Global Sensitivity Analysis of the Rodgers and Rowland Model for Prediction of Tissue: Plasma Partitioning Coefficients: Assessment of the Key Physiological and Physicochemical Factors That Determine Small-Molecule Tissue Distribution

Application of partition coefficient methods to predict tissue:plasma affinities in common farm animals: Influence of ionisation state

Tissue affinities are conventionally determined from in vivo steady-state tissue and plasma or plasma-water chemical concentration data. In silico approaches were initially developed for preclinical species but standardly applied and tested in human physiologically-based kinetic (PBK) models. Recently, generic PBK models for farm animals have been made available and require partition coefficients as input parameters. In the current investigation, data for species-specific tissue compositions have been collected, and prediction of chemical distribution in various tissues of livestock species for cattle, chicken, sheep and swine have been performed. Overall, tissue composition was very similar across the four farm animal species. However, small differences were observed in moisture, fat and protein content in the various organs within each species. Such differences could be attributed to factors such as variations in age, breed, and weight of the animals and general conditions of the animal itself. With regards to the predictions of tissue:plasma partition coefficients, 80 %, 71 %, 77 % of the model predictions were within a factor 10 using the methods of Berezhkovskiy (2004), Rodgers and Rowland (2006) and Schmitt (2008). The method of Berezhkovskiy (2004) was often providing the most reliable predictions except for swine, where the method of Schmitt (2008) performed best. In addition, investigation of the impact of chemical classes on prediction performance, all methods had very similar reliability. Notwithstanding, no clear pattern regarding specific chemicals or tissues could be detected for the values predicted outside a 10-fold change in certain chemicals or specific tissues. This manuscript concludes with the need for future research, particularly focusing on lipophilicity and species differences in protein binding.

Relative Performance of Volume of Distribution Prediction Methods for Lipophilic Drugs with Uncertainty in LogP Value

PURPOSE

The goal was to assess, for lipophilic drugs, the impact of logP on human volume of distribution at steady-state (VDss) predictions, including intermediate fut and Kp values, from six methods: Oie-Tozer, Rodgers-Rowland (tissue-specific Kp and only muscle Kp), GastroPlus, Korzekwa-Nagar, and TCM-New.

METHOD

A sensitivity analysis with focus on logP was conducted by keeping pKa and fup constant for each of four drugs, while varying logP. VDss was also calculated for the specific literature logP values. Error prediction analysis was conducted by analyzing prediction errors by source of logP values, drug, and overall values.

RESULTS

The Rodgers-Rowland methods were highly sensitive to logP values, followed by GastroPlus and Korzekwa-Nagar. The Oie-Tozer and TCM-New methods were only modestly sensitive to logP. Hence, the relative performance of these methods depended upon the source of logP value. As logP values increased, TCM-New and Oie-Tozer were the most accurate methods. TCM-New was the only method that was accurate regardless of logP value source. Oie-Tozer provided accurate predictions for griseofulvin, posaconazole, and isavuconazole; GastroPlus for itraconazole and isavuconazole; Korzekwa-Nagar for posaconazole; and TCM-New for griseofulvin, posaconazole, and isavuconazole. Both Rodgers-Rowland methods provided inaccurate predictions due to the overprediction of VDss.

CONCLUSIONS

TCM-New was the most accurate prediction of human VDss across four drugs and three logP sources, followed by Oie-Tozer. TCM-New showed to be the best method for VDss prediction of highly lipophilic drugs, suggesting BPR as a favorable surrogate for drug partitioning in the tissues, and which avoids the use of fup.

A minimal PBPK model to accelerate preclinical development of drugs against tuberculosis

Introduction: Understanding drug exposure at disease target sites is pivotal to profiling new drug candidates in terms of tolerability and efficacy. Such quantification is particularly tedious for anti-tuberculosis (TB) compounds as the heterogeneous pulmonary microenvironment due to the infection may alter lung permeability and affect drug disposition. Murine models have been a longstanding support in TB research so far and are here used as human surrogates to unveil the distribution of several anti-TB compounds at the site-of-action via a novel and centralized PBPK design framework. Methods: As an intermediate approach between data-driven pharmacokinetic (PK) models and whole-body physiologically based (PB) PK models, we propose a parsimonious framework for PK investigation (minimal PBPK approach) that retains key physiological processes involved in TB disease, while reducing computational costs and prior knowledge requirements. By lumping together pulmonary TB-unessential organs, our minimal PBPK model counts 9 equations compared to the 36 of published full models, accelerating the simulation more than 3-folds in Matlab 2022b. Results: The model has been successfully tested and validated against 11 anti-TB compounds-rifampicin, rifapentine, pyrazinamide, ethambutol, isoniazid, moxifloxacin, delamanid, pretomanid, bedaquiline, OPC-167832, GSK2556286 - showing robust predictability power in recapitulating PK dynamics in mice. Structural inspections on the proposed design have ensured global identifiability and listed free fraction in plasma and blood-to-plasma ratio as top sensitive parameters for PK metrics. The platform-oriented implementation allows fast comparison of the compounds in terms of exposure and target attainment. Discrepancies in plasma and lung levels for the latest BPaMZ and HPMZ regimens have been analyzed in terms of their impact on preclinical experiment design and on PK/PD indices. Conclusion: The framework we developed requires limited drug- and species-specific information to reconstruct accurate PK dynamics, delivering a unified viewpoint on anti-TB drug distribution at the site-of-action and a flexible fit-for-purpose tool to accelerate model-informed drug design pipelines and facilitate translation into the clinic.

A Machine Learning Framework to Improve Rat Clearance Predictions and Inform Physiologically Based Pharmacokinetic Modeling

During drug discovery and development, achieving appropriate pharmacokinetics is key to establishment of the efficacy and safety of new drugs. Physiologically based pharmacokinetic (PBPK) models integrating in vitro-to-in vivo extrapolation have become an essential in silico tool to achieve this goal. In this context, the most important and probably most challenging pharmacokinetic parameter to estimate is the clearance. Recent work on high-throughput PBPK modeling during drug discovery has shown that a good estimate of the unbound intrinsic clearance (CLint,u,) is the key factor for useful PBPK application. In this work, three different machine learning-based strategies were explored to predict the rat CLint,u as the input into PBPK. Therefore, in vivo and in vitro data was collected for a total of 2639 proprietary compounds. The strategies were compared to the standard in vitro bottom-up approach. Using the well-stirred liver model to back-calculate in vivo CLint,u from in vivo rat clearance and then training a machine learning model on this CLint,u led to more accurate clearance predictions (absolute average fold error (AAFE) 3.1 in temporal cross-validation) than the bottom-up approach (AAFE 3.6-16, depending on the scaling method) and has the advantage that no experimental in vitro data is needed. However, building a machine learning model on the bias between the back-calculated in vivo CLint,u and the bottom-up scaled in vitro CLint,u also performed well. For example, using unbound hepatocyte scaling, adding the bias prediction improved the AAFE in the temporal cross-validation from 16 for bottom-up to 2.9 together with the bias prediction. Similarly, the log Pearson r2 improved from 0.1 to 0.29. Although it would still require in vitro measurement of CLint,u., using unbound scaling for the bottom-up approach, the need for correction of the fu,inc by fu,p data is circumvented. While the above-described ML models were built on all data points available per approach, it is discussed that evaluation comparison across all approaches could only be performed on a subset because ca. 75% of the molecules had missing or unquantifiable measurements of the fraction unbound in plasma or in vitro unbound intrinsic clearance, or they dropped out due to the blood-flow limitation assumed by the well-stirred model. Advantageously, by predicting CLint,u as the input into PBPK, existing workflows can be reused and the prediction of the in vivo clearance and other PK parameters can be improved.

Modeled Rat Hepatic and Plasma Concentrations of Chemicals after Virtual Administrations Using Two Sets of in Silico Liver-to-Plasma Partition Coefficients

The hepatic elimination of chemical substances in pharmacokinetic models requires hepatic intrinsic clearance (CLh,int) parameters for unbound drug in the liver, and these are regulated by the liver-to-plasma partition coefficients (Kp,h). Both Poulin and Theil and Rodgers and Rowland have proposed in silico expressions for Kp,h for a variety of chemicals. In this study, two sets of in silico Kp,h values for 14 model substances were assessed using experimentally reported in vivo steady-state Kp,h data and time-dependent virtual internal exposures in the liver and plasma modeled by forward dosimetry in rats. The Kp,h values for 14 chemicals independently calculated using the primary Poulin and Theil method in this study were significantly correlated with those obtained using the updated Rodgers and Rowland method and with reported in vivo steady-state Kp,h data in rats. When pharmacokinetic parameters were derived based on individual in vivo time-dependent data for diazepam, phenytoin, and nicotine in rats, the modeled liver and plasma concentrations after intravenous administration of the selected substrates in rats using two sets of in silico Kp,h values were mostly similar to the reported time-dependent in vivo internal exposures. Similar results for modeled liver and plasma concentrations were observed with input parameters estimated by machine-learning systems for hexobarbital, fingolimod, and pentazocine, with no reference to experimental pharmacokinetic data. These results suggest that the output values from rat pharmacokinetic models based on in silico Kp,h values derived from the primary Poulin and Theil model would be applicable for estimating toxicokinetics or internal exposure to substances.

A "middle-out approach" for the prediction of human drug disposition from preclinical data using simplified physiologically based pharmacokinetic (PBPK) models

Simplified physiologically based pharmacokinetic (PBPK) models using estimated tissue-to-unbound plasma partition coefficients (Kpus) were previously investigated by fitting them to in vivo pharmacokinetic (PK) data. After optimization with preclinical data, the performance of these models for extrapolation of distribution kinetics to human were evaluated to determine the best approach for the prediction of human drug disposition and volume of distribution (Vss) using PBPK modeling. Three lipophilic bases were tested (diazepam, midazolam, and basmisanil) for which intravenous PK data were available in rat, monkey, and human. The models with Kpu scalars using k-means clustering were generally the best for fitting data in the preclinical species and gave plausible Kpu values. Extrapolations of plasma concentrations for diazepam and midazolam using these models and parameters obtained were consistent with the observed clinical data. For diazepam and midazolam, the human predictions of Vss after optimization in rats and monkeys were better compared with the Vss estimated from the traditional PBPK modeling approach (varying from 1.1 to 3.1 vs. 3.7-fold error). For basmisanil, the sparse preclinical data available could have affected the model performance for fitting and the subsequent extrapolation to human. Overall, this work provides a rational strategy to predict human drug distribution using preclinical PK data within the PBPK modeling strategy.

Investigation of simplified physiologically-based pharmacokinetic models in rat and human

Whole-body physiologically-based pharmacokinetic (PBPK) models have many applications in drug research and development. It is often necessary to inform these models with animal or clinical data, updating model parameters, and making the model more predictive for future applications. This provides an opportunity and a challenge given the large number of parameters of such models. The aim of this work was to propose new mechanistic model structures with reduced complexity allowing for parameter optimization. These models were evaluated for their ability to estimate realistic values for unbound tissue to plasma partition coefficients (Kpu) and simulate observed pharmacokinetic (PK) data. Two approaches are presented: using either established kinetic lumping methods based on tissue time constants (drug-dependent) or a novel clustering analysis to identify tissues sharing common Kpu values or Kpu scalars based on similarities of tissue composition (drug-independent). PBPK models derived from these approaches were assessed using PK data of diazepam in rats and humans. Although the clustering analysis produced minor differences in tissue grouping depending on the method used, two larger groups of tissues emerged. One including the kidneys, liver, spleen, gut, heart, and lungs, and another including bone, brain, muscle, and pancreas whereas adipose and skin were generally considered distinct. Overall, a subdivision into four tissue groups appeared most physiologically relevant in terms of tissue composition. Several models were found to have similar abilities to describe diazepam i.v. data as empirical models. Comparability of estimated Kpus to experimental Kpu values for diazepam was one criterion for selecting the appropriate PK model structure.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.

Can We Predict Clinical Pharmacokinetics of Highly Lipophilic Compounds by Integration of Machine Learning or In Vitro Data into Physiologically Based Models? A Feasibility Study Based on 12 Development Compounds

While high lipophilicity tends to improve potency, its effects on pharmacokinetics (PK) are complex and often unfavorable. To predict clinical PK in early drug discovery, we built human physiologically based PK (PBPK) models integrating either (i) machine learning (ML)-predicted properties or (ii) discovery stage in vitro data. Our test set was composed of 12 challenging development compounds with high lipophilicity (mean calculated log P 4.2), low plasma-free fraction (50% of compounds with fu,p < 1%), and low aqueous solubility. Predictions focused on key human PK parameters, including plasma clearance (CL), volume of distribution at steady state (V_ss), and oral bioavailability (%F). For predictions of CL, the ML inputs showed acceptable accuracy and slight underprediction bias [an average absolute fold error (AAFE) of 3.55; an average fold error (AFE) of 0.95]. Surprisingly, use of measured data only slightly improved accuracy but introduced an overprediction bias (AAFE = 3.35; AFE = 2.63). Predictions of V_ss were more successful, with both ML (AAFE = 2.21; AFE = 0.90) and in vitro (AAFE = 2.24; AFE = 1.72) inputs showing good accuracy and moderate bias. The %F was poorly predicted using ML inputs [average absolute prediction error (AAPE) of 45%], and use of measured data for solubility and permeability improved this to 34%. Sensitivity analysis showed that predictions of CL limited the overall accuracy of human PK predictions, partly due to high nonspecific binding of lipophilic compounds, leading to uncertainty of unbound clearance. For accurate predictions of %F, solubility was the key factor. Despite current limitations, this work encourages further development of ML models and integration of their results within PBPK models to enable human PK prediction at the drug design stage, even before compounds are synthesized. Further evaluation of this approach with more diverse chemical types is warranted.

Evaluation of the Success of High-Throughput Physiologically Based Pharmacokinetic (HT-PBPK) Modeling Predictions to Inform Early Drug Discovery

Minimizing in vitro and in vivo testing in early drug discovery with the use of physiologically based pharmacokinetic (PBPK) modeling and machine learning (ML) approaches has the potential to reduce discovery cycle times and animal experimentation. However, the prediction success of such an approach has not been shown for a larger and diverse set of compounds representative of a lead optimization pipeline. In this study, the prediction success of the oral (PO) and intravenous (IV) pharmacokinetics (PK) parameters in rats was assessed using a “bottom-up” approach, combining in vitro and ML inputs with a PBPK model. More than 240 compounds for which all of the necessary inputs and PK data were available were used for this assessment. Different clearance scaling approaches were assessed, using hepatocyte intrinsic clearance and protein binding as inputs. In addition, a novel high-throughput PBPK (HT-PBPK) approach was evaluated to assess the scalability of PBPK predictions for a larger number of compounds in drug discovery. The results showed that bottom-up PBPK modeling was able to predict the rat IV and PO PK parameters for the majority of compounds within a 2- to 3-fold error range, using both direct scaling and dilution methods for clearance predictions. The use of only ML-predicted inputs from the structure did not perform well when using in vitro inputs, likely due to clearance miss predictions. The HT-PBPK approach produced comparable results to the full PBPK modeling approach but reduced the simulation time from hours to seconds. In conclusion, a bottom-up PBPK and HT-PBPK approach can successfully predict the PK parameters and guide early discovery by informing compound prioritization, provided that good in vitro assays are in place for key parameters such as clearance.

A latent variable approach to account for correlated inputs in global sensitivity analysis

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed.

An integrated computational methodology with data-driven machine learning, molecular modeling and PBPK modeling to accelerate solid dispersion formulation design

Drugs in solid dispersion (SD) take advantage of fast and extended dissolution, thus attains a higher bioavailability than the crystal form. However, current development of SD relies on a random large-scale formulation screening method with low efficiency. Current research aims to integrate various computational tools, including machine learning (ML), molecular dynamic (MD) simulation and physiologically based pharmacokinetic (PBPK) modeling, to accelerate the development of SD formulations. Firstly, based on a dataset consisting of 674 dissolution profiles of SD, the random forest algorithm was used to construct a classification model to distinguish two types of dissolution profiles: "spring-and-parachute" and "maintain supersaturation", and a regression model to predict the time-dependent dissolution profiles. Both of the two prediction models showed good prediction performance. Moreover, feature importance was performed to help understand the key information that contributes to the model. After that, the vemurafenib (VEM) SD formulation in previous report was used as an example to validate the models. MD simulation was used to investigate the dissolution behavior of two SD formulations with two polymers (HPMCAS and Eudragit) at the molecular level. The results showed that the HPMCAS-based formulation resulted in faster dissolution than the Eudragit formulation, which agreed with the reported experimental results. Finally, a PBPK model was constructed to accurately predict the human pharmacokinetic profile of the VEM-HPMCAS SD formulation. In conclusion, combined computational tools have been developed to in silico predict formulation composition, in vitro release and in vivo absorption behavior of SD formulations. The integrated computational methodology will significantly facilitate pharmaceutical formulation development than the traditional trial-and-error approach in the laboratory.

Predicting Volume of Distribution in Humans: Performance of In Silico Methods for a Large Set of Structurally Diverse Clinical Compounds

Volume of distribution at steady state (V_D,ss) is one of the key pharmacokinetic parameters estimated during the drug discovery process. Despite considerable efforts to predict V_D,ss, accuracy and choice of prediction methods remain a challenge, with evaluations constrained to a small set (<150) of compounds. To address these issues, a series of in silico methods for predicting human V_D,ss directly from structure were evaluated using a large set of clinical compounds. Machine learning (ML) models were built to predict V_D,ss directly and to predict input parameters required for mechanistic and empirical V_D,ss predictions. In addition, log D, fraction unbound in plasma (fup), and blood-to-plasma partition ratio (BPR) were measured on 254 compounds to estimate the impact of measured data on predictive performance of mechanistic models. Furthermore, the impact of novel methodologies such as measuring partition (Kp) in adipocytes and myocytes (n = 189) on V_D,ss predictions was also investigated. In predicting V_D,ss directly from chemical structures, both mechanistic and empirical scaling using a combination of predicted rat and dog V_D,ss demonstrated comparable performance (62%–71% within 3-fold). The direct ML model outperformed other in silico methods (75% within 3-fold, r² = 0.5, AAFE = 2.2) when built from a larger data set. Scaling to human from predicted V_D,ss of either rat or dog yielded poor results (<47% within 3-fold). Measured fup and BPR improved performance of mechanistic V_D,ss predictions significantly (81% within 3-fold, r² = 0.6, AAFE = 2.0). Adipocyte intracellular Kp showed good correlation to the V_D,ss but was limited in estimating the compounds with low V_D,ss.

Inter-compound and Intra-compound Global Sensitivity Analysis of a Physiological Model for Pulmonary Absorption of Inhaled Compounds

In recent years, global sensitivity analysis (GSA) has gained interest in physiologically based pharmacokinetics (PBPK) modelling and simulation from pharmaceutical industry, regulatory authorities, and academia. With the case study of an in-house PBPK model for inhaled compounds in rats, the aim of this work is to show how GSA can contribute in PBPK model development and daily use. We identified two types of GSA that differ in the aims and, thus, in the parameter variability: inter-compound and intra-compound GSA. The inter-compound GSA aims to understand which are the parameters that mostly influence the variability of the metrics of interest in the whole space of the drugs' properties, and thus, it is useful during the model development. On the other hand, the intra-compound GSA aims to highlight how much the uncertainty associated with the parameters of a given drug impacts the uncertainty in the model prediction and so, it is useful during routine PBPK use. In this work, inter-compound GSA highlighted that dissolution- and formulation-related parameters were mostly important for the prediction of the fraction absorbed, while the permeability is the most important parameter for lung AUC and MRT. Intra-compound GSA highlighted that, for all the considered compounds, the permeability was one of the most important parameters for lung AUC, MRT and plasma MRT, while the extraction ratio and the dose for the plasma AUC. GSA is a crucial instrument for the quality assessment of model-based inference; for this reason, we suggest its use during both PBPK model development and use.

Potential for pharmacokinetic interactions between Schisandra sphenanthera and bosutinib, but not imatinib: in vitro metabolism study combined with a physiologically-based pharmacokinetic modelling approach

AIMS

This study aimed to investigate the potential interaction between Schisandra sphenanthera, imatinib and bosutinib combining in vitro and in silico methods.

METHODS

In vitro metabolism of imatinib and bosutinib using recombinant enzymes and human liver microsomes were investigated in the presence and absence of Schisandra lignans. Physiologically-based pharmacokinetic (PBPK) models for the lignans accounting for reversible and mechanism-based inhibitions and induction of CYP3A enzymes were built in the Simcyp Simulator (version 17) and evaluated for their capability to predict interactions with midazolam and tacrolimus. Their potential effect on systemic exposures of imatinib and bosutinib were predicted using PBPK in silico simulations.

RESULTS

Schisantherin A and schisandrol B, but not schisandrin A, potently inhibited CYP3A4-mediated metabolism of imatinib and bosutinib. All three compounds showed a strong reversible inhibition on CYP2C8 enzyme with k_i of less than 0.5 μmol L^-1 . The verified PBPK models were able to describe the increase in systemic exposure of midazolam and tacrolimus due to co-administration of S. sphenanthera, consistent with the reported changes in the corresponding clinical interaction study (AUC ratio of 2.0 vs 2.1 and 2.4 vs 2.1, respectively). The PBPK simulation predicted that at recommended dosing regimens of S. sphenanthera, co-administration would result in an increase in bosutinib exposure (AUC ratio 3.0) but not in imatinib exposure.

CONCLUSION

PBPK models for Schisandra lignans were successfully developed. Interaction between imatinib and Schisandra lignans was unlikely to be of clinical importance. Conversely, S. sphenanthera at a clinically-relevant dose results in a predicted three-fold increase in bosutinib systemic exposure.