Characterizing variability and uncertainty for parameter subset selection in PBPK models.

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models.

In vitro and computational approaches to predict developmental toxicity: Integrating PBPK models with cell-based assays.

This study aimed to develop a physiologically-based pharmacokinetic (PBPK) model to predict the maximum plasma concentration (Cmax) and trough concentration (Ctrough) at steady-state of olaparib (OLA) in Caucasian, Japanese and Chinese. Furthermore, the PBPK model was combined with mean and 95% confidence interval to predict optimal dosing regimens of OLA when co-administered with CYP3A4 modulators and administered to patients with hepatic/renal impairment. The dosing regimens were determined based on safety and efficacy PK threshold Cmax (< 12,500 ng/mL) and Ctrough (772–2500 ng/mL). The population PBPK model for OLA was successfully developed and validated, demonstrating good consistency with clinically observed data. The ratios of predicted to observed values for Cmax and Ctrough fell within the range of 0.5 to 2.0. When OLA was co-administered with a strong or moderate CYP3A4 inhibitor, the recommended dosing regimens should be reduced to 100 mg BID and 150 mg BID, respectively. Additionally, the PBPK model also suggested that OLA could be not recommended with a strong or moderate CYP3A4 inducer. For patients with moderate hepatic and renal impairment, the dosing regimens of OLA were recommended to be reduced to 200 mg BID and 150 mg BID, respectively. In cases of severe hepatic and renal impairment, the PBPK model suggested a dosing regimen of 100 mg BID for OLA. Overall, this present PBPK model can determine the optimal dosing regimens for various clinical scenarios involving OLA.

A physiologically based pharmacokinetic (PBPK) model was developed for inhaled ethylbenzene (EB) in B6C3F1 mice. The mouse physiological parameters were obtained from the literature, but the blood:air and tissue:air partition coefficients were determined by vial equilibration technique. The maximal velocity for hepatic metabolism (Vmax) obtained from a previously published rat study was increased by a factor of ∼3 to account for enzyme induction during repeated exposures. The Michaelis affinity constant (Km) for hepatic metabolism of EB, obtained from a previously published rat PBPK modeling study, was kept unchanged during single and repeated exposure scenarios. Hepatic metabolism alone could not adequately describe the clearance of EB from mouse blood. Additional metabolism was assumed to be localized in the lung. The parameters for pulmonary metabolism were obtained by optimization of PBPK model fits to kinetic data collected following exposures to 75–1000 ppm. The PBPK model successfully predicted all available blood and tissue concentration data in mice exposed to 75 or 750 ppm EB. Overall, the results indicate that the rate of EB clearance is markedly higher in B6C3F1 mice than rats or humans and exceeds the hepatic metabolism capacity. Available biochemical evidence is consistent with a significant role for pulmonary metabolism; however, the extent to which the extrahepatic metabolism is localized in the lung is unclear. Overall, the PBPK model developed for the mouse adequately simulated the blood and tissue kinetics of EB by accounting for its high rate of clearance.

Physiologically based pharmacokinetic (PBPK) modeling is a mechanistic concept, which helps to judge the effects of biopharmceutical properties of drug product such as in vitro dissolution on its pharmacokinetic and in vivo performance. With the application of virtual bioequivalence (VBE) study, the drug product development using model-based approach can help in evaluating the possibility of extending BCS-based biowaiver. Therefore, the current study was intended to develop PBPK model as well as in vitro in vivo extrapolation (IVIVE) for BCS class III drug i.e. cefadroxil.A PBPK model was created in GastroPlus™ 9.8.3 utilizing clinical data of immediate-release cefadroxil formulations. By the examination of simulated and observed plasma drug concentration profiles, the predictability of the proposed model was assessed for the prediction errors. Furthermore, mechanistic deconvolution was used to create IVIVE, and the plasma drug concentration profiles and pharmacokinetic parameters were predicted for different virtual formulations with variable cefadroxil in vitro release. Virtual bioequivalence study was also executed to assess the bioequivalence of the generic verses the reference drug product (Duricef®).The developed PBPK model satisfactorily predicted Cmax and AUC0-t after cefadroxil single and multiple oral dose administrations, with all individual prediction errors within the limits except in a few cases. Second order polynomial correlation function obtained accurately predict in vivo drug release and plasma concentration profile of cefadroxil test and reference (Duricef®) formulation. The VBE study also proved test formulation bioequivalent to reference formulation and the statistical analysis on pharmacokinetic parameters reported 90% confidence interval for Cmax and AUC0-t in the FDA acceptable limits.The analysis found that a validated and verified PBPK model with a mechanistic background is as a suitable approach to accelerate generic drug development.

This study aimed to conduct an integrated and probabilistic risk assessment of gold nanoparticles (AuNPs) based on recently published in vitro and in vivo toxicity studies coupled to a physiologically based pharmacokinetic (PBPK) model. Dose–response relationships were characterized based on cell viability assays in various human cell types. A previously well-validated human PBPK model for AuNPs was applied to quantify internal concentrations in liver, kidney, skin, and venous plasma. By applying a Bayesian-based probabilistic risk assessment approach incorporating Monte Carlo simulation, probable human cell death fractions were characterized. Additionally, we implemented in vitro to in vivo and animal-to-human extrapolation approaches to independently estimate external exposure levels of AuNPs that cause minimal toxicity. Our results suggest that under the highest dosing level employed in existing animal studies (worst-case scenario), AuNPs coated with branched polyethylenimine (BPEI) would likely induce ∼90–100% cellular death, implying high cytotoxicity compared to <10% cell death induced by low-to-medium animal dosing levels, which are commonly used in animal studies. The estimated human equivalent doses associated with 5% cell death in liver and kidney were around 1 and 3 mg/kg, respectively. Based on points of departure reported in animal studies, the human equivalent dose estimates associated with gene expression changes and tissue cell apoptosis in liver were 0.005 and 0.5 mg/kg, respectively. Our analyzes provide insights into safety evaluation, risk prediction, and point of departure estimation of AuNP exposure for humans and illustrate an approach that could be applied to other NPs when sufficient data are available.

Systems pharmacokinetic (PK) models that can characterize and predict whole body disposition of antibody-drug conjugates (ADCs) are needed to support (i) development of reliable exposure-response relationships for ADCs and (ii) selection of ADC targets with optimal tumor and tissue expression profiles. Towards this goal, we have developed a translational physiologically based PK (PBPK) model for ADCs, using T-DM1 as a tool compound. The preclinical PBPK model was developed using rat data. Biodistribution of DM1 in rats was used to develop the small molecule PBPK model, and the PK of conjugated trastuzumab (i.e., T-DM1) in rats was characterized using platform PBPK model for antibody. Both the PBPK models were combined via degradation and deconjugation processes. The degradation of conjugated antibody was assumed to be similar to a normal antibody, and the deconjugation of DM1 from T-DM1 in rats was estimated using plasma PK data. The rat PBPK model was translated to humans to predict clinical PK of T-DM1. The translation involved the use of human antibody PBPK model to characterize the PK of conjugated trastuzumab, use of allometric scaling to predict human clearance of DM1 catabolites, and use of monkey PK data to predict deconjugation of DM1 in the clinic. PBPK model-predicted clinical PK profiles were compared with clinically observed data. The PK of total trastuzumab and T-DM1 were predicted reasonably well, and slight systemic deviations were observed for the PK of DM1-containing catabolites. The ADC PBPK model presented here can serve as a platform to develop models for other ADCs.

Uncertainty and sensitivity analysis of cooling and heating loads for building energy planning

Biological monitoring and physiologically-based pharmacokinetic (PBPK) modelling are useful complementary tools in quantifying human exposure to elements in the environment. In this work, we used PBPK models to determine the optimal time for collecting biological samples in a longitudinal study to determine if participants who consumed allotment produce had been exposed to arsenic, cadmium, chromium, nickel or lead. There are a number of PBPK models for these elements published in the literature, which vary in size, complexity and application, given the differences in physiochemical properties of the elements, organs involved in metabolism and exposure pathways affected. We selected PBPK models from the literature to simulate the oral ingestion pathway from consumption of allotment produce. Some models required modification by reducing or removing selected compartments whilst still maintaining their original predictability. The performance of the modified models was evaluated by comparing the predicted urinary and blood elemental levels with experimental data and other model simulations published in the literature. Overall, the model predictions were consistent with literature data (r > 0.7, p < 0.05), and were influential in predicting when samples should be collected. Our results demonstrate the use of mathematical modelling in informing and optimising the design of longitudinal studies.

Development of protein therapeutics for ocular disorders, particularly age-related macular degeneration (AMD), is a highly competitive and expanding therapeutic area. However, the application of a predictive and translatable ocular PK model to better understand ocular disposition of protein therapeutics, such as a physiologically-based pharmacokinetic (PBPK) model, is missing from the literature. Here, we present an expansion of an antibody platform PBPK model towards rabbit and incorporate a novel anatomical and physiologically relevant ocular component. Parameters describing all tissues, flows, and binding events were obtained from existing literature and fixed a priori. First, translation of the platform PBPK model to rabbit was confirmed by evaluating the model's ability to predict plasma PK of a systemically administered exogenous antibody. Then, the PBPK model with the new ocular component was validated by estimation of serum and ocular (i.e. aqueous humor, retina, and vitreous humor) PK of two intravitreally administered monoclonal antibodies. We show that the proposed PBPK model is capable of accurately (i.e. within twofold) predicting ocular exposure of antibody-based drugs. The proposed PBPK model can be used for preclinical-to-clinical translation of antibodies developed for ocular disorders, and assessment of ocular toxicity for systemically administered antibody-based therapeutics.

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fup) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.

Conducting clinical trials to understand the exposure risk/benefit relationship of cannabis use is not always feasible. Alternatively, physiologically based pharmacokinetic (PBPK) models can be used to predict exposure of the psychoactive cannabinoid (-)-Δ9-tetrahydrocannabinol (THC) and its active metabolite 11-hydroxy-Δ9-tetrahydrocannabinol (11-OH-THC). Here, we first extrapolated in vitro mechanistic pharmacokinetic information previously quantified to build a linked THC/11-OH-THC PBPK model and verified the model with observed data after intravenous and inhalation administration of THC in a healthy, nonpregnant population. The in vitro to in vivo extrapolation of both THC and 11-OH-THC disposition was successful. The inhalation bioavailability (Finh) of THC after inhalation was higher in chronic versus casual cannabis users (Finh = 0.35 and 0.19, respectively). Sensitivity analysis demonstrated that 11-OH-THC but not THC exposure was sensitive to alterations in hepatic intrinsic clearance of the respective compound. Next, we extrapolated the linked THC/11-OH-THC PBPK model to pregnant women. Simulations showed that THC plasma area under the curve (AUC) does not change during pregnancy, but 11-OH-THC plasma AUC decreases by up to 41%. Using a maternal-fetal PBPK model, maternal and fetal THC serum concentrations were simulated and compared with the observed THC serum concentrations in pregnant women at term. To recapitulate the observed THC fetal serum concentrations, active placental efflux of THC needed to be invoked. In conclusion, we built and verified a linked THC/11-OH-THC PBPK model in healthy nonpregnant population and demonstrated how this mechanistic physiologic and pharmacokinetic platform can be extrapolated to a special population, such as pregnant women. SIGNIFICANCE STATEMENT: Although the pharmacokinetics of cannabinoids have been extensively studied clinically, limited mechanistic pharmacokinetic models exist. Here, we developed and verified a physiologically based pharmacokinetic (PBPK) model for (-)-Δ9-tetrahydrocannabinol (THC) and its active metabolite, 11-hydroxy-Δ9-tetrahydrocannabinol (11-OH-THC). The PBPK model was verified in healthy, nonpregnant population after intravenous and inhalation administration of THC, and then extrapolated to pregnant women. The THC/11-OH-THC PBPK model can be used to predict exposure in special populations, predict drug-drug interactions, or impact of genetic polymorphism.

The potential of inhibitory metabolites of perpetrator drugs to contribute to drug-drug interactions (DDIs) is uncommon and underestimated. However, the occurrence of unexpected DDI suggests the potential contribution of metabolites to the observed DDI. The aim of this study was to develop a physiologically-based pharmacokinetic (PBPK) model for bupropion and its three primary metabolites—hydroxybupropion, threohydrobupropion and erythrohydrobupropion—based on a mixed “bottom-up” and “top-down” approach and to contribute to the understanding of the involvement and impact of inhibitory metabolites for DDIs observed in the clinic. PK profiles from clinical researches of different dosages were used to verify the bupropion model. Reasonable PK profiles of bupropion and its metabolites were captured in the PBPK model. Confidence in the DDI prediction involving bupropion and co-administered CYP2D6 substrates could be maximized. The predicted maximum concentration (Cmax) area under the concentration-time curve (AUC) values and Cmax and AUC ratios were consistent with clinically observed data. The addition of the inhibitory metabolites into the PBPK model resulted in a more accurate prediction of DDIs (AUC and Cmax ratio) than that which only considered parent drug (bupropion) P450 inhibition. The simulation suggests that bupropion and its metabolites contribute to the DDI between bupropion and CYP2D6 substrates. The inhibitory potency from strong to weak is hydroxybupropion, threohydrobupropion, erythrohydrobupropion, and bupropion, respectively. The present bupropion PBPK model can be useful for predicting inhibition from bupropion in other clinical studies. This study highlights the need for caution and dosage adjustment when combining bupropion with medications metabolized by CYP2D6. It also demonstrates the feasibility of applying the PBPK approach to predict the DDI potential of drugs undergoing complex metabolism, especially in the DDI involving inhibitory metabolites.