Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse Laplace transform (FILT)

Implementing PRED Subroutine of NONMEM for Versatile Pharmacokinetic Analysis Using Fast Inversion of Laplace Transform (FILT)

In pharmacokinetic (PK) analysis, conventional models are described by ordinary differential equations (ODE) that are generally solved in their Laplace transformed forms. The solution in the Laplace transformed forms is inverse Laplace transformed to derive an analytical solution. However, inverse Laplace transform is often mathematically difficult. Consequently, numerical inverse Laplace transform methods have been developed. In this study, we focus on extending the modeling functions of Nonlinear Mixed Effect Model (NONMEM), a standard software for PK and population pharmacokinetic (PPK) analyses, by adding the Fast Inversion of Laplace Transform (FILT) method, one of the representative numerical inverse Laplace transform methods. We implemented PREDFILT, a specialized PRED subroutine, which functions as an internal model unit in NONMEM to enable versatile FILT analysis with second-order precision. The calculation results of the compartment models and a dispersion model are in good agreement with the ordinary analytical solutions and theoretical values. Therefore, PREDFILT ensures enhanced flexibility in PK or PPK analyses under NONMEM environments.

Modeling bacterial clearance using stochastic-differential equations

Capillary - tissue fluid exchange is controlled by the blood pressure in the capillary and the osmotic pressure of blood (pressure of the tissue fluid outside the capillaries). In this paper, we develop a mathematical model to simulate the movement of bacteria into and within a capillary segment. The model is based on Fokker-Planck equation and Navier-Stocks equations that accounts for different boundary conditions. Also, we model the transportation through capillary walls by means of anisotropic diffusivity that depends on the pressure difference across the capillary walls. By solving the model with a numerical method, it was possible to predict the concentration of bacteria at points within the capillary. However, numerical analysis consumes computational time and resources. To efficiently simulate the bacterial clearance, we propose a segmentation model that is based on breaking the capillary network into smaller sections with pre-defined properties in order to reduce the overall computational time. The proposed model shows a great reduction in computational time and provides accurate results when compared to the numerical analysis.

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.

Influence of erythrocytes on the hepatic distribution kinetics of urea and thiourea

The role of erythrocyte on the hepatic distribution kinetics of urea and thiourea was investigated in the in situ isolated perfused rat liver. Perfusion experiments were conducted using Krebs-bicarbonate buffer delivered via the portal vein in a single pass mode at a total flow rate of 15 ml/min. With urea, superimposable unimodal effluent curves were obtained in the presence and absence of erythrocytes, indicating that its distribution kinetics is not affected by erythrocytes. With thiourea, effluent curves were unimodal in the absence of erythrocytes but bimodal in the presence of erythrocytes. The maximum frequency output at the first peak increased from 0.017+/-0.002 to 0.042+/-0.006 s(-1) with an increase in the bolus hematocrit from 0.40 to 0.75, indicating that some thiourea fraction is retained by the erythrocytes on transit through the liver. Although the fractional output associated with the first peak was very similar (11.9% versus 11.5%), whether the perfusate contained unlabelled thiourea or not, this fraction was reduced from 17 to 5% with a decrease in the incubation time before injection from 30 min to 40s. However, there was no evidence for a capacity limitation; a 30-min period of pre-incubation of either radiolabelled thiourea alone or combined with a high concentration of unlabelled thiourea had minimal effect on effluent profiles.

Excipient effects on gastrointestinal transit and drug absorption in beagle dogs

Previous work has shown that polyethylene glycol 400 (PEG 400) has an accelerating effect on gastrointestinal transit and a modulating influence on drug absorption in humans. The aim of this study was to assess the impact of various excipients, PEG 400, propylene glycol, d-alpha-tocopheryl-polyethylene glycol-1000 succinate (TPGS) and Labrasol on gastrointestinal transit and drug absorption in four beagle dogs using scintigraphy. Each dog received, on five separate occasions, water (control) or a dose of excipient equivalent to 1 g PEG 400, 2 g propylene glycol, 1 g TPGS or 2 g Labrasol dissolved in water and administered in the form of two capsules. The model drugs ampicillin (200mg) and antipyrine (100mg) were co-administered in the capsules. The capsule solutions were radiolabelled with technetium-99m to follow their transit using a dual-headed gamma camera, and blood samples were collected to determine drug pharmacokinetics. On a separate occasion, the drugs were dissolved in saline and given intravenously. The capsules rapidly disintegrated in the stomach liberating their liquid contents. The mean small intestinal transit times for the different treatments (control, PEG 400, propylene glycol, TPGS and Labarasol) were 183, 179, 195, 168 and 154 min, respectively. The corresponding mean absolute oral bioavailability figures were 36, 32, 39, 42 and 32% for ampicillin and 76, 74, 85, 73 and 74% for antipyrine, respectively. The transit and bioavailability data for the excipient treatments were not significantly different from the control. In summary, these excipients, at the doses administered, have limited influence on gastrointestinal transit and drug in beagle dogs.

A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time t(mu) and its variance sigma were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2sigma = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.

Analysis of hepatic disposition of galactosylated cationic liposome/plasmid DNA complexes in perfused rat liver

PURPOSE

To determine the intrahepatic disposition characteristics of galactosylated liposome/plasmid DNA (pDNA) complexes in perfused rat liver.

METHODS

Galactosylated liposomes containing N-[1-(2,3-dioleyloxy)propyl]-N,N,N-trimethylammonium chloride (DOTMA), cholesterol (Chol), and cholesten-5-yloxy-N-14-[(1-imino-2-D-thiogalactosylethyl)amino]butyl] formamide (Gal-C4-Chol) were prepared. The liposome/[32P]-labeled pDNA complexes were administered to perfused liver, and the venous outflow patterns were analyzed based on a two-compartment dispersion model.

RESULTS

The single-pass hepatic extraction of pDNA complexed with DOTMA/Chol/Gal-C4-Chol liposomes was greater than that with control DOTMA/Chol liposomes. A two-compartment dispersion model revealed that both the tissue binding and cellular internalization rate were higher for the DOTMA/Chol/Gal-C4-Chol liposome complexes compared with the control liposome complexes. The tissue binding was significantly reduced by the presence of 20 mM galactose. When their cellular localization in the perfused liver at 30 min postinjection was investigated, it was found that the parenchymal uptake of the DOTMA/Chol/Gal-C4-Chol liposome complexes was greater than that of the control liposome complexes. The parenchymal cell/ nonparenchymal cell uptake ratio was as high as unity.

CONCLUSION

Galactosylation of the liposome/pDNA complexes increases the tissue binding and internalization rate via an asialoglycoprotein receptor-mediated process. Because of the large particle size of the complexes (approximately 150 nm), however, penetration across the fenestrated sinusoidal endothelium appears to be limited.

Analysis Methods and Recent Advances in Nonlinear Pharmacokinetics from In Vitro through In Loci to In Vivo

An attempt has been made to review the nonlinearities in the disposition in vitro, in situ, in loci and in vivo mainly from a theoretical point of view. Parallel Michaelis-Menten and linear (first-order) eliminations are often observed in the cellular uptake, metabolism and efflux of drugs. The well-stirred and parallel-tube models are mainly adopted under steady-state conditions in perfusion experiments, whereas distribution, tank-in-series and dispersion models are often used under nonsteady-state conditions with a pulse input. The analysis of the nonlinear local disposition in loci is reviewed from two points of view, namely an indirect method involving physiologically based pharmacokinetics (PBPK) and a direct (two or three samplings) method using live animals. The nonlinear global pharmacokinetics in vivo is reviewed with regard to absorption, elimination (metabolism and excretion) and distribution.

A novel method for determining hepatic sinusoidal oxygen permeability in the isolated perfused rat liver using [15O]O2

Measurement of hepatic sinusoidal permeability of oxygen and other substrates may help elucidate the mechanisms responsible for impaired liver function in cirrhosis. However studies of sinusoidal oxygen permeability in normal liver and various disease states have been limited due to the considerable technical difficulties involved in the use of standard techniques. We have developed a new method for measuring sinusoidal oxygen permeability in the isolated perfused rat liver that overcomes the difficulties of previous methods by using [(15)O]O(2) and an in-line fluid monitor. This method uses data obtained from impulse response curves of radiolabelled red cells, albumin and oxygen that are fitted mathematically using the axial dispersion model to yield rate constants that describe oxygen transit through the liver. We have demonstrated the utility and reproducibility of this method by comparing multiple injections and permeability determinations in the same preparation. This approach could be used in isolated perfused organs to study oxygen permeability in a range of disease states.

Analysis of Hepatic Disposition of Native and Galactosylated Polyethylenimine Complexed with Plasmid DNA in Perfused Rat Liver

We studied the intrahepatic disposition characteristics of galactosylated polyethylenimine (Gal-PEI)/plasmid DNA (pDNA) complexes using rat liver perfusion experiment. After intraportal administration, transfection activity in liver of Gal-PEI complexes was approximately 26-fold higher than that of native PEI complexes. To evaluate the relationship between hepatic gene expression and disposition profiles, hepatic disposition of Gal-PEI complexes were pharmacokinetically analyzed by use of perfused rat liver, which enables uptake characteristics intrinsic to the liver to be elucidated. Moment analysis revealed that both complexes exhibited very high single-pass extraction. To characterize each kinetic process in hepatic uptake of Gal-PEI complexes, their outflow profiles were analyzed based on a two-compartment dispersion model. Consequently, the tissue binding affinity of Gal-PEI complexes was 3.0-fold larger than that of native PEI complexes, suggesting the increasing of hepatic binding affinity much enhanced the hepatic gene transfection efficiency. In contrast, galactosylation of PEI did not affected internalization (and/or sequestration) rate.

Gastrointestinal transit and drug absorption

The gastrointestinal (GI) absorption of orally administered drugs is determined by not only the permeability of GI mucosa but also the transit rate in the GI tract. It is well known that the gastric emptying rate is an important factor affecting the plasma concentration profile of orally administered drugs, and the intestinal transit rate also has a significant influence on the drug absorption, since it determines the residence time of the drug in the absorption site. The reason why the residence time is also a critical factor for drug absorption is that there is the site difference in absorbability for some drugs. We have developed the GI-Transit-Absorption Model (GITA Model) to analyze and predict the drug absorption kinetics by taking into account both the two factors, ie. GI transit and drug absorbability including its site difference. GITA Model has been already evidenced to be very useful for estimating the absorption kinetics of drugs with various characteristics and applied to assess the human data in combination with the gamma scintigraphy. In this review, the importance of GI transit rate in determining the absorption kinetics and the bioavailability of orally administered drugs is discussed mainly employing GITA Model and the results obtained by the model.

Quantitative evaluation of capacity-limited hepatobiliary transport based on hepatocellular diffusion model by MULTI(FEM)

The dose-dependency of hepatic uptake and hepatobiliary transport of a drug was evaluated by means of a nonlinear least square program incorporating the finite element method, MULTI(FEM). A perfusion experiment using isolated rat livers following a pulse input (i.e., under nonsteady-state conditions) was performed at three dose levels of cefpiramide as a model drug. The hepatic extraction ratio (E(H)) of cefpiramide decreased with an increase in dose, which demonstrates that the hepatic uptake is capacity-limited. The outflow time-profiles from the liver were represented by a two-compartment dispersion model with central Michaelis-Menten elimination, and the maximal elimination rate per central compartment volume (Vmax) and the Michaelis constant (Km) were estimated to be 1420 microg/ml/min and 235 microg/ml, respectively. The biliary mean transit time (t(bile)) increased slightly with an increase in dose. The hepatocellular diffusion model under non-steady-state conditions considering nonlinear transport across the bile canalicular membrane was adopted to evaluate dose-dependency in the biliary excretion of cefpiramide. The maximal penetration velocity across the bile canalicular membrane per liver (V=(bcm)max) and the affinity constant of penetration across the bile canalicular membrane (k(bcm)m = K(bcm)m A(H)L) were estimated to be 40.1 microg/min and 123 microg, respectively. Considering that the volume of a rat liver (A(H)L) is approximately 10 ml, the Michaelis constant of penetration (K(bcm)m), which is an apparent parameter, was estimated to be approximately 12.3 microg/ml. In conclusion, MULTI(FEM) is useful for evaluation of capacity-limited local disposition.

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.

Notes on the inverse Gaussian distribution and choice of boundary conditions for the dispersion model in the analysis of local pharmacokinetics

The dispersion model has been widely used to analyze local pharmacokinetics in the organs and the tissues since the 1980's. However, an ambiguity still remains in selecting the boundary conditions which are necessary to solve the basic equation of the model. In this note, theoretical considerations are given to this problem and we present here some deficiencies of the mixed boundary conditions. It seems that theoretical confusion exists in the literature for the mixed boundary conditions. It is well-known that the solution of the dispersion model with a bolus input is the inverse Gaussian distribution for the mixed boundary conditions. However, it is rarely recognized that the inverse Gaussian distribution requires an open boundary at either the inlet or the outlet. For the analysis of local pharmacokinetics, the use of the classical Danckwerts (or closed) boundary conditions is recommended.

Carbon monoxide disposition in the perfused rat liver

A simple method for determining carbon monoxide (CO) disposition in the rat liver perfused with erythrocyte-free buffer was developed. Wash-in experiments were performed with buffer containing tracer quantities of [14C]sucrose and 3H2O and equilibrated with CO. Outflow samples were collected into tubes containing human erythrocytes, which avidly bind CO. Outflow curves were analyzed using compartmental models. Fractional recovery of CO was 1.07 +/- 0. 17, and the apparent volume of distribution was 1.37 +/- 0.30 ml/g of liver (n = 8). A flow-limited model fitted the data most effectively, although estimates of the permeability-to-surface area product were attempted using a barrier-limited model. This technique will facilitate investigation of the effects of disease on gaseous substrate disposition in perfused organs.

Interconnected-tubes model of hepatic elimination: steady-state considerations

In the interconnected-tubes model of hepatic transport and elimination, intermixing between sinusoids was modelled by the continuous interchange of solutes between a set of parallel tubes. In the case of strongly interconnected tubes and for bolus input of solute, a zeroth-order approximation led to the governing equation of the dispersion model. The dispersion number was expressed for the first time in terms of its main physiological determinants: heterogeneity of flow and density of interconnections. The interconnected-tubes model is now applied to steady-state hepatic extraction. In the limit of strong interconnections, the expression for output concentrations is predicted to be similar in form to those predicted by the distributed model for a narrow distribution of elimination rates over sinusoids, and by the dispersion model in the limit of a small dispersion number D(N). More generally, the equations for the predicted output concentrations can be expressed in terms of a dimensionless 'heterogeneity number'H(N), which characterizes the combined effects of variations in enzyme distribution and flow rates between different sinusoids, together with the effects of interconnections between sinusoids. A comparative analysis of the equations for the dispersion and heterogeneity numbers shows that the value of H(N)can be less than, greater than or equal to the value of D(N)for a correlation between distributions of velocities and elimination rates over sinusoids, anticorrelation between them, and when all sinusoids have the same elimination rate, respectively. Simple model systems are used to illustrate the determinants of H(N)and D(N).

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.

Structure-hepatic disposition relationships for phenolic compounds

Phenolic compounds are widely used in therapeutic, environmental, and industrial applications. The present work seeks to define the hepatic disposition of 11 phenolic compounds with varying lipophilicities and molecular weights. The hepatic disposition kinetics were studied in a once-through in situ rat liver perfusion preparation in order to avoid extra-hepatic metabolism and recirculation effects. The phenols were administered using the impulse-response technique and the time course of hepatic venous effluent concentration was examined by moments and a two-compartment dispersion model. While the extraction of the phenolic compounds was relatively independent of lipophilicity, the estimated permeability-surface area (PS) product for influx of solutes into the hepatocytes could be related to the compounds' octanol-buffer partition coefficients (log Papp). This log PS-logPapp relationship was consistent with that reported earlier for another series of solutes with a wide range of lipophilicity. The metabolites produced from each of the phenolic compounds used in this study had mean transit times similar to those of their corresponding parent phenols, suggesting that the metabolites were not trapped in the liver as a consequence of their higher polarity. It is concluded that the strong solute lipophilicity-toxicity and lipophilicity-skin penetration relationships often seen for aqueous solutions of phenols are not evident for the hepatic extraction of these compounds. Such a conclusion is consistent with the hepatic extraction of phenolic compounds being mainly determined by a blood flow limitation in delivery of the phenol to the liver, rather than the intrinsic liver metabolic enzyme activities at the doses injected.

Analysis program based on finite element method, MULTI(FEM), for evaluation of dose-dependent local disposition of drug in liver

A curve-fitting program based on the Finite Element Method, MULTI(FEM), was developed to model nonlinear local disposition of a drug in the liver under non-steady-state conditions. The program was written in FORTRAN on an IBM-compatible personal computer. The validity of MULTI(FEM) was confirmed by analyzing the outflow kinetics of oxacillin (a model drug) following a pulse input to isolated, perfused rat livers, according to both linear and nonlinear dispersion models. Four dose levels (300, 1000, 3000, and 5000 microg) of oxacillin were administered to observe the dose-dependency in the hepatic local disposition. First, the individual outflow time-profiles at the same dose were averaged, and the average time-profile was analyzed by MULTI(FEM) based on linear dispersion models to yield a single curve fit. The fitted parameters at each dose level were compared with parameters estimated using MULTI(FILT), a program based on fast inverse Laplace transform, to analyze linear pharmacokinetics. The estimated parameters by MULTI(FEM) were in good agreement with those by MULTI(FILT). The apparent elimination rate constant (ke) decreased with an increase in dose, whereas other parameters showed no discernible dependency on an increase of dose. Second, the average outflow time-profiles at the four dose levels were simultaneously analyzed by MULTI(FEM) based on dispersion models featuring Michaelis-Menten elimination. The outflow time-profiles of oxacillin were well approximated by a two-compartment dispersion model with central Michaelis-Menten elimination. The maximum elimination rate constant (Vmax) and the Michaelis constant (Km) were estimated to be 1520 microg/mL/min and 41.3 microg/mL, respectively. Thus, the capability of MULTI(FEM) was demonstrated in evaluating capacity-limited local disposition in the liver.

Pharmacokinetic curve fitting using numerical inverse Laplace transformation

The combination of the nonlinear regression program ADAPT II with Talbot's method of numerical Laplace transformation, that allows parameter estimation when the model function is given only in the Laplace domain, is described and successfully applied to pharmacokinetic problems. The accuracy and precision of the method has been found satisfactory; its performance is comparable to that achieved in parameter estimation based on functions defined in the time domain.

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.

Analysis of nonlinear hepatic clearance of a cyclopentapeptide, BQ-123, with the multiple indicator dilution method using the dispersion model

PURPOSE

To bridge in vitro, in situ and in vivo kinetic analyses of the hepatic clearance of a cyclopentapeptide, BQ-123, by using dispersion models that assume nonlinear pharmacokinetics.

METHODS

Rat livers were perfused by the multiple indicator dilution method with doses of BQ-123 ranging from 1-1000 microg. The outflow dilution curves were fitted to a two-compartment dispersion model that was solved numerically by the finite difference method. Further, in vivo plasma concentrations of BQ-123 after bolus injection were analyzed with a hybrid physiological model that incorporates the hepatic dispersion model.

RESULTS

The calculated Michaelis-Menten constants (Km = 12.0 microM, Vmax = 321 pmol/min/10(6) cells, P(dif) = 1.2 microl/min/10(6) cells) were comparable to those obtained previously from the in vitro isolated hepatocyte experiment (Km = 9.5 microM, Vmax = 517 pmol/min/l0(6) cells, P(dif) = 1.1 microl/min/10(6) cells). The plasma concentrations of BQ-123 at doses of 1-25 mg/kg were explained well by the hybrid physiological model.

CONCLUSIONS

These results suggest that carrier-mediated transport on the sinusoidal membrane was responsible for the in vivo hepatic elimination of BQ-123.

Analysis of nonlinear and nonsteady state hepatic extraction with the dispersion model using the finite difference method

A numerical calculation method for dispersion models was developed to analyze nonlinear and nonsteady hepatic elimination of substances. The finite difference method (FDM), a standard numerical calculation technique, was utilized to solve nonlinear partial differential equations of the dispersion model. Using this method, flexible application of the dispersion model becomes possible, because (i) nonlinear kinetics can be incorporated anywhere, (ii) the input function can be altered arbitrarily, and (iii) the number of compartments can be increased as needed. This method was implemented in a multipurpose nonlinear least-squares fitting computer program, Napp (Numeric Analysis Program for Pharmacokinetics). We simulated dilution curves for several nonlinear two-compartment hepatic models in which the saturable process is assumed in transport or metabolism, and investigated whether they could definitely be discriminated from each other. Preliminary analysis of the rat liver perfusion data of a cyclic pentapeptide, BQ-123, was performed by this method to demonstrate its applicability.

Absorption behavior of orally administered drugs in rats treated with propantheline

The effect of gastrointestinal (GI) transit rate on the absorption behavior of orally administered drugs was investigated using rats pretreated with propantheline. The propantheline-treatment reduced the transit rate in all segments to approximately 50%. The absorption behavior was examined for three model drugs with different absorption characteristics: theophylline as a highly absorbable drug without the first-pass elimination, ampicillin as a poorly absorbable one, and cephalexin as a highly absorbable one via carrier-mediated transport system. In the GI transit-retarded state, the Tmax of the plasma concentration-time curve was delayed in all the three drugs. However, the extent of bioavailability was not changed in theophylline and cephalexin. On the other hand, the extent of bioavailability of ampicillin was increased in rats pretreated with propantheline. This might be caused by the increased residence time in the absorption site, i.e., small intestine. These results were generally predicted by use of the convolution method based on the GI-Transit-Absorption Model, which was developed in our previous study, using the GI transit rate parameters in rats pretreated with propantheline. The analysis using this model could clarify that the substantial absorption site of cephalexin moved to the upper region of the small intestine by the reduction of the GI transit rate.

Relative dispersions of intra-albumin transit times across rat and elasmobranch perfused livers, and implications for intra- and inter-species scaling of hepatic clearance using microsomal data

It is recognized that vascular dispersion in the liver is a determinant of high first-pass extraction of solutes by that organ. Such dispersion is also required for translation of in-vitro microsomal activity into in-vivo predictions of hepatic extraction for any solute. We therefore investigated the relative dispersion of albumin transit times (CV2) in the livers of adult and weanling rats and in elasmobranch livers. The mean and normalized variance of the hepatic transit time distribution of albumin was estimated using parametric non-linear regression (with a correction for catheter influence) after an impulse (bolus) input of labelled albumin into a single-pass liver perfusion. The mean+/-s.e. of CV2 for albumin determined in each of the liver groups were 0.85+/-0.20 (n = 12), 1.48+/-0.33 (n = 7) and 0.90+/-0.18 (n = 4) for the livers of adult and weanling rats and elasmobranch livers, respectively. These CV2 are comparable with that reported previously for the dog and suggest that the CV2 of the liver is of a similar order of magnitude irrespective of the age and morphological development of the species. It might, therefore, be justified, in the absence of other information, to predict the hepatic clearances and availabilities of highly extracted solutes by scaling within and between species livers using hepatic elimination models such as the dispersion model with a CV2 of approximately unity.

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.

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.

Contribution of cytochrome P450 3A pathway to bromocriptine metabolism and effects of ferrous iron and hypoxia-re-oxygenation on its elimination in the perfused rat liver

The contribution of the cytochrome P450 3A pathway to bromocriptine metabolism, and the effects of ferrous iron and hypoxia-re-oxygenation on its elimination, were evaluated with the perfused rat liver. Outflow profiles of bromocriptine after bolus administration were estimated by moment analysis and dispersion model analysis. Kinetic parameters were not significantly changed by troleandomycin, a P450 3A inhibitor. The inhibition of bromocriptine metabolism by troleandomycin was 5.7 +/- 2.4%. These findings indicate that cytochrome P450 3A does not play an important role in bromocriptine elimination with the perfused rat liver. Elimination rate constant (ka) values were significantly increased by ferrous iron perfusion or hypoxia-re-oxygenation. Free-radical generation can, therefore, affect bromocriptine elimination. Our observations suggest that bromocriptine might be eliminated by scavenging of free radicals in the liver.

Prediction of the plasma concentration profiles of orally administered drugs in rats on the basis of gastrointestinal transit kinetics and absorbability

A new method based on gastrointestinal transit kinetics has been developed for estimation of the absorption profiles of drugs administered orally as aqueous solutions. The utility of the method was evaluated in rats. The gastrointestinal transit profile for each segment was estimated by in-vivo studies using phenol red, an unabsorbable marker. The gastrointestinal transit profile of phenol red was well explained by a linear gastrointestinal transit kinetic model with eight segments. We also introduced the absorption process into the gastrointestinal transit kinetic model and the plasma profile was predicted by the convolution method. The absorbability of drugs in each segment was assessed by an in-situ absorption study. The validity of the model was evaluated for model drugs with different absorption characteristics. The plasma profiles predicted for ampicillin, theophylline and cephalexin were in good agreement with those observed. The overestimated plasma profile of propranolol suggests that the low bioavailability of propranolol is a result of first-pass metabolism by the intestine wall and the liver, because the calculated absolute absorption is almost perfect. This proposed model is also suitable for estimation of segmental absorption, which is useful for the development of drug delivery systems. We have demonstrated that the plasma profile of orally administered drugs can be predicted by use of gastrointestinal transit and segmental absorbability information and that this method is especially useful for estimating separately the effect of absolute absorption and first-pass metabolism on the bioavailability of drugs.

Research to develop a predicting system of mammalian subacute toxicity, (3). Construction of a predictive toxicokinetics model

A new predictive toxicokinetics model was developed to estimate subacute toxicity (target organs, severity, etc.) of non-congeneric industrial chemicals, where the chemical structures and physico-chemical properties are only available. Thus, a physiological pharmacokinetics model, which consists of blood, liver, kidney (these were experimentally found as major toxicological targets), muscle and fat compartments, was established to simulate the chemical concentrations in organs/tissues with pharmacokinetic parameters by means of Runge-Kutta-Gill algorithm. The pharmacokinetic parameters, i.e. absorption rate, absorption ratio, hepatic extraction ratio of metabolism and renal clearance were calculated by using separately established Quantitative Structure-Pharmacokinetics Relationship equations. The developed predictive model was then applied to simulations of 43 non-congeneric industrial chemicals. The chemical concentrations in organs/tissues after single oral administration were simulated, and their maximum concentrations (Cmax's) and area under the concentration-time curves (AUC's) were calculated. Fast Inverse Laplace Transform was newly applied for the purpose of simulation of 28-day repeated dose toxicity. Simulated concentrations of 28 days repeated dose were, however, found to be the same as those of simple repetitions of a single administration per day because of the short half-lives of non-congeneric industrial chemicals. A comparison of subacute toxicity data with Cmax's and AUC's in a single dose scenario suggested that the organs/tissues with relatively high concentrations of tested chemical substances were the most sensitive targets within a chemical. Chemical concentrations in liver, for instance, were correlated with the severity of hepatotoxicity among the chemicals. It was also suggested that to improve and widen the present approach, data of metabolite and reactivity of non-congeneric industrial chemicals to organs/tissues, receptors, etc. should be incorporated into the model.

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.

Evidence that cytochrome P-4502E1 contributes to ethanol elimination at low doses: effects of diallyl sulfide and 4-methyl pyrazole on ethanol elimination in the perfused rat liver

The roles of cytochrome P-4502E1 and alcohol dehydrogenase (ADH) on ethanol (EtOH) hepatic elimination was examined in the perfused rat liver. EtOH concentration-time curves of outflow after instantaneous administration (0.46 mg) through the portal vein with or without perfusion of diallyl sulfide (DAS), a selective cytochrome P-450E1 inhibitor, and/or 4-methyl pyrazole (4-MP), a classical ADH inhibitor, were analyzed by the statistical moment analysis and the compartment dispersion model. Recovery ratios obtained by moment analysis significantly changed with perfusion of inhibitors (p < 0.01). Values of the hepatic volume of distribution and the relative dispersion were significantly higher by the perfusion of DAS and 4-MP (p < 0.01). In the two-compartment dispersion model, the partition ratio (K') and the first-order elimination constant (K0) were decreased significantly by DAS (p < 0.05). By the addition of 4-MP, the blood volume of distribution (VB) and the backward partition rate constant (k21) were increased significantly (p < 0.05). K sigma values were decreased significantly to 0 (p < 0.001). The decrease of elimination rates by DAS and/or 4-MP shows the inhibition of metabolic pathways. The change of V beta and k21 caused by DAS and 4-MP indicates that EtOH taken into hepatic tissues was not metabolized and flowed out into the perfusates. Inhibition rates calculated from the efficiency number with addition of DAS and DAS + 4-MP were 40.7 and 99.3%. Therefore, cytochrome P-4502E1 and ADH accounted for 40 and 60% of the hepatic EtOH elimination at low doses.

Hepatic saturation mechanism of ethanol: application of mathematical models to ethanol outflow profiles in the perfused rat liver

The saturation mechanism of hepatic ethanol (EtOH) elimination was studied in the perfused rat liver. EtOH outflow profiles after the instantaneous administration of 3 (mg/ml) x 0.4(ml), 12 x 0.1, 24 x 0.1, and 3 x 0.1 mg (as a dose concentration x a volume) through the portal vein were analyzed by the statistical moment analysis and mathematical models (i.e., dispersion models). Results for 3 x 0.1 and 12 x 0.1 mg doses by moment analysis were similar. This demonstrated that the elimination exhibits linear kinetics. Recovery ratio and hepatic volume of distribution for 3 x 0.4 and 24 x 0.1 mg were larger than those for 3 x 0.1 and 12 x 0.1 mg doses and were similar. Kinetics after administration of 3 x 0.4 and 24 x 0.1 mg may be nonlinear. A difference in the relative dispersion (CV2) obtained by moment analysis between 3 x 0.4 and 24 x 0.1 mg doses indicated different properties of the nonlinear elimination kinetics. There were no differences in all the parameters in the one-compartment dispersion model between 3 x 0.4 and 24 x 0.1 mg doses. In the two-compartment dispersion model, there were differences in the blood volume (VB) and the forward partition rate constant (k12) between 3 x 0.4 and 24 x 0.1 mg (p < 0.05), whereas the elimination rate constant (k sigma) and the dispersion number values for these doses were similar. These findings demonstrated that there is difference in the no-equilibrium process between 3 x 0.4 and 24 x 0.1 mg doses. Therefore, we suggest that the continuous EtOH input into the liver causes the saturation of enzyme pathways and the change of the nonequilibrium process.

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.

Moment analysis of hepatic local disposition of allopurinol and oxipurinol: metabolism kinetics from allopurinol to oxipurinol in the rat isolated perfused liver

Drug metabolism in the liver was examined by the rat isolated perfused liver using the single-pass bolus-input technique. The test compounds, allopurinol and its metabolite oxipurinol, were independently introduced into the liver from the portal vein, and the concentration profiles in the venous outflow were monitored and kinetically analysed by moment theory. The recovery ratios of allopurinol and oxipurinol after the individual administration of each drug were estimated to be 0.17 (+/- 0.08 s.d.) and 1.03 (+/- 0.02 s.d.), respectively. The outflow recovery ratio of oxipurinol as the metabolite after allopurinol administration was estimated to be 0.80 (+/- 0.07 s.d.). These results indicate that the combined outflow recovery of the precursor and the metabolite after allopurinol administration is almost 100% in the rat liver.

Alternative continuous infusion method for analysis of enterohepatic circulation and biliary excretion of cefixime in the rat

The enterohepatic circulation and biliary excretion of cefixime during continuous infusion were evaluated in rats based on the recirculatory concept. The Laplace-transformed equations for the enterohepatic circulation according to this concept were derived by means of the combination of transfer function. The transformed equations were simultaneously fitted to the time courses of plasma concentration in rats with laparotomy and with bile duct cannula by means of a nonlinear regression program, MULTI(FILT), into which the fast inverse Laplace transform was incorporated. The optimum model was selected on the basis of Akaike's information criterion (AIC). The time course of drug accumulation in the bile during infusion starts with a relatively gentle slope and finally approaches the asymptote with a constant slope. The kinetic significance of this asymptote was explained using the time courses of the cumulative amount excreted into the bile of rats with bile duct cannulation. The local moment characteristics for a single pass through enterohepatic circulation were further calculated from the time courses of both the plasma concentration and the excreted amount into the bile. The recovery ratio (Fc) and the mean circulatory time (tc) through a single pass of enterohepatic circulation were estimated to be 31.1% and 0.925 h, respectively. The recovery ratio (Fa) and the mean transit time (ta) for the complicated process from the access to the bile duct into the systemic circulation such as transport through the bile duct, absorption from the intestinal tract, and transit through the portal system were 76.4% and 0.0231 h, respectively. The recovery ratio (Fb) and the mean transit time (tb) for the disposition process through the systemic circulation into the bile were 40.7% and 0.902 h, respectively.

Generalized theory of the kinetics of tracers in biological systems

Most theoretical analyses of tracer kinetics in capillaries contain an implicit assumption that the tissues to which they are connected have homogeneous material properties. The microscopic description of the exchange of tracer molecules and tissues is then modeled in terms of first-order kinetics. We consider a class of more general models allowing us to assess the robustness of simplifying assumptions made above. It is shown that when amorphous properties are important the kinetics of the system may differ considerably from those predicted by standard theories.

Physiological pharmacokinetics of solutes in the isolated perfused rat hindlimb: characterization of the physiology with changing perfusate flow, protein content, and temperature using statistical moment analysis

Distribution of Evans Blue (EB), sucrose, and water into the isolated perfused rat hindlimb was studied under various conditions using the multiple indicator dilution (MID) technique. Statistical moment analysis of the outflow profiles for the EB, sucrose, and water were used to define the vascular, extravascular, and total water spaces, respectively. The varied perfusion conditions included albumin content (2, 4.7, and 7%), temperature (25, 37, and 42 C), perfusate flow rate (2, 4, 8, and 12 ml/min) and the presence/absence of red blood cells. The range of studies undertaken were chosen to represent the variety of conditions used in the preparation of both isolated animal and human limbs, the latter being particularly important in cytotoxic therapy for recurrent malignant melanoma. The distribution volumes of EB, sucrose, and water were dependent on the flow rate and the albumin content of perfusate. The normalized variances (CV2) of the markers were of the following order: sucrose (2.18) > water (1.58) > EB (0.68), indicating that some disequilibrium occurs during the capillary exchange of water and sucrose. It is suggested that a Krebs-Henseleit buffer containing 2% BSA is a suitable perfusate for most studies of the isolated rat hindlimb perfusion. The effect of albumin concentration manifests itself only at higher flows.

Physiologic models of hepatic drug clearance: influence of altered protein binding on the elimination of diclofenac in the isolated perfused rat liver

The single-pass perfused rat liver preparation was used to assess the influence of binding to human serum albumin on the steady-state hepatic extraction of diclofenac (n = 8). In the absence of binding protein, the extraction ratio of diclofenac approached unity (range, 0.975-0.992), such that its clearance was perfusion-rate limited. As the binding of diclofenac to protein was increased by the addition of human serum albumin to the perfusion medium, its extraction ratio decreased dramatically, and clearance eventually became capacity limited. The relationship between diclofenac availability and fraction unbound was analyzed with various physiologic models of hepatic drug clearance. The dispersion model, which contains a parameter (the dispersion number) that quantifies the axial spreading of a substrate as it passes along the liver length, provided a significantly better description of the data (p < 0.05) than the undistributed parallel-tube model, which assumes that an eliminated substrate travels through the liver as an undispersed plug, and the well stirred (venous equilibrium) model, which assumes that substrate undergoes infinite mixing as soon as it enters the liver. The dispersion number estimated for diclofenac (mean, 3.03; range, 0.89-7.56) was significantly greater than that predicted from considerations of the transverse heterogeneity of blood flow within the hepatic sinusoidal bed, suggesting that additional factors influenced the relationship between availability and fraction unbound for this compound. Such factors may include transverse heterogeneity of the metabolizing enzyme system(s), axial flux of substrate created by diffusion within hepatic tissue, and protein-facilitated transfer of substrate across an unstirred fluid layer adjacent to the hepatocyte surface.

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)