of VA from the system. L(I,J)s refer to the fractional transfer of pool J to pool I per day, U(1) refers to intake of dietary VA, and the asterisks (*) represent the site of tracer input. VA, vitamin A.

FIGURE 2

Representative fractions of the dose in serum compared with time and resulting models from a single woman given 13C-retinyl acetate representing different study lengths: (A) 14 d; inset is same model with altered axes; (B), 27 d; (C), 52 d; and (D), 152 d. Models that used data ≤14 d and 27 d (A and B) required only 1 extravascular compartment to adequately fit data, whereas models containing data ≤52 d and 152 d (C and D) required 2 extravascular compartments to adequately fit data.

FIGURE 3

Representative TTRs/doses (equivalent to fraction of dose/compartment mass) for a single woman given 13C-retinyl acetate. (A) Model truncated to 14 d. (B) Full model plotted only to 50 d. (C) Full model with all data plotted. The model with data through 14 d required 1 extravascular pool, whereas the full model required 2. TTR, tracer-to-tracee ratio.

FIGURE 4

Comparison plots of model-calculated total traced mass and short-term isotope dilution TBS (Equation 2) in US women. Each data point represents 1 participant. Short 4-d TBS were determined by the following equation: TBS = Fa × S × dose × (1/TTR), with factors Fa and S customized for each participant with the corresponding model. (A) Total traced mass and customized Fa and S for each participant from the statistically preferred model with data ≤27 d. (B) Total traced mass and customized Fa and S for each participant from the statistically preferred model with all data. Fa, the fraction of the administered dose absorbed and in store; S, ratio of specific activities or TTRs of retinol in serum to that in stores; TBS, total body stores; TTR, tracer-to-tracee ratio.

FIGURE 5

Kinetic data and model outcomes for an additional woman given 17.5 µmol 13C4-retinyl acetate with 1825 d of follow-up. (A) Observed data and model-predicted fraction of oral dose in serum over time for the full model. Inset is same model with altered axes. (B) Total traced mass compared with truncated study length. Lines represent total body VA stores estimated from isotope dilution equations. (C) Vitamin A half-life compared with truncated study length. (D) Time-to-dose equilibration (time at which S = 1) compared with truncated study length. (E) Value of S at final equilibration (time to infinity) compared with truncated study length. All data for panels B–E represent the statistically preferred compartmental model (1 compared with 2 extravascular pools); 2 pools were required for models with >64 d of follow-up. S, ratio of specific activities or TTRs of retinol in serum to that in stores; TTR, tracer-to-tracee ratio; VA, vitamin A.