A whole-body physiologically based pharmacokinetic model incorporating dispersion concepts: short and long time characteristics

The Application of a Physiologically Based Toxicokinetic Model in Health Risk Assessment

Toxicokinetics plays a crucial role in the health risk assessments of xenobiotics. Classical compartmental models are limited in their ability to determine chemical concentrations in specific organs or tissues, particularly target organs or tissues, and their limited interspecific and exposure route extrapolation hinders satisfactory health risk assessment. In contrast, physiologically based toxicokinetic (PBTK) models quantitatively describe the absorption, distribution, metabolism, and excretion of chemicals across various exposure routes and doses in organisms, establishing correlations with toxic effects. Consequently, PBTK models serve as potent tools for extrapolation and provide a theoretical foundation for health risk assessment and management. This review outlines the construction and application of PBTK models in health risk assessment while analyzing their limitations and future perspectives.

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.

Exploring the Pharmacokinetic Mysteries of the Liver: Application of Series Compartment Models of Hepatic Elimination

Among the basic hepatic clearance models, the dispersion model (DM) is the most physiologically sound compared with the well-stirred model and the parallel tube model. However, its application in physiologically-based pharmacokinetic (PBPK) modeling has been limited due to computational complexities. The series compartment models (SCM) of hepatic elimination that treats the liver as a cascade of well-stirred compartments connected by hepatic blood flow exhibits some mathematical similarities to the DM but is easier to operate. This work assesses the quantitative correlation between the SCM and DM and demonstrates the operation of the SCM in PBPK with the published single-dose blood and liver concentration-time data of six flow-limited compounds. The predicted liver concentrations and the estimated intrinsic clearance (CLint ) and PBPK-operative tissue-to-plasma partition coefficient (Kp ) values were shown to depend on the number of liver sub-compartments (n) and hepatic enzyme zonation in the SCM. The CLint and Kp decreased with increasing n, with more remarkable differences for drugs with higher hepatic extraction ratios. Given the same total CLint , the SCM yields a higher Kp when the liver perivenous region exhibits a lower CLint as compared with a high CLint at this region. Overall, the SCM nicely approximates the DM in characterizing hepatic elimination and offers an alternative flexible approach as well as providing some insights regarding sequential drug concentrations in the liver. SIGNIFICANCE STATEMENT: The SCM nicely approximates the DM when applied in PBPK for characterizing hepatic elimination. The number of liver sub-compartments and hepatic enzyme zonation are influencing factors for the SCM resulting in model-dependent predictions of total/internal liver concentrations and estimates of CLint and the PBPK-operative Kp . Such model-dependency may have an impact when the SCM is used for in vitro-to-in vivo extrapolation (IVIVE) and may also be relevant for PK/PD/toxicological effects when it is the driving force for such responses.

Hepatic transporter drug-drug interactions: an evaluation of approaches and methodologies

INTRODUCTION

Drug-drug interactions (DDIs) continue to account for 5% of hospital admissions and therefore remain a major regulatory concern. Effective, quantitative prediction of DDIs will reduce unexpected clinical findings and encourage projects to frontload DDI investigations rather than concentrating on risk management ('manage the baggage') later in drug development. A key challenge in DDI prediction is the discrepancies between reported models. Areas covered: The current synopsis focuses on four recent influential publications on hepatic drug transporter DDIs using static models that tackle interactions with individual transporters and in combination with other drug transporters and metabolising enzymes. These models vary in their assumptions (including input parameters), transparency, reproducibility and complexity. In this review, these facets are compared and contrasted with recommendations made as to their application. Expert opinion: Over the past decade, static models have evolved from simple [I]/k_i models to incorporate victim and perpetrator disposition mechanisms including the absorption rate constant, the fraction of the drug metabolised/eliminated and/or clearance concepts. Nonetheless, models that comprise additional parameters and complexity do not necessarily out-perform simpler models with fewer inputs. Further, consideration of the property space to exploit some drug target classes has also highlighted the fine balance required between frontloading and back-loading studies to design out or 'manage the baggage'.

Exploration of PBPK Model-Calculation of Drug Time Course in Tissue Using IV Bolus Drug Plasma Concentration-Time Profile and the Physiological Parameters of the Organ

An uncommon innovative consideration of the well-stirred linear physiologically based pharmacokinetic model and the drug plasma concentration-time profile, which is measured in routine intravenous bolus pharmacokinetic study, was applied for the calculation of the drug time course in human tissues. This cannot be obtained in the in vivo pharmacokinetic study. The physiological parameters of the organ such as organ tissue volume, organ blood flow rate, and its vascular volume were used in the calculation. The considered method was applied to calculate the time course of midazolam, alprazolam, quinidine, and diclofenac in human organs or tissues. The suggested method might be applied for the prediction of drug concentration-time profile in tissues and consequently the drug concentration level in the targeted tissue, as well as the possible undesirable toxic levels in other tissues.

A PBPK model describing a xenobiotic with a short PK event scale

Physiologically-based pharmacokinetic (PBPK) modeling has been widely used in human risk assessment and in early drug development to predict human PK from in vitro and/or in vivo animal data. Recently, the application of PBPK modeling has been extended to the evaluation of drug-drug interactions. For most xenobiotic agents, the PK event scale such as elimination is in hours or days. This is much longer than the transit time of the agent in the body, and a PBPK model can be significantly simplified through lumping based on the physiochemical properties, mass transfer, and biotransformation. However, for a xenobiotic agent with a short PK event scale, e.g. in minutes, such an approach is not applicable. In this manuscript, the authors used the observed PK data from an ultrasound contrast agent to illustrate the role of a short PK event scale in the development of a suitable PBPK model. The model development process showed that a PBPK model assuming uniform venous and arterial blood pools, with a static lung model including alveolar and tissue regions, was unable to adequately capture the characteristics of the PK of the agent. Detailed information describing the pulmonary and cardiovascular circulation, and a heterogeneous dynamic lung model became necessary for the model. This exercise once again demonstrates the importance of the principles and methodologies that have been established since the 1960s that need to be followed during PBPK model development.

A 3-D mathematical model to identify organ-specific risks in rats during thermal stress

Early prediction of the adverse outcomes associated with heat stress is critical for effective management and mitigation of injury, which may sometimes lead to extreme undesirable clinical conditions, such as multiorgan dysfunction syndrome and death. Here, we developed a computational model to predict the spatiotemporal temperature distribution in a rat exposed to heat stress in an attempt to understand the correlation between heat load and differential organ dysfunction. The model includes a three-dimensional representation of the rat anatomy obtained from medical imaging and incorporates the key mechanisms of heat transfer during thermoregulation. We formulated a novel approach to estimate blood temperature by accounting for blood mixing from the different organs and to estimate the effects of the circadian rhythm in body temperature by considering day-night variations in metabolic heat generation and blood perfusion. We validated the model using in vivo core temperature measurements in control and heat-stressed rats and other published experimental data. The model predictions were within 1 SD of the measured data. The liver demonstrated the greatest susceptibility to heat stress, with the maximum temperature reaching 2°C higher than the measured core temperature and 95% of its volume exceeding the targeted experimental core temperature. Other organs also attained temperatures greater than the core temperature, illustrating the need to monitor multiple organs during heat stress. The model facilitates the identification of organ-specific risks during heat stress and has the potential to aid in the development of improved clinical strategies for thermal-injury prevention and management.

YAGYOPATHY VERSUS ORAL AND IV DRUG ADMINISTRATION: EVALUATION FOR PULMONARY TUBERCULOSIS USING COMPARTMENT MODELING

With pulmonary drug administration gaining more and more importance, there is an obvious need for improvement in the existing methods and search for the newer ones. We have carried out the first ever study on the potentials of yagyopathy in this regard. While introducing this new mode of pulmonary drug administration, we also highlight some preliminary clinical and empirical results on drug inhalation characterization of yagyopathy that indicate its effectiveness in the treatment of pulmonary tuberculosis and thus motivate the present study. We construct mathematical models to evaluate the efficacy of this method of herbal cure vis-à-vis the common modes of oral and intravenous medication. The models are analyzed mathematically for the availability of the drug and other important pharmacokinetic features for the case when the site of infection and hence of desired activation is located in the lungs. Computer simulation experiments and validation are also carried out using available data from relevant empirical studies. The results further support significant potential of yagyopathy especially in terms of higher lung deposits, (bio)availability and residence time. The scope of yagyopathy and related research directions are discussed.

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

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

Physiologically-based pharmacokinetics in drug development and regulatory science

The application of physiologically-based pharmacokinetic (PBPK) modeling is coming of age in drug development and regulation, reflecting significant advances over the past 10 years in the predictability of key pharmacokinetic (PK) parameters from human in vitro data and in the availability of dedicated software platforms and associated databases. Specific advances and contemporary challenges with respect to predicting the processes of drug clearance, distribution, and absorption are reviewed, together with the ability to anticipate the quantitative extent of PK-based drug-drug interactions and the impact of age, genetics, disease, and formulation. The value of this capability in selecting and designing appropriate clinical studies, its implications for resource-sparing techniques, and a more holistic view of the application of PK across the preclinical/clinical divide are considered. Finally, some attention is given to the positioning of PBPK within the drug development and approval paradigm and its future application in truly personalized medicine.

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.

Comparison of three physiologically-based pharmacokinetic models for the prediction of contrast agent distribution measured by dynamic MR imaging

PURPOSE

To compare the performance of three physiologically-based pharmacokinetic (PBPK) models for predicting gadolinium contrast agent concentration-time curves (Gd-CTCs) obtained in superior sagittal sinus (SSS), cerebral cortex, and psoas muscle.

MATERIALS AND METHODS

Three published whole-body PBPK models were modified to predict Gd-CTCs in normal-appearing tissue. The models differed in the number of organs modeled and total number of compartments, and were designated as the "well-mixed," "delay," and "dispersion" models. The suitability of the three models to predict Gd-CTC was studied using data from dynamic contrast-enhanced MR perfusion imaging obtained at 1.5T from 10 patients with glioblastoma multiforme and at 3.0T from five patients with liver metastases.

RESULTS

The dispersion model produced better fits than the delay model in the SSS (P < 0.0001) and cerebral cortex (P < 0.0001), and better fits than the well-mixed model in psoas muscle (P < 0.005). No model produced better fits than the dispersion model at any of the three locations.

CONCLUSION

In this evaluation, the dispersion model was most robust for prediction of Gd-CTCs derived from dynamic contrast-enhanced (DCE)-MRI. This represents a preliminary step in the development of a PBPK model useful for predicting Gd-CTCs at a time resolution appropriate for dynamic MRI applications.

Whole-body physiologically based pharmacokinetic models

This review summarizes the most recent developments in and applications of physiologically based pharmacokinetic (PBPK) modeling methodology originating from both the pharmaceutical and environmental toxicology areas. It focuses on works published in the last 5 years, although older seminal papers have also been referenced. After a brief introduction to the field and several essential definitions, the main body of the text is structured to follow the major steps of a typical PBPK modeling exercise. Various applications of the methodology are briefly described. The major future trends and perspectives are outlined. The main conclusion from the review of the available literature is that PBPK modeling, despite its obvious potential and recent incremental developments, has not taken the place it deserves, especially in pharmaceutical and drug development sciences.

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

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

Evaluation of antiangiogenic treatment effects on tumors' microcirculation by Bayesian physiological pharmacokinetic modeling and magnetic resonance imaging

A physiological pharmacokinetic (PBPK) model was used to estimate tumor microcirculation in nude mice with a grafted tumor. The kinetics of a rapid clearance blood pool agent, Vistarem, were investigated by dynamic MRI after bolus administration. Signal enhancements were recorded in arterial blood and in tumor tissue. To analyze these data, we developed a whole-body mathematical model of the agent's biodistribution using physiological parameters. The model included six compartments: arterial and venous plasma, tumor (split into capillaries and interstitium), and the rest of the body (also split into capillaries and interstitium). As an application, changes in tumor microcirculation parameters were evaluated in mice receiving either an antiangiogenic treatment (ZD4190) or a placebo. The analysis was performed in a Bayesian framework, and the model was fitted to experimental data using Markov Chain Monte Carlo techniques. Results showed a significant difference in tumor microcirculation between the two groups of mice when the microcirculation parameters are considered together. This whole-body physiological model enables to analyze jointly data in tumor tissue and in arterial blood. This leads to accurate estimates of microcirculation parameters and the evaluation of their uncertainty.

Human physiologically based pharmacokinetic model for propofol

Background

Propofol is widely used for both short-term anesthesia and long-term sedation. It has unusual pharmacokinetics because of its high lipid solubility. The standard approach to describing the pharmacokinetics is by a multi-compartmental model. This paper presents the first detailed human physiologically based pharmacokinetic (PBPK) model for propofol.

Methods

PKQuest, a freely distributed software routine , was used for all the calculations. The "standard human" PBPK parameters developed in previous applications is used. It is assumed that the blood and tissue binding is determined by simple partition into the tissue lipid, which is characterized by two previously determined set of parameters: 1) the value of the propofol oil/water partition coefficient; 2) the lipid fraction in the blood and tissues. The model was fit to the individual experimental data of Schnider et. al., Anesthesiology, 1998; 88:1170 in which an initial bolus dose was followed 60 minutes later by a one hour constant infusion.

Results

The PBPK model provides a good description of the experimental data over a large range of input dosage, subject age and fat fraction. Only one adjustable parameter (the liver clearance) is required to describe the constant infusion phase for each individual subject. In order to fit the bolus injection phase, for 10 or the 24 subjects it was necessary to assume that a fraction of the bolus dose was sequestered and then slowly released from the lungs (characterized by two additional parameters). The average weighted residual error (WRE) of the PBPK model fit to the both the bolus and infusion phases was 15%; similar to the WRE for just the constant infusion phase obtained by Schnider et. al. using a 6-parameter NONMEM compartmental model.

Conclusion

A PBPK model using standard human parameters and a simple description of tissue binding provides a good description of human propofol kinetics. The major advantage of a PBPK model is that it can be used to predict the changes in kinetics produced by variations in physiological parameters. As one example, the model simulation of the changes in pharmacokinetics for morbidly obese subjects is discussed.

Position of the American Dietetic Association and Dietitians of Canada: nutrition intervention in the care of persons with human immunodeficiency virus infection

Infection with the human immunodeficiency virus (HIV) and the development of acquired immunodeficiency syndrome (AIDS) have had a significant impact on domestic and global health, social, political, and economic outcomes. Prevention and treatment efforts to control HIV infection are more demanding than in previous decades. Achieving food and nutrition security, and managing nutrition-related complications of HIV infection and the multiple aspects of disease initiated by or surrounding HIV infection, referred to as HIV disease, remain challenges for patients and for those involved with HIV/AIDS prevention, care, and treatment efforts. Confounding clinical issues include medication interactions, coinfection with other infections and diseases, wasting, lipodystrophy, and others. Dietetics professionals, other health care professionals, and people infected with HIV will need to understand and address multiple complex aspects of HIV infection and treatment to improve survival, body functions, and overall quality of life. Individualized nutrition care plans will be an essential feature of the medical management of persons with HIV infection and AIDS.

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.

In silico prediction of ADME and pharmacokinetics. Report of an expert meeting organised by COST B15

The computational approach is one of the newest and fastest developing techniques in pharmacokinetics, ADME (absorption, distribution, metabolism, excretion) evaluation, drug discovery and toxicity. However, to date, the software packages devoted to ADME prediction, especially of metabolism, have not yet been adequately validated and still require improvements to be effective. Most are 'open' systems, under constant evolution and able to incorporate rapidly, and often easily, new information from user or developer databases. Quantitative in silico predictions are now possible for several pharmacokinetic (PK) parameters, particularly absorption and distribution. The emerging consensus is that the predictions are no worse than those made using in vitro tests, with the decisive advantage that much less investment in technology, resources and time is needed. In addition, and of critical importance, it is possible to screen virtual compounds. Some packages are able to handle thousands of molecules in a few hours. However, common experience shows that, in part at least for essentially irrational reasons, there is currently a lack of confidence in these approaches. An effort should be made by the software producers towards more transparency, in order to improve the confidence of their consumers. It seems highly probable that in silico approaches will evolve rapidly, as did in vitro methods during the last decade. Past experience with the latter should be helpful in avoiding repetition of similar errors and in taking the necessary steps to ensure effective implementation. A general concern is the lack of access to the large amounts of data on compounds no longer in development, but still kept secret by the pharmaceutical industry. Controlled access to these data could be particularly helpful in validating new in silico approaches.

A dispersion model for cellular signal transduction cascades

PURPOSE

The purpose of this study was to evaluate the ability of the dispersion model to describe pharmacokinetic-pharmacodynamic data containing contributions from signal transduction cascades.

METHODS

The partial differential equations and appropriate boundary conditions describing the dispersion model for signal transduction were obtained. Explicit analytical solutions to the dispersion equation were not available, and a numerical approach was necessary. Solutions were obtained by numerical inversion of the output Laplace transform. Generalized least square fitting was used to obtain parameter estimates for a variety of experimental data sets.

RESULTS

The parameters of the dispersion model estimate the relative roles of diffusion, convection, and chemical reaction in signal transduction. The model is capable of describing messenger RNA and protein expression kinetics induced by drug action.

CONCLUSIONS

The dispersion model may find potential applications in pharmacokinetic-pharmacodynamic models involving delayed drug effects mediated by transcriptional changes.

Predicting ADME properties in silico: methods and models

Unfavourable absorption, distribution, metabolism and elimination (ADME) properties have been identified as a major cause of failure for candidate molecules in drug development. Consequently, there is increasing interest in the early prediction of ADME properties, with the objective of increasing the success rate of compounds reaching development. This review explores in silico approaches and selected published models for predicting ADME properties from chemical structure alone. In particular, we provide a comparison of methods based on pattern recognition to identify correlations between molecular descriptors and ADME properties, structural models based on classical molecular mechanics and quantum mechanical techniques for modelling chemical reactions.

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.