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1.  Using Bayesian-PBPK modeling for assessment of inter-individual variability and subgroup stratification 
Purpose
Inter-individual variability in clinical endpoints and occurrence of potentially severe adverse effects represent an enormous challenge in drug development at all phases of (pre-)clinical research. To ensure patient safety it is important to identify adverse events or critical subgroups within the population as early as possible. Hence, a comprehensive understanding of the processes governing pharmacokinetics and pharmacodynamics is of utmost importance. In this paper we combine Bayesian statistics with detailed mechanistic physiologically-based pharmacokinetic (PBPK) models. On the example of pravastatin we demonstrate that this combination provides a powerful tool to investigate inter-individual variability in groups of patients and to identify clinically relevant homogenous subgroups in an unsupervised approach. Since PBPK models allow the identification of physiological, drug-specific and genotype-specific knowledge separately, our approach supports knowledge-based extrapolation to other drugs or populations.
Methods
PBPK models are based on generic distribution models and extensive collections of physiological parameters and allow a mechanistic investigation of drug distribution and drug action. To systematically account for parameter variability within patient populations, a Bayesian-PBPK approach is developed rigorously quantifying the probability of a parameter given the amount of information contained in the measured data. Since these parameter distributions are high-dimensional, a Markov chain Monte Carlo algorithm is used, where the physiological and drug-specific parameters are considered in separate blocks.
Results
Considering pravastatin pharmacokinetics as an application example, Bayesian-PBPK is used to investigate inter-individual variability in a cohort of 10 patients. Correlation analyses infer structural information about the PBPK model. Moreover, homogeneous subpopulations are identified a posteriori by examining the parameter distributions, which can even be assigned to a polymorphism in the hepatic organ anion transporter OATP1B1.
Conclusions
The presented Bayesian-PBPK approach systematically characterizes inter-individual variability within a population by updating prior knowledge about physiological parameters with new experimental data. Moreover, clinically relevant homogeneous subpopulations can be mechanistically identified. The large scale PBPK model separates physiological and drug-specific knowledge which allows, in combination with Bayesian approaches, the iterative assessment of specific populations by integrating information from several drugs.
Electronic supplementary material
The online version of this article (doi:10.1186/2193-9616-1-6) contains supplementary material, which is available to authorized users.
doi:10.1186/2193-9616-1-6
PMCID: PMC4230716  PMID: 25505651
Physiologically-based pharmacokinetic modeling; Bayesian approaches; Markov chain Monte Carlo; Inter-individual variability; OATP1B1; Drug development; Pravastatin
2.  Physiologically Based Pharmacokinetic Modeling: Methodology, Applications, and Limitations with a Focus on Its Role in Pediatric Drug Development 
The concept of physiologically based pharmacokinetic (PBPK) modeling was introduced years ago, but it has not been practiced significantly. However, interest in and implementation of this modeling technique have grown, as evidenced by the increased number of publications in this field. This paper demonstrates briefly the methodology, applications, and limitations of PBPK modeling with special attention given to discuss the use of PBPK models in pediatric drug development and some examples described in detail. Although PBPK models do have some limitations, the potential benefit from PBPK modeling technique is huge. PBPK models can be applied to investigate drug pharmacokinetics under different physiological and pathological conditions or in different age groups, to support decision-making during drug discovery, to provide, perhaps most important, data that can save time and resources, especially in early drug development phases and in pediatric clinical trials, and potentially to help clinical trials become more “confirmatory” rather than “exploratory”.
doi:10.1155/2011/907461
PMCID: PMC3118302  PMID: 21716673
3.  Applications of linking PBPK and PD models to predict the impact of genotypic variability, formulation differences, differences in target binding capacity and target site drug concentrations on drug responses and variability 
This study aimed to demonstrate the added value of integrating prior in vitro data and knowledge-rich physiologically based pharmacokinetic (PBPK) models with pharmacodynamics (PDs) models. Four distinct applications that were developed and tested are presented here. PBPK models were developed for metoprolol using different CYP2D6 genotypes based on in vitro data. Application of the models for prediction of phenotypic differences in the pharmacokinetics (PKs) and PD compared favorably with clinical data, demonstrating that these differences can be predicted prior to the availability of such data from clinical trials. In the second case, PK and PD data for an immediate release formulation of nifedipine together with in vitro dissolution data for a controlled release (CR) formulation were used to predict the PK and PD of the CR. This approach can be useful to pharmaceutical scientists during formulation development. The operational model of agonism was used in the third application to describe the hypnotic effects of triazolam, and this was successfully extrapolated to zolpidem by changing only the drug related parameters from in vitro experiments. This PBPK modeling approach can be useful to developmental scientists who which to compare several drug candidates in the same therapeutic class. Finally, differences in QTc prolongation due to quinidine in Caucasian and Korean females were successfully predicted by the model using free heart concentrations as an input to the PD models. This PBPK linked PD model was used to demonstrate a higher sensitivity to free heart concentrations of quinidine in Caucasian females, thereby providing a mechanistic understanding of a clinical observation. In general, permutations of certain conditions which potentially change PK and hence PD may not be amenable to the conduct of clinical studies but linking PBPK with PD provides an alternative method of investigating the potential impact of PK changes on PD.
doi:10.3389/fphar.2014.00258
PMCID: PMC4244809  PMID: 25505415
PBPK linked PD models; CYP P450 genotypes and response; heart drug concentration and QTc; formulation effects on drug response; target site concentrations and response
4.  Development of a Paediatric Population-Based Model of the Pharmacokinetics of Rivaroxaban 
Clinical Pharmacokinetics  2013;53(1):89-102.
Background
Venous thromboembolism has been increasingly recognised as a clinical problem in the paediatric population. Guideline recommendations for antithrombotic therapy in paediatric patients are based mainly on extrapolation from adult clinical trial data, owing to the limited number of clinical trials in paediatric populations. The oral, direct Factor Xa inhibitor rivaroxaban has been approved in adult patients for several thromboembolic disorders, and its well-defined pharmacokinetic and pharmacodynamic characteristics and efficacy and safety profiles in adults warrant further investigation of this agent in the paediatric population.
Objective
The objective of this study was to develop and qualify a physiologically based pharmacokinetic (PBPK) model for rivaroxaban doses of 10 and 20 mg in adults and to scale this model to the paediatric population (0–18 years) to inform the dosing regimen for a clinical study of rivaroxaban in paediatric patients.
Methods
Experimental data sets from phase I studies supported the development and qualification of an adult PBPK model. This adult PBPK model was then scaled to the paediatric population by including anthropometric and physiological information, age-dependent clearance and age-dependent protein binding. The pharmacokinetic properties of rivaroxaban in virtual populations of children were simulated for two body weight-related dosing regimens equivalent to 10 and 20 mg once daily in adults. The quality of the model was judged by means of a visual predictive check. Subsequently, paediatric simulations of the area under the plasma concentration–time curve (AUC), maximum (peak) plasma drug concentration (Cmax) and concentration in plasma after 24 h (C24h) were compared with the adult reference simulations.
Results
Simulations for AUC, Cmax and C24h throughout the investigated age range largely overlapped with values obtained for the corresponding dose in the adult reference simulation for both body weight-related dosing regimens. However, pharmacokinetic values in infants and preschool children (body weight <40 kg) were lower than the 90 % confidence interval threshold of the adult reference model and, therefore, indicated that doses in these groups may need to be increased to achieve the same plasma levels as in adults. For children with body weight between 40 and 70 kg, simulated plasma pharmacokinetic parameters (Cmax, C24h and AUC) overlapped with the values obtained in the corresponding adult reference simulation, indicating that body weight-related exposure was similar between these children and adults. In adolescents of >70 kg body weight, the simulated 90 % prediction interval values of AUC and C24h were much higher than the 90 % confidence interval of the adult reference population, owing to the weight-based simulation approach, but for these patients rivaroxaban would be administered at adult fixed doses of 10 and 20 mg.
Conclusion
The paediatric PBPK model developed here allowed an exploratory analysis of the pharmacokinetics of rivaroxaban in children to inform the dosing regimen for a clinical study in paediatric patients.
Electronic supplementary material
The online version of this article (doi:10.1007/s40262-013-0090-5) contains supplementary material, which is available to authorized users.
doi:10.1007/s40262-013-0090-5
PMCID: PMC3889826  PMID: 23912563
5.  Cutting Edge PBPK Models and Analyses: Providing the Basis for Future Modeling Efforts and Bridges to Emerging Toxicology Paradigms 
Journal of Toxicology  2012;2012:852384.
Physiologically based Pharmacokinetic (PBPK) models are used for predictions of internal or target dose from environmental and pharmacologic chemical exposures. Their use in human risk assessment is dependent on the nature of databases (animal or human) used to develop and test them, and includes extrapolations across species, experimental paradigms, and determination of variability of response within human populations. Integration of state-of-the science PBPK modeling with emerging computational toxicology models is critical for extrapolation between in vitro exposures, in vivo physiologic exposure, whole organism responses, and long-term health outcomes. This special issue contains papers that can provide the basis for future modeling efforts and provide bridges to emerging toxicology paradigms. In this overview paper, we present an overview of the field and introduction for these papers that includes discussions of model development, best practices, risk-assessment applications of PBPK models, and limitations and bridges of modeling approaches for future applications. Specifically, issues addressed include: (a) increased understanding of human variability of pharmacokinetics and pharmacodynamics in the population, (b) exploration of mode of action hypotheses (MOA), (c) application of biological modeling in the risk assessment of individual chemicals and chemical mixtures, and (d) identification and discussion of uncertainties in the modeling process.
doi:10.1155/2012/852384
PMCID: PMC3413973  PMID: 22899915
6.  Physiologically based pharmacokinetic model of lapatinib developed in mice and scaled to humans 
Lapatinib is an oral 4-anilinoquinazoline derivative that dually inhibits epidermal growth factor receptor and human epidermal growth factor receptor 2 (HER2). This drug is a mere decade old and has only been approved by the FDA for the treatment of breast cancer since 2007. Consequently, the intricacies of the pharmacokinetics are still being elucidated. In the work presented herein, we determined the biodistribution of orally administered lapatinib in mouse plasma, brain, heart, lung, kidney, intestine, liver, muscle and adipose tissue. Using this data, we subsequently developed a physiologically based pharmacokinetic (PBPK) model of lapatinib in mice that accurately predicted the tissue concentrations after doses of 30, 60 and 90 mg/kg. By taking into account interspecies differences in physiology and physiochemistry, we then extrapolated the mouse PBPK model to humans. Our model predictions closely reflected lapatinib plasma pharmacokinetics in healthy subjects. Additionally, we were also able to simulate the pharmacokinetics of this drug in the plasma of patients with solid malignancies by incorporating a decrease in liver metabolism into the model. Finally, our PBPK model also facilitated the estimation of various human tissue exposures to lapatinib, which harmonize with the organ-specific toxicities observed in clinical trials. This first-generation PBPK model of lapatinib can be further improved with a greater understanding of lapatinib absorption, distribution, metabolism and excretion garnered from subsequent in vitro and in vivo studies and expanded to include other pharmacokinetic determinants, including efflux transporters, metabolite generation, combination dosing, etc., to better predict lapatinib disposition in both mouse and man.
doi:10.1007/s10928-012-9295-8
PMCID: PMC3897212  PMID: 23315145
Breast cancer; Lapatinib; Physiologically based pharmacokinetic modeling; Tyrosine kinase inhibitor
7.  Physiologically Based Pharmacokinetic Models in the Prediction of Oral Drug Exposure Over the Entire Pediatric Age Range—Sotalol as a Model Drug 
The AAPS Journal  2014;16(2):226-239.
In recent years, the increased interest in pediatric research has enforced the role of physiologically based pharmacokinetic (PBPK) models in pediatric drug development. However, an existing lack of published examples contributes to some uncertainties about the reliability of their predictions of oral drug exposure. Developing and validating pediatric PBPK models for oral drug application shall enrich our knowledge about their limitations and lead to a better use of the generated data. This study was conducted to investigate how whole-body PBPK models describe the oral pharmacokinetics of sotalol over the entire pediatric age. Two leading software tools for whole-body PBPK modeling: Simcyp® (Simcyp Ltd, Sheffield, UK) and PK-SIM® (Bayer Technology Services GmbH, Leverkusen, Germany), were used. Each PBPK model was first validated in adults before scaling to children. Model input parameters were collected from the literature and clinical data for 80 children were used to compare predicted and observed values. The results obtained by both models were comparable and gave an adequate description of sotalol pharmacokinetics in adults and in almost all pediatric age groups. Only in neonates, the mean ratio(Obs/Pred) for any PK parameter exceeded a twofold error range, 2.56 (95% confidence interval (CI), 2.10–3.49) and 2.15 (95% CI, 1.77–2.99) for area under the plasma concentration-time curve from the first to the last concentration point and maximal concentration (Cmax) using SIMCYP® and 2.37 (95% CI, 1.76–3.25) for time to reach Cmax using PK-SIM®. The two PBPK models evaluated in this study reflected properly the age-related pharmacokinetic changes and predicted adequately the oral sotalol exposure in children of different ages, except in neonates.
doi:10.1208/s12248-013-9555-6
PMCID: PMC3933580  PMID: 24399240
administration (oral); child; computer simulation; pharmacokinetics; sotalol
8.  Physiologically based pharmacokinetic models for everolimus and sorafenib in mice 
Cancer chemotherapy and pharmacology  2013;71(5):1219-1229.
Purpose
Everolimus is a mammalian target of rapamycin (mTOR) inhibitor approved as an immunosuppressant and for second-line therapy of hepatocellular carcinoma (HCC) and renal cell carcinoma (RCC). Sorafenib is a multikinase inhibitor used as first-line therapy in HCC and RCC. This study assessed the pharmacokinetics (PK) of everolimus and sorafenib alone and in combination in plasma and tissues, developed physiologically based pharmacokinetic (PBPK) models in mice, and assessed the possibility of PK drug interactions.
Methods
Single and multiple oral doses of everolimus and sorafenib were administered alone and in combination in immunocompetent male mice and to severe combined immune-deficient (SCID) mice bearing low-passage, patient-derived pancreatic adenocarcinoma in seven different studies. Plasma and tissue samples including tumor were collected over a 24-h period and analyzed by liquid chromatography-tandem mass spectrometry (LC–MS/MS). Distribution of everolimus and sorafenib to the brain, muscle, adipose, lungs, kidneys, pancreas, spleen, liver, GI, and tumor was modeled as perfusion rate-limited, and all data from the diverse studies were fitted simultaneously using a population approach.
Results
PBPK models were developed for everolimus and sorafenib. PBPK analysis showed that the two drugs in combination had the same PK as each drug given alone. A twofold increase in sorafenib dose increased tumor exposure tenfold, thus suggesting involvement of transporters in tumor deposition of sorafenib.
Conclusions
The developed PBPK models suggested the absence of PK interaction between the two drugs in mice. These studies provide the basis for pharmacodynamic evaluation of these drugs in patient-derived primary pancreatic adenocarcinomas explants.
doi:10.1007/s00280-013-2116-y
PMCID: PMC3755750  PMID: 23455451
Everolimus; Sorafenib; Pancreatic cancer; PBPK; Patient-derived pancreatic adenocarcinoma
9.  Physiologically-based pharmacokinetic tissue compartment model selection in drug development and risk assessment 
Journal of Pharmaceutical Sciences  2011;101(1):424-435.
The well-stirred tank (WST) has been the predominant flow-limited tissue compartment model in physiologically-based pharmacokinetic (PBPK) modeling. Recently, we developed a two-region asymptotically reduced (TAR) PBPK tissue compartment model through an asymptotic approximation to a two-region vascular-extravascular system to incorporate more biophysical detail than the WST model. To determine the relevance of the novel flow-limited approach (F-TAR), 75 structurally diverse drugs are evaluated herein using a priori predicted tissue:plasma partition coefficients along with hybrid and whole-body PBPK of eight rat tissues to determine the impact of model selection on simulation and optimization. Simulations show the F-TAR model significantly improves the ability to predict drug exposure, with hybrid and whole-body WST model error approaching 50% for tissues with larger vascular volumes. When optimization is used to fit F-TAR and WST models to pseudo data, WST-optimized drug partition coefficients more appropriately represent curve-fitting parameters rather than biophysically meaningful partition coefficients. Median F-TAR-optimized error ranged from -0.4 to 0.3%, while WST-optimized median error ranged from -22.2 to 1.8%. These studies demonstrate the use of F-TAR represents a more accurate, biophysically realistic PBPK tissue model for predicting tissue exposure to drug and should be considered for use in drug development and regulatory review.
doi:10.1002/jps.22768
PMCID: PMC3314064  PMID: 21968734
Pharmacokinetics; Physiological model; Well stirred model; Tissue partition; In silico modeling; Physicochemical; Singular perturbation; Asymptotic matching; Flow-limited; Compartmental modeling
10.  A Simplified PBPK Modeling Approach for Prediction of Pharmacokinetics of Four Primarily Renally Excreted and CYP3A Metabolized Compounds During Pregnancy 
The AAPS Journal  2013;15(4):1012-1024.
During pregnancy, a drug’s pharmacokinetics may be altered and hence anticipation of potential systemic exposure changes is highly desirable. Physiologically based pharmacokinetics (PBPK) models have recently been used to influence clinical trial design or to facilitate regulatory interactions. Ideally, whole-body PBPK models can be used to predict a drug’s systemic exposure in pregnant women based on major physiological changes which can impact drug clearance (i.e., in the kidney and liver) and distribution (i.e., adipose and fetoplacental unit). We described a simple and readily implementable multitissue/organ whole-body PBPK model with key pregnancy-related physiological parameters to characterize the PK of reference drugs (metformin, digoxin, midazolam, and emtricitabine) in pregnant women compared with the PK in nonpregnant or postpartum (PP) women. Physiological data related to changes in maternal body weight, tissue volume, cardiac output, renal function, blood flows, and cytochrome P450 activity were collected from the literature and incorporated into the structural PBPK model that describes HV or PP women PK data. Subsequently, the changes in exposure (area under the curve (AUC) and maximum concentration (Cmax)) in pregnant women were simulated. Model-simulated PK profiles were overall in agreement with observed data. The prediction fold error for Cmax and AUC ratio (pregnant vs. nonpregnant) was less than 1.3-fold, indicating that the pregnant PBPK model is useful. The utilization of this simplified model in drug development may aid in designing clinical studies to identify potential exposure changes in pregnant women a priori for compounds which are mainly eliminated renally or metabolized by CYP3A4.
Electronic supplementary material
The online version of this article (doi:10.1208/s12248-013-9505-3) contains supplementary material, which is available to authorized users.
doi:10.1208/s12248-013-9505-3
PMCID: PMC3787241  PMID: 23835676
PBPK models; pharmacokinetics; physiological changes; pregnancy; systemic exposure
11.  The pharmacokinetics of the interstitial space in humans 
Background
The pharmacokinetics of extracellular solutes is determined by the blood-tissue exchange kinetics and the volume of distribution in the interstitial space in the different organs. This information can be used to develop a general physiologically based pharmacokinetic (PBPK) model applicable to most extracellular solutes.
Methods
The human pharmacokinetic literature was surveyed to tabulate the steady state and equilibrium volume of distribution of the solutes mannitol, EDTA, morphine-6-glucuronide, morphine-3-glucuronide, inulin and β-lactam antibiotics with a range of protein binding (amoxicillin, piperacillin, cefatrizine, ceforanide, flucloxacillin, dicloxacillin). A PBPK data set was developed for extracellular solutes based on the literature for interstitial organ volumes. The program PKQuest was used to generate the PBPK model predictions. The pharmacokinetics of the protein (albumin) bound β-lactam antibiotics were characterized by two parameters: 1) the free fraction of the solute in plasma; 2) the interstitial albumin concentration. A new approach to estimating the capillary permeability is described, based on the pharmacokinetics of the highly protein bound antibiotics.
Results
About 42% of the total body water is extracellular. There is a large variation in the organ distribution of this water – varying from about 13% of total tissue water for skeletal muscle, up to 70% for skin and connective tissue. The weakly bound antibiotics have flow limited capillary-tissue exchange kinetics. The highly protein bound antibiotics have a significant capillary permeability limitation. The experimental pharmacokinetics of the 11 solutes is well described using the new PBPK data set and PKQuest.
Conclusions
Only one adjustable parameter (systemic clearance) is required to completely characterize the PBPK for these extracellular solutes. Knowledge of just this systemic clearance allows one to predict the complete time course of the absolute drug concentrations in the major organs. PKQuest is freely available .
doi:10.1186/1472-6904-3-3
PMCID: PMC194216  PMID: 12890292
12.  Simulation of the pharmacokinetics of bisoprolol in healthy adults and patients with impaired renal function using whole-body physiologically based pharmacokinetic modeling 
Acta Pharmacologica Sinica  2012;33(11):1359-1371.
Aim:
To develop and evaluate a whole-body physiologically based pharmacokinetic (WB-PBPK) model of bisoprolol and to simulate its exposure and disposition in healthy adults and patients with renal function impairment.
Methods:
Bisoprolol dispositions in 14 tissue compartments were described by perfusion-limited compartments. Based the tissue composition equations and drug-specific properties such as log P, permeability, and plasma protein binding published in literatures, the absorption and whole-body distribution of bisoprolol was predicted using the 'Advanced Compartmental Absorption Transit' (ACAT) model and the whole-body disposition model, respectively. Renal and hepatic clearances were simulated using empirical scaling methods followed by incorporation into the WB-PBPK model. Model refinements were conducted after a comparison of the simulated concentration-time profiles and pharmacokinetic parameters with the observed data in healthy adults following intravenous and oral administration. Finally, the WB-PBPK model coupled with a Monte Carlo simulation was employed to predict the mean and variability of bisoprolol pharmacokinetics in virtual healthy subjects and patients.
Results:
The simulated and observed data after both intravenous and oral dosing showed good agreement for all of the dose levels in the reported normal adult population groups. The predicted pharmacokinetic parameters (AUC, Cmax, and Tmax) were reasonably consistent (<1.3-fold error) with the observed values after single oral administration of doses ranging from of 5 to 20 mg using the refined WB-PBPK model. The simulated plasma profiles after multiple oral administration of bisoprolol in healthy adults and patient with renal impairment matched well with the observed profiles.
Conclusion:
The WB-PBPK model successfully predicts the intravenous and oral pharmacokinetics of bisoprolol across multiple dose levels in diverse normal adult human populations and patients with renal insufficiency.
doi:10.1038/aps.2012.103
PMCID: PMC4011361  PMID: 23085739
bisoprolol; whole-body physiologically based pharmacokinetic model; drug absorption; drug distribution; renal function impairment
13.  Issues in the Pharmacokinetics of Trichloroethylene and Its Metabolites 
Environmental Health Perspectives  2006;114(9):1450-1456.
Much progress has been made in understanding the complex pharmacokinetics of trichloroethylene (TCE). Qualitatively, it is clear that TCE is metabolized to multiple metabolites either locally or into systemic circulation. Many of these metabolites are thought to have toxicologic importance. In addition, efforts to develop physiologically based pharmacokinetic (PBPK) models have led to a better quantitative assessment of the dosimetry of TCE and several of its metabolites. As part of a mini-monograph on key issues in the health risk assessment of TCE, this article is a review of a number of the current scientific issues in TCE pharmacokinetics and recent PBPK modeling efforts with a focus on literature published since 2000. Particular attention is paid to factors affecting PBPK modeling for application to risk assessment. Recent TCE PBPK modeling efforts, coupled with methodologic advances in characterizing uncertainty and variability, suggest that rigorous application of PBPK modeling to TCE risk assessment appears feasible at least for TCE and its major oxidative metabolites trichloroacetic acid and trichloroethanol. However, a number of basic structural hypotheses such as enterohepatic recirculation, plasma binding, and flow- or diffusion-limited treatment of tissue distribution require additional evaluation and analysis. Moreover, there are a number of metabolites of potential toxicologic interest, such as chloral, dichloroacetic acid, and those derived from glutathione conjugation, for which reliable pharmacokinetic data is sparse because of analytical difficulties or low concentrations in systemic circulation. It will be a challenge to develop reliable dosimetry for such cases.
doi:10.1289/ehp.8691
PMCID: PMC1570093  PMID: 16966104
metabolism; pharmacokinetics; physiologically based pharmacokinetic model; risk assessment; trichloroethylene
14.  BioDMET: a physiologically based pharmacokinetic simulation tool for assessing proposed solutions to complex biological problems 
We developed a detailed, whole-body physiologically based pharmacokinetic (PBPK) modeling tool for calculating the distribution of pharmaceutical agents in the various tissues and organs of a human or animal as a function of time. Ordinary differential equations (ODEs) represent the circulation of body fluids through organs and tissues at the macroscopic level, and the biological transport mechanisms and biotransformations within cells and their organelles at the molecular scale. Each major organ in the body is modeled as composed of one or more tissues. Tissues are made up of cells and fluid spaces. The model accounts for the circulation of arterial and venous blood as well as lymph. Since its development was fueled by the need to accurately predict the pharmacokinetic properties of imaging agents, BioDMET is more complex than most PBPK models. The anatomical details of the model are important for the imaging simulation endpoints. Model complexity has also been crucial for quickly adapting the tool to different problems without the need to generate a new model for every problem. When simpler models are preferred, the non-critical compartments can be dynamically collapsed to reduce unnecessary complexity. BioDMET has been used for imaging feasibility calculations in oncology, neurology, cardiology, and diabetes. For this purpose, the time concentration data generated by the model is inputted into a physics-based image simulator to establish imageability criteria. These are then used to define agent and physiology property ranges required for successful imaging. BioDMET has lately been adapted to aid the development of antimicrobial therapeutics. Given a range of built-in features and its inherent flexibility to customization, the model can be used to study a variety of pharmacokinetic and pharmacodynamic problems such as the effects of inter-individual differences and disease-states on drug pharmacokinetics and pharmacodynamics, dosing optimization, and inter-species scaling. While developing a tool to aid imaging agent and drug development, we aimed at accelerating the acceptance and broad use of PBPK modeling by providing a free mechanistic PBPK software that is user friendly, easy to adapt to a wide range of problems even by non-programmers, provided with ready-to-use parameterized models and benchmarking data collected from the peer-reviewed literature.
Electronic supplementary material
The online version of this article (doi:10.1007/s10928-011-9229-x) contains supplementary material, which is available to authorized users.
doi:10.1007/s10928-011-9229-x
PMCID: PMC3258408  PMID: 22161221
PBPK modeling; Whole body model; Biodistribution; Pharmacokinetics; Mechanistic model; Imaging
15.  Use of Probabilistic Modeling within a Physiologically Based Pharmacokinetic Model To Predict Sulfamethazine Residue Withdrawal Times in Edible Tissues in Swine 
The presence of antimicrobial agents in edible tissues of food-producing animals remains a major public health concern. Probabilistic modeling techniques incorporated into a physiologically based pharmacokinetic (PBPK) model were used to predict the amounts of sulfamethazine residues in edible tissues in swine. A PBPK model for sulfamethazine in swine was adapted to include an oral dosing route. The distributions for sensitive parameters were determined and were used in a Monte Carlo analysis to predict tissue residue times. Validation of the distributions was done by comparison of the results of a Monte Carlo analysis to those obtained with an external data set from the literature and an in vivo pilot study. The model was used to predict the upper limit of the 95% confidence interval of the 99th percentile of the population, as recommended by the U.S. Food and Drug Administration (FDA). The external data set was used to calculate the withdrawal time by using the tolerance limit algorithm designed by FDA. The withdrawal times obtained by both methods were compared to the labeled withdrawal time for the same dose. The Monte Carlo method predicted a withdrawal time of 21 days, based on the amounts of residues in the kidneys. The tolerance limit method applied to the time-limited data set predicted a withdrawal time of 12 days. The existing FDA label withdrawal time is 15 days. PBPK models can incorporate probabilistic modeling techniques that make them useful for prediction of tissue residue times. These models can be used to calculate the parameters required by FDA and explore those conditions where the established withdrawal time may not be sufficient.
doi:10.1128/AAC.01355-05
PMCID: PMC1489760  PMID: 16801411
16.  Evaluation of a Catenary PBPK Model for Predicting the In Vivo Disposition of mAbs Engineered for High-Affinity Binding to FcRn 
The AAPS Journal  2012;14(4):850-859.
Efforts have been made to extend the biological half-life of monoclonal antibody drugs (mAbs) by increasing the affinity of mAb–neonatal Fc receptor (FcRn) binding; however, mixed results have been reported. One possible reason for a poor correlation between the equilibrium affinity of mAb–FcRn binding and mAb systemic pharmacokinetics is that the timecourse of endosomal transit is too brief to allow binding to reach equilibrium. In the present work, a new physiologically based pharmacokinetic (PBPK) model has been developed to approximate the pH and time-dependent endosomal trafficking of immunoglobulin G (IgG). In this model, a catenary sub-model was utilized to describe the endosomal transit of IgG and the time dependencies in IgG–FcRn association and dissociation. The model performs as well as a previously published PBPK model, with assumed equilibrium kinetics of mAb–FcRn binding, in capturing the disposition profile of murine mAb from wild-type and FcRn knockout mice (catenary vs. equilibrium model: r2, 0.971 vs. 0.978; median prediction error, 3.38% vs. 3.79%). Compared to the PBPK model with equilibrium binding, the present catenary PBPK model predicts much more moderate changes in half-life with altered FcRn binding. For example, for a 10-fold increase in binding affinity, the catenary model predicts <2.5-fold change in half-life compared to an ∼8-fold increase as predicted by the equilibrium model; for a 100-fold increase in binding affinity, the catenary model predicts ∼7-fold change in half-life compared to >70-fold increase as predicted by the equilibrium model. Predictions of the new catenary PBPK model are more consistent with experimental results in the published literature.
Electronic supplementary material
The online version of this article (doi:10.1208/s12248-012-9395-9) contains supplementary material, which is available to authorized users.
doi:10.1208/s12248-012-9395-9
PMCID: PMC3475865  PMID: 22956476
endosomal transit; FcRn; mAb; PBPK; pharmacokinetics
17.  A Detailed Physiologically Based Model to Simulate the Pharmacokinetics and Hormonal Pharmacodynamics of Enalapril on the Circulating Endocrine Renin-Angiotensin-Aldosterone System 
The renin-angiotensin-aldosterone system (RAAS) plays a key role in the pathogenesis of cardiovascular disorders including hypertension and is one of the most important targets for drugs. A whole body physiologically based pharmacokinetic (wb PBPK) model integrating this hormone circulation system and its inhibition can be used to explore the influence of drugs that interfere with this system, and thus to improve the understanding of interactions between drugs and the target system. In this study, we describe the development of a mechanistic RAAS model and exemplify drug action by a simulation of enalapril administration. Enalapril and its metabolite enalaprilat are potent inhibitors of the angiotensin-converting-enzyme (ACE). To this end, a coupled dynamic parent-metabolite PBPK model was developed and linked with the RAAS model that consists of seven coupled PBPK models for aldosterone, ACE, angiotensin 1, angiotensin 2, angiotensin 2 receptor type 1, renin, and prorenin. The results indicate that the model represents the interactions in the RAAS in response to the pharmacokinetics (PK) and pharmacodynamics (PD) of enalapril and enalaprilat in an accurate manner. The full set of RAAS-hormone profiles and interactions are consistently described at pre- and post-administration steady state as well as during their dynamic transition and show a good agreement with literature data. The model allows a simultaneous representation of the parent-metabolite conversion to the active form as well as the effect of the drug on the hormone levels, offering a detailed mechanistic insight into the hormone cascade and its inhibition. This model constitutes a first major step to establish a PBPK-PD-model including the PK and the mode of action (MoA) of a drug acting on a dynamic RAAS that can be further used to link to clinical endpoints such as blood pressure.
doi:10.3389/fphys.2013.00004
PMCID: PMC3567458  PMID: 23404365
physiologically based pharmacokinetic model; cardiovascular; renin-angiotensin-aldosterone system; enalapril; enalaprilat
18.  Application of biologically based computer modeling to simple or complex mixtures. 
Environmental Health Perspectives  2002;110(Suppl 6):957-963.
The complexity and the astronomic number of possible chemical mixtures preclude any systematic experimental assessment of toxicology of all potentially troublesome chemical mixtures. Thus, the use of computer modeling and mechanistic toxicology for the development of a predictive tool is a promising approach to deal with chemical mixtures. In the past 15 years or so, physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling has been applied to the toxicologic interactions of chemical mixtures. This approach is promising for relatively simple chemical mixtures; the most complicated chemical mixtures studied so far using this approach contained five or fewer component chemicals. In this presentation we provide some examples of the utility of PBPK/PD modeling for toxicologic interactions in chemical mixtures. The probability of developing predictive tools for simple mixtures using PBPK/PD modeling is high. Unfortunately, relatively few attempts have been made to develop paradigms to consider the risks posed by very complex chemical mixtures such as gasoline, diesel, tobacco smoke, etc. However, recent collaboration between scientists at Colorado State University and engineers at Rutgers University attempting to use reaction network modeling has created hope for the possible development of a modeling approach with the potential of predicting the outcome of toxicology of complex chemical mixtures. We discuss the applications of reaction network modeling in the context of petroleum refining and its potential for elucidating toxic interactions with mixtures.
PMCID: PMC1241278  PMID: 12634125
19.  PRELIMINARY PHYSIOLOGICALLY BASED PHARMACOKINETIC MODELS FOR BENZO[A]PYRENE AND DIBENZO[DEF, P]CHRYSENE IN RODENTS 
Toxicology and applied pharmacology  2011;257(3):365-376.
Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental contaminants generated as byproducts of natural and anthropogenic combustion processes. Despite significant public health concern, physiologically based pharmacokinetic (PBPK) modeling efforts for PAHs have so far been limited to naphthalene, plus simpler PK models for pyrene, nitropyrene, and benzo[a]pyrene (B[a]P). The dearth of published models is due in part to the high lipophilicity, low volatility, and myriad metabolic pathways for PAHs, all of which present analytical and experimental challenges. Our research efforts have focused upon experimental approaches and initial development of PBPK models for the prototypic PAH, B[a]P, and the more potent, albeit less studied transplacental carcinogen, dibenzo[def, p]chrysene (DBC). For both compounds, model compartments included arterial and venous blood, flow limited lung, liver, richly perfused and poorly perfused tissues, diffusion limited fat, and a two compartment theoretical gut (for oral exposures). Hepatic and pulmonary metabolism was described for both compounds, as were fractional binding in blood and fecal clearance. Partition coefficients for parent PAH along with their diol and tetraol metabolites were estimated using published algorithms and verified experimentally for the hydroxylated metabolites. The preliminary PBPK models were able to describe many, but not all, of the available data sets, comprising multiple routes of exposure (oral, intravenous) and nominal doses spanning several orders of magnitude. Supported by Award Number P42 ES016465 from the National Institute of Environmental Health Sciences.
doi:10.1016/j.taap.2011.09.020
PMCID: PMC3226888  PMID: 22001385
PBPK modeling; benzo[a]pyrene; dibenzo[def; p]chrysene; polycyclic aromatic hydrocarbons
20.  A Semi-Physiologically Based Pharmacokinetic Pharmacodynamic Model for Glycyrrhizin-Induced Pseudoaldosteronism and Prediction of the Dose Limit Causing Hypokalemia in a Virtual Elderly Population 
PLoS ONE  2014;9(12):e114049.
Glycyrrhizin (GL) is a widely used food additive which can cause severe pseudoaldosteronism at high doses or after a long period of consumption. The aim of the present study was to develop a physiologically based pharmacokinetic (PBPK) pharmacodynamic (PD) model for GL-induced pseudoaldosteronism to improve the safe use of GL. Since the major metabolite of GL, glycyrrhetic acid (GA), is largely responsible for pseudoaldosteronism via inhibition of the kidney enzyme 11β-hydroxysteroiddehydrogenase 2 (11β-HSD 2), a semi-PBPK model was first developed in rat to predict the systemic pharmacokinetics of and the kidney exposure to GA. A human PBPK model was then developed using parameters either from the rat model or from in vitro studies in combination with essential scaling factors. Kidney exposure to GA was further linked to an Imax model in the 11β-HSD 2 module of the PD model to predict the urinary excretion of cortisol and cortisone. Subsequently, activation of the mineralocorticoid receptor in the renin-angiotensin-aldosterone-electrolyte system was associated with an increased cortisol level. Experimental data for various scenarios were used to optimize and validate the model which was finally able to predict the plasma levels of angiotensin II, aldosterone, potassium and sodium. The Monte Carlo method was applied to predict the probability distribution of the individual dose limits of GL causing pseudoaldosteronism in the elderly according to the distribution of sensitivity factors using serum potassium as an indicator. The critical value of the dose limit was found to be 101 mg with a probability of 3.07%.
doi:10.1371/journal.pone.0114049
PMCID: PMC4252094  PMID: 25463381
21.  Applications of physiologic pharmacokinetic modeling in carcinogenic risk assessment. 
Environmental Health Perspectives  1994;102(Suppl 11):37-50.
The use of physiologically based pharmacokinetic (PBPK) models has been proposed as a means of estimating the dose of the reactive metabolites of carcinogenic xenobiotics reaching target tissues, thereby affording an opportunity to base estimates of potential cancer risk on tissue dose rather than external levels of exposure. In this article, we demonstrate how a PBPK model can be constructed by specifying mass-balance equations for each physiological compartment included in the model. In general, this leads to a system of nonlinear partial differential equations with which to characterize the compartment system. These equations then can be solved numerically to determine the concentration of metabolites in each compartment as functions of time. In the special case of a linear pharmacokinetic system, we present simple closed-form expressions for the area under the concentration-time curves (AUC) in individual tissue compartments. A general relationship between the AUC in blood and other tissue compartments is also established. These results are of use in identifying those parameters in the models that characterize the integrated tissue dose, and which should therefore be the primary focus of sensitivity analyses. Applications of PBPK modeling for purposes of tissue dosimetry are reviewed, including models developed for methylene chloride, ethylene oxide, 1,4-dioxane, 1-nitropyrene, as well as polychlorinated biphenyls, dioxins, and furans. Special considerations in PBPK modeling related to aging, topical absorption, pregnancy, and mixed exposures are discussed. The linkage between pharmacokinetic models used for tissue dosimetry and pharmacodynamic models for neoplastic transformation of stem cells in the target tissue is explored.
PMCID: PMC1566756  PMID: 7737040
22.  Approaches to developing alternative and predictive toxicology based on PBPK/PD and QSAR modeling. 
Environmental Health Perspectives  1998;106(Suppl 6):1385-1393.
Systematic toxicity testing, using conventional toxicology methodologies, of single chemicals and chemical mixtures is highly impractical because of the immense numbers of chemicals and chemical mixtures involved and the limited scientific resources. Therefore, the development of unconventional, efficient, and predictive toxicology methods is imperative. Using carcinogenicity as an end point, we present approaches for developing predictive tools for toxicologic evaluation of chemicals and chemical mixtures relevant to environmental contamination. Central to the approaches presented is the integration of physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) and quantitative structure--activity relationship (QSAR) modeling with focused mechanistically based experimental toxicology. In this development, molecular and cellular biomarkers critical to the carcinogenesis process are evaluated quantitatively between different chemicals and/or chemical mixtures. Examples presented include the integration of PBPK/PD and QSAR modeling with a time-course medium-term liver foci assay, molecular biology and cell proliferation studies. Fourier transform infrared spectroscopic analyses of DNA changes, and cancer modeling to assess and attempt to predict the carcinogenicity of the series of 12 chlorobenzene isomers. Also presented is an ongoing effort to develop and apply a similar approach to chemical mixtures using in vitro cell culture (Syrian hamster embryo cell transformation assay and human keratinocytes) methodologies and in vivo studies. The promise and pitfalls of these developments are elaborated. When successfully applied, these approaches may greatly reduce animal usage, personnel, resources, and time required to evaluate the carcinogenicity of chemicals and chemical mixtures.
Images
PMCID: PMC1533423  PMID: 9860897
23.  A Workflow Example of PBPK Modeling to Support Pediatric Research and Development: Case Study with Lorazepam 
The AAPS Journal  2013;15(2):455-464.
The use of physiologically based pharmacokinetic (PBPK) models in the field of pediatric drug development has garnered much interest of late due to a recent Food and Drug Administration recommendation. The purpose of this study is to illustrate the developmental processes involved in creation of a pediatric PBPK model incorporating existing adult drug data. Lorazepam, a benzodiazepine utilized in both adults and children, was used as an example. A population-PBPK model was developed in PK-Sim v4.2® and scaled to account for age-related changes in size and composition of tissue compartments, protein binding, and growth/maturation of elimination processes. Dose (milligrams per kilogram) requirements for children aged 0–18 years were calculated based on simulations that achieved targeted exposures based on adult references. Predictive accuracy of the PBPK model for producing comparable plasma concentrations among 63 pediatric subjects was assessed using average-fold error (AFE). Estimates of clearance (CL) and volume of distribution (Vss) were compared with observed values for a subset of 15 children using fold error (FE). Pediatric dose requirements in young children (1–3 years) exceeded adult levels on a linear weight-adjusted (milligrams per kilogram) basis. AFE values for model-derived concentration estimates were within 1.5- and 2-fold deviation from observed values for 73% and 92% of patients, respectively. For CL, 60% and 80% of predictions were within 1.5 and 2 FE, respectively. Comparatively, predictions of Vss were more accurate with 80% and 100% of estimates within 1.5 and 2 FE, respectively. Using the presented workflow, the developed pediatric model estimated lorazepam pharmacokinetics in children as a function of age.
doi:10.1208/s12248-013-9451-0
PMCID: PMC3675728  PMID: 23344790
lorazepam; PBPK; pediatrics
24.  Human physiologically based pharmacokinetic model for propofol 
BMC Anesthesiology  2005;5:4.
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.
doi:10.1186/1471-2253-5-4
PMCID: PMC1090550  PMID: 15847680
25.  Transforming Medical Imaging: The First SCAR TRIP™ Conference 
Journal of Digital Imaging  2006;19(1):6-16.
The First Society for Computer Applications in Radiology (SCAR) Transforming the Radiological Interpretation Process (TRIP™) Conference and Workshop, “Transforming Medical Imaging” was held on January 31–February 1, 2005 in Bethesda, MD. Representatives from all areas of medical and scientific imaging—academia, research, industry, and government agencies—joined together to discuss the future of medical imaging and potential new ways to manage the explosion in numbers, size, and complexity of images generated by today's continually advancing imaging technologies. The two-day conference included plenary, scientific poster, and breakout sessions covering six major research areas related to TRIP™. These topic areas included human perception, image processing and computer-aided detection, data visualization, image set navigation and usability, databases and systems integration, and methodology evaluation and performance validation. The plenary presentations provided a general status review of each broad research field to use as a starting point for discussion in the breakout sessions, with emphasis on specific topics requiring further study. The goals for the breakout sessions were to define specific research questions in each topic area, to list the impediments to carrying out research in these fields, to suggest possible solutions and near- and distant-future directions for each general topic, and to report back to the general session. The scientific poster session provided another mechanism for presenting and discussing TRIP™-related research. This report summarizes each plenary and breakout session, and describes the group recommendations as to the issues facing the field, major impediments to progress, and the outlook for radiology in the short and long term. The conference helped refine the definition of the SCAR TRIP™ Initiative and the problems facing radiology with respect to the dramatic growth in medical imaging data, and it underscored a present and future need for the support of interdisciplinary translational research in radiology bridging bench-to-bedside. SCAR will continue to fund research grants exploring TRIP™ solutions. In addition, the organization proposes providing an infrastructure to foster collaborative research partnerships between SCAR corporate and academic members in the form of a TRIP™ Imaging Informatics Network (TRIPI2N).
doi:10.1007/s10278-006-9712-x
PMCID: PMC3043951  PMID: 16511675
Large data sets; radiological image interpretation paradigm; medical imaging informatics

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