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

Abstract

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.

Study Highlights.

WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

A whole‐body physiologically based pharmacokinetic (PBPK) modeling approach is frequently used for the extrapolation of nonclinical pharmacokinetics to humans. Mismatches could, however, occur between model predictions and observations in preclinical species; thus, model parameters need to be adjusted before any translation.

WHAT QUESTION DID THIS STUDY ADDRESS?

Can we develop a systematic strategy to integrate preclinical data and optimize simplified PBPK models to successfully predict the distribution of small molecules in human?

WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

Compared with the traditional PBPK approach, the strategy proposed provided an easy and systematic alternative for optimizing drug distribution in PBPK models in preclinical species and predicted better or similar accuracy of human drug distribution for diazepam and midazolam.

HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

The proposed strategy can improve the quality of predictions used to support candidate drug selection and internal decision making during preclinical development. Potentially this strategy for PBPK models of drug distribution could be applied to translation within species, for example, from the adult to pediatric population.

INTRODUCTION

During drug discovery and development, characterizing the pharmacokinetic (PK) properties of a drug in the early stage is crucial to avoid failures attributed to poor PK properties. Prediction of human PK helps to design the optimal phase I studies and to select a starting dose that is safe and effective to maintain a rapid dose escalation, saving time and cost. ¹ Different strategies for predicting human PK profiles based on preclinical data have been proposed. ² , ³ , ⁴ , ⁵ Among them, whole‐body physiologically based PK (WBPBPK) modeling has the advantage of providing a biological and mechanistic understanding for inter‐ and intraspecies scaling as well as a better understanding of the drug behavior. ⁶ , ⁷ , ⁸ Several studies showed better accuracy of the physiologically based PK (PBPK) modeling approach for predicting PK compared with empirical and allometric approaches. ⁹ , ¹⁰ , ¹¹ , ¹²

PBPK model development is a “bottom‐up” approach and an iterative “predict, learn, confirm” process. ¹³ , ¹⁴ , ¹⁵ However, when comparing WBPBPK model predictions with observed PK data, mismatches often occur, and thus model parameters need to be adjusted. Generally, the PBPK model is fitted to the observed data to estimate unknown or uncertain model parameters (so‐called “middle‐out approach”). ¹⁶ , ¹⁷ , ¹⁸ However, estimation is challenging because of the large number of parameters and paucity of observed data available (especially preclinical in vivo data). One common practice is to fix some parameters and estimate others, yet the decision on which parameters to fix or estimate is subjective. ¹⁶ , ¹⁹ Our previous work ²⁰ showed the possibility of using simplified PBPK models for fitting PK data. In these models, tissue distribution was described by mechanistic equations that calculate tissue‐to‐unbound plasma partition coefficients (Kpus). ²¹ , ²² Kinetically lumped models based on tissue time constants ²³ were investigated together with PBPK models with common tissue Kpus or common tissue scaling factors. The commonality in tissue partitioning was considered when observing similar behavior of tissue Kpus across compounds with different properties. ²⁴ The kinetically lumped model may not extrapolate well across species because of interspecies differences in tissue blood flows and volumes. In contrast, PBPK models with a full structure and either common Kpus or scalar may perform better in terms of translation across species or within a species due to stronger similarity of tissue composition, assuming an identical model structure across species and species independence of Kpus or scaling factors.

Therefore, the aim of this work was to develop and evaluate a strategy for the extrapolation of drug distribution from preclinical species to humans using the simplified PBPK models and subsequently improving the quality of predictions used to support candidate drug selection and internal decision making during preclinical development. Herein, a proof of concept is presented using diazepam, midazolam, and basmisanil as model drugs for which intravenous (i.v.) PK data in rats, monkeys, and humans were available for the fitting and evaluation of the human prediction.

METHOD

The proposed models were applied to the following three weakly basic compounds: diazepam, midazolam, and basmisanil. Criteria for compound selection were the availability of i.v. plasma concentration profiles in rats, monkeys, and humans and the availability of relevant in vitro information for Kpu predictions (octanol–water partition coefficient [LogP], fraction unbound of drug [fup], and blood–plasma ratio [BP]).

Experimental data

Physicochemical and in vitro data for diazepam, midazolam, and basmisanil are provided in Table S1. For diazepam and midazolam, the literature was searched for PK studies where plasma (or blood or serum) concentrations were reported following an i.v. administration in rats, Cynomolgus monkeys, and humans. These studies provided a mixture of average profiles and individual concentration‐time profiles that were digitized using WebPlotDigitizer (Version 4.2; https://automeris.io/WebPlotDigitizer). For basmisanil, data were collected from in‐house PK studies that are described in the Appendix S1. The PK data available for each compound can be found in Table S2. Diazepam data originate from a total of 13 studies (n = 5 in rat, n = 1 in monkey, n = 7 in human) with a mixture of average and individual profiles and doses ranging from 0.04 to 5 mg/kg. Midazolam data originate from a total of 21 studies (n = 6 in rat, n = 3 in monkey, n = 12 in human) with a mixture of average and individual profiles and doses ranging from 0.075 to 10 mg/kg. Basmisanil data originate from a total of three studies (one for each species) with individual profiles and doses ranging from 0.001 to 4.3 mg/kg.

Fitting and extrapolation approach of the simplified PBPK models

The development of the simplified PBPK models was previously described, ²⁰ and these models were applied here for translation between species. A list of these models is presented in Table 1.

TABLE 1.

Models and details of tissue grouping.

Model	Model description	Tissue grouping (by lumping or clustering)
1	Lumped three‐compartment model	Kpu1: blood, lungs, kidneys, heart, spleen, liver, pancreas, gut, stomach, bone, brain Kpu2: adipose, muscle, rest of body Kpu3: skin
2A	14‐compartment PBPK model with three common Kpus (H)	Kpu1: adipose, bone, brain, muscle, pancreas, muscle, rest of body Kpu2: lung, gut, stomach, kidney, heart, spleen, liver Kpu3: skin
2B	14‐compartment PBPK model with four common Kpus (H)	Kpu1: bone, brain, muscle, pancreas, muscle, rest of body Kpu2: lung, gut, stomach, kidney, heart, spleen, liver Kpu3: skin Kpu4: adipose
2C	14‐compartment PBPK model with three common Kpus (Km)	Kpu1: adipose, bone, brain, muscle, pancreas, rest of body Kpu2: kidney, spleen, liver Kpu3: skin, lung, gut, stomach, heart
2D	14‐compartment PBPK model with four common Kpus (Km)	Kpu1: bone, brain, muscle, pancreas, rest of body Kpu2: kidney, spleen, liver Kpu3: skin, lung, gut, stomach, heart Kpu4: adipose
2 E	14‐compartment PBPK model with three common Kpus (ss)	Kpu1: adipose, bone, brain, muscle, pancreas, muscle, rest of body, skin, gut, stomach, heart, spleen Kpu2: kidney, liver Kpu3: lung
2F	14‐compartment PBPK model with four common Kpus (ss)	Kpu1: adipose, bone, brain, muscle, pancreas, muscle, rest of body, skin, gut, stomach, heart, spleen Kpu2: kidney Kpu3: liver Kpu4: lung
3A	14‐compartment PBPK model with three scalars (H)	SF1: adipose, bone, brain, muscle, pancreas, muscle, rest of body SF2: lung, gut, stomach, kidney, heart, spleen, liver SF3: skin
3B	14‐compartment PBPK model with four scalars (H)	SF1: bone, brain, muscle, pancreas, muscle, rest of body SF2: lung, gut, stomach, kidney, heart, spleen, liver SF3: skin SF4: adipose
3C	14‐compartment PBPK model with three scalars (Km)	SF1: adipose, bone, brain, muscle, pancreas, rest of body SF2: kidney, spleen, liver SF3: skin, lung, gut, stomach, heart
3D	14‐compartment PBPK model with four scalars (Km)	SF1: bone, brain, muscle, pancreas, rest of body SF2: kidney, spleen, liver SF3: skin, lung, gut, stomach, heart SF4: adipose
3E	14‐compartment PBPK model with three scalars (ss)	SF1: adipose, bone, brain, muscle, pancreas, muscle, rest of body, skin, gut, stomach, heart, spleen SF2: kidney, liver SF3: lung
3F	14‐compartment PBPK model with four scalars (ss)	SF1: adipose, bone, brain, muscle, pancreas, muscle, rest of body, skin, gut, stomach, heart, spleen SF2: kidney SF3: liver SF4: lung

Abbreviations: H, hierarchical clustering on rat tissue composition data; Km, k‐means clustering on rat tissue composition data; Kpu, tissue‐to‐unbound plasma partition coefficient; PBPK, physiologically based pharmacokinetic; ss, clustering on in vivo rat tissue‐to‐plasma partition coefficient data; SF, scaling factor.

Optimization of the distribution parameters with preclinical data and model evaluation

The performance of the developed models in preclinical species was assessed by comparing the simulated concentration‐time profiles with experimental data of i.v. studies (Table S2). For diazepam and midazolam, as the data originated from various studies with different designs, a model‐based meta‐analysis was first performed to estimate the volume of distribution (Vss) and clearance (CL) from the observed data using compartmental analysis. For basmisanil, the Vss and CL of the observed data were obtained by noncompartmental analysis (NCA) of the PK studies. The observed Vss were considered as the reference values. When fitting the simplified PBPK models to the animal PK data, the CL was fixed to the observed CL value to ensure comparable disposition model performance assessment between the different investigated models. In each species, the CL value was estimated by compartmental analysis for diazepam and midazolam, and NCA was used for basmisanil.

The PBPK models were fitted in NONMEM 7.3 (ICON Development Solutions) using first‐order with interaction (FO‐I), and when this failed as a result of model complexity or data sparsity, first‐order conditional estimation with interaction (FOCE‐I) or stochastic approximation expectation‐maximization with interaction/importance sampling (SAEM‐I/IMP) methods were used. ²⁵ , ²⁶ Initial values for lumped Kpu and common Kpu parameters were calculated as a weighted sum of all the tissue Kpus (predicted by the Rodgers and Rowland [RR] model) that are lumped or clustered together. Likewise, the initial common scalars were chosen to be one. Several criteria were used to evaluate the model performance and determine its suitability for extrapolation to human: Bayesian information criterion (BIC), convergence assessment, goodness‐of‐fit plots, precision of estimates, physiological plausibility of Kpus, and closeness of estimated Vss to the observed Vss. For each compound, models that matched all of these criteria were considered the best models. ²⁰

The i.v. prediction of the simplified model in human

For diazepam and midazolam, as the clinical observations were from PK studies with different doses and lengths of infusion, it was not feasible to use a single visual predictive check plot to compare the predicted versus observed data. Therefore, a common study design was simulated using the R package RxODE. ²⁷ The human PK was simulated from a reference two or three compartmental that was used to fit the PK data of diazepam or midazolam. The 1000 concentration‐time profiles were simulated for a single i.v. dose and infusion rate to achieve a steady‐state plasma concentration determined by the drug elimination rate. A 16.1‐h infusion of 10 mg for diazepam and a 0.01‐h infusion of 5 mg for midazolam were chosen to illustrate the different kinetic phases. For basmisanil, CL was fixed to the value calculated from NCA in the clinical study (7.26 L/h) and simulations were overlaid with the PK observations of the reported clinical study (Table S2).

In the kinetically lumped model and the 14‐compartment PBPK model with common Kpus, the assumption is that tissue compositions are similar and Kpus are the same across species. While adjusting for the differences in species physiology and species fup and BP, the tissue‐to‐plasma partition coefficients (Kps) of human were estimated by assuming Kpu_human is equal to Kpu_species, where species correspond to rat or monkey as shown by Equation (1).

$$\mathrm{K}{\mathrm{p}}_{\text{human}}=\mathrm{Kp}{\mathrm{u}}_{\text{species}}\bullet \mathrm{fu}{\mathrm{p}}_{\text{human}}$$ (1)

In the 14‐compartment PBPK model with common scalars, the assumption is that the bias from the Kpu predicted using RR equations ²¹ , ²² and the “true” Kpu is the same across species while adjusting for the differences in species physiology, fup, and BP. The Kp_human were estimated by assuming Kpu_human is equal to KpuRR_human $\bullet$ SF_species, where SF_species correspond to the scalar estimated in preclinical species, and KpuRR is the tissue‐to‐plasma unbound partition coefficient calculated using the RR method.

$$\mathrm{K}{\mathrm{p}}_{\text{human}}=\left({\text{KpuRR}}_{\text{human}}\bullet {\mathrm{SF}}_{\text{species}}\right)*\mathrm{fu}{\mathrm{p}}_{\text{human}}$$ (2)

Interspecies extrapolation was conducted using the species‐specific blood flow rates, volumes, and composition for each tissue when using the models with common scalars (Tables S3–S6).

Assessment of human prediction accuracy/performance assessment of extrapolation

For the studied compounds, simulation of i.v. concentration‐time profiles in human using the best models were compared against the simulation using the traditional WBPBPK modeling approach with 16 compartments and tissue Kpus calculated from the RR equations. For each best model, the human blood Vss (Vss,b) was calculated ²⁰ and assessed against the observed Vss. When Vss in plasma (Vss,p) was reported in the literature study, Vss,p was converted to Vss,b ($\mathrm{Vss},\mathrm{b}=\mathrm{Vss},\mathrm{p}\bullet \mathrm{BP}$).

In addition, simulated concentration profiles from each best model (“middle‐out approach”) and from the traditional WBPBPK model (“bottom‐up approach”) were compared against the median observed concentration profile by calculating the root mean square error (RMSE) to assess the prediction accuracy. ²⁸

RESULTS

Diazepam was the first compound selected for optimization due to the number of PK studies in humans (n = 36), monkeys (n = 2), and rats (n = 5). Based on the preliminary results of the model fitting to rat data, it was decided to reduce the number of models to be further tested for the model fitting of the diazepam to monkey data. The number of models tested was also reduced for the fitting of midazolam and basmisanil. The best simplified models fitted in rat were 3C and 3D for diazepam (Table 2), 3D for midazolam (Table S7), and none for basmisanil (Table S9). The best models in monkey were 3C and 3D for diazepam (Table 3), 3C and 3D for midazolam (Table S8), and none for basmisanil (Table S10).

TABLE 2.

Parameter estimates of the investigated model for diazepam in rat.

Model	BIC	Kpu1/SF1 (RSE%)	Kpu2/SF2 (RSE%)	Kpu3/SF3 (RSE%)	Kpu4/SF4 (RSE%)	IIV CL as %CV (RSE%)	Proportional error (RSE%)	Vss,b estimated (L)	Vss within 20% (YYY), 25% (YY), 30% (Y)
1	−209.012	40.3 (2730)	26.4 (2.5)	199.5 (12.5)	N/A	26.8 (25.4)	19.5 (14.5)	1.11	YY
2A	−208.136	28.4 (12)	307 (45.9)	88.2 (13.9)	N/A	29.2 (21.8)	20.3 (8.6)	1.34	N/A
2B	−169.673	29.4 (12.7)	309 (44.1)	88.1 (13.9)	23.1 (7.1)	28.8 (21.8)	20.2 (8.6)	1.34	N/A
2C	−211.201	27.3 (11.6)	427 (19.5)	87.3 (13.5)	N/A	26.4 (20.8)	19.8 (7.1)	1.14	Y
2D	−172.823	29.1 (12.6)	438 (11.4)	87.3 (13.6)	17.8 (12.9)	26.9 (20.6)	19.8 (7.1)	1.15	Y
2E	−169.818	47.0 (6.8)	334 (7.3)	424 (59.1)	N/A	33.6 (33.6)	29.3 (9.9)	1.22	N/A
2F	−135.196	46.9 (6.8)	334 (8.4)	3.11 (24.2)	505 (69.5)	31.6 (19.7)	29.2 (9.9)	1.3	N/A
3A	−198.144	1.92 (28.9)	27.3 (20.7)	1.77 (18.7)	N/A	30.6 (18.9)	21.5 (7.8)	1.71	N/A
3B	−169.725	3.20 (11.7)	19.5 (31.9)	2.03 (13.9)	0.394 (7.7)	29.8 (21.1)	20.2 (8.8)	1.56	N/A
3C	−206.274	3.33 (9.5)	19.5 (27.6)	0.11 (23.8)	N/A	26.2 (21)	20.1 (9.2)	1.06	YYY
3D	−173.892	3.2 (11.2)	23.5 (23.7)	2.02 (13.8)	0.265 (20.9)	26 (21.7)	19.6 (8.8)	1.11	YY
3E	−204.291	1.77 (11.5)	42.9 (18.7)	0.894 (5.8)	N/A	26.3 (20.3)	20.5 (6.8)	0.99	YYY
3F	−170.095	1.76 (11.4)	42.4 (18.8)	757 (17.2)	0.009 (10,600)	25.9 (21.2)	20.4 (7.4)	1.86	N/A

Note: Estimates were reported with RSEs in parentheses. To obtain the RSEs in the domain of the reported original parameter instead of the log‐transformed domain, normal/log‐normal reverse algebra was applied (see the Appendix S1).

Abbreviations: %CV, coefficient of variation; BIC, Bayesian information criterion; CL, clearance; IIV, intraindividual variability; Kpu, tissue‐to‐unbound plasma partition coefficient; N/A, not available; RSE, relative standard error; RSE%, relative standard error percentage; SF, scaling factor; Vss, volume of distribution; Vss,b, blood volume of distribution.

TABLE 3.

Parameter estimates of the investigated model for diazepam in monkey

Model	BIC	SF1 (RSE%)	SF2 (RSE%)	SF3 (RSE%)	SF4 (RSE%)	Proportional error (RSE%)	Vss,b estimated (L)	Vss within 20% (YYY), 25% (YY), 30% (Y)
3A	−140.543	0.153 (52.9)	44.0.5 (100)	3.34 (3.9)	N/A	51.4 (14.9)	50.9	N/A
3B	−137.609	0.289 (20.7)	21.0 (94.2)	3.30 (4.4)	1.20 (10.4)	55.8 (4.6)	28.8	N/A
3C	−138.918	0.500 (23.9)	12.9 (10.9)	3.47 (7.4)	N/A	64.3 (6.5)	12.17	YYY
3D	−136.666	0.425 (26.6)	14.8 (8.9)	3.38 (4.4)	1.20 (25.4)	62.8 (6.6)	12.16	YYY
3E	−132.007	1.23 (5.7)	0.453 (5.7)	121 (10.0)	N/A	63.2 (7.3)	14.9	N/A
3F	−129.234	1.23 (5.7)	0.921 (34.7)	8.33 (148)	120 (10.5)	63.2 (7.3)	14.8	N/A

Note: Estimates were reported with RSEs in parentheses. To obtain the RSEs in the domain of the reported original parameter instead of the log‐transformed domain, normal/log‐normal reverse algebra was applied (see the Appendix S1).

Abbreviations: BIC, Bayesian information criterion; N/A, not available; RSE, relative standard error; RSE%, relative standard error percentage; SF, scaling factor; Vss, volume of distribution; Vss,b, blood volume of distribution.

Abbreviations for models are defined in Table 1.

Results shown were based on using FO‐I or FOCE‐I algorithms in NONMEM. ²⁵ , ²⁶ They generally performed well but sometimes failed to converge. Estimation of distribution parameters (scalars or clustered Kpu) using the SAEM‐I/IMP method was then considered. SAEM‐I/IMP could improve the estimation accuracy or convergence success at the expense of a longer running time and more parameter tuning (results not shown).

Rat

The PK data for diazepam in rat were extracted from literature studies (Table S2). Using a blood CL of 0.915 L/h in rat, the concentration‐time profiles were analyzed with all the investigated models. The estimated parameters are listed in Table 2, and the goodness of fit plots of the best models are shown in Figures S1 and S2. All model parameters were estimated with reasonable precision (relative standard error percentage [RSE%] < 50%) except for the Kpu of the central compartment (2730%) in the lumped model (Table 2). This lack of precision is surprising but may be attributed to insufficient flexibility of the model structure: the lung Kpu is highly influenced by the assumptions made around the other tissue kinetics and the nonapplicability to diazepam, that is, it is not a compound with low Kpus. Among the compartment models, several models could capture an estimated Vss,b close to the rat observed Vss,b (0.91 L) within 20% (Models 3C and 3E), 25% (Model 3D), and 30% error (Models 2C and 2D) (Table 2). Models 3C and 3D gave plausible estimates for Kpus (Table 2). In addition, the estimated rat Kpus were biologically plausible as the values obtained were close to tissue Kpus measured in rat (Table S11). For diazepam, tissue concentrations were derived and compared with observed tissue concentrations from rat studies (Figures S3 and S4). Although differences exist between the estimated and observed Kpu values, tissue concentrations were still well predicted (e.g., liver, kidney). Thus, Models 3C and 3D were the best for fitting the diazepam data in rats and were then used for extrapolation to human (Figure 1). The extrapolated human PK profiles from Models 3C and 3D showed a major improvement compared with the simulation using the traditional WPBPK modeling approach (RMSE 4.9 and 10.2 vs. 28). Similarly, the Vss,b in human estimated from Models 3C (132 L) and 3D (97 L) were within 1.1‐ and 1.5‐fold error of the Vss,b observed (152 L), which is considerably better than the Vss,b estimated from the traditional WPBPK modeling approach (41 L, 3.7‐fold error). Thus, the approach using the 14 compartments with common scalars (especially Models 3C and 3D) seemed more promising for translation. The PK data of midazolam and basmisanil in rat were extracted from literature studies (Table S2) and an internal PK study, respectively. Using a blood CL of 1.30 and 0.824 L/h, respectively, the concentration‐time profiles were analyzed with the models with scalars (Models 3A–F). The estimated parameters are listed in Tables S7 and S9, respectively. In general, the relative standard errors (RSEs) were low (<50%), with certain exceptions (Table S7) for midazolam. Models 3C and 3D could capture an estimated Vss,b close to the Vss,b observed (0.64 L) within 20% error. Considering the different criteria (precision of estimates, physiological plausibility of Kpu estimates, and estimated Vss value), Model 3D was the best for fitting the midazolam data in rats. Moreover, the estimated rat Kpus were biologically plausible as the values obtained were mostly within twofold of Kpu measurements in rat available from the literature (Figure S3). Model 3D was subsequently selected for extrapolation to human (Figure 2). The simulated human PK profiles from Model 3D was slightly better than the simulation using the traditional WPBPK modeling approach (RMSE 0.021 vs. 0.018). The Vss,b in human estimated from Model 3D in rat (183 L, which is within a 1.3‐fold error) was also closer to the Vss,b observed (141 L) compared with the Vss,b estimated from the traditional WPBPK modeling approach (202 L, which is within a 1.5‐fold error). No interindividual variability was estimated for basmisanil as there were only two subjects in the PK study. Model 3F did not converge. Although some models were able to produce parameter estimates with reasonable RSEs (<50%), none of them provided an estimated Vss,b close to the Vss,b observed (0.91 L) within 20% error. The models' performance could be limited by the sparse sampling in the rat studies, particularly in the terminal phase. In the absence of any additional data to improve the optimization in rat, the decision was to perform the prediction in human using the traditional PBPK model approach (Figure 3). The simulated human PK profiles from the traditional WPBPK modeling approach was within a threefold error of the Vss,b in human (38 L vs. 84 L). Therefore, the traditional WPBPK modeling approach gave a good prediction in human for basmisanil.

FIGURE 1.

Simulated human pharmacokinetic profiles of diazepam from the most suitable simplified physiologically based pharmacokinetic models optimized in rat (left) and in monkey (monkey) versus the traditional whole‐body physiologically based pharmacokinetic (WBPBPK) modeling approach. The dashed red line represents the median concentrations, and the semitransparent red field represents a simulation‐based 90% confidence interval for the median using the reference model (empirical three‐compartmental model). The solid lines represent the median concentrations using the traditional WBPBPK model approach (black), the Model 3C (green), and the Model 3D (light blue).

FIGURE 2.

Simulated human pharmacokinetic profiles of midazolam from the most suitable simplified physiologically based pharmacokinetic models optimized in rat (left) and in monkey (monkey) versus the traditional whole‐body physiologically based pharmacokinetic (WBPBPK) modeling approach. The dashed red line represents the median concentrations, and the semitransparent red field represents a simulation‐based 90% confidence interval for the median using the reference model (empirical three‐compartmental model). The solid lines represent the median concentrations using the traditional WBPBPK model approach (black), the Model 3C (green), and the Model 3D (light blue).

FIGURE 3.

Simulated human pharmacokinetic profiles of basmisanil (intravenous infusion of 0.1 mg for 15 min). The red dots represent the observed data. The solid lines represent the median concentrations using the traditional whole‐body physiologically based pharmacokinetic model approach (black), the Model 3C (green), and the Model 3E (brown).

Monkey

The PK data in monkey were extracted from literature studies (Table S2) for diazepam and midazolam and from an internal PK study for basmisanil. Using a blood CL of 9.97 L/h, 6.4 L/h, and 0.824 L/h, respectively, the concentration‐time profiles in monkey were analyzed with the approach of simplified models with scalars (Models 3A–F). The estimated parameters are listed in Table 3 for diazepam and in Tables S8 and S10 for midazolam and basmisanil, respectively. For diazepam and midazolam, Models 3C and 3D presented parameter estimates with reasonable RSEs (<50%) (Table 3 and Table S8). The physiological plausibility of Kpu estimates of these two models was reasonable for both compounds. Models 3C and 3D recaptured an estimated Vss,b close to the Vss,b observed (11.1 L for diazepam and 8.8 L for midazolam) within 20% error (Table 3 and Table S8). Moreover, the obtained Kpus of the two models were physiologically plausible, and these models were the best for fitting the diazepam and midazolam data in monkeys and were subsequently selected for extrapolation to human (Figures 1 and 2). It should be noted that the traditional WBPBPK modeling approach for midazolam gave good prediction in human (which was not the case for diazepam). The simulated human PK profiles from these selected models showed improvement compared with the simulation using the traditional WPBPK modeling approach for diazepam (RMSE 26 and 20 vs. 28) and were comparable for midazolam (RMSE 0.018 and 0.019 vs. 0.018). The Vss,b in human estimated from Models 3C (Vss,b = 47 L for diazepam and 131 L for midazolam) and 3D (respectively, Vss,b = 57 L and 302 L) were within 3.1 to 1.1‐fold error of the Vss,b observed (respectively, Vss,b = 152 L and 141 L), which were overall better than the Vss,b estimated from the traditional WPBPK modeling approach (Vss,b = 41 L, 3.7‐fold error and 202 L, 1.5‐fold error, respectively). On the other hand, for basmisanil convergence failure was encountered with most of the models when using FOCE‐I. The parameters estimated using SAEM‐I/IMP are listed in Table S10. None of the models were able to produce parameter estimates with reasonable RSEs (<50%); also, none of them provided an estimated Vss,b close to the Vss,b observed (24 L) within 20% or 30% error. This could be due to the heterogeneity of PK profiles and the small number of subjects (n = 3) as the proportional errors were very large (>68%). Similarly, as with the rat data, the decision was to perform the prediction in human using the traditional PBPK model approach in the absence of any additional data to improve the optimization in monkey (Figure 3).

DISCUSSION

In this work, several approaches and PBPK models were presented for cross‐species extrapolation. The Kp prediction method used here was the RR method, ²¹ , ²² but other methods could also be used. ⁴ , ²⁹ , ³⁰ , ³¹ In general, they strongly rely on drug properties such as LogP, acid‐base dissociation constant (pKa), fup, and BP, which are expected to be well characterized. A low confidence in the measurement of these values may subsequently prevent parameter estimation from in vivo data and increase uncertainty around the human predictions. ²⁴

In the kinetic lumping approach, one model structure was assumed to be common across species. The lumped model was based on human, the target species for extrapolation. This approach assigned similar tissue kinetics between species that potentially alter the model mechanistic realism in preclinical species. For most tissues, the ratio of blood flows to tissue volumes were similar between species except for adipose and skin (Tables S3–S6). In human, skin and adipose volumes account for 3.9% and 24% of total tissue volume, respectively; they account for 19% and 8.4%, respectively, in rats, and for 11% and 3% in monkeys. Adipose tissue can be key for drug distribution in human due to its size and characteristics (lowest tissue water, high neutral lipids, and low phospholipids), and thus having adipose separately can help to better describe the PK in human. However, rats and monkeys are lean animals, and adipose does not represent such an important organ for drug distribution. Optimization of the “human” lumped model may limit its use and interpretation in preclinical species. Therefore, the cross‐species extrapolation using this approach may not work well and be challenging especially for drugs that distribute largely in the adipose tissue, such as highly lipophilic compounds.

In the 14‐compartment PBPK models approach with tissue commonalities, parameters could be separated into system‐ and drug‐specific components, which allowed the extrapolation of mechanistic knowledge from a reference species (rat or monkey) to a target species (human) like in a traditional WBPBPK model. Species differences in organ size and blood flow rates were accounted for by extrapolation in all of the models. In the models with common scalars, species differences in tissue composition are considered, and different Kpu values are allowed for tissues, whereas this is less flexible in the models with common Kpus. In addition, in the latter models, Kpus are assumed to be the same across species, whereas in the former models it is assumed that the same bias from RR Kpus exist across species, which gives a better translational value providing physiologically relevant predictions of tissue distribution while analyzing plasma profiles only.

The aim of this work was to propose a PBPK strategy for extrapolating drug distribution from preclinical species to human. Based on the findings obtained for three compounds (lipophilic weak bases), a strategy is proposed in Figure 4. These three compounds were provided as examples on how human PK profiles could be predicted by optimizing simplified models in rats and monkeys while using only plasma concentrations that are more readily available. Other studies often require plasma and various tissue concentrations in rats to estimate Kps and predict human PK. ³² , ³³ , ³⁴ , ³⁵ The predictive performance of simplified models for extrapolation was compared retrospectively to the traditional WBPBPK approach for diazepam and midazolam. Sparse data resulted in parameter estimation issues for basmisanil, and subsequently it is not recommended to further extrapolate the “best” worst animal model as it could be inconsistent and impair human predictions. Therefore, when data are scarce, the better choice is to use the traditional PBPK modeling approach (Figure 4). Generating good‐quality data (full PK profile, high confidence in in vitro data) should be a prerequisite for the extrapolation; however, this might be limited due to animal welfare constrains.

FIGURE 4.

Optimized PBPK modeling strategy for distribution. This is a preliminary recommendation that needs to be refined by investigating more compounds from a larger and more diverse chemical space. RR, Rodgers and Rowland; fup, fraction unbound of drug; BP, blood–plasma ratio; BIC, Bayesian information criterion; GoF, goodness of fit; Kpu, tissue‐to‐unbound plasma partition coefficient; PBPK, physiologically based pharmacokinetic; PK, pharmacokinetic; Vss, steady‐state volume; Vss,obs, steady‐state volume observed; Vuss, unbound volume of distribution.

When limited data are available at early sampling times, it could also affect the model optimization in preclinical species, causing deviations in initial phase predictions in human. Nevertheless, the 14‐compartment model assumes the lumped central compartment (blood and lungs) as the initial dilution space, which increases accuracy and stability for fitting the initial PK decline phases. This simplified PBPK approach reduced the number of parameters to be estimated from 16 to only three or four, therefore resolving parameter identifiability issues when trying to fit WBPBPK models to data. ²⁰ The insensitivity of one parameter for the overall PK profiles may explain the low precision in some of the models. Nevertheless, the high precision for the parameter estimates in the best models in animals indicated good model performance, although fittings for some of the digitized data are only approximate. The presented approach can be combined with commercial PBPK software (e.g., SimCYP®, PK‐Sim®, or Gastroplus®) by using the optimized parameters to derive the tissue Kpu or scalar values needed as inputs. For diazepam and midazolam, if the Vss and the CL were well characterized, the model described the overall profile in animals and would reasonably predict the concentration‐time profiles in human (vs. traditional WBPBPK modeling). Based on this approach, the recommendation is to start with the models with scalars, especially those using k‐means clustering as they generally performed well for fitting and extrapolation. Alternatively, other simplified PBPK models could be explored. If none of the models performed well in animals (basmisanil example), the extrapolation could be done using the traditional WBPBPK modeling approach, although confidence in prediction accuracy will be in the realms of traditional PBPK models. It is, however, not recommended to use the models with poor fitting to preclinical data, as the predictions in human are uncertain and could be poor.

This work has some limitations due to the assumptions and data sources. Relevant physiological data and evidence may be lacking to address the potential limitations of cross‐species translation. Although monkey is generally considered to be the most suitable preclinical species for translation, the case study showed better results using rat. This could be attributed to the lack of information regarding monkey tissue composition, which was a hybrid of rat, human, and monkey data (Table S5). Therefore, better knowledge on species‐specific physiological parameters could improve the fitting and prediction accuracy across species. Another explanation could be the interspecies difference in Vss for diazepam. Rat Vuss,p (30 L/kg) was 4.6 times lower than human unbound volume of distribution in plasma (Vuss,p) (139 L/kg), whereas monkey Vuss,p (18 L/kg) was surprisingly 7.8 times lower. Besides insufficient data, this analysis also highlighted the need for good‐quality PK data in animal studies to avoid parameter fitting issues and consequently the suitability of models for prediction in human. Low numbers of animals and variable methods for bioanalysis in the different preclinical studies might also have influence on the model fitting.

PBPK modeling is increasingly applied in drug development and regulatory review. ³⁶ , ³⁷ , ³⁸ , ³⁹ , ⁴⁰ Recent regulatory guidance regarding PBPK modeling ⁴¹ , ⁴² highlighted the need for a more systematic approach to establish confidence in PBPK models, especially when estimating model parameters (middle‐out approach). Overall, this work provided a rational and systematic strategy to predict human PK using preclinical data in a PBPK modeling strategy. The extrapolation is focused on selected best‐fitted models and plausible parameters that are not arbitrarily chosen, thus bringing a more rational way to translate PBPK models for drug distribution between species. The strategy was applied to a dataset of three weak bases, mostly due to the limited availability of PK data simultaneously in several species. The validation of this framework would require further assessment with a large dataset of compounds with diverse physicochemical properties. It should be noted that the predictive performance of the models in preclinical species was not validated with independent preclinical data as new data are generally not generated due to 3R (Replacement, Reduction and Refinement) principles. Following the development and verification of models in rats, it can be suggested to have an additional step for validating the predictive performance of these models using monkey data when they become available to increase confidence before predictions in human. In addition, this strategy mainly focused on drug distribution, which is only one key component of drug PK. Indeed, it did not consider challenges related to absorption and CL ⁴³ , ⁴⁴ by considering only i.v. administration and assuming a fitted CL, which would have further increased the degree of complexity and potential uncertainty. For example, there were interspecies differences in plasma CL, which was very rapid and large in rat compared with man and monkey for diazepam, whereas rat blood CL was higher than hepatic blood flow rate for midazolam.

In this work, the PBPK modeling strategy was mainly focused on an application for interspecies extrapolation from animals to human. However, it could also be used for intraspecies extrapolation from a base population to pediatrics or a special population. ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁴⁸ If some mechanisms are modified in the target population, this knowledge should be updated and incorporated in the model.

AUTHOR CONTRIBUTIONS

E.Y., M.G., and A.O‐M. wrote the manuscript. E.Y., M.G., A.O‐M., K.O., and L.A. designed the research. E.Y. performed the research. E.Y. analyzed the data.

FUNDING INFORMATION

This work has been funded by F. Hoffmann‐La Roche.

CONFLICT OF INTEREST STATEMENT

E.Y., M.G., and A.O‐M. are employees of F. Hoffmann‐La Roche. All other authors declared no competing interests for this work.

Supporting information

Appendix S1:

Yau E, Gertz M, Ogungbenro K, Aarons L, Olivares‐Morales A. A “middle‐out approach” for the prediction of human drug disposition from preclinical data using simplified physiologically based pharmacokinetic (PBPK) models. CPT Pharmacometrics Syst Pharmacol. 2023;12:346‐359. doi: 10.1002/psp4.12915