Use of Theoretical Women and Model-Based Compartmental Analysis to Evaluate the Impact of Vitamin A Intake with or without a Daily Vitamin A Supplement on Vitamin A Total Body Stores and Balance During Lactation.

BACKGROUND: Inadequate vitamin A (VA) intake is common among lactating women in many communities worldwide, but high-dose VA supplementation for postpartum women is not recommended by the World Health Organization as an effective intervention. OBJECTIVES: To simulate the impact of VA intake via diet and daily VA supplements on VA total body stores (TBS) and balance in theoretical lactating women with low/moderate TBS. METHODS: We studied 6 theoretical subjects with assigned values for TBS from 219-624 µmol. Using Simulation, Analysis, and Modeling software and a previously published compartmental model for whole-body VA metabolism, we simulated TBS over 6 mo of established lactation for each subject under 4 conditions: 1) prelactation VA intake was increased to maintain VA balance (LSS); 2) prelactation VA intake was maintained (NLSS); 3) VA intake was the same as 2) but a daily VA supplement (2.8 µmol/d) was added (NLSS+S); and 4) VA intake was as 1) and the daily VA supplement was included (LSS+S). RESULTS: To compensate for the loss of VA via milk while VA balance was maintained (LSS) over 6 mo of lactation, VA intake had to increase by 0.8-1.87 µmol/d (n = 6) compared with NLSS. Over 6 mo of NLSS treatment, VA balance was negative (geometric mean, -0.77 µmol/d) compared with LSS, whereas balance was positive under NLSS+S and LSS+S conditions (0.75 and 1.5 µmol/d, respectively). For LSS, the proportion of total VA disposal was 37% via breastmilk, 32% from VA stores, and 32% from nonstorage tissues. CONCLUSIONS: Adding a daily VA supplement (2.8 µmol/d) to the diet of lactating women with suboptimal VA intake may effectively counterbalance the negative VA balance resulting from the output of VA via breastmilk and thus benefit both mother and infant by maintaining or increasing VA stores and breastmilk VA concentration.

Use of Compartmental Modeling and Retinol Isotope Dilution to Determine Vitamin A Stores in Young People with Sickle Cell Disease Before and After Vitamin A Supplementation.

BACKGROUND: Suboptimal plasma retinol concentrations have been documented in US children with sickle cell disease (SCD) hemoglobin SS type (SCD-HbSS), but little is known about vitamin A kinetics and stores in SCD. OBJECTIVES: The objectives were to quantify vitamin A total body stores (TBS) and whole-body retinol kinetics in young people with SCD-HbSS and use retinol isotope dilution (RID) to predict TBS in SCD-HbSS and healthy peers as well as after vitamin A supplementation in SCD-HbSS subjects. METHODS: Composite plasma [13C10]retinol response data collected from 22 subjects with SCD-HbSS for 28 d after isotope ingestion were analyzed using population-based compartmental modeling ("super-subject" approach); TBS and retinol kinetics were quantified for the group. TBS was also calculated for the same individuals using RID, as well as for healthy peers (n = 20) and for the subjects with SCD-HbSS after 8 wk of daily vitamin A supplements (3.15 or 6.29 µmol retinol/d [900 or 1800 µg retinol activity equivalents/d]). RESULTS: Model-predicted group mean TBS for subjects with SCD-HbSS was 428 µmol, equivalent to ∼11 mo of stored vitamin A; vitamin A disposal rate was 1.3 µmol/d. Model-predicted TBS was similar to that predicted by RID at 3 d postdosing (mean, 389 µmol; ∼0.3 µmol/g liver); TBS predictions at 3 compared with 28 d were not significantly different. Mean TBS in healthy peers was similar (406 µmol). RID-predicted TBS for subjects with SCD-HbSS was not significantly affected by vitamin A supplementation at either dose. CONCLUSIONS: Despite differences in plasma retinol concentrations, TBS was the same in subjects with SCD-HbSS compared with healthy peers. Because 56 d of vitamin A supplementation at levels 1.2 to 2.6 times the Recommended Dietary Allowance did not increase TBS in these subjects with SCD-HbSS, further work will be needed to understand the effects of SCD on retinol metabolism. This trial was registered as NCT03632876 at clinicaltrials.gov.

Use of Theoretical Subjects to Develop a Method for Assessing Equivalence of Dietary Vitamin A in a Mixed Diet.

BACKGROUND: Although the vitamin A (VA) equivalency of provitamin A carotenoids from single foods or capsules has been studied using several approaches, there is currently no reliable method to determine VA equivalency for mixed diets. OBJECTIVES: To reach the objective of identifying a method to determine the VA equivalency of provitamin A carotenoids in mixed diets, we tested a new approach using preformed VA as proxy for provitamin A. METHODS: We studied 6 theoretical subjects who were assigned physiologically plausible values for dietary VA intake, retinol kinetic parameters, plasma retinol pool size, and VA total body stores. Using features in the Simulation, Analysis and Modeling software, we specified that subjects ingested a tracer dose of stable isotope-labeled VA on day 0 followed by 0-µg supplemental VA or 200, 400, 800, 1200, 1600, and 2000 µg VA daily from day 14 to day 28; we assigned VA absorption to be 75%. For each supplement level, we simulated plasma retinol specific activity (SAp) over time and calculated the mean decrease in SAp relative to 0 µg. Group mean data were fitted to a regression equation to calculate predicted VA equivalency at each supplement level on day 28. RESULTS: For each subject, higher VA supplement loads resulted in lower SAp, with the magnitude of the decrease differing among subjects. The mean predicted amount of absorbed VA was within 25% of individual subjects' assigned amount for 4 of the 6 subjects, and the mean ratio of predicted to assigned amount of absorbed VA over all supplement loads ranged from 0.60 to 1.50, with an overall mean ratio of 1.0. CONCLUSIONS: Results for preformed VA suggest that this protocol may be useful for determining VA equivalency of provitamin A carotenoids in free-living subjects if mixed diets with known provitamin A content were substituted for the VA supplements.

Direct Use of Plasma or Milk Vitamin A Specific Activity Data to Model Retinol Kinetics and Predict Vitamin A Stores in Theoretical Lactating Women.

BACKGROUND: Many applications of the Simulation, Analysis and Modeling software use data on the fraction of an orally administered tracer dose (FD) in plasma; thus, researchers must scale-up measured analyte concentration to the total plasma pool. For studies in lactating women, estimating breast milk pool size is challenging. OBJECTIVES: The objectives were to determine whether the standard vitamin A modeling approach using FD data could be modified to use vitamin A specific activity in milk (SAm) and/or plasma (SAp) for compartmental analysis of vitamin A kinetics and status in theoretical lactating women. METHODS: Using 12 previously studied theoretical subjects with a wide range of assigned values for vitamin A total body stores (TBS) and the coefficient ("FaS") needed to predict TBS using a retinol isotope dilution equation, we simulated data for SAp and SAm for 49 d after oral administration of labeled vitamin A. Then we modeled datasets for SAp and SAm, as well as only SAp or SAm, incorporating a linear scaling factor to automatically convert SA to FD and including several physiologically reasonable constraints as input data. As outcomes, we compared model-predicted TBS and FaS to assigned values. RESULTS: Scaling factors effectively adjusted SA data to adequately predict vitamin A mass in plasma and breast milk pools. Data for SAp and SAm provided model predictions of TBS that were comparable to assigned values (range: 85-107%); using only SAp, ratios ranged from 92% to 108% and for SAm from 85% to 108%. Parallel results were obtained for simulated FaS. CONCLUSIONS: Results show that SA data from plasma and/or milk can be used directly for modeling vitamin A during lactation in theoretical subjects, providing accurate estimates of TBS and FaS. Results suggest that, in free-living lactating women, researchers might measure only SAp or only SAm and adequately describe whole-body vitamin A metabolism and status.

Use of Compartmental Modeling and Datasets for Theoretical Lactating Women to Determine Conditions under Which Vitamin A-Specific Activity in Breast Milk Provides Accurate Estimates of Vitamin A Total Body Stores by Retinol Isotope Dilution.

BACKGROUND: Vitamin A concentrations in breast milk are related to maternal vitamin A intake and status. OBJECTIVES: Our objective was to identify conditions under which vitamin A specific activity in breast milk (SAm) could be used instead of retinol specific activity in plasma (SAp) to predict vitamin A total body stores (TBS) by retinol isotope dilution (RID). METHODS: We used 12 previously-studied theoretical lactating women with assigned values for TBS (219-1348 µmol) and retinol kinetic parameters; we assumed subjects ingested a dose of stable isotope-labeled vitamin A. We expanded a 9-compartment steady state tracer model to include a parallel model for tracee (unlabeled retinol) and then adapted that model so vitamin A intake entered the system in 3 meals each day. Using compartmental analysis, we first simulated SAm and SAp after an overnight fast (as in actual RID experiments) and then with vitamin A intake also restricted in sequential meals on the day before sampling for RID. RESULTS: After an overnight fast, SAm at day 21 postdosing was lower than SAp. However, if vitamin A intake was also restricted in 1, 2, or 3 meals before sampling, SAm/SAp (mean ± SD) was 0.92 ± 0.042,  0.96 ± 0.016,  or 0.99 ± 0.004,  respectively; results for days 14 and 28 were similar. When either SAp or SAm was used to predict TBS by RID on day 21 after 1-d restriction, predictions for all subjects were within 25% of assigned TBS. CONCLUSIONS: Results indicate that, for theoretical lactating women with a wide range of vitamin A status, SAm will accurately predict TBS by RID at 2-4 wk postdosing if vitamin A intake is restricted for 1 d before sampling. If confirmed in community settings, results suggest that vitamin A status in lactating women can be determined without collecting blood.

Does the Amount of Stable Isotope Dose Influence Retinol Kinetic Responses and Predictions of Vitamin A Total Body Stores by the Retinol Isotope Dilution Method in Theoretical Children and Adults?

BACKGROUND: To minimize both cost and perturbations to the vitamin A system, investigators limit the amount of stable isotope administered when estimating vitamin A total body stores (TBS) by retinol isotope dilution (RID). OBJECTIVES: We hypothesized that reasonable increases in the mass of stable isotope administered to theoretical subjects would have only transient impacts on vitamin A kinetics and minimal effects on RID-predicted TBS. METHODS: We adapted previously used theoretical subjects (3 children, 3 adults) with low, moderate, or high assigned TBS and applied compartmental analysis to solve a steady state model for tracer and tracee using assigned values for retinol kinetic parameters and plasma retinol. To follow retinol trafficking when increasing amounts of stable isotope were administered [1.39-7 (children) and 2.8-14 µmol retinol (adults)], we added assumptions to an established compartmental model so that plasma retinol homeostasis was maintained. Using model-simulated data, we plotted retinol kinetics versus time and applied the RID equation TBS = FaS/SAp [Fa, fraction of dose in stores; S, retinol specific activity (SA) in plasma/SA in stores; SAp, SA in plasma] to calculate vitamin A stores. RESULTS: The model predicted that increasing the stable isotope dose caused transient early increases in hepatocyte total retinol; increases in plasma tracer were accompanied by decreases in tracee to maintain plasma retinol homeostasis. Despite changes in kinetic responses, RID accurately predicted assigned TBS (98-105%) at all loads for all theoretical subjects from 1 to 28 d postdosing. CONCLUSIONS: Results indicate that, compared with doses of 1.4-3.5 µmol used in recent RID field studies, doubling the stable isotope dose should not affect the accuracy of TBS predictions, thus allowing for experiments of longer duration when including a super-subject design (Ford et al., J Nutr 2020;150:411-8) and/or studying retinol kinetics.

The Use of Datasets for Theoretical Subjects to Validate Vitamin A-Related Methods and Experimental Designs.

We review recent work in which model-based compartmental analysis has been applied to data for theoretical human subjects in order to study questions related to vitamin A kinetics and metabolism. Using model simulations in this way, one can validate experimental designs, evaluate or improve vitamin A assessment methods, study the influence of perturbations on assessment methods, and/or advance information related to retinol kinetics. We also provide some information on the rationale for assigning physiologically appropriate values for specified characteristics [e.g., plasma retinol concentration, vitamin A total body stores (TBS), vitamin A intake] to hypothetical individuals, and in addition, we outline how one might first select an appropriate compartmental model for whole-body vitamin A metabolism and then specify physiologically reasonable values for the associated retinol kinetic parameters. In the studies discussed here, the Simulation, Analysis, and Modeling software was used to simulate responses in key model compartments for hypothetical subjects so that model predictions could be compared to assigned values or projected outcomes. For example, in the case of the retinol isotope dilution (RID) method that is used to assess vitamin A status, application of this approach has provided a way to evaluate the accuracy of TBS predictions under different steady state and non-steady state conditions, thus increasing confidence about the validity of RID results obtained in the field. Although datasets for theoretical subjects have been used to evaluate protocols in pharmacokinetics, to our knowledge, other nutrition researchers have not previously used approaches such as those described here. Our results to date indicate that this strategy has the potential to provide useful information related not only to vitamin A but perhaps to other nutrients as well.

Influence of Vitamin A Status on the Choice of Sampling Time for Application of the Retinol Isotope Dilution Method in Theoretical Children.

BACKGROUND: Vitamin A status may influence the choice of a blood sampling time for applying the retinol isotope dilution (RID) equation to predict vitamin A total body stores (TBS) in children. OBJECTIVES: We aimed to identify time(s) after administration of labeled vitamin A that provide accurate estimates of TBS in theoretical children with low or high TBS. METHODS: We postulated 2- to 5-y-old children (12/group) with low (<200 µmol) or high TBS (≥700 µmol) and used compartmental analysis to simulate individual subject values for the RID equation TBS =   FaS/SAp (Fa, fraction of dose in stores; S, retinol specific activity in plasma/in stores; SAp, retinol specific activity in plasma). Using individual SAp and group geometric mean FaS values from 1-28 d, we calculated individual and group mean TBS and compared them to assigned values. RESULTS: Mean TBS was accurately predicted for both groups at all times. For individuals, predicted and assigned TBS were closest when the CV% for FaS was low [12-14%; 4-13 d (low), 12-28 d (high)]. The mean percentage error for TBS was <10% from 2-19 d (low) and 7-28 d (high). Predicted TBS was within 25% of assigned TBS for ≥80% of children from 3-23 d (low) and 9-28 d (high). Within groups, RID tended to overestimate lower TBS and underestimate higher TBS. CONCLUSIONS: Using a good estimate for FaS, accurate RID predictions of TBS for individuals will be obtained at many times. If vitamin A status is low, results indicate that early sampling (e.g., 4-13 d) is optimal; if vitamin A status is high, sampling at 12-28 d is indicated. When vitamin A status is unknown, sampling at 14 d is recommended, or a super-subject design can be used to obtain the group mean FaS at various times for RID prediction of TBS in individuals.

Use of Model-Based Compartmental Analysis and Theoretical Data to Further Explore Choice of Sampling Time for Assessing Vitamin A Status in Groups and Individual Human Subjects by the Retinol Isotope Dilution Method.

BACKGROUND: An optimal blood sampling time for application of the retinol isotope dilution (RID) method for predicting vitamin A total body stores (TBS) (i.e., vitamin A status) has not been established. OBJECTIVES: Objectives were to identify sampling times that provide accurate estimates of TBS by RID in groups and individuals by applying compartmental modeling to data for theoretical adults and children. METHODS: We selected previously generated hypothetical adults and children (20 per group) that had a wide range of assigned values for TBS and vitamin A kinetic parameters. We used the Simulation, Analysis and Modeling software to simulate individual kinetic responses; then we calculated geometric mean values for the RID equation coefficients and each individual's plasma retinol specific activity at various times, using those values to predict group mean and individual subject TBS. Predicted values for TBS were compared with assigned values. RESULTS: Accurate estimates of group mean TBS were obtained at all sampling times from 1 to 30 d in both adults and children. For individuals, correlations between RID-predicted TBS and assigned values increased with time in the adults (R2 = 0.80 at day 14, 0.96 at day 21, and 0.99 at day 28); a similar trend was observed for the children, with R2 = 0.82 at day 7 and increasing to 0.97 at days 21 and 28 (P < 0.001 for all comparisons). CONCLUSIONS: Although no single, unique time provided the most accurate prediction of TBS for all individuals within these groups, applying the RID method at 21 or 28 d yielded predictions that were within 25% of assigned values for 90% or 95% of adults, respectively; corresponding values for children were 80% from 10 to 20 d, and 85% at 21 and 28 d. For most subjects, early times (<14 d for adults and <10 d for children) provided less accurate predictions.

Development of a Compartmental Model to Investigate the Influence of Inflammation on Predictions of Vitamin A Total Body Stores by Retinol Isotope Dilution in Theoretical Humans.

BACKGROUND: Inflammation, both acute and chronic, is associated with reductions in the synthesis of retinol-binding protein (RBP) and the concentration of retinol in plasma. Consequently, it is currently recommended that the retinol isotope dilution (RID) method not be used to estimate vitamin A total body stores (TBS) in subjects with inflammation. OBJECTIVES: To apply compartmental analysis to study the effects of inflammation on hepatic apo-RBP input, plasma retinol pool size, and RID-predicted TBS in theoretical subjects with known steady state values for these parameters. METHODS: We selected 6 previously generated hypothetical subjects who ingested a dose of stable isotope-labeled vitamin A (day 0). Starting with each subject's published steady state model for retinol tracer kinetics, we developed a parallel model for unlabeled retinol and RBP that incorporated links between these entities and tied liver retinol secretion to RBP availability. Then we perturbed the steady state model by initiating chronic or acute inflammation on day 0 or acute inflammation on day 3 or 9 and simulating results for RBP, plasma retinol, and TBS. RESULTS: Chronic inflammation led to substantial reductions in RID-predicted TBS for at least 2 weeks after tracer administration. In contrast, acute inflammation induced on day 0 or 3 resulted in less dramatic impacts on TBS (37% or 20% reduction, respectively, from steady state levels, with levels rebounding by 14 days). When inflammation was induced 9 days after administration of the tracer, the effects on predicted TBS were minimal. Overall, for acute inflammation initiated at 0, 3, or 9 days, accurate predictions of TBS were obtained by 2 weeks. CONCLUSIONS: Compartmental analysis can be applied in the novel way described here to study the influence of perturbations such as inflammation on predictions of vitamin A status using RID. Such an approach has potential value for studying other perturbations and different nutrients.

A Compartmental Model Describing the Kinetics of ß-Carotene and ß-Carotene-Derived Retinol in Healthy Older Adults.

BACKGROUND: Descriptive and quantitative information on ß-carotene whole-body kinetics in humans is limited. OBJECTIVES: Our objective was to advance the development of a physiologically based, working hypothesis compartmental model describing the metabolism of ß-carotene and ß-carotene-derived retinol. METHODS: We used model-based compartmental analysis (Simulation, Analysis and Modeling software) to analyze previously published data on plasma kinetics of [2H8]ß-carotene, [2H4]ß-carotene-derived retinol, and [2H8]retinyl acetate-derived retinol in healthy, older US adults (3 female, 2 male; 50-68 y); subjects were studied for 56 d after consuming doses of 11 µmol [2H8]ß-carotene and, 3 d later, 9 µmol [2H8]retinyl acetate in oil. RESULTS: We developed a complex model for labeled ß-carotene and ß-carotene-derived retinol, as well as preformed vitamin A, using simulations to augment observed data during model calibration. The model predicts that mean (range) ß-carotene absorption (bioavailability) was 9.5% (5.2-14%) and bioefficacy was 7.3% (3.6-14%). Of the absorbed ß-carotene, 41% (25-58%) was packaged intact in chylomicrons and the balance was converted to retinol, with 58% (42-75%) transported as retinyl esters in chylomicrons and 0-2% by retinol-binding protein. Most (95%) chylomicron ß-carotene was cleared by the liver. Later data revealed differences in the metabolism of retinyl acetate- versus ß-carotene-derived retinol; data required that both ß-carotene and derived retinol be recycled from extrahepatic tissues (e.g. adipose) in HDL. Of total bioconversion [73% (47-99%)], 82% occurred in the intestine, 17% in the liver, and 0.83% in other tissues. CONCLUSIONS: Our model advances knowledge about whole-body ß-carotene metabolism in healthy adults, including the kinetics of transport in all lipoprotein species, and suggests hypotheses to be tested in future studies, such as the possibility that retinol derived from hepatic conversion over a long period of time might contribute to plasma retinol homeostasis and total body vitamin A stores.

Vitamin A Absorption Efficiency Determined by Compartmental Analysis of Postprandial Plasma Retinyl Ester Kinetics in Theoretical Humans.

BACKGROUND: Better methods are needed for determining vitamin A absorption efficiency in humans to support development of dietary recommendations and to improve the accuracy of predictions of vitamin A status. OBJECTIVES: We developed and evaluated a method for estimating vitamin A absorption efficiency based on compartmental modeling of theoretical data on postprandial plasma retinyl ester (RE) kinetics. METHODS: We generated data on plasma RE and retinol kinetics (30 min to 8 h or 56 d, respectively) after oral administration of labeled vitamin A for 12 theoretical adults with a range of values assigned for vitamin A absorption (55-90%); we modeled all data to obtain best-fit values for absorption and other parameters using Simulation, Analysis, and Modeling software. We then modeled RE data only (16 or 10 samples), with or without added random error, and compared assigned to predicted absorption values. We also compared assigned values to areas under RE response curves (RE AUCs). RESULTS: We confirmed that a unique value for vitamin A absorption cannot be identified by modeling plasma retinol tracer kinetics. However, when RE data were modeled, predicted vitamin A absorptions were within 1% of assigned values using data without error and within 12% when 5% error was included. When the sample number was reduced, predictions were still within 13% for 10 of the 12 subjects and within 23% overall. Assigned values for absorption were not correlated with RE AUC (P = 0.21). CONCLUSIONS: We describe a feasible and accurate method for determining vitamin A absorption efficiency that is based on compartmental modeling of plasma RE kinetic data collected for 8 h after a test meal. This approach can be used in a clinical setting after fasting subjects consume a fat-containing breakfast meal with a known amount of vitamin A or a stable isotope label.

Vitamin A Absorption Determined in Rats Using a Plasma Isotope Ratio Method.

BACKGROUND: Better methods are needed for determining vitamin A absorption efficiency. OBJECTIVE: Our objective was to measure vitamin A absorption in rats by adapting a plasma isotope ratio method previously used to determine cholesterol absorption. METHODS: Male Sprague-Dawley rats [n = 14; 340 ± 16 g (mean ± SD)] received an oral tracer dose of [3H]retinyl acetate in oil plus an intravenous dose of [14C]vitamin A-labeled lymph prepared in a donor rat that had received [14C]retinyl acetate intraduodenally. Blood samples were collected on days 1, 2, 3, 6, 9, and 12, and plasma was analyzed for 3H and 14C; vitamin A absorption was calculated for each sample as (fraction of oral dose/fraction of intravenous dose) × 100. Radioactivity was also measured in feces and urine collected as pools on days 3, 6, 9, and 12 and in liver and remaining carcass on day 12. RESULTS: Vitamin A absorption calculated as the plasma isotope ratio was >100% on day 1, 78% ± 5% on day 6, 76% ± 5% on day 9, and 74% ± 5% on day 12; fitting the data to an exponential function plus a constant predicted an absorption of 75% by day 14. Recovery of the oral dose in feces (day 0 to day 6) was low (6.2% ± 0.84%, n = 10) and the mean isotope ratio in day 9-12 urine pool was lower than that in plasma. CONCLUSIONS: The plasma isotope ratio holds promise for estimating vitamin A absorption, but additional work is needed to determine how long studies need to be and if the doses should be administered simultaneously. For application of this method in humans, artificial chylomicrons labeled with a stable isotope of retinyl acetate could be used for the intravenous dose, with a different isotope required for the oral dose.

Use of Model-Based Compartmental Analysis and a Super-Child Design to Study Whole-Body Retinol Kinetics and Vitamin A Total Body Stores in Children from 3 Lower-Income Countries.

BACKGROUND: Model-based compartmental analysis has been used to describe and quantify whole-body vitamin A metabolism and estimate total body stores (TBS) in animals and humans. OBJECTIVES: We applied compartmental modeling and a super-child design to estimate retinol kinetic parameters and TBS for young children in Bangladesh, Guatemala, and the Philippines. METHODS: Children ingested [13C10]retinyl acetate and 1 or 2 blood samples were collected from each child from 6 h to 28 d after dosing. Temporal data for fraction of dose in plasma [13C10]retinol were modeled using WinSAAM software and a 6-component model with vitamin A intake included as weighted data. RESULTS: Model-predicted TBS was 198, 533, and 1062 µmol for the Bangladeshi (age, 9-17 mo), Filipino (12-18 mo), and Guatemalan children (35-65 mo). Retinol kinetics were similar for Filipino and Guatemalan groups and generally faster for Bangladeshi children, although fractional transfer of plasma retinol to a larger exchangeable storage pool was the same for the 3 groups. Recycling to plasma from that pool was ∼2.5 times faster in the Bangladeshi children compared with the other groups and the recycling number was 2-3 times greater. Differences in kinetics between groups are likely related to differences in vitamin A stores and intakes (geometric means: 352, 727, and 764 µg retinol activity equivalents/d for the Bangladeshi, Filipino, and Guatemalan children, respectively). CONCLUSIONS: By collecting 1 or 2 blood samples from each child to generate a composite plasma tracer data set with a minimum of 5 children/time, group TBS and retinol kinetics can be estimated in children by compartmental analysis; inclusion of vitamin A intake data increases confidence in model predictions. The super-child modeling approach is an effective technique for comparing vitamin A status among children from different populations. These trials were registered at www.clinicaltrials.gov as NCT03000543 (Bangladesh), NCT03345147 (Guatemala), and NCT03030339 (Philippines).

Better Predictions of Vitamin A Total Body Stores by the Retinol Isotope Dilution Method Are Possible with Deeper Understanding of the Mathematics and by Applying Compartmental Modeling.

Retinol isotope dilution (RID) is a well-accepted technique for assessing vitamin A status [i.e., total body stores (TBS)]. Here, in an effort to increase understanding of the method, we briefly review RID equations and discuss their included variables and their coefficients (i.e., assumptions that account for the efficiency of absorption of an orally administered tracer dose of vitamin A, mixing of the dose with endogenous vitamin A, and loss due to utilization). Then, we focus on contributions of another technique, model-based compartmental analysis and especially the "super-person" approach, that advance the RID method. Specifically, we explain how adding this modeling component, which involves taking 1 additional blood sample from each subject, provides population-specific estimates for the RID coefficients that can be used in the equation instead of values derived from the literature; using model-derived RID coefficients results in improved confidence in predictions of TBS for both a group and its individuals. We note that work is still needed to identify the optimal time for applying RID in different groups and to quantify vitamin A absorption efficiency. Finally, we mention other contributions of modeling, including the use of theoretical data to verify the accuracy of RID predictions and the additional knowledge that model-based compartmental analysis provides about whole-body vitamin A kinetics.

Addition of Vitamin A Intake Data during Compartmental Modeling of Retinol Kinetics in Theoretical Humans Leads to Accurate Prediction of Vitamin A Total Body Stores and Kinetic Parameters in Studies of Reasonable Duration.

BACKGROUND: Mathematical modeling of theoretical data has been used to validate experimental protocols and methods in several fields. OBJECTIVES: We hypothesized that adding dietary vitamin A intake data as an input during compartmental modeling of retinol kinetics would lead to accurate prediction of vitamin A total body stores (TBS) at 2 specified study lengths and would reduce study duration required to accurately define the system. METHODS: We generated reference values for state variables (including TBS and intake) and kinetic parameters for 12 theoretical individuals (4 each of children, younger adults, and older adults) based on modeling plasma retinol tracer data for 365 d. We compared TBS predictions using data to 28 d (children) or 56 d (adults) without and with intake included in the model to reference values for each subject. Then, by truncating data sets from 365 d, we determined the shortest study duration required to accurately define the system without and with inclusion of vitamin A intake. RESULTS: Reference values for TBS ranged from 30 to 3023 µmol. Study durations of 28 and 56 d were sufficient to accurately predict TBS for 6 of the 12 subjects without intake; adding intake resulted in accurate predictions of TBS for all individuals. When intake was not included as a modeling input, durations of 35-310 d were required to define the system; inclusion of intake data substantially reduced the time required to 10-42 d. CONCLUSIONS: Inclusion of vitamin A intake as additional data input when modeling vitamin A kinetics allows investigators to accurately predict TBS and define the vitamin A system in studies of reasonable length (4 wk in children and 8 wk in adults). Because it is generally possible to obtain estimates/measures of intake, including such data increases confidence in model predictions while also making studies more feasible.

Inclusion of Vitamin A Intake Data Provides Improved Compartmental Model-Derived Estimates of Vitamin A Total Body Stores and Disposal Rate in Older Adults.

BACKGROUND: Sampling times and study duration impact estimates of kinetic parameters and variables including total body stores (TBS) and disposal rate (DR) when compartmental analysis is used to analyze vitamin A kinetic data. OBJECTIVE: We hypothesized that inclusion of dietary intake (DI) of vitamin A as an additional input would improve confidence in predictions of TBS and DR when modeling results appear to indicate that studies are not long enough to accurately define the terminal slope of the plasma retinol isotope response curve. METHODS: We reanalyzed previously published data on vitamin A kinetics monitored over 52 d in 7 US and 6 Chinese adults (means: 56 y, BMI 26.6 kg/m2, 38% males), adding an estimate for vitamin A intake [2.8 µmol/d (mean RDA)] as an input during application of the Simulation, Analysis and Modeling software. RESULTS: Use of a model with 1 extravascular compartment (1 EV), as in the original analysis, resulted in predictions of vitamin A intake that were higher than physiologically reasonable; inclusion of intake data in a model with 2 extravascular compartments (2 EV DI) resulted in more realistic estimates of intake and DR. Specifically, predictions of DR by the 2 EV DI (versus 1 EV) model were 2.10 compared with 12.2 µmol/d (US) and 2.21 compared with 5.13 µmol/d (Chinese). Predictions of both TBS [2056 compared with 783 µmol (US) and 594 compared with 219 µmol (Chinese)] and days of vitamin A stores [981 compared with 64 d (US) and 269 compared with 43 d (Chinese)] were higher using the new approach. CONCLUSIONS: Inclusion of vitamin A intake as additional data input when modeling vitamin A kinetics can compensate for less-than-optimal study duration, providing more realistic predictions of vitamin A TBS and DR. This approach advances the application of compartmental analysis to the study of vitamin A and, potentially, other nutrients.

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.

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 (Rs  = 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.

Intestinal ß-carotene bioconversion in humans is determined by a new single-sample, plasma isotope ratio method and compared with traditional and modified area-under-the-curve methods.

The vitamin A value (bioefficacy) of provitamin A carotenoids is determined by absorption of the carotenoid (bioavailability) and its subsequent conversion to retinol (bioconversion). Here we show that intestinal bioconversion of ß-carotene can be estimated based on analysis of a single plasma sample collected 6 h after subjects ingest a test dose of stable isotope-labeled ß-carotene from the ratio of retinyl esters to retinyl esters plus ß-carotene. Plasma isotope ratio predictions of bioconversion ranged from 50 to- 93% (mean 76%) for 45 healthy young adults with low vitamin A stores. Results were the same as predictions made by a traditional area-under-the-curve method calculated from 0 to- 8 h or a modified area-under-the-curve method calculated from 0 to- 12 h. The modified method may provide better estimates of bioconversion between 8 and 24 h after ingestion of a carotenoid dose when stable isotopes cannot be used due to cost or logistics. Furthermore, because the plasma isotope ratio method requires only one blood sample and no isolation of triglyceride-rich lipoproteins, its use will facilitate estimation of provitamin A carotenoid bioconversion in human subjects and especially children, in whom repeated blood sampling is not feasible.

A Simple Plasma Retinol Isotope Ratio Method for Estimating ß-Carotene Relative Bioefficacy in Humans: Validation with the Use of Model-Based Compartmental Analysis.

Background: Provitamin A carotenoids are an important source of dietary vitamin A for many populations. Thus, accurate and simple methods for estimating carotenoid bioefficacy are needed to evaluate the vitamin A value of test solutions and plant sources. ß-Carotene bioefficacy is often estimated from the ratio of the areas under plasma isotope response curves after subjects ingest labeled ß-carotene and a labeled retinyl acetate reference dose [isotope reference method (IRM)], but to our knowledge, the method has not yet been evaluated for accuracy.Objectives: Our objectives were to develop and test a physiologically based compartmental model that includes both absorptive and postabsorptive ß-carotene bioconversion and to use the model to evaluate the accuracy of the IRM and a simple plasma retinol isotope ratio [(RIR), labeled ß-carotene-derived retinol/labeled reference-dose-derived retinol in one plasma sample] for estimating relative bioefficacy.Methods: We used model-based compartmental analysis (Simulation, Analysis and Modeling software) to develop and apply a model that provided known values for ß-carotene bioefficacy. Theoretical data for 10 subjects were generated by the model and used to determine bioefficacy by RIR and IRM; predictions were compared with known values. We also applied RIR and IRM to previously published data.Results: Plasma RIR accurately predicted ß-carotene relative bioefficacy at 14 d or later. IRM also accurately predicted bioefficacy by 14 d, except that, when there was substantial postabsorptive bioconversion, IRM underestimated bioefficacy. Based on our model, 1-d predictions of relative bioefficacy include absorptive plus a portion of early postabsorptive conversion.Conclusion: The plasma RIR is a simple tracer method that accurately predicts ß-carotene relative bioefficacy based on analysis of one blood sample obtained at ≥14 d after co-ingestion of labeled ß-carotene and retinyl acetate. The method also provides information about the contributions of absorptive and postabsorptive conversion to total bioefficacy if an additional sample is taken at 1 d.