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.     

A dispersion model of hepatic elimination: 3. Application to metabolite formation and elimination kinetics

A dispersion model of hepatic elimination is presented to describe metabolite formation and elimination kinetics within the liver, consistent with the known physiology and biochemistry of this organ. The model is based on the spread in residence times of blood flowing through the liver. This dispersion model is shown to be more consistent with transient and steady-state data obtained after the single passage of phenacetin and acetaminophen through the liver (both normal and retrograde perfusions) than other models of hepatic elimination. The dispersion model is suitable for the evaluation of enzyme heterogeneity using experimentally obtained metabolite data.     

A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations

A dispersion model of hepatic elimination, based on the residence time distribution of blood elements within the liver, is presented. The general rate equations appropriate for describing the hepatic output concentration of a tracer solute are derived. Particular consideration is given to events following a bolus input dose of a tracer. The model is shown to be compatible with the known hepatic architecture and hepatic physiology. The model has been fitted to hepatic outflow data for red blood cells, albumin, and other noneliminated solutes. The experimental data suggest a high degree of dispersion of blood elements within the liver. The model has also been used to evaluate the effects of changes in enzyme activity, hepatic cell permeability, blood flow, and protein binding on the outflow concentration vs. time profiles of solutes.     

A comparative investigation of hepatic clearance models: Predictions of metabolite formation and elimination

Liver clearance models serve to improve our understanding of the relationships between the physiological determinants and hepatic clearance and predict changes in the disposition of substrates when homeostasis of the organ is perturbed. Their ability to describe metabolism was presently extended to the sequential formation and elimination of primary (M₁), secondary (M₂), and tertiary (M₃) metabolites during a single passage of drug (P) across the liver, under steady state and first-order conditions. The well-stirred model is distinct from other models in that metabolite formation and elimination is independent of enzymic distributions, the number of steps involved in metabolite formation, and the intrinsic clearances of the precursors. This model predicts that the extraction ratio of a formed primary metabolite derived from drug (E{M₁, P}) is identical to that for the preformed primary metabolite (E{M₁}), and that the extraction ratios of a secondary metabolite derived from drug (E{M₂, P}) and primary metabolite (E{M₂, M₁}) or preformed secondary metabolite (E{M₂}) are identical. For the more physiologically acceptable, parallel-tube and dispersion models, metabolite sequential elimination is highly influenced by the intrinsic clearances of the precursors and the enzymic distributions that mediate removal of precursor species and the metabolites. Furthermore, the extent of sequential metabolism recedes as the number of steps involved for metabolite formation increases. These models predict that E{M₁, P}1}, and E{M₂, P}2, M₁}2}, with the magnitude of the changes being less for the dispersion model than for the parallel-tube model. Competing pathways that divert substrate from entering the sequential pathway were found to exert only minimal influence on the sequential pathway.This work was supported by the Medical Research Council, Canada (DG-263, MA-9104, and MA-9765), and USHHS (NIH, GM-38250). M. V. St-Pierre was a recipient of the University Toronto Open Fellowship and the Ontario Ministry of Health Fellowship,. K. S. Pang and P. I. Lee are recipients of Faculty Development Awards, MRC, Canada.     

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

The application of the axial dispersion model to diazepam hepatic elimination was evaluated using data obtained for several conditions using the single-pass isolated perfused rat liver preparation. The influence of alterations in the fraction unbound in perfusate (fu) and perfusate flow (Q) on the availability (F) of diazepam was studied under steady conditions (n=4 in each case). Changes in fu were produced by altering the concentration of human serum albumin (HSA) in the perfusion medium while maintaining diazepam concentration at 1 mg L^–1. In the absence of protein (fu = 1), diazepam availability was 0.011 ±0.005 (¯x±SD). >As fu decreased, availability progressively increased and at a HSA concentration of 2% (g/100 ml), whenfu was 0.023, diazepam availability was 0.851 ±0.011. Application of the axial dispersion model to the relationship betweenfu andF provided estimates for the dispersion numbe (D _N) of 0.337±0.197, and intrinsic clearance (CL _int) of 132±34 ml min^–1. The availability of diazepam during perfusion with protein-free media was also studied at three different flow rates (15, 22.5, and 30 ml min^–1). Diazepam availability always progressively increased as perfusate flow increased, with the axial dispersion model yielding estimates forD _N of 0.393 ± 0.128 andCL _int of 144 ±38 ml min^–1. The transient form of the two-compartment dispersion model was also applied to the output concentration versus time profile of diazepam after bolus input of a radiolabeled tracer into the hepatic portal vein (n=4), providingD _N andCL _int estimates of 0.251 ±0.093 and 135±59 ml min^–1, respectively. Hence, all methods provided similar estimates forD _N andCL _int. Furthermore, the magnitude of D_Nis similar to that determined for noneliminated substances such as erythrocytes, albumin, sucrose, and water. These findings suggest that the dispersion of diazepam in the perfused rat liver is determined primarily by the architecture of the hepatic microvasculature.This work was supported by the Commission of the European Communities and the Medical Research Council. One of us (A.M.E.) was partially supported by a Merck, Sharp & Dohme Fellowship. We are grateful to Roche (Switzerland) for the supply of diazepam and 2-[¹⁴C]-diazepam, and Kabi AB (Sweden) for the supply of human serum albumin.     

Hepatic structure-pharmacokinetic relationships: The hepatic disposition and metabolite kinetics of a homologous series of O-acyl derivatives of salicylic acid

1. The hepatic disposition and metabolite kinetics of a homologous series of O-acyl (acetyl, propionyl, butanoyl, pentanoyl, hexanoyl and octanoyl) esters of salicylic acid (C2SA, C3SA, C4SA, C5SA, C6SA and C8SA, respectively) was determined using a single-pass, in-situ rat liver preparation.
2. The hepatic venous outflow profiles for the parent esters and the generated metabolite, salicylic acid (SA) were analysed by HPLC. Non-parametric moments analysis was used to determine the area under the curve (AUC′), mean transit time (MTT) and normalized variance (CV²) for the parent esters and generated SA.
3. Pregenerated SA ([¹⁴C]-salicylic acid) was injected into each liver with the parent ester to determine its distribution characteristics.
4. The overall recovery of ester plus metabolite was 89% of the ester dose injected and independent of the ester carbon number, suggesting that ester extraction was due to hepatic metabolism to salicylic acid.
5. The metabolite AUC′ value increased directly with the lipophilicity of the parent ester (from 0.12 for C2SA to 0.95 for C8SA). By contrast, the parent AUC′ decreased with the lipophilicity (from 0.85 for C2SA to zero for C8SA). The metabolite MTT value also showed a trend to increase with the lipophilicity of the parent ester (from 15.72 s for C3SA to 61.97 s for C8SA). However, the parent MTT value shows no significant change across the series.
6. The two-compartment dispersion model was used to derive the kinetic parameters for parent ester, pregenerated SA and generated SA. Consequently, these parameters were used to estimate the values of AUC′, MTT and CV² for the parent ester and metabolite. The moments values obtained using the two-compartment dispersion model show similar trends to the corresponding moments values obtained from the outflow profiles using a non-parametric approach.
7. The more lipophilic aspirin analogues are more confined to the portal circulation after oral administration than aspirin due to their more extensive hepatic elimination avoiding systemic prostacyclin inhibition. Given that aspirin''s selectivity as an anti-thrombotic agent has been postulated to be due to selective anti-platelet effects in the portal circulation, the more lipophilic and highly extracted analogues are potentially more selective anti-thrombotic agents than aspirin.

     

A dispersion model of hepatic elimination: 2. Steady-state considerations-influence of hepatic blood flow,binding within blood,and hepatocellular enzyme activity

The dispersion model of hepatic elimination is based on the distribution of residence times of blood elements within the liver. The model has two asymptotic solutions corresponding to the wellstirred model (complete mixing of blood elements) and the parallel-tube model (no variation in residence times of blood elements). The steady-state form of the dispersion model relevant to pharmacokinetic analysis is developed and explored with respect to changes in blood flow, in binding within blood, and in hepatocellular enzyme activity. Literature data are used to evaluate discrepancies among the predictions of the dispersion, well-stirred, and tube models. It is concluded that the dispersion model is consistent-with the data. The limitations of steady-state perfusion experiments to estimate the residence time distribution of blood elements within the liver are considered.     

Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. I. Derivations and theoretical analysis

The approach presented enables a model independent representation of the pharmacokinetics of drugs with a linear disposition and some drugs with a nonlinear disposition. The approach is based on a decomposition of the drug disposition into an elimination function q(c) and a distribution function h(t). The qfunction represents the net effect of all disposition processes which work toward a reduction in the systemic drug level. The hfunction represents the net effect of all disposition processes which slow down the rate of decline of the systemic drug level by returning drug from the peripheral environment to the systemic circulation. Several theorems relating qand hto the drug disposition are presented which uniquely define these functions mathematically. The disposition decomposition is of particular significance in three main areas of pharmacokinetics: (1) evaluation of drug absorption, (2) drug level predictions including steady state predictions, and (3)elucidation of drug disposition kinetics. The practical significance of the decomposition method in these three areas is discussed, and various procedures for the application of the method are proposed. The decomposition method represents a model independent alternative to pharmacokinetic models such as linear compartmental models, the recirculation model, and some physiologic models. This also includes nonlinear forms of such models, as long as the nonlinearity is due to a central nonlinear elimination. The greatest promise and significance of the disposition decomposition approach appears to be its application to nonlinear pharmacokinetics. In contrast to linear pharmacokinetics the kinetic analysis in such cases has been limited to model dependent methods employing specific pharmacokinetic models, due to the lack of model independent alternatives. The novel development presented offers such alternatives. For some applications these alternatives appear more rational in the sense that the analysis becomes more general and objective and may be based on fewer assumptions.     

Effects of cardiac output on disposition kinetics of sorbitol: recirculatory modelling

1   The purpose of this study was to determine the effects of cardiac output on distribution and elimination kinetics of the marker compound sorbitol.
2   The disposition kinetics of sorbitol were investigated after rapid intravenous injection and arterial sampling in nine patients who had undergone cardiac catheterization whereby the cardiac output was measured.
3   A minimal circulatory model consisting of pulmonary and systemic subsystems, both of which were characterized by an inverse Gaussian transit time density function, fitted the data very well. The method involves numerical inverse Laplace transform of the model equations.
4   The mixing clearance introduced as a novel non-compartmental parameter of distribution dynamics was significantly correlated with cardiac output. The steady-state volume of 14 l matched the extracellular volume. The systemic extraction ratio of 23% may reflect the fractional liver blood flow.
5   This pharmacokinetic model can be applied when an independent observation of cardiac output is available. In contrast to the conventional compartmental (or sum of exponential) approach it contains fewer adjustable parameters which can be more readily interpreted in physiological terms.     

A new method for assessment of drug disposition in muscle: Application of statistical moment theory to local perfusion systems

A new experimental system is used to determine exact information concerning local drug disposition. Rabbit hind leg is perfused in situusing a single-pass technique, and outflow curves of drugs are analyzed using statistical moment theory. By the introduction of Chromatographic concepts and the application of the well-stirred model to the local perfusion system, physiologically and/or physicochemically meaningful parameters are derived from the first three moments. Moreover, in the assessment, drug disposition is divided into elimination and distribution. The elimination process is also evaluated with respect to rate and extent. This system is used to elucidate the disposition characteristics of mitomycin C and its lipophilic derivative nonyloxycarbonyl mitomycin C.     

Residence time distributions of solutes in the perfused rat liver using a dispersion model of hepatic elimination: 1. Effect of changes in perfusate flow and albumin concentration on sucrose and taurocholate

The residence time distributions of sucrose and taurocholate have been determined from the outflow concentration-time profiles after bolus input into an in situperfused rat liver preparation. The normalized variance (and the dispersion number) appeared to be independent of perfusate flow rate (10 to 37ml/mm) and perfusate albumin concentration (0–5%). The apparent volume of distribution for sucrose appeared to increase with flow rate but was unaffected by the concentration of albumin (0–5%) present in the perfusate. The changes in taurocholate availability with flow rate were adequately accounted for by the dispersion model, whereas taurocholate availabilityprotein binding changes required an albumin-mediated transport model to be used in conjunction with the dispersion model.This study was supported by the National Health and Medical Research Council of Australia and the Dean's MRC (NZ) Fund.     

Models of hepatic elimination: Comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution,enzyme heterogeneity,and systemic recycling on hepatic elimination

The residence time distribution of noneliminated solutes in the liver can be represented by a variety of stochastic models. The dispersion model (closed and mixed boundary conditions), gamma distribution, log normal distribution and normal distribution models were used to describe output concentration-time profiles after bolus injections into the liver of labeled erythrocytes and albumin. The dispersion model and log normal distribution model provide the best representation of the data and give similar estimates of relative dispersion and availability for varying hepatocellular enzyme activity. The availability of solutes eliminated from the liver by first-order kinetics is determined by the residence time distribution of the solute in the liver and not on events occurring in the liver when a uniform enzyme distribution is assumed. Both enzyme heterogeneity (axial or transverse) and hepatocyte permeability may affect solute availability. A more complex model accounting for enzyme distribution and the micromixing of solute within the liver is required for solutes undergoing saturable kinetics.     

Stepwise determination of multicompartment disposition and absorption parameters from extravascular concentration-time data. Application to mesoridazine,flurbiprofen, flunarizine,labetalol, and diazepam

When disposition is monoexponential, extravascular concentrationtime (C, t) data yield both disposition and absorption parameters, the latter via the Wagner-Nelson method or deconvolution which are equivalent. Classically, when disposition is multiexponential, disposition parameters are obtained from intravenous administration and absorption data are obtained from extravascular C, tdata via the Loo-Riegelman or Exact Loo-Riegelman methods or via deconvolution. Thus, in multiexponential disposition one assumes no intrasubject variation in disposition, a hypothesis that has not been proven for most drugs. Based on the classical two and threecompartment open models with central compartment elimination, and using postabsorptive extravascular C, tdata only, we have developed four equations to estimate k₁₀ when disposition is biexponential and two other equations to estimate k₁₀ when disposition is triexponential. The other disposition rate constants are readily obtained without intravenous data. We have analyzed extravascular data of flurbiprofen (12 sets), mesoridazine (20 sets), flunarizine (5 sets), labetalol (9 sets), and diazepam (4 sets). In the case of diazepam intravenous C, tdata were also available for analysis. After disposition parameters had been estimated from the extravascular data the Exact Loo-Riegelman method with the Proost modification was applied to the absorptive extravascular data to obtain A_T/V_p as a function of time. These latter data for each subject and each drug studied were found to befitted by a function indicating either simple firstorder absorption, two consecutive firstorder processes, or zero order absorption. After absorption and disposition parameters had been estimated, for each set of extravascular data analyzed, a reconstruction trend line through the original C, tdata was made. The new methods allow testing of the hypothesis of constancy of disposition with any given drug. There is also a need for new methods of analysis since the majority of drugs have no marketed intravenous formulation, hence the classical methods cannot be applied.     

The effects of dose, route, and repeated dosing on the disposition and kinetics of tetrabromobisphenol A in male F-344 rats.

Studies were conducted to characterize the metabolic and dispositional fate of (14)C-tetrabromobisphenol A (TBBPA)-a commonly used brominated flame retardant, in male Fischer-344 rats. The percent of dose eliminated as total radioactivity in feces at 72 h following three different single oral doses (2, 20, or 200 mg/kg) of (14)C-TBBPA was 90% or greater for all doses. Most of the dose was eliminated in the first 24 h. At 72 h after administration of the highest dose, the amounts of (14)C found in the tissues were minimal (0.2-0.9%). With repeated daily oral doses (20 mg/kg) for 5 or 10 days, the cumulative percent dose eliminated in the feces was 85.1+/-2.8 and 97.9+/-1.1, respectively. In all studies radioactivity recovered in urine was minimal, <2%. Repeated dosing did not lead to retention in tissues. Following iv administration, feces was also the major route of elimination. Following iv administration of TBBPA, the radiolabel found in the blood decreased rapidly and could be described by a biexponential equation, consistent with a two-compartment model. The key calculated kinetic parameters are terminal elimination half-life (t(1/2)beta)=82 min; area under the blood concentration-time curve from time 0 to infinity (AUC)=1440 mug x min/ml; and apparent clearance (CL)=2.44 ml/min. Although readily absorbed from the gut, systemic bioavailability of TBBPA is low (<2%). It is extensively extracted and metabolized by the liver and the metabolites (glucuronides) exported into the bile. About 50% of an oral dose (20 mg/kg) was found in the bile within 2 h. This extensive extraction and metabolism by the liver greatly limits exposure of internal tissues to TBBPA following oral exposures.     

A pharmacokinetic model to differentiate preabsorptive,gut epithelial,and hepatic first-pass metabolism

A combined perfusion/ compartmental pharmacokinetic model has been developed to describe the time course of drugs that are subject to preabsorptive, intestinal epithelial, and hepatic first-pass metabolism. Equations are derived to estimate the fraction of the administered dose which is metabolized at each of the three sites and to establish the limits of the true absorption rate constant. The model is tested using literature data for phenacetin.     

Residence time distributions of solutes in the perfused rat liver using a dispersion model of hepatic elimination: 2. Effect of pharmacological agents,retrograde perfusions,and enzyme inhibition on evans blue,sucrose, water,and taurocholate

The effect of altered physiological conditions on the residence time distributions of sucrose, water, and taurocholate in the rat liver were studied using a bolus injection and quantifying fraction of total outflow per ml-time profiles. Retrograde perfusions increased the residence times of sucrose and water markedly and were associated with very low hepatic availabilities for taurocholate. Resistance by the inlet sinusoids sphincters, which become outlet sphincters during retrograde perfusions, is suggested as the explanation for the observation. Infusions of noradrenaline, propranolol, and lidocaine resulted in relatively small changes in the mean residence times for sucrose and water with no apparent relationship existing between the efficiency number of taurocholate and volumes of either water or sucrose. Taurochenodeoxycholate resulted in an increase in the availability and mean residence time for taurocholate relative to no infusion.This study was supported by the National Health and Medical Research Council of Australia and the Dean's MRC (NZ) Fund.     

A dispersion model of hepatic elimination: 3. Application to metabolite formation and elimination kinetics

A dispersion model of hepatic elimination is presented to describe metabolite formation and elimination kinetics within the liver, consistent with the known physiology and biochemistry of this organ. The model is based on the spread in residence times of blood flowing through the liver. This dispersion model is shown to be more consistent with transient and steady-state data obtained after the single passage of phenacetin and acetaminophen through the liver (both normal and retrograde perfusions) than other models of hepatic elimination. The dispersion model is suitable for the evaluation of enzyme heterogeneity using experimentally obtained metabolite data.     

Conflicting alterations in hepatic expression of CYP3A and enzyme kinetics in rats exposed to 5-fluorouracil: relevance to pharmacokinetics of midazolam

Abstract

1. 5-Fluorouracil (5-FU) is a pyrimidine derivative widely used for the treatment of cancer. In this study, we investigated the effects of 5-FU on the protein expression of hepatic CYP3A and their enzyme activity for metabolizing midazolam (MDZ), a typical substrate of CYP3A, in rat liver microsomes. We also examined the pharmacokinetic behavior of intravenously administered MDZ in rats treated with 5-FU (120?mg/kg, ip).

2. 5-FU was shown to induce hepatic CYP3A2 protein 2?days after administration without changing the expression of CYP3A1/3A23. However, affinity of 5-FU-inducible CYP3A protein to MDZ for its 4- and 1′-hydroxylation was decreased. Furthermore, the susceptibility of MDZ hydroxylation activity to a CYP3A inhibitor differed between the control and 5-FU groups.

3. Pharmacokinetic analysis of the MDZ disposition demonstrated no significant differences in the total clearance (CL_tot) and elimination rate constant (k_e) between the control and 5-FU-treated rats. Lack of alteration in the metabolic clearance of MDZ may be attributable to the induction of CYP3A protein with reduced affinity for the substrate of CYP3A enzymes.

4. Our findings provide novel information regarding the manifestation of inductive and interfering actions of 5-FU toward hepatic CYP3A to help in assessing the pharmacokinetics of CYP3A substrate drugs.