Predicting Drug Transfer Into Human Milk With the Simcyp Simulator: A Contribution From the ConcePTION Project

ABSTRACT

Physiologically‐based pharmacokinetic (PBPK) modeling can support decision‐making on maternal medication use during breastfeeding. This study aimed to enhance lactation PBPK models in two ways. First, the utility of integrating permeability‐ versus perfusion‐limited distribution to human milk was explored using the Simcyp Simulator. Secondly, for permeability‐limited models, drug‐specific bidirectional intrinsic clearance across the blood‐milk barrier, predicted from drug physicochemical properties, was incorporated into lactation PBPK models. Initially, reference PBPK models were developed and verified against published clinical data. Geometric Mean Fold Error (GMFE; ~accuracy) and Average Fold Error (AFE; ~bias) for these models ranged from 1.13–1.51 and 0.68–1.42, respectively. These verified models were then extended to lactation PBPK models applying either permeability‐ or perfusion‐limited assumptions for drug distribution across the blood‐milk barrier. The lactation PBPK models were applied to predict drug concentrations in human milk and relative infant doses (RID) for 11 small molecule drugs with diverse physicochemical and disposition profiles. The models successfully predicted observed plasma PK, human milk concentration‐time profiles, and milk‐to‐plasma ratios. Nine drugs had RID values below the safety threshold of 25%, while levetiracetam and nevirapine showed relatively higher RIDs (up to 21%). Based on these findings, a decision tree is proposed to guide the selection between permeability‐ or perfusion‐limited distribution models in future lactation PBPK applications using Simcyp. This workflow can be extended beyond the 11 model drugs evaluated, supporting broader infant risk assessment for maternal medication during lactation.

Summary.

• What is the current knowledge on the topic?

  • ○
    Physiologicallybased pharmacokinetic (PBPK) models enable simulation of drug secretion in human milk followed by estimation of daily infant dosage, thus informing infant risk assessment in cases of maternal medication.
• What question did this study address?

  • ○
    Can the predictive performance of lactation PBPK models be enhanced within the Simcyp simulator by integrating mechanistic models of the blood‐milk barrier, such as perfusion‐ and permeability‐limited models, along with bidirectional barrier clearance prediction algorithms based on drug physicochemical properties ?
• What does this study add to our knowledge?

  • ○
    Considering mechanistic models for the blood‐milk barrier, along with a drug‐specific physiochemistry‐based model for the permeability of this barrier, enhances the predictive performance of lactation PBPK models and enables estimating the amount of drug secreted in human milk. This is the first time that the Simcyp Simulator has been used to develop lactation PBPK models for 11 drugs by integrating a semi‐mechanistic concept of the blood‐milk barrier.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    Applying the developed workflow for lactation PBPK model‐based simulations to other drugs, as well as to xenobiotics and drug candidates, will benefit infant safety during breastfeeding and support future drug development programs.

1. Introduction

According to Wang et al., less than 5% of approved drugs include human lactation‐related data in their labeling [1]. This lack of information presents a significant challenge for breastfeeding women, who often weigh the need for therapeutic treatment against the well‐established maternal and infant health benefits of continued breastfeeding. Therefore, generating information regarding the use and safety of drugs throughout postpartum is relevant for the development and labeling of drugs used in this population.

With the aim to generate information on drugs used during pregnancy and breastfeeding, the Innovative Medicines Initiative (IMI) project ConcePTION was launched in 2019. Work Package 3 (WP3) of ConcePTION aimed to generate a non‐clinical testing platform to determine drug transfer into human milk and subsequent infant exposure. While this platform relies on non‐clinical and computational methodologies (i.e., in vivo animal, in vitro, and in silico), the predicted outcomes are of clinical relevance (e.g., concentration‐time profiles of drugs in maternal blood and human milk).

Physiologically‐based pharmacokinetic (PBPK) modeling and simulation represent a quantitative and mechanistic approach that relies on the physicochemical properties of a xenobiotic (i.e., marketed drug or drug candidate) along with its absorption, distribution, metabolism, and excretion (ADME) profile. This compound‐specific information is combined with system‐specific data and clinical trial design. By integrating these data, PBPK modeling and simulation generate concentration‐time profiles in plasma or human milk, enabling simulation of various (patho)physiological conditions and accounting for physiological and developmental changes.

In a previous publication from our research group [2], a generic lactation PBPK modeling and simulation framework was developed in PK‐Sim to predict drug concentration‐time profiles for 10 medicines in human milk at 3 months postpartum. This framework parameterized drug transfer between plasma and milk with drug‐specific bidirectional clearance values across the blood‐milk barrier according to the semi‐mechanistic model developed by Koshimichi and collaborators [3]. This also involved estimating the drug‐specific clearance values across the blood‐milk barrier based on a Quantitative Structure–Property Relationship (QSPR) model that predicted the M/P ratio based on lipophilicity, polar surface area, and molecular weight. The models developed in our previous work accurately captured the drug concentrations in human milk for 8 out of 10 selected drugs, also allowing the estimation of daily infant dosage (DID) and relative infant dose (RID).

The aim of the present study was to further explore lactation PBPK model performance with the more recently launched Simcyp Simulator for 11 small molecule drugs with diverse physicochemical properties (including the same 10 drugs previously simulated in PK‐Sim, with addition of sildenafil as the 11 compound). The outcome of this study resulted in an optimized workflow for lactation PBPK model development. In addition, a decision tree was proposed to decide using either a perfusion‐limited or permeability‐limited model for drug milk distribution. Those distribution models relied on either the log‐transformed phase distribution model by Atkinson and Begg [4] or the semi‐mechanistic concept by Koshimichi et al. [3].

2. Methods

2.1. Selected Model Drugs

Eleven physico‐chemically diverse small molecules, exhibiting various elimination pathways and with available lactation data, were selected for this study. Additionally, these model drugs were chosen based on their clinical relevance and common use for pharmacotherapy in lactating women [2]: amoxicillin (AMX), levetiracetam (LEV), caffeine (CAF), zidovudine (ZDV), metformin (MET), cetirizine (CET), tenofovir (TNF), valproic acid (VPA), sertraline (SER), nevirapine (NVP), and sildenafil (SIL). Physicochemical properties of these model drugs are summarized in Tables S1 and S2.

2.2. PBPK Modeling Strategy

As described in Figure 1, PBPK models were developed for each model drug (or reproduced from literature with modifications) for healthy volunteers and verified against published clinical data. All model building was conducted with the Simcyp Population‐based Simulator (Version 21, Certara, L.P., Sheffield, UK). In a subsequent phase, lactation PBPK models were established using the Simcyp built‐in lactation module (v21) and verified against available published data. Upon successful model verification, the predicted average concentrations in human milk were used to estimate the DID and, subsequently, the RID.

FIGURE 1.

General workflow of PBPK model development in adult healthy volunteers (or patients) and in lactating women. The training dataset, containing studies after single intravenous (iv) or oral administration, was used to develop the adult healthy volunteers (reference) PBPK models. At this stage, if necessary, parameter estimation was performed to fit the observed data. A second (i.e., verifying) dataset was used to assess the performance of each compound‐specific PBPK model. The verifying dataset contained multiple studies after single or multiple iv and oral administrations. After successful model verification, PBPK models were applied to breastfeeding women to establish corresponding lactation PBPK models, enabling prediction of drug concentration in human milk as well as estimating the daily infant dosage received via human milk.

2.3. Adult Healthy Volunteer PBPK Model

The initial PBPK models were built based on available clinical studies in adults, which could include either healthy volunteers or patients without diseases that affect PK. Within the Simcyp Simulator, the virtual population used was the Simcyp Healthy Volunteer (Sim‐Healthy Volunteers, HV) population for all simulations in healthy subjects. Virtual populations were selected to closely match the enrolled individuals in the respective clinical trials when details on participants characteristics were available, such as dosing regimen, route of administration, gender ratio, and age range. In the absence of information on these parameters, the default age range of 20–50 years and a female proportion of 0.5 were used (See Supporting Information for drug‐specific reports).

2.4. Predictive Performance of the Adult Healthy Volunteer PBPK Model

The predictive performance of the developed adult PBPK models was evaluated by comparing the predicted PK parameters and plasma concentration‐time profiles against the available clinical observations of each drug reported in the literature (More information can be found in the Supporting Information as drug‐specific reports). All systemic PK data were based on plasma concentrations. For PK predictions, the maximal plasma concentration (C _max) and the area under the curve (AUC) ratios were expressed as the geometric mean (GM) and percent coefficient of variation (CV%) of GM. The PBPK model was deemed adequate when the main descriptive PK parameters (i.e., C _max and AUC) were predicted within a two‐fold range [5] compared to observed clinical data, as outlined by the European Medicines Agency in 2018 and Food and Drug Administration in 2020 [6, 7]. The average fold error (AFE; overall bias) and the geometric mean fold error (GMFE; average accuracy) values were calculated using the GM C_max or AUC ratios from all studies for all tested drugs [8, 9, 10] (Equations 1 and 2, respectively).

$$\mathrm{AFE}={10}^{\frac{\sum {\log }_{10}\left(\frac{\text{pred}\mathrm{PK}\text{parameter}}{\mathrm{obs}\mathrm{PK}\text{parameter}}\right)}{n}}$$ (1)

$$\text{GMFE}={10}^{\frac{\sum \left|{\mathit{log}}_{10}\left(\frac{\text{pred}\mathrm{PK}\text{parameter}}{\mathrm{obs}\mathrm{PK}\text{parameter}}\right)\right|}{n}}$$ (2)

2.5. Lactation PBPK Model

The built‐in lactation module from Simcyp (v21) was selected to establish the lactation PBPK models for each drug‐specific model. This lactation module provides two human milk distribution models: permeability‐ and perfusion‐limited models. Data on milk properties and physiology (i.e., milk volume, pH, Creamatocrit) were collected and used to specify parameters in the Simcyp lactation module [11].

2.6. Perfusion‐ Versus Permeability‐Limited Models of the Blood‐Milk Barrier

The built‐in Simcyp lactation module requires selecting either the permeability—or perfusion‐limited model for drug distribution into human milk. Of note, only the perfusion‐limited model option is available when a minimal PBPK model is constructed in Simcyp version 21. To allow incorporation of uptake and efflux transporter kinetics as part of a permeability‐limited model, a full PBPK modeling approach must be selected. Considering the impact of the blood‐milk barrier model selection, a decision tree was developed to guide the choice between perfusion‐ and permeability‐limited models (Figure 2). More information can be found in the Supporting Information.

FIGURE 2.

Decision tree for the development of the lactation PBPK model within the Simcyp simulator (version 21). PBPK, physiologically‐ based pharmacokinetic; m‐PBPK, minimal physiologically based‐ pharmacokinetic model; CL_int, intrinsic clearance, determined by: (i) back‐calculating with the Well‐Stirred Model from in vivo Clearance values as predicted with the QSPR models of Koshimichi et al. [3] or (ii) the In vitro permeability as determined across mammary epithelial cells in vitro model; Papp, apparent permeability coefficient; SA, total surface area of mammary glands; Q, breast blood flow of 9.09 L/h (Simcyp V21).

Once the human milk distribution model was selected, to ensure a standardized approach and for feasibility reasons, lactation PBPK models were developed and evaluated for subjects at 3 months postpartum. This approach was taken because many physiological parameters are expected to be back to pre‐pregnancy levels at 3 months postpartum. In this way, we mitigated the practical challenges in obtaining consistent and reliable physiological data in earlier postpartum. A virtual population was created with female subjects between 30 and 30.3 years old, i.e., 3 months postpartum (geometric mean bodyweight of 65.78 kg). Simulations were performed for 10 trials with 10 individuals each, assuming a milk volume of 0.5 L (coefficient of variation of 33%) and a milk pH of 7.2 (as reported by Koshimichi et al. [3]). For each simulation, the administration protocol was adapted to the clinical study design as reported. See Supporting Information for drug‐specific reports.

The performance of the lactation PBPK models was evaluated by visual inspection of the predicted geometric mean for plasma and median for milk concentration over time profiles against clinical data available in the literature.

2.7. Infant Dose Estimation

PBPK simulations at steady state were carried out to predict DID, at the therapeutic dosing regimen for each drug. The dose received via human breast milk to the infant (i.e., DID, mL/kg/day) was calculated based on the predicted average concentration in human milk (C _{average, milk} as described in Equation 3), and the volume of infant daily milk intake, as described in Equation (4). For safety risk assessment purposes, two scenarios were considered: (i) a daily milk intake of 150 mL/kg/day and (ii) an assumed daily milk intake of 200 mL/kg/day [12]. Subsequently, the DID was compared with the maternal dosage to evaluate the RID, %, as described in Equation (5).

$$C_{\text{average},\text{milk}}=\frac{{\mathrm{AUC}}_{\text{milk}}}{\tau }$$ (3)

$$\begin{array}{c}\text{Daily infant dosage}\left(\mathrm{mg}/\mathrm{kg}/\mathrm{day}\right)=C_{\text{average},\text{milk}}\hfill \\ \times \text{volume of daily milk intake}\hfill \end{array}$$ (4)

$$\begin{array}{c}\text{Relative infant dose}\left(\mathrm{RID},\%\right)\hfill \\ =\frac{\text{Daily infant dosage}\left(\mathrm{mg}/\mathrm{kg}/\mathrm{day}\right)}{\text{Maternal dosage}\left(\mathrm{mg}/\mathrm{kg}/\mathrm{day}\right)}\times 100\hfill \end{array}$$ (5)

where AUC area under the curve, $\tau$ is dosing interval. The maternal dosage was adjusted according to the maternal weight of a virtual lactating population aged between 30 and 30.3 years old, with a mean weight of 65.78 kg (Simcyp v21).

Additionally, to assess drug intake during the breastfeeding period, a comparison between the estimated DID and the daily therapeutic dosage of the drug in infants, when available, was applied for risk assessment by calculating the relative therapeutic infant dose (RID_therapeutic, %), according to Equation (6).

$$\begin{array}{c}\text{Relative therapeutic infant dose}\left(\mathrm{RID},\text{therapeutic},\%\right)\hfill \\ =\frac{\text{Daily infant dosage}\left(\mathrm{mg}/\mathrm{kg}/\mathrm{day}\right)}{\text{Daily therapeutic infant dosage}\left(\mathrm{mg}/\mathrm{kg}/\mathrm{day}\right)}\times 100\hfill \end{array}$$ (6)

3. Results

3.1. Adult Healthy Volunteer (Reference) PBPK Models

PBPK models were developed, reproduced, or adapted from literature for 11 model drugs in adult healthy volunteers [13, 14, 15, 16, 17, 18] and verified against in vivo published data. These PBPK models were able to adequately capture the plasma concentration‐time profiles as well as the descriptive PK parameters (i.e., C _max and AUC) in adult healthy volunteers after oral, intravenous, and single/multiple dose administration at different dose levels. The predicted C _max and AUC were within 1.5‐fold for cetirizine, valproic acid, tenofovir, nevirapine, and sildenafil, and within twofold for levetiracetam, caffeine, amoxicillin, sertraline, and metformin when compared to the observed clinical data used for both model development and evaluation (Figure 3). The accuracy (GMFE) and bias (AFE) of predictions are summarized in Table 1 for all compounds. The GMFE and AFE values ranged from 1.13–1.51 and 1.08–1.43 for AUC, and from 0.68–1.42 and 0.85–1.31 for C _max, respectively (Table 1). More information about the model development and evaluation of the individual PBPK models can be found in the drug‐specific reports (See Supporting Information). This confirms that the PBPK models are verified and can be used to establish the lactation PBPK models.

FIGURE 3.

Predictive performance plots of the PBPK models comparing predicted and observed AUC (A) and C _max (B) in healthy adults at different dose levels. Symbols represent the clinical data used for model development and model validation. The solid bold line represents the line of unity, while the dashed lines and solid lines represent the 2.0‐ and 1.5‐fold deviation from unity, respectively.

TABLE 1.

GMFE and AFE values for prediction of AUC and C _max of model drugs in adult healthy volunteers (reference population).

Drug (number of clinical studies used for model development and verification)	GMFE		AFE
	AUC	C max	AUC	C max
Amoxicillin (12)	1.26	1.36	1.01	0.85
Levetiracetam (11)	1.41	1.08	1.41	1.02
Caffeine (10)	1.25	1.13	0.93	0.94
Zidovudine (6)	1.42	1.21	1.08	0.88
Metformin (22)	1.51	1.40	1.42	1.31
Cetirizine (7)	1.13	1.10	1.07	1.00
Tenofovir (6)	1.49	1.15	0.68	0.87
Valproic acid (25)	1.23	1.15	1.00	0.93
Sertraline (23)	1.48	1.43	1.19	1.18
Nevirapine (13)	1.13	1.16	0.96	1.07
Sildenafil (7)	1.38	1.08	0.79	0.97

Abbreviations: AFE, average fold error; AUC, area under the curve; C _max, maximal plasma concentration; GMFE, geometric mean fold error.

3.2. Lactation PBPK Models

The lactation PBPK models established either using perfusion‐ or permeability‐limited models were in agreement with the predicted plasma or human milk concentration profiles when these were overlaid with the available in vivo clinical data (Figures 4, 5, 6, 7).

FIGURE 4.

Comparison of observed and predicted milk‐to‐plasma ratio values for selected drugs. Blue symbols represent the predicted milk‐to‐plasma ratio values for amoxicillin, levetiracetam, caffeine, zidovudine, metformin, cetirizine, and tenofovir based on the ratio of AUC_milk over AUC_plasma (using the permeability‐limited model). Red symbols represent the calculated milk‐to‐plasma ratio values for valproic acid, sertraline, nevirapine, and sildenafil using the log transformed phase‐distribution model by Atkinson and Begg (using the perfusion‐limited model). Solid bold line represents the line of unity. Dotted and dashed lines represent 1.5‐ and 2‐fold deviations from unity, respectively.

FIGURE 5.

Predicted and observed plasma (left) and milk (right) concentration time profiles of (A) Amoxicillin (B) Levetiracetam (C) Caffeine and (D) Zidovudine. The red solid line represents the geometric mean predicted plasma concentration profile, and the blue line represents the arithmetic mean predicted milk concentration profile. Dashed lines represent the 5^th and 95^th percentile of arithmetic mean predictions. Symbols represent observed data after (A) a single oral dose of 1000 mg [19] (B) multiple oral administrations of 1500 mg twice a day [20] (C), single oral dose of 64 mg [21], (D) multiple oral administrations of 300 mg twice a day [22].

FIGURE 6.

Predicted and observed plasma (left) and milk (right) concentration time profiles of (A) Metformin (B, C) Cetirizine and (D) Tenofovir. The red solid line represents the geometric mean predicted plasma concentration profile, and the blue line represents the arithmetic mean predicted milk concentration profile. Dashed lines represent the 5^th and 95^th percentiles of predictions. Symbols represent observed data after (A) multiple oral doses of 500 mg twice a day [23] (B) oral administration of 10 mg [24] (C) oral administration of 10 mg [25] (D) multiple oral administrations of 300 mg twice a day [26, 27, 28, 29, 30].

FIGURE 7.

Predicted and observed plasma (left) and milk (right) concentration time profiles of (A) valproic acid, (B) sertraline, (C) nevirapine, (D) and Sildenafil. The red solid lines represent the geometric mean predicted plasma concentration profile and the blue lines represent the arithmetic mean predicted milk concentration profile. Dashed lines represent the 5^th and 95^th percentile of predictions. Symbols represent observed data after (A) multiple oral dose of 2100 mg once a day [31], (B) multiple oral administration of 100 mg once a day [32], (C) multiple oral doses of 200 mg twice a day [22], (D) and multiple oral administration of 20 mg twice a day [33].

For four drugs (i.e., cetirizine, nevirapine, sertraline, and sildenafil), the intrinsic clearance values were higher or equal to 80% when compared to the breast blood flow of 9.09 L/h, indicating a perfusion‐limited flow‐limited process. Additionally, using a “classical” cut‐off value of 0.7 instead of 0.8 resulted in the same model classification, indicating that the choice of threshold did not affect the final outcome (Figure S2, Figure 2).

The intrinsic clearance of all selected drugs was also (retrograde) calculated using the parallel tube model [34] (Figure S2). Both well‐stirred and parallel tube models resulted in similar intrinsic clearance values for all drugs. Given that the well‐stirred model has demonstrated better overall performance [35], it was chosen to calculate intrinsic clearance.

For seven drugs (amoxicillin, levetiracetam, caffeine, zidovudine, metformin, and tenofovir), the lactation PBPK models were developed using a permeability‐limited model for the blood‐milk barrier. Based on parameter sensitivity analyses, varying the maternal passive diffusion clearance (CL_PD) between blood (“extracellular”) and breast cells (“intracellular”) value from 10 L/h to 10⁶ L/h had no impact on the prediction of plasma AUC and C_max as well as human milk concentrations (see drug‐specific reports in the Supporting Information). For permeability‐limited PBPK models, the M/P ratio values, calculated based on milk/plasma AUC values (Equation 11, Supporting Information), are listed in Table 2. The predicted M/P ratio for amoxicillin was 0.14. However, only one clinical study is available in the literature, reporting three M/P ratio values, each based on a single time point at the (anticipated) plasma peak concentration. Since the peak concentration in human milk typically occurs later than in plasma, these values may underestimate the true M/P ratio. To account for this, the M/P ratio was calculated from the peak plasma concentration and the highest measured concentration in human milk. Additionally, a non‐compartmental analysis was applied to estimate an AUC‐based M/P ratio, assuming similar elimination slopes in plasma and human milk [19]. The estimated M/P ratio for levetiracetam was 1.37, which aligned with literature‐reported values [36, 37, 38, 39]. The estimated caffeine M/P ratio of 1.41 was slightly higher than the observed range (0.52–1.16 [21, 40, 41]). The predicted M/P ratio values of zidovudine (1.30), tenofovir (0.05), metformin (0.16) were in agreement with observed values [22, 23, 42, 43, 44, 45, 46, 47, 48].

TABLE 2.

Predicted milk‐to‐plasma ratio, daily infant dosage, and relative infant dose of selected drugs using the developed lactation PBPK models.

Drug	Maternal dosing regimen (mg)	Predicted GM concentration in milk (90% CI) (mg/L)	Predicted GM M/P ratio (90% CI) c	DID d (mg/kg/day) (RID, %)
				Daily milk volume 150 mL	Daily milk volume 200 mL
Amoxicillin a	1000/TID	0.66 (0.62–0.69)	0.14 (0.13–0.14)	0.10 (0.22)	0.13 (0.29)
Levetiracetam a	1500/BID	47.44 (45.56–49.41)	1.37 (1.37–1.38)	7.12 (15.6)	9.49 (20.8)
Caffeine a	100/TID	3.17 (2.80–3.59)	1.41 (1.41–1.42)	0.48 (10.43)	0.63 (13.90)
Zidovudine a	300/BID	0.57 (0.51–0.61)	1.30 (1.29–1.30)	0.09 (0.94)	0.11 (1.25)
Metformin a	500/BID	0.11 (0.11–0.12)	0.16 (0.162–1.16)	0.017 (0.11)	0.023 (0.15)
Cetirizine a	10/QD	0.025 (0.019–0.034)	0.16 (0.14–0.19)	0.00375 (2.47)	0.005 (3.29)
Tenofovir a	300/QD	0.009 (0.008–0.010)	0.08 (0.084–0.009)	0.0014 (0.07)	0.0018 (0.04)
Valproic acid b	2100/QD	4.13 (3.96–4.30)	0.05	0.62 (1.94)	0.83 (2.59)
Sertraline b	50/QD	0.05 (0.043–0.051)	1.62	0.00705 (0.93)	0.0094 (1.24)
Nevirapine b	200/BID	6.09 (5.79–6.40)	1.06	0.91 (15.0)	1.22 (20.0)
Sildenafil b	20/TID	0.0053 (0.0049–0.0057)	0.08	0.00075 (0.08)	0.001 (0.11)

Abbreviations: BID, twice a day administration; CI, confidence interval; DID, daily infant dosage; GM, geometric mean; M/P ratio, milk‐to‐plasma ratio; QD, once a day administration; RID, relative infant dosage; TID, three times a day administration.

^a Lactation PBPK model using permeability‐limited model.

^b Lactation PBPK model using perfusion‐limited model.

^c The M/P ratio was estimated (i) based on the ratio of AUC_milk over AUC_plasma (Equation 11) for permeability‐limited models and (ii) using the log transformed phase‐distribution by Atkinson and Begg (Equations 12 and 13) for perfusion‐limited models.

^d Daily infant dosage estimated assuming daily milk volume of either 150 mL or 200 mL.

The lactation PBPK models for five drugs (cetirizine, nevirapine, sertraline, sildenafil, and valproic acid) were developed using the perfusion‐limited model. For perfusion‐limited models, the M/P ratio values were calculated and used as input to predict drug concentration‐time profiles in human milk, as listed in Table 2. The calculated M/P ratio values of cetirizine (0.24), valproic acid (0.05), sertraline (1.62), and nevirapine (1.06) were in agreement with literature [22, 24, 25, 31, 39, 42, 43, 45, 49, 50, 51, 52, 53, 54, 55, 56]. The sildenafil calculated M/P ratio (0.08) was slightly underpredicted compared to reported data (0.09–0.14) [33, 57].

Overall, the predicted M/P ratios (AUC‐based or relying on the log transformed phase‐distribution model) were comparable with the observed values as reported in literature for all drugs (Table 2 and Figure 4) with AFE of 0.82 and GMFE of 1.74 across all the drugs. Most of the in vivo observed clinical data were within the 90% confidence interval of predictions (Figures 5, 6, 7) allowing the reliable PBPK‐based estimation of the DID and RID of the selected model drugs.

3.3. Infant Dose Estimation

The values reflecting the predicted amount of a drug transferred to the infant through human milk relative to the maternal dose (RID) are reported in Table 2. The lactation PBPK models estimated very low RID values (< 1%) for amoxicillin (observed range; 0.22%–0.29%), zidovudine (range 0.91%–1.25%), metformin (range 0.11%–0.15%), tenofovir (range 0.036%–0.04%), sertraline (range 0.93%–1.24%), and sildenafil (range 0.08%–0.11%). Cetirizine and valproic acid were predicted to have a low RID of < 5%, ranging from 2.47% to 3.29% and from 1.94% to 2.59%, respectively. For caffeine, levetiracetam, and nevirapine, the estimated RID values ranged from 10% to 25%. The estimated RID values for caffeine, levetiracetam, and nevirapine aligned with observed RID values, reported to range from 7% to 10%, from 15.6% to 20.8%, and from 15.0% to 20.0%, respectively [39, 44, 45].

The DID (mg/kg/day) was calculated based on the PBPK‐based simulations of human milk average concentrations at steady state and assuming a high maternal therapeutic dose for each drug. The DID was compared to the recommended therapeutic dosage for pediatrics, if available (Table 3). The results revealed that the estimated DIDs represented less than 25% of the recommended infant dosing (Table 3).

TABLE 3.

Predicted daily infant dosage as a percentage of the pediatric therapeutic dose.

Drug	Therapeutic pediatric dose (reference dose) (mg/kg/day)	RID, therapeutic (%), assuming 150 mL daily milk intake	RID, therapeutic (%), assuming 200 mL daily milk intake
Amoxicillin	50	0.20	0.26
Levetiracetam	40	17.8	23.7
Caffeine a	5	9.6	12.6
Zidovudine	24	0.38	0.46
Metformin	N/A	N/A	N/A
Cetirizine	0.5	0.75	1.00
Tenofovir	6.5	0.02	0.03
Valproic acid	40	1.55	2.08
Sertraline	N/A	N/A	N/A
Nevirapine	12	7.58	10.17
Sildenafil b	6	0.013	0.017

Abbreviations: DID, daily infant dosage; N/A, not applicable; RID, relative infant dose.

^a Caffeine therapeutic dosage recommendation only to preterm population.

^b Sildenafil therapeutic dosage recommendation only to neonate population.

4. Discussion

Regulatory agencies encourage the use of PBPK modeling and simulation, especially in the early stages of drug development [58]. Lactation PBPK models, in particular, can support risk assessment on maternal drug exposure during lactation and ultimately be instrumental in predicting lactation‐related medication exposure in infants. Our group previously reported the utility of PBPK modeling and simulation in the PK‐Sim software platform for predicting concentrations of 10 physicochemically diverse model drugs in human milk [2]. The present study extends this structured effort, relying on the same set of model drugs in addition to sildenafil, and using the more recently launched lactation module in Simcyp. The suitability of permeability‐limited versus perfusion‐limited distribution models for drug transfer into human milk was specifically explored. The present work also aligned with the WP3 ambitions of IMI ConcePTION to pursue European Medicines Agency (EMA) qualification advice/opinion for non‐clinical methods for drug milk distribution assessment.

In a first phase of the present study, adult reference PBPK models were developed and verified to predict the pharmacokinetic behavior of each drug in adult healthy volunteers. Subsequently, the Simcyp Simulator was used to develop corresponding lactation PBPK models for the 11 model drugs. The Simcyp Simulator includes a built‐in lactation module, featuring both perfusion‐limited and permeability‐limited models. Initially, the approach was to develop lactation PBPK models by applying the generic framework previously published to predict drug concentration in human milk using the built‐in permeability‐limited model [2]. Such an approach is also compatible (and consistent) with the previously introduced semi‐mechanistic lactation model by Koshimichi et al. [3], indeed assuming that the drug distribution between plasma and milk was not always in rapid equilibrium. The secretion and reuptake clearances are estimated based on drug physicochemical properties via two QSPR models. Moreover, as the drug transfer rate is also affected by the unbound fraction in human milk, the proposed model requires knowledge of the drug unbound fractions in plasma and milk. The estimation of fraction unbound in milk was assumed using the model proposed by Atkinson and Begg [4]. For 6 out of 11 compounds, the Simcyp Simulator permeability‐limited lactation module was configured to reflect two instead of three compartments (Figure S1), ensuring compatibility with the Koshimichi concept.

For some compounds (i.e., cetirizine, sertraline, nevirapine, and sildenafil), a flow‐limited clearance was apparent when intrinsic clearance was calculated; i.e., intrinsic clearance values were higher than the breast blood flow of 9.09 L/h (Figure S2). Furthermore, a perfusion‐limited lactation model also had to be applied for valproic acid. Perfusion‐limited lactation models are essentially consistent with the semi‐mechanistic models proposed by Atkinson and Begg in 1990 to estimate the M/P ratio of a given drug [4], thereby assuming rapid equilibrium between plasma and milk. Within the Simcyp Simulator lactation module, the M/P calculated with the QSPR model of Atkinson and Begg is subsequently used to generate the concentration‐time profile in human milk.

Taken together, a selection of a perfusion‐limited versus permeability‐limited lactation model for milk distribution appeared key for successful lactation PBPK model development in the present study, and as a practical outcome of the present study, a decision tree (Figure 2) was proposed to guide the future development of lactation PBPK models within the Simcyp Simulator.

The models developed using either a permeability‐limited or a perfusion‐limited approach were able to predict drug concentration‐time profiles in human milk across various dose regimens. The predicted and/or estimated M/P ratios were in agreement with the observed ratios in the literature (See Figure 4 and Supporting Information for drug‐specific reports). In this context, it is important to consider that the M/P ratio is dose‐independent for drugs with linear pharmacokinetics, simplifying extrapolation across different dosing regimens. However, for new drugs with unknown pharmacokinetics, potential non‐linearity, especially when transporters at the blood‐milk barrier are involved, could cause the M/P ratio to vary with dose. This could introduce challenges in predicting drug exposure in breastfed infants when extrapolating from limited clinical data at specific dose levels. Of note, non‐linearity in absorption or elimination processes are not expected to have a substantial impact on the M/P ratio, but further studies are required to address this.

Evaluation of the lactation PBPK models against clinical data from literature obviously represented a key element of the present study. However, amoxicillin is one of the examples where only one dataset in human milk was available for model development and subsequent evaluation, illustrating a significant limitation of the present effort. This is complicated by the high inter‐individual variability often observed in clinical data, which may be due to substantial physiological differences within the studied populations [59].

Regulatory agencies have recently issued guidance on conducting clinical lactation studies [12, 60], recommending standardized sampling methods, including the timing and frequency of milk and plasma samples. This guidance marks an important advance toward improving and increasing the availability of clinical data in a manner that minimizes risk to participants while providing essential information on drug transfer into human milk, one step to generate reliable data that supports model validation.

Regardless of verification, the limitations of the QSPR models currently used to inform the lactation module of the PBPK models should be acknowledged. For instance, these QSPR models are based on a limited number of compounds and do not account for transporters at the blood–milk barrier. Some drugs are expected to be transported into human milk via a carrier‐mediated mechanism, as transporters, such as the breast cancer resistance protein (BCRP), are present on the basal and apical membranes of the mammary epithelial cells. One example is tenofovir, which is thought to be excreted into human milk through BCRP, with the expression of this transporter varying throughout the postpartum period [61].

Importantly, by predicting milk concentration time profiles, lactation PBPK models can also aid in estimating DIDs and the RID, providing valuable information to assess drug safety in breastfed infants. The appropriate threshold to be considered when evaluating these results is still debated. Some authors suggest that a 10% RID can be considered a safety threshold in risk assessment, while an RID higher than 25% is considered a major safety threshold [62, 63, 64, 65]. Except for levetiracetam, caffeine, and nevirapine, all estimated RID values obtained based on the PBPK models in the present study are < 10% (Table 2). In contrast, levetiracetam and nevirapine have a relatively higher transfer rates into human milk. In the literature, this suggests the need for careful consideration and potentially closer monitoring when levetiracetam or nevirapine is used by breastfeeding mothers. Additionally, as recommended in regulatory guidelines [12], we compared the estimated DID to the pediatric therapeutic dose. The RID therapeutic values (Table 3) were less than 25% compared to the dosing used for pediatric therapeutic treatment, indicating (relatively) low risk of side effects in infants.

A more comprehensive understanding of infant exposure can be assessed by integrating the information generated from the maternal model (e.g., DID) into a verified infant PBPK model. This integration accounts for the pharmacokinetic processes (ontogeny and physiological maturation) of the drug in pediatrics to assess the potential exposure in this population [66]. Furthermore, extending the model incorporating the impact of human milk fat content, milk pH, changes in organ volume and flow, and postpartum time could potentially lead to a better investigation and understanding of systemic infant exposure [59].

While our models focus on the 3‐month postpartum time point, we recognize that an exploration of the safety risk evolution over time, especially during the first few weeks postpartum, could provide a more comprehensive understanding of the potential safety risks for the infant [59, 67]. Future work may include employing a dynamic physiological model to account for milk changes over the postpartum time period and further validating the models using data from clinical milk studies conducted within the ConcePTION project. Additional modifications should aim to refine the lactation PBPK models by integrating experimentally determined in vitro permeability coefficient values for the blood‐milk barrier. Furthermore, the increased availability of clinical data will allow for the development of more comprehensive PBPK models that account for interindividual variability, reducing the uncertainty that currently surrounds drug safety in breastfeeding mothers. This should subsequently improve confidence in the quality of information available to support shared informed decisions by healthcare providers and patients. Ongoing efforts in our lab aim to develop infant PBPK models for further inclusion in maternal–infant PBPK models to assess lactation‐related medication exposure.

5. Conclusion

The present study succeeded in the development of lactation PBPK models for 11 small molecule drugs within the Simcyp simulator. Drug distribution between plasma and human milk was implemented either with perfusion‐limited or permeability‐limited semi‐mechanistic models informed by drug physicochemical properties. Despite some limitations (e.g., not accounting for transport‐mediated human milk distribution), the models were able to capture human milk profiles and estimate milk‐to‐plasma ratios as compared to clinical reports, allowing for the estimation of DID, mg/kg/day and RID, %. The estimated RID remained below 10% for all drugs except for levetiracetam, caffeine, and nevirapine, illustrating the utility of the developed lactation PBPK models to inform risk assessment. Future work aims to incorporate in vitro permeability data across the blood‐milk barrier and further integration of the maternal PBPK models with infant PBPK models to assess relative infant exposure.

Author Contributions

All authors wrote the manuscript. P.A., A.S., and K.A. designed the research. J.M., N.N., J.M.B., R.H.B., and M.‐C.H. performed the research. J.M., N.N., J.M.B., R.H.B., M.‐C.H., M.V.N., A.S., K.A., H.N., M.H., F.S.M., and P.A. analyzed the data.

Conflicts of Interest

P.A. is co‐owner of the company BioNotus. The remaining authors declare no conflicts of interest. The research project leading to these results was conducted as part of the ConcePTION consortium. This manuscript reflects the personal views of the stated authors.

Supporting information

Table S1. Summary of the drug physicochemical properties for the development of lactation PBPK model using the permeability‐limited model.

Table S2. Summary of the drug physicochemical properties for the development of lactation PBPK model using perfusion‐limited model.

Table S3. Estimated unbound fraction in skimmed and whole milk as well as secretion and reuptake milk clearances used to develop the permeability rate‐limited lactation models for 7 drugs.

Table S4. Estimated unbound fraction in skimmed and whole milk as well as the unionized fraction in plasma and milk used to determine the milk‐to‐plasma ratio within the lactation perfusion‐limited model for 4 drugs.

Table S5. Compound‐specific values used for passive diffusion clearance (CL_PD) between extracellular and intracellular compartments in Simcyp, along with resulting AUC and Cmax in plasma, extracellular water (EW) and intracellular water (IW). Values shown are geometric mean values.

Figure S1. The default permeability‐limited model structure in the Simcyp simulator (v21) is shown in panel (A) and the modified structure of the permeability‐limited model, that was used to describe the passage of drugs across the blood‐milk barrier as part of the lactation PBPK models used in the present study, is shown in panel (B). In the Simcyp model, drug transfer between plasma and milk is originally represented by a three‐compartment system (extracellular, intracellular, and milk compartments). However, to align with the two‐compartment structure described in the Koshimichi model while maintaining physiological relevance, the passive diffusion clearance (CL_PD breast passive diffusion clearance) (bidirectional black arrow) between maternal blood (~extracellular) and mammary epithelial cells (~intracellular) was increased to the maximum value allowed by Simcyp, effectively combining the extracellular and intracellular compartments. CL_PD milk was set to zero (default). Qbreast: breast blood flow, CLsec: secretion clearance, CLre: reuptake clearance calculated according to Koshimichi et al., black arrow from the milk compartment represents the drug removal from the milk compartment.

Figure S2. Comparison of intrinsic secretion clearance back‐calculated with the well‐stirred model and parallel tube model. The red dashed line represents the breast blood flow of 9.09 L/h.