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

Process and System Clearances in Pharmacokinetic Models: Our Basic Clearance Concepts Are Correct

Clearances are important parameters in pharmacokinetic (PK) models. All clearances in PK models are either process clearances that include diffusion, transport, and metabolism clearances or system clearances that include organ and systemic clearance. Clearance and volume of distribution are two independent parameters that characterize drug disposition in both individual compartments and systems of compartments. In this minireview, we show that systemic and organ clearances are net clearances that can be easily derived by partition analysis. When drugs are eliminated from the central compartment by first-order processes, systemic clearance is constant. When drugs are eliminated from a peripheral compartment, instantaneous systemic clearance will vary with time. However, average clearance and clearance at steady state will be constant and will equal dose divided by area under the curve. We show that peripheral elimination will not have a large impact on most pharmacokinetic analyses and that standard models of organ and systemic clearance are useful and appropriate. SIGNIFICANCE STATEMENT: There are two basic kinds of clearances used in pharmacokinetic models, process and system clearances. We show that organ and systemic clearances are net clearances with blood or plasma as the driving concentration. For linear pharmacokinetics, clearance is constant for elimination from the central compartment but varies with time for peripheral elimination. Despite the different kinds of clearance parameters and models, standard clearance models and concepts remain valid.

Development of an intracellular quantitative assay to measure compound binding kinetics

Contemporary drug discovery typically quantifies the effect of a molecule on a biological target using the equilibrium-derived measurements of IC50, EC50, or KD. Kinetic descriptors of drug binding are frequently linked with the effectiveness of a molecule in modulating a disease phenotype; however, these parameters are yet to be fully adopted in early drug discovery. Nanoluciferase bioluminescence resonance energy transfer (NanoBRET) can be used to measure interactions between fluorophore-conjugated probes and luciferase fused target proteins. Here, we describe an intracellular NanoBRET competition assay that can be used to quantify cellular kinetic rates of compound binding to nanoluciferase-fused bromodomain and extra-terminal (BET) proteins. Comparative rates are generated using a cell-free NanoBRET assay and by utilizing orthogonal recombinant protein-based methodologies. A screen of known pan-BET inhibitors is used to demonstrate the value of this approach in the investigation of kinetic selectivity between closely related proteins.

Tailored Pharmacokinetic model to predict drug trapping in long-term anesthesia

Introduction

In long-term induced general anesthesia cases such as those uniquely defined by the ongoing Covid-19 pandemic context, the clearance of hypnotic and analgesic drugs from the body follows anomalous diffusion with afferent drug trapping and escape rates in heterogeneous tissues. Evidence exists that drug molecules have a preference to accumulate in slow acting compartments such as muscle and fat mass volumes. Currently used patient dependent pharmacokinetic models do not take into account anomalous diffusion resulted from heterogeneous drug distribution in the body with time varying clearance rates.

Objectives

This paper proposes a mathematical framework for drug trapping estimation in PK models for estimating optimal drug infusion rates to maintain long-term anesthesia in Covid-19 patients. We also propose a protocol for measuring and calibrating PK models, along with a methodology to minimize blood sample collection.

Methods

We propose a framework enabling calibration of the models during the follow up of Covid-19 patients undergoing anesthesia during their treatment and recovery period in ICU. The proposed model can be easily updated with incoming information from clinical protocols on blood plasma drug concentration profiles. Already available pharmacokinetic and pharmacodynamic models can be then calibrated based on blood plasma concentration measurements.

Results

The proposed calibration methodology allow to minimize risk for potential over-dosing as clearance rates are updated based on direct measurements from the patient.

Conclusions

The proposed methodology will reduce the adverse effects related to over-dosing, which allow further increase of the success rate during the recovery period.

Hepatic clearance concepts and misconceptions: Why the well-stirred model is still used even though it is not physiologic reality?

The liver is the most important drug metabolizing organ, endowed with a plethora of metabolizing enzymes and transporters to facilitate drug entry and removal via metabolism and/or biliary excretion. For this reason, much focus surrounds the development of clearance concepts, which are based on normalizing the rate of removal to the input or arterial concentration. By so doing, some authors have recently claimed that it implies one specific model of hepatic elimination, namely, the widely used well-stirred or venous equilibration model (WSM). This commentary challenges this claim and aims to provide a comprehensive discussion of not only the WSM but other currently applied hepatic clearance models - the parallel tube model (PTM), the dispersion model (DM), the zonal liver model (ZLM), and the heterogeneous capillary transit time model of Goresky and co-workers (GM). The WSM, PTM, and DM differ in the patterns of internal blood flow, assuming bulk, plug, and dispersive flows, respectively, which render different degrees of mixing within the liver that are characterized by the magnitudes of the dispersion number (D_N), resulting in different implications concerning the (unbound) substrate concentration in liver (Cu_H). Early models assumed perfusion rate-limited distribution, which have since been modified to include membrane-limited transport. The recent developments associated with the misconceptions and the sensitivity of the models are hereby addressed. Since the WSM has been and will likely remain widely used, the pros and cons of this model relative to physiological reality are further discussed.

Better prediction of the local concentration-effect relationship: the role of physiologically based pharmacokinetics and quantitative systems pharmacology and toxicology in the evolution of model-informed drug discovery and development

Model-informed drug discovery and development (MID3) is an umbrella term under which sit several computational approaches: quantitative systems pharmacology (QSP), quantitative systems toxicology (QST) and physiologically based pharmacokinetics (PBPK). QSP models are built using mechanistic knowledge of the pharmacological pathway focusing on the putative mechanism of drug efficacy; whereas QST models focus on safety and toxicity issues and the molecular pathways and networks that drive these adverse effects. These can be mediated through exaggerated on-target or off-target pharmacology, immunogenicity or the physiochemical nature of the compound. PBPK models provide a mechanistic description of individual organs and tissues to allow the prediction of the intra- and extra-cellular concentration of the parent drug and metabolites under different conditions. Information on biophase concentration enables the prediction of a drug effect in different organs and assessment of the potential for drug-drug interactions. Together, these modelling approaches can inform the exposure-response relationship and hence support hypothesis generation and testing, compound selection, hazard identification and risk assessment through to clinical proof of concept (POC) and beyond to the market.

Reproducible pharmacokinetics

Reproducibility is a highly desired feature of scientific investigation in general, and it has special connotations for research in pharmacokinetics, a vibrant field with over 500,000 publications to-date. It is important to be able to differentiate between genuine heterogeneity in pharmacokinetic parameters from heterogeneity that is due to errors and biases. This overview discusses efforts and opportunities to diminish the latter type of undesirable heterogeneity. Several reporting and research guidance documents and standards have been proposed for pharmacokinetic studies, but their adoption is still rather limited. Quality problems in the methods used and model evaluations have been examined in some empirical studies of the literature. Standardization of statistical and laboratory tools and procedures can be improved in the field. Only a small fraction of pharmacokinetic studies become pre-registered and only 9995 such studies have been registered in ClinicalTrials.gov as of August 2018. It is likely that most pharmacokinetic studies remain unpublished. Publication bias affecting the results and inferences has been documented in case studies, but its exact extent is unknown for the field at-large. The use of meta-analyses in the field is still limited. Availability of raw data, detailed protocols, software and codes is hopefully improving with multiple ongoing initiatives. Several research practices can contribute to greater transparency and reproducibility for pharmacokinetic investigations.

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.

Fractal properties and morphological investigation of Nano hydrochlorothiazide is used to treat hypertension

PURPOSE

High blood pressure (hypertension) is a relatively common condition that increases blood pressure in the arteries abnormally, causing problems such as heart disease and stroke. Blood pressure is a force that is felt through the walls of the blood vessels and has a direct relationship to the power of pumping the heart and vascular resistance to the blood flow. One of the lowing of blood pressure medications is hydrochlorothiazide (Hctz) which is used to treat high blood pressure and swelling from heart failure, liver damage, and other minor actions.

PROCEDURES

This study explains the effectiveness of Hctz with the help of "fractal dimension". To perfect investigate the fractal dimension, we used the Hctz drug nanoparticle form then using MATLAB software, homogeneity levels or heterogeneity of Nano Hctz using SEM images were computed.

RESULTS

We calculated histogram plot with SEM image by MATLAB software which that its standard deviation was eclose to zero and it can explain that the scattering of data is low and their amount is in one suffering. Fractal dimensions obtained from Matlab and SPSS software for normal distribution, correlation, standard deviation, mean, cumulative frequency and variance analysis were analyzed.

CONCLUSIONS

In this research, the association between Hctz treatment effects with the point of view of the fractal dimension of the drug was demonstrated to prove the properties of the drug in the body. in the near future, drug fractal studies can improve the development of new drugs and treatments with minimal cost than clinical approaches by linking chemistry, mathematical sciences and pharmaceutical sciences.

Drug Transporters in Xenobiotic Disposition and Pharmacokinetic Prediction

Drug transporters are widely expressed in organs and tissue barriers throughout human and animal bodies. Studies over the last two decades have identified various ATP-binding cassette and solute carrier transporters that play critical roles in the absorption, distribution, metabolism, and elimination of drugs and xenobiotics. This special section contains more than 20 original manuscripts and reviews that cover the most recent advances in the areas of drug transporter research, including the basic biology and function of transporters, expression of drug transporters in organ and tissue barriers, the mechanisms underlying regulation of transporter expression, transporter-mediated drug disposition in animal models, and the development and utilization of new technologies in drug transporter study, as well as pharmacokinetic modeling and simulation to assess transporter involvement in drug disposition and drug-drug interactions. We believe that the topics covered in this special section will advance our understanding of the roles of transporters in drug disposition, efficacy, and safety.

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.

Unrepaired Tetralogy of Fallot-related Pathophysiologic Changes Reduce Systemic Clearance of Etomidate in Children

BACKGROUND

Pathophysiologic changes in children with congenital heart disease may alter the effect of drugs by influencing the pharmacokinetics (PK). Considering the limited literature that describes the PK of etomidate in pediatric patients, especially in those with tetralogy of Fallot (TOF), our aim was to characterize the PK of etomidate and explore the effects of TOF.

METHODS

Twenty-nine pediatric patients (15 with TOF and 14 with normal cardiac anatomy) scheduled to undergo elective surgery under general anesthesia were recruited in the study. All children received etomidate 60 μg/kg/min intravenously until a bispectral index of ≤50 was reached for 5 seconds during anesthesia induction. Arterial blood samples were drawn and analyzed. Population analysis was performed by using NONMEM to define PK characteristics. The estimates were standardized to a 70-kg adult using a per-kilogram model.

RESULTS

Data consisting of 244 samples from 29 children with a mean age of 236 days (range, 86-360 days) were used, including a TOF group with a mean age of 250 days (range, 165-360 days) and a normal cardiac anatomy group with a mean age of 221 days (range, 86-360 days). A 3-compartment disposition model was best fitted to describe the PK of etomidate. The introduction of TOF as a covariate for systemic clearance (Cl1) improved the model and resulted in a significant reduction of objective function (Δobjective function = -7.33; P = .0068), which means that TOF was a significant covariate of Cl1, and the etomidate Cl1 in children with TOF (1.67 × (weight [WT]/70 kg) L/min) was lower than those with normal cardiac anatomy (2.28 × (WT/70 kg) L/min). Other PK parameter values were as follows: V1 = 8.05 × (WT/70 kg) L; V2 = 13.7 × (WT/70 kg) L; V3 = 41.3 × (WT/70 kg) L; Cl2 = 3.35 × (WT/70 kg) L/min; Cl3 = 0.563 × (WT/70 kg) L/min.

CONCLUSIONS

A decreased systemic clearance for etomidate in children with TOF resulted in a lower required infusion rate and variation with time to achieve the same plasma concentration and maintain an equivalent target concentration or have longer sedation and recovery times after bolus or continuous infusion than normal children.

The virtual cell based assay: Current status and future perspectives

In order to replace the use of animals in toxicity testing, there is a need to predict in vivo toxic doses from concentrations that cause toxicological effects in relevant in vitro systems. The Virtual Cell Based Assay (VCBA) estimates time-dependent concentration of a test chemical in the cell and cell culture for a given in vitro system. The concentrations in the different compartments of the cell and test system are derived from ordinary differential equations, physicochemical parameters of the test chemical and properties of the cell line. The VCBA has been developed for a range of cell lines including BALB/c 3T3 cells, HepG2, HepaRG, lung A459 cells, and cardiomyocytes. The model can be used to design and refine in vitro experiments and extrapolate in vitro effective concentrations to in vivo doses that can be applied in risk assessment. In this paper, we first discuss potential applications of the VCBA: i) design of in vitro High Throughput Screening (HTS) experiments; ii) hazard identification (based on acute systemic toxicity); and iii) risk assessment. Further extension of the VCBA is discussed in the second part, exploring potential application to i) manufactured nanomaterials, ii) additional cell lines and endpoints, and considering iii) other opportunities.

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VCBA as an alternative approach can be applied in the domain of nanotoxicology.

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VCBA can support better testing strategies in acute toxicity.

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Refinement of the VCBA taking into account biological oscillators could improve toxicity prediction.

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Extensions of the VCBA can capture effects related to additional subcellular compartments.

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.

Multiscale modelling approaches for assessing cosmetic ingredients safety

The European Union's ban on animal testing for cosmetic ingredients and products has generated a strong momentum for the development of in silico and in vitro alternative methods. One of the focus of the COSMOS project was ab initio prediction of kinetics and toxic effects through multiscale pharmacokinetic modeling and in vitro data integration. In our experience, mathematical or computer modeling and in vitro experiments are complementary. We present here a summary of the main models and results obtained within the framework of the project on these topics. A first section presents our work at the organelle and cellular level. We then go toward modeling cell levels effects (monitored continuously), multiscale physiologically based pharmacokinetic and effect models, and route to route extrapolation. We follow with a short presentation of the automated KNIME workflows developed for dissemination and easy use of the models. We end with a discussion of two challenges to the field: our limited ability to deal with massive data and complex computations.

A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Background

One of the major issues in current pharmaceutical development is potential hepatotoxicity and drug-induced liver damage. This is due to the unique metabolic processes performed in the liver to prevent accumulation of a wide range of chemicals in the blood. Recently, we developed a physiologically-based lattice model to address the transport and metabolism of drugs in the liver lobule (liver functional unit).

Method

In this paper, we extend our idealized model to consider structural and spatial variability in two and three dimensions. We introduce a hexagonal-based model with one input (portal vein) and six outputs (hepatic veins) to represent a typical liver lobule. To capture even more realistic structures, we implement a novel sequential diffusion-limited aggregation (DLA) method to construct a morphological sinusoid network in the lobule. A 3D model constructed with stacks of multiple 2D sinusoid realizations is explored to study the effects of 3D structural variations. The role of liver zonation on drug metabolism in the lobule is also addressed, based on flow-based predicted steady-state O₂ profiles used as a zonation indicator.

Results

With this model, we analyze predicted drug concentration levels observed exiting the lobule with their detailed distribution inside the lobule, and compare with our earlier idealized models. In 2D, due to randomness of the sinusoidal structure, individual hepatic veins respond differently (i.e. at different times) to injected drug. In 3D, however, the variation of response to the injected drug is observed to be less extreme. Also, the production curves show more diffusive behavior in 3D than in 2D.

Conclusion

Although, the individual producing ports respond differently, the average lobule production summed over all hepatic veins is more diffuse. Thus the net effect of all these variations makes the overall response smoother. We also show that, in 3D, the effect of zonation on drug production characteristics appears quite small. Our new biophysical structural analysis of a physiologically-based 3D lobule can therefore form the basis for a quantitative assessment of liver function and performance both in health and disease

Electronic supplementary material

The online version of this article (doi:10.1186/s12976-016-0034-5) contains supplementary material, which is available to authorized users.

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.

Practical permeability-based hepatic clearance classification system (HepCCS) in drug discovery

Background: The use of liver microsomes and hepatocytes to predict total in vivo clearance is standard practice in the pharmaceutical industry; however, metabolic stability data alone cannot always predict in vivo clearance accurately. Results: Apparent permeability generated from Mardin–Darby canine kidney cells and rat hepatocyte uptake for 33 discovery compounds were obtained. Conclusion: When there is underprediction of in vivo clearance, compounds with low apparent permeability (less than 3 × 10-6 cm/s) all exhibited hepatic uptake. A systematic approach in the form of a classification system (hepatic clearance classification system) and decision tree that will help drug discovery scientists understand in vitro–in vivo clearance prediction disconnect early is proposed.

Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Physiologically realistic geometric models of the vasculature in the liver are indispensable for modelling hepatic blood flow, the main connection between the liver and the organism. Current in vivo imaging techniques do not provide sufficiently detailed vascular trees for many simulation applications, so it is necessary to use algorithmic refinement methods. The method of Constrained Constructive Optimization (CCO) (Schreiner et al., 2006) is well suited for this purpose. Its results after calibration have been previously compared to experimentally acquired human vascular trees (Schwen and Preusser, 2012). The goal of this paper is to extend this calibration to the case of rodents (mice and rats), the most commonly used animal models in liver research. Based on in vivo and ex vivo micro-CT scans of rodent livers and their vasculature, we performed an analysis of various geometric features of the vascular trees. Starting from pruned versions of the original vascular trees, we applied the CCO procedure and compared these algorithmic results to the original vascular trees using a suitable similarity measure. The calibration of the postprocessing improved the algorithmic results compared to those obtained using standard CCO. In terms of angular features, the average similarity increased from 0.27 to 0.61, improving the total similarity from 0.28 to 0.40. Finally, we applied the calibrated algorithm to refine measured vascular trees to the (higher) level of detail desired for specific applications. Having successfully adapted the CCO algorithm to the rodent model organism, the resulting individual-specific refined hepatic vascular trees can now be used for advanced modeling involving, e.g., detailed blood flow simulations.

Spatio-temporal simulation of first pass drug perfusion in the liver

The liver is the central organ for detoxification of xenobiotics in the body. In pharmacokinetic modeling, hepatic metabolization capacity is typically quantified as hepatic clearance computed as degradation in well-stirred compartments. This is an accurate mechanistic description once a quasi-equilibrium between blood and surrounding tissue is established. However, this model structure cannot be used to simulate spatio-temporal distribution during the first instants after drug injection. In this paper, we introduce a new spatially resolved model to simulate first pass perfusion of compounds within the naive liver. The model is based on vascular structures obtained from computed tomography as well as physiologically based mass transfer descriptions obtained from pharmacokinetic modeling. The physiological architecture of hepatic tissue in our model is governed by both vascular geometry and the composition of the connecting hepatic tissue. In particular, we here consider locally distributed mass flow in liver tissue instead of considering well-stirred compartments. Experimentally, the model structure corresponds to an isolated perfused liver and provides an ideal platform to address first pass effects and questions of hepatic heterogeneity. The model was evaluated for three exemplary compounds covering key aspects of perfusion, distribution and metabolization within the liver. As pathophysiological states we considered the influence of steatosis and carbon tetrachloride-induced liver necrosis on total hepatic distribution and metabolic capacity. Notably, we found that our computational predictions are in qualitative agreement with previously published experimental data. The simulation results provide an unprecedented level of detail in compound concentration profiles during first pass perfusion, both spatio-temporally in liver tissue itself and temporally in the outflowing blood. We expect our model to be the foundation of further spatially resolved models of the liver in the future.

A multi-scale modeling framework for individualized, spatiotemporal prediction of drug effects and toxicological risk

In this study, we focus on a novel multi-scale modeling approach for spatiotemporal prediction of the distribution of substances and resulting hepatotoxicity by combining cellular models, a 2D liver model, and whole body model. As a case study, we focused on predicting human hepatotoxicity upon treatment with acetaminophen based on in vitro toxicity data and potential inter-individual variability in gene expression and enzyme activities. By aggregating mechanistic, genome-based in silico cells to a novel 2D liver model and eventually to a whole body model, we predicted pharmacokinetic properties, metabolism, and the onset of hepatotoxicity in an in silico patient. Depending on the concentration of acetaminophen in the liver and the accumulation of toxic metabolites, cell integrity in the liver as a function of space and time as well as changes in the elimination rate of substances were estimated. We show that the variations in elimination rates also influence the distribution of acetaminophen and its metabolites in the whole body. Our results are in agreement with experimental results. What is more, the integrated model also predicted variations in drug toxicity depending on alterations of metabolic enzyme activities. Variations in enzyme activity, in turn, reflect genetic characteristics or diseases of individuals. In conclusion, this framework presents an important basis for efficiently integrating inter-individual variability data into models, paving the way for personalized or stratified predictions of drug toxicity and efficacy.

Evaluation of the intestinal toxicity and transport of xenobiotics utilizing precision-cut slices

1.The precision-cut intestinal slice (PCIS) technology is a relatively new addition to the battery of in vitro assays for evaluation of xenobiotic toxicity, metabolism, and transport. 2.The intestine is an important target for drug-induced toxicity due to its high exposure after oral administration. Therefore, the prediction of drug-induced intestinal side effects remains a significant safety issue in pharmaceutical development. Although animal experiments have been proven useful, species differences and the requirement for reduction of animal use warrant the development of in vitro methods which can apply human tissue. 3.The enterocytes lining the villi express high activities of enzymes and transporters involved in drug disposition. They vary highly in activities: along the length of the intestine and along the villi, gradients of expression levels of the enzymes and proteins exist, which necessitates an in vitro model that can reflect the different regions of the intestine. 4.In this chapter, the application of PCIS in studies on transport and toxicity of xenobiotics is reviewed. PCIS can be prepared from each region of the intestine and from various species in a similar manner, and the results published so far indicate that they represent a promising model to evaluate intestinal toxicity and transport.

System approach to modeling of liver glucose metabolism with physiologically interpreted model parameters outgoing from [18F]FDG concentrations measured by PET

New mathematical models from physiologically interpreted parameters capable of evaluating glucose metabolism within the liver and/or the whole body were developed. The group of pigs in a fasting state and the group of pigs with euglycemic supraphysiological hyperinsulinemia were scanned by positron emission tomography after a single dose of [(18)F]FDG tracer. Simultaneously frequent sampling of the dynamic data of [(18)F]FDG plasma concentration in artery, portal vein and hepatic vein was obtained. A system approach to the liver and/or the whole-body system by the tools of linear dynamic sysztem theory was used. Three kinds of structural models, single input and single output or multiple outputs and multiple inputs and single output, were identified. Differences between the group of fasting pigs and the group of pigs in euglycemic supraphysiological hyperinsulinemia were identified by estimated parameters of the structural models. The suitability of the structural mathematical models for the estimation of physiologically interpreted parameters from PET was validated.

Using modeling to help understand vaginal microbicide functionality and create better products

A summary is presented of a range of mathematical models that relate to topical microbicidal molecules, applied vaginally to inhibit HIV transmission. These models contribute to the fundamental understanding of the functioning of those molecules, as introduced in different delivery systems. They also provide computational tools that can be employed in the practical design and evaluation of vaginal microbicide products. Mathematical modeling can be implemented, using stochastic principles, to understand the probability of infection by sexually transmitted HIV virions. This provides a frame of reference for the deterministic models of the various processes that underlie HIV transmission and its inhibition, including: the temporal and spatial history of HIV migration from semen to vaginal epithelial surfaces and thence to the underlying stroma; the time and spatial distribution of microbicidal drugs as delivered by various vehicles (e.g., gels, rings, films, and tablets)-this is central to understanding microbicide product pharmacokinetics; and the time and space history of the drug interactions with HIV directly and with host cells for HIV within the vaginal environment-this informs the understanding of microbicide pharmacodynamics. Models that characterize microbicide functionality and performance should and can interface with both in vitro and in vivo experimental studies. They can serve as a rapidly applied, inexpensive tool, to facilitate microbicide R&D, in advance of more costly and time consuming clinical trials.

Diverse approaches for the enhancement of oral drug bioavailability

In conscious and co-operating patients, oral drug delivery remains the preferable route of drug administration. However, not all drugs possess the desirable physicochemical and pharmacokinetic properties which favor oral administration mainly due to poor bioavailability. This has in some cases led to the choice of other routes of administration, which may compromise the convenience and increase the risk of non-compliance. Poor bioavailability has necessitated the administration of higher than normally required oral doses which often leads to economic wastages, risk of toxicity, erratic and unpredictable responses. The challenge over the years has been to design techniques that will allow oral administration of most drugs, irrespective of their properties, to achieve a therapeutic systemic availability. This will be a worthy achievement since over 90% of therapeutic compounds are known to possess oral bioavailability limitations. In this review, an attempt has been made to explore various approaches that have been used in recent years to improve oral drug bioavailability, including physical and chemical means. This review strives to provide a comprehensive overview of advances made over the past 10 years (2000-2010) in the improvement of the oral bioavailability of drugs. Briefly, the design of prodrugs to bypass metabolism or to enhance solubility as well as modification of formulation techniques such as the use of additives, permeation enhancers, solubilizers, emulsifiers and non-aqueous vehicles have been discussed. Arising approaches, such as formulation modification techniques; novel drug delivery systems, which exploit the gastrointestinal regionality of drugs, and include the pharmaceutical application of nanotechnology as an emerging area in drug delivery; inhibition of efflux pumps; and inhibition of presystemic metabolism have been more extensively addressed. This critical review sought to assess each method aimed at enhancing the oral bioavailability of drugs in terms of the purpose, scientific basis, limitations, commercial application, as well as the areas in which current research efforts are being focused and should be focused in the future.

Long-lasting target binding and rebinding as mechanisms to prolong in vivo drug action

An increasing number of examples in the literature suggest that the in vivo duration of drug action not only depends on macroscopic pharmacokinetic properties like plasma half-life and the time needed to equilibrate between the plasma and the effect compartments, but is also influenced by long-lasting target binding and rebinding. The present review combines information from different research areas and simulations to explore the nature of these mechanisms and the conditions in which they are most prevalent. Simulations reveal that these latter phenomena become especially influential when there is no longer sufficient free drug around to maintain high levels of receptor occupancy. There is not always a direct link between slow dissociation and long-lasting in vivo target protection, as the rate of free drug elimination from the effect compartment is also a key influencing factor. Local phenomena that hinder the diffusion of free drug molecules away from their target may allow them to consecutively bind to the same target and/or targets nearby (denoted as 'rebinding') even when their concentration in the bulk phase has already dropped to insignificant levels. The micro-anatomic properties of many effect compartments are likely to intensify this phenomenon. By mimicking the complexity of tissues, intact cells offer the opportunity to investigate both mechanisms under the same, physiologically relevant conditions.

Rebinding: or why drugs may act longer in vivo than expected from their in vitro target residence time

IMPORTANCE OF THE FIELD

It is well established that the in vivo duration of drug action not only depends on macroscopic pharmacokinetic properties like its plasma half-life, but also on the residence time of the drug-target complexes. However, drug 'rebinding' (i.e., the consecutive binding of dissociated drug molecules to the original target and/or targets nearby) can be influential in vivo as well.

AREAS COVERED IN THIS REVIEW

Information about rebinding is available since the 1980s but it is dispersed in the life sciences literature. This review compiles this information. In this respect, neurochemists and biopohysicians advance the same equations to describe drug rebinding.

WHAT THE READER WILL GAIN

The rebinding mechanism is explained according to the prevailing viewpoint in different life science disciplines. There is a general consensus that high target densities, high association rates and local phenomena that hinder the diffusion of free drug molecules away from their target all promote rebinding.

TAKE HOME MESSAGE

Simulations presented here for the first time suggest that rebinding may increase the duration and even the constancy of the drug's clinical action. Intact cell radioligand dissociation and related ex vivo experiments offer useful indications about a drug's aptitude to experience target rebinding.

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.

Interplay of transporters and enzymes in drug and metabolite processing

This review highlights the "interplay" between enzymes and transporters, essential components of eliminating organs for drug removal. The understanding of the interplay is important in terms of deciphering the change of one eliminatory pathway on compensatory mechanisms in drug disposal, and, ultimately, their importance in drug-drug interactions. Controversy existed on the explanation underlying the interplay between transporters and enzymes in the Caco-2 cell monolayer or cell culture systems, but less so on eliminating organs such as the intestine and liver. For the Caco-2 system, the increase in the mean residence time (MRT) accompanying increased secretion had been construed as the basis for increased metabolism. We hold the opposite view and assert that increased secretion should evoke a decrease in metabolism due to the competition between the enzyme and apical efflux transporter for the drug within the cell. To illustrate this point, simulations on the MRT, fraction of dose metabolized (f(met)) and the extraction ratio (ER) as defined by various investigators under linear and nonlinear metabolic conditions were compared to observed data and the trends upon induction/inhibition of secretion. The conclusion is that the f(met) is the more appropriate index to reflect the extent of metabolism in transporter-enzyme interplay, since the parameter captures drug metabolism in the cell when its contents in the apical, cell, and basolateral compartments or the entire dose is considered to be available for metabolism. This parameter for metabolism (f(met)) bears a reciprocal relationship to the secretory intrinsic clearance and is in concordance with the notion that both the enzyme and apical transporter compete for the cellular substrate within. For the liver and intestine, several physiologically based pharmacokinetic (PBPK) models that contain transporters and enzymes were utilized, together with the solved equations for the area under the curve (AUC), metabolic, excretory, and total clearance (CL) to shed meaningful insight of how the inhibition of one pathway can result in a higher AUC and therefore a reduced total clearance for drug, but a higher apparent clearance of the alternate pathway; induction of the same pathway would lead to an increased total clearance but decreased drug AUC, and reduced clearance of the alternate pathway. The use of an increased MRT to explain increased extents of metabolism upon increased apical excretion is not tenable in these organs or "open systems" since the MRT of drug in the cell is reduced with irreversible loss from biliary excretion or hastened gastrointestinal transit of the secreted drug in the lumen. Data in the literature for the Caco-2 system, knockout animals and organ perfusion systems were discussed in relation to these concepts on clearance based on fundamental, pharmacokinetic theory. The shortcomings in data interpretation were discussed. The general conclusion is that a reciprocal relationship exists between the clearances related to enzymes and apical transporters due to their competition for the substrate within the cell, and is a relationship independent of the MRT of drug in the system.

Caco-2 cell monolayers as a tool to study simultaneous phase II metabolism and metabolite efflux of indomethacin, paracetamol and 1-naphthol

The human intestinal cell line, Caco-2, was used to study compounds - indomethacin, paracetamol and 1-naphthol - that undergo intestinal phase II metabolism followed by apical and/or basolateral efflux of the metabolites and/or parent compounds. The interplay was studied during permeability experiments across fully differentiated Caco-2 cell monolayers. The parent compounds and their glucuronide and/or sulfate metabolites were detected by LC-MS/MS. Conjugation of the model compounds and effluxes of their metabolites were observed. The efflux of indomethacin glucuronide was apical, but complementary basolateral efflux was observed at the highest indomethacin concentration (500 microM), probably due to apical saturation. Paracetamol glucuronide was not formed in these experiments, but apical and basolateral effluxes of paracetamol sulfate were observed. A typical bell-shaped inhibition curve was observed for the formation of 1-naphthol glucuronides, indicating substrate or product inhibition of the UGT enzyme(s) at higher 1-naphthol concentrations (200 microM and 500 microM). Based on these results, the fully differentiated Caco-2 cell monolayers can be applied as a platform for qualitative in vitro studies, where phase II metabolism and efflux activities are ongoing simultaneously.