Introduction

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The multiple indicator dilution (MID)¹ technique has been used to assess the kinetics of transport and metabolism of substrates in intact organs such as the liver (Goresky, 1963; Goresky and Groom, 1984). It is based on bolus injection of labeled parent drug/metabolite and noneliminated reference indicators (labeled red blood cells, labeled albumin and sucrose, and labeled water to trace the sinusoidal blood volume, interstitial or Disse space, and cellular water space, respectively) at the inflow of the liver and has been used frequently to examine transport and metabolic processing in the dog liver (Goresky et al., 1973) or in the perfused rat liver preparation (Schwab et al., 1985; Pang et al., 1995). The theoretical basis of MID developed until now generally assumes constant enzyme activity along the sinusoidal flow path. In contrast to this, there is considerable experimental evidence that drug-metabolizing activities are heterogeneously distributed among the zonal regions of the acinus, the functional microcirculatory unit (Rappaport, 1958). The enzymes and their associated metabolic activities may be predominantly localized in the upstream [periportal (pp) or zone 1] or the downstream [perivenous (pv) or zone 3] region of the acinus (Pang and Terrell, 1981; Pang et al., 1983; Anundi et al., 1986; El Mouelhi and Kauffman, 1986; Morris et al., 1988; Xu and Pang, 1989; Pang and Chiba, 1994) or evenly distributed (Chiba et al., 1998).

A useful experimental protocol for probing enzyme zonation within the intact liver is perfusion of the liver in the prograde mode, with perfusate entering at the portal vein and leaving at the hepatic vein, versus the retrograde mode, with perfusate flowing in the opposite direction, from hepatic vein to portal vein (Pang and Terrell, 1981; Pang et al., 1983; St-Pierre et al., 1989). Retrograde perfusion effectively reverses the enzymic distributions. If outflow profiles or their moments are dependent on the localization of enzymes along the acinus, the observation of changes with reversal of the perfusion mode may be used to assess enzyme zonation.

The kinetics of drug elimination in the presence of enzyme zonation has been extensively studied in the steady state. Enzyme zonation will influence net rates of metabolism among sequential (Pang and Terrell, 1981; Pang and Stillwell, 1983; Xu and Pang, 1989) and parallel (Pang et al., 1983; Morris et al., 1988; Xu and Pang, 1989) pathways. However, the impact of enzyme zonation on the outflow profiles of formed metabolite after pulse injection of the drug has not been addressed previously. Although there is one such account on the use of metabolite data after pulse dosing to the liver preparation to ascribe enzyme zonation (Ballinger et al., 1995), the basis has been explained only in intuitive terms. This issue was explored in this communication because enzyme zonation is an important determinant in drug and metabolite processing. We formulated algebraic expressions for the zeroth, first, and second moments of both drug and metabolite after bolus pulse injection of drugs and we extended these to describe cases where the enzyme for metabolite formation is not evenly distributed, that is, when enzyme zonation is exclusively or predominantly pp or pv.

	Theory

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For simplicity, the microcirculation of an organ is represented by a single sinusoid, or alternately, by an array of identical sinusoids perfused in parallel. A two-zone model was developed with stepwise (incremental or decremental) change in enzymic activity half way along the acinar flow path. Influx and efflux of parent drug and metabolite across cellular membranes of parenchymal cells, including the canalicular membrane for excretion, are assumed to occur uniformly over the whole sinusoidal flow path.

The specific model for the description of the hepatocellular entry of drug and formation of a metabolic product behind a membrane barrier is depicted in Fig. 1. The differential equations describing the transport and metabolism in a single hepatic sinusoidal flow path after pulse input have been presented previously (Goresky et al., 1993b). Due to the presence of ample fenestration of hepatic endothelial cells, the sinusoidal and the interstitial (Disse) spaces in the liver may be viewed as kinetically identical for solutes such that these are combined to form the expanded plasma space (Goresky and Groom, 1984). For a non-recirculating system (as in single pass liver perfusion), the differential equations are given as follows:

(1)

(2)

(3)

(4)

where C₁ and C₂ are dose-normalized tracer concentrations (fraction of dose per milliliter) of parent drug and metabolite, respectively, in the expanded (sinusoidal + interstitial) plasma space, C₃, and C₄ are the corresponding dose-normalized concentrations of drug and metabolite in hepatocytes, t is time,  is a space variable representing the cumulative transit time of a reference indicator from the entrance point of the sinusoid, or the ratio of the cumulative expanded plasma volume to sinusoidal flow, Q is the plasma flow through the liver,  is the ratio of the accessible cellular water space to the sinusoidal plasma volume, and ' = /(1 + _ref), where _ref is the volume ratio of extracellular space of the reference indicator to the sinusoidal plasma volume. It must be noted that the reference indicator is one that occupies the same proportion of the combined sinusoidal and interstitial spaces as the tracer substance to be studied, but does not penetrate parenchymal cells (Goresky et al., 1992; Chiba et al., 1998). The value of _ref may differ for the parent drug and the metabolite due to differences in vascular binding. However, _ref is taken to be the same for drug and metabolite for this consideration, for the sake of simplication.

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Model structure for parent drug and intracellularly formed metabolite. The interconnecting transfer coefficients are ratios of the rates to the amount present in the compartment from which the fluxes originate. The coefficient k34 represents that for the biotransformation of drug to metabolite with enzymes that are heterogeneously distributed. The coefficient k30 refers to pathways other than formation of the given metabolite, and is zero for all simulations.

The transfer of the tracer label between the compartmental pools is described by a set of transfer coefficients k_ij, each of which represents the fractional amount of tracer transferred from pool i to pool j per unit time in the source pool i. Thus k₁₃ and k₃₁ are coefficients for influx of tracer precursor into, and efflux from, parenchymal cells; k₂₄ and k₄₂ are the corresponding coefficients for the metabolite; k₃₄ is the coefficient for enzymic conversion of parent to metabolite; k₃₀ is that for sequestration (removal) of the parent drug (other than formation of the metabolite), and k₄₀ is that for sequestration of the metabolite (Fig. 1). The influx and efflux rate constants, k₁ and k₁, have been defined previously by Goresky et al. (1973) as ratios of permeability-surface area products to the accessible cellular water space. They are related to the transfer coefficients defined in Fig. 1 according to the relations k₁₃ = f_uk₁' and k₃₁ = f_tk₁, where f_u and f_t are the unbound fractions of drug in plasma and tissue, respectively. Similar relations apply to the transport coefficients for the metabolite, k₂₄ and k₄₂. The term 1/Q(t)() (where  is the unit impulse function) represents rapid bolus injection of the tracer dose. The solutions of eqs. 1 to 4 for the extracellular concentrations thus represent the impulse response of the system. Normalization of these solutions by multiplying by Q yields the unit impulse response per unit dose, which is equivalent to the frequency or permeability density function of transit times (Lassen and Perl, 1979; Bronikowski et al., 1987).

Algebraic Expressions for Laplace Transforms and Moments. Analytical solutions of eqs. 1 to 4 in the Laplace domain for the homogeneous case were the same as found previously (Goresky et al., 1993b; Mellick et al., 1997). The formulations of parent and metabolite in the extracellular space are:

(5)

(6)

where ₁(s) and ₂(s) are the Laplace transforms of C₁ and C₂, respectively, s is the Laplace variable, and the exponential coefficients, ₁ and ₂, are:

(7)

(8)

The area under the curve (AUC) or zeroth moment is obtained from the following equation:

(9)

The recovery (survival fraction, or availability, F) is obtained as:

(10)

The mean transit time (MTT) or first moment is obtained from the following equation:

(11)

Finally, the variance of the transit time (VTT) or the second moment is obtained from the following equation:

(12)

The relative dispersion (the square of the coefficient of variation) defined as:

(13)

Similar relations are obtained for the corresponding moments for the metabolite, AUC_M, MTT_M, VTT_M and CV_M² from the metabolite curve, C₂(t).

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Enzyme Zonation. The transfer coefficient for metabolic transformation is treated as a function of  to represent enzyme zonation, whereas rate constants for transmembrane transport are treated as constants. For the formulation of Laplace transforms and moments of outflow profiles, the sinusoid was considered as two half sinusoids arranged in series, each with  = 0.5 MTT_ref. A stepwise change at  = 0.5 was assumed such that

(21)

(22)

where ₃₄ is the length-averaged value of k₃₄() and r is a heterogeneity parameter with values between 1 and 1. In our designation, positive values of r denote predominantly pp enzyme distribution and negative values predominantly pv enzyme distribution. The special cases considered included the even or uniform enzyme distribution with r = 0, the exclusively pp enzyme distribution with r = 1, and the exclusively pv enzyme distribution with r = 1. Various values of r, ranging from 1 to +1, were used in the above expressions (eqs. 21 and 22) to explore the impact of intermediate enzyme zonation on the moments of drugs and metabolites.

(23)

(24)

(25)

Calculations. The outflow profiles (impulse responses) shown in Figs. 2 and 3 were calculated according to eqs. 1 to 4 using a finite difference method with analytical evaluation of discontinuities along the front as described previously (Schwab, 1984). Alternatively, eqs. 5 and 6 were used to calculate Laplace transforms, which were then used with numerical Laplace inversion using a Fortran subroutine Inlap from IMSL (Visual Numerics, Inc., Houston, TX). The results were found to be the same with reasonable accuracy (generally <1% error). Both procedures were further verified by comparing the results for uniform enzyme distribution with those obtained with published analytical solutions (Goresky et al., 1973; 1993b). These methods provide only the returning component of the parent drug. The throughput component is denoted as an impulse function of the form 1/Q e^k₁₃(t  MTT_ref), where (t  MTT_ref) is the delta or unit impulse function at t = MTT_ref.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Outflow profiles of parent drug from a single sinusoid with and without enzyme zonation. Fractions recovered per unit transit time of the reference indicator, C(t) × Q × MTTref, were plotted versus normalized time, t/MTTref. Transfer coefficients for influx (k13), efflux (k31), and enzymic conversion (k34) were k13 = k31 = k34 = 4 × MTTref1 (Data Set A), k13 = 4 × MTTref1, k31 = k34 = 0.25 × MTTref1 (Set B), and k13 = k31 = k34 = 0.25 × MTTref1 (Set C). Only the returning components are shown. Each throughput component consists of an impulse function ("spike") at unit normalized time (t/MTTref = 1) with an integral of 0.018 (Sets A and B) or 0.78 (Set C).

View larger version (30K): [in this window] [in a new window]   Fig. 3.   Outflow profiles of metabolites from a single sinusoid, with and without enzyme zonation. Fractions recovered per unit transit time of the reference indicator, C(t) × Q × MTTref were plotted versus normalized time, t/MTTref. Data Sets 1 to 6 correspond to different sets of transfer coefficients for membrane transport and enzymic conversion, as compiled in Table 2.

(26)

(27)

(28)

	Results

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For the sake of simplification, emphasis was given to representative outflow profiles and values of moments (F, MTT, and CV²) for the cases on homogeneous (even), exclusively pp (with enzymes within the first half of the liver, r = 1), and exclusively pv (with enzymes within the second half of the liver, r = 1) enzymic distributions are reported in Fig. 2 and Table 1 for the parent drug, and in Fig. 3 and Table 2 for the formed metabolite; the effect of the elimination constant of the metabolite, k₄₀, on the MTT_Ms is summarized in Fig. 4. For other enzymic distributions that were intermediate between the exclusively pp and exclusively pv cases (defined within the limits, 1 < r < 1), values for AUC_M, MTT_M, and CV_M² are further shown in Fig. 5.

View larger version (25K): [in this window] [in a new window]   Fig. 4.   Change of metabolite mean transit time (MTTM) with the transfer coefficient for metabolite elimination, k40. The latter has been normalized by the transit time for a single sinusoid (MTTref) for the varying enzyme distributions. The ratio of MTT with pp or pv enzyme distribution to that with uniform (even) enzyme distribution is plotted versus k40. Other transfer coefficients are those summarized in Table 2 for data Sets 1 to 6.

View larger version (15K): [in this window] [in a new window]   Fig. 5.   Dependence of moments for the parent drug on the degree of enzyme heterogeneity. The values of the AUCs (continuous lines), MTTs (long-dashed lines), and (CV2s (short-dashed lines) at various r were normalized to those for even enzyme distribution (r = 0). A stepwise increase or decrease of enzyme concentration along the flow path according to eqs. 21 and 22 was effected by varying the value of the heterogeneity parameter r between pp (r = 1) and pv (r = +1); for even enzymic distribution, r = 0.

Outflow Profiles of Parent Drug. The outflow profiles after pulse injection for uniform enzyme distribution have been described previously for a sequestered tracer (Goresky et al., 1973; 1993b) and are now compared with those of pp and pv enzymic distributions. Normally, the outflow profiles for the parent drug consisted of two parts: the throughput component and the returning component. However, for pulse injection, the throughput component consisted of an impulse function (a "spike") at unit normalized time (t/MTT_ref = 1), with an integral of 0.78 for Sets 6 and 6A, and of 0.018 for all other sets. Only the returning component was shown in Fig. 2. As expected for irreversible conversion, the dilution outflow profiles for the parent drug were independent of the transfer coefficients for the metabolite. Values for AUC, MTT, and CV² were found to be always larger in the exclusive pp or pv enzyme cases than in the homogeneous enzyme case, but the outflow profiles for exclusively pp and pv enzyme distributions were necessarily identical because for the cases examined, the exclusive pp and pv enzyme distributions were mirror images of each other (Table 1). The MTTs of the parent drug increased with increasing influx-efflux ratio (or cellular-sinusoidal distribution ratio, k₁₃/k₃₁). For example, increasing k₁₃/k₃₁ from 1 to 16 (compare Sets A or C to B, Fig. 2) resulted in concentrative uptake of the drug and yielded protracted outflow profiles for the parent drug and increased MTTs. Decreasing the influx and efflux coefficients while maintaining their ratios constant (compare Sets A and C) led to an increased throughput component and yielded a reduced and protracted returning component without changing the overall MTT of the drug (Table 1).

Metabolite Outflow Profiles for Even, pp, and pv Cases in the Absence of Metabolite Elimination (k₄₀ = 0). For all cases, the condition where formation of the metabolite from the parent drug is the only elimination pathway of the parent drug was examined (k₃₀ = 0, all data sets in Table 2, Fig. 3). With lack of elimination of metabolite (Sets 1 to 6, k₄₀ = 0), the sum of the venous recoveries of parent drug and metabolite equals unity. AUC_M was always smaller when enzyme heterogeneity was present, and there was no difference between the examples on the exclusive pp and pv enzyme distributions.

Metabolite Outflow Profiles for Even, pp, and pv Cases in the Presence of Metabolite Elimination (k₄₀ > 0). The above relationships were found to be modified with elimination of the metabolite, for example, biliary excretion. When the metabolite is eliminated (k₄₀ > 0), AUC_M and MTT_M were diminished with respect to the case where k₄₀ = 0 (compare Sets 1 to 6 with their counterparts, Sets 1A to 6A, Table 2 and Fig. 3) and the sum of the outflow recoveries of parent drug and metabolite was <1. Metabolic zonation exerted a definitive effect; the AUC_Ms were found to be always larger for pv than for pp regardless of the values of the transport parameters because elimination of the metabolite occurred along the entire acinus.

1

Intermediate Enzyme Zonation. When stepwise enzyme distribution along the acinar flow path was considered (1 < r < 1), the values for the moments for the drug (Fig. 5) metabolites (Fig. 6) were generally found to vary in a monotonous fashion between those for exclusively pp (r = 1) or pv (r = 1) and those for even distribution (r = 0). Exceptions were the values of CV_M², which in some cases (Sets 2, 2A, 4, and 4A) exhibited M-shaped patterns with distinct maxima at intermediate degrees of heterogeneity (1 < r < 0 or 0 < r < +1). Although the values of AUC, MTT, and CV² of the parent compound depend on the degree of heterogeneity, r, a symmetrical pattern is obtained such that no change occurs with reversal of enzyme distribution (change of the sign of r, Fig. 5). In the case of the metabolite, the dependence of AUC_M, MTT_M, and CV_M² on r shows a symmetrical pattern only for Sets 1 and 5 in which drug and metabolite show equal partitioning into cells (Fig. 6).

View larger version (24K): [in this window] [in a new window]   Fig. 6.   Dependence of moments for the metabolite on the degree of enzyme heterogeneity. The values of the AUCMs (lines), MTTMs (lines), and CVM2s (lines) at various r were normalized to those for even enzyme distribution (r = 0). A stepwise increase or decrease of enzyme concentration along the flow path according to eqs. 21 and 22 was effected by varying the value of the heterogeneity parameter r between pp (r = 1) and pv (r = +1); for even enzymic distribution, r = 0.

View larger version (24K): [in this window] [in a new window]   Fig. 7.   Effect of flow reversal on moments for the metabolite at various degrees of enzyme heterogeneity. Each moment ratio is the ratio of AUCM (continuous lines), MTTM (long-dashed lines), or CVM2 (short-dashed lines) at a positive value of r (r = +|r|) to the corresponding moment at the negative value of r with the same absolute value |r| (r = |r|). These ratios represent the change in moment with predominantly pp enzyme distribution upon reversal of perfusion from prograde to retrograde; predominantly pv enzyme distribution would yield the reciprocals of these ratios. A stepwise increase or decrease of enzyme concentration along the flow path according to eqs. 21 and 22 was effected by varying the value of the heterogeneity parameter |r| between even (|r| = 0) and exclusively pp or pv (|r| = ±1).

	Discussion

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The distinct differences in outflow dilution profiles between the pp and pv enzyme distributions revealed in the present exploration suggest that the prograde/retrograde perfusion protocol may indeed be used to assess enzyme zonation. The effect of reversal of the perfusion mode (prograde to retrograde) will be most pronounced if an enzyme is located exclusively in one of two zones, but will still be present, albeit to a lesser extent, with more uniform enzyme distributions (Fig. 5).

Theoretical considerations predict that when a barrier is present between the vasculature and the enzyme within the cell, the extraction ratio and the outflow profile of the parent drug will be altered in the presence of uneven enzyme distribution (Sato et al., 1986; Goresky et al., 1993a; Cai et al., 1995). However, they will be the same for the pp and pv cases because these are mirror images of each other. The prograde/retrograde perfusion protocol does not provide information on enzyme zonation if only the outflow profile of the parent drug is assessed (Sato et al., 1986; Goresky et al., 1993a). We have therefore extended the theoretical treatment to include analysis of metabolite data. We have included these aspects in our analysis by deriving analytical expressions for a two-zone model. Although there existed other previous exploration on the moments of metabolite profiles (Mellick et al., 1997), enzyme zonation was not considered.

For linear systems, recoveries of metabolites obtained by integration of outflow dilution profiles are equivalent to those obtained at steady state (Meier and Zierler, 1954; Lassen and Perl, 1979) and can thus be used as a means of assessing enzyme heterogeneities in the same way as in steady-state approaches (Pang and Terrell, 1981; Pang et al., 1983; St-Pierre et al., 1989). An important observation is that in the prograde mode, the recovery of a metabolite that is itself eliminated is larger with pv than with pp enzyme distribution if the elimination system for the metabolite is evenly distributed (Pang and Terrell, 1981; Pang and Stillwell, 1983). Consequently, the ratio of AUC_Ms for prograde to retrograde flow, if smaller than unity, suggests a pp enzyme distribution, and, if greater than unity, suggests a pv enzyme distribution (Tables 2 and 3). When the metabolite is not eliminated, AUC_M is the same for prograde and retrograde perfusion and will not be useful for the assessment of enzyme zonation.

A useful alternative would be the observation of changes in MTT_M after switching between prograde and retrograde flow, whereas changes in CV_M² would not be interpretable because their direction may depend on the degree of heterogeneity (Fig. 7, Set 4A). The changes in MTT_M are dependent on the relative magnitudes of k₁₃/k₃₁, k₂₄/k₄₂, and k₄₀. In many experimental settings, the parent drug is lipophilic and distributes readily in parenchymal cells, whereas the metabolite is hydrophilic and distributes only poorly in parenchymal cells, such that k₁₃/k₃₁ > k₂₄/k₄₂. If this is the case, the ratio of the MTT_M during prograde to retrograde flow, if smaller than unity, suggests a pp enzyme distribution, and, if larger than unity, suggests a pv enzyme distribution (Table 3). When k₁₃/k₃₁ < k₂₄/k₄₂ interpretation of the observed prograde/retrograde ratio of MTT_Ms becomes less defined because the ratio of the MTT_Ms further depends on the value of k₄₀ (Fig. 4, Set 2A).

Expectedly, there are additional factors that affect the shapes of the dilution profiles and therefore data interpretation of the moments for both drugs and metabolites. Experimentally, retrograde flow is known to bring about distention of the hepatic vascular spaces. For rat livers perfused even at low flow rates [10 or 12 ml/min with erythrocytes (20%) and albumin (1%)], distention of the extracellular spaces, and increases in the transit times of labeled red cells, albumin, or sucrose were observed although there was only little change in the accessible cellular water space; the increase in the extracellular spaces intensifies with greater retrograde flow (St-Pierre et al., 1989; Xu et al., 1990). A valid comparison of the AUC_Ms and MTT_Ms during prograde and retrograde flow therefore requires correction by subtraction of the mean transit time of the reference indicator, MTT_ref.

Very few studies have been reported on the use of the MID technique together with prograde and retrograde liver perfusion. One example, however, was reported for the almost exclusive metabolism of [¹⁴C]phenol (at tracer concentrations) to [¹⁴C]phenyl sulfate in the perfused rat liver because formation of [¹⁴C]phenyl--glucuronide was minor (<1%; Ballinger et al., 1995). A pp distribution of sulfation activity towards phenol was inferred because a higher MTT was observed for phenol during retrograde flow in comparison with that with prograde perfusion. The interpretation is at variance with the present theoretical prediction of a lack of change in the MTT for the drug. Our analysis to this, however, differed. Because phenol, a lipophilic and neutral substrate, and not phenol sulfate, is expected to undergo extensive partitioning into hepatocytes (k₁₃/k₃₁ > k₂₄/k₄₂), the additional observation on increase in MTT_M with retrograde perfusion could be attributed to the pp localization of phenol sulfoconjugation activity if the effect were above and beyond that caused by distention of the vasculature. However, in these preparations, retrograde flow had increased dramatically the observed MTT of water and the accessible cellular water space. The large changes in the accessible cellular water space observed in these erythrocyte-free preparations were at variance with previous investigations with erythrocyte-containing perfusate (St-Pierre et al., 1989; Xu et al., 1990) and suggest edema and damage to the liver. Upon normalization to the MTT of accessible cellular water, the MTT of formed phenol sulfate, MTT_M, actually became smaller with retrograde than with prograde perfusion. This, according to Table 3, suggests a pv localization of sulfoconjugation activity, and the conclusion is inconsistent with the pp sulfation activity inferred towards harmol (Pang et al., 1983), acetaminophen (Pang and Terrell, 1981), gentisamide (Morris et al., 1988), and salicylamide (Xu and Pang, 1989). It is highly probable that in these studies, the large increases in the MTTs of the noneliminated reference indicators and of the accessible water space with retrograde flow had masked the changes on the MTT of drug and metabolite, and this severely compromised the use of the MTTs of phenol and phenol sulfate on interpreting enzyme zonation. It must be further noted that the normalization of MTT_M to that of cellular water is not always appropriate because distribution of a lipophilic drug in cellular lipids is unaffected by an increase of the cellular water space.

Another example is on the deacetylation of acetylsalicylic acid in perfused liver (Mellick and Roberts, 1996). In this study, the sum of the recoveries for the parent drug (acetylsalicylic acid) and the metabolite (salicylate) was complete and hepatic metabolism of salicylate could be viewed as insignificant. The MTT of the preformed salicylate was much larger than that of the parent drug, and the observation is reasonable with the absence of elimination of salicylate (k₄₀ = 0). Although the observed difference in MTT_M between progradely and retrogradely perfused livers was insignificant, a shorter MTT_M resulted in four of five experiments with retrograde perfusion upon subtraction of the MTTs of sucrose, the reference indicator. There was, however, no report on k₁₃/k₃₁ or k₂₄/k₄₂ although these could have been deduced from the MID data. The lack of these essential data precludes the proper interpretation of enzyme zonation.

A third study is on 4-methylumbelliferyl sulfate (4MUS), which furnished similar recoveries of the desulfated metabolite 4-methylumbelliferone (4MU) during steady state with prograde and retrograde flows (Chiba et al., 1998). Unfortunately, the recoveries from the outflow dilution profiles of labeled 4MU were too low to define the MTT_M properly. The influx-efflux ratio for 4MUS (k₁₃/k₃₁), though predicted to be less than that for 4MU (k₂₄/k₄₂), becomes irrelevant in the interpretation of the data because the desulfation activity of 4MUS is evenly distributed (Anundi et al., 1986; El Mouelhi and Kauffman, 1986; Chiba et al., 1998).

In summary, the present study has successfully extended the theory on outflow dilution profiles of a parent drug to its metabolite(s) generated after pulse dosing of the parent to the perfused rat liver preparation in MID experiments. It was found that zonal metabolic activity for formation of the metabolite is an important determinant of metabolite outflow profiles, and of its MTT and relative dispersion in MID studies. When coupled with prograde and retrograde flow, the MID experiments augment our ability in the assessment of zonal metabolic heterogeneity in the liver, as outlined in the changes in AUC_M and MTT_M of the metabolite predicted with the presence of enzyme zonation, if the cell-plasma partitioning characteristics of the parent and metabolite and elimination of the metabolite are considered. The usefulness of the method, however, needs to be re-assessed when drug removal is complicated by the presence of multiple metabolic pathways.