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

Distribution Clearance: Significance and Underlying Mechanisms

PURPOSE

Evaluation of distribution kinetics is a neglected aspect of pharmacokinetics. This study examines the utility of the model-independent parameter whole body distribution clearance (CLD) in this respect.

METHODS

Since mammillary compartmental models are widely used, CLD was calculated in terms of parameters of this model for 15 drugs. The underlying distribution processes were explored by assessment of relationships to pharmacokinetic parameters and covariates.

RESULTS

The model-independence of the definition of the parameter CLD allowed a comparison of distributional properties of different drugs and provided physiological insight. Significant changes in CLD were observed as a result of drug-drug interactions, transporter polymorphisms and a diseased state.

CONCLUSION

Total distribution clearance CLD is a useful parameter to evaluate distribution kinetics of drugs. Its estimation as an adjunct to the model-independent parameters clearance and steady-state volume of distribution is advocated.

Interpretation of Non-Clinical Data for Prediction of Human Pharmacokinetic Parameters: In Vitro-In Vivo Extrapolation and Allometric Scaling

Extrapolation of pharmacokinetic (PK) parameters from in vitro or in vivo animal to human is one of the main tasks in the drug development process. Translational approaches provide evidence for go or no-go decision-making during drug discovery and the development process, and the prediction of human PKs prior to the first-in-human clinical trials. In vitro-in vivo extrapolation and allometric scaling are the choice of method for projection to human situations. Although these methods are useful tools for the estimation of PK parameters, it is a challenge to apply these methods since underlying biochemical, mathematical, physiological, and background knowledge of PKs are required. In addition, it is difficult to select an appropriate methodology depending on the data available. Therefore, this review covers the principles of PK parameters pertaining to the clearance, volume of distribution, elimination half-life, absorption rate constant, and prediction method from the original idea to recently developed models in order to introduce optimal models for the prediction of PK parameters.

Trospium chloride is absorbed from two intestinal "absorption windows" with different permeability in healthy subjects

Intestinal P-glycoprotein is regio-selectively expressed and is a high affinity, low capacity efflux carrier for the cationic, poorly permeable trospium. Organic cation transporter 1 (OCT1) provides lower affinity but higher capacity for trospium uptake. To evaluate regional intestinal permeability, absorption profiles after gastric infusion of trospium chloride (30mg/250ml=[I]₂) for 6h and after swallowing 30mg immediate-release tablets in fasted and fed healthy subjects, were evaluated using an inverse Gaussian density function to model input rate and mean absorption time (MAT). Trospium chloride was slowly absorbed (MAT ∼10h) after gastric infusion involving two processes with different input rates, peaking at about 3h and 7h. Input rates and MAT were influenced by dosage form and meal. In conclusion, trospium is absorbed from two "windows" located in the jejunum and cecum/ascending colon, whose uptake capacity might result from local abundance and functional interplay of P-glycoprotein and OCT1.

A new parameter estimation method for solute transport in a column

To study contaminant transport in groundwater, an essential requirement is robust and accurate estimation of the transport parameters such as dispersion coefficient. The commonly used inverse error function method (IEFM) may cause unacceptable errors in dispersion coefficient estimation using the breakthrough curves (BTCs) data. We prove that the random error in the measured concentrations, which might be described by a normal distribution, would no longer follow the normal distribution after the IEFM transformation. In this study, we proposed a new method using the weighted least squares method (WLSM) to estimate the dispersion coefficient and velocity of groundwater. The weights were calculated based on the slope of the observed BTCs. We tested the new method against other methods such as genetic algorithm and CXTFIT program and found great agreement. This new method acknowledged different characteristics of solute transport at early, intermediate, and late time stages and divided BTCs into three sections for analysis. The developed method was applied to interpret three column tracer experiments by introducing continuous, constant-concentration of sodium chloride (NaCl) into columns filled with sand, gravel, and sand-gravel media. This study showed that IEFM performed well only when the observed data points were located in the linear (intermediate time) section of BTCs; it performed poorly when data points were in the early and late time stages. The new WLSM method, however, performed well for data points scattering over the entire BTCs and appeared promising in parameter estimation for solute transport in a column.

Hepatocellular necrosis, fibrosis and microsomal activity determine the hepatic pharmacokinetics of basic drugs in right-heart-failure-induced liver damage

PURPOSE

To explore how liver damage arising from cardio-hepatic syndromes in RHF affect the hepatic pharmacokinetics of basic drugs.

METHODS

The hepatic pharmacokinetics of five selected basic drugs with different physicochemical properties were studied in IPRL from control rats and rats with RHF. Hepatic pharmacokinetic modelling was performed with a two-phase physiologically-based organ pharmacokinetic model with the vascular space and dispersion evaluated with the MID technique. The liver damage arising from RHF was assessed by changes in liver biochemistry and histopathology. The expression of various CYP isoforms was evaluated by real-time RT-PCR analysis.

RESULTS

Four of the five basic drugs had a significantly lower E in RHF rat livers compared to the control rat livers. Hepatic pharmacokinetic analysis showed that both the CL int and PS were significantly decreased in the RHF rat livers. Stepwise regression analysis showed that the alterations in the pharmacokinetic parameters (E, CL int and PS) can be correlated to the observed histopathological changes (NI, CYP concentration and FI) as well as to the lipophilicity of the basic drugs (logP app).

CONCLUSIONS

Serious hepatocellular necrosis and fibrosis induced by RHF affects both hepatic microsomal activity and hepatocyte wall permeability, leading to significant impairment in the hepatic pharmacokinetics of basic drugs.

A model for transit time distributions through organs that accounts for fractal heterogeneity

It has been shown that density functions of organ transit time distributions of vascular markers (washout curves) are characterized by a power-law tail, reflecting the fractal nature of the vascular network. Yet, thus far, no closed-form model is available that can be fitted to such organ outflow data. Here we propose a model that accounts for the existing data. The model is a continuous mixture of inverse Gaussian densities, implying flow heterogeneity in the organ. It has been fitted to outflow data from the rabbit heart and rat liver. The power-law decay with exponent -3 observed in the heart, corresponds to an intra-organ flow distribution with a relative dispersion of about 35%.

A physiologically based model of hepatic ICG clearance: interplay between sinusoidal uptake and biliary excretion

Although indocyanine green (ICG) has long been used for the assessment of liver function, the respective roles of sinusoidal uptake and canalicular excretion in determining hepatic ICG clearance remain unclear. Here this issue was addressed by incorporating a liver model into a minimal physiological model of ICG disposition that accounts of the early distribution phase after bolus injection. Arterial ICG concentration-time data from awake dogs under control conditions and from the same dogs while anesthetized with 3.5% isoflurane were subjected to population analysis. The results suggest that ICG elimination in dogs is uptake limited since it depends on hepatocellular uptake capacity and on biliary excretion but not on hepatic blood flow. Isoflurane caused a 63% reduction in cardiac output and a 33% decrease in the ICG biliary excretion rate constant (resulting in a 26% reduction in elimination clearance) while leaving unchanged the sinusoidal uptake rate. The terminal slope of the concentration-time curve, K, correlated significantly with elimination clearance. The model could be useful for assessing the functions of sinusoidal and canalicular ICG transporters.

Pharmacokinetic analysis of continuous erythropoietin receptor activator disposition in adult sheep using a target-mediated, physiologic recirculation model and a tracer interaction methodology

The pharmacokinetics (PK) of continuous erythropoietin receptor activator (CERA), a PEGylated erythropoietin (EPO) derivative, was studied in sheep after bone marrow (BM) busulfan ablation by using a receptor-based recirculation model and tracer interaction method (TIM) experiments. The nontracer CERA component of the TIM was analyzed using a noncompartmental approach. In contrast to EPO elimination that is linear after the BM ablation, CERA elimination remains nonlinear. After busulfan treatment, initial EPO receptors (EPOR) normalized production rate constant, EPOR degradation rate constant, and CERA-EPOR complex internalization rate constant decreased (p < 0.01), whereas no change in CERA/EPOR equilibrium dissociation constant was detected (p > 0.05). After BM ablation, noncompartmental analysis showed that CERA-PK parameters underwent 1) a decrease in plasma clearance (p < 0.01); 2) a concomitant increase in elimination half-life and mean residence time; and 3) no significant change in volume of distribution, distribution half-life, or distributional clearance (p > 0.05). These results suggest that CERA elimination is mediated through saturable hematopoietic and nonhematopoietic EPOR pathways, with possible contribution of another EPOR-independent pathway(s). Compared with the nonhematopoietic EPOR population, the hematopoietic receptors have similar affinity to CERA but are significantly more involved in CERA's in vivo elimination. The saturable nature of the nonerythropoietic, non-BM pathway(s) for CERA in contrast to EPO predicts two fundamental differences: 1) an increasing fraction of CERA is used for erythropoiesis for increasing concentrations; and 2) the clearance of CERA becomes more limited for increasing concentrations. Taken together, these differences favor a more efficacious and prolonged action for CERA.

Drug structure-transport relationships

Malcolm Rowland has greatly facilitated an understanding of drug structure–pharmacokinetic relationships using a physiological perspective. His view points, covering a wide range of activities, have impacted on my own work and on my appreciation and understanding of our science. This overview summarises some of our parallel activities, beginning with Malcolm’s work on the pH control of amphetamine excretion, his work on the disposition of aspirin and on the application of clearance concepts in describing the disposition of lidocaine. Malcolm also spent a considerable amount of time developing principles that define solute structure and transport/pharmacokinetic relationships using in situ organ studies, which he then extended to involve the whole body. Together, we developed a physiological approach to studying hepatic clearance, introducing the convection–dispersion model in which there was a spread in blood transit times through the liver accompanied by permeation into hepatocytes and removal by metabolism or excretion into the bile. With a range of colleagues, we then further developed the model and applied it to various organs in the body. One of Malcolm’s special interests was in being able to apply this knowledge, together with an understanding of physiological differences in scaling up pharmacokinetics from animals to man. The description of his many other activities, such as the development of clearance concepts, application of pharmacokinetics to the clinical situation and using pharmacokinetics to develop new compounds and delivery systems, has been left to others.

Sulphonylurea physicochemical-pharmacokinetic relationships in the pancreas and liver

This study examined the physicochemical-pharmacokinetic relationships for the sulphonylureas in the perfused rat pancreas and liver. Multiple indicator dilution studies were conducted with bolus injections of tolbutamide, chlorpropamide, gliclazide, glipizide, glibenclamide and glimepiride, and a reference marker albumin, in the perfused pancreas and liver. Individual solute pharmacokinetics were analysed using nonparametric moment analysis and nonlinear regression assuming a physiologically based pharmacokinetic model. All solutes had similar shaped outflow concentration-time profiles in both the pancreas and liver, but varied in extraction. Negligible drug extraction was evident in the pancreas. Hepatic extraction ranged from 0.03 (tolbutamide) to 0.52 (glibenclamide) and could be related to solute lipophilicity and perfusate protein binding. The sulphonylurea mean transit times in both the pancreas and liver varied four- and ninefold respectively and were related to the lipophilicity and perfusate protein binding of the drug. The permeability surface area product of sulphonylureas from the perfusate into the organs were greater in the liver and were mainly determined by lipophilicity (pancreas, r2 = 0.89; liver, r2 = 0.80). The distribution of the sulphonylureas in both the perfused pancreas and perfused liver was dependent on their lipophilicity and perfusate protein binding.

A minimal physiological model of thiopental distribution kinetics based on a multiple indicator approach

Currently available models of thiopental disposition kinetics using only plasma concentration-time data neglect the influence of intratissue diffusion and provide no direct information on tissue partitioning in individual subjects. Our approach was based on a lumped-organ recirculatory model that has recently been applied to unbound compounds. The goal was to find the simplest model that accounts for the heterogeneity in tissue partition coefficients and accurately describes initial distribution kinetics of thiopental in dogs. To ensure identifiability of the underlying axially distributed capillary-tissue exchange model, simultaneously measured disposition data of the vascular indicator, indocyanine green, and the marker of whole body water, antipyrine, were analyzed together with those of thiopental. A model obtained by grouping the systemic organs in two subsystems containing fat and nonfat tissues, successfully described all data and allowed an accurate estimation of model parameters. The estimated tissue partition coefficients were in accordance with those measured in rats. Because of the effect of tissue binding, the diffusional equilibration time characterizing intratissue distribution of thiopental is longer than that of antipyrine. The approach could potentially be used in clinical pharmacokinetics and could increase our understanding of the effect of obesity on the disposition kinetics of lipid-soluble drugs.

Advanced pharmacokinetic models based on organ clearance, circulatory, and fractal concepts

Three advanced models of pharmacokinetics are described. In the first class are physiologically based pharmacokinetic models based on in vitro data on transport and metabolism. The information is translated as transporter and enzyme activities and their attendant heterogeneities into liver and intestine models. Second are circulatory models based on transit time distribution and plasma concentration time curves. The third are fractal models for nonhomogeneous systems and non-Fickian processes are presented. The usefulness of these pharmacokinetic models, with examples, is compared.

Circulatory transport and capillary-tissue exchange as determinants of the distribution kinetics of inulin and antipyrine in dog

A pharmacokinetic model was developed to estimate physiologically meaningful parameters of distribution kinetics from plasma concentration-time data. The model is based on simultaneously measured disposition curves of drug and vascular marker. Employing residence time distribution theory, a recirculatory model with two subsystems, the pulmonary and systemic circulation, was constructed. In addition to intravascular mixing, the axially distributed model of the systemic circulation accounts for transcapillary transport of solutes, quantified by permeability-surface area product (PS) and diffusional equilibration time. Parameters of ICG, inulin, and antipyrine were estimated from disposition data obtained in awake dogs under control conditions and during an isoproterenol infusion or moderate hypovolemia. Results suggest that distribution kinetics is (1) governed by extravascular diffusion and (2) its dependency on cardiac output decreases with increasing diffusional resistance. Hemorrhage decreased the effective PS of inulin. In conclusion, this novel mechanistic model effectively described both the permeability-limited distribution of inulin into interstitial fluid and the flow-limited distribution of antipyrine into total body water and might be useful for other drugs.

Residence Time Dispersion as a General Measure of Drug Distribution Kinetics: Estimation and Physiological Interpretation

PURPOSE

To evaluate distribution kinetics of drugs by the relative dispersion of disposition residence time and demonstrate its uses, interpretation and limitations.

MATERIALS AND METHODS

The relative dispersion was estimated from drug disposition data of inulin and digoxin fitted by three-exponential functions, and calculated from compartmental parameters published for fentanyl and alfentanil. An interpretation is given in terms of a lumped organs model and the distributional equilibration process in a noneliminating system.

RESULTS

As a measure of the deviation from mono-exponential disposition (one-compartment behavior), the relative dispersion provides information on the distribution kinetics of drugs, i.e., diffusion-limited distribution or slow tissue binding, without assuming a specific structural model. It also defines the total distribution clearance which has a clear physical meaning.

CONCLUSION

The residence time dispersion is a model-independent measure that can be used to characterize the distribution kinetics of drugs and to reveal the influence of disease states. It can be estimated with high precision from drug disposition data.

Characterization of the Physiological Spaces and Distribution of Tolbutamide in the Perfused Rat Pancreas

PURPOSE

To set up and validate a viable perfused rat pancreas model suitable for pharmacokinetic studies.

MATERIALS AND METHODS

We setup and conducted multiple indicator dilution studies in the single pass perfused rat pancreas. The distribution of the reference markers [99mTc]-red blood cells (RBC), [14C]-sucrose, and [3H]-water, and tolbutamide were analysed using both non-parametric and parametric methods.

RESULTS

The perfusion preparation was observed to be viable by oxygen consumption, outflow perfusate pH, lactate release and insulin release in response to glucose. Parametric analysis of the outflow profiles suggested that the transport of water and tolbutamide from the vascular space was permeability limited. Parametric and nonparametric estimates of Vd for RBC and sucrose were similar and were 0.14+/-0.01, 0.15 0.005 and 0.35+/-0.01 ml/g. The parametric estimate for water, 1.04+/-0.05 ml/g was greater than the nonparametric estimate, 0.89+/-0.02 ml/g. The multiple indicator dilution method Vd of tolbutamide of 0.75+0.08 ml/g was similar to the reported value of 0.73+/-0.04 ml/g estimated by tissue partitioning studies.

CONCLUSIONS

A viable single pass pancreas perfusion model was established and applied to define distribution spaces of reference markers and the distribution kinetics of tolbutamide.

Mechanistic modeling of digoxin distribution kinetics incorporating slow tissue binding

This study aims to develop a mechanistic pharmacokinetic model that accounts for the kinetics of tissue binding in order to evaluate the effect of slow binding of digoxin to skeletal muscular Na(+)/K(+)-ATPase in humans. The approach is based on a minimal circulatory model with a systemic transit time density function that accounts for vascular mixing, transcapillary permeation and extravascular binding of the drug. The model parameters were estimated using previously published disposition data of digoxin in healthy volunteers and physiological distribution volumes taken from the literature. A time constant of the binding process of 34min was estimated indicating that receptor binding and not permeation clearance is the rate-limiting step of the distribution process. Model simulations suggest that up- or downregulation of sodium pumps, typically observed under physiological or pathophysiological conditions, could be detected with this method. The model allows a quantitative prediction of the effect of changes in skeletal muscular sodium pump activity on plasma levels of digoxin.

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.

Dermal capillary clearance: physiology and modeling

Substances applied to the skin surface may permeate deeper tissue layers and pass into the body's systemic circulation by entering blood or lymphatic vessels in the dermis. The purpose of this review is an in-depth analysis of the dermal clearance/exchange process and its constituents: transport through the interstitium, permeability of the microvascular barrier and removal via the circulation. We adapt an 'engineering' viewpoint with emphasis on quantifying the dermal microcirculatory physiology, providing the theoretical framework for the physics of key transport processes and reviewing the available computational clearance models in a comparative manner. Selected experimental data which may serve as valuable input to modeling attempts are also reported.

Reduced hepatic extraction of palmitate in steatosis correlated to lower level of liver fatty acid binding protein

Nonalcoholic fatty liver disease is the most common of all liver diseases. The hepatic disposition [(3)H]palmitate and its low-molecular-weight metabolites in perfused normal and steatotic rat liver were studied using the multiple indicator dilution technique and a physiologically based slow diffusion/bound pharmacokinetic model. The steatotic rat model was established by administration of 17 alpha-ethynylestradiol to female Wistar rats. Serum biochemistry markers and histology of treated and normal animals were assessed and indicated the presence of steatosis in the treatment group. The steatotic group showed a significantly higher alanine aminotransferase-to-aspartate aminotransferase ratio, lower levels of liver fatty acid binding protein and cytochrome P-450, as well as microvesicular steatosis with an enlargement of sinusoidal space. Hepatic extraction for unchanged [(3)H]palmitate and production of low-molecular-weight metabolites were found to be significantly decreased in steatotic animals. Pharmacokinetic analysis suggested that the reduced extraction and sequestration for palmitate and its metabolites was mainly attributed to a reduction in liver fatty acid binding protein in steatosis.

Disposition kinetics of propranolol isomers in the perfused rat liver

The aim of this study was to define the determinants of the linear hepatic disposition kinetics of propranolol optical isomers using a perfused rat liver. Monensin was used to abolish the lysosomal proton gradient to allow an estimation of propranolol ion trapping by hepatic acidic vesicles. In vitro studies were used for independent estimates of microsomal binding and intrinsic clearance. Hepatic extraction and mean transit time were determined from outflow-concentration profiles using a nonparametric method. Kinetic parameters were derived from a physiologically based pharmacokinetic model. Modeling showed an approximate 34-fold decrease in ion trapping following monensin treatment. The observed model-derived ion trapping was similar to estimated theoretical values. No differences in ion-trapping values was found between R(+)- and S(-)-propranolol. Hepatic propranolol extraction was sensitive to changes in liver perfusate flow, permeability-surface area product, and intrinsic clearance. Ion trapping, microsomal and nonspecific binding, and distribution of unbound propranolol accounted for 47.4, 47.1, and 5.5% of the sequestration of propranolol in the liver, respectively. It is concluded that the physiologically more active S()-propranolol differs from the R(+)-isomer in higher permeability-surface area product, intrinsic clearance, and intracellular binding site values.

Ion-trapping, microsomal binding, and unbound drug distribution in the hepatic retention of basic drugs

This study investigated the relative contribution of ion-trapping, microsomal binding, and distribution of unbound drug as determinants in the hepatic retention of basic drugs in the isolated perfused rat liver. The ionophore monensin was used to abolish the vesicular proton gradient and thus allow an estimation of ion-trapping by acidic hepatic vesicles of cationic drugs. In vitro microsomal studies were used to independently estimate microsomal binding and metabolism. Hepatic vesicular ion-trapping, intrinsic elimination clearance, permeability-surface area product, and intracellular binding were derived using a physiologically based pharmacokinetic model. Modeling showed that the ion-trapping was significantly lower after monensin treatment for atenolol and propranolol, but not for antipyrine. However, no changes induced by monensin treatment were observed in intrinsic clearance, permeability, or binding for the three model drugs. Monensin did not affect binding or metabolic activity in vitro for the drugs. The observed ion-trapping was similar to theoretical values estimated using the pHs and fractional volumes of the acidic vesicles and the pKa values of drugs. Lipophilicity and pKa determined hepatic drug retention: a drug with low pKa and low lipophilicity (e.g., antipyrine) distributes as unbound drug, a drug with high pKa and low lipophilicity (e.g., atenolol) by ion-trapping, and a drug with a high pKa and high lipophilicity (e.g., propranolol) is retained by ion-trapping and intracellular binding. In conclusion, monensin inhibits the ion-trapping of high pKa basic drugs, leading to a reduction in hepatic retention but with no effect on hepatic drug extraction.

Kinetic analysis of pulmonary neutrophil retention in vivo using the multiple-indicator-dilution technique

Multiple-indicator-dilution experiments were performed in the lungs of 13 anesthetized dogs by simultaneous bolus injection of 111In-labeled neutrophils, 51Cr-labeled red blood cells, and Evans blue-labeled albumin. Concomitant counts of unlabeled neutrophils were similar in pulmonary artery and aortic blood samples, demonstrating a dynamic balance across the lungs in the physiological state. Outflow profiles of labeled neutrophils were analyzed on the basis of a recirculatory pharmacokinetic model of labeled albumin. The outflow profiles of the recovered neutrophils were composed of a throughput component of circulating neutrophils and a component of reversibly marginated neutrophils. They were interpreted by a model incorporating neutrophil margination (transfer coefficient = 0.195 +/- 0.081 s-1), rapid demargination (0.054 +/- 0.027 s-1), and transfer to a slow marginated pool (0.023 +/- 0.018 s-1). It will be interesting to apply the analysis in future studies aimed at determining whether it could be a useful research tool to investigate the interactions between the pulmonary endothelium and neutrophils in physiological and diseased states.

Fatty acid binding protein is a major determinant of hepatic pharmacokinetics of palmitate and its metabolites

Disposition kinetics of [(3)H]palmitate and its low-molecular-weight metabolites in perfused rat livers were studied using the multiple-indicator dilution technique, a selective assay for [(3)H]palmitate and its low-molecular-weight metabolites, and several physiologically based pharmacokinetic models. The level of liver fatty acid binding protein (L-FABP), other intrahepatic binding proteins (microsomal protein, albumin, and glutathione S-transferase) and the outflow profiles of [(3)H]palmitate and metabolites were measured in four experimental groups of rats: 1) males; 2) clofibrate-treated males; 3) females; and 4) pregnant females. A slow-diffusion/bound model was found to better describe the hepatic disposition of unchanged [(3)H]palmitate than other pharmacokinetic models. The L-FABP levels followed the order: pregnant female > clofibrate-treated male > female > male. Levels of other intrahepatic proteins did not differ significantly. The hepatic extraction ratio and mean transit time for unchanged palmitate, as well as the production of low-molecular-weight metabolites of palmitate and their retention in the liver, increased with increasing L-FABP levels. Palmitate metabolic clearance, permeability-surface area product, retention of palmitate by the liver, and cytoplasmic diffusion constant for unchanged [(3)H]palmitate also increased with increasing L-FABP levels. It is concluded that the variability in hepatic pharmacokinetics of unchanged [(3)H]palmitate and its low-molecular-weight metabolites in perfused rat livers is related to levels of L-FABP and not those of other intrahepatic proteins.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-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 bloodflow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Distribution kinetics of solutes in the isolated in-situ perfused rat head using the multiple indicator dilution technique and a physiological two-barrier model

The purpose of this study was to determine the pharmacokinetics of [14C]diclofenac, [14C]salicylate and [3H]clonidine using a single pass rat head perfusion preparation. The head was perfused with 3-[N-morpholino] propane-sulfonic acid-buffered Ringer's solution. 99mTc-red blood cells and a drug were injected in a bolus into the internal carotid artery and collected from the posterior facial vein over 28 min. A two-barrier stochastic organ model was used to estimate the statistical moments of the solutes. Plasma, interstitial and cellular distribution volumes for the solutes ranged from 1.0 mL (diclofenac) to 1.6 mL (salicylate), 2.0 mL (diclofenac) to 4.2 mL (water) and 3.9 mL (salicylate) to 20.9 mL (diclofenac), respectively. A comparison of these volumes to water indicated some exclusion of the drugs from the interstitial space and salicylate from the cellular space. Permeability-surface area (PS) products calculated from plasma to interstitial fluid permeation clearances (CL(PI)) (range 0.02-0.40 mL s(-1)) and fractions of solute unbound in the perfusate were in the order: diclofenac > salicylate > clonidine > sucrose (from 41.8 to 0.10 mL s(-1)). The slow efflux of diclofenac, compared with clonidine and salicylate, may be related to its low average unbound fraction in the cells. This work accounts for the tail of disposition curves in describing pharmacokinetics in the head.

Skeletal muscle kinetics of propofol in anaesthetized sheep: effect of altered muscle blood flow

1. The kinetics of propofol were studied in vivo in a skeletal muscle bed of the hindlimb of the anaesthetized sheep at normal and low rates of blood flow. 2. Propofol kinetics in muscle were determined during and after a 20-min i.v. infusion of propofol (10 mg min-1) via paired arteriofemoral venous blood sampling. One-and-a-half hours later, the study was repeated but with a concurrent left femoral artery infusion of adrenaline (0.004 mg min-1) to lower the muscle blood flow by vasoconstriction. 3. Muscle blood flow in the low flow state was 28% of that in the normal state. The kinetics were poorly described by a single flow-limited compartment model, but were better described by a model with a flow-limited component and a deeper distribution component. There were no significant differences in muscle retention of propofol between normal and low flow states. 4. There was an apparent arteriovenous shunt of approximately 24% of total muscle blood flow for the low flow state, but not for the normal blood flow state.

Kinetics of propranolol uptake in muscle, skin, and fat of the isolated perfused rat hindlimb

The tissue distribution kinetics of a highly bound solute, propranolol, was investigated in a heterogeneous organ, the isolated perfused limb, using the impulse-response technique and destructive sampling. The propranolol concentration in muscle, skin, and fat as well as in outflow perfusate was measured up to 30 min after injection. The resulting data were analysed assuming (1) vascular, muscle, skin and fat compartments as well mixed (compartmental model) and (2) using a distributed-in-space model which accounts for the noninstantaneous intravascular mixing and tissue distribution processes but consists only of a vascular and extravascular phase (two-phase model). The compartmental model adequately described propranolol concentration-time data in the three tissue compartments and the outflow concentration-time curve (except of the early mixing phase). In contrast, the two-phase model better described the outflow concentration-time curve but is limited in accounting only for the distribution kinetics in the dominant tissue, the muscle. The two-phase model well described the time course of propranolol concentration in muscle tissue, with parameter estimates similar to those obtained with the compartmental model. The results suggest, first that the uptake kinetics of propranolol into skin and fat cannot be analysed on the basis of outflow data alone and, second that the assumption of well-mixed compartments is a valid approximation from a practical point of view (as, e.g., in physiological based pharmacokinetic modelling). The steady-state distribution volumes of skin and fat were only 16 and 4%, respectively, of that of muscle tissue (16.7 ml), with higher partition coefficient in fat (6.36) than in skin (2.64) and muscle (2.79).

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.

Use of a single-pass in situ perfused rat hindlimb to study tissue distribution kinetics. Method development and experiences with Evans blue

A single-pass in situ rat hindlimb preparation has been developed as an alternative to the isolated perfused preparation to study tissue drug distribution kinetics with minimal disturbance of the animal physiology. Evans blue (EB), a vascular marker, was administered (in saline or plasma) as a bolus into the femoral artery, and the total outflow blood was collected at timed intervals from the corresponding femoral vein. Donor blood was infused through the jugular vein at a rate that matched the loss. No changes in the blood flow or development of edema were observed. The outflow profile was characterized using statistical moments. Regardless of the injected solution, the estimated vascular volume (10% of the hindlimb wet weight) was higher than that reported for the isolated rat hindlimb (4.1%) but closer to the in vivo blood volume (6.8-8.1% of body weight for 250-g rat) and sum of vascular volumes of its composite tissues (6.9% of tissue weights). The large normalized variance (CV(2)) of the outflow (2.2+/-0.1) confirms the known heterogeneity of the hindlimb. Entrapment in the limb (approximately 4%) and escape to the rest of the body could explain the incomplete recovery (79-89%) of the dye.

An isolated in-situ rat head perfusion model for pharmacokinetic studies

PURPOSE

To develop a viable, single pass rat head perfusion model useful for pharmacokinetic studies.

METHODS

A viable rat head preparation, perfused with MOPS-buffered Ringer's solution, was developed. Radiolabelled markers (red blood cells, water and sucrose) were injected in a bolus into the internal carotid artery and collected from the posterior facial vein over 28 minutes. The double inverse Gaussian function was used to estimate the statistical moments of the markers.

RESULTS

The viability of the perfusion was up to one hour, with optimal perfusate being 2% bovine serum albumin at 37 degrees C, pH 7.4. The distribution volumes for red blood cells, sucrose and water (from all studies, n = 18) were 1.0 +/- 0.3 ml, 6.4 +/- 4.2 ml and 18.3 +/- 11.9 ml, respectively. A high normalised variance for red blood cells (3.1 +/- 2.0) suggests a marked vascular heterogeneity. A higher normalised variance for water (6.4 +/- 3.3) is consistent with additional diffusive/permeability limitations.

CONCLUSIONS

Analysis of the physiological parameters derived from the moments suggested that the kinetics of the markers were consistent with distribution throughout the head (weight 25 g) rather than just the brain (weight 2 g). This model should assist in studying solute pharmacokinetics in the head.

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).

The anomalous pharmacokinetics of amiodarone explained by nonexponential tissue trapping

Conventional pharmacokinetic (PK) concepts fail to describe the long-term pharmacokinetics of the extremely cationic amphiphilic drug amiodarone. A nonclassical model based on the phenomenon of trapping at tissue binding sites with very long release times is presented, which implies that a volume of distribution and a steady-state level cannot be defined. In agreement with clinical PK data available in the literature, the model well describes not only single-dose disposition curves but also the persistently increasing plasma concentration-time curve during long-term treatment (up to 5 years) and the washout curve following cessation of therapy. The novel aspect is a long-tailed tissue residence time distribution which is incorporated into a recirculatory model leaving the initial distribution process and the clearance concept unchanged. The underlying theoretical approach, which is known as "strange or anomalous" kinetics in physical sciences, and the fractal scaling property of the model may enhance our understanding of the PK of extremely hydrophobic xenobiotics.

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.

Cellular pharmacokinetics: effects of cytoplasmic diffusion and binding on organ transit time distribution

Distribution between well-stirred compartments is the classical paradigm in pharmacokinetics. Also in capillary-issue exchange modeling a barrier-limited approach is mostly adopted. As a consequence of tissue binding, however, drug distribution cannot be regarded as instantaneous even at the cellular level and the distribution process consists of at least two components: transmembrane exchange and cytoplasmic transport. Two concepts have been proposed for the cytoplasmic distribution process of hydrophobic or amphipathic molecules, (i) slowing of diffusion due to instantaneous binding to immobile cellular structures and (ii) slow binding after instantaneous distribution throughout the cytosol. The purpose of this study was to develop a general approach for comparing both models using a stochastic model of intra- and extravascular drug distribution. Criteria for model discrimination are developed using the first three central moments (mean, variance, and skewness) of the cellular residence time and organ transit time distribution, respectively. After matching the models for the relative dispersion the remaining differences in relative skewness are predicted, discussing the relative roles of membrane permeability, cellular binding and cytoplasmic transport. It is shown under which conditions the models are indistinguishable on the basis of venous organ outflow concentration-time curves. The relative dispersion of cellular residence times is introduced as a model-independent measure of cytoplasmic equilibration kinetics, which indicates whether diffusion through the cytoplasm is rate limiting. If differences in outflow curve shapes (their relative skewness) cannot be detected, independent information on binding and/or diffusion kinetics is necessary to avoid model misspecification. The method is applied to previously published hepatic outflow data of enalaprilat, triiodothyronine, and diclofenac. It provides a general framework for the modeling of cellular pharmacokinetics.

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.

Diffusion-limited, but not perfusion-limited, compartmental models describe cerebral nitrous oxide kinetics at high and low cerebral blood flows

This study aimed to evaluate the relative importance of diffusion-limited vs. perfusion-limited mechanisms in compartmental models of blood-tissue inert gas exchange in the brain. Nitrous oxide concentrations in arterial and brain efferent blood were determined using gas chromatographic analysis during and after 15 min of nitrous oxide inhalation, at separate low and high steady states of cerebral blood flow (CBF) in five sheep under halothane anesthesia. Parameters and model selection criteria of various perfusion- or diffusion-limited structural models of the brain were estimated by simultaneous fitting of the models to the mean observed brain effluent nitrous oxide concentration for both blood flow states. Perfusion-limited models returned precise, credible estimates of apparent brain volume but fit the low CBF data poorly. Diffusion-limited models provided better overall fit of the data, which was best described by exchange of nitrous oxide between a perfusion-limited brain compartment and an unperfused compartment. In individual animals, during the low CBF state, nitrous oxide kinetics displayed either fast, perfusion-limited behavior or slow, diffusion-limited behavior. This variability was exemplified in the different parameter estimates of the diffusion limited models fitted to the individual animal data sets. Results suggest that a diffusion limitation contributes to cerebral nitrous oxide kinetics.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

BACKGROUND/AIMS

Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system. The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats.

METHODS

A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data.

RESULTS

The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats.

CONCLUSIONS

These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing. The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

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.

Pulmonary disposition of lipophilic amine compounds in the isolated perfused rabbit lung

We measured the pulmonary venous concentration vs. time curves for [3H]alfentanil, [14C]lidocaine, and [3H]codeine after the bolus injection of each of these lipophilic amine compounds (LAC) and a vascular-reference indicator (fluorescein isothiocyanate-dextran) into the pulmonary artery of isolated perfused rabbit lungs. A range of flows and perfusate albumin concentrations was studied. To evaluate the information content of the data, we developed a kinetic model describing the pulmonary disposition of these LAC that was based on indicator dilution theory, and we sought a robust approach for interpreting the estimated model parameters. We found that the distribution of the kinetic model rate constants of the lipophilic amine-tissue interactions can be described by alpha, H, and psi, where alpha is a measure of the capacity of the rapidly equilibrating interactions between the lipophilic amine and the tissue; H is a measure of the equilibrium capacity of the slowly equilibrating interactions between the lipophilic amine and the tissue; and psi is the mean sojourn time. The values of alpha, H, and psi were 0.8 +/- 0.1 (SE), 0.6 +/- 0.1, and 1.6 +/- 0.5 s; 1.9 +/- 0.1, 5.3 +/- 0.4, and 5.6 +/- 0.5 s; and 1.1 +/- 0.1, 9.8 +/- 0.4, and 4.7 +/- 0.2 s for alfentanil, lidocaine, and codeine, respectively. These values for alpha, H, and psi reveal the relative dominance of the slowly equilibrating interactions for lidocaine and codeine in comparison with alfentanil. This approach to data analysis may have utility for the potential use of LAC to reveal and to quantify changes in lung tissue composition associated with lung disease.

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.