A Simulation study on the effect of a uniform diffusional barrier across hepatocytes on drug metabolism by evenly or unevenly distributed uni-enzyme in the liver

Journal of Pharmaceutical

Sciences January 1986 Volume 75, Number 1

~~ ~

k publication of the American Pharmaceutical Association

A RTlCL ES

A Simulation Study on the Effect of a Uniform Diffusional Barrier Across Hepatocytes on Drug Metabolism by Evenly or Unevenly Distributed Uni-enzyme in the Liver

HITOSHI SATO, YUlCHl SUGIYAMA, SElJl MIYAUCHI, YASUFUMI SAWADA, TATSUJI lGAX, AND MANABU HANANO Received May 17, 1985, from the Faculty of Pharmaceutical Sciences, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan. for publication September 26. 1985.

Accepted

Abstract 0 The effect of a uniform diffusional barrier on hepatic extraction of the parent drug by evenly or unevenly distributed uni- enzyme was quantitatively determined by the present simulation study. Five models of enzymic distribution were defined with regard to the hepatic blood flow path, and the extraction ratios were calculated or simulated under the various conditions of average intrinsic clearances and diffusion clearances across hepatocytes. Differences in the extraction ratios among the five models were evaluated by the “relative extraction ratios,” which are the extraction ratios in each model divided by that in the model where the enzymatic activity is evenly distributed. It was found that when a diffusion clearance was’ high compared to the intrinsic clearance, enzymic distribution was not an Important determi- nant of the extent of hepatic extraction. By contrast, when a diffusional barrier across hepatocytes exists, i.e., the diffusion clearance is low or intermediate compared to the intrinsic clearance, extraction ratios differed widely among the models of enzymic distribution, especially at intermediate average intrinsic clearances. In the presence of a diffusional barrier, the more skewed the distributlon of the enzymatic activity is, the lesser the amount of drug eliminated at steady state. The most efficient metabolism occurred when the enzymatic activity was evenly distributed.

Three models of hepatic elimination have been developed in recent years; the “well-stirred” model,’ the “parallel tube” model,“ and the “distributed” mode1.3.4 The well-stirred model assumes that the liver is a single well-mixed compartment and that the unbound drug in the emergent blood is in equilibrium with the unbound drug in the liver, while the parallel tube model assumes that the liver is composed of a series of identical and parallel tubes, along which the drug concentration decreases progressively in the direction of the hepatic blood flow. The distributed model assumes that the liver is composed of sinusoids arranged in a parallel fashion and that blood flow and enzyme contents per sinusoid are statistically distributed over the sinusoids. The feasibility of these models depends on a given drug, and a general theory to predict the kinetics of drugs in the perfused liver prepara- tions is still controversia1.”13

Pang and Stillwell14 recently described a computer-aided simulation of the metabolite kinetics in the “enzyme-distributed” model assuming a tubular flow path, as an extension of the parallel tube model. They determined the least or most efficient patterns of enzymic distribution for sequential metabolism. In the enzyme-distributed model, providing a perfusion limitation (or a rapid equilibrium between blood and hepatocytes) is assumed, it can be easily shown by a mathematical analysis that the distribution of metabolizing enzymes in the liver does not affect the hepatic extraction ratio for the parent drug.“ However, the assumption of a rapid equilibrium dose not necessarily hold true. Slow equilibrium between blood and certain extrahepatic and hepatic tissues was observed for several water-soluble drugs, i.e., phenobar- bital,16 methotrexate,’s and actinomycin D,17 while a diffusional barrier across hepatocytes exists for a few drugs such as enalaprilat.18 Moreover, the rate of hepatic extraction of organic anions such as tose bengal, sulfobromophthalein and indocyanine green, which are transported into the liver by facilitated diffusion systems,19 is affected by the carrier- transport process and the sequestration process (metabolism or biliary excretion). The effect of a diffusional barrier between blood and hepatocytes on drug metabolism has been studied before for an even distribution of enzymesa2”22 How- ever, no one has ever quantitatively determined the effect of a diffusional barrier across hepatocytes on drug metabolism by unevenly distributed enzymes.

The purpose of the present simulation study is to deter- mine quantitatively the effect of a uniform transmembrane diffusional barrier on hepatic extraction of the parent drug by evenly or unevenly distributed uni-enzyme in the liver.

Theoretical Section A single-pass liver perfusion a t steady state was used as a

condition for the simulation, in which a constant output concentration of the drug (C,,J is reached when a constant

0022-3549/86/0 1 00-0003$0 1 . 0010 0 1986, American Pharmaceutical Association

Journal of Pharmaceutical Sciences / 3 Vol. 75, No. 7, January 7986

input concentration of the drug (Cln) was infused at a constant hepatic blood flow rate (&I into the liver. Several assumptions made in the simulations are the same as those made by Pang and Stillwell14 except that only the parent drug is dealt with and that a passive or facilitated diffusion process across hepatocytes is involved in the enzyme-distributed model. Binding of the drug to blood components remains constant along the flow path in the liver, i.e, the unbound fraction of drug in blood ( f ~ ) is constant throughout all the sinusoids in the liver. The rate of drug removal at steady state is due either to metabolism by hepatocellular enzymes or to biliary excretion,Z3 and both of them are designated as “metabolism” hereafter for the simplicity of description. The avera e hepatic metabolic intrinsic clearance is designated as &. Since the passive diffusion clearance and the rate of facilitated diffusion by transport carriers are equivalent in the present mathematical analysis, both of them are designated as “diffusion clearance” between blood and hepatocytes. The average diffusion clearance is designated as P. CL,,, and P are presented as multiples of 8. Other basic assumptions are made as follows:

1. The average intrinsic clearance along the flow path, L, is held constant, i.e.:

L

= \ (cLint,,x/L)dx (1)

P = I, (Px/L)dx (2)

0

where CL,,,,, is the intrinsic clearance at any point x along the flow path.

2. The average diffusion clearance between blood and hepatocytes is held constant, i.e.:

L

where P, is the diffusion clearance a t any point x along the flow path.

3. The rate of drug removal from hepatocytes is linear; that is, CLlnt, is equal to the ratio of Vm,xlK,,24 where V,,,, and K , are the maximal elimination rate and the Michaelis constant, respectively, a t any point x along the Aow path. The value of K, is held constant among hepatocytes.

4. In the case of a facilitated diffusion, the carrier- mediated transport rate is linear; that is, P, is equal to the ratio of V$&Jp2ff,26 where vd&. and K“2ff are the maximal transport velocity and the Michaelis constant, respectively, at any point x along the flow path. The value of Kd2‘ is held constant along the flow path.

5. Only the unbound drug in the hepatocytes is metabo- lized, so that the rate of metabolism of the drug is equal to the product of CL,ntJ and the unbound drug concentration in the hepatocytes at point x , or fTxcTq.

6. Transmembrane diffusion across hepatocytes occurs only to the unbound drug in blood, so that the rate of passive or facilitated diffusion at any point x is equal to the product of P, and that unbound drug concentration in hepatic blood, or

The following mass balance differential equations hold a t f B c x .

steady -state:

(4) where V, and VT are the hepatic extracellular and intracellular volumes, respectively; C, and CTx represent the concen-

trations of the drug at any point, x , (0 5 x 5 L) of the flow path in the blood and hepatocytes, respectively. The value f T x is the drug unbound fraction in hepatocytes a t any point x . Solving for CT, in eq. 4 yields:

Substituting for CT, in eq. 3 according to eq. 5 and rear- rangement yields:

This differential equation indicates that C, is independent from fTx; that is, intracellular binding of the drug does not affect the concentration profile in the liver sinusoids along the hepatic blood flow path at steady state, while it is related to the apparent distribution volume of the drug.26

Furthermore, symmetry of Px and CLint, in eq. 6 indicates that the following two cases are mathematically equivalent: (a) A uniform diffusional barrier between blood and hepatocytes, whether passive or facilitated, exists under an uneven distribution of the metabolizing uni-enzyme and (b) an uneven distribution of the diffusional clearance exists under an even distribution of the metabolizing uni-enzyme.

Definite integration of eq. 6 from 0 to L for x gives:

In (C,,JCin) = -Z (7)

where:

Since the ratio of CoutlCin is the availability, F, transformation of eq. 7 gives:

F = exp(-Z) (9)

(10)

Extraction ratio (E) is expressed as

E = 1 - F = 1 - exp(-Z) Condition 1-If P, approaches infinity in eq. 8, Z is ex-

pressed as:

It follows from eq. 1 that:

z = - . fB Q

(11)

(12)

This equation is the same as the one derived by Pang and Rowland5 when a transport barrier across hepatocytes is absent and the enzymatic activity is distributed evenly along the hepatic blood flow path as in the parallel tube model.

Condition 2-When P, has a low enough value relative to CLint, in eq. 8 at any point x, Z is expressed as:

It follows from eq. 2 that:

z = - f B F

Q (15)

4 [Journal of Pharmaceutical Sciences Vol. 75, No. 1, January 1986

so that:

E = 1 - exp(-fBP/Q) (16) Condition 3-By substituting a given function G(x) for

CLintr in eq. 8, we obtain

(17)

On the other hand, substitution of the function G(L - x ) , which is symmetric with G(x) at x = L12, for CLintJ in eq. 8 gives:

Transformation of the left-hand side of eq. 18 by replacing L - x by a variance y results in:

when P, is constant, i.e., P, is equal to P L - ~ at any point x , we obtain:

z1 = 2 2 (20) It follows from eqs. 20 and 10 that the extraction ratios for any two models with symmetric patterns of enzymic distribution are necessarily the same, if the transmembrane diffusion clearance is constant along the hepatic blood flow path.

Experimental Section As shown in Fig. 1, we defined five models on enzymic distribution

in the direction of the hepatic blood flow, where the transmembrane diffusion clearance between blood and the hepatocytes remains constant. In models I-IV, we biased what enzymic distribution mainly to the periportal region, since any two models with symmetric patterns of enzymic distribution give the same extraction ratio for a given drug, as proved in the Theoretical Section. In Model I, the activity of the enzyme is evenly distributed in the first half of the liver, but is absent in the second half of the liver. In model 11, the enzymatic activity decreases exponentially along the flow path, as

* a 5

1 , ‘....!,LLi OLl L 1 2 L O L / i L O L12 t

Length of Liver

Flgure 1-Distribution patterns of drug metabolizing uni-enzyme along the hepatic blood flow path in the liver, utilized in the present simulation study. The average intrinsic clearance &J is set equal to the hepatic blood flow rate (0).

defined by CLintp = 4.08 exp(-WL). In Model 111, the activity of the enzyme decreases linearly to zero at the end of the flow path. In model IV, the activity of the enzyme decreases linearly, but not to zero at the end of the flow path. In model V (parallel tube model), the activity of the enzyme is evenly distributed throughout the liver along the flow path.

For model 11, extraction ratios were obtained by simulating C, from x = 0 (inlet) to x = L (outlet) in eq. 6 using the Runge-Kutta- Gill method at a suitable interval (1/1000 of the flow path) and calculating as E = 1 - CJCo on a microcomputer. For the models except model 11, extraction ratios were obtained by calculating Z values in eq. 8 and substituting into eq. 10. For example, the Z value for model 111, where CLint, is expressed as 2=(1 - x/L), can be calculated as follows:

= . . . etc.

Values for Z were calculated using the integrated forms of eq. 8 as follows: Model I:

Model 111:

z = - f B P

Q Model IV:

z = - f B P

Q Model V:

- P + 0.5CLint 1 + = ln (-

CLin, P + 1.5CLint (23)

(24)

For the simplicity of the calculation of eqs. 21-24 or the simulation of eq. 6, f B is fixed at f B = 1 and the average values of and P are expressed as multiples of Q. Calculation and simulation were per- formed under 30 combinations of P and = to obtain the values of E and F of the parent drug for each model of enzymic distribution. The value of I5 was varied as 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, and 100 times Q. The value of was varied as 0.1,1, and 10 times Q. The differences among models I-V in eliminating the parent drug were assessed by the ratio of E for each model (I-IV) to E for model V, which is designated as the “relative extraction ratio.” The ratio of F for each model (I-IV) to F for model V is designated as the “relative availability.”

Results Extraction ratios (E) were calculated or simulated for each

model presented under the various conditions of the average intrinsic clearances (G) and diffusion clearances (P) and are listed in Table I. The activity of the metabolizing uni- enzyme system is differently distributed among the five models, while the transmembrane diffusion clearance remains constant along the hepatic blood flow path, i.e., P, equals P.

Journal of Pharmaceutical Sciences / 5 Vol. 75, No. 1, January 1986

Table I-Calculated or Simulated Extractlon Ratlos for the Flve EnzymeDlstrlbuted Models at Varlous Condltlons of Average Hepatic lntrlnslc Clearances and Average Dlffuslon Clearances

- - -- Model Motel Model Mod$ Model Ille IV v g CL,nJQ” PIQb PICLin, 11

10 10 10 10 10 10 10 10 10 10

1 1 1 1 1 1 1 1 1 1

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

100 10 1.00 1.00 1.00 1.00 1.00 50 5 0.999 0.999 1.00 1.00 1.00 20 2 0.993 0.995 0.998 0.999 1.00 10 1 0.964 0.974 0.989 0.993 0.993 5 0.5 0.865 0.925 0.950 0.962 0.964 2 0.2 0.597 0.747 0.781 0.807 0.811 1 0.1 0.379 0.548 0.572 0.594 0.597 0.5 0.05 0.216 0.354 0.365 0.378 0.379 0.2 0.02 0.0943 0.172 0.174 0.178 0.178 0.1 0.01 0.0485 0.0924 0.0928 0.0942 0.0943

100 100 0.625 0.625 0.627 0.628 0.629 50 50 0.618 0.618 0.623 0.624 0.625 20 20 0.597 0.598 0.609 0.613 0.616 10 10 0.565 0.567 0.587 0.595 0.597 5 5 0.511 0.517 0.548 0.561 0.565 2 2 0.394 0.416 0.459 0.480 0.487 1 1 0.284 0.322 0.363 0.387 0.394 0.5 0.5 0.181 0.229 0.258 0.279 0.284 0.2 0.2 0.0869 0.128 0.141 0.152 0.154 0.1 0.1 0.0465 0.0763 0.0813 0.0862 0.0869

100 1000 50 500 20 200 10 100 5 50 2 20 1 10 0.5 5 0.2 2 0.1 1

0.0950 0.0951 0.0951 0.0950 0.0951 0.0948 0.0950 0.0949 0.0950 0.0950 0.0943 0.0944 0.0946 0.0947 0.0947 0.0934 0.0935 0.0940 0.0942 0.0943 0.0917 0.0918 0.0928 0.0932 0.0934 0.0869 0.0870 0.0895 0.0905 0.0908 0.0780 0.0803 0.0846 0.0863 0.0869 0.0689 0.0702 0.0763 0.0791 0.0800 0.0488 0.0524 0.0595 0.0633 0.0645 0.0328 0.0381 0.0441 0.0477 0.0488

“The average intrinsic clearances (z) are expressed as multiples otthe hepatic blood flow rate (0). bThe average diffusion clearances (P) are expressed as multiples of the hepatic blood flow rate (0). CCalculated by eqs. 21 and 10. dSimulated by eq. 6, using the Rung- Kutta-Gill method. eCalculated by eqs. 22 and 10. ‘Calculated by eqs. 23 and 10. gCalculated by eqs. 24 and 10.

Figure 2 shows the relationship between average intrinsic clearances and extraction ratios for the average diffusion clearances of 0.1,0.5,1,2,10, and 100 times the hepatic blood flow, in model I (panel A) and model V (panel B). As shown in Figs. 2A and 2B, irrespective of the patterns of enzymic distribution, extraction ratios were sensitive to changes in the average intrinsic clearance at high and intermediate average diffusion clearances (>0.2 times A), but relatively insensitive at low average diffusion clearances ( s0 .2 times Q), as readily understood by the examination of eqs. 21 and 24. This trend was also consistent in other models presented (models from I1 to IV).

Flgure 2- Relationship between the extraction ratio and the average intrinsic clearance (expressed as multiples of hepatic blood flow) in model l (A) and model V (B) for the average diffusion clearances of 0.1, 0.5, 1, 2, 10, and 100 times the hepatic blood flow (0).

When comparing absolute extraction ratios among the five models with each other on varying average diffusion clearances, it turned out that the differences in the extraction ratios were not large enough to graphically discriminate among the models, especially at low average diffusion clearances (low extraction ratios). Therefore, in order to evaluate the differences in extraction ratios among the five models of enzymic distribution, we presented relative extraction ratios normalized by the extraction ratios for model V at various conditions of P and CL,,t.

Figures 3A-3C represent the relationship between average diffusion clearances and the “relative extraction ratio” at the average intrinsic clearances of 10 (panel A), 1 (panel B), and 0.1 (panel C) times Q. There was little difference in extraction ratios between model V and model IV at any condition of the average intrinsic and diffusion clearances. The order of increasing efficiency of the models for hepatic extraction was from model I to model V. These figures visualize the region of conditions where the differences in hepatic extraction among the models of enzymic distribution are most or least marked. At high average diffusion clearances relative to the average intrinsic clearance, enzymic distribution will not alter E among models. On the other hand, at intermediate and low average diffusion clearances, extraction ratios will change according to enzymic distribution, especially at intermediate average intrinsic clearances. Interestingly, there was the condition of the average diffusion clearance where the relative extraction ratios were minimal for models 11, 111, and IV (not shown in Fig. 3C).

Figures 4A-4C depict the relationship between average diffusion clearances and “relative availability” at the average intrinsic clearances of 10 (panel A), 1 (panel B), and 0.1 (panel C) times Q. The differences in the availability among the five models are most remarkable when the average intrinsic clearances are high and the average diffusion clearances are also high but not very high.

0.61 - F/Q

0. I I 10 100

Flgure 3-Relationship between the relative extraction ratio and the average diffusion clearance f/Q) (expressed as multiples of the hepatic blood flow, Q) in models I-IV for the average intrinsic clearances of 10 (A), 1 (B), and 0.1 (C) times the hepatic blood flow. For model V, the relative extraction ratio is defined as 1, as a reference (not shown).

6 /Journal of Pharmaceutical Sciences Vol. 75, No. 1, January 1986

0. I 10 I00 R.2

Figure &Relationship between the relative availability and the average diffusion clearance P/Q) (expressed as multiples of the hepatic blood flow, 0) in models I-lV for the average intrinsic clearances of 10 (A), 7 (B), and 0.7 (C) times the hepatic blood flow. For model V, the relative availability is defined as 7 , as a reference (not shown).

Discussion Unless a rapid equilibrium between blood and hepatocytes

is assumed, the apparent intrinsic clearance (CLTZpP), obtained by in vivo or in situ experiments, is expressed as the following equation either in the well-stirred or parallel-tube model:

(25)

so that CL?$‘ is equal to or less than P and CLint. If the diffusion clearance has a lower value than the intrinsic clearance, the apparent intrinsic clearance which is directly related to the extraction ratio turns out to be lower than the intrinsic clearance, as previously described by Gillette and Pangzo with respect to the well-stirred model. Goresky et a1.21.22 examined the effect of a diffusional barrier with respect to the distributed model assuming an even distribu-

estimating the diffusion clearance between blood and the hepatocytes. It is notable that the diffusion clearance across hepatocytes for a given drug may be determined by the multiple indicator dilution rnethod.21-32.33

Recently, Pang and Stillwell14 have emphasized the impor- tance of an uneven enzymic distribution for metabolite formation and sequential elimination of the generated metabolite in a tubular-flow model. Moreover, Pang et al.’* have given evidence that the presence of a diffusional barrier is another important element for metabolite kinetics. When the hepatic clearance for the drug is “blood flow-limited” (i.e., the extraction ratio is high) the apparent intrinsic clearance (and therefore both P and should be high compared to hepatic blood flow, and the clearance is flow-limited. In this regard, the patterns of enzymatic distribution will not influ- ence the clearance or the extraction ratio of the drug. When the hepatic clearance is “apparent intrinsic clearance-limited,” i.e., the extraction ratio is low or intermediate, there are two cases in which the apparent intrinsic clearance is “intrinsic clearance-limited” and “diffusion clearance-limited”, respectively. “Diffusion clearance-limited” (or “membrane- limited”) cases have been observed for water-soluble drugsla and some organic anions22 in hepatic elimination.

In the present simulation study, we examined the hepatic extraction ratios of a drug among five models of enzymic distribution in a tubular-flow model assuming a transmembrane-diffusion process. We determined the effect of a uniform diffusional barrier on drug metabolism under conditions where the enzyme system is evenly or unevenly distributed in the liver. When a diffusional barrier was absent, i.e., the diffusion clearances were high relative to the intrinsic clearances, extraction ratios were not affected by the enzymic distribution. However, when a diffusional barrier was present, i.e., the diffusion clearances were intermediate or low relative to the intrinsic clearances, extraction ratios differed widely among the five models of eczymic distribution, especially at intermediate average intrinsic clearances (Fig. 3). The most efficient metabolism occurred in the model where the enzymatic activity was evenly distributed along the hepatic blood flow path, and the least efficient metabolism occurred in the model where the enzymatic activity was located only in one-half of the liver (Table I and Fig. 3). The order of increasing efficiency of the five models for hepatic extraction suggested that the more skewed the distribution of the enzymatic activity is along the blood flow path a t the same average intrinsic clearance, the lesser the amount of drug eliminated by the liver at steady state. When the enzymatic activity was evenly distributed within the limited region along the flow path, i.e., from x = L(1/2 - lln) to x = L(1/2 + l/n) (n a 2), then the intrinsic clearance is expressed as the following function using the parameter n:

n- L ZCLint ( Ix - 2’ 2)

0 (IX+) L (1132) (27)

tion of enzymes along the flow path, andconcluded that the existence of a diffusional barrier caused the decrease in metabolic sequestration. The conclusions in these earlier studies qualitatively hold in model V (parallel-tube model) in the present study.

Again, if a diffusional barrier across hepatocytes exists, the

CLi,t,(n) =

apparent intrinsic clearance is limited not by the hepatocellular enzymatic metabolism but by the slow diffusion into Substitution of eq. 27 into eq. 8 and integration yields: hepatocytes. There are some drugs reported, the hepatic

2 intrinsic clearances of which could be well estimated from in

pened because those drugs could reach their eliminating Q - n- n enzymes rapidly in vivo and because neither the denatur- ation of metabolic enzymes nor the insufficiency of enzyme cofactors occurred in homogenates in vitro. On the other hand, if there is a diffusional barrier across hepatocytes for a given drug, the rate of in vitro degradation cannot be extrapolated to that of in vivo or in situ elimination without

-n __ P-CLint

P + -CLint (n 3 2) (28) vitro experiments using liver h o m o g e n a t e ~ . ~ ~ 3 ~ This hap- Z(n) = f B . - 2 . -

2 If n approaches infinity in eq. 28,Zb-d becomes zero and the extraction ratio also equals zero according to eq. 10, though such an extreme distribution of enzymes was not observed.

A qualitative explanation for the effect of a diffusional

Journal of Pharmaceutical Sciences / 7 Vol, 75, No. 1, January 7986

barrier on drug metabolism by an uneven distribution of enzymes, is that because the elimination is limited not by the rate of metabolism but by the diffusion rate into hepatocytes, a high density of enzymatic activity is diminished to some extent, while the low (but not blank) density of enzymatic activity effectively reacts with its substrate. Therefore, the most marked dissociation of extraction ratios among the five models was observed at intermediate average intrinsic clearances, e.g., G I Q = 1, because the extent of extraction by the diminished and effectively employed enzymatic activities differ more widely at intermediate intrinsic clearances than at high or low average intrinsic clearance%.

As for availabilities, the most marked dissociation of availabilities among the five models was observed when the average intrinsic clearances were high and the average diffusion clearances were also high but not very high (Fig. 4A). By contrast, when the average intrinsic clearances were low or intermediate, little difference between high availabilities was observed (Figs. 4B and 4 0 . Therefore, availability is sensitive to the enzymic distribution if the drugs are highly or completely extracted by the liver.

Inspection of eq. 6 indicates that P, and CLint, are inter- changeable with each other. Therefore it follows that the case simulated in the present study, in which the diffusion clearance is held constant and the enzymatic activity is unevenly distributed, is mathematically equivalent to the case in which the intrinsic clearance is held constant and the diffusion clearance is unevenly distributed in the sinusoid along the hepatic blood flow path. Diffusional transport may vary along the sinusoidal flow path. Therefore, by the analogy of the former case as elucidated so far, we can conclude that extraction ratios differ widely among the different patterns for the diffusion clearance when the average intrinsic clearances are intermediate or low compared to the average diffusion clearance. By contrast, extraction ratios are un- changed at high average intrinsic clearances, irrespective of different patterns for ths diffusion clearance. The most efficient elimination occurs in the model where the diffusion clearance is evenly distributed along the hepatic blood flow path. The more skewed the distribution of the diffusion clearance, the lesser the amount of drug eliminated by the liver at steady state.

The conclusions here might qualitatively hold in the distributed model, because the above conclusions on the effect of a diffusional barrier on drug metabolism under an uneven distribution of uni-enzyme along the flow path, consistent in each parallel sinusoid, could be extended to the whole liver where the enzyme content and blood flow per sinusoid CV,, and Q per sinusoid) were assumed to be statistically distributed over the sinusoids constituting the liver. However, a quantitative determination needs to be made by a mathematical analysis.

Conclusions If a uniform diffusional barrier across hepatocytes exists

for a given drug, i.e., the diffusion clearance is low or intermediate relative to the intrinsic clearance, the extrac-

tion ratio of the drug is dependent on the distribution patterns of hepatocellular uni-enzyme along the hepatic blood flow path. The highest extraction of the drug was obtained in the model where the enzymatic activity was evenly distributed among the models examined.

1.

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32. 33.

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Forker, E. L.; Luxon, B. Am. J. Physiol. 1978,235, E648-E660. Pang, K. S.; Rowland, M. J. Pharmacokinet. Biopharm. 1977,5,

Ahmad, A. B.; Bennett, P. N.; Rowland, M. J. Pharm. Pharmu- col. 1982,35, 219-224. Rowland, M.; Leitch, D.; Fleming, G.; Smith, B. J. Pharmaco- kinet. BioDharm. 1984.12. 129-147.

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Jones, D: B.; Morgan, D. J.; Mihaly, G. W. Webster, L. K.; Smallwood, R. A. J. Pharrnacol. Exp. Ther. 1984,229,522-526. Keiding, S.; Priisholm, K. Biochern. Pharmacol. 1984,33,3209- ‘30- n JOll. Wagner, J. G.; Szpunar, G. J.; Ferry, J . J. Drug Metab. Dispos. 1984,12,385388. Wagner, J. G. Drug Metab. Dispos. 1985, 13, 119-120. B ne, A. J.; Morgan, D. J.; Harrison, P. M.; McLean, A. J . J. P g r m . Sci. 1985, 74, 205-207. Sawada, Y.; Su iyama, Y.; Miyamoto, Y.; Iga, T.; Hanano, M. Chem. Pharm. lh. 1985,33, 319-326. Pang, K. S.; Stillwell, R. N. J . Pharmacokinet. Biopharm. 1983,

Igari, Y.; Sugiyama, Y.; Awazu, S.; Hanano, M. J. Pharrnuco- kinet. Bio harm. 1982, 10, 53-75. Dedrick, fl. L.; Zaharko, D. S.; Lutz, R. J. J. Pharrn. Sci. 1973,

Lutz, R. J.; Galbraith, W. M.; Dedrick, R. L.; Shrager, R.; Mel- lett, L. B. J. Pharmacol. Ex Pang, K. S.; Cherry, W. (’ Terrell, J . A.; Ulm, E. H. Drug Metab. Dispos. 1984, 12, 309-313. Scharschmidt, B. F.; Waggoner, J . G.; Berk, P. D. J. Clin. Invest. 1975,56, 1280-1292. Gillette, J. R.; Pang, K. S. Clin Pharmucol. Ther. 1977,22, 623- 639

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Goresky, C. A.; Bach, G. G.; Nadeau, B. E. J. Clin. Invest. 1973, 52.991-1009. Goresky, C. A.; Bach, G. G.; Rose, C. P. Am. J. Physiol. 1983, 244, G215-G232. Klaassen, C. 0.; Watkins, 111, J. B. Pharmucol. Rev. 1984,36, 1- 67 Eiilette, J. R. Ann. N.Y. Acad. Sci. 1971, 179, 43-46. Stein, W. D. “The Movement of Molecules Across Cell Mem- branes”; Academic Press: New York; pp 126-176. Gibaldi, M.; Perrier, D. “Pharmacokinetics,” 2nd ed.; Marcel Dekker: New York, 1982; pp 199-219. Dedrick, R. L.; Forester, D. D.; Ho, D. W. Biochem. Pharmucol. 1972.21. 1-16. Rane, A:;-Wiikinson, G. R.; Shand, D. G. J. Pharmacol. Exp. Ther. 1977,200,420-424. Lin, J. H.; Sugiyama, Y .; Awazu, S.; Hanano, M. J. Pharmuca- kinet. BioDharm. 1982.10.649-661.

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8 /Journal of Pharmaceutical Sciences Vol. 75, No. 1, January 1986

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A Simulation study on the effect of a uniform diffusional barrier across hepatocytes on drug metabolism by evenly or unevenly distributed uni-enzyme in the liver