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(Journal of Nutrition. 2001;131:1854-1861.)
© 2001 The American Society for Nutritional Sciences


Articles

Accuracy of Simple Techniques for Estimating Fractional Zinc Absorption in Humans1

David M. Shames*, Leslie R. Woodhouse{dagger}, Nicola M. Lowe** and Janet C. King{dagger}2

* Department of Radiology, University of California, San Francisco, CA 94143, {dagger} Western Human Nutrition Research Center, U.S. Department of Agriculture, Agricultural Research Service, University of California, Davis CA 95616 and ** Department of Biological Sciences, University of Central Lancashire, Preston PR1 2HE, UK

2To whom correspondence should be addressed. E-mail: jking{at}whnrc.usda.gov


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The theoretical basis of the accuracy of a number of simple techniques for estimating fractional zinc absorption (FZA) in humans using stable isotopic tracers has not been evaluated. These techniques include fecal monitoring (FM), deconvolution analysis (DA), double isotopic tracer ratio (DITR) and indicator dilution methods. Using a compartmental model, we investigated the accuracy and logic of each of these techniques. Time-dependent estimates of FZA based on the simple techniques were simulated using the compartmental model and compared with the known FZA derived from the model. The analysis elucidated logical errors in some of the FM techniques, and even when these problems were corrected, the FM technique was still prone to errors due to incomplete fecal tracer recovery and variable gastrointestinal (GI) transit time. Although logically correct, the indicator dilution techniques were also highly sensitive to incomplete fecal tracer recovery and variable GI transit time. The DA and DITR techniques were the most robust in that they were logically correct and were insensitive to incomplete fecal tracer recovery and variable GI transit time. Although all of the DA and DITR methods provided similarly good estimates of FZA relative to the compartmental model, the DITR technique performed on a spot urine specimen obtained several days after tracer administration was the preferred choice because of its simplicity and minimal requirements for patient compliance.


KEY WORDS: zincstable isotopic tracerszinc absorptioncompartmental modeling


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
A number of relatively simple techniques have been described for estimating fractional zinc absorption (FZA)3 in humans using stable isotopic tracers of zinc. Each of these methods can be grouped into one of four broad categories [fecal monitoring (FM), deconvolution analysis (DA), double isotopic tracer ratio (DITR) and indicator dilution (ID)]. The FM techniques use measurement of zinc tracer in feces after oral tracer administration alone (1Citation 2Citation 3)Citation or in combination with intravenous tracer administration (4)Citation . DA requires detailed plasma or cumulative urine measurements of both orally and intravenously administered zinc tracers (5Citation ,6)Citation . DITR requires single measurements in plasma or urine of both orally and intravenously administered tracers (7)Citation . Finally, ID requires measurement of zinc tracer in feces and plasma (8)Citation or feces and urine (5)Citation after a single administration of intravenous tracer. This technique also requires measurement of the zinc tracee in feces and plasma (8)Citation or in urine (5)Citation . Despite the plethora of techniques for estimation of FZA, no attempt has been made to evaluate their relative accuracy or time dependence primarily because no gold standard for measuring FZA is available in humans.

We have formulated a detailed compartmental model (9)Citation of zinc metabolism from dynamic zinc tracer and tracee data. The model is based on six normal women in whom zinc tracer and tracee measurements were performed in plasma, urine and feces for up to 12 d after simultaneous administration of both oral and intravenous stable isotopic tracers of zinc. The model is consistent with zinc metabolism as currently understood, contains the minimal degree of mathematical structure required to explain all of the data and is mathematically unique, meaning that all 11 adjustable rate constants are determinable from the data with good precision. Such large relatively complex models of metabolic systems, based on rich databases of information, can be used to evaluate the adequacy of simpler models that focus on specific features (in this case FZA) of the larger metabolic system described by the detailed compartmental model (10)Citation .

A recent report by us (11)Citation compared the results of the simple techniques for estimation of FZA based on six individual datasets with the FZA obtained from the compartmental model also applied to each of the datasets. Because of the experimental and biological variability in each of the datasets, the results reflected this variability within the data as well as the logical adequacy of each of the simpler techniques with respect to the compartmental model. To overcome these problems, the current study was designed to simulate time-dependent values for FZA for the simple techniques using the compartmental model, and then compared these estimates with the known FZA derived from the detailed model. This procedure eliminated any confounding effects due to analytical variations and inadequate data sampling, so that the underlying logic for the simple techniques of estimating FZA can be evaluated, i.e., how well do the simpler techniques of FZA estimation recover the value for FZA encoded into the compartmental model assuming noiseless data with very fine temporal resolution. In addition, the ideal time at which or over which the simple technique should be applied to provide the best estimate of FZA can be determined.


    METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Simple measures of FZA

    FM technique. The FM method for estimating zinc absorption is based on the amount of orally administered tracer cumulatively excreted during a 12-d fecal collection period (2)Citation . The cumulative fecal excretion of tracer expressed as a fraction of the orally administered dose, fo, is measured from which FZA is estimated by

(1)

This measure of FZA, FM, no correction (FM-N), is known to be an underestimate of FZA because fo contains endogenously secreted oral tracer, which has already been absorbed as well as the unabsorbed oral tracer.

To correct for the resecretion of absorbed oral tracer, which contributes to fo, English et al. (3)Citation presented a technique detailed by Krebs et al. (1)Citation in which the cumulative excretion of tracer, expressed as the percentage of administered dose, is plotted against time. The rate of increase of fecal accumulation of tracer defined as the slope between successive data points, rises rapidly at the beginning of fecal collection due to the passage of unabsorbed tracer directly into the feces and then decreases to an apparent slightly positive slope of < 1%/d. It is assumed that this final positive slope is due entirely to the resecretion of absorbed tracer back into the intestine and subsequent excretion into the feces. To correct for this endogenous excretion, a line is fitted by linear regression to the data points comprising the slightly positive slope on the cumulative tracer excretion plot and extrapolated back to the y-axis. The percentage of the never absorbed oral tracer dose excreted in the stools is then estimated as the intercept of this line on the y-axis, y(0), under which conditions FZA is then given by

(2)

Values for FZA using Equation 2 are subsequently referred to as FM, English correction (FM-E).

Another correction for the resecretion of absorbed oral tracer appearing in the feces has been developed by Rauscher and Fairweather-Tait (4)Citation . It takes advantage of the fecal accumulation of a second tracer administered intravenously at the same time as the oral tracer. They define an equation for apparent fractional absorption of zinc exactly as that formulated in Equation 1 and convert it to FZA using additional information provided by the fraction of an intravenously administered tracer accumulated in the feces, fiv. They suggest that:

(3)

The product, (fo)(fiv), is assumed to correct for resecretion of absorbed oral tracer collected in the feces as part of fo. This measure of FINF>), is assumedZA is subsequently referred to as FM, Raucher correction (FM-R).

We have developed an alternative formulation of the double tracer FM technique based on different logic. Rewriting Equation 3 as

(4)

It is seen that the final term of Equation 4 is given by the fraction of oral tracer absorbed, FZA, multiplied by the fraction of intravenously administered zinc tracer plasma tracer excreted in the feces, fiv. Thus, Equation 4 becomes

(5)

which reduces to

(6)

Values for FZA determined using Equation 6 are subsequently referred to as FM, Shames correction (FM-S).

    DA technique. DA, used primarily as a method for estimating calcium absorption (6Citation ,12)Citation , can also be used to determine zinc absorption (5)Citation . In this method, the first pass absorption of an oral tracer dose can be determined if the tracer concentration responses in plasma to both oral and intravenously administered tracers are measured. Typically, the experiment is carried out by administering different oral and intravenous tracers simultaneously, so that plasma sampling has to be implemented only once. Under these conditions, the function describing the tracer response in the plasma, Rp,o(t), (% dose) to an orally administered tracer is given by the convolution integral:

(7)

where E(t) is the function describing the rate of first pass entry of the orally administered tracer into the plasma compartment (% dose h-1) and Rp,iv(t) is the function describing the plasma response to an intravenously administered tracer (% dose). Because FZA is given by the integration of E(t) from 0 to infinity and the integration of Eq 7 from 0 to infinity is

(8)

FZA can be expressed as

(9)

This value for FZA can be approximated by the ratio of the integrals from zero to time t, assuming that t is great enough for the first pass absorption process to be completed such that

(10)

In practice, the numerator and denominator are plasma concentrations rather than total amounts of tracer in plasma, and consequently their ratio is equivalent to that in Equation 10 .

Because the amounts of oral and intravenous tracers in cumulative urine are given by {lambda} {int}0t Rp,o({theta})d{theta} and {lambda} {int}0t Rp,iv({theta})d{theta}, respectively, where {lambda} is a proportionality constant describing the fractional rate of transfer of tracer from plasma to urine, the ratio of oral to intravenous tracers in cumulative urine reduces to the same expression as that seen in Equation 10 because {lambda} cancels out in both the numerator and denominator.

    DITR method. The DITR method was first proposed for measuring FZA by Friel et al. (7)Citation . They noticed that both the oral and intravenous tracers in plasma and urine seemed to decline with the same slope after a period of a day or 2 after simultaneous tracer administration and assumed that the ratio of oral to intravenous tracer concentrations in plasma or urine would be a good measure of FZA after correcting for different tracer doses. These measures for FZA are given by the following three equations for plasma, spot urine and cumulative 24-h urine, respectively.

(11)


(12)


(13)

where uo(t) and uiv(t) are concentrations of oral and intravenous tracer in a single spot urine specimen at any time t (d) > 2 and uo'(d) and uiv'(d) are concentrations of oral and intravenous tracer in a complete 24-h urine collection beginning after d 2. Estimates of FZA using Equations 11–13 are subsequently referred to as DITR in plasma (DITRP), DITR in spot urine (DITRU) and DITR in 24-h urine (DITR24H), respectively.

    ID techniques. ID techniques for estimating FZA, FZAID, described by Yergey (5)Citation and Jackson et al. (8)Citation , are based on the accumulation of intravenously injected zinc tracer in feces and urine or feces and plasma, respectively, and provide a measure of the rate of endogenous fecal zinc (EFZ) excretion, EFZ (mg · d-1). When combined with metabolic balance data on total dietary zinc and total fecal zinc, these techniques can be used to estimate FZA. Assuming intravenous administration of a unit dose of zinc tracer, one can show that the ratio of EFZ to the rate of urinary excretion of zinc tracee, U, (mg · d-1) is given by

(14)

where f* and u* are the accumulation of intravenously administered zinc tracer in feces and urine, respectively, from time 0 to infinity. Assuming that this ratio reaches a limiting value at some number of days t after tracer administration, Equation 14 can be approximated by

(15)

Because

(16)

where p(t) is the amount of zinc tracer in the plasma compartment at any time t, P is the steady-state zinc tracee mass in the plasma compartment (mg) and {lambda} is the fractional transfer of zinc tracer and tracee from the plasma into the urine (d-1), substitution into Equation 15 yields

(17)

where p'(t) is the zinc tracer-tracee ratio in plasma. Another formulation of Equation 17 is given by

(18)

where f'(t) is the zinc tracer-tracee ratio in feces and F is the rate of fecal excretion of zinc tracee (mg · d-1). Any of these three equations for EFZ can be used to estimate FZA by the steady-state balance equation

(19)

where D and F are the dietary intake and fecal excretion, respectively, of zinc tracee (mg · d-1).

    Compartmental model simulations and reference value for FZA. The compartmental model from which the simulated values for FZA were generated according to the simpler techniques (Eqs. 1–3 , 6, 10–13, 15, and 17–19) is based on stable isotopic tracer studies from six normal women (9)Citation . The structure of this model with average values for the rate constants (pools · d-1) used in the simulations is shown in Figure 1ACitation , and the steady-state solution of zinc masses (mg) and fluxes (mg · d-1), based on the average plasma zinc mass of 2.02 mg, is shown in Figure 1BCitation . Using this model, simulations of tracer content in plasma, urine and feces were performed for both intravenous and oral administrations. The plasma responses for both tracers up to d 20 are shown in Figure 2Citation ; cumulative urine and fecal tracer responses also for 20 d are shown in Figure 3ACitation for intravenous tracer and in Figure 3BCitation for oral tracer. Because the compartmental model used for all simulations is based on data obtained only to d 12 (9)Citation , extrapolation of the model simulations is required between d 12 and 20. Although such extrapolation does lead to an element of uncertainty in the simulated results beyond d 12, this uncertainty is likely small due to the limited dynamic range of the model responses between d 12 and 20. Most importantly, the longer simulation of the FZA results beyond d 12 for some of the simple techniques provides additional insight into the logical adequacy of each of the simple techniques not completely appreciated up to d 12.



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Figure 1. Compartmental model of zinc metabolism from Lowe et al. (9)Citation . Average values (A) for rate constants (pools · d-1) obtained from fits of compartmental model to plasma, urine and fecal zinc tracer and tracee data in six subjects after simultaneous administration of intravenous (open bullets and arrow) and oral (solid black bullets and arrow) tracers. Steady-state solution (B) with compartmental masses (mg; center of compartments) and fluxes (mg · d-1, adjacent to flux arrows) based on average rate constants in A and average plasma zinc mass of 2.02 mg. FZA of compartmental model is given by k1,5/(k1,5 + k6,5), where ki,j are rate constants describing the fractional transfer rate of zinc tracer or mass to compartment i from compartment j.

 


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Figure 2. Simulations of plasma zinc responses (% of dose) to intravenous (heavy line) and oral (light line) tracers based on average compartmental model shown in Figure 1Citation . Detailed response over d 1 (A) and more prolonged response over 20 d (B).

 


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Figure 3. Simulations (% dose) of fecal (heavy line) and urinary (light line) responses to intravenous (A) and oral (B) tracer administrations.

 
The FZA of the compartmental model given by the ratio of k(1,5) to k(1,5) + k(6,5) is 0.279. Application of the compartmental model to each of the simpler measures of FZA allowed calculation of FZA as a function of time, FZAcalc (t) for each of the simpler techniques. These measures of FZA were expressed as percentages of the FZA implied in the model, FZAmod by

(20)

All simulations were generated using the SAAM II computer program (SAAM Institute, Seattle, WA). Values for FZA using the simple methods were determined at multiple times over the course of the theoretical experiment to evaluate the optimal time interval for use of each method. Slope estimates obtained using the FM-E method were calculated daily beginning at d 5 using the simulated cumulative excretion values for the oral tracer for that day and the previous 2 d (total of three points for each regression line). Because of the suspicion that the FM and ID methods were sensitive to percent recovery of excreted tracer and gastrointestinal (GI) transit time, simulations of %FZA(t) were also performed assuming that fecal tracer recovery was only 95% complete and that the GI transit time was twice the average value used in the initial simulations.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The results of the simple techniques for determining FZA simulated from the compartmental model are shown in Figures 4Citation , 5Citation and 6Citation . Figure 4Citation shows that the estimates of FZA by DA (Eq. 10) and the DITR techniques in plasma (DITRP; Eq. 11 ), in spot urine samples (DITRU; Eq. 12 ) and in complete 24 h urine collections (DITR24H; Eq. 13 ) all provided close approximations (within 5%) to the reference FZA value from the model, when the DA technique was carried out to at least 3–4 d and when the DITR estimates were applied between d 2 and 7 after dual tracer administration. The DA technique was always an underestimate of FZA and approached the expected FZA value asymptotically with time. The DITR methods were always overestimates and did not asymptotically approach the expected FZA with time. By d 2, the DITR method in the 24-h and in the spot urine samples provided nearly identical results.



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Figure 4. Application of DA and DITR techniques for estimation of % FZA in combination with Equation 20 using compartmental model of Figure 1Citation . The reference FZA (FZA expected if accuracy of method is perfect) is shown as the 100% line. The results ({Delta}) given by Equation 10 for DA (A) shown for varying durations of time after tracer administration up to 10 d. The DITR values ({Delta}) for FZA in plasma samples (B) based on Eq 11 shown frequently during d 1 and then daily up to 10 d after tracer administration. The DITR values in 24-h urine samples ({Delta}) and in spot urine samples (O) based on Equations 13 and 12 , respectively, shown on a daily basis (C) up to 10 d after tracer administration.

 


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Figure 5. Application of the four variations of the FM technique for estimation of % FZA in combination with Equation 20 using compartmental model of Figure 1Citation . The reference FZA of the compartmental model is shown as the 100% line. Results given by Equations 1 , 2, 3 and 6 are plotted daily (representing fecal collection periods ending on that day) for the FM-N ({Delta}), FM-E (O), FM-R (X) and FM-S (+) methods, respectively. Each FZA value for the FM-E method ({Delta}) is the result of a regression line fitted to the values of the cumulative fecal tracer on the day plotted along with the values on the previous 2 d.

 


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Figure 6. Application of the ID technique for estimation of % FZA in combination with Equation 20 using the compartmental model of Figure 1Citation . The reference FZA of the compartmental model is shown as the 100% line. Results are given by Equation 19 , where EFZ is a function of time based on Equations 15 , 17 or 18 calculated daily.

 
The results of the FM techniques applied to the simulated cumulative fecal tracer data are shown in Figure 5Citation . The FM-S method (Eq. 6) was the only FM technique that approached the 100% line asymptotically at ~7 or 8 d after tracer administration. The FM-N (Eq. 1) and FM-E (Eq. 2) methods provided overestimates of FZA initially and then crossed the expected FZA value (at 4–5 d for FM-N and at d 9 for FM-E) and became underestimates thereafter. The degree of the underestimate was less for FM-E than for FM-N. The worst of the techniques was FM-R (Eq. 3) , which always overestimated FZA, the smallest overestimate (13%) occurred at d 6. Before and after d 6, the overestimates of FZA by FM-R became progressively worse.

The results for the ID technique, FZAID (Eq. 19) , are shown in Figure 6Citation . This technique, like DA, provided an underestimate of FZA that approximated FZAmod asymptotically over time but was less accurate than the DA technique for a given time, t. At d 5 after tracer administration, FZAID returned a value just over 84% of the expected value and not until d 11 was the estimate > 95% of the expected FZA.

The simulated effects on FZA estimates using the FM and ID methods resulting from incomplete fecal tracer recovery (95%) and prolonged GI transit times (twice average) are shown in Figures 7Citation and 8Citation . A 5% loss of both oral and intravenous fecal tracer (Fig. 7A)Citation had a huge effect on these FZA estimates. The theoretically most accurate of the FM methods, that of FM-S, provided an overestimate of 15% and no longer approached the expected value asymptotically. Values of FZA from both FM-N and FM-E were increased for both short and long fecal collection periods and paradoxically provided better estimates of FZA for long fecal collections than would be the case assuming complete recovery of fecal tracer. Values obtained using the FM-R method were also higher for all fecal collection periods with the best value again occurring at d 6 and providing a 25% overestimate of FZA. The effects of a longer GI transit time (Fig. 7B)Citation revealed similar shapes to those responses seen in Figure 5Citation but were considerably delayed in time. The FM-S method was again the most accurate, although it did not approach the expected FZA value until d 14 or 15. Both FM-N and FM-E were, again, overestimates of FZA early and underestimates later in the fecal collection period, with the crossover point being significantly delayed compared with the shorter GI transit time. The overestimate of FZA provided by FM-R was somewhat worse than that seen in Figure 5Citation , the best value being approximately a 20% overestimate occurring at d 10.



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Figure 7. Application of the four variations of the FM technique for determination of % FZA using the compartmental model as in Figure 5Citation assuming fecal tracer recovery over a given fecal collection period only 95% complete (A) and assuming GI transit time of zinc twice the average value (B). Results given by Equations 1 , 2, 3 and 6 are plotted daily (representing fecal collection periods ending on that day) for the FM-N ({Delta}), FM-E (O), FM-R (X) and FM-S (+) methods, respectively. Each FZA value for the FM-E method ({Delta}) is the result of a regression line fitted to the values of the cumulative fecal tracer on the day plotted along with the values on the previous 2 d.

 


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Figure 8. Application of the ID technique for estimation of % FZA as in Figure 6Citation , assuming fecal tracer recovery over each fecal collection period is only 95% complete ({Delta}) and assuming GI transit time of zinc twice average value (O). Reference FZA of the compartmental model is shown as the 100% line. Results are given by Equation 19 , where EFZ is a function of time based on Equations 15 , 17 or 18 calculated daily.

 
Simulations of FZAID(t) based on incomplete (95%) zinc recovery in feces, i.e., an underestimate of f* in Equations 15 and 17 and an underestimate of F in Equation 18 , are shown in Figure 8Citation . This response no longer approximated the expected FZA asymptotically but was an underestimate of FZA up to 5 d post-tracer administration and an overestimate thereafter. Also shown in Figure 8Citation is the response of FZAID(t) based on a twice normal GI transit time. Here, the response was an underestimate of FZA approximating the correct value asymptotically but was considerately delayed in time. At d 5, the estimate was only 69% of the correct value and did not reach 95% of the model FZA until d 17.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Stable isotopic tracers are useful tools for determining mineral absorption. Although a number of relatively simple techniques for estimating FZA have been proposed, the logic of these techniques, i.e., how well they return the correct value for FZA, has not been fully investigated. In this study, we evaluated commonly used simple techniques for estimating FZA simulated with the compartmental model to the known FZA of the model. This process is equivalent to applying the simple techniques for FZA estimation to a noise-free dataset of very high temporal resolution generated from a detailed compartmental model having known FZA. This procedure allowed a comparison of the simpler methods without the confounding effects produced by experimental and analytical errors and insufficient data sampling. Any deviation from the expected FZA of the compartmental model provided by a particular technique, therefore, must be due to logical errors in that technique. In addition, the process provided an understanding of the time sensitivity of the simple techniques, i.e., at what time after tracer administration the technique should be applied for optimal accuracy.

The DA and DITR techniques (both using two tracers) were the most robust of the simple methods because they were easy to perform and provide relatively accurate estimates of FZA that were insensitive to incomplete tracer collection and variability in colonic transit time. The DITR estimates in urine were virtually the same as those in plasma a few days after tracer administration, and little difference was found between the DITR estimates in spot versus complete 24-h urine collections (Fig. 4)Citation . Although the DITR values for FZA anytime after the 1st d after tracer administration were overestimates, that provided by DA was an underestimate of FZA, which approximates the correct value asymptotically from below. In this analysis, based on zinc tracer kinetics in six normal women, the DITR measures of FZA at times between 3 and 8 d after tracer administration were slightly more accurate than that provided by DA, although eventually (e.g., at 20 d) the DA estimate becomes more accurate. The DA and DITR estimates are both ratio measurements and are insensitive to incomplete tracer collection because both oral and intravenous stable isotopic tracers are measured in the same sample of either plasma or urine. The colonic mean transit time is also not a factor because measurement of fecal zinc tracer or mass is not needed for the estimation.

All of the FM methods can lead to overestimates and underestimates of FZA as shown in Figures 5Citation and 7Citation . Wastney and Henkin (13)Citation show, and we confirmed (Fig. 5)Citation , that use of FM-N (Eq. 1) overestimates FZA for short fecal collections and underestimates it for longer collections. The uncorrected technique provides an accurate value for FZA only over a narrow band of days after tracer administration. Because this ideal collection period depends on a number of variables (rates of fractional absorption, fractional secretion and GI transit time) the unknown values for which differ in every subject, Wastney and Henkin (13)Citation argue that this technique should not be used to estimate FZA. They point out that the critical problem with this technique is the fecal excretion of previously absorbed and resecreted oral tracer along with the unabsorbed oral tracer.

An attempted solution to this problem of endogenous secretion of absorbed oral tracer (FM-E; Eq. 2 ) has been developed and carefully described in a review by Krebs et al. (1)Citation based on work presented earlier (3)Citation . The underlying assumption of this technique is that the rate of excretion of resecreted absorbed tracer is constant and can be determined from the slope of the fecal accumulation of tracer plotted as a function of time after all of the unabsorbed oral tracer has passed through the GI tract into the feces. Once determined, this slope can be extrapolated back to zero time to, thereby, account for all of the resecreted oral tracer that has been absorbed. As shown in Figure 5Citation , this correction, just like that for FM-N, also leads to an early overestimation and a later underestimation of FZA, although not as great an underestimation as that which occurs with no correction at all. The underestimation of FZA by the FM-E method at later times results from the fact that the rate of endogenous secretion of absorbed tracer is not constant but falls with time probably in proportion to the fall in concentration of the tracer in plasma, the latter peaking in the first 6 h after oral administration (see Fig. 2Citation ). Because the magnitude of the correction slope is underestimated, Y(0) is overestimated and, therefore, does not allow for complete correction for resecreted oral tracer in the feces. The early overestimation of FZA using FM-E results from the regression slope being applied to the cumulative fecal tracer data before all of the unabsorbed oral tracer has exited the colon producing a spuriously low value for Y(0).

Rauscher and Fairweather-Tait (4)Citation provide another method for correcting for the secretion of absorbed oral tracer (FM-R; Eq. 3 ). This correction uses a second tracer administered intravenously at the same time as oral tracer administration and assumes that the fractions of absorbed oral and intravenously administered tracers ending up in the feces would be the same. They estimate this amount of absorbed but subsequently fecally excreted oral tracer as the product of fo and fiv, where fo and fiv are the fractions of administered oral and intravenous tracers, respectively, ending up in the feces. This amount of tracer is then added back to the apparent absorption given by FM-N to correct for the underestimate of FZA afforded by FM-N alone. As shown in Figure 5Citation , the formulation offered by Rauscher and Fairweather-Tait (4)Citation is inaccurate and overcorrects the underestimate of FZA by FM-N, thereby producing an overestimate of FZA. This overestimation by FM-R results from the substitution of f0 for FZA in the correction term of Equation 3 . Because f0 is nearly always greater than FZA (except perhaps in instances of FZA being very high in instances of severe zinc deficiency), FM-R will always be an overestimate, greater in relative terms at lower FZA and becoming a better estimate at higher FZA when values for f0 and FZA become more similar.

The correct formulation of FZA using the FM technique with intravenous and oral zinc tracers was derived by us in Equation 6 and referred to as FM-S. It provides the correct value for FZA if fecal collections are carried out long enough for the unabsorbed oral tracer to completely exit the GI tract as shown in Figure 5Citation . The correct value for FZA is approached asymptotically from above at roughly 7 d after tracer administration corresponding in this case to between 5 and 6 GI transit times.

The effects on FZA provided by the four FM methods due to incomplete (95%) fecal tracer recovery and twice average GI transit time are shown in Figure 7Citation . Incomplete fecal tracer recovery (due either to measurement error or inadequate subject compliance) increased the estimate of FZA in all four FM methods. The magnitude of the error due to incomplete fecal tracer recovery is amplified by the FM calculations. For example, a 5% loss of tracer results in a 15% overestimate of FZA by FM-S. Ironically, a spurious increase in FZA due to fecal tracer loss could convert what would have been a significant underestimate of FZA by the FM-N method into a more accurate result.

The problems associated with the FM techniques are further compounded by the possibility of a delayed GI transit time as shown in Figure 7BCitation . All four of the FM responses shown in Figure 7BCitation are significantly delayed in time. The FM-S method again asymptotically approaches the correct value for FZA, but not until 13–15 d after tracer administration. Terminating fecal collections before d 13–15 would result in larger FZA values for all four of the methods compared with values based on shorter GI transit times (Fig. 5)Citation . Such an effect, like that due to incomplete fecal tracer recovery, leads to an apparent improvement in the accuracy of the FM-N method. The GI transit time used in the simulations shown in Figure 7BCitation of 2.66 d (twice the average of our six subjects) is well within the 95% confidence limits determined by us using compartmental analysis (9)Citation ; it is still less than half of the average value reported by Wastney et al. (14)Citation based on a similar compartmental analysis of 25 normal subjects. Using their estimate of average GI transit time of > 5 d, fecal collection would have to be done for > 20 d to exclude the confounding effects of incomplete GI transit of unabsorbed tracer. Thus, even if fecal tracer recovery was complete, a 13- to 15-d fecal collection period may not be long enough to obtain an accurate estimate of FZA if GI transit is long. Because of the high variability in GI transit time in normal subjects, even the most accurate of the FM techniques, FM-S, is not recommended for careful estimation of FZA.

Although logically correct, the estimate of FZA provided by the ID technique (Eq. 19 using EFZ estimates from Eqs. 15 , 17 or 18) requires a longer data collection period than the other correct methods to provide the same degree of accuracy (Fig. 6)Citation . Moreover, this accuracy is significantly degraded by incomplete zinc tracer and tracee recovery in feces and prolonged GI transit time (Fig. 8)Citation .

The results of the theoretical analysis discussed above are generally corroborated by our recent report (11)Citation in which each of six detailed zinc tracer studies (9)Citation is analyzed according to the simple techniques for FZA and then compared with the FZA obtained from the compartmental model applied to that dataset. Methodological problems with this study detailed in a Letter to the Editor (15)Citation include the experimental and biological variability in each dataset, the specific sampling frequency used and the limited number of studies. By focusing in the current report on a theoretical dataset with zero noise and very fine sampling frequency, the logical adequacy of each of the simple techniques for FZA estimation can be better compared with the FZA of the compartmental model (from which the theoretical data were simulated) outside of the any confounding effects resulting from noisy data with limited temporal resolution.

In summary, theoretical comparisons of the FM, DA, DITR and ID techniques for estimating FZA using a detailed compartmental model show that the FM technique, even when properly corrected for resecretion of absorbed oral tracer (FM-S), can lead to serious overestimates of FZA. The technique is highly sensitive to incomplete fecal tracer recovery (due either to inadequate subject compliance or analytical error) and prolonged GI transit time for zinc. Neither of these conditions is easily amenable to careful control, and the latter is highly variable among normal subjects. Because of these deficiencies, the FM technique cannot be recommended for accurate estimation of FZA. Nevertheless, when venous access is not possible or when only one zinc tracer is available, the FM-E technique may be the only technique applicable for estimation of FZA. Under such conditions, the FM-E technique may still be useful for relative nonquantitative FZA estimates in the same subject if careful attention is paid to complete fecal tracer recovery and maintenance of constant GI transit times between studies. Although logically correct, the ID technique based on a single intravenous injection of zinc tracer requires longer collection times than the DA and DITR methods for the same degree of accuracy. Moreover, the accuracy of the technique is seriously degraded by incomplete recoveries of fecal zinc tracer and mass and prolonged GI transit times. The DA and DITR techniques provide accurate estimates of FZA in both theory and practice. The DA technique requires multiple blood draws over a number of days to define the response of the orally and intravenously administered tracers in plasma with subject confinement for the first 7–8 h of the 1st d during which time high temporal resolution plasma zinc tracer measurements must be made. Alternatively, careful cumulative 24-h urine collections must be made over several days after oral and intravenous tracer administration. In contrast, the DITR technique requires only a single plasma sample, a 24-h urine or spot urine sample obtained 2 or more d after tracer administration. The spot urine sample requires the least amount of subject involvement of all the procedures. We, therefore, recommend the DITR technique, using a spot urine sample collected at least 2 d after tracer administration (or the average of several spot urine samples), as the method of choice for simple estimation of FZA when detailed compartmental modeling and the data acquisition it requires cannot be performed.


    FOOTNOTES
 
1 Supported in part by a gift from Bristol-Myers Squibb/Mead Johnson and by the University of California Agricultural Experimental Station Department of Nutritional Sciences, University of California at Berkeley, CA 94720. Back

3 Abbreviations used: DA, deconvolution analysis; DITR, double isotopic tracer ratio; DITRP, double isotopic tracer ratio in plasma; DITRU, double isotopic tracer ratio in spot urine; DITR24H, double isotopic tracer ratio in 24-h urine; EFZ, endogenous fecal zinc; FM, fecal monitoring; FM-E, fecal monitoring, English correction; FM-N, fecal monitoring, no correction; FM-R, fecal monitoring, Raucher correction; FM-S, fecal monitoring, Shames correction; FZA, fractional zinc absorption; GI, gastrointestinal; ID, indicator dilution. Back

Manuscript received December 13, 2000. Initial review completed February 5, 2001. Revision accepted March 23, 2001.


    REFERENCES
 TOP
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 RESULTS
 DISCUSSION
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