Comparison of Vitamin A Total Body Stores Calculated by Two Retinol Isotope Dilution Equations with Known Values Derived from Modeling
Authors: Ford Jennifer Lynn , Green Michael Henry , Green Joanne Balmer , Novotny Janet 
Published: November 2023

Isotope dilution equations are used to assess vitamin A (VA) status following oral administration of stable isotope‐labeled vitamin A (2H or 13C). The “Olson equation” (Furr et al., Am J Clin Nutr. 1989;49:713) is used to calculate VA total body stores (TBS) based on plasma isotope enrichment after dose equilibration with endogenous VA (typically 21 d after dosing) and the dose mass, and correction factors that account for dose absorption and retention, VA specific activity (SA) in plasma vs. stores after equilibration, and the system fractional catabolic rate (FCR). A more recently applied isotope‐balance equation (Valentine et al., Am J Clin Nutr. 2013;98:1192) calculates TBS from the fractional abundance of 13C in the dose of 13C‐retinyl acetate, the mass of the dose, the pre‐dose fractional abundance of 13C in plasma retinol, and the fractional abundance of 13C in plasma retinol after the dose has mixed with endogenous stores. Both of these equations were originally developed for closed homogeneous systems, but correction factors are included in the currently used versions to accommodate open, heterogeneous systems in which there is input of dietary VA and loss of VA metabolites. The correction factor related to loss (i.e., the FCR) is assumed to be very low (0.5%/d). To evaluate the accuracy of the prediction equations as currently applied, we used model‐based compartmental analysis (the Simulation, Analysis and Modeling software [WinSAAM]) to provide known values for TBS in seven theoretical subjects whose kinetic parameters were derived from actual plasma retinol kinetics in healthy adults with a wide range of TBS. First, we postulated a two compartment model in which labeled retinol in plasma exchanges with VA in extravascular tissues (TBS), where there is metabolism of VA and excretion of retinoid metabolites as well as VA storage. Then, model parameters plus the mass of retinol in plasma were used to calculate actual TBS for each theoretical subject. Values ranged from 71 to 2493 μmol. As expected, the ratio of tracee (unlabeled retinol) to tracer in plasma increased with time in all subjects. When we compared model‐generated values for TBS to predictions made by the isotope dilution equations, we found that predicted TBS was not constant but rather increased with time. TBS was overestimated by 2.4 times using 21 d data in the Olson equation and by 5.6 times using 28 d data in the isotope‐balance equation; agreement with the model‐generated values was best at higher TBS, coinciding with lower FCR. We conclude that the major problems with both equations are (a) the assumption of an incorrect (too low) value for FCR as the correction factor for loss and (b) the need for an accurate value for the difference in plasma and extravascular retinol SA. When we used modeling results to obtain accurate, time‐variant values for the correction factors, we found that both equations correctly estimate the steady state value for TBS. Since the influence of FCR increases with time, it is important when FCR is not accurately known to sample blood for the TBS calculation soon after dosing (e.g., 3–5 d).