Application of the axial dispersion model of hepatic drug elimination to the kinetics of diazepam in the isolated perfused rat liver

How predictive are isolated perfused liver data of in vivo hepatic clearance? A meta-analysis of isolated perfused rat liver data

Isolated perfused rat liver (IPRL) experiments have been used to answer clearance-related questions, including evaluating the impact of pathological and physiological processes on hepatic clearance (CLH). However, to date, IPRL data has not been evaluated for in vivo CLH prediction accuracy.In addition to a detailed overview of available IPRL literature, we present an in-depth analysis of the performance of IPRL in CLH prediction.While the entire dataset poorly predicted CLH (GAFE = 3.2; 64% within 3-fold), IPRL conducted under optimal experimental conditions, such as in the presence of plasma proteins and with a perfusion rate within 2-fold of physiological liver blood flow and corrected for unbound fraction in the presence of red blood cells, can accurately predict rat CLH (GAFE = 2.0; 78% within 3-fold). Careful consideration of experimental conditions is needed to allow proper data analysis.Further, isolated perfused liver experiments in other species, including human livers, may allow us to address the current in vitro-in vivo disconnects of hepatic metabolic clearance and improve our methodology for CLH predictions.

A Complete Extension of Classical Hepatic Clearance Models Using Fractional Distribution Parameter fd in Physiologically Based Pharmacokinetics

The classical organ clearance models have been proposed to relate the plasma clearance CLp to probable mechanism(s) of hepatic clearance. However, the classical models assume the intrinsic capability of drug elimination (CLu,int) that is physically segregated from the vascular blood but directly acts upon the unbound drug concentration in the blood (fubCavg), and do not handle the transit-time delay between the inlet/outlet concentrations in their closed-form clearance equations. Therefore, we propose unified model structures that can address the internal blood concentration patterns of clearance organs in a more mechanistic/physiological manner, based on the fractional distribution parameter fd operative in PBPK. The basic partial/ordinary differential equations for four classical models are revisited/modified to yield a more complete set of extended clearance models, i.e., the Rattle, Sieve, Tube, and Jar models, which are the counterparts of the dispersion, series-compartment, parallel-tube, and well-stirred models. We demonstrate the feasibility of applying the resulting extended models to isolated perfused rat liver data for 11 compounds and an example dataset for in vitro-in vivo extrapolation of the intrinsic to the systemic clearances. Based on their feasibilities to handle such real data, these models may serve as an improved basis for applying clearance models in the future.

Utility of Minimal Physiologically Based Pharmacokinetic Models for Assessing Fractional Distribution, Oral Absorption, and Series-Compartment Models of Hepatic Clearance

Minimal physiologically based pharmacokinetic (mPBPK) models are physiologically relevant, require less information than full PBPK models, and offer flexibility in pharmacokinetics (PK). The well-stirred hepatic model (WSM) is commonly used in PBPK, whereas the more plausible dispersion model (DM) poses computational complexities. The series-compartment model (SCM) mimics the DM but is easier to operate. This work implements the SCM and mPBPK models for assessing fractional tissue distribution, oral absorption, and hepatic clearance using literature-reported blood and liver concentration-time data in rats for compounds mainly cleared by the liver. Further handled were various complexities, including nonlinear hepatic binding and metabolism, differing absorption kinetics, and sites of administration. The SCM containing one to five (n) liver subcompartments yields similar fittings and provides comparable estimates for hepatic extraction ratio (ER), prehepatic availability (Fg ), and first-order absorption rate constants (ka ). However, they produce decreased intrinsic clearances (CLint ) and liver-to-plasma partition coefficients (Kph ) with increasing n as expected. Model simulations demonstrated changes in intravenous and oral PK profiles with alterations in Kph and ka and with hepatic metabolic zonation. The permeability (PAMPA P) of the various compounds well explained the fitted fractional distribution (fd ) parameters. The SCM and mPBPK models offer advantages in distinguishing systemic, extrahepatic, and hepatic clearances. The SCM allows for incorporation of liver zonation and is useful in assessing changes in internal concentration gradients potentially masked by similar blood PK profiles. Improved assessment of intraorgan drug concentrations may offer insights into active moieties driving metabolism, biliary excretion, pharmacodynamics, and hepatic toxicity. SIGNIFICANCE STATEMENT: The minimal physiologically based pharmacokinetic model and the series-compartment model are useful in assessing oral absorption and hepatic clearance. They add flexibility in accounting for various drug- or system-specific complexities, including fractional distribution, nonlinear binding and saturable hepatic metabolism, and hepatic zonation. These models can offer improved insights into the intraorgan concentrations that reflect physiologically active moieties often driving disposition, pharmacodynamics, and toxicity.

Assumptions Underlying Hepatic Clearance Models: Recognizing the Influence of Saturable Protein Binding on Driving Force Concentration and Discrimination Between Models of Hepatic Clearance

One underlying assumption of hepatic clearance models is often underappreciated. Namely, plasma protein binding is assumed to be nonsaturable within a given drug concentration range, dependent only on protein concentration and equilibrium dissociation constant. However, in vitro hepatic clearance experiments often use low albumin concentrations that may be prone to saturation effects, especially for high-clearance compounds, where the drug concentration changes rapidly. Diazepam isolated perfused rat liver literature datasets collected at varying concentrations of albumin were used to evaluate the predictive utility of four hepatic clearance models (the well-stirred, parallel tube, dispersion, and modified well-stirred model) while both ignoring and accounting for potential impact of saturable protein binding on hepatic clearance model discrimination. In agreement with previous literature findings, analyses without accounting for saturable binding showed poor clearance prediction using all four hepatic clearance models. Here we show that accounting for saturable albumin binding improves clearance predictions across the four hepatic clearance models. Additionally, the well-stirred model best reconciles the difference between the predicted and observed clearance data, suggesting that the well-stirred model is an appropriate model to describe diazepam hepatic clearance when considering appropriate binding models. SIGNIFICANCE STATEMENT: Hepatic clearance models are vital for understanding clearance. Caveats in model discrimination and plasma protein binding have sparked an ongoing scientific discussion. This study expands the understanding of the underappreciated potential for saturable plasma protein binding. Fraction unbound must correspond to relevant driving force concentration. These considerations can improve clearance predictions and address hepatic clearance model disconnects. Importantly, even though hepatic clearance models are simple approximations of complex physiological processes, they are valuable tools for clinical clearance predictions.

Exploring the Pharmacokinetic Mysteries of the Liver: Application of Series Compartment Models of Hepatic Elimination

Among the basic hepatic clearance models, the dispersion model (DM) is the most physiologically sound compared with the well-stirred model and the parallel tube model. However, its application in physiologically-based pharmacokinetic (PBPK) modeling has been limited due to computational complexities. The series compartment models (SCM) of hepatic elimination that treats the liver as a cascade of well-stirred compartments connected by hepatic blood flow exhibits some mathematical similarities to the DM but is easier to operate. This work assesses the quantitative correlation between the SCM and DM and demonstrates the operation of the SCM in PBPK with the published single-dose blood and liver concentration-time data of six flow-limited compounds. The predicted liver concentrations and the estimated intrinsic clearance (CLint ) and PBPK-operative tissue-to-plasma partition coefficient (Kp ) values were shown to depend on the number of liver sub-compartments (n) and hepatic enzyme zonation in the SCM. The CLint and Kp decreased with increasing n, with more remarkable differences for drugs with higher hepatic extraction ratios. Given the same total CLint , the SCM yields a higher Kp when the liver perivenous region exhibits a lower CLint as compared with a high CLint at this region. Overall, the SCM nicely approximates the DM in characterizing hepatic elimination and offers an alternative flexible approach as well as providing some insights regarding sequential drug concentrations in the liver. SIGNIFICANCE STATEMENT: The SCM nicely approximates the DM when applied in PBPK for characterizing hepatic elimination. The number of liver sub-compartments and hepatic enzyme zonation are influencing factors for the SCM resulting in model-dependent predictions of total/internal liver concentrations and estimates of CLint and the PBPK-operative Kp . Such model-dependency may have an impact when the SCM is used for in vitro-to-in vivo extrapolation (IVIVE) and may also be relevant for PK/PD/toxicological effects when it is the driving force for such responses.

Plasma Protein-Mediated Uptake and Contradictions to the Free Drug Hypothesis: A Critical Review

According to the free drug hypothesis (FDH), only free, unbound drug is available to interact with biological targets. This hypothesis is the fundamental principle that continues to explain the vast majority of all pharmacokinetic and pharmacodynamic processes. Under the FDH, the free drug concentration at the target site is considered the driver of pharmacodynamic activity and pharmacokinetic processes. However, deviations from the FDH are observed in hepatic uptake and clearance predictions, where observed unbound intrinsic hepatic clearance (CL_int,u) is larger than expected. Such deviations are commonly observed when plasma proteins are present and form the basis of the so-called plasma protein-mediated uptake effect (PMUE). This review will discuss the basis of plasma protein binding as it pertains to hepatic clearance based on the FDH, as well as several hypotheses that may explain the underlying mechanisms of PMUE. Notably, some, but not all, potential mechanisms remained aligned with the FDH. Finally, we will outline possible experimental strategies to elucidate PMUE mechanisms. Understanding the mechanisms of PMUE and its potential contribution to clearance underprediction is vital to improving the drug development process.

Precisely adjusting the hepatic clearance of highly extracted drugs using the modified well-stirred model

Hepatic clearance has been widely studied for over 50 yr. Many models have been developed using either theoretical or empirical tests to predict drug metabolism. The well-stirred, parallel-tube, and dispersion metabolic models have been extensively discussed. However, to our knowledge, these models cannot fully describe all relevant scenarios in hepatic clearance. We addressed this issue using the isolated perfused rat liver technique with minor modifications. Diazepam was selected to illustrate different levels of drug plasma-protein binding by changing the added concentration of human serum albumin. The free fractions of diazepam at different albumin concentrations were assayed by rapid equilibrium dialysis. The experimental data provide new insights concerning an accepted formula used to describe hepatic clearance. Regarding drug concentrations passing through the liver, the driving force concentration (C_H,ss) in terms of C_in (influx in the liver) or C_out (efflux from the liver) needs to be carefully considered when determining drug hepatic and intrinsic clearances. The newly established model, termed the modified well-stirred model, which was derived from the original formula, successfully estimated hepatic drug metabolism. Using the modified well-stirred model, a theoretical driving force concentration of diazepam passing through the liver was evaluated. The model was further used to assess the predictability of in vitro to in vivo extrapolation. This study was not intended to refute the existing models, but rather to augment them using experimental data. The results stress the importance of proper calculation of dose when the drug clearance deviates from the prediction of the well-stirred model.

Are There Any Experimental Perfusion Data that Preferentially Support the Dispersion and Parallel-Tube Models over the Well-Stirred Model of Organ Elimination?

In reviewing previously published isolated perfused rat liver studies, we find no experimental data for high-clearance metabolized drugs that reasonably or unambiguously support preference for the dispersion and parallel-tube models versus the well-stirred model of organ elimination when only entering and exiting drug concentrations are available. It is likely that the investigators cited here may have been influenced by: 1) the unphysiologic aspects of the well-stirred model, which may have led them to undervalue the studies that directly test the various hepatic disposition models for high-clearance drugs (for which model differences are the greatest); 2) experimental assumptions made in the last century, which are no longer valid today, related to the predictability of in vivo outcomes from in vitro measures of drug elimination and the influence of albumin in hepatic drug uptake; and 3) a lack of critical review of previously reported experimental studies, resulting in inappropriate interpretation of the available experimental data. The number of papers investigating the theoretical aspects of the dispersion, parallel-tube, and well-stirred models of hepatic elimination greatly outnumber the papers that actually examine the experimental evidence available to substantiate these models. When all experimental studies that measure organ elimination using entering and exiting drug concentrations at steady state are critically reviewed, the simple but unphysiologic well-stirred model is the only model that can describe all trustworthy published available data. SIGNIFICANCE STATEMENT: Although the dispersion model of hepatic elimination more adequately reflects physiologic reality, there are no convincing experimental data that unambiguously favor this model. The well-stirred model can describe all well-designed perfusion studies with high-clearance drugs and nondrug substrates, but the field has not recognized this because of hesitation to accept a nonphysiologic model and flawed attempts to utilize in vitro-in vivo extrapolation approaches.

Protein Binding and Hepatic Clearance: Re-Examining the Discrimination between Models of Hepatic Clearance with Diazepam in the Isolated Perfused Rat Liver Preparation

This study re-examined the hepatic extraction for diazepam, the only drug for which isolated perfused rat liver (IPRL) studies have been reported not to be consistent with the well stirred model of organ elimination when only entering and exiting liver concentration measurements are available. First, the time dependency of diazepam equilibrium fraction unbound measurements from 4 to 24 hours was tested, reporting the continuing increases with time. The results showed that the time dependency of equilibrium protein-binding measurements for very highly bound drugs may be an issue that is not readily overcome. When examining C out/C in (F obs) measurements for diazepam when no protein is added to the incubation media, IPRL outcomes were consistent with previous reports showing marked underpredictability of in vivo clearance from in vitro measures of elimination in the absence of protein for very highly bound drugs, which is markedly diminished in the presence of albumin. F obs for diazepam at additional low concentrations of protein that would allow discrimination of the models of hepatic elimination produced results that were not consistent with the dispersion and parallel-tube models. Therefore, although the outcomes of this study were similar to those reported by Rowland and co-workers, when no protein is added to the perfusion media, these IPRL results for diazepam cannot be reasonably interpreted as proving that hepatic organ elimination is model-independent or as supporting the dispersion and parallel-tube models of organ elimination. SIGNIFICANCE STATEMENT: The only drug experiments for which isolated perfusion rat liver studies do not support hepatic clearance being best described by the well stirred model have been carried out with diazepam at zero protein concentration. This study repeated those studies, confirming the previous results at zero protein concentration, but the addition of low protein-binding conditions capable of differentiating the various models of hepatic elimination are more consistent with the well stirred model of hepatic elimination. These experimental studies do not support the preference for alternate models of hepatic elimination or the proposal that hepatic organ clearance is model-independent.

Hepatic clearance concepts and misconceptions: Why the well-stirred model is still used even though it is not physiologic reality?

The liver is the most important drug metabolizing organ, endowed with a plethora of metabolizing enzymes and transporters to facilitate drug entry and removal via metabolism and/or biliary excretion. For this reason, much focus surrounds the development of clearance concepts, which are based on normalizing the rate of removal to the input or arterial concentration. By so doing, some authors have recently claimed that it implies one specific model of hepatic elimination, namely, the widely used well-stirred or venous equilibration model (WSM). This commentary challenges this claim and aims to provide a comprehensive discussion of not only the WSM but other currently applied hepatic clearance models - the parallel tube model (PTM), the dispersion model (DM), the zonal liver model (ZLM), and the heterogeneous capillary transit time model of Goresky and co-workers (GM). The WSM, PTM, and DM differ in the patterns of internal blood flow, assuming bulk, plug, and dispersive flows, respectively, which render different degrees of mixing within the liver that are characterized by the magnitudes of the dispersion number (D_N), resulting in different implications concerning the (unbound) substrate concentration in liver (Cu_H). Early models assumed perfusion rate-limited distribution, which have since been modified to include membrane-limited transport. The recent developments associated with the misconceptions and the sensitivity of the models are hereby addressed. Since the WSM has been and will likely remain widely used, the pros and cons of this model relative to physiological reality are further discussed.

Exploration of PBPK Model-Calculation of Drug Time Course in Tissue Using IV Bolus Drug Plasma Concentration-Time Profile and the Physiological Parameters of the Organ

An uncommon innovative consideration of the well-stirred linear physiologically based pharmacokinetic model and the drug plasma concentration-time profile, which is measured in routine intravenous bolus pharmacokinetic study, was applied for the calculation of the drug time course in human tissues. This cannot be obtained in the in vivo pharmacokinetic study. The physiological parameters of the organ such as organ tissue volume, organ blood flow rate, and its vascular volume were used in the calculation. The considered method was applied to calculate the time course of midazolam, alprazolam, quinidine, and diclofenac in human organs or tissues. The suggested method might be applied for the prediction of drug concentration-time profile in tissues and consequently the drug concentration level in the targeted tissue, as well as the possible undesirable toxic levels in other tissues.

The influence of old age and poloxamer-407 on the hepatic disposition of diazepam in the isolated perfused rat liver

BACKGROUND AND PURPOSE

The normal liver sinusoidal endothelium is thin and punctuated with fenestrations 50-200 nm in diameter that filter endobiotics and xenobiotics. Defenestration of the liver sinusoidal endothelium in old age and after pre-treatment with poloxamer-407 (P407) has been shown to prevent the transfer of small chylomicrons across the liver sinusoidal endothelium. The aim of this study was to investigate the impact of liver sinusoidal endothelium fenestrations on the hepatic uptake of the highly protein-bound drug diazepam. We hypothesized that defenestration will reduce the hepatic extraction of drugs which are highly bound to albumin.

METHODOLOGY

The isolated perfused rat liver (IPRL) model and multiple indicator dilution technique were used to investigate the effect of fenestrations in the liver sinusoidal endothelium on the hepatic disposition of diazepam in old and young rats, and in young rats treated with P407 or vehicle. A bolus dose of (14)C-diazpeam and non-extracted tracers ((3)H-sucrose and Evans blue) was injected into the portal vein. The single-pass recovery of diazepam and markers and the apparent volume of distribution were determined.

RESULTS

Scanning electron microscopy confirmed reduced porosity of the liver sinusoidal endothelial cells in P407-treated rats and old rats compared to young and control rats. The fractional recovery of diazepam was significantly increased in P407-treated rats compared to controls (0.20 ± 0.16, n = 12, P407; 0.08 ± 0.05, n = 8, controls; p = 0.0029), and in old rats compared to young rats (0.15 ± 0.03, n = 11, old; 0.10 ± 0.02, n = 11, young; p = 0.0004) following a single pass.

CONCLUSION

Defenestration due to age-related pseudocapillarization and treatment with P407 resulted in reduced hepatic extraction of diazepam after a single pass through the IPRL. These results highlight the importance of the liver sinusoidal endothelium in the ultrafiltration of highly protein-bound drugs, and may also provide an additional mechanism for reduced hepatic clearance of diazepam in conditions associated with defenestration.

On the influence of protein binding on pharmacological activity of drugs

The effect of variable protein binding (taken as independent parameter) on pharmacological activity of drugs is considered in terms of the exposure or the steady state concentration of unbound drug at targeted tissue. Based on the application of the parallel tube or dispersion models it is shown that for the most common case of orally administered drugs eliminated mainly by hepatic metabolism the increase of protein binding may be beneficial for drug action. In contrary, consideration of this case using the well-stirred model suggests that changes in protein binding do not influence drug efficiency. The relatively simplistic well-stirred model appears not accurate enough to reveal the influence of variation in protein binding on drug exposure. The conclusion in favor of the predictions based on parallel tube or dispersion models is supported by experimental data. In case of the oral dosing of drugs that are subjected to nonhepatic elimination as well as for parenteral drug administration with arbitrary routes of elimination the decrease in protein binding would lead to the increase of unbound drug exposure and thus may enhance drug efficiency. An advanced approach to evaluation of drug activity based on the assumption of the necessity to exceed certain minimal drug concentration at action site is implied. Such a consideration leads to the conclusion that there should be an optimal value of protein binding which provides maximum drug activity. The case when drug action is determined by binding to targeted receptors is discussed in terms of equilibrium binding and kinetics.

Application of the dispersion model to describe disposition kinetics of markers in the dual perfused rat liver

The liver receives two blood supplies, portal and hepatic, yet most in situ studies use only portal perfusion. A model based on dispersion principles was developed to provide baseline data of the dual perfused rat liver preparation by characterizing the temporal outflow profiles of noneliminated reference markers (vascular marker, red blood cells; extracellular markers, albumin, sucrose; and intracellular markers, urea, water). The model consists of two components: the common and a specific arterial space operating in parallel. The common space receives all the portal flow and some of the arterial flow; the remaining arterial flow perfuses the specific space. Each space is divided into three subspaces: vascular, interstitial, and intracellular. The extent of axial spreading of solute on passage through the common and specific spaces is characterized by their respective dispersion numbers, D(N). The model was fully characterized by analysis of the outflow data following independent bolus administration into the portal vein and hepatic artery. The model provided a good fit of the data for all reference compounds. The estimate of the fraction of the total space assigned to the specific arterial space varied from 4 to 11%, with a mean value of 9%. The estimated D(N) was always small (<0.25) and tended to be greater for the common space (0.08-0.23) than the specific space (0.05-0.12). However, for each space, there was no significant difference in the D(N) value among all reference markers; this is assumed to arise because all markers are reflecting a common feature, the heterogeneity of the microvasculature.

A whole-body physiologically based pharmacokinetic model incorporating dispersion concepts: short and long time characteristics

In whole-body physiologically based pharmacokinetic (PBPK) models, each tissue or organ is frequently portrayed as a single well-mixed compartment with distribution, perfusion rate limited. However, single-pass profiles from isolated organ studies are more adequately described by models which display an intermediate degree of mixing. One such model is the dispersion model, which successfully describes the outflow profiles from the liver and the perfused hindlimb of many compounds, under a variety of conditions. A salient parameter of this model is the dispersion number, a dimensionless term, which characterizes the relative axial spreading of compound on transit through the organ. We have developed a whole-body PBPK model wherein the distribution of drug on transit through each organ is described by the dispersion model with closed boundary conditions incorporated. The model equations were numerically solved using finite differencing methods, in particular, the method of lines. An integrating routine suitable for solving stiff sets of equations was used. Physiological parameters, blood flows, and tissue volumes, were taken from the literature, as were the tissue dispersion numbers, which characterize the mixing properties of each tissue; where none could be found, the value was set as that for liver. On solution, tissue, venous and arterial blood concentration-time profiles are generated. The profiles exhibited both short and long time characteristics. Oscillations were observed in the venous and arterial profiles over the first 10 min of simulation for the rat. On scale-up to human, the effects were seen over a 30 min period. Longer time effects of tissue distribution involve buildup of drug in the large tissues of distribution: skeletal muscle, skin, and adipose. The extent of distribution in the large tissues was somewhat dependent on the magnitude of the dispersion number, the lower the dispersion number, the greater the extent of distribution after an intravenous bolus dose. The model has a distinct advantage over the well-stirred organ whole-body PBPK model in its ability to describe both short and long time characteristics.

Cytoplasmic binding and disposition kinetics of diclofenac in the isolated perfused rat liver

1. The binding kinetics of diclofenac to hepatocellular structures were evaluated in the perfused rat liver using the multiple indicator dilution technique and a stochastic model of organ transit time density. 2. The single-pass, in situ rat liver preparation was perfused with buffer solution (containing 2% albumin) at 30 ml min(-1). Diclofenac and [(14)C]-sucrose (extracellular reference) were injected simultaneously as a bolus dose into the portal vein (six experiments in three rats). An analogous series of experiments was performed with [(14)C]-diclofenac and [(3)H]-sucrose. 3. The diclofenac outflow data were analysed using three models of intracellular distribution kinetics, assuming (1) instantaneous distribution and binding (well-mixed model), (2) 'slow' binding at specific intracellular sites after instantaneous distribution throughout the cytosol (slow binding model), and (3) 'slowing' of cytoplasmic diffusion due to instantaneous binding (slow diffusion model). 4. The slow binding model provided the best description of the data. The rate constants for cellular influx and sequestration were 0.126+/-0. 026 and 0.013+/-0.009 s(-1), respectively. The estimated ratio of cellular initial distribution volume to extracellular volume of 2.82 indicates an almost instantaneous distribution in the cellular water space, while the corresponding ratio of 5.54 estimated for the apparent tissue distribution volume suggests a relatively high hepatocellular binding. The non-instantaneous intracellular equilibration process was characterized by time constants of the binding and unbinding process of 53.8 and 49.5 s, respectively. The single-pass availability of diclofenac was 86%. The results obtained with [(14)C]-diclofenac and [(3)H]-sucrose were not statistically different.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and unweighted conventional convection-dispersion models decreases as hepatic extraction increases. A correspondence of more than 95% in F and Cl exists for all solute extractions. In addition, the analysis showed that the outflow concentration-time profiles for both the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in both experimental and clinical situations.

Pharmacokinetics in organs and the intact body: model validation and reduction

Physiological pharmacokinetic models are based on the structure of the circulatory system reflecting the convective transport of drug by blood flow to the various organs and tissues. Distribution kinetics at the organ level is mostly simplified as transfer between well-stirred compartments neglecting a priori the effects of intravascular dispersion and diffusion within tissue parenchyma. Recirculatory models based on residence time theory overcome these structural limitations since they allow in a most general way the decomposition of the body into its natural subsystems. Because of the unidentifiability of the global multi-organ model on the basis of plasma concentration-time curves the following methods/experimental designs will be discussed which provide quantitative information regarding the subsystems under in vivo conditions: (i) determination of tissue concentration-time profiles (destructive sampling), (ii) estimation of the organ transit time density from input/output profiles and (iii) application of a recirculatory model with reduced complexity to clinical pharmacokinetic data.

Optimal experimental design for precise estimation of the parameters of the axial dispersion model of hepatic elimination

The axial dispersion model of hepatic drug elimination is characterized by two dimensionless parameters, the dispersion number, DN, and the efficiency number, RN, corresponding to the relative dispersion of material on transit through the organ and the relative efficiency of elimination of drug by the organ, respectively. Optimal design theory was applied to the estimation of these two parameters based on changes in availability (F) of drug at steady state for the closed boundary condition model, with particular attention to variations in the fraction of drug unbound in the perfusate (fuB). Sensitivity analysis indicates that precision in parameter estimation is greatest when F is low and that correlation between RN and DN is high, which is desirable for parameter estimation, when DN lies between 0.1 and 100. Optimal design points were obtained using D-optimization, taking into account the error variance model. If the error variance model is unknown, it is shown that choosing Poisson error model is reasonable. Furthermore, although not optimal, geometric spacing of fuB values is often reasonable and definitively superior to a uniform spacing strategy. In practice, the range of fuB available for selection may be limited by such practical considerations as assay sensitivity and acceptable concentration range of binding protein. Notwithstanding, optimal design theory provides a rational approach to precise parameter estimation.

Application of the dispersion model for description of the outflow dilution profiles of noneliminated reference indicators in rat liver perfusion studies

The dispersion model (DM) is a stochastic model describing the distribution of blood-borne substances within organ vascular beds. It is based on assumptions of concurrent convective and random-walk (pseudodiffusive) movements in the direction of flow, and is characterized by the mean transit time (t) and the dispersion number (inverse Peclet number), DN. The model is used with either closed (reflective) boundary conditions at the inflow and the outflow point (Danckwerts conditions) or a closed condition at the inflow and an open (transparent) condition at the outflow (mixed conditions). The appropriateness of DM was assessed with outflow data from single-pass perfused rat liver multiple indicator dilution (MID) experiments, with varying lengths of the inflow and outflow catheters. The studies were performed by injection, of bolus doses of 51Crlabeled red blood cells (vascular indicator), 125I-labeled albumin and [14C] sucrose (interstitual indicators), and [3H]2O (whole tissue indicator) into the portal vein at a perfusion rate of 12 ml/ min. The outflow profiles based on the DM were convolved with the transport function of the catheters, then fitted to the data. A fairly good fit was obtained for most of the MID curve, with the exception of the late-in-time data (prolonged tail) beyond 3 x [symbol: see text]. The fitted DNS were found to differ among the indicators, and not with the length of the inflow and outflow catheters. But the differences disappeared when a delay parameter, t0 = 4.1 +/- 0.7 sec (x +/- SD), was included as an additional fitted parameter for all of the indicators except water. Using the short catheters, the average DN for the model with delay was 0.31 +/- 0.13 for closed and 0.22 +/- 0.07 for mixed boundary conditions, for all reference indicators. Mean transit times and the variances of the fitted distributions were always smaller than the experimental ones (on average, by 6.8 +/- 3.7% and 58 +/- 19%, respectively). In conclusion, the DM is a reasonable descriptor of dispersion for the early-in-time data and not the late-in-time data. The existence of a common DN for all noneliminated reference indicators suggests that intrahepatic dispersion depends only on the geometry of the vasculature rather than the diffusional processes. The role of the nonsinusoidal ("large") vessels can be partly represented by a simple delay.

Effect of altered tissue binding on the disposition of barbital in the isolated perfused rat liver: application of the axial dispersion model

To examine the dependence of hepatic dispersion on tissue binding, the distribution kinetics of barbital under varying conditions of barbiturate perfusate concentrations was studied in the isolated perfused rat liver preparation (n = 5). The in situ liver was perfused in a single-pass mode with protein-free Krebs bicarbonate medium (15 mL/min). During steady-state infusion with various barbiturate concentrations (barbital, 1 g/L; butethal, 0.1, 1 g/L), a bolus containing [3H]water (cellular space marker) and [14C]barbital was injected into the portal vein. The recoveries of [3H]water and [14C]barbital were complete. The mean transit time and hence the volume of distribution for barbital in the absence of bulk barbiturate concentration (56 s and 1.24 mL/g) were about 2-fold higher than those for water (29 s and 0.58 mL/g), and they decreased progressively as the perfusate barbiturate concentration increased, indicating a decrease in tissue binding. However, the relative dispersion values (CV2H) of water (0.60) and barbital (0.66) were about the same magnitude and independent of the bulk concentration of barbiturate. The one-compartment dispersion model adequately described the data of barbital with a constant DN (dispersion number) value of 0.35. The results indicate that varying the tissue binding of barbital does not change the magnitude of DN; as such it offers a new experimental approach to examine the hepatic dispersion of solutes with a large distribution volume.

Impulse-response studies on tracer doses of [14C]lignocaine and its multiple metabolites in the perfused rat liver

The outflow-concentration-time profiles for lignocaine (lidocaine) and its metabolites have been measured after bolus impulse administration of [14C]lignocaine into the perfused rat liver. Livers from female Sprague-Dawley rats were perfused in a once-through fashion with red-blood-cell-free Krebs-Henseleit buffer containing 0 or 2% bovine serum albumin. Perfusate flow rates of 20 and 30 mL min-1 were used and both normal and retrograde flow directions were employed. Significant amounts of metabolite were detected in the effluent perfusate soon after lignocaine injection. The early appearance of metabolite contributed to bimodal outflow profiles observed for total 14C radioactivity. The lignocaine outflow profiles were well characterized by the two-compartment dispersion model, with efflux rate << influx rate. The profiles for lignocaine metabolites were also characterized in terms of a simplified two-compartment dispersion model. Lignocaine was found to be extensively metabolized under the experimental conditions with the hepatic availability ranging between 0.09 and 0.18. Generally lignocaine and metabolite availability showed no significant change with alterations in perfusate flow rate from 20 to 30 mL min-1 or protein content from 0 to 2%. A significant increase in lignocaine availability occurred when 1200 microM unlabelled lignocaine was added to the perfusate. Solute mean transit times generally decreased with increasing flow rate and with increasing perfusate protein content. The results confirm that lignocaine pharmacokinetics in the liver closely follow the predictions of the wellstirred model. The increase in lignocaine availability when 1200 microM unlabelled lignocaine was added to the perfusate is consistent with saturation of the hydroxylation metabolic pathways of lignocaine metabolism.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximately by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as an alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models.

A physiologically based pharmacokinetic model incorporating dispersion principles to describe solute distribution in the perfused rat hindlimb preparation

A physiologically based pharmacokinetic model incorporating dispersion principles has been developed to describe outflow data from the isolated perfused rat hindlimb preparation, for the three reference markers 14C-sucrose, 14C-urea, and 3H-water and three 14C-labeled 5-n-alkyl-5-ethyl barbiturates; the methyl, butyl, and nonyl homologues. Also 51Cr-RBC and 125I-albumin were studied. The model consists of four parallel components representing each of the tissues comprising the hindlimb: skeletal muscle, skin, bone, and adipose. Attempts to simplify the model by using the principle of tissue lumping were made by examining the tissue equilibration rate constant k tau for each of respective tissues for each compound. It was found that simplification was only possible in the case of 3H-water data. The model took into account a possible shunting component in the skin tissue and incomplete mass but not volumetric recovery from the system. The dispersion model characterizes the relative spreading of solute on transit through a tissue bed by a dimension-less parameter DN. The estimated dispersion numbers (DN) obtained were in the region of 2.7-4.72, 8.39-15.54, 0.61-2.74, and 6.02-14.0 for skeletal muscle, skin, bone, and adipose, respectively, and were independent of the compound studied. These values are much larger than the range reported in the literature for hepatic outflow data, DN = 0.2-0.5, and suggest a greater heterogeneity of vascular flow in the different component tissues of the rat hindlimb.

Metabolite mean transit times in the liver as predicted by various models of hepatic elimination

Predicted area under curve (AUC), mean transit time (MTT) and normalized variance (CV2) data have been compared for parent compound and generated metabolite following an impulse input into the liver. Models studied were the well-stirred (tank) model, tube model, a distributed tube model, dispersion model (Danckwerts and mixed boundary conditions) and tanks-in-series model. It is well known that discrimination between models for a parent solute is greatest when the parent solute is highly extracted by the liver. With the metabolite, greatest model differences for MTT and CV2 occur when parent solute is poorly extracted. In all cases the predictions of the distributed tube, dispersion, and tanks-in-series models are between the predictions of the tank and tube models. The dispersion model with mixed boundary conditions yields identical predictions to those for the distributed tube model (assuming an inverse gaussian distribution of tube transit times). The dispersion model with Danckwerts boundary conditions and the tanks-in series models give similar predictions to the dispersion (mixed boundary conditions) and the distributed tube. The normalized variance for parent compound is dependent upon hepatocyte permeability only within a distinct range of permeability values. This range is similar for each model but the order of magnitude predicted for normalized variance is model dependent. Only for a one-compartment system is the MTT for generated metabolite equal to the sum of MTTs for the parent compound and preformed metabolite administered as parent.

On the degree of solute mixing in liver models of drug elimination

One of the fundamental differences between various liver models regards the underlying assumptions on the intrahepatic mixing process. A model-independent method for the evaluation of the departure from the perfectly mixed system is proposed which is based on an application of the relative entropy concept to hepatic transit time distributions of intravascular markers. This approach provides a measure of the distance between two probability distributions. Available data measured in isolated perfused livers indicate that sinusoidal solute mixing is nearly optimal. The suggestion of maximum mixedness in the liver may explain the discrepancy between the apparent validity of the venous equilibrium model and the physiological irrelevance of the underlying well-stirred assumption. In terms of the dispersion model the results are in accordance with the model equation obtained for mixed boundary conditions.

Effects of albumin on the disposition of morphine and morphine-3-glucuronide in the rat isolated perfused liver

1. The effect of albumin on the disposition of morphine and hepatically generated morphine-3-glucuronide (M3G) was investigated in the single-pass rat isolated perfused liver. 2. Using a balanced cross-over design, each of 10 livers was perfused at 30 mL/min with medium containing 2.7 mumol/L morphine in the presence and absence of 10 g/L bovine serum albumin (BSA). 3. Both bile flow rate and hepatic oxygen consumption were significantly higher (P < 0.005) when BSA was present in the perfusion medium, suggestive of a change in the functional performance of the perfused liver. 4. The binding of morphine and M3G was negligible in both BSA-free and -containing perfusate. 5. Outflow perfusate contained both morphine and M3G, while the metabolite but not morphine was found in bile. The recovery of the administered morphine was approximately 100% and was not altered (P > 0.05) by the presence or absence of BSA. 6. The fraction of morphine escaping heptic extraction in the absence of BSA (mean +/- SD; 0.41 +/- 0.14) was not altered significantly (P > 0.05) by the presence of the protein in perfusate (0.35 +/- 0.13), indicating no change in the intrinsic clearance or morphine despite the difference in oxygen consumption. 7. The fraction of hepatically generated M3G excreted in bile was significantly higher (P < 0.005) when BSA was present in the perfusate than when it was not (0.44 +/- 0.14 vs 0.38 +/- 0.16, respectively). 8. The results are consistent with the concept that BSA modifies the ability of solutes, including M3G, to move through the paracellular pathway from the canalicular to the vascular space. 9. It is concluded that because albumin may modify not only the unbound fraction of a ligand in perfusate, but also the functional performance of the liver, care is needed in the interpretation of studies examining the influence of the protein on the hepatic disposition of drugs and their metabolites.

Inhibitory effect of pentobarbital on biliary excretion of diclofenac in a rat liver perfusion system

The effect of pentobarbital on the biliary excretion of diclofenac was investigated in a rat liver perfusion system following a pulse input of the drug. Without albumin in the perfusate, a trace amount of diclofenac was detected in the outflow from the liver (< 0.1%). The total biliary excretion of diclofenac (intact diclofenac plus its glucuronide) decreased from 23.8% (diclofenac 6.01, glucuronide 17.8%) to 16.3% (diclofenac 5.09, glucuronide 11.2%) with an increase in the perfusate concentration of pentobarbital from 0 to 2.5 micrograms mL-1. At pentobarbital concentrations exceeding 2.5 micrograms mL-1, the biliary excretion of diclofenac and its glucuronide (14% total diclofenac) was not reduced further. The mean local excretion times of both diclofenac and its glucuronide were approximately 17 min and were unchanged at all pentobarbital concentrations tested. The ratios of biliary excreted diclofenac and its glucuronide to total diclofenac were 22 and 78%, respectively, and these values were virtually constant at all concentrations of pentobarbital in the perfusate. These results suggest that the glucuronidation of diclofenac and the biliary excretion of its glucuronide are rapid processes and that pentobarbital blocks a step before glucuronidation.

The disposition of morphine and morphine-3-glucuronide in the isolated perfused rat liver: effects of altered perfusate flow rate

The rat single-pass isolated perfused liver preparation was used to study the effects of altered perfusate flow rate on the hepatic disposition of morphine and its polar metabolite morphine-3-glucuronide (M3G). Using a balanced, cross-over design, livers of female Sprague-Dawley rats (n = 6) were perfused at 15 and 30 mL min-1 with erythrocyte- and protein-free perfusion medium containing a constant concentration of morphine (2.7 microM). After reaching steady-state, inflow and outflow perfusate and bile samples were collected and morphine and M3G were measured by HPLC. Doubling of perfusate flow rate was associated with a significant increase (P < 0.05) in the availability of morphine (mean +/- s.d. of 0.19 +/- 0.06 at 15 mL min-1 and 0.29 +/- 0.08 at 30 mL min-1). The magnitude of the change in morphine availability was consistent with the predictions of the well-stirred model of hepatic elimination. The fate of hepatically generated M3G was assessed by the biliary extraction ratio of M3G; alterations in perfusate flow rate had no significant effect on this ratio (mean +/- s.d. of 0.49 +/- 0.14 at a perfusate flow rate of 15 mL min-1 and 0.47 +/- 0.22 at 30 mL min-1). A physiologically-based mathematical model, in which the vascular and intracellular spaces of the liver were represented by two well-mixed compartments, was utilized to derive an equation for the biliary extraction ratio of M3G. According to the model, the value of this extraction ratio will become insensitive to changes in perfusate flow rate when the permeability for M3G of the membrane separating the intracellular and vascular compartments is low compared with perfusate flow rate. Hence, the experimental results are consistent with the concept that the hepatic sinusoidal membrane represents a diffusional barrier to M3G.

Tissue distribution kinetics as determinant of transit time dispersion of drugs in organs: application of a stochastic model to the rat hindlimb

A stochastic theory of drug transport in a random capillary network with permeation across the endothelial barrier is coupled with a model of tissue residence time of drugs assuming radial intratissue diffusion. Axial diffusion is neglected both in tissue as well as in the radially well-mixed vascular phase. The convective transport through the microcirculatory network is characterized by an experimentally determined transit time distribution of a nonpermeating vascular indicator. This information is used to identify three adjustable model parameters characterizing permeation, diffusion, and steady-state distribution into tissue. Predictions are made for the influence of distribution volume, capillary permeability, and tissue diffusion on transit time distributions. The role of convection (through the random capillary network), permeation, and diffusion as determinants of the relative dispersion of organ transit times has been examined. The relationship to previously proposed models of capillary exchange is discussed. Results obtained for lidocaine in the isolated perfused hindleg in rats indicate that although the contribution of intratissue diffusion to the dispersion process is relatively small in quantitative terms, it has a pronounced influence on the shape of the impulse response curve. The theory suggests that the rate of diffusion in muscle tissue is about two orders of magnitude slower than in water.

Availability and mean transit times of phenol and its metabolites in the isolated perfused rat liver: normal and retrograde studies using tracer concentrations of phenol

Phenolic compounds are frequently detoxified by the formation of sulphate and glucuronic acid conjugates in the liver. These conjugates are formed in the hepatocytes and then either transported into the bile or back into the blood. In this study, we examined the transport kinetics of phenol and its metabolites in the isolated perfused rat liver by monitoring the outflow profiles of these compounds after a bolus input in a single pass preparation. Phenol was almost exclusively metabolized to phenyl sulphate (97%) at the trace concentrations used, with the amount of phenol and metabolites excreted into the bile being minimal (3.5%). The metabolite formed was rapidly transported back into the perfusate, with mean transit times of 17.4 and 12.3 s anterograde and 24.9 and 24.2 s retrograde at flow rates of 15 and 30 mL min-1 respectively, which were intermediate between those of Evans blue and water. The outflow concentration-time profile for phenyl sulphate formation was unaffected by the addition of another organic anion (bromosulphophthalein). The effect of enzyme zonation on outflow concentration-time profiles was also investigated using retrograde perfusions. The transit time ratios for generated metabolite to water for anterograde perfusions (0.6) was found to be more than twice that for retrograde perfusions (0.23) at 15 mL min-1 and approximately 1.6 times greater at 30 mL min-1, being 0.58 and 0.37 respectively. The relative ratios obtained are consistent with previous findings that normalized variance of solutes in the retrograde perfusions is greater than that for anterograde perfusions.

Discrepancies in pharmacokinetic parameter estimation between bolus and infusion studies in the perfused rat hindlimb

Isolated, perfused rat hindlimb consists of skeletal muscle, skin, bone, and adipose. Hence, it is a heterogeneous preparation composed of slowly equilibrating tissues of different characteristics and fractional flow rates. This paper shows how caution should be exercised in interpreting the results following bolus administration and subsequent statistical moment analysis of intravascular markers (51Cr-erythrocytes and 125I-albumin) and lipophilic barbiturates. For the intravascular markers, the events in the hindlimb are overshadowed by events in the connecting tubing and cannulas, due to their comparable volumes. For the barbiturates, these estimates appear to apply to short-term effects as the volume estimates obtained following infusion to steady state are greater than after bolus administration. For the extravascular markers, 14C-sucrose, 14C-urea, and 3H-water, no such time dependency was shown. However, it is only from the outflow profiles following bolus administration that events in the tissue beds can be elucidated.

New hepatocellular diffusion model for analysis of hepatobiliary transport processes of drugs

A new hepatocellular diffusion model was developed to kinetically evaluate the hepatobiliary transport processes of drugs in the perfusion system, based on the physiological structure of the liver. Since the equations describing the hepatocellular diffusion phenomena were derived as image forms in the Laplace domain, the fast inverse Laplace transform (FILT) was adopted to manipulate the image equations. Cefixime and cefpiramide were selected as model drugs. The concentrations in the perfusate and the excreted amounts into the bile were simultaneously measured at appropriate intervals after the rapid administration of each drug into the portal vein. The hepatocellular diffusion model was fitted to the biliary excretion profiles from rat livers, by means of a nonlinear least squares program, MULTI(FILT). According to this model, the hepatobiliary transport process of drug is kinetically separated into three steps, that is, the diffusion into and through the hepatocytes, the transfer from the hepatocytes into the bile canaliculi, and the movement through the bile canaliculi to the outlet of bile duct. These steps are characterized by the diffusion rate constant through hepatocytes (kdif), the permeability rate constant into the bile canaliculi (kbmc) and the transit time through the bile canaliculi to the outlet of bile duct (tcan), respectively. It was demonstrated that kdif of cefixime (0.023 min-1) was significantly smaller than that of cefpiramide (0.044 min-1), while the differences in kbmc and tcan were not obvious between cefixime and cefpiramide. kbmc and tcan of both drugs were about 1.2 min-1 and about 1.0 min, respectively. These parameters were correlated to the excretion ratio into the bile (Fbile) and the mean transit time from the sinusoid through the hepatocytes to the outlet of bile duct (tbile).

Accuracy of numerical inversion of Laplace transforms for pharmacokinetic parameter estimation

Numerical inversion of the Laplace transform is a useful technique for pharmacokinetic modeling and parameter estimation when the model equations can be solved in the Laplace domain but the solutions cannot be inverted back to the time domain. The accuracy of numerical inversion of the Laplace transform using an infinite series approximation due to Hosono was systematically studied by reference to 17 widely differing functions having known inverse transforms. The error of inversion was found to be very sensitive to the details of the computer implementation of the method; for example, double-precision artihmetic is essential. The method used to sum the series in the least-squares program Multi(Filt) was often unable to achieve a relative error of less than 10(-4), and a Monte Carlo simulation showed that this method is insufficiently accurate for reliable least-squares parameter estimation. Improvements to the algorithm are described whereby a better method of applying Euler's transformation is used and the number of terms summed is determined automatically by the rate of convergence of the series. The improved algorithm is more efficient in inverting easy functions and more reliable in inverting difficult functions, especially those involving a time lag. With its use, pharmacokinetic parameter estimation can be performed with essentially the same accuracy as when the function is defined in the time domain.

Distribution kinetics of salicylic acid in the isolated perfused rat liver assessed using moment analysis and the two-compartment axial dispersion model

The distribution kinetics of salicylic acid in the single-pass isolated perfused rat liver has been investigated under varying conditions of perfusate flow (15 to 30 ml min-1) and of salicylate perfusate concentration (0, 100, 200 mg l-1) using statistical moment analysis and the two-compartment axial dispersion model. Salicylic acid was not metabolised during the experiment. The perfusate did not contain binding protein. As flow rate was increased, the maximum fraction output per second (f(t)max) increased and the mean transit time (MTTH) decreased, while tmax became shorter for both tritiated water and 14C-salicylic acid. Increasing the salicylate perfusate concentration profoundly affected the frequency outflow profile of 14C-salicylic acid, but not that of tritiated water. The one-compartment axial dispersion model adequately described the frequency outflow profile for tritiated water, whereas the two-compartment form, which incorporates a cellular permeability barrier, provided a better description of the 14C-salicylic acid outflow data. The estimated two-compartment axial dispersion model parameters for 14C-salicylic acid, DN, the dispersion number (0.08 +/- 0.03), k12, the influx rate constant (0.56 +/- 0.04 sec-1) and k21, the efflux rate constant (0.095 +/- 0.01 sec-1) were independent of perfusate flow rate. The in situ permeability-surface area product for 14C-salicylic acid (4.6 +/- 0.7 ml min-1g-1 liver) was in good agreement with literature estimates obtained from in vitro hepatocyte experiments, suggesting that the permeability barrier is at the hepatocyte membrane. Whereas DN and k12 were uninfluenced by, k21 displayed a positive correlation with, salicylate perfusate concentration. This correlation was most likely due to decreased intracellular salicylate binding.

Influence of albumin on the distribution and elimination kinetics of diclofenac in the isolated perfused rat liver: analysis by the impulse-response technique and the dispersion model

The impulse-response technique was used to investigate the influence of changes in the perfusate concentration of human serum albumin (HSA; 1.5-25 g/L) on the distribution and elimination kinetics of [14C]diclofenac in the isolated perfused rat liver. Output data were analyzed by a linear systems approach in combination with the axial dispersion model of hepatic elimination. This stochastic model is characterized by a dimensionless parameter (the dispersion number, DN) that quantifies the relative spreading of a substance as it passes through the liver. The two-compartment form of the axial dispersion model, which assumes that the radial transfer of a substance between the vascular and cellular spaces proceeds at a finite rate, was used to describe the output profiles for diclofenac, thereby providing estimates for DN and the first-order rate constants for the transfer of drug between the vascular and cellular compartments (k12 and k21) and its sequestration from the cellular compartment (kel). With a change in perfusate HSA concentration, the only one of these parameters to alter significantly (analysis of variance, p < 0.05) was the uptake rate constant (k12), which increased from 0.091 +/- 0.016 (mean +/- standard deviation) to 0.79 +/- 0.09 s-1 as HSA decreased from 25 to 1.5 g/L. Most of this change could be accounted for by an increase in the fraction of diclofenac unbound in perfusate, from 0.0030 to 0.0407 as HSA decreased from 25 to 1.5 g/L.(ABSTRACT TRUNCATED AT 250 WORDS)