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

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.

Convective transport of highly plasma protein bound drugs facilitates direct penetration into deep tissues after topical application

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT

Many products are applied to human skin for local effects in deeper tissues. Animal studies suggest that deep dermal and/or subcutaneous delivery may be facilitated by both dermal diffusion and transport via the cutaneous vasculature. However, the relationship between the extent and pathways of penetration, drug physicochemical properties and deeper tissue physiology is not well understood.

WHAT THIS STUDY ADDS

We have used a physiologically based pharmacokinetic model to analyze published human cutaneous microdialysis data, complemented by our own in vitro skin penetration studies. We found that convective blood, lymphatic and interstitial flow led to significant deep tissue concentrations for drugs that are highly plasma protein bound. In such cases, deeper tissue concentrations will occur earlier and may be several orders of magnitude greater than predicted by passive dermal diffusion alone.

AIMS

To relate the varying dermal, subcutaneous and muscle microdialysate concentrations found in man after topical application to the nature of the drug applied and to the underlying physiology.

METHODS

We developed a physiologically based pharmacokinetic model in which transport to deeper tissues was determined by tissue diffusion, blood, lymphatic and intersitial flow transport and drug properties. The model was applied to interpret published human microdialysis data, estimated in vitro dermal diffusion and protein binding affinity of drugs that have been previously applied topically in vivo and measured in deep cutaneous tissues over time.

RESULTS

Deeper tissue microdialysis concentrations for various drugs in vivo vary widely. Here, we show that carriage by the blood to the deeper tissues below topical application sites facilitates the transport of highly plasma protein bound drugs that penetrate the skin, leading to rapid and significant concentrations in those tissues. Hence, the fractional concentration for the highly plasma protein bound diclofenac in deeper tissues is 0.79 times that in a probe 4.5 mm below a superficial probe whereas the corresponding fractional concentration for the poorly protein bound nicotine is 0.02. Their corresponding estimated in vivo lag times for appearance of the drugs in the deeper probes were 1.1 min for diclofenac and 30 min for nicotine.

CONCLUSIONS

Poorly plasma protein bound drugs are mainly transported to deeper tissues after topical application by tissue diffusion whereas the transport of highly plasma protein bound drugs is additionally facilitated by convective blood, lymphatic and interstitial transport to deep tissues.

Physiologically based structure of mean residence time

A mean residence time (MRT) is an important pharmacokinetic parameter. To the author's knowledge, however, a physiologically based structure of MRT (thereafter MRT structure) has not been published so far. Primarily this is because MRT structures cannot be identified by traditional pharmacokinetic methods used for the determination of MRT. Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. The MRT structure identified is physiologically meaningful. Accordingly, it seems that the MRT structure identified may contribute to already established knowledge about MRT.

Hepatic pharmacokinetics of cationic drugs in a high-fat emulsion-induced rat model of nonalcoholic steatohepatitis

The hepatic pharmacokinetics of five selected cationic drugs (propranolol, labetalol, metoprolol, antipyrine, and atenolol) was studied in the liver from control rats and from those with high-fat emulsion-induced nonalcoholic steatohepatitis (NASH). Studies were undertaken using an in situ-perfused rat liver and multiple indicator dilution, and outflow data were analyzed with a physiologically based organ pharmacokinetic model. Hepatic extraction (E) was significantly lower in the NASH model, and lipophilicity was the main solute structural determinant of the observed differences in intrinsic elimination clearance (CL(int)) and permeability-surface area product (PS) with pK(a) defining the extent of sequestration in the liver [apparent distribution ratio (K(v))]. The main pathophysiological determinants were liver fibrosis, leading to a decreased PS, liver fat causing an increase in K(v), and an increase in both total liver cytochrome P450 (P450) concentration and P450 isoform expression for Cyp3a2 and Cyp2d2, causing an increase CL(int) in NASH rat livers compared with control livers. Changes in hepatic pharmacokinetics (PS, K(v), CL(int), and E ratio) as a result of NASH were related to the physicochemical properties of drugs (lipophilicity or pK(a)) and hepatic histopathological changes (fibrosis index, steatosis index, and P450 concentration) by stepwise regression analysis. Thus, it appears that in NASH, counteracting mechanisms to facilitate hepatic removal are created in NASH-induced P450 expression, whereas NASH-induced fibrosis and steatohepatitis inhibit E by decreasing hepatocyte permeability through fibrosis and hepatic sequestration.

Effect of adjuvant-induced systemic inflammation in rats on hepatic disposition kinetics of taurocholate

It has been reported that the adjuvant-induced inflammation could affect drug metabolism in liver. Here we further investigated the effect of inflammation on drug transport in liver using taurocholate as a model drug. The hepatic disposition kinetics of [(3)H]taurocholate in perfused normal and adjuvant-treated rat livers were investigated by the multiple indicator dilution technique and data were analyzed by a previously reported hepatobiliary taurocholate transport model. Real-time RT-PCR was also performed to determine the mRNA expression of liver bile salt transporters in normal and diseased livers. The uptake and biliary excretion of taurocholate were impaired in the adjuvant-treated rats as shown by decreased influx rate constant k(in) (0.65 ± 0.09 vs. 2.12 ± 0.30) and elimination rate constant k(be) (0.09 ± 0.02 vs. 0.17 ± 0.04) compared with control rat group, whereas the efflux rate constant k(out) was greatly increased (0.07 ± 0.02 vs. 0.02 ± 0.01). The changes of mRNA expression of liver bile salt transporters were found in adjuvant-treated rats. Hepatic taurocholate extraction ratio in adjuvant-treated rats (0.86 ± 0.05, n = 6) was significantly reduced compared with 0.93 ± 0.05 (n = 6) in normal rats. Hepatic extraction was well correlated with altered hepatic ATP content (r(2) = 0.90). In conclusion, systemic inflammation greatly affects hepatic ATP content/production and associated transporter activities and causes an impairment of transporter-mediated solute trafficking and pharmacokinetics.

Cloud computing and validation of expandable in silico livers

BACKGROUND

In Silico Livers (ISLs) are works in progress. They are used to challenge multilevel, multi-attribute, mechanistic hypotheses about the hepatic disposition of xenobiotics coupled with hepatic responses. To enhance ISL-to-liver mappings, we added discrete time metabolism, biliary elimination, and bolus dosing features to a previously validated ISL and initiated re-validated experiments that required scaling experiments to use more simulated lobules than previously, more than could be achieved using the local cluster technology. Rather than dramatically increasing the size of our local cluster we undertook the re-validation experiments using the Amazon EC2 cloud platform. So doing required demonstrating the efficacy of scaling a simulation to use more cluster nodes and assessing the scientific equivalence of local cluster validation experiments with those executed using the cloud platform.

RESULTS

The local cluster technology was duplicated in the Amazon EC2 cloud platform. Synthetic modeling protocols were followed to identify a successful parameterization. Experiment sample sizes (number of simulated lobules) on both platforms were 49, 70, 84, and 152 (cloud only). Experimental indistinguishability was demonstrated for ISL outflow profiles of diltiazem using both platforms for experiments consisting of 84 or more samples. The process was analogous to demonstration of results equivalency from two different wet-labs.

CONCLUSIONS

The results provide additional evidence that disposition simulations using ISLs can cover the behavior space of liver experiments in distinct experimental contexts (there is in silico-to-wet-lab phenotype similarity). The scientific value of experimenting with multiscale biomedical models has been limited to research groups with access to computer clusters. The availability of cloud technology coupled with the evidence of scientific equivalency has lowered the barrier and will greatly facilitate model sharing as well as provide straightforward tools for scaling simulations to encompass greater detail with no extra investment in hardware.

Computational strategies unravel and trace how liver disease changes hepatic drug disposition

Liver disease changes the disposition properties of drugs, complicating drug therapy management. We present normal and "diseased" versions of an abstract, agent-oriented In Silico Livers (ISLs), and validate their mechanisms against disposition data from perfused normal and diseased rat livers. Dynamic tracing features enabled spatiotemporal tracing of differences in dispositional events for diltiazem and sucrose across five levels, including interactions with representations of lobular microarchitectural features, cells, and intracellular factors that sequester and metabolize. Differences in attributes map to measures of histopathology. We measured disease-causing differences in local, intralobular ISL effects, obtaining until now unavailable views of how and where hepatic drug disposition may differ in normal and diseased rat livers from diltiazem's perspective. Exploration of disposition in less and more advanced stages of disease is feasible. The approach and technology represent an important step toward unraveling the complex changes from normal to disease states and their influences on drug disposition.

In silico representation of the liver-connecting function to anatomy, physiology and heterogeneous microenvironments

We have built a collection of flexible, hepatomimetic, in silico components. Some are agent-based. We assemble them into devices that mimic aspects of anatomic structures and the behaviors of hepatic lobules (the primary functional unit of the liver) along with aspects of liver function. We validate against outflow profiles for sucrose administered as a bolus to isolated, perfused rat livers (IPRLs). Acceptable in silico profiles are experimentally indistinguishable from those of the in situ referent based on similarity measure values. The behavior of these devices is expected to cover expanding portions of the behavior space of real livers and their components. These in silico livers will provide powerful tools for understanding how the liver functions in normal and diseased states, at multiple levels of organization.

Development and application of physiologically based pharmacokinetic-modeling tools to support drug discovery

Physiologically based pharmacokinetic (PBPK) modeling integrates physicochemical (PC) and in vitro pharmacokinetic (PK) data using a mechanistic framework of principal ADME (absorption, distribution, metabolism, and excretion) processes into a physiologically based whole-body model. Absorption, distribution, and clearance are modeled by combining compound-specific PC and PK properties with physiological processes. Thereby, isolated in vitro data can be upgraded by means of predicting full concentration-time profiles prior to animal experiments. The integrative process of PBPK modeling leads to a better understanding of the specific ADME processes driving the PK behavior in vivo, and has the power to rationally select experiments for a more focussed PK project support. This article presents a generic disposition model based on tissue-composition-based distribution and directly scaled hepatic clearance. This model can be used in drug discovery to identify the critical PK issues of compound classes and to rationally guide the optimization path of the compounds toward a viable development candidate. Starting with a generic PBPK model, which is empirically based on the most common PK processes, the model will be gradually tailored to the specifics of drug candidates as more and more experimental data become available. This will lead to a growing understanding of the 'drug in the making', allowing a range of predictions to be made for various purposes and conditions. The stage is set for a wide penetration of PK modeling and simulations to form an intrinsic part of a project starting from lead discovery, to lead optimization and candidate selection, to preclinical profiling and clinical trials.

Physiologically based synthetic models of hepatic disposition

Current physiologically based pharmacokinetic (PBPK) models are inductive. We present an additional, different approach that is based on the synthetic rather than the inductive approach to modeling and simulation. It relies on object-oriented programming. A model of the referent system in its experimental context is synthesized by assembling objects that represent components such as molecules, cells, aspects of tissue architecture, catheters, etc. The single pass perfused rat liver has been well described in evaluating hepatic drug pharmacokinetics (PK) and is the system on which we focus. In silico experiments begin with administration of objects representing actual compounds. Data are collected in a manner analogous to that in the referent PK experiments. The synthetic modeling method allows for recognition and representation of discrete event and discrete time processes, as well as heterogeneity in organization, function, and spatial effects. An application is developed for sucrose and antipyrine, administered separately and together. PBPK modeling has made extensive progress in characterizing abstracted PK properties but this has also been its limitation. Now, other important questions and possible extensions emerge. How are these PK properties and the observed behaviors generated? The inherent heuristic limitations of traditional models have hindered getting meaningful, detailed answers to such questions. Synthetic models of the type described here are specifically intended to help answer such questions. Analogous to wet-lab experimental models, they retain their applicability even when broken apart into sub-components. Having and applying this new class of models along with traditional PK modeling methods is expected to increase the productivity of pharmaceutical research at all levels that make use of modeling and simulation.

Membrane binding proteins are the major determinants for the hepatocellular transmembrane flux of long-chain fatty acids bound to albumin

PURPOSE

The hepatic transmembrane flux of long-chain fatty acids (LCFA) occurs through passive and fatty acid transport protein facilitated processes from blood. The extent that these transport processes can be related to the unbound and protein-bound fractions of LCFA in blood is not clear.

METHODS

We used hepatocyte suspensions, hepatoma monolayers, and perfused rat livers to quantitate the transport of purified [(3)H]palmitate ([(3)H]PA) and 12-(N-methyl)-N-[(7-nitrobenz-2oxa-1,3-diazol-4yl-)amino]octadecanoicacid (12-NBDS) from solutions with a constant unbound LCFA concentration with varying bovine serum albumin (BSA) concentrations and in the presence and absence of antisera raised against cytosolic liver fatty acid binding protein (L-FABP).

RESULTS

In the absence of L-FABP antisera, using an unbound ligand concentration that was adjusted to remain constant at each BSA concentration, hepatocyte [(3)H]PA and 12-NBDS uptake rates increased linearly with an increase in BSA concentration (p < 0.0001). In the presence of L-FABP antisera, [(3)H]PA uptake showed a greater reduction in the presence of 100 muM BSA than 5 muM BSA. The calculated permeability surface area product (PS) confirmed that both unbound and bound fractions of LCFA contributed to the overall flux, but only the PS for the protein-bound fraction was reduced in the presence of L-FABP antisera. In situ rat liver perfusion studies showed that the only rate process for the disposition of [(3)H]PA in the liver inhibited by L-FABP antisera was that for influx, as defined by PS, and that it reduced PS in the perfused liver by 42%.

CONCLUSION

These results suggest that, at physiological albumin concentrations, most of the LCFA uptake is mediated from that bound to albumin by a hepatocyte basolateral membrane transport protein, and uptake of unbound LCFA occurring by passive diffusion contributes a minor component.

Whole body pharmacokinetic models

The aim of the current review is to summarise the present status of physiologically based pharmacokinetic (PBPK) modelling and its applications in drug research, and thus serve as a reference point to people interested in the methodology. The review is structured into three major sections. The first discusses the existing methodologies and techniques of PBPK model development. The second describes some of the most interesting PBPK model implementations published. The final section is devoted to a discussion of the current limitations and the possible future developments of the PBPK modelling approach. The current review is focused on papers dealing with the pharmacokinetics and/or toxicokinetics of medicinal compounds; references discussing PBPK models of environmental compounds are mentioned only if they represent considerable methodological developments or reveal interesting interpretations and/or applications.The major conclusion of the review is that, despite its significant potential, PBPK modelling has not seen the development and implementation it deserves, especially in the drug discovery, research and development processes. The main reason for this is that the successful development and implementation of a PBPK model is seen to require the investment of significant experience, effort, time and resources. Yet, a substantial body of PBPK-related research has been accumulated that can facilitate the PBPK modelling and implementation process. What is probably lagging behind is the expertise component, where the demand for appropriately qualified staff far outreaches availability.

Cationic drug pharmacokinetics in diseased livers determined by fibrosis index, hepatic protein content, microsomal activity, and nature of drug

The disposition kinetics of six cationic drugs in perfused diseased and normal rat livers were determined by multiple indicator dilution and related to the drug physicochemical properties and liver histopathology. A carbon tetrachloride (CCl(4))-induced acute hepatocellular injury model had a higher fibrosis index (FI), determined by computer-assisted image analysis, than did an alcohol-induced chronic hepatocellular injury model. The alcohol-treated group had the highest hepatic alpha(1)-acid glycoprotein, microsomal protein (MP), and cytochrome P450 (P450) concentrations. Various pharmacokinetic parameters could be related to the octanol-water partition coefficient (log P(app)) of the drug as a surrogate for plasma membrane partition coefficient and affinity for MP or P450, the dependence being lower in the CCl(4)-treated group and higher in the alcohol-treated group relative to controls. Stepwise regression analysis showed that hepatic extraction ratio, permeability-surface area product, tissue-binding constant, intrinsic clearance, partition ratio of influx (k(in)) and efflux rate constant (k(out)), and k(in)/k(out) were related to physicochemical properties of drug (log P(app) or pK(a)) and liver histopathology (FI, MP, or P450). In addition, hepatocyte organelle ion trapping of cationic drugs was evident in all groups. It is concluded that fibrosis-inducing hepatic disease effects on cationic drug disposition in the liver may be predicted from drug properties and liver histopathology.

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.

Catheter effects in organ perfusion experiments

In a typical isolated organ perfusion experiment, a substance is injected upstream of an organ and then collected at some distance downstream. To reach the organ from the injection site, and then from the organ to the collector, a solute passes through catheters, usually tubes with circular cross-sections. Catheters cause distortion to the concentration-time profile of the perfusion. In this paper, we analyse catheter distribution kinetics from a mathematical point of view, develop the function most suitable for modeling this distribution and successfully apply this function to experimental data.

Commentary: using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyama in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application.