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

Hepatic OATP1B zonal distribution: Implications for rifampicin-mediated drug-drug interactions explored within a PBPK framework

OATP1B facilitates the uptake of xenobiotics into hepatocytes and is a prominent target for drug-drug interactions (DDIs). Reduced systemic exposure of OATP1B substrates has been reported following multiple-dose rifampicin; one explanation for this observation is OATP1B induction. Non-uniform hepatic distribution of OATP1B may impact local rifampicin tissue concentrations and rifampicin-mediated protein induction, which may affect the accuracy of transporter- and/or metabolizing enzyme-mediated DDI predictions. We incorporated quantitative zonal OATP1B distribution data from immunofluorescence imaging into a PBPK modeling framework to explore rifampicin interactions with OATP1B and CYP substrates. PBPK models were developed for rifampicin, two OATP1B substrates, pravastatin and repaglinide (also metabolized by CYP2C8/CYP3A4), and the CYP3A probe, midazolam. Simulated hepatic uptake of pravastatin and repaglinide increased from the periportal to the pericentral region (approximately 2.1-fold), consistent with OATP1B distribution data. Simulated rifampicin unbound intracellular concentrations increased in the pericentral region (1.64-fold) compared to simulations with uniformly distributed OATP1B. The absolute average fold error of the rifampicin PBPK model for predicting substrate maximal concentration (Cmax) and area under the plasma concentration-time curve (AUC) ratios was 1.41 and 1.54, respectively (nine studies). In conclusion, hepatic OATP1B distribution has a considerable impact on simulated zonal substrate uptake clearance values and simulated intracellular perpetrator concentrations, which regulate transporter and metabolic DDIs. Additionally, accounting for rifampicin-mediated OATP1B induction in parallel with inhibition improved model predictions. This study provides novel insight into the effect of hepatic OATP1B distribution on site-specific DDI predictions and the impact of accounting for zonal transporter distributions within PBPK models.

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

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

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

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

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Understanding Inter-individual Variability in the Drug Interaction of a Highly Extracted CYP1A2 Substrate Tizanidine: Application of a Permeability-limited Multi-compartment Liver Model in a Population Based PBPK Framework

Tizanidine, a centrally acting skeletal muscle relaxant, is predominantly metabolised by CYP1A2 and undergoes extensive hepatic first-pass metabolism following oral administration. As a highly extracted drug, the systemic exposure to tizanidine exhibits considerable inter-individual variability and is altered substantially when co-administered with CYP1A2 inhibitors or inducers. The aim of the current study was to compare the performance of a permeability-limited multi-compartment liver (PerMCL) model, which operates as an approximation of the dispersion model (DM), and the well-stirred model (WSM) for predicting tizanidine DDIs. Physiologically-based pharmacokinetic (PBPK) models were developed for tizanidine, incorporating the PerMCL model and the WSM, respectively, to simulate the interaction of tizanidine with a range of CYP1A2 inhibitors and inducers. While the WSM showed a tendency to under-predict the fold change of tizanidine AUC (AUC ratio) in the presence of perpetrators, the use of PerMCL model increased precision (absolute average-fold error: 1.32 - 1.42 versus 1.58) and decreased bias (average-fold error: 0.97 - 1.25 versus 0.63) for the predictions of mean AUC ratios as compared to the WSM. The PerMCL model captured the observed range of individual AUC ratios of tizanidine as well as the correlation between individual AUC ratios and CYP1A2 activities without interactions, whereas the WSM was not able to capture these. The results demonstrate the advantage of using the PerMCL model over the WSM in predicting the magnitude and inter-individual variability of DDIs for a highly extracted sensitive substrate tizanidine. Significance Statement This study demonstrates the advantages of the permeability-limited multi-compartment liver (PerMCL) model, which operates as an approximation of the dispersion model (DM), in mitigating the tendency of the well-stirred model (WSM) to under-predict the magnitude and variability of DDIs of a highly extracted CYP1A2 substrate tizanidine when it is administered with CYP1A2 inhibitors or inducers. The PBPK modelling approach described herein is valuable to the understanding of drug interactions of highly extracted substrates and the source of its inter-individual variability.

Topical drug delivery: History, percutaneous absorption, and product development

Topical products, widely used to manage skin conditions, have evolved from simple potions to sophisticated delivery systems. Their development has been facilitated by advances in percutaneous absorption and product design based on an increasingly mechanistic understanding of drug-product-skin interactions, associated experiments, and a quality-by-design framework. Topical drug delivery involves drug transport from a product on the skin to a local target site and then clearance by diffusion, metabolism, and the dermal circulation to the rest of the body and deeper tissues. Insights have been provided by Quantitative Structure Permeability Relationships (QSPR), molecular dynamics simulations, and dermal Physiologically Based PharmacoKinetics (PBPK). Currently, generic product equivalents of reference-listed products dominate the topical delivery market. There is an increasing regulatory interest in understanding topical product delivery behavior under 'in use' conditions and predicting in vivo response for population variations in skin barrier function and response using in silico and in vitro findings.

Relating transdermal delivery plasma pharmacokinetics with in vitro permeation test (IVPT) findings using diffusion and compartment-in-series models

Increasing emphasis is being placed on using in vitro permeation test (IVPT) results for topical products as a surrogate for their in vivo behaviour. This study sought to relate in vivo plasma concentration - time pharmacokinetic (PK) profiles after topical application of drug products to IVPT findings with mechanistic diffusion and compartment models that are now widely used to describe permeation of solutes across the main skin transport barrier, the stratum corneum. Novel in vivo forms of the diffusion and compartment-in-series models were developed by combining their IVPT model forms with appropriate in vivo disposition functions. Available in vivo and IVPT data were then used with the models in data analyses, including the estimation of prediction intervals for in vivo plasma concentrations derived from IVPT data. The resulting predicted in vivo plasma concentration - time profiles for the full models corresponded closely with the observed results for both nitroglycerin and rivastigmine at all times. In contrast, reduced forms of these in vivo models led to discrepancies between model predictions and observed results at early times. A two-stage deconvolution procedure was also used to estimate the in vivo cumulative amount absorbed and shown to be linearly related to that from IVPT, with an acceptable prediction error. External predictability was also shown using a separate set of in vitro and in vivo data for different nitroglycerin patches. This work suggests that mechanistic and physiologically based pharmacokinetic models can be used to predict in vivo behaviour from IVPT data for topical products.

A multiscale modelling approach to assess the impact of metabolic zonation and microperfusion on the hepatic carbohydrate metabolism

The capacity of the liver to convert the metabolic input received from the incoming portal and arterial blood into the metabolic output of the outgoing venous blood has three major determinants: The intra-hepatic blood flow, the transport of metabolites between blood vessels (sinusoids) and hepatocytes and the metabolic capacity of hepatocytes. These determinants are not constant across the organ: Even in the normal organ, but much more pronounced in the fibrotic and cirrhotic liver, regional variability of the capillary blood pressure, tissue architecture and the expression level of metabolic enzymes (zonation) have been reported. Understanding how this variability may affect the regional metabolic capacity of the liver is important for the interpretation of functional liver tests and planning of pharmacological and surgical interventions. Here we present a mathematical model of the sinusoidal tissue unit (STU) that is composed of a single sinusoid surrounded by the space of Disse and a monolayer of hepatocytes. The total metabolic output of the liver (arterio-venous glucose difference) is obtained by integration across the metabolic output of a representative number of STUs. Application of the model to the hepatic glucose metabolism provided the following insights: (i) At portal glucose concentrations between 6–8 mM, an intra-sinusoidal glucose cycle may occur which is constituted by glucose producing periportal hepatocytes and glucose consuming pericentral hepatocytes, (ii) Regional variability of hepatic blood flow is higher than the corresponding regional variability of the metabolic output, (iii) a spatially resolved metabolic functiogram of the liver is constructed. Variations of tissue parameters are equally important as variations of enzyme activities for the control of the arterio-venous glucose difference.

Glucose homeostasis is one of the central liver functions. The liver extracts glucose from the blood when plasma glucose levels are high and produces glucose when plasma glucose levels are low. To fulfill this function the liver is organized in smallest functional units, the sinusoidal tissue units (STUs). These STUs consist of a single sinusoid surrounded by linear arranged hepatocytes. Liver zonation describes the spatial separation of metabolic pathways along the STUs. As blood flows through the sinusoid the plasma nutrient and hormone composition changes and in conjunction with the heterogeneous endowment of metabolic enzymes this leads to big differences in the metabolic performance of hepatocytes depending on their position within the sinusoid. This makes liver zonation and blood flow two central determinants for the functional output of the liver. In this work we present a tissue model of hepatic carbohydrate metabolism that combines liver zonation and microperfusion within the STU. We show that structural properties, enzymatic properties and regional bloodflow are equally important for the understanding of liver functionality. With our work we provide a true multi-scale model bridging the scale from the cellular to the tissue level.

A Computational Model of Hepatic Energy Metabolism: Understanding Zonated Damage and Steatosis in NAFLD

In non-alcoholic fatty liver disease (NAFLD), lipid build-up and the resulting damage is known to occur more severely in pericentral cells. Due to the complexity of studying individual regions of the sinusoid, the causes of this zone specificity and its implications on treatment are largely ignored. In this study, a computational model of liver glucose and lipid metabolism is presented which treats the sinusoid as the repeating unit of the liver rather than the single hepatocyte. This allows for inclusion of zonated enzyme expression by splitting the sinusoid into periportal to pericentral compartments. By simulating insulin resistance (IR) and high intake diets leading to the development of steatosis in the model, we identify key differences between periportal and pericentral cells accounting for higher susceptibility to pericentral steatosis. Secondly, variation between individuals is seen in both susceptibility to steatosis and in its development across the sinusoid. Around 25% of obese individuals do not show excess liver fat, whilst 16% of lean individuals develop NAFLD. Furthermore, whilst pericentral cells tend to show higher lipid levels, variation is seen in the predominant location of steatosis from pericentral to pan-sinusoidal or azonal. Sensitivity analysis was used to identify the processes which have the largest effect on both total hepatic triglyceride levels and on the sinusoidal location of steatosis. As is seen in vivo, steatosis occurs when simulating IR in the model, predominantly due to increased uptake, along with an increase in de novo lipogenesis. Additionally, concentrations of glucose intermediates including glycerol-3-phosphate increased when simulating IR due to inhibited glycogen synthesis. Several differences between zones contributed to a higher susceptibility to steatosis in pericentral cells in the model simulations. Firstly, the periportal zonation of both glycogen synthase and the oxidative phosphorylation enzymes meant that the build-up of glucose intermediates was less severe in the periportal hepatocyte compartments. Secondly, the periportal zonation of the enzymes mediating β-oxidation and oxidative phosphorylation resulted in excess fats being metabolised more rapidly in the periportal hepatocyte compartments. Finally, the pericentral expression of de novo lipogenesis contributed to pericentral steatosis when additionally simulating the increase in sterol-regulatory element binding protein 1c (SREBP-1c) seen in NAFLD patients in vivo. The hepatic triglyceride concentration was predicted to be most sensitive to inter-individual variation in the activity of enzymes which, either directly or indirectly, determine the rate of free fatty acid (FFA) oxidation. The concentration was most strongly dependent on the rate constants for β-oxidation and oxidative phosphorylation. It also showed moderate sensitivity to the rate constants for processes which alter the allosteric inhibition of β-oxidation by acetyl-CoA. The predominant sinusoidal location of steatosis meanwhile was most sensitive variations in the zonation of proteins mediating FFA uptake or triglyceride release as very low density lipoproteins (VLDL). Neither the total hepatic concentration nor the location of steatosis showed strong sensitivity to variations in the lipogenic rate constants.

Representative Sinusoids for Hepatic Four-Scale Pharmacokinetics Simulations

The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the body. The corresponding biochemical processes are typically subject to spatial variations at different length scales. Zonal enzyme expression along sinusoids leads to zonated metabolization already in the healthy state. Pathological states of the liver may involve liver cells affected in a zonated manner or heterogeneously across the whole organ. This spatial heterogeneity, however, cannot be described by most computational models which usually consider the liver as a homogeneous, well-stirred organ.

The goal of this article is to present a methodology to extend whole-body pharmacokinetics models by a detailed liver model, combining different modeling approaches from the literature. This approach results in an integrated four-scale model, from single cells via sinusoids and the organ to the whole organism, capable of mechanistically representing metabolization inhomogeneity in livers at different spatial scales. Moreover, the model shows circulatory mixing effects due to a delayed recirculation through the surrounding organism.

To show that this approach is generally applicable for different physiological processes, we show three applications as proofs of concept, covering a range of species, compounds, and diseased states: clearance of midazolam in steatotic human livers, clearance of caffeine in mouse livers regenerating from necrosis, and a parameter study on the impact of different cell entities on insulin uptake in mouse livers.

The examples illustrate how variations only discernible at the local scale influence substance distribution in the plasma at the whole-body level. In particular, our results show that simultaneously considering variations at all relevant spatial scales may be necessary to understand their impact on observations at the organism scale.

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.

Tissue-level modeling of xenobiotic metabolism in liver: An emerging tool for enabling clinical translational research

This review summarizes some of the recent developments and identifies critical challenges associated with in vitro and in silico representations of the liver and assesses the translational potential of these models in the quest of rationalizing the process of evaluating drug efficacy and toxicity. It discusses a wide range of research efforts that have produced, during recent years, quantitative descriptions and conceptual as well as computational models of hepatic processes such as biotransport and biotransformation, intra- and intercellular signal transduction, detoxification, etc. The above mentioned research efforts cover multiple scales of biological organization, from molecule-molecule interactions to reaction network and cellular and histological dynamics, and have resulted in a rapidly evolving knowledge base for a "systems biology of the liver." Virtual organ/organism formulations represent integrative implementations of particular elements of this knowledge base, usually oriented toward the study of specific biological endpoints, and provide frameworks for translating the systems biology concepts into computational tools for quantitative prediction of responses to stressors and hypothesis generation for experimental design.

An improved nonlinear model describing the hepatic pharmacokinetics of digoxin: evidence for two functionally different uptake systems and saturable binding

PURPOSE

To develop a semi-distributed liver model for the evaluation of saturable sinusoidal uptake and binding kinetics of the Oatp1a4 substrate digoxin.

METHODS

In the perfused rat liver, two successive digoxin doses of 42 and 125 microg were administered, and the outflow concentration was determined by LC/MS/MS. [14C]-sucrose was used as vascular reference. The data were analyzed simultaneously by a population approach using sucrose to determine the sinusoidal mixing of digoxin.

RESULTS

The results suggest the existence of a high-affinity, low-capacity system, and a low-affinity, high-capacity system for sinusoidal uptake with apparent Michaelis constants (K(M)) of 0.24 and 332 microg/ml, respectively. Incorporation of saturable sinusoidal binding of digoxin considerably improved the fit, and the parameter estimates were consistent with those of binding to hepatic Na,K-ATPase. Simpler models that neglect the concentration gradient in flow direction failed to describe the outflow data in the high dose range.

CONCLUSION

The semi-distributed liver model with saturable uptake should be useful for a functional characterization of transporters in the in situ rat liver.

Prediction of human pharmacokinetics—evaluation of methods for prediction of hepatic metabolic clearance

Methods for prediction of hepatic clearance (CLH) in man have been evaluated. A physiologically-based in-vitro to in-vivo (PB-IVIV) method with human unbound fraction in blood (fu,bl) and hepatocyte intrinsic clearance (CLint)-data has a good rationale and appears to give the best predictions (maximum ∼2-fold errors; < 25% errors for half of CL-predictions; appropriate ranking). Inclusion of an empirical scaling factor is, however, needed, and reasons include the use of cryopreserved hepatocytes with low activity, and inappropriate CLint- and fu,bl-estimation methods. Thus, an improvement of this methodology is possible and required. Neglect of fu,bl or incorporation of incubation binding does not seem appropriate. When microsome CLint-data are used with this approach, the CLH is underpredicted by 5- to 9-fold on average, and a 106-fold underprediction (attrition potential) has been observed. The poor performance could probably be related to permeation, binding and low metabolic activity. Inclusion of scaling factors and neglect of fu,bl for basic and neutral compounds improve microsome predictions. The performance is, however, still not satisfactory. Allometry incorrectly assumes that the determinants for CLH relate to body weight and overpredicts human liver blood flow rate. Consequently, allometric methods have poor predictability. Simple allometry has an average overprediction potential, > 2-fold errors for ∼1/3 of predictions, and 140-fold underprediction to 5800-fold overprediction (potential safety risk) range. In-silico methodologies are available, but these need further development. Acceptable prediction errors for compounds with low and high CLH should be ∼50 and ∼10%, respectively. In conclusion, it is recommended that PB-IVIV with human hepatocyte CLint and fu,bl is applied and improved, limits for acceptable errors are decreased, and that animal CLH-studies and allometry are avoided.

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

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