Modeling Whole-Body Dynamic PET Microdosing Data to Predict the Whole-Body Pharmacokinetics of Glyburide in Humans

Abstract

Introduction

Whole-body dynamic (WB4D) positron emission tomography (PET) imaging data using radiolabeled analogs of drugs are mostly analyzed using descriptive approaches, with no relationship to traditional pharmacokinetic studies based on blood sampling. Here, we build a pharmacokinetic (PK) model from WB4D PET data obtained using a microdose of radiolabeled glyburide ([¹¹C]glyburide) in humans, aiming to describe the biodistribution of this drug and compare estimated pharmacokinetic parameters with the parameters obtained in standard PK studies.

Methods

The present work analyzes data acquired over 40 min after injection of [¹¹C]glyburide in 16 healthy subjects using non-linear mixed-effect models (NLMEM). In 10 subjects, a second PET acquisition was performed after rifampicin administration, which may cause a drug–drug interaction and inhibit the liver uptake transport of glyburide. Arterial blood, liver, kidneys, pancreas, and spleen kinetics were modeled using NLMEM. The model-building strategy involved selecting the structural model using baseline [¹¹C]glyburide PET data and then selecting the covariate model (rifampicin, age, and gender) and refining the structure of the interindividual variability model using both administration periods. Model selection was based on the corrected Bayesian information criterion and implemented in Monolix software.

Results

The final model included seven compartments, with two compartments each for the Liver and kidneys to account for within-tissue exchanges. Rifampicin decreased the Liver distribution by 261%.

Discussion

The estimated central volume of distribution (V = 3.6 L) and elimination rate (k = 0.8 h^-1) were consistent with the known pharmacokinetics of glyburide, which is a promising first step in leveraging microdose data to study the WB4D biodistribution.

Registration

EudraCT identifier no. 2017-001703-69

Supplementary Information

The online version contains supplementary material available at 10.1007/s40262-025-01562-9.

Key Points

Microdosing PET studies represent an opportunity to safely and dynamically follow the kinetics of radiolabeled drugs in the entire human body. Clinical pharmacokinetic parameters can therefore be obtained at an earlier stage, during phase 0 rather than phase I in the traditional process.

We used glyburide as a model drug to build a PK model from dynamic PET imaging using compartmental approaches and relate it to the results of standard pharmacological approaches.

Our model describes the biodistribution of this drug in five major organs and the influence of an inhibition of a key liver transporter.

Introduction

One of the key tasks in early drug development is to untangle the absorption, distribution, metabolism, and excretion (ADME) phases of new chemical entities and integrate these data for the prediction of human pharmacokinetics (PK). Simulation of the human PK profile remains challenging and provides key data to guide the selection of lead compounds and the adequate dose for the first-in-human administration of the investigational drug (phase I) [1]. Today, early prediction of human PK and biodistribution mainly relies on in silico, in vitro, and in vivo PK data obtained in animals. However, considerable species differences exist in terms of ADME, and clinical translation of PK profiles is not straightforward [2]. To overcome these limitations, allometric scaling and physiologically based pharmacokinetic (PBPK) models, integrating in vitro data, have been proposed [3].

Microdosing approaches benefit from a relatively facilitating regulatory framework, allowing subtherapeutic doses of drug candidates (< 100 µg, 1/100th of the no-adverse-event level) to be used in healthy volunteers or directly in the targeted patients. This approach can be carried out rapidly, upstream of the traditional phase I, and is therefore referred to as “phase 0” by some authors [4]. Assuming that humans are probably the best model to predict human PK, decisive clinical PK data can theoretically be obtained at a very early stage compared with the traditional development process. This approach is gaining particular interest with the rise of PK studies using radiolabeled compounds for positron emission tomography (PET) imaging. PET imaging is a quantitative, kinetic, and sensitive imaging technique [5]. Whole-body dynamic (WB4D) PET imaging data can theoretically inform investigational drugs’ whole-body PK (WBPK) and enrich available PK data classically obtained from the concentration of drugs and metabolites in blood and body fluids. However, examples and adequate methods are needed to establish the predictive value of this approach for anticipating the PK at the therapeutic dose, usually estimated during phase I, and/or identifying rate-limiting factors that may impact the clinical PK of investigational drugs. Here, we propose to use population approaches to model distribution and elimination from WB4D PET data as well as investigate keys sources of interindividual variability. This concept is gaining particular interest because microdosing with radiolabeled compounds allows the collection of detailed whole-body PK data in humans very early in development, without significant pharmacological effects or safety risks. It provides a unique opportunity to characterize human pharmacokinetics before administering therapeutic doses. [4]

Glyburide (also called glibenclamide) is a widely prescribed glucose-lowering drug for which much PK data are available. The objective of this work was to build a PK model from WB4D PET data obtained using a microdose of radiolabeled glyburide ([¹¹C]glyburide) in humans, with the aim to describe the biodistribution of this drug and compare estimated pharmacokinetic parameters with the parameters obtained in standard PK studies involving pharmacological doses in later phases of development. The hepatobiliary elimination of glyburide is mainly mediated by liver transporters of the organic anion-transporting polypeptide (OATP) family, and the expression of these transporters has been shown to change with age and with gender [6]. We therefore tested the influence of age, gender, and coadministration with rifampicin, an inhibitor of OATP transporters [7], on model parameters.

Methods

Study Design and Data Acquisition

Study Design

The data used in this work were collected in a study comparing the WBPK of radiolabeled glyburide ([¹¹C]glyburide) in the absence or the presence of rifampicin, a potent OATP inhibitor [9]. The study was designed to investigate the impact of age and sex on OATP function. Therefore, 16 healthy volunteers (5 females and 11 males) were included to compare males > 50 years old with males < 30 years old (age effect) and males > 50 years old with females > 50 years old (sex effect). Table 1 presents the demographic characteristics of each group.

Table 1.

Demographic characteristics of the 16 subjects included in the two imaging sessions of the study

	Group 1 Men > 50 years old	Group 2 Women > 50 years old	Group 3 Men < 30 years old
Nb of subjects with imaging after Glyburide/Glyburide+Rifampicin	4/1	5/4	7/5
Age (years) Median (Min–Max)	59 (50–64)	60 (59–65)	25 (20–30)
Body weight (kg) Median (Min−Max)	81 (74–88)	66 (53–72)	73 (59–87)

All subjects underwent a baseline WB4D PET acquisition, which started with the injection of a microdose of [¹¹C]glyburide (intravenous [i.v.] bolus). In total, 10 of the 16 subjects underwent a second [¹¹C]glyburide scan in the presence of OATP inhibition, at least 3 h after the end of the first acquisition to allow for decay of carbon-11 radioactivity [10] (half-life = 20.4 min). To this end, an infusion of rifampicin (9 mg/kg diluted in glucose 5% perfused over 30 min) was administered immediately before [¹¹C]glyburide injection and WB4D PET acquisition. Potential carryover of drug within occasion was not taken into account, as the radioactivity from the first dose had completely disappeared and the amount of residual drug was negligible.

The study protocol was approved by an ethics committee (CPP IDF5: 17041, study reg. no. EudraCT 2017-001703-69). Experiments were conducted with respect to the 1975 Declaration of Helsinki. Written informed consent was provided after the subjects had received a medical examination and been given all information about the study. A blood sample was collected for pharmacogenetic analysis of OATP transporter genes. Polymorphism of the SLCO1B1 gene coding for OATP1B1 (c.521T>C genotype, rs4149015) is relatively common in Caucasian and Asian populations, with a frequency of about 15–20%, but rare in subjects of African origin [11]. Homozygous carriers of the C allele (CC) show lower elimination rates, higher plasma exposure, and enhanced toxicity risk to OATP1B1 substrates such as statins or some antidiabetic drugs [12, 13]. Consequently, the subject harboring the CC allele in our study showed a ~60% increase in plasma exposure to [¹¹C]glyburide associated with a ~48% decrease in its liver-uptake transfer rate) and a lower response to rifampicin [6]. Therefore, this subject was excluded from model building to avoid skewing the results with one outlier.

PET Data

WB4D PET acquisitions were performed using a Signa positron emission tomography–magnetic resonance imaging (PET–MR) scanner (GE Healthcare, USA). First, dynamic mono-bed acquisition focused on the abdomen was performed for 3 min after the injection of [¹¹C]glyburide to capture early time-points (16 frames of 10 s) in the Liver, spleen, pancreas, kidneys, and myocardium. Then, 15 whole-body PET images (five bed positions, every 2.5 min) were acquired over 37 min (Fig. 1).

Fig. 1.

Whole-body PET images of [¹¹C]glyburide distribution in healthy volunteers, without and with pre-infusion of rifampicin. Three subjects were randomly selected, one from each group: subject 14 (group 1), subject 9 (group 2), and subject 3 (group 3).

PET images were reconstructed using a three-dimensional (3D) iterative reconstruction algorithm, and WB4D PET images were generated to capture the kinetics of radioactivity in the different organs over 40 min. Volumes of interest (VOIs) were manually delineated for each patient for selected tissues (liver, kidneys, spleen, myocardium, pancreas, brain, testis, muscle, and eyes) using PMOD^® software (version 3.9) on the last images of the acquisition and used to compute the radioactivity per mL. An additional VOI was delineated over the left ventricle and the aorta representing arterial blood pool. Kinetics in this VOI have been previously validated as an image-derived input for [¹¹C]glyburide, which is a metabolically stable probe.

Concentrations of radioactivity expressed in kBq/mL were extracted. Measurements were then converted for pharmacokinetic modeling to concentrations in $\mathrm{\mu }$ g/mL using radioactivity expressed as concentrations ($C_{\text{radioactivity}}$ in kBq/mL), specific radioactivity (SRA; in kBq/$\mathrm{\mu }$ mol), and the molar mass of glyburide ($M_{\text{Gb}}$) is 494 $\mathrm{\mu }$ g/$\mathrm{\mu }$ mol.

$$C=\frac{C_{\text{radioactivity}}}{\text{SRA}}\times M_{\text{Gb}}$$ 1

The same conversion was used to convert the individually injected radioactivity to a dose in grams.

Pharmacokinetic Modeling of PET Data

Statistical Model

Supplementary Fig. S1 shows the total radioactivity, expressed in percentage of injected dose corrected by radioactive decay, as a function of time in the different organs. From these data, we decided to model only the organs in which most of the radioactivity was found to be concentrated. Brain, muscle, and eye tissue were not included in the dataset for modeling because the levels of radioactivity in these organs were negligible. Bladder and gallbladder presented very different profiles, with a marked accumulation with time and very high interindividual variability. As attempts to include them in the model were unsuccessful, we present the modeling performed for only the following five organs: blood, kidney, liver, spleen, as well as pancreas as the active site of action of glyburide.

We denote $y_{\text{ijko}}$ the ${\text{j}}^{\text{th}}$ concentration observed in subject i at time t_ijko in tissue k, where k denotes the tissue by its first letter, i.e., B(lood), L(iver), K(kidney), P(ancreas), and S(pleen), at occasion o (= 1 for [¹¹C]glyburide alone and 2 when [¹¹C]glyburide was administered after rifampicin infusion). To account for intervariability (IIV) across subjects (i = 1,..N) and interoccasion (IOV) variability over the two acquisition periods, we describe observed concentrations through the following non-linear mixed-effect model:

$$y_{\text{ijko}}=f_{\text{k}}(t_{\text{ijko}},{\psi }_{\text{io}})+g_{\text{k}}(t_{\text{ijko}},{\psi }_{\text{io}},{\sigma }_{\text{k}}){\epsilon }_{\text{ijko}}$$ 2

$${\psi }_{\text{io}}=H(\mu ,c_{\text{io}},{\eta }_{\text{i}},{\kappa }_{\text{io}},\beta )$$

$${\eta }_{\text{i}}\sim N(0,\mathrm{\Omega })$$

$${\kappa }_{\text{io}}\sim N(0,\mathrm{\Gamma })$$

$${\epsilon }_{\mathit{ijko}}\sim N(\text{0,1})$$

$f_{\text{k}}$ describes the structural model associated with tissue k, and g_k quantifies the variance of the residual error for this tissue, with ${\epsilon }_{\text{ijko}}$ a normally distributed random intervariable with a variance of 1. For each tissue, the error model was either a constant ($g_{\text{k}}=a_{\text{k}}$), proportional to the predicted concentration ($g_{\text{k}}=b_{\text{k}}{f}_{\text{k}}$) or a combined error model ($g_{\text{k}}=a_{\text{k}}+b_{\text{k}}{f}_{\text{k}}$). ${\sigma }_{\text{k}}$ will denote the vector of parameters of the error model, ${\sigma }_{\text{k}}=(a_{\text{k}},b_{\text{k}})$. We assumed that the vector ${\psi }_{\text{io}}$ of individual parameters was log-normally distributed by modeling it as the exponential of a linear combination of fixed effects $\mu$, covariate effects $\beta$ multiplying known individual covariates $c_{\text{io}}$, individual random effects ${\eta }_{\text{i}}$, and occasion-level random effects ${\kappa }_{\text{io}}$ (H = exponential in equation 2). We assumed multivariate normal distributions for ${\eta }_{\text{i}}$ and ${\kappa }_{\text{io}}$ with variance–covariance matrices $\mathrm{\Omega }$ and $\mathrm{\Gamma }$, respectively (${\eta }_{\text{i}}\sim N(0,\mathrm{\Omega })$, IIV, and ${\kappa }_{\text{io}}\sim N(0,\mathrm{\Gamma })$, IOV).

We introduce the covariate effect in the model. We investigated the effect of weight, age (known to affect liver and kidney function), sex (which can influence drug exposure through differences in enzyme activity and hormone levels), and rifampicin coadministration (which can affect hepatic transport). Covariates were introduced in the model as:

$${\psi }_{\text{i},\text{o}}={\psi }_{\text{pop}}+{\beta }_{\mathrm{\psi },\text{c}}\text{cov}\left({\text{c}}_{\text{i},\text{o}}\right)+{\eta }_{\text{i}}+{\kappa }_{\text{i},\text{o}}$$

$\text{with cov}\left(c_{\text{i},\text{o}}\right)=H^{-1}\left(c_{\text{i},\text{o}},)-H^{-1}(,c_{\text{pop}}\right)$ if the covariate is continuous and $\text{cov}\left(c_{\text{i},\text{o}}\right)=1_{{\{c}_{\text{i},\text{o}}=1\}}$ if the covariate is categorical. Here, ${\psi }_{\text{io}}$ is the vector of individual parameters of subject i for occasion o, $\left(c_{\text{i},\text{o}}\right)$ is the corresponding vector of covariates, ${\eta }_{\text{i}}\sim \mathcal{N}(0,\mathrm{\Omega })$ (respectively ${\kappa }_{\text{i},\text{o}}\sim \mathcal{N}(0,\mathrm{\Gamma })$) is the vector of random effect, which describes the interindividual variability (respectively intraindividual variability), and ${\beta }_{\psi ,c}$ is the effect of covariate c on parameter $\psi$.

For weight, ${\beta }_{\mathrm{\psi },\text{WT}}$ was fixed according to the allometric model to 1 for weight.

We denote $\theta =(\mu ,\mathrm{\Omega },\kappa ,\sigma )$ the population parameters of the model to estimate. Thereafter, we used the Stochastic Approximation Expectation-Maximization (SAEM) algorithm for parameter estimation [14]. Parameter uncertainty was estimated using the Fisher information matrix, computed using a first-order linearization of the model.

Model Building

Each tissue was represented by at least one compartment in equilibrium with the blood compartment. Some tissues could be represented by subcompartments, one compartment connected to the blood and others connected to this compartment.

In the first step, the structural model was built using the data collected after [¹¹C]glyburide was administered alone. Each tissue was first modeled separately. We used the log-likelihood ratio test (LRT) to determine the appropriate number of compartments and to obtain initial parameter estimates. For model building purposes, we excluded one woman who had a CC mutation on gene SLCO1B1, as she presented a markedly different kinetic profile with much higher blood concentrations and much lower liver concentrations. In addition, we considered the splenectomy that one man had undergone by considering this tissue was missing for this subject. A joint model was then fitted simultaneously including the data for all five tissues, with a combined error model for all tissues. For each tissue, we selected the number of compartments, testing linear and non-linear processes for distribution and elimination, and finally chose the residual error model by testing additive and proportional error models separately for each tissue. For the pancreas and spleen, which showed rapid distribution, we also tested a simple model with a linear relationship between the tissue and blood concentrations, representing a fast equilibrium. Indeed, if the rate $k_{\text{PB}}$ (respectively $k_{\text{SB}}$) is much smaller than $k_{\text{BP}}$ (respectively $k_{\text{BS}}$), we can model the pancreas (respectively spleen) concentration as a ratio of the blood concentration. For the liver and kidney, we also tested a two-compartment structure with a superficial compartment exchanging with blood and a deep compartment exchanging with the first (Fig. 2). The model corresponding to the best corrected Bayesian information criterion (BICc) was selected:

$${\text{BIC}}_{\text{C}}=-2{\text{LL}}_{\text{y}}(\widehat{\theta })+\text{dim}({\theta }_{\text{R}})\text{log}(N)+\text{dim}({\theta }_{\text{F}})\text{log}(n_{\text{tot}})$$ 3

where $\widehat{\theta }$ is the maximum likelihood estimate of $\theta$ that maximizes the log-likelihood function ${\text{LL}}_{\text{y}}(\theta )$, ${\theta }_{\text{R}}$ represents the variances of the random effects, ${\theta }_{\text{F}}$ represents the fixed effects, and $n_{\text{tot}}$ represents the total number of observations [15].

Fig. 2.

Diagram of the method. Each tissue is represented by a colored background and a letter that is used to index the volume of the corresponding compartment: blood (B, red), liver (L, yellow), kidneys (K, purple), pancreas (P, pink), and spleen (S, blue). Each block represents a modeling step. The text in gray represents the elements tested, while the text in bold black represents the elements included in the final model. B blood, L liver, K kidneys, S spleen, P pancreas, V volume, Cc concentration, k exchange rate between tissues, kₑ elimination rate, BW body weight, Rif rifampicin, COSSAC Conditional Sampling Use for Stepwise Approach Based on Correlation Tests, IIV interindividual variability, IOV interoccasion variability

We then tested the effect of body weight (BW) on the volumes of distribution using an allometric model. Allometric scaling was kept if the BICc did degrade by > 3 points.

In the second step, the model selected using [¹¹C]glyburide alone was applied to the full dataset, including both administrations. Interoccasion variability (IOV) was introduced on all parameters (transfer rate constants between tissues, and volumes of distribution). We performed an exploratory analysis of parameter–covariate relationships using the Conditional Sampling Use for Stepwise Approach Based on Correlation Tests (COSSAC) algorithm [16], considering as potential covariates rifampicin, age, gender, and combined age-gender groups. The COSSAC algorithm uses the correlation between conditional samples of individual parameters and covariates to include the most relevant parameter–covariate relationship iteratively. The covariate model can include continuous covariates (such as body weight or age) and categorical covariates (such as sex, group, or rifampicin effect). The model with IOV on all parameters proved unstable. We therefore used a stepwise bottom-up approach for covariate building, including the effect of rifampicin first. For this, we introduced IOV only on the parameters associated with the liver and kidney (transfer rate constants between blood and liver or kidney), adding a fixed effect corresponding to a systematic change in these parameters when coadministered with rifampicin. Those relationships were tested one by one, removing both the IOV and the fixed rifampicin effect on parameters when the relative standard error (RSE) on the fixed effect exceeded 100%. The IOV for the effects remaining in the model was then fixed to 0.01 to help parameter identification. At this stage, we refined the covariance structure: We removed interindividual variabilities if their relative standard error (RSE) exceeded 100%, and we tested for correlations between parameters.

In a final step, we tested each covariate highlighted by the exploratory COSSAC proposal one by one and kept the covariate if the BICc improved. The error models were also refined by testing proportional, combined, or additive error models for each compartment.

Model Evaluation

The final model was evaluated using graphical diagnostics: prediction-corrected visual predictive check (pcVPC) [17] and normalized prediction distribution errors (NPDE) [18]. The pcVPC compares empirical percentiles (observed data) with theoretical percentiles and prediction intervals computed using data simulated under the estimated model. In our case, we chose to compare the 10th, 50th, and 90th percentiles (80% confidence interval [CI]). The corrected predictions take into account the large variability in actual dose received, a variability built in the computation of the NPDE. The NPDE was plotted against time and against predicted concentrations and can be interpreted as residuals for non-linear mixed-effect models. The goal is to align the empirical percentiles with the theoretical percentiles.

Convergence assessment was performed at key steps in the analysis to calibrate the number of iterations and chains. We ran five models starting from different initial estimates (within 20% of the final estimates) and assessed the stability of parameter and likelihood estimates by visual diagnostics of the confidence intervals (CI).

In a sensitivity analysis, we applied the final model to the full dataset including the subject with a mutation on SLCO1B1.

Implementation

We used Python for data management and analysis, and Monolix-2023R1 for population parameter estimates. Algorithm settings included four chains, and the minimum number of iterations was 300. The maximum number of iterations was chosen for stability, starting with 500 iterations and increasing to 1000 if run assessments showed instability in parameter estimates.

Results

Modeling [11C]glyburide Alone

Figure 2 shows the different steps of the analysis. The first column shows the different models tested and retained (in bold) for each tissue, with a different color for each tissue. The final structural model, shown in Fig. 3, included six compartments. The liver and kidney required two compartments each, representing within-tissue exchanges, while the spleen and pancreas could be described using one compartment each. The differential equation system describing the whole system is given, where Q__k represents amount in tissue k and C__k the corresponding concentration, and I(t) represents a perfusion with an estimated duration Tk0:

$$\begin{array}{c}\frac{{\text{dA}}_{\text{B}}}{\text{dt}}=I(t)+k_{\text{L}1\text{B}}{A}_{\text{L}1}+k_{\text{K}1\text{B}}{A}_{\text{K}1}+k_{\text{SB}}{A}_{\text{S}}\\ -(k_{\text{BL}1}+k_{\text{BK}1}+k_{\text{BS}}+k_{\text{e}})A_{\text{B}}\\ \frac{{\text{dA}}_{\text{L}1}}{\text{dt}}=k_{\text{BL}1}{A}_{\text{B}}+k_{\text{L}2\text{L}1}{A}_{\text{L}2}-(k_{\text{L}1\text{B}}+k_{\text{L}1\text{L}2})A_{\text{L}1}\\ \frac{{\text{dA}}_{\text{L}2}}{\text{dt}}=k_{\text{L}1\text{L}2}{A}_{\text{L}1}-k_{\text{L}2\text{L}1}{A}_{\text{L}2}\\ \frac{{\text{dA}}_{\text{K}1}}{\text{dt}}=k_{\text{BK}1}{A}_{\text{B}}+k_{\text{K}2\text{K}1}{A}_{\text{K}2}-(k_{\text{K}1\text{B}}+k_{\text{K}1\text{K}2})A_{\text{K}1}\\ \frac{{\text{dA}}_{\text{K}2}}{\text{dt}}=k_{\text{K}1\text{K}2}{A}_{\text{K}1}-k_{\text{K}2\text{K}1}{A}_{\text{K}2}\\ \frac{{\text{dA}}_{\text{S}}}{\text{dt}}=k_{\text{BS}}{A}_{\text{B}}-k_{\text{SB}}{A}_{\text{S}}\\ \frac{{\text{dA}}_{\text{P}}}{\text{dt}}=k_{\text{BP}}{A}_{\text{B}}-k_{\text{PB}}{A}_{\text{P}}\end{array},and\begin{array}{c}{C}_{\text{B}}=\frac{A_{\text{B}}}{V_{\text{B}}}\\ C_{\text{L}}=\frac{A_{\text{L}1}+A_{\text{L}2}}{V_{\text{L}}}\\ C_{\text{K}}=\frac{A_{\text{K}1}+A_{\text{K}2}}{V_{\text{K}}}\\ C_{\text{S}}=\frac{A_{\text{S}}}{V_{\text{S}}}\\ C_{\text{P}}=\frac{A_{\text{P}}}{V_{\text{P}}}\end{array}$$ 5

Fig. 3.

Diagram of the structural model. Each tissue is represented by a colored background and a letter that is used to index the volume of the corresponding compartment: blood (B, red), liver (L, yellow), kidneys (K, purple), pancreas (P, pink), and spleen (S, blue). Exchanges between tissues are symbolized by arrows, called k_xy. where x denotes the origin and y the destination. For example, k_BL1 denotes the rate constant of transfer from blood to the first liver compartment. The kidneys and liver are divided into two subcompartments with total volumes V_K and V_L, respectively. The rifampicin effect is highlighted by the green star. Finally, k_e denotes the elimination rate. B blood, L liver, K kidneys, S spleen, P pancreas, V volume, k exchange rate between tissues, kₑ elimination rate, I(t) perfused amount, Tk0 estimated duration of the perfusion, $V_{\text{B}}$ estimated blood volume, $V_{\text{L}}$ estimated liver volume, $V_{\text{K}}$ estimated kidney volume, $V_{\text{S}}$ estimated spleen volume, $V_{\text{P}}$ estimated pancreas volume, $k_{\text{L}1\text{B}}$ exchange rate between liver and blood, $k_{\text{BL}1}$ exchange rate between blood and liver, $k_{\text{L}1\text{L}2}$ exchange rate between “liver 1” and “liver 2”, $k_{\text{L}2\text{L}1}$ exchange rate between “liver 2” and “liver 1”, $k_{\text{K}1\text{B}}$ exchange between kidneys and blood, $k_{\text{BK}1}$ exchange between blood and kidneys, $k_{\text{K}1\text{K}2}$ exchange between “kidney 1” and “kidney 2”, $k_{\text{K}2\text{K}1}$ exchange between “kidney 2” and “kidney 1”, $k_{\text{BS}}$ exchange between blood and spleen, $k_{\text{SB}}$ exchange between spleen and blood, $k_{\text{BP}}$ exchange between blood and pancreas, $k_{\text{PB}}$ exchange between pancreas and blood, ${\beta }_{\text{L}1{\text{B}}_{\text{Rif}}}$, rifampicin effect on the liver–blood exchange.

For the Liver and kidney, the proportional term in the residual error model was estimated close to 0, with a large RSE. However, removing it increased the BICc, so a combined error model was kept for all tissues for the following steps of the analysis. Using an allometric model for the effect of body weight on volumes resulted in a degraded BICc, both when applied to all tissues simultaneously and when applied to individual tissues; therefore, we did not include body weight in the model.

Modeling [¹¹C]glyburide

The model developed in the first step was then applied to the full dataset, adding IOV on all parameters. An exploratory analysis using the COSSAC algorithm suggested an effect of rifampicin on $V_{\text{B}},k_{\text{e}},k_{\text{L}1\text{B}},k_{\text{L}2\text{L}1},V_{\text{K}},k_{\text{K}1\text{K}2},{\text{and}k}_{\text{K}2\text{K}1}$; a group effect on $k_{\text{BL}1}$ and $V_{\text{K}}$; and an age effect on $V_{\text{S}}$ and $k_{\text{BP}}$, but including all these covariates in our model degraded the BICc at this stage, and the model was unstable, with large RSEs for some of the variability parameters.

We therefore reduced the number of parameters with IOV, considering only liver and kidney rate constants. The stepwise search selected an effect of rifampicin on the exchange rate between the liver and blood, $k_{\mathrm{L}1\mathrm{B}}$, with the efflux increased by 166% (RSE = 2%). The IOV for this parameter was subsequently fixed to 0.01, with no change in the BICc. At this stage, interindividual variability parameters were tested one by one, and column 6 in Fig. 2 shows the IIV remaining in the model.

We then tested one by one the relationships suggested by the exploratory COSSAC analysis performed previously, but none of them led to a better BICc. The final step in our analysis was to simplify the error model. The proportional term of the combined error model was very small, with a large RSE for the liver and kidneys. Although the BICc was higher, using a constant model for these tissues did not degrade the model in terms of parameter estimates, RSE, and graphical diagnostics.

We present the estimated parameters and their respective relative standard errors in Table 2. The value of $k_{\text{L}1\text{B}}$ increases on average from 20 h⁻¹ to 55 h⁻¹ in the presence of rifampicin. The spleen and pancreas show a rapid equilibration with the blood, as indicated by markedly asymmetric exchange rate constants. For the spleen, the rate of transfer from spleen to blood $(k_{\text{SB}}=131$ h⁻¹) greatly exceeds the reverse ($k_{\text{BS}}=5.9$ h⁻¹), and a similar pattern is observed for the pancreas, where $k_{\text{PB}}=138$ h⁻¹ is higher than $k_{\text{BP}}=5.9$ h⁻¹. In contrast, the liver and kidneys exhibit slower distribution kinetics, attributable to their representation by two-compartment models. The exchange ratios for these organs are more moderate, with $\frac{k_{\text{L}1\text{B}}}{k_{\text{BL}1}}=2.3$ for the liver and $\frac{k_{\text{K}1\text{B}}}{k_{\text{BK}1}}=2.9$ for the kidneys. Regarding the model parameters, in a compartmental model, k represents transfer between tissues, k_e elimination rate constants, and V volume parameter. The relation between clearance (CL), volume of distribution (V), and elimination rate constant (k_e) is given by: $\text{CL}=V_{\text{B}}\times k_{\text{e}}=2.84\text{L}/\text{h}$. The volume V is the theoretical volume that reflects how extensively a drug distributes into tissues. The estimated β value quantifies the effect of covariates (continuous or categorical) on the parameter, allowing us to adjust individual predictions.

Table 2.

Population parameter estimates

We used the same color code and letters as in Fig. 3. The first three columns show the parameter estimates for the fixed effects, with pop as the index for the population parameter and β for covariate effects. For example, $k_{L1B,pop}$ denotes the population value estimated for the transfer rate constant from the first liver compartment to blood, and its value in subject i at occasion o, $k_{L1B,i,o}$, was modeled as: $k_{L1B,i,o}=k_{L1B,pop}{e}^{{\beta }_{L1B,Rif}\times 1_{\{Ri{f}_o=1\}}}{e}^{{\eta }_i+{\kappa }_{i,o}}$. The next three columns show the estimated interindividual variability (IIV), expressed as the standard deviation of the corresponding random effect, if estimated. For small IIV, this is roughly equivalent to the coefficient of variation of the parameter. Only ${\gamma }_{k_{L1B}}$ had interoccasion variability in the final model, and the value of the IOV was fixed at 0.01. The final group of three columns shows the estimated error model terms for each organ, with a and b representing the additive and proportional terms, respectively. Each parameter is given along with the estimated relative standard error (RSE), expressed as percentage of the population estimate. Each IIV is given with the coefficient of variation (CV).

The run assessment showed unstable estimates for these parameters (Supplementary Fig. S3), varying three-fold for Vp (and eight-fold for Vs) over five successive runs with different starting values. A matching three-fold variation was found for k_bp, following Vp. The other parameters vary by less than two-fold (Supplementary Information). For these two compartments (pancreas and spleen), we estimated a 20-fold difference in the rate constants representing the distribution to and from the tissue (6 to 130), which suggests a very fast equilibrium.

We also tested an alternative model assuming instant equilibrium, through a ratio of tissue to blood concentrations, assuming that pancreas and spleen concentrations were proportional to blood concentrations, to reduce the number of parameters. This model showed a degradation of the pcVPC for blood and spleen on occasion 2. The results are presented in Supplementary Table S2. The BICc was also higher. Similarly, we tested different parameterizations to improve the large uncertainty on some parameters remaining in the model, expressing the two sub-compartments in the liver or kidney as fractions of the total volume, but this did not improve the estimates.

Finally, we also compared the results of the full model with those of a model including only the blood and liver compartment, finding very similar parameter and uncertainty estimates (Supplementary Figs. S4–6 and Supplementary Table S3). With only these two organs in the model, model stability was also improved, suggesting that the high uncertainty in the full model does not substantially affect the estimates of the parameters related to liver transport or to elimination.

Model Evaluation

Figure 4 shows the individual fits color-coded by tissue, with one column for each occasion. In the three rows, we show individual profiles. We randomly selected one subject in each group (first row: man > 50 years old; second row: woman > 50 years old; and third row: man < 30 years old). The pcVPC (Supplementary Fig. S2) evaluates the population model over all subjects. They demonstrate reasonably good fits for the typical profiles in the different tissues. Note that given the Limited number of subjects, the empirical percentiles for the 10th and 90th bounds of the prediction intervals correspond to the most extreme subject in each case and may therefore not be particularly representative of the variability in the general population. The size of the prediction intervals was large, particularly in the liver and pancreas, suggesting a larger sample would be necessary to better identify the IIV. For some tissues, notably the spleen and to a lesser extent blood, the model slightly underpredicted the median concentration, suggesting the effect of rifampicin is not fully captured. The observations versus individual prediction plots highlight the excellent predictive performance for liver concentrations and good performance for the other organs. NPDE profiles show some deviations, particularly in the NPDE versus population predictions plot.

Fig. 4.

Individual fits. We used the same color code as shown in Fig. 3. Each row corresponds to three randomly selected subjects (one from each group) to compare the real data (blue points) and the estimation (purple curve). Each column corresponds to a specific tissue on one occasion

We then re-estimated the parameters of this final model in a dataset including the subject with a mutation. The estimates are shown in Supplementary Table S1. The variabilities remained stable, and the pcVPC was not degraded, showing that the model could also fit this atypical subject. Although we could not include the genotype as a covariate for OATP transport given the small sample size, it would be interesting to investigate further given the frequency of this mutation in Caucasian and Asian populations.

Discussion

In this study, we developed a model to describe the WBPK of glyburide from the WB4D PET data of [¹¹C]glyburide obtained in a cohort of healthy volunteers. We analyzed the WBPK in the presence and absence of rifampicin, an inhibitor of liver transporters. Kinetic modeling of dynamic PET data is the state-of-the-art method to estimate the tissue distribution and specific binding of PET radioligands in one selected organ [19]. Repeated whole-body PET acquisition is routinely used to estimate the radiation dosimetry associated with innovative radiopharmaceuticals but is not designed to inform on the WBPK from a drug-development or pharmacology perspective [20]. The originality of this work was to validate a strategy and a kinetic modeling framework that makes the best use of WB4D PET data to predict the WBPK of a drug.

Glyburide was selected as a test drug to validate our approach because of (1) the availability of [¹¹C]glyburide in a cohort of different ages and sexes, (2) the acquisition of WB4D [¹¹C]glyburide PET data with high-frequency time-framing (2.5 min [7, 9]), (3) the limited contribution of [¹¹C]glyburide radiometabolites to the PET signal during PET acquisition, which ensures correct estimation of PK parameters [5], and (5) the availability of conventional clinical PK data to compare the outcome parameters with the gold-standard approach.

Rifampicin is a widely employed index inhibitor used to assess the impact of OATP1B inhibition on investigational drugs for drug–drug interaction (DDI) studies [21, 22]. A single dose of 600 mg rifampicin (~9 mg/kg for 70 kg), which corresponds to its pharmacological dose to treat tuberculosis, is expected to have minimal enzyme/transporter induction activity; thus, it is the preferred dosing regimen to safely achieve OATP1B inhibition. In a population similar to ours, Zheng and colleagues showed that an i.v. infusion of a 600mg dose of rifampicin, which is in the same range as in our study, significantly increased the plasma area under the curve (AUC) of orally administered glyburide by 125 ± 51.5% compared with the baseline situation [23]. The magnitude of the impact was much higher than the change observed in our study (+24 ± 24%, [6]), which may be explained by methodological differences. First, [¹¹C]glyburide was given i.v. at microdoses (12.5 ± 6.2 µg), while Zheng et al. administered glyburide orally at the pharmacological glucose-lowering dose of 1.25 mg. Above all, our PET data were obtained only 30 min after injection, thus predominantly reflecting the distribution phase, while the plasma PK study reported by Zheng et al. was carried out over 24 h, mainly reflecting the elimination phase. This suggests that early PET data may underestimate the overall impact of transporter-mediated DDI on drug elimination, especially when hepatic elimination is involved. Hence, microdose PK PET data provide an insight into clinical WBPK but should be interpreted in the light of known plasma PK.

In addition to the blood where glyburide circulates, our model describes the distribution of glyburide in five tissues. The high PET signal of [¹¹C]glyburide in the vasculature is probably due to its strong binding to plasma protein (> 99%, [7]). The liver and kidneys were selected as the organ involved in the elimination, and the pancreas was included as the site of action where glyburide affects insulin production [24], although regulation of glucose metabolism by glyburide in the liver has been suggested [25]. The spleen, which showed significant glyburide accumulation was also included in the model. We chose to ignore the other tissues owing to their limited contribution to the total radioactivity, suggesting limited impact on WBPK. We did consider adding a hypothetical rest compartment representing the sum of all other radioactivity. However, the exchange constants between the blood compartment and the dummy compartment were very small, even negligible. Moreover, adding this dummy compartment severely degraded the BICc.

In our model, we did not manage to include two organs where a significant amount of radioactivity collected during the study. Concentrations in the bladder presented an unusual profile, with a first peak followed by a dip and subsequent rapid increase, which could be an artefact due to the measurement of the VOI at the end of the study while the bladder increases in volume over time. The individual profiles in the gallbladder showed extreme variability, with some patients remaining almost flat but most of the patients increasing to very high levels at times ranging from 10 min to 40 min. From the modeling point of view, both organs represent a sink for glyburide elimination from the rest of the system, as the gallbladder would be expected not to empty during the acquisition. A perspective of this work would be to integrate these two organs with a more complex structure taking into account the link between the liver and gallbladder and kidney and bladder, as well as metabolism, which could help to strengthen the estimation of k_e.

Model selection was performed sequentially, starting with an initial step for each organ considered independently. This was necessary to determine starting values for the parameters when estimating the full model. Indeed, the small number of subjects made it difficult to identify all the parameters in the model despite the very rich dynamic resolution (high-frequency time-framing) compared with classical PK or preclinical biodistribution studies. Moreover, run assessments showed high instability in some parameters, even in the final model. Part of the complexity lay in the large number of parameters and associated variabilities, which could not all be estimated from the limited number of subjects in the study.

In the liver, glyburide is predominantly taken up into the hepatocytes across the sinusoidal membrane via active OATP-mediated uptake [26]. From a physiological perspective, assuming limited passive diffusion of glyburide from blood to the liver, the “liver 1” compartment may reflect the OATP-mediated accumulation of [¹¹C]glyburide in hepatocytes, whereas “liver 2” may reflect the concentration of [¹¹C]glyburide radiometabolites that are further eliminated in bile ducts, as suggested by Li and colleagues [27]. Therefore, the PET signal in the bile could consist in radiometabolites rather than parent [¹¹C]glyburide. Furthermore, we can assume limited enterohepatic circulation of radiometabolites within the short timeframe of PET acquisition (40 min) and consider the gallbladder as a sink for this study, and, while taking it into account might improve the estimation of k_e, the large interindividual variability and the sharp and variable increase in some subjects made its integration complicated. Importantly, the PET signal represents total radioactivity and does not differentiate between parent glyburide and radiolabeled metabolites. Consequently, it remains unclear whether the observed accumulation corresponds to the unchanged drug or to one or more metabolites. This distinction is critical for accurately assessing the contribution of the gallbladder to the active elimination of glyburide and for interpreting its pharmacokinetic relevance.

At the kidney level, glyburide is mainly eliminated as metabolites [27], which was confirmed with [¹¹C]glyburide in humans [8]. The “kidney 1” compartment may reflect the interstitial space, and “kidney 2” may represent the intracellular uptake of radiometabolites that are then eliminated in the urine, which again act as a sink compartment in our model. Of note, the renal elimination of glyburide metabolites is mediated by transporters other than OATP that are not inhibited by rifampicin [27].

We can compare our findings with those from a traditional compartmental PK modeling of glyburide based on blood samples [28]. In their study, Savic et al. estimated a central volume of distribution of 3.8 L, very close to our estimate of 3.6 L. As we used non-linear mixed-effect models (NLMEM) approaches, we interpret the volume in classical PK modeling, representing the volume in which the drug distributes. With this approach, we can estimate PK volumes for the different organs in which glyburide distributes. Interestingly, summing the volumes of distribution estimated here for all organs but blood, we find a total volume of distribution of 3.3 L, which is in the same ballpark although slightly higher than previous estimates (2 L, 95% CI derived from the estimates reported in the paper: 1.3–3.2 L)[28]. Savic et al. also estimated a slightly higher elimination rate (1.1 h⁻¹) than the value of 0.79 h⁻¹ that we estimate here. Similarly, Rydberg et al. estimated the elimination rate at 1.59 h⁻¹, and the central volume of distribution was estimated to be 3.63 L [29]

From the individual profiles in the liver where glyburide is metabolized (Fig. 4), we can see that the concentrations in the Liver have not really started to decline at the end of the 40-min acquisition period, making it more difficult to estimate the final elimination rate. Although this parameter is reported with a good precision (15%, Table 2), run assessments show variations around 30% from run to run with different starting values, underscoring that caution is needed when extrapolating from a short acquisition time. However, the estimate is very close to the value obtained by Savic et al. [28] in a traditional PK study using a pharmacological dose, which is promising. A contributing factor to the underestimation of elimination could also be that in our model, we assumed total radioactivity was entirely attributable to the parent drug PET. For glyburide, blood sampling performed in the subjects during the study showed that the proportion of radiometabolites was < 10% by the end of PET acquisition [7], supporting this approximation. Using longer acquisitions would require taking into account a significant proportion of circulating radiometabolites for kinetic modeling. However, correct determination of the parent fraction of carbon-11 radioligands in late samples is difficult due to the radioactive decay of this isotope (half-life = 20.4 min).

Model instability also manifested during the search for covariates. We attempted to use the COSSAC algorithm built in the Monolix software for automated covariate model building [16], which suggested a rifampicin effect on the parameters governing the distribution to and from the kidneys. However, this covariate effect when entered in the model led to worse performance, with unstable estimated parameters and a degradation of the BICc. We used BICc for model selection and, for consistency, we applied the same criterion to the covariate modeling step, as suggested by Delattre et al. [15]. The Conditional Sampling Use for Stepwise Approach Based on Correlation Tests (COSSAC) algorithm relies on samples from the conditional distribution of the individual parameters, a by-product of the SAEM algorithm refined after the final model fit and on iterative model evaluations and selection via the log-likelihood ratio test. Although COSSAC was found to perform well in a number of cases including a small number of subjects [16], it was not tested in such a complex model as the one we have here. Despite some covariates being picked up during the COSSAC runs, the final model only included an effect of rifampicin on the rate constant governing the distribution from the first liver compartment back to blood. In particular, we did not keep a gender effect on the parameters for the liver, and as a result our model was unable to reproduce the difference in liver AUC that was detected in the same data by non-compartment modeling by Marie et al. [9]. The final model does show a significant reduction in hepatic radioactivity following OATP inhibition, suggesting altered liver distribution, a finding consistent with previous non-compartmental analyses [7]. However, the estimate parameters ($k_{\text{BL}1}$ = 9, $k_{\text{L}1\text{B}}$ = 21 without rifampicin and $k_{\text{L}1\text{B}}$ = 55 with rifampicin) do not fully capture OATP transport activity. Nevertheless, the ratio $\frac{k_{\text{BL}1}}{k_{\text{L}1\text{B}}}$ decreases from 0.43 to 0.16 in the presence of rifampicin, an expected reduction consistent with OATP inhibition. The allometry model increased the BICc, so weight was not included in the model either.

Finally, the rich temporal resolution allowed us to estimate transfer rate constants with very different magnitudes, as for example in the pancreas, where there was a 20-fold difference in the estimates of the transfer rates to and from blood. This suggests a very rapid equilibrium between blood and pancreas concentrations, which could explain the model’s identifiability issue, which is apparent from the estimation errors that could not be estimated for the corresponding volume of distribution. However, an alternative model in which we used a ratio to represent the fast equilibrium had a worse BICc and perturbed the estimation of V_b.

This study was a first attempt at modeling PET data obtained from microdose studies, and, as such, our objective was to apply compartmental models without using additional information such as previous parameter estimates from the literature. This raised a number of issues, as shown in our results, in particular with regard to parameter identifiability and uncertainty, which could indeed be addressed in future studies by combining different types of data. Given the limits of our analysis, a perspective would be to combine non-linear mixed-effect models with PBPK modeling. PBPK models have been developed in the software SimCyp [30, 31] using the standard distribution, metabolism, and elimination processes applied to the characteristics of glyburide. A first perspective of this work could then be to examine whether the predictions obtained by these models match the time course of PET data in the different organs. However, the parameters used to define the building blocks in a PBPK model are derived from various sources ranging from in vitro experiments to preclinical animal models providing tissue samples. Moreover, dynamic data are rarely available, as tissue samples in particular are obtained by preclinical ex vivo determination of drugs and metabolites in tissues. A more interesting perspective would therefore be to combine the underlying structure and physicochemical parameters built in the PBPK model and the dynamic PET data [32] to estimate select individual parameters and quantify interindividual variability. This would be more representative of organ structure, which we approached here in the liver by considering two compartments within that organ in a more physiological manner. Currently, however, the estimation methods implemented in mainstream PBPK software such as SimCyp [33] or PKSim [34] are limited to individual regression and do not allow the sharing of information across subjects that mixed-effect models provide, although work coupling PBPK software and mixed-effect modeling is ongoing [35]. We could consider including physiological elements such as hepatic transport processes or liver structure, similar to PBPK approaches (e.g., nonlinear exchange processes and parameters from the literature). This would lead to a hybrid model combining a simplified structure for the whole body with a more physiologically detailed liver submodel (or a simplified liver model including transporter dynamics) to improve parameter estimation and stability. In addition, a simpler model accounting only for blood and Liver compartments yielded similar parameter estimates without the estimation and stability issues we encountered using the full model. Building Limited scope models using the organs of interest could therefore be an interesting approach to leverage phase 0 PET data to predict elimination and anticipate liver toxicity using probes for drug–drug interactions such as rifampicin.

This approach also opens perspectives for the broader use of PET microdosing studies to predict pharmacokinetics and inform first-in-human study design. Beyond characterizing biodistribution, PET with radiolabeled microdoses can be used to explore potential drug–drug interactions by assessing the impact of coadministered compounds, including known inhibitors or inducers, on the tissue distribution of the drug. This enables early identification of interaction risks without exposing subjects to pharmacologically active doses. In addition, the non-invasive and longitudinal nature of PET imaging reduces reliance on animal models, which often require terminal procedures and preclude repeated measurements in the same subject.

However, some limitations must be considered. Not all compounds can be readily radiolabeled, and differences in pharmacokinetics between micro and therapeutic doses, particularly due to non-linear processes such as transporter saturation, may limit direct extrapolation. One approach to tackle these challenges would be to integrate PET data into hybrid models, including physiologically based pharmacokinetic models, to bridge microdose findings with therapeutic scenarios and improve the predictive power of early clinical studies.

In conclusion, PET studies represent a fascinating opportunity to safely and dynamically follow the kinetics of radiolabeled drugs in the entire body. They can also be used in animals with the potential to improve preclinical studies by drastically reducing the number of animals needed. A novelty of our study was to model via compartmental approaches the whole-body data obtained through PET imaging, which provides a higher frequency of samples compared with traditional pharmacokinetics, as well as access to drug distribution within tissue compartments. This increased temporal resolution provides a more detailed and dynamic picture of the drug’s behavior within the human body. The modeling however presented several challenges, including selecting appropriate organs and constructing a robust model accounting for metabolic processes. Logistic challenges include on-site production of [¹¹C]glyburide, as the radiolabeled drug decays quickly, good coordination with PET imaging, and manageable duration of the acquisition for the volunteers. Despite these issues, PET data offer an opportunity to estimate PK parameters early in drug development, thereby guiding the subsequent construction of PK/PD models.

Supplementary Information

Below is the link to the electronic supplementary material.

Author Contributions

N.T., E.C., and S.Z. initiated the project. S.M. and N.T. participated in the data acquisition. E.C. and L.C. performed the PK data analysis and constructed the model. L.C., E.C., and N.T. drafted the manuscript. All authors performed a critical review of the manuscript draft and approved the final version of the manuscript.

Funding

Open access funding provided by Université Paris-Saclay. This study was supported by a grant from Inserm and the French Ministry of Health (MESSIDORE 2022, ref. no. Inserm-MESSIDORE N° 94).

Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code Availability

Not applicable.

Declarations

Conflict of Interest

Léa Comin, Solène Marie, Moreno Ursino, Sarah Zohar, Nicolas Tournier, and Emmanuelle Comets have no conflicts of interest that are directly relevant to the content of this article.

Ethics Approval

The study protocol was approved by an ethics committee (CPP IDF5: 17041, study reg. no. EudraCT 2017-001703-69).

Consent to Participate

Written informed consent was obtained from all participants.

Consent for Publication

Not applicable.