Applications of minimal physiologically-based pharmacokinetic models

Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue (usually total body weight) volumes, fractions (f _d ) of cardiac output with Fick??s Law of Perfusion, tissue/blood partitioning (K _p ), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mammillary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated K _p values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common K _p and f _d values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.     

Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models

In drug discovery and development, classical compartment models and physiologically based pharmacokinetic (PBPK) models are successfully used to analyze and predict the pharmacokinetics of drugs. So far, however, both approaches are used exclusively or in parallel, with little to no cross-fertilization. An approach that directly links classical compartment and PBPK models is highly desirable. We derived a new mechanistic lumping approach for reducing the complexity of PBPK models and establishing a direct link to classical compartment models. The proposed method has several advantages over existing methods: Perfusion and permeability rate limited models can be lumped; the lumped model allows for predicting the original organ concentrations; and the volume of distribution at steady state is preserved by the lumping method. To inform classical compartmental model development, we introduced the concept of a minimal lumped model that allows for prediction of the venous plasma concentration with as few compartments as possible. The minimal lumped parameter values may serve as initial values for any subsequent parameter estimation process. Applying our lumping method to 25 diverse drugs, we identified characteristic features of lumped models for moderate-to-strong bases, weak bases and acids. We observed that for acids with high protein binding, the lumped model comprised only a single compartment. The proposed lumping approach established for the first time a direct derivation of simple compartment models from PBPK models and enables a mechanistic interpretation of classical compartment models.     

A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples

An overview is provided of the present population analysis methods and an assessment of which software packages are most appropriate for various PK/PD modeling problems. Four PK/PD example problems were solved using the programs NONMEM VI beta version, PDx-MCPEM, S-ADAPT, MONOLIX, and WinBUGS, informally assessed for reasonable accuracy and stability in analyzing these problems. Also, for each program we describe their general interface, ease of use, and abilities. We conclude with discussing which algorithms and software are most suitable for which types of PK/PD problems. NONMEM FO method is accurate and fast with 2-compartment models, if intra-individual and interindividual variances are small. The NONMEM FOCE method is slower than FO, but gives accurate population values regardless of size of intra- and interindividual errors. However, if data are very sparse, the NONMEM FOCE method can lead to inaccurate values, while the Laplace method can provide more accurate results. The exact EM methods (performed using S-ADAPT, PDx-MCPEM, and MONOLIX) have greater stability in analyzing complex PK/PD models, and can provide accurate results with sparse or rich data. MCPEM methods perform more slowly than NONMEM FOCE for simple models, but perform more quickly and stably than NONMEM FOCE for complex models. WinBUGS provides accurate assessments of the population parameters, standard errors and 95% confidence intervals for all examples. Like the MCPEM methods, WinBUGS's efficiency increases relative to NONMEM when solving the complex PK/PD models.     

Development of multi-route physiologically-based pharmacokinetic models for ethanol in the adult,pregnant, and neonatal rat

Biofuel blends of 10% ethanol (EtOH) and gasoline are common in the USA, and higher EtOH concentrations are being considered (15–85%). Currently, no physiologically-based pharmacokinetic (PBPK) models are available to describe the kinetics of EtOH-based biofuels. PBPK models were developed to describe life-stage differences in the kinetics of EtOH alone in adult, pregnant, and neonatal rats for inhalation, oral, and intravenous routes of exposure, using data available in the open literature. Whereas ample data exist from gavage and intravenous routes of exposure, kinetic data from inhalation exposures are limited, particularly at concentrations producing blood and target tissue concentrations associated with developmental neurotoxicity. Compared to available data, the three models reported in this paper accurately predicted the kinetics of EtOH, including the absorption, peak concentration, and clearance across multiple datasets. In general, model predictions for adult and pregnant animals matched inhalation and intravenous datasets better than gavage data. The adult model was initially better able to predict the time-course of blood concentrations than was the neonatal model. However, after accounting for age-related changes in gastric uptake using the calibrated neonate model, simulations consistently reproduced the early kinetic behavior in blood. This work provides comprehensive multi-route life-stage models of EtOH pharmacokinetics and represents a first step in development of models for use with gasoline-EtOH blends, with additional potential applicability in investigation of the pharmacokinetics of EtOH abuse, addiction, and toxicity.     

Computational estimation of errors generated by lumping of physiologically-based pharmacokinetic (PBPK) interaction models of inhaled complex chemical mixtures

Many cases of environmental contamination result in concurrent or sequential exposure to more than one chemical. However, limitations of available resources make it unlikely that experimental toxicology will provide health risk information about all the possible mixtures to which humans or other species may be exposed. As such, utilizing computational models in order to make toxicological predictions is a useful tool in complementing experimental efforts which examine mixtures in health risk assessment. This paper outlines a novel mathematical method which reduces the complexity of a mixtures model and increases computational efficiency via a biologically-based lumping methodology (BBLM). In contrast to previous chemical lumping methodologies, BBLM allows the computation of error as a measure of the difference between the lumped simulation based on BBLM and the full mathematical model. As a consequence, the modeler has the opportunity to find the optimal configuration in the tradeoff between simplification and accuracy in order to determine an acceptable number and composition of lumped chemicals. To demonstrate this method, lumped equations based on a typical inhalation physiologically-based pharmacokinetic (PBPK) model assuming a competitive inhibition interaction mechanism are developed for a mixture of arbitrary size. The novel methodology is further tested using literature data for a mixture of 10 volatile organic chemicals (VOCs). Through simulation of these chemicals, BBLM is shown to produce good approximations when compared to the unlumped simulation and experimental data.     

Development of multi-route physiologically-based pharmacokinetic models for ethanol in the adult, pregnant, and neonatal rat

Biofuel blends of 10% ethanol (EtOH) and gasoline are common in the USA, and higher EtOH concentrations are being considered (15-85%). Currently, no physiologically-based pharmacokinetic (PBPK) models are available to describe the kinetics of EtOH-based biofuels. PBPK models were developed to describe life-stage differences in the kinetics of EtOH alone in adult, pregnant, and neonatal rats for inhalation, oral, and intravenous routes of exposure, using data available in the open literature. Whereas ample data exist from gavage and intravenous routes of exposure, kinetic data from inhalation exposures are limited, particularly at concentrations producing blood and target tissue concentrations associated with developmental neurotoxicity. Compared to available data, the three models reported in this paper accurately predicted the kinetics of EtOH, including the absorption, peak concentration, and clearance across multiple datasets. In general, model predictions for adult and pregnant animals matched inhalation and intravenous datasets better than gavage data. The adult model was initially better able to predict the time-course of blood concentrations than was the neonatal model. However, after accounting for age-related changes in gastric uptake using the calibrated neonate model, simulations consistently reproduced the early kinetic behavior in blood. This work provides comprehensive multi-route life-stage models of EtOH pharmacokinetics and represents a first step in development of models for use with gasoline-EtOH blends, with additional potential applicability in investigation of the pharmacokinetics of EtOH abuse, addiction, and toxicity.     

Computational estimation of errors generated by lumping of physiologically-based pharmacokinetic (PBPK) interaction models of inhaled complex chemical mixtures

Many cases of environmental contamination result in concurrent or sequential exposure to more than one chemical. However, limitations of available resources make it unlikely that experimental toxicology will provide health risk information about all the possible mixtures to which humans or other species may be exposed. As such, utilizing computational models in order to make toxicological predictions is a useful tool in complementing experimental efforts which examine mixtures in health risk assessment. This paper outlines a novel mathematical method which reduces the complexity of a mixtures model and increases computational efficiency via a biologically-based lumping methodology (BBLM). In contrast to previous chemical lumping methodologies, BBLM allows the computation of error as a measure of the difference between the lumped simulation based on BBLM and the full mathematical model. As a consequence, the modeler has the opportunity to find the optimal configuration in the tradeoff between simplification and accuracy in order to determine an acceptable number and composition of lumped chemicals. To demonstrate this method, lumped equations based on a typical inhalation physiologically-based pharmacokinetic (PBPK) model assuming a competitive inhibition interaction mechanism are developed for a mixture of arbitrary size. The novel methodology is further tested using literature data for a mixture of 10 volatile organic chemicals (VOCs). Through simulation of these chemicals, BBLM is shown to produce good approximations when compared to the unlumped simulation and experimental data.     

Use of partition coefficients in flow-limited physiologically-based pharmacokinetic modeling

Permeability-limited two-subcompartment and flow-limited, well-stirred tank tissue compartment models are routinely used in physiologically-based pharmacokinetic modeling. Here, the permeability-limited two-subcompartment model is used to derive a general flow-limited case of a two-subcompartment model with the well-stirred tank being a specific case where tissue fractional blood volume approaches zero. The general flow-limited two-subcompartment model provides a clear distinction between two partition coefficients typically used in PBPK: a biophysical partition coefficient and a well-stirred partition coefficient. Case studies using diazepam and cotinine demonstrate that, when the well-stirred tank is used with a priori predicted biophysical partition coefficients, simulations overestimate or underestimate total organ drug concentration relative to flow-limited two-subcompartment model behavior in tissues with higher fractional blood volumes. However, whole-body simulations show predicted drug concentrations in plasma and lower fractional blood volume tissues are relatively unaffected. These findings point to the importance of accurately determining tissue fractional blood volume for flow-limited PBPK modeling. Simulations using biophysical and well-stirred partition coefficients optimized with flow-limited two-subcompartment and well-stirred models, respectively, lead to nearly identical fits to tissue drug distribution data. Therefore, results of whole-body PBPK modeling with diazepam and cotinine indicate both flow-limited models are appropriate PBPK tissue models as long as the correct partition coefficient is used: the biophysical partition coefficient is for use with two-subcompartment models and the well-stirred partition coefficient is for use with the well-stirred tank model.     

External evaluation of population pharmacokinetic models of vancomycin in neonates: the transferability of published models to different clinical settings

Aims

Vancomycin is one of the most evaluated antibiotics in neonates using modeling and simulation approaches. However no clear consensus on optimal dosing has been achieved. The objective of the present study was to perform an external evaluation of published models, in order to test their predictive performances in an independent dataset and to identify the possible study-related factors influencing the transferability of pharmacokinetic models to different clinical settings.

Method

Published neonatal vancomycin pharmacokinetic models were screened from the literature. The predictive performance of six models was evaluated using an independent dataset (112 concentrations from 78 neonates). The evaluation procedures used simulation-based diagnostics [visual predictive check (VPC) and normalized prediction distribution errors (NPDE)].

Results

Differences in predictive performances of models for vancomycin pharmacokinetics in neonates were found. The mean of NPDE for six evaluated models were 1.35, −0.22, −0.36, 0.24, 0.66 and 0.48, respectively. These differences were explained, at least partly, by taking into account the method used to measure serum creatinine concentrations. The adult conversion factor of 1.3 (enzymatic to Jaffé) was tested with an improvement in the VPC and NPDE, but it still needs to be evaluated and validated in neonates. Differences were also identified between analytical methods for vancomycin.

Conclusion

The importance of analytical techniques for serum creatinine concentrations and vancomycin as predictors of vancomycin concentrations in neonates have been confirmed. Dosage individualization of vancomycin in neonates should consider not only patients'' characteristics and clinical conditions, but also the methods used to measure serum creatinine and vancomycin.     

老年患者万古霉素群体药代动力学模型验证

目的:利用已发表的成人万古霉素群体药代动力学模型对本院使用万古霉素的老年患者治疗药物监测数据进行拟合;探讨已发表的模型对不同临床机构的适用性,选择较为适合本院老年患者的万古霉素群体药代动学模型。方法:分析已发表的成人万古霉素群体药代动力学模型,提取人口学信息及模型参数,将模型参数固定后,利用NONMEM 7.3.0.(Icon Development Solution,USA)软件及PDx-Pop Version 5软件进行拟合,并用RStudio软件作图。根据实测浓度-预测浓度(DV-PRED)图及可视化预测检验(VPC)评估拟合效果。结果:共收集2014-2015年42例老年患者88个稳态谷浓度点,年龄范围为66~93岁;共检索到15个成人万古霉素群体药代动力学模型,一房室模型6个,二房室模型9个。对一房室模型进行拟合,模型拟合图形显示模型2、5及6的拟合效果较好,其中模型5为老年人模型。结论:可以尝试利用拟合结果良好的模型在本院进行前瞻性临床实践,并逐步建立本院老年患者的万古霉素群体模型。     

Fundamentals of population pharmacokinetic modelling: validation methods

Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition; and population pharmacokinetic modelling provides an estimation of drug pharmacokinetic parameters. This method's defined outcome aims to understand how participants in population pharmacokinetic studies are representative of the population as opposed to the healthy volunteers or highly selected patients in traditional pharmacokinetic studies. This review focuses on the fundamentals of population pharmacokinetic modelling and how the results are evaluated and validated. This review defines the common aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. The concept of validation, as applied to population pharmacokinetic models, is explored focusing on the lack of consensus regarding both terminology and the concept of validation itself. Population pharmacokinetic modelling is a powerful approach where pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. Given the lack of consensus on the best approaches in model building and validation, sound fundamentals are required to ensure the selected methodology is suitable for the particular data type and/or patient population. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and the results relied upon.     

Quantitative justification for target concentration intervention--parameter variability and predictive performance using population pharmacokinetic models for aminoglycosides

AIMS: [1] To quantify the random and predictable components of variability for aminoglycoside clearance and volume of distribution [2] To investigate models for predicting aminoglycoside clearance in patients with low serum creatinine concentrations [3] To evaluate the predictive performance of initial dosing strategies for achieving an aminoglycoside target concentration. METHODS: Aminoglycoside demographic, dosing and concentration data were collected from 697 adult patients (> or =20 years old) as part of standard clinical care using a target concentration intervention approach for dose individualization. It was assumed that aminoglycoside clearance had a renal and a nonrenal component, with the renal component being linearly related to predicted creatinine clearance. RESULTS: A two compartment pharmacokinetic model best described the aminoglycoside data. The addition of weight, age, sex and serum creatinine as covariates reduced the random component of between subject variability (BSVR) in clearance (CL) from 94% to 36% of population parameter variability (PPV). The final pharmacokinetic parameter estimates for the model with the best predictive performance were: CL, 4.7 l h(-1) 70 kg(-1); intercompartmental clearance (CLic), 1 l h(-1) 70 kg(-1); volume of central compartment (V1), 19.5 l 70 kg(-1); volume of peripheral compartment (V2) 11.2 l 70 kg(-1). CONCLUSIONS: Using a fixed dose of aminoglycoside will achieve 35% of typical patients within 80-125% of a required dose. Covariate guided predictions increase this up to 61%. However, because we have shown that random within subject variability (WSVR) in clearance is less than safe and effective variability (SEV), target concentration intervention can potentially achieve safe and effective doses in 90% of patients.     

Global sensitivity analysis in physiologically-based pharmacokinetic/pharmacodynamic models of inhaled and opioids anesthetics and its application to generate virtual populations

Journal of Pharmacokinetics and Pharmacodynamics - The integration between physiologically-based pharmacokinetics (PBPK) models and pharmacodynamics (PD) models makes it possible to describe the...     

A priori prediction of tissue:plasma partition coefficients of drugs to facilitate the use of physiologically-based pharmacokinetic models in drug discovery

The tissue:plasma (P(t:p)) partition coefficients (PCs) are important drug-specific input parameters in physiologically based pharmacokinetic (PBPK) models used to estimate the disposition of drugs in biota. Until now the use of PBPK models in early stages of the drug discovery process was not possible, since the estimation of P(t:p) of new drug candidates by using conventional in vitro and/or in vivo methods is too time and cost intensive. The objectives of the study were (i) to develop and validate two mechanistic equations for predicting a priori the rabbit, rat and mouse P(t:p) of non-adipose and non-excretory tissues (bone, brain, heart, intestine, lung, muscle, skin, spleen) for 65 structurally unrelated drugs and (ii) to evaluate the adequacy of using P(t:p) of muscle as predictors for P(t:p) of other tissues. The first equation predicts P(t:p) at steady state, assuming a homogenous distribution and passive diffusion of drugs in tissues, from a ratio of solubility and macromolecular binding between tissues and plasma. The ratio of solubility was estimated from log vegetable oil:water PCs (K(vo:w)) of drugs and lipid and water levels in tissues and plasma, whereas the ratio of macromolecular binding for drugs was estimated from tissue interstitial fluid-to-plasma concentration ratios of albumin, globulins and lipoproteins. The second equation predicts P(t:p) of drugs residing predominantly in the interstitial space of tissues. Therefore, the fractional volume content of interstitial space in each tissue replaced drug solubilities in the first equation. Following the development of these equations, regression analyses between P(t:p) of muscle and those of the other tissues were examined. The average ratio of predicted-to-experimental P(t:p) values was 1.26 (SD = 1.40, r = 0.90, n = 269), and 85% of the 269 predicted values were within a factor of three of the corresponding literature values obtained under in vivo and in vitro conditions. For predicted and experimental P(t:p), linear relationships (r > 0.9 in most cases) were observed between muscle and other tissues, suggesting that P(t:p) of muscle is a good predictor for the P(t:p) of other tissues. The two previous equations could explain the mechanistic basis of these linear relationships. The practical aim of this study is a worthwhile goal for pharmacokinetic screening of new drug candidates.