A multiscale PBPK‐PD model of oxytocin‐induced uterine excitation and contraction

Abstract

Abstract

Coordinated excitation of uterine smooth muscle cells (USMCs) is the physiological basis of labour, and several mathematical models have been developed to understand the function of USMCs. However although the key role of oxytocin in parturition has been established, most existing USMC models still rely on external electrical stimulation to initiate action potentials rather than including oxytocin as a stimulus. This study developed a multiscale dynamic model. First a pregnancy physiologically based pharmacokinetic (PBPK) model was built to describe pulsatile oxytocin release, systemic transport and clearance. This PBPK model was coupled to a cell‐level model via local myometrial oxytocin exposure. This model explicitly captures oxytocin binding to and dissociation from the oxytocin receptor (OXTR), as well as downstream OXTR signalling. The cell‐level model incorporates excitation–contraction coupling, enabling the simulation of USMC excitation and contractile responses without external electrical stimulation. The model aligns with published data across multiple key endpoints, including oxytocin pharmacokinetic parameters, maternal venous and umbilical arterial and umbilical venous concentrations, and the duration and amplitude of cellular excitation and contraction. The results also show that an increased oxytocin association rate constant $k_{\mathrm{on}}$ lowers the half‐maximal effective concentration (EC₅₀) and is a key determinant of USMC sensitivity to oxytocin. This model provides a quantitative framework to explain oxytocin's role in uterine excitability during pregnancy and to investigate pathological conditions such as preterm labour and uterine atony.

Key points

• Oxytocin is a major physiological regulator of labour contractions, but most existing uterine smooth muscle cell models still require external electrical stimulation to trigger excitation, rather than recapitulating oxytocin‐induced myometrial activity.

• We developed a multiscale physiologically based pharmacokinetic‐pharmacodynamic (PBPK‐PD) model that links pulsatile endogenous oxytocin release, maternal–fetal distribution, oxytocin receptor binding, IP₃‐mediated Ca²⁺ signalling and excitation–contraction coupling in uterine smooth muscle cells.

• The model reproduced published ranges for key pharmacokinetic and pharmacodynamic endpoints, including oxytocin half‐life and clearance, maternal and fetal oxytocin concentrations, intracellular Ca²⁺ responses, membrane potential, contraction duration and active stress.

• Simulations showed that the oxytocin association rate constant and oxytocin receptor abundance strongly influence the oxytocin dose–response relationship, shifting EC50 and modulating uterine excitability.

• This work provides a quantitative framework for studying how endogenous oxytocin can induce uterine excitation and contraction, and offers a basis for investigating abnormal uterine activity such as preterm labour and uterine atony.

Abstract figure legend Schematic overview of the multiscale pregnancy PBPK‐PD framework linking endogenous oxytocin (OXT) release to uterine smooth muscle cell (USMC) excitation and contraction. The framework includes a pregnancy physiologically based pharmacokinetic (P‐PBPK) module, in which OXT from maternal and fetal hypothalamic neurohypophyseal sources is transported through maternal and fetal blood circulation, with placental exchange, to determine local myometrial OXT exposure. At the cellular level OXT binds the oxytocin receptor (OXTR) to form OXT–OXTR complexes (OXTRCs), followed by receptor cycling, inositol 1,4,5‐trisphosphate (IP₃) generation, activation of the IP₃ receptor (IP₃R) and sarcoplasmic reticulum (SR) Ca²⁺ release. Ca²⁺ signalling, together with Na⁺, K⁺, Ca²⁺ and Cl⁻ channel activity, regulates membrane excitation and cross‐bridge cycling, thereby triggering USMC excitation and contraction. Created in BioRender. Yang, Y. (2026) https://BioRender.com/wvaa9vl.

Introduction

Coordinated, rhythmic contractions of the myometrium are essential for normal parturition and also play a key role in maintaining appropriate control of postpartum blood loss. Conversely abnormal uterine contractions can lead to serious pregnancy complications, including preterm birth and postpartum haemorrhage (Koutras et al., 2021). Globally approximately 15 million preterm infants are born annually, with preterm birth accounting for 35% of neonatal deaths (Blencowe et al., 2013). Surviving pre‐term infants often face long‐term health challenges, including neurodevelopmental disorders, respiratory diseases and metabolic issues. Postpartum haemorrhage, accounting for 27% of maternal deaths worldwide, is another leading cause of maternal mortality (Say et al., 2014). Uterine smooth muscle cell (USMC) excitation refers to the process by which USMCs transition from a resting membrane potential to an action potential (AP), accompanied by calcium ion influx, thereby triggering filament sliding, which directly causes uterine muscle contraction (Garfield & Maner, 2007). Unlike cardiac tissue the existence of specialized pacemaker cells within the uterus remains a subject of ongoing debate, with no consistent evidence supporting their presence (Yang et al., 2024). The absence of a defined pacemaker makes it challenging to elucidate the precise mechanisms underlying the initiation and coordination of uterine contractions (Garfield et al., 1977; Wray et al., 2003). EHG real‐time monitoring systems have provided valuable information for predicting preterm birth (Goldsztejn & Nehorai 2023). However they are not suitable for investigating the mechanistic origins of uterine contractions, as the signals are influenced by numerous physiological and environmental factors. Computational modelling provides a systematic framework for evaluating mechanistic hypotheses, allowing researchers to integrate experimental data, test competing models of excitation and explore how cell and tissue‐level processes interact to generate coordinated uterine activity.

Early uterine USMC models primarily focused on describing the dynamic changes in intracellular calcium ion concentrations and the role of calcium ions in membrane depolarization (Bursztyn et al., 2007) and stress generation (Hai & Murphy, 1988). Subsequent models have incorporated the dynamics of an increasing number of ion channels, including potassium, sodium and chloride ions, significantly enhancing the representation of electrical activity in USMCs (Tong et al., 2011). For instance Tong et al. (2014) developed a mathematical model incorporating 19 ion channels, enabling the simulation of long‐lasting bursting APs. Some models have further expanded to include detailed descriptions of sarcoplasmic reticulum (SR) calcium ion channels (Testrow et al., 2018). The integrated model developed by Testrow et al. (2018) incorporates SR calcium storage and release, a four‐component mechanical model and a dynamic cross‐bridge model. This model successfully coupled electrochemical and mechanical dynamics, representing one of the most detailed USMC models to date. Recent studies have aimed to robustly identify potential model simplifications for future applications in multiscale modelling of uterine contractility (Means et al., 2023; Sheldon et al., 2013). Most tissue‐level models incorporate either spontaneously oscillating cell models (Means et al., 2025) or detailed cell models (Atia et al., 2016) that rely on external electrical stimulation to induce APs, thereby deviating from physiological processes.

Increasing evidence suggests that oxytocin, a potent uterotonic agent, plays a pivotal role in initiating and sustaining uterine contractions during labour (Uvnäs‐Moberg, 2024). Oxytocin is widely used to induce or augment labour by enhancing the frequency and intensity of uterine contractions and to prevent postpartum haemorrhage (Buckley et al., 2023). In vitro studies have demonstrated that oxytocin can directly elicit myometrial contractions, even in absence of other physiological stimuli (Uvnäs‐Moberg et al., 2019). As pregnancy progresses, particularly during the third trimester, maternal oxytocin levels gradually increase and reach their peak at the onset of labour (Uvnäs‐Moberg, 2024). In parallel the expression of oxytocin receptors (OXTRs) on USMCs is upregulated, rendering the myometrium more sensitive to oxytocin (Kimura et al., 1996). This concurrent elevation in oxytocin levels and receptor sensitivity aligns with the need for efficient uterine contractions in late pregnancy to facilitate fetal expulsion. Both the frequency and amplitude of oxytocin pulses increase as labour progresses, with a typical frequency of three to five pulses per 10 min (Uvnäs‐Moberg, 2024). This pattern closely aligns with the uterine contraction cycle, suggesting oxytocin's fundamental role in initiating and coordinating contractions.

In humans endogenous oxytocin is primarily released from the posterior pituitary. Nevertheless a comprehensive mechanistic model that integrates pituitary oxytocin secretion with its downstream binding to myometrial OXTRs and the ensuing signalling cascades that drive uterine contractions is currently lacking. PBPK modelling offers a mechanistic understanding of oxytocin pharmacokinetics (PK) by linking its systemic release and distribution to tissue‐specific concentrations and receptor‐mediated effects in the uterus. Oxytocin binds to G‐protein‐coupled receptors (OXTRs) on USMCs, promoting the hydrolysis of phosphatidylinositol 4,5‐bisphosphate (PIP₂) to generate inositol 1,4,5‐trisphosphate (IP₃), which in turn induces calcium release from the SR, driving the initiation and modulation of uterine electrical activity (Woll & Van Petegem, 2022).

This study aims to develop and validate a multiscale pregnancy‐specific PBPK‐PD model to characterize oxytocin‐induced uterine excitation and contraction. This model provides a framework to elucidate mechanisms underlying abnormal preterm contractions and uterine atony, and may support future optimization of drug dosing during labour induction to improve pregnancy and postpartum management.

Methods

The framework consists of two coupled models. The PBPK model, with key physiological parameters adjusted for gestational week, captures endogenous oxytocin release, distribution, metabolism and clearance across organs. The OXTR signalling model translates these dynamic exposure profiles into cell‐level electrophysiological responses including ligand–receptor binding, internalization, recycling and excitation–contraction coupling in a USMC. Together the modules establish a multiscale link between maternal–fetal PK and myometrial cellular activity.

P‐PBPK model

Accurately modelling oxytocin's effects on uterine contractions requires capturing its changing concentrations throughout the body during pregnancy. Accurate concentrations can be achieved using a physiologically based pharmacokinetic (PBPK) model that mathematically describes the complex pharmacological, physiological, anatomical and physical processes involved in absorption, distribution, metabolism and excretion (ADME) (Peters, 2021). The model includes both a maternal (m‐PBPK) and fetal (f‐PBPK) component (Fig. 1). Placental exchange of oxytocin bidirectionally couples the maternal and fetal models, allowing the interchange of the modelled substance (Peters, 2021).

Figure 1. Physiologically based pharmacokinetic model for pregnancy (P‐PBPK) model.

Abbreviations: DA, ductus arteriosus; DV, ductus venosus; FO, foramen ovale; LA, left atrium; LV, left ventricle; PA, pulmonary artery; PO, portal vein; PV, pulmonary vein; RA, right atrium; RV, right ventricle; UA, umbilical artery; UV, umbilical vein; VC, vena cava.

PBPK models generally consist of a number of body ‘compartments’ corresponding to organs or tissues. These compartments are connected based on blood flow. By considering the concentration or amount of a chemical substance produced in, eliminated from or transported through each compartment, differential equations can be formulated using conservation principles.

To determine how a substance distributes across the body's compartments, it is essential to consider its PK. In PBPK modelling, concentrations are often expressed per unit plasma volume (i.e. plasma concentration), whereas mass balance and transport are governed by blood flow and blood volume. Therefore plasma concentrations are commonly converted to whole‐blood concentrations using the blood to plasma ratio ($\mathrm{B}:\mathrm{P}$), which relates concentrations defined per plasma volume to those defined per blood volume. In addition substances in the body can bind reversibly to proteins in the blood plasma. It is often the unbound fraction in plasma ($f_{\mathrm{u},\mathrm{p}}$) that is available to interact with targets.

For any compartment $i,$ the amount of substance in the compartment $A_i(t)$ should conserve mass, and thus the rate of change of the concentration of a substance in the compartment is given by the rate of change of the substance going into the compartment ($R_{\mathrm{in}}(t)$), plus the rate of change of production by the compartment ($R_{\mathrm{prod}}(t)$), minus the rate of change of substance going out of the compartment ($R_{\mathrm{out}}(t)$), minus the rate of change of elimination of the substance ($R_{\mathrm{elim}}(t)$), in the compartment, that is, for compartment $i$,

$$\begin{array}{ccc}\hfill \frac{d{A}_i\left(t\right)}{dt}& =& V_i\frac{d{C}_i\left(t\right)}{dt}\hfill \\ & =& R_{\mathrm{in}}\left(t\right)+R_{\mathrm{prod}}\left(t\right)-R_{\mathrm{out}}\left(t\right)-R_{\mathrm{elim}}\left(t\right)\hfill \end{array}$$ (1)

where $C_i(t)$ represents the concentration of the substance in compartment $i$, and $V_i$ represents the volume of compartment $i$.

For compartments fed by an arterial blood supply the rate of substance flowing into a compartment is given by

$$R_{\mathrm{in}}\left(t\right)=Q_i\left(t\right)·C_{\mathrm{A}}\left(t\right)$$ (2)

where $Q_i(t)$ is the blood flow rate of compartment $i$, and $C_{\mathrm{A}}(t)$ is the concentration of the substance in arterial blood.

For blood‐flow‐limited compartments, the rate of the substance flowing out is given by the rate of decrease in the substance from the draining venous blood after distribution to the compartment tissues, which is given by

$$R_{\mathrm{out}}\left(t\right)=Q_i\left(t\right)·C_{v_i}\left(t\right)$$ (3)

where $C_{v_i}(t)$ is the concentration of the substance in the venous blood leaving tissue $i$ given by

$$C_{{\mathrm{v}}_i}\left(t\right)=\frac{C_i\left(t\right)·\mathrm{B}:\mathrm{P}}{{K_{\mathrm{p},\mathrm{u}}}_i·f_{\mathrm{u},\mathrm{p}}}$$ (4)

where $\mathrm{B}:\mathrm{P}$ is the blood to plasma concentration ratio of the substance, ${K_{\mathrm{p},\mathrm{u}}}_i$ is the tissue to unbound plasma partition coefficient and $f_{\mathrm{u},\mathrm{p}}$ is the fraction of the substance that is unbound in the plasma. The blood to plasma ratio, $\mathrm{B}:\mathrm{P}$, is given by

$$\mathrm{B}:\mathrm{P}=\frac{\mathrm{RBC}:\mathrm{P}·\mathrm{H}+\left(1-H\right)}{f_{\mathrm{u},\mathrm{p}}}$$ (5)

where $H$ is the haematocrit and $\mathrm{RBC}:\mathrm{P}$ is the red blood cell to plasma ratio, which gives the extent to which the substance partitions into red blood cells.

The compartmental elimination rate of oxytocin, $R_{\mathrm{elim}}(t)$, is given by

$$R_{\mathrm{elim}}\left(t\right)=\mathrm{C}{\mathrm{L}}_i·f_{\mathrm{u},\mathrm{p}}·C_i\left(t\right)$$ (6)

where $\mathrm{C}{\mathrm{L}}_i$ denotes the clearance of oxytocin in compartment $i$.

${\mathrm{K}}_{p,u}$ calculations

Oxytocin is a peptide hormone composed of a chain of nine amino acids. As a peptide hormone it is water‐soluble and fat‐insoluble. As such oxytocin is primarily distributed in the extracellular space of tissues (Lozic & Ludwig, 2022). We assume that:

1. Intracellular accumulation is negligible. The drug is mainly in the interstitial fluid. There is no significant partition into cells, organelles or membrane lipids.

2. Trans‐epithelial active transport is negligible. An unbound drug rapidly equilibrates between interstitial fluid and plasma. Unbound concentrations in these two spaces are approximately equal.

3. Only binding to soluble proteins in plasma and interstitial fluid is considered.

After derivation (Appendix A), we obtain:

$$f_{\mathrm{u},\mathrm{ISF}}=\frac{f_{\mathrm{u},\mathrm{p}}}{f_{\mathrm{u},\mathrm{p}}+\mathrm{I}:\mathrm{P}\left(1-f_{\mathrm{u},\mathrm{p}}\right)}$$ (7)

where $f_{\mathrm{u},\mathrm{ISF}}$ denotes the unbound fraction in interstitial fluid, and $\mathrm{I}:\mathrm{P}$ is the interstitial‐to‐plasma protein ratio. For proteins this tends to be in the range 0.3–0.6 (Levick, 2004). The tissue‐to‐unbound plasma ratios ($K_{\mathrm{p},\mathrm{u}}$) is given by:

$$K_{\mathrm{p},\mathrm{u}}=\frac{K_{\mathrm{p}}}{f_{\mathrm{u},\mathrm{p}}}=\frac{f_{\mathrm{ISF}}·\left(f_{\mathrm{u},\mathrm{p}}+\mathrm{I}:\mathrm{P}\left(1-f_{u,p}\right)\right)}{f_{\mathrm{u},\mathrm{p}}}$$ (8)

where $f_{\mathrm{ISF}}$ is the interstitial fluid fraction for the compartment of interest.

It has been reported that approximately 60% of oxytocin is bound to immunoglobulin G (IgG) (Værøy et al., 2023). Using Table 1 in Rafidi et al. (2022), we obtained the ratios of IgG content in each tissue to that in the serum ($I:P$ in Table 1). Data for the myometrium and placenta were not available; we used skeletal muscle as a proxy. From Table 2 in Bruno (2016) and Table A2 in Dallmann et al. (2017), we obtained the interstitial fluid fractions $f_{\mathrm{ISF}}$ for each tissue ($f_{\mathrm{ISF}}$ in Table 1). Specifically to account for the haematoencephalic (blood–brain) barrier, the calculated $K_{\mathrm{p},\mathrm{u}}$ value for the brain was multiplied by 0.0001 to obtain the final $K_{\mathrm{p},\mathrm{u}}$ for the brain compartment. With $f_{\mathrm{u},\mathrm{p}}$= 0.4 we calculated the $f_{\mathrm{u},\mathrm{ISF}}$ and $K_{\mathrm{p},\mathrm{u}}$ for all organ/tissue compartments, as shown in Table 1.

Table 1.

Tissue/organ‐to‐unbound plasma partition coefficients ($K_{\mathrm{p},\mathrm{u}}$)

	Tissue/organ	$I:P$	f u, ISF	$f_{\mathrm{ISF}}$	$K_{\mathrm{p},\mathrm{u}}$
Maternal organs	Brain	0.0185	0.973	0.16	1.64e−5
	Fat	0.075	0.899	0.14	0.156
	Gut	0.185	0.783	0.28	0.358
	Kidney	0.032	0.954	0.27	0.283
	Liver	0.25	0.727	0.16	0.22
	Heart	0.051	0.783	0.32	0.409
	Lung	0.0215	0.969	0.34	0.351
	Myometrium	0.345	0.659	0.422	0.64
	Placenta	0.35	0.656	0.20303	0.31
	Other	/	/	/	0.81
Fetal organs	Brain	0.0185	0.973	0.16	3.75e−5
	Gut	0.185	0.783	0.28	0.816
	Kidney	0.032	0.954	0.27	0.283
	Liver	0.25	0.727	0.16	0.502
	Lung	0.0215	0.969	0.34	0.8
	Placenta	0.35	0.656	0.20303	0.31
	Other	/	/	/	1.85

Table 2.

Comparison between simulated and measured results

Simulated variable	Simulated value	Measured variable	Measured value	Ref.
Duration of oxytocin secretion	5 s	Oxytocin neuron discharge timing	5s	Yaguchi et al. (2023)
Distribution volume of oxytocin	15 L	Distribution volume of oxytocin	15 L	Dawood et al. (1980)
Half‐life (t 1/2)	2.04 min	Half‐life (t 1/2)	1–6 min	Knox et al. (2024)
Total body clearance	5.09 L·min−1	Total body clearance	1.3–7.1 L·min−1	Thornton et al. (1990)
Oxytocin concentration in venous blood	0–100 pg·mL−1	Oxytocin concentration in venous blood	1.7–725 pg·mL−1	Uvnäs‐Moberg et al. (2019)
Fetal umbilical artery concentration	15.8 pg·mL−1	Fetal umbilical artery concentration	15–50 pg·mL−1	Buckley et al. (2023), Nathan et al. (2021)
Fetal umbilical vein concentration	1.8 pg·mL−1	Fetal umbilical vein concentration	4–12 pg·mL−1	Buckley et al. (2023), Nathan et al. (2021)
Intracellular calcium concentration	0.1–0.4 µM	Intracellular calcium concentration	0.1–0.4 µM	Matthew et al. (2004)
Membrane potential	−50 to −5 mV	Membrane potential	−60 to 5 mV	Testrow et al. (2018)
Active stress	0–75 mmHg	IUP	20–100 mmHg	Das et al. (2020)
Excitation duration	36.4 s	Excitation duration	30–90 s	Rhomadona et al. (2019)
EC50 of oxytocin effect	2.31–5.65 nM	EC50 of oxytocin effect	2.91–14.5 nM	Willets et al. (2009), Dubey et al. (2024)

Oxytocin release from the pituitary

In humans oxytocin is mainly synthesized by neurons in the supraoptic and paraventricular nuclei (Hermesch et al., 2024), axonally transported to the maternal posterior pituitary and released into the circulation in a pulsatile manner in response to neural firing (Fuchs, 1983). This pulsatile release is considered an efficient mechanism for maintaining uterine contractility while preventing overstimulation (Fuchs, 1983; Russell et al., 2003). In vivo evidence shows that during the active phase of labour, oxytocinergic neurons fire in bursts of APs; each burst triggers a pulse of oxytocin release (Russell et al., 2003), with firing lasting approximately 5 s (Yaguchi et al., 2023) and yielding venous oxytocin concentrations of roughly 20–700 pg·mL⁻¹ (Uvnäs‐Moberg et al., 2019). In the literature the exact amount of oxytocin released during human labour has not been directly measured. Report on Animal Experiments by Pitzel et al. (1981) reported that maximal stimulation of isolated rat posterior pituitary lobes with high physiological bursting released much less than 20% of the pituitary pool during labour, whereas the human posterior pituitary contains approximately 21 µg of oxytocin (Leng & Sabatier, 2016), 1.05% of release (21 µg $\times$0.0105 = 0.2205  µg) into 2.5 L (venous plasma) (Gaohua et al., 2012), which will give rise to 88 pg·mL⁻¹.

In this study oxytocin release from the posterior pituitary was represented as a ∼5 s burst composed of 40 Gaussian‐shaped pulses (20 ms each) delivered at 125 ms inter‐pulse intervals (8 Hz; Leng et al., 2017), yielding a total burst duration of $((40-1)\times 125\mathrm{ms}+20\mathrm{ms}\approx 5s)$. Each pulse event is expressed as

$$R_{\mathrm{pituitary}}^{\mathrm{m}}\left(\mathrm{GA},t\right)=\frac{A}{\sqrt{2\pi }·\sigma }·\mathrm{ex}{\mathrm{p}}^{-\frac{{\left(t-t_0\right)}^2}{2{\sigma }^2}}$$ (9)

Here $t$ is the current time, $A$ = 5.5 ng denotes the amount of oxytocin released per single pulse (the total release of 40 pulses is 5.5 ng $\times$ 40 = 220 ng, corresponding to about 1.05% release from the posterior pituitary); with a Gaussian pulse of width σ = 20 ms, this corresponds to a peak release rate of ng·ms⁻¹. To mimic uterine contractions during the active phase of labour, we imposed a recurring secretion event with a period of 200 s, corresponding to a contraction frequency of three events per 10 min, as reported clinically (De Geest et al., 1985).

Previous studies also showed that there is an increased fetal plasma oxytocin concentration during pregnancy (Preslock, 2019). Oxytocin is present in the fetal pituitary gland as early as 14–17 weeks of gestation; unlike to maternal posterior pituitary pulsatile nature, fetal plasma concentration did not show a clear pulsatile pattern (Dawood et al., 1978). Therefore the secretion of oxytocin from the fetal pituitary gland is modelled as follows:

$$F_{\mathrm{pituitary}}^{\mathrm{f}}\left(\mathrm{GA}\right)=1340.907·{\mathrm{e}}^{0.14018·\mathrm{GA}}$$ (10)

$$R_{\mathrm{pituitary}}^{\mathrm{f}}\left(\mathrm{GA},t\right)=F_{pituitary}^{\mathrm{f}}\left(\mathrm{GA}\right)·R_{\mathrm{pituitary},\mathrm{basse}}$$ (11)

where $F_{\mathrm{pituitary}}^{\mathrm{f}}(\mathrm{GA})$ denotes the gestational‐age‐dependent growth factor for fetal pituitary oxytocin secretion. This factor is derived by fitting an exponential function to the oxytocin content measured in fetal pituitaries at different gestational weeks by Khan‐Dawood and Dawood (1984). $R_{\mathrm{pituitary},\mathrm{basse}}$= 5.5 ng·min⁻¹ represents the baseline rate of fetal oxytocin secretion in early pregnancy reported by Dawood et al. (1978). $\mathrm{GA}$ denotes gestational age (in weeks).

Oxytocin elimination

Oxytocin is cleared in vivo via two pathways: (1) metabolic clearance by the liver and kidneys and (2) enzymatic hydrolysis.

In pharmacokinetic modelling the fraction of tissue perfused where enzymes are accessible ($f_{\mathrm{IVS}}$) and the intrinsic clearance ($\mathrm{C}{\mathrm{L}}_{\mathrm{int}}$) of enzymes are key determinants of organ‐specific drug metabolism. Organ clearance is commonly described using physiologically based perfusion models that couple blood flow with effective intrinsic clearance (Wilkinson & Shand, 1975):

$$F=1-E=\frac{Q}{Q+f_{\mathrm{up}}·\mathrm{C}{\mathrm{L}}_{\mathrm{int}}}\to E=\frac{f_{\mathrm{up}}·\mathrm{C}{\mathrm{L}}_{\mathrm{int}}}{Q+f_{\mathrm{up}}·\mathrm{C}{\mathrm{L}}_{\mathrm{int}}}$$ (12)

$$\mathrm{CL}=Q·E$$ (13)

Here $\mathrm{CL}$ denotes the organ clearance, $F$ is the organ availability and $E$ represents the fraction of drug removed during a single pass through the organ (0‐1). A larger $E$ indicates greater extraction by the organ and, consequently, a higher organ clearance.

For hepatic elimination empirical compartmental approaches treat the liver as a single well‐mixed compartment where unbound drug in blood is accessible to hepatocytes (Pang & Rowland, 1977). In this work we set the hepatic extraction ratio to 0.9 (E _H = 0.9), yielding a maternal hepatic clearance rate of 1.1574 L·min⁻¹, assuming a blood flow of 1.28 L· min⁻¹ at 40 weeks of gestation. Analogously the fetal hepatic clearance rate ${\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{f}}$ is estimated to be 59.4 mL·min⁻¹ (liver blood flow = 0.0678 L·min⁻¹ at 40 weeks of pregnancy), which agrees with the fetal oxytocin clearance of approximately 30–60 mL·min⁻¹ (Glatz et al., 1980). Previous studies indicate that less than 1% of oxytocin is cleared by the kidneys, corresponding to a renal clearance of 5.5 mL·min⁻¹ (Amico et al., 1987).

Oxytocinase, also known as placental leucine aminopeptidase (P‐LAP) or insulin‐regulated aminopeptidase (IRAP), belongs to the leucyl/cystoyl aminopeptidase family (LNPEP) and is mainly derived from the placenta (e.g. syncytiotrophoblast) (Tsujimoto et al., 2021). During pregnancy oxytocinase activity markedly increases in the maternal circulation (Yamahara et al., 2000), whereas oxytocinase activity in fetal blood remains very low (Oya et al., 1974). These additional enzymatic pathways significantly enhance oxytocin degradation and can produce a several‐fold increase in whole‐body metabolic clearance during late gestation, with reported maternal clearance rates reaching up to 5.7 L·min⁻¹ (Thornton et al., 1990). Therefore in this study, oxytocinase‐mediated enzymatic degradation of oxytocin in maternal blood was modelled using Michaelis–Menten kinetics:

$$\frac{d\left[P\right]}{dt}=\frac{V_{\max }·\left[S\right]}{K_{\mathrm{m}}+\left[S\right]}$$ (14)

where $S$ is the substrate concentration (oxytocin), $V_{\max }$ is the maximum reaction rate at saturating substrate concentration and $K_{\mathrm{m}}$ is the Michaelis constant (the substrate concentration at which the reaction rate equals $V_{\max }/2$).

CAPI and CAPII represent two distinct molecular forms of unbound, circulating oxytocinase (Dziechciowski & Klimek, 2001; Itoh et al., 1997; Yamahara et al., 2000). For PBPK models we must scale the in vitro Michaelis–Menten kinetic parameters to those of the whole organ. $K_{\mathrm{m}}$ remains unchanged because it is an affinity (concentration) term that is not dependent on the total amount of enzyme. Itoh et al. (1997) found that the Michaelis–Menten kinetic parameters for the hydrolysis of oxytocin are $K_{\mathrm{m},\mathrm{CAPI}}$ = 5.6 µm for CAPI and $K_{\mathrm{m},\mathrm{CAPII}}$ = 38 µm for CAPII. For the $V_{\max }$ the total organ reaction rate will be dependent on the total amount of enzyme present in the organ. Experimental studies reported serum oxytocinase (CAPI and CAPII) activity during pregnancy (Klimek, 2005), and fits to these data suggest

$$V_{\max ,\mathrm{CAPI}}=0.30416·\mathrm{ex}{\mathrm{p}}^{0.08529·\mathrm{GA}}$$ (15)

$${\mathrm{V}}_{\max ,\mathrm{CAPII}}=0.81887·\mathrm{ex}{\mathrm{p}}^{0.0521·\mathrm{GA}}$$ (16)

where GA is expressed in weeks, and $V_{\max ,\mathrm{CAPI}}$ and $V_{\max ,\mathrm{CAPII}}$ are expressed in µmol·L⁻¹·min⁻¹.

For oxytocinase Kleiner et al. (1980) measured the relative concentrations of CAPI and CAPII and found that, on average, at physiological pH, there was approximately 55% CAPI and 45% CAPII. The effective clearance rate of oxytocin in veins and artery is calculated as follows:

$$\begin{array}{ccc}\hfill {\mathrm{CL}}_{\mathrm{ven}}^m\left(\mathrm{GA},t\right)& =& \frac{f_{\mathrm{CAPI}}·V_{\max ,\mathrm{CAPI}}·V_{\mathrm{ven}}^m}{K_{\mathrm{m},\mathrm{CAPI}}+f_{\mathrm{u},\mathrm{p}}^{\mathrm{m}}·C_{\mathrm{ven}}^{\mathrm{m}}\left(t\right)}\hfill \\ & & +\frac{f_{\mathrm{CAPII}}·V_{\max ,\mathrm{CAPII}}·V_{\mathrm{ven}}^{\mathrm{m}}}{K_{\mathrm{m},\mathrm{CAPII}}+f_{\mathrm{u},\mathrm{p}}^{\mathrm{m}}·C_{\mathrm{ven}}^{\mathrm{m}}\left(t\right)}\hfill \end{array}$$ (17)

$$\begin{array}{ccc}\hfill {\mathrm{CL}}_{\mathrm{art}}^m\left(\mathrm{GA},t\right)& =& \frac{f_{\mathrm{CAPI}}·V_{\max ,\mathrm{CAPI}}·V_{\mathrm{art}}^{\mathrm{m}}}{K_{\mathrm{m},\mathrm{CAPI}}+f_{\mathrm{u},\mathrm{p}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)}\hfill \\ & & +\frac{f_{\mathrm{CAPII}}·V_{\max ,\mathrm{CAPII}}·V_{\mathrm{art}}^{\mathrm{m}}}{K_{\mathrm{m},\mathrm{CAPII}}+f_{\mathrm{u},\mathrm{p}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)}\hfill \end{array}$$ (18)

where ${\mathrm{CL}}_{\mathrm{ven}}^m(\mathrm{GA},t)$ is the clearance rate of oxytocin in the maternal venous, ${\mathrm{CL}}_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA},t)$ is the clearance rate of oxytocin in maternal arterial blood, $V_{\mathrm{ven}}^{\mathrm{m}}$ is the maternal venous volume, $V_{\mathrm{art}}^{\mathrm{m}}$ is the maternal arterial blood volume, $C_{\mathrm{ven}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in maternal venous blood, $C_{\mathrm{art}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in maternal arterial blood, and $f_{\mathrm{CAPI}}$ and $f_{\mathrm{CAPII}}$ represent the relative concentrations of CAPI and CAPII, respectively. For 40 weeks of gestation venous and arterial clearance rates are about 1.22 L·min⁻¹ and 2.45 L·min⁻¹, respectively.

In dually perfused ex vivo human placenta experiments, Nathan et al. observed that the maternal concentration of oxytocin declined over time, with only ∼31 % of the administered compound remaining after 180 min (Nathan et al., 2021). This cumulative loss demonstrates significant placental metabolism, but the single‐pass extraction is moderate, with an estimated upper bound of E < 0.69. Physiologically the primary oxytocin‐metabolizing enzyme in the placenta is CAP/LNPEP. It is membrane‐bound and accessible to maternal plasma in the intervillous space (Nomura et al., 2005). According to eqn (12) the maximum organ clearance cannot exceed the organ blood flow (i.e.$E\le 1$). Because the intervillous space occupies roughly 40% of the placental volume (Luo et al., 2017), only a fraction of the oxytocin is exposed to the enzyme in a single pass; if $E=0.4$, the effective placental clearance is estimated to be approximately 0.246 L·min⁻¹ at 40 weeks of pregnancy (${\mathrm{CL}}_{\mathrm{pla}}^{\mathrm{m}}=0.4·Q_{\mathrm{pla}}^{\mathrm{m}}$, $Q_{pla}^{\mathrm{m}}$ is the blood flow rate of the placenta).

Experimental studies show that oxytocin interactions in the myometrium occur primarily in a limited receptor compartment rather than via high‐capacity enzyme activity. In depolarized rat myometrium oxytocin clearance is confined to a small extracellular receptor compartment rather than the entire tissue, consistent with low effective metabolic exposure of circulating oxytocin in uterine smooth muscle (Pliska & Jutz, 2022). The elimination rate ($K_{\mathrm{r}}$) was found to be 0.137 min⁻¹ (Pliska & Jutz, 2022), giving rise to a clearance rate of approximately 0.0103 L·min⁻¹ at 40 weeks of pre‐pregnancy (${\mathrm{CL}}_{\mathrm{myo}}^{\mathrm{m}}=K_{\mathrm{r}}·V_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}$).

To sum up the total clearance rate is about 5.09 L·min⁻¹ at 40 weeks of pregnancy. These tissue‐specific differences in $f_{\mathrm{IVS}}$ and enzymatic capacity explain the dominant roles of the liver, blood and placenta in oxytocin metabolism and the negligible clearance by the myometrium, guiding accurate PBPK predictions.

OXTR signalling

Oxytocin binding

Oxytocin binds to OXTR in the myometrium to form the OXTRC (Fig. 2) (Dubey et al., 2024).

$$\mathrm{OXT}+\mathrm{OXTR}\rightleftarrows \mathrm{OXTRC}$$ (19)

where OXT is oxytocin concentration, OXTR is oxytocin receptor and OXTRC is oxytocin receptor complex.

Figure 2. Oxytocin receptor signalling model.

[OXT] and [OXTR] denote the oxytocin concentration in the myometrial compartment and the oxytocin receptor concentration on the surface of myometrial cells, respectively. [OXTRC] represents the oxytocin–oxytocin receptor complex, while [OXTRC]_int represents the internalized oxytocin–oxytocin receptor complex. [PLC_act] denotes the active form of phospholipase C_β stimulated by the Gq α‐subunit; PIP₂ is phosphatidylinositol 4,5‐bisphosphate; and DAG and IP₃ are diacylglycerol and inositol 1,4,5‐trisphosphate, respectively.

This binding process is regulated by the dissociation rate k _off and the association rate k _on, which together determine the binding affinity (k _d = k _off/k _on) (Monga et al., 1996). A lower $K_{\mathrm{d}}$ value indicates a higher binding affinity, resulting in a more stable complex, whereas a higher $K_{\mathrm{d}}$ value reflects a weaker binding capability (Monga et al., 1996). Reported values in the literature show considerable variability. Dubey et al. (2024) performed a meta‐analysis of studies reporting OXTR binding, finding $K_{\mathrm{d}}$ values ranging from 0.56 nm to 9.32 nm, with an average of approximately 1.48 nm, indicating high receptor affinity. For human myometrial cells reported kinetic parameters include: $k_{\mathrm{on}}$ = 6.8×10⁵ L·mol⁻¹·min⁻¹ and $k_{\mathrm{off}}$ = 0.0011 min⁻¹; $k_{\mathrm{on}}$ = 8.8×10⁶ L·mol⁻¹·min⁻¹ and $k_{\mathrm{off}}$ = 0.005 min⁻¹ ($K_{\mathrm{d}}$ = 0.56 nm) (Gulliver, 2021). The highest k _on of 4×10⁷ L·mol⁻¹·min⁻¹ was reported by Pliska and Jutz (2018). Literature indicates that $k_{\mathrm{on}}$ increases progressively throughout pregnancy and reaches its peak during the active phase of labour (Gulliver, 2021). In this study to reproduce uterine contractions during active labour, we set $k_{\mathrm{on}}$ = 4×10⁷ L·mol⁻¹·min⁻¹, $k_{\mathrm{off}}$ = 0.0224 min⁻¹, resulting in $K_{\mathrm{d}}$ = 0.56 nm, consistent with high‐affinity receptor binding.

In vivo, activated OXTR undergoes rapid desensitization, involving β‐arrestin‐mediated uncoupling from G proteins followed by receptor internalization (Fig. 2). Desensitization is the process by which a receptor's responsiveness to a ligand decreases after prolonged exposure, and in the case of OXTR, it involves GRK‐mediated phosphorylation of the receptor promotes binding of β‐arrestins to the phosphorylated receptor, thereby blocking its interaction with G proteins (Fig. 2) (Kim et al., 2024). Internalization is the subsequent removal of the oxytocin–oxytocin receptor complex (OXTRC) from the cell surface into the cell. Internalized OXTRC undergo dissociation within the cell, and the released OXTRs are recycled back to the cell membrane, thereby restoring receptor function (Fig. 2) (Kim et al., 2024). Desensitization and internalization of OXTRs are crucial mechanisms for modulating receptor signalling to prevent cells from overstimulation during prolonged exposure to oxytocin (Kim et al., 2024). In the present model we did not explicitly separate membrane desensitization from internalization; instead receptor internalization was used as the main kinetic representation of OXTR desensitization, which exhibits non‐linear, concentration‐dependent kinetics that can be described using Michaelis–Menten kinetics (Kim et al., 2024). It is assumed that receptor recycling to the membrane $k_{\mathrm{rec}}$ occurs at the same rate as internalization $k_{\mathrm{int}}$, maintaining a steady‐state equilibrium (Kim et al., 2024). In the myometrium internalized OXTRC may also undergo irreversible degradation. In the model implementation we followed the receptor‐binding framework of Dubey et al. (2024) and explicitly incorporated (i) membrane‐level degradation and internalization of the complex, and (ii) receptor recycling. The rates of OXTRC internalization and receptor recycling were modelled according to Kim et al. (2024), as follows:

$$\begin{array}{ccc}\hfill \frac{d{C}_{\mathrm{oxtr}}}{dt}& =& -k_{\mathrm{on}}·C_{\mathrm{oxt}}·C_{\mathrm{oxtr}}+k_{\mathrm{off}}·C_{\mathrm{oxtrc}}\hfill \\ & & +k_{\mathrm{rec}}·C_{\mathrm{oxtrc},\mathrm{int}}\hfill \end{array}$$ (20)

$$\begin{array}{ccc}\hfill \frac{d{C}_{\mathrm{oxtrc}}}{dt}& =& k_{\mathrm{on}}·C_{\mathrm{oxt}}·C_{\mathrm{oxtr}}-k_{\mathrm{off}}·C_{\mathrm{oxtrc}}\hfill \\ & & -k_{\mathrm{int}}·C_{\mathrm{oxtrc}}-k_{\mathrm{des}}·C_{\mathrm{oxtrc}}\hfill \end{array}$$ (21)

$$\frac{d{C}_{\mathrm{oxtrc},\mathrm{int}}}{dt}=k_{\mathrm{int}}·C_{\mathrm{oxtrc}}-k_{\mathrm{rec}}·C_{\mathrm{oxtrc},\mathrm{int}}$$ (22)

$$k_{\mathrm{int}}=\frac{k_{\mathrm{int},\max }·C_{\mathrm{oxtrc}}}{k_{\mathrm{phos}}+C_{\mathrm{oxtrc}}}$$ (23)

$$k_{\mathrm{rec}}=k_{\mathrm{int}}$$ (24)

where $k_{\mathrm{on}}$ is the association rate constant and $k_{\mathrm{off}}$ is the dissociation rate constant. $k_{\mathrm{int}}$ is the internalization rate of the OXTRC. $k_{\mathrm{rec}}$ is the receptor recycling rate (the rate at which receptors return to the cell surface). $C_{\mathrm{oxtr}}$ denotes the OXTR concentration, and $C_{\mathrm{oxtrc},\mathrm{int}}$ is the concentration of internalized OXTRC. $C_{\mathrm{oxt}}$ is the oxytocin concentration in the myometrium compartment. $k_{\mathrm{des}}$ is the OXTRC degradation rate. $k_{\mathrm{int},\max }$ is the maximal receptor internalization rate. $k_{\mathrm{phos}}$ is the OXTR phosphorylation constant. In this work we used $k_{\mathrm{int},\max }$= 1 min⁻¹ and $k_{\mathrm{phos}}$= 40 nm for β2AR (Kim et al., 2024). Willet et al. (2009) reported a 30% responsiveness after 30 s, giving rise to $k_{des}$= 2.41 min⁻¹. The relevant parameters are located in Table A1.

IP₃ production

After oxytocin binds OXTR in the myometrium, the OXTRC activates the Gq/11 G‐protein (Fig. 2). The Gq α‐subunit then stimulates phospholipase C_β (PLC_β), which hydrolyses PIP₂ in the plasma membrane. This reaction produces inositol 1,4,5‐trisphosphate (IP₃) (Fig. 2) (Navaratnarajah et al., 2017; Woll & Van Petegem, 2022). The formulation of IP₃ production and degradation dynamics in the cytosol is based on the Swillens–Mercan model (Yang & Jafri, 2015).

$$\mathrm{PL}{\mathrm{C}}_{\beta }+C_{\mathrm{oxtrc}}\to \mathrm{PL}{\mathrm{C}}_{\beta \mathrm{act}}$$ (25)

where

$$\begin{array}{ccc}\hfill \left[\mathrm{PLC}{\beta }_{\mathrm{act}}\right]& =& \left[\mathrm{PLC}{\beta }_{\mathrm{total}}\right]·\frac{C_{\mathrm{oxtrc}}}{C_{\mathrm{oxtrc}}+K_{\mathrm{d}}^{\mathrm{PLC}\beta }}=133.3·\hfill \\ & & \frac{C_{\mathrm{oxtrc}}}{C_{\mathrm{oxtrc}}+100}=0.02799\mathrm{nM}\hfill \end{array}$$ (26)

where $K_{\mathrm{d}}^{\mathrm{PLC}\beta }=100\mathrm{nM}$ (Navaratnarajah et al., 2017), $C_{\mathrm{oxtrc}}$ is 0.21 nm [the peak $C_{\mathrm{oxtrc}}$ concentration predicted by eqn (21) when A = 5.5 ng in eqn (9) and $C_{\mathrm{oxtr}}$ = 216 nm in eqn (20)]. PLCβ₃ interacts with its regulatory partners with sub‐micromolar affinity, for example ∼120–240 nM for Gαq providing experimentally grounded values for use in models of IP₃/Ca²⁺ signalling (Navaratnarajah et al., 2017). Quantitative immunoblot data indicated that the concentration of PLCβ₃ protein in human primary USMCs is of ∼17–20 ng·µg⁻¹ of total cell lysate protein. Using a molecular weight of ∼150 kDa (Zhong et al., 2008) assuming ∼1 mg·mL⁻¹ total protein supported by standard protocols (Bass et al., 2017), we obtain an estimated PLC_β3 concentration of approximately 133.3 nm.

$$\begin{array}{ccc}\hfill v_{\mathrm{PLC}}& =& k_{\mathrm{cat}}·\left[\mathrm{PLC}{\beta }_{\mathrm{act}}\right]=56.9\ast 0.02799\mathrm{nM}\hfill \\ & =& 1.59\mathrm{nM}·{\mathrm{s}}^{-1}\hfill \end{array}$$ (27)

where $k_{\mathrm{cat}}=56.9{\mathrm{s}}^{-1}$ (Falzone & MacKinnon, 2024) is the rate of PIP₂ turnover by PLC.

The concentration of IP₃ is given by the following formula:

$$\begin{array}{ccc}\hfill \mathrm{I}{\mathrm{P}}_3& =& \mathrm{PLC}{\beta }_{\mathrm{total}}·\frac{k_{\mathrm{cat}}·C_{\mathrm{oxtrc}}}{C_{\mathrm{oxtrc}}+K_{\mathrm{d}}^{\mathrm{PLC}\beta }}-\frac{v_5}{1+\frac{k_5^{\mathrm{I}{\mathrm{P}}_3}}{\mathrm{I}{\mathrm{P}}_3}}\hfill \\ & & -\frac{v_6}{\left(1+\frac{k_6^{\mathrm{I}{\mathrm{P}}_3}}{\mathrm{I}{\mathrm{P}}_3}\right)·\left(1+\frac{k_7^{\mathrm{I}{\mathrm{P}}_3}}{\mathrm{C}{\mathrm{a}}_i}\right)}\hfill \end{array}$$ (28)

Here $v_5$ is the maximal rate of dephosphorylation IP₃ by a 5‐phosphatase governed by the binding constant $k_5^{\mathrm{I}{\mathrm{P}}_3}$. The third term represents the rate of IP₃ phosphorylation to inositol 1,3,4,5‐tetrakisphosphate by a 3‐kinase with a maximal rate $v_6$ and binding constant $k_6^{\mathrm{I}{\mathrm{P}}_3}$ that is increased by $\mathrm{C}{\mathrm{a}}_i$ with a binding constant $k_7^{\mathrm{I}{\mathrm{P}}_3}$. $\mathrm{C}{\mathrm{a}}_i$ denotes the intracellular Ca²⁺ concentration. The relevant parameters are located in Table A2.

SR Ca²⁺ channels

IP₃ opens IP₃R (IP₃ receptor) on the SR, releasing Ca²⁺ into the cytosol (Fig. 3) (Woll & Van Petegem, 2022). Following Testrow et al. (2018) we modelled the SR as two compartments: an IP₃‐driven release pool and a SERCA‐mediated uptake pool. Release increases with IP3 and saturates at high levels; SERCA returns Ca²⁺ to the SR, restoring basal calcium levels. Flux formulations for release and uptake followed (Mandge & Manchanda, 2018; Pallippadan Johny, 2016; Shuai & Jung, 2003; Testrow et al., 2018), with an explicit passive SR leak per Shuai and Jung (2003). We implemented the Li–Rinzel model to faithfully reproduce intracellular calcium (Ca²⁺) oscillations (Li & Rinzel, 1994).

$$J_{\mathrm{rel}}=v_{\mathrm{I}{\mathrm{P}}_3\mathrm{R}}·{\left(\frac{\mathrm{I}{\mathrm{P}}_3}{d_4+\mathrm{I}{\mathrm{P}}_3}·\frac{\mathrm{C}{\mathrm{a}}_i}{d_5+\mathrm{C}{\mathrm{a}}_i}·h\right)}^3\left(\mathrm{C}{\mathrm{a}}_u-\mathrm{C}{\mathrm{a}}_i\right)$$ (29)

$$\begin{array}{c}{J}_{\mathrm{up}}=v_{\mathrm{SERCA}}·\frac{{{\mathrm{Ca}}_i}^2}{{k_{\mathrm{SERCA}}}^2+{{\mathrm{Ca}}_i}^2}\end{array}$$ (30)

$$h=\frac{\alpha }{\alpha +\beta }$$ (31)

$$\alpha =a·d_2·\frac{\mathrm{I}{\mathrm{P}}_3+d_1}{\mathrm{I}{\mathrm{P}}_3+d_3}$$ (32)

$$\beta =a·\mathrm{C}{\mathrm{a}}_i$$ (33)

$$J_{\mathrm{soc}}=k_{\mathrm{SR}\_\mathrm{leak}}·\left(\mathrm{C}{\mathrm{a}}_u-\mathrm{C}{\mathrm{a}}_i\right)$$ (34)

$$J_{\mathrm{t}}=J_{\mathrm{rel}}+J_{\mathrm{soc}}-J_{\mathrm{up}}$$ (35)

$$I_{\mathrm{eq}}=-z_{\mathrm{ca}}·F·\frac{J_{\mathrm{rel}}-J_{\mathrm{up}}+J_{\mathrm{soc}}}{Av·C_{\mathrm{m}}·\mathrm{buff}}$$ (36)

Figure 3. Oxytocin receptor signalling and uterine myocyte excitation–contraction coupling.

OXT represents oxytocin in the myometrium; OXTR represents the oxytocin receptor; PLC represents phospholipase C; PIP₂ represents phosphatidylinositol 4,5‐bisphosphate; DAG represents diacylglycerol; IP₃ represents inositol trisphosphate; IP₃R represents the inositol trisphosphate receptor; [Na⁺]_i represents the intracellular sodium ion concentration; [K⁺]_i represents the intracellular potassium ion concentration; [Cl⁻]_i represents the intracellular chloride ion concentration; [Ca²⁺]_i represents the intracellular calcium ion concentration; [Ca²⁺]_u represents the calcium ion concentration within the sarcoplasmic reticulum; $J_{\mathrm{rel}}$ represents the calcium release flux from the sarcoplasmic reticulum; $J_{\mathrm{up}}$ represents the calcium reuptake flux into the sarcoplasmic reticulum; $J_{\mathrm{soc}}$ represents the calcium flux through the SR leak channel; $I_{\mathrm{NSCC}}$ is the non‐selective cation current; $I_{\mathrm{NaK}}$ is the sodium‐potassium pump current; $J_{\mathrm{PMCA}}$ represents the plasma membrane Ca²⁺‐ATPase; $I_{\mathrm{CaT}}$ is the T‐type calcium channel current; $I_{\mathrm{Cl}(\mathrm{Ca})}$ is the calcium‐activated chloride current; $I_{\mathrm{Na}}$ is the sodium ion channel current; $I_{\mathrm{h}}$ is the hyperpolarization‐activated current; $I_{\mathrm{CaL}}$ is the L‐type calcium channel current; $I_{K(\mathrm{HERG})}$ is the delayed rectifier K⁺ current from the HERG channel; $I_{\mathrm{KCNQ}5}$ is the delayed rectifier K⁺ current from the KCNQ5 channel; $I_{\mathrm{KCNQ}4}$ is the delayed rectifier K⁺ current from the KCNQ4 channel; $I_{\mathrm{KCNQ}1}$ is the delayed rectifier K⁺ current from the KCNQ1 channel; $I_{K1}$ and $I_{K2}$ are potassium channel currents; $I_{K(\mathrm{Ca})}$ is the calcium‐activated potassium current; $I_{\mathrm{NaCa}}$ is the Na⁺/Ca²⁺ exchanger current; MLCK is myosin light chain kinase;$\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$ represents the attached phosphorylated cross‐bridge state; $\mathrm{AM}$ represents the attached dephosphorylated cross‐bridge state; $M$ represents the free cross‐bridge state; ${\mathrm{M}}_{\mathrm{p}}$ represents the phosphorylated cross‐bridge state; $k_1$ is the rate of conversion from $M$ to $M_{\mathrm{p}}$; $k_6$ is the rate of conversion from $\mathrm{AM}$ to $\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$; $k_2$ is the rate of conversion from $M\mathrm{p}$ to $M$; $k_3$ is the rate of conversion from $M_{\mathrm{p}}$ to $\mathrm{AMp}$; $k_4$ is the rate of conversion from $\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$ to $M_{\mathrm{p}}$; $k_5$ is the rate of conversion from $\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$ to $\mathrm{AM}$ and $k_7$ is the conversion rate from AM to M.

Here $J_{\mathrm{rel}}$ denotes the Ca²⁺ release flux from the SR, $J_{\mathrm{up}}$ denotes the Ca²⁺ uptake flux mediated by the SERCA pump, $J_{\mathrm{soc}}$ denotes the Ca²⁺ leak flux from the SR and $I_{\mathrm{eq}}$ represents the total ionic current associated with Ca²⁺ movement across the SR membrane. $\mathrm{C}{\mathrm{a}}_i$ is the cytosolic calcium concentration. $v_{\mathrm{I}{\mathrm{P}}_3\mathrm{R}}$ is the rate of IP₃ binding to receptors, and $h$ denotes the inactivation gating variable, whose dynamics are governed by the activation rate $\alpha$ and the inactivation rate $\beta$. Parameter $d_1$ is the dissociation constant for IP₃ binding to IP₃R, $d_2$ is a scaling factor controlling $\alpha$ and $d_3$ is the IP₃‐related dissociation constant appearing in $\alpha$. Parameter $d_5$ represents the dissociation constant of the Ca²⁺ activation site on IP₃R, whereas $d_4$ is a constant associated with IP3R activation that modulates the receptor's overall activation strength. $\mathrm{C}{\mathrm{a}}_u$ represent the calcium concentration in the SR, $v_{\mathrm{SERCA}}$ is the maximum uptake rate of the SERCA channel, $k_{\mathrm{SERCA}}$ is the rate constant for calcium uptake via the SERCA channel, $k_{\mathrm{SR}\_\mathrm{leak}}$ is the rate constant for calcium leakage, $z_{\mathrm{ca}}$ is the valence of calcium ions, $F$ is the Faraday constant, $Av$ is the volume‐to‐membrane area ratio of USMC, $C_{\mathrm{m}}$ is the membrane capacitance and $\mathrm{buff}$ is the buffering coefficient.

Using the original parameter set at an IP₃ concentration of 50 nm resulted in a strongly suppressed recovery rate and oscillation periods of several seconds. To obtain a more IP₃‐sensitive recovery regime: consistent with reported variability across IP₃ receptor isoforms and regulatory states, we increased parameter d ₁ from 0.13 to 0.5 µM and decreased $d_3$ from 0.94 to 0.3 µM. These adjustments increased the effective recovery rate by approximately one order of magnitude, producing oscillation periods in the experimentally observed ∼1 s range (Callamaras & Parker, 2000) while preserving the model's qualitative dynamics.

The maximal IP₃ receptor flux ($v_{\mathrm{I}{\mathrm{P}}_3\mathrm{R}}$) was tuned to balance cytoplasmic Ca²⁺ fluxes at rest, ensuring zero net SR Ca²⁺ flux ($J_{\mathrm{t}}$ ≈ 0 mM·ms^{− 1}; Mandge & Manchanda, 2018), while allowing transient dominance of Ca²⁺ release during contraction. Stable oscillatory behaviour was obtained for v _IP3R = 1.95 s^{− 1} and v _SERCA = 0.5 s^{− 1}. Specifically v_IP3R was experimentally determined to achieve stable oscillation, and k_{SR_leak =} 0.018 s⁻¹ was set to obtain balanced cytosolic flux ($J_{\mathrm{t}}$ ≈ 0 mM·ms^{− 1}; Mandge & Manchanda, 2018). The relevant parameters are located in Table A3.

Integrating oxytocin with the Tong USMC model

Aside from the mechanisms described above we use the previously published Tong et al. USMC model (Tong et al., 2014). SR Ca²⁺ release elevates cytosolic Ca²⁺, activating non‐selective cation channels (NSCCs) and the Na⁺/Ca²⁺ exchanger (NCX) to produce a modest depolarization (Noble et al., 2014). Once the threshold is reached voltage‐gated Ca²⁺ channels (L‐type/T‐type) open and trigger APs (Tong et al., 2014), thereby reproducing oxytocin‐induced myometrial cell excitation. Membrane voltage and total current arise from the sum of ionic currents and their time integration (Fig. 3). The total membrane current and the membrane potential are given as follows.

$$\begin{array}{ccc}\hfill I_{\mathrm{tot}}& =& I_{\mathrm{h}}+I_{\mathrm{Na}}+I_{\mathrm{CaL}}+I_{\mathrm{CaT}}+I_{\mathrm{Cl}\left(\mathrm{Ca}\right)}+I_{\mathrm{NSCC}}+I_{\mathrm{NaCa}}\hfill \\ & & +J_{\mathrm{PMCA}}+I_{\mathrm{NaK}}+I_{K\left(\mathrm{Ca}\right)}+I_{\mathrm{Ka}}+I_{K1}+I_{K2}\hfill \\ & & +I_{\mathrm{KCNQ}1}+I_{\mathrm{KCNQ}4}+I_{\mathrm{KCNQ}5}+I_{K\left(\mathrm{HERG}\right)}\hfill \end{array}$$ (37)

$$\frac{dV}{dt}=-\left(I_{\mathrm{tot}}+I_{\mathrm{eq}}\right)$$ (38)

where $I_{\mathrm{tot}}$ is the total ionic current, $I_{\mathrm{h}}$ represents the hyperpolarization‐activated current, $I_{\mathrm{Na}}$ denotes the sodium current, $I_{\mathrm{CaL}}$ is the L‐type calcium current and $I_{\mathrm{CaT}}$ signifies the T‐type calcium current. $I_{\mathrm{Cl}(\mathrm{Ca})}$ is identified as the calcium‐activated chloride current, $I_{\mathrm{NSCC}}$ as the non‐selective cation current and $I_{\mathrm{NaCa}}$ as the membrane current from the $\mathrm{N}{\mathrm{a}}^{+}/\mathrm{C}{\mathrm{a}}^{2+}$ exchanger. $J_{\mathrm{PMCA}}$ represents the plasma membrane $\mathrm{C}{\mathrm{a}}^{2+}$ ATPase, $I_{\mathrm{NaK}}$ is the sodium‐potassium pump current, $I_{K(\mathrm{Ca})}$ is known as the calcium‐activated potassium current, $I_{\mathrm{Ka}}$ as the A‐type transient potassium current, and $I_{\mathrm{K}1}$ and $I_{\mathrm{K}2}$ are the voltage‐dependent potassium currents. $I_{\mathrm{KCNQ}1}$, $I_{\mathrm{KCNQ}4}$ and $I_{\mathrm{KCNQ}5}$ represent delayed rectifying $K^{+}$ currents from KCNQ channels, and $I_{K(\mathrm{HERG})}$ represents delayed rectifying $K^{+}$ currents from HERG channels.

Active stress was modelled with a four‐state cross‐bridge scheme (Fig. 3):

$$\mathrm{MLCK}=\frac{\mathrm{MLC}{\mathrm{K}}_{\max }}{1+\frac{\mathrm{c}{\mathrm{a}}_i}{K_{\mathrm{MLCK}}}}$$ (39)

$$k_1=\frac{\mathrm{MLCK}}{1+{\left(\frac{K_{\mathrm{CaMLCK}}}{\mathrm{c}{\mathrm{a}}_i}\right)}^{\mathrm{nm}}}$$ (40)

$$\frac{dM}{dt}=-k_1·M+k_2·M_{\mathrm{p}}+k_7·\mathrm{AM}$$ (41)

$$\frac{d{M}_{\mathrm{p}}}{dt}=k_4·\mathrm{A}{\mathrm{M}}_{\mathrm{p}}+k_1·M-\left(k_2+k_3\right)·M_p$$ (42)

$$\frac{d\mathrm{AM}}{dt}=k_5·\mathrm{A}{\mathrm{M}}_{\mathrm{p}}-\left(k_6+k_7\right)·\mathrm{AM}$$ (43)

$$\frac{d\mathrm{A}{\mathrm{M}}_{\mathrm{p}}}{dt}=k_3·M_{\mathrm{p}}+k_6·\mathrm{AM}-\left(k_4+k_5\right)·\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$$ (44)

$$k_6=k_1$$ (45)

Here $\mathrm{MLCK}$ represents the concentration of myosin light chain kinase, $\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$ represents the attached phosphorylated cross‐bridge, $\mathrm{AM}$ represents the attached dephosphorylated cross‐bridge, $M$ represents the free cross‐bridge and $M_p$ represents the phosphorylated cross‐bridge. $K_1$ is the rate of conversion from $M$ to $M_{\mathrm{p}}$. $K_6$ is the rate of conversion from $\mathrm{AM}$ to $\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$.

Assuming, at a given length/shortening velocity, a nearly constant average force per cross‐bridge and equal weighting of the attached phosphorylated and latch states ($\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$ and $\mathrm{AM}$), the active stress ($\sigma$) is proportional to the fraction of load‐bearing bridges:

$$\sigma =k_{\sigma }·\left(\mathrm{A}{\mathrm{M}}_{\mathrm{p}}+\mathrm{AM}\right)·\lambda$$ (46)

Here $k_{\sigma }$ is a calibration coefficient used to map the phosphorylation proportion to tissue level stress (Pa). In this study we set $k_{\sigma }=14000\mathrm{Pa}$, based on the whole‐region mean of all four stages in Fig. 3 of Vila Pouca et al. (2019). $\lambda$ = 0.0075 was used to convert Pa to mmHg. The relevant parameters are located in Table A4.

Simulation experiment design

To evaluate the model's sensitivity to oxytocin we first compared the model‐predicted dose–response of oxytocin‐modulated cytosolic Ca²⁺ with previously reported experimental data (Fig. 4), thereby assessing whether the model reproduces the overall trend and sensitivity within the tested concentration range. While keeping the binding affinity constant we examined how varying $k_{\mathrm{on}}$ and OXTR concentration shifts the position and shape of the dose–response curve, and adjusted k _off accordingly to satisfy the $K_{\mathrm{d}}$ constraint. Oxytocin was scanned over 0.01–1000 nm (Willets et al., 2009; Dubey et al., 2024), and EC₅₀ (the oxytocin concentration required to elicit 50% of the maximal effect) was used as the primary metric.

Figure 4. Dose–response curve of intracellular Ca²⁺ concentration of oxytocin concentration.

(A) obtained under different $k_{\mathrm{on}}$ conditions and compared with the experimental measurements reported by Willetts et al. (2009) and Dubey et al. (2024); (B) obtained under different receptor concentrations.

Next we simulated the complete cascade from oxytocin secretion to USMC excitation contraction output to evaluate model accuracy. We then extracted venous oxytocin, intracellular Ca²⁺, membrane potential amplitude, stress and contraction duration, and benchmarked these outputs against clinically reported typical ranges to assess physiological plausibility.

To investigate how oxytocin release magnitude modulates USMC excitability, we increased the total amount of a single oxytocin pulse stepwise while holding all other parameters constant, and computed contraction duration and Montevideo units (MVU) for each simulation. MVU was defined as the number of contractions within 10 min multiplied by the difference between peak stress and resting stress for each contraction (Uvnäs‐Moberg et al., 2019).

We performed a local sensitivity analysis covering all parameters appearing in the governing equations of Sections oxytocin release, oxytocin binding, oxytocin elimination, IP₃ production and SR Ca²⁺ channels, together with key maternal physiological covariates (gestational age, body weight and $f_{u,p}$). Unless otherwise specified, each parameter was perturbed by ±10% around its nominal value (Mi et al., 2024). For parameters with literature‐reported bounds, we used the corresponding ranges: $f_{\mathrm{u},\mathrm{p}}$= 0.4–0.9, $GA$ = 28–40 weeks (late pregnancy) and $K_{\mathrm{d}}^{\mathrm{PLC}\beta }$ = 100–200 nm. Parameter influence on the key output (peak stress) was quantified using normalized sensitivity coefficients (|NSC|) (Mi et al., 2024), yielding a sensitivity ranking and identifying dominant determinants. The oxytocin transport rate was discussed separately in the preceding paragraph because it directly governs cross‐compartment delivery to the uterine target site; nevertheless it was also included in the sensitivity analysis parameter set.

Because there exist different types of myometrial Aps in uterine myometrium cell, we also attempted to generate the plateau type to further validate the model. Plateau‐type APs arise from a balance between inward Ca²⁺ currents and outward K⁺ currents. To improve this balance the extracellular potassium concentration ($K\circ$) was reduced from 6.0 to 5.4 mm. This adjustment shifts the potassium equilibrium potential to more negative values, increases the driving force for K⁺ efflux and enhances repolarization, thereby promoting the generation of a stable plateau‐type AP. Because the oxytocin‐mediated inward current produced by pulsatile stimulation is considerably smoother than that generated by an externally applied current step, the half‐effect concentration governing Ca²⁺‐dependent inactivation of the L‐type Ca²⁺ current ($K_{\mathrm{m},\mathrm{caL}}$) was reduced from 1.0 to 0.6 µm. This modification increases the sensitivity of L‐type Ca^{2 +} channels to intracellular Ca²⁺, thereby strengthening Ca²⁺‐dependent inactivation. The values of both $K\circ$ and $K_{\mathrm{m},\mathrm{caL}}$ were selected with reference to the uterine myocyte model developed by Testrow et al. (2018). Finally pituitary oxytocin release was increased from 5.5 to 7.0 ng per pulse to provide sufficient oxytocin‐mediated stimulation for generating plateau‐type APs.

Statistical analysis

This study was based on a deterministic computational modelling framework rather than repeated experimental measurements. Therefore no experimental group comparisons or inferential statistical tests were performed. Accordingly no P values, confidence intervals or summary statistics for experimental replicates are reported.

Results

Figure 4 summarizes the simulated dose–response relationship between oxytocin concentration and the model output (normalized response), under different settings of $k_{\mathrm{on}}$ and OXTR abundance. In Fig. 4A , our simulated curves (with k _off adjusted to maintain a constant k _d) are shown together with literature‐reported dose–response curves from Willets et al. (2009) and Dubey et al. (2024). In Fig. 4B we further illustrate how varying OXTR concentration shifts the dose–response curve. Open and filled markers indicate the threshold concentration and EC50, respectively, and the corresponding vertical dashed lines project these values onto the concentration axis. Increasing $k_{\mathrm{on}}$ shifted the curve leftward: when $k_{\mathrm{on}}$= 1×108 L·mol⁻¹·min⁻¹, the threshold was approximately $0.15$ nM and EC50 was $\sim 2.31$ nM; when $k_{\mathrm{on}}$= 4×107 L·mol⁻¹·min⁻¹, the threshold was $\sim 0.35$ nM and EC50 was $\sim 5.65$ nM. These EC50 values fall within the range reported by Willets et al. (2009) (2.91 nm at OXTR = 63.7 nm) and Dubey et al. (2024). (14.5 nm at OXTR = 254 nm). Consistently increasing OXTR concentration also produced a leftward shift with a reduced EC50 (Fig. 4B ).

Figure 5 schematically summarizes an example of oxytocin release from the posterior pituitary, systemic distribution, receptor binding in the uterine myometrium and downstream excitation–contraction coupling in USMCs. Posterior pituitary oxytocin secretion was modelled as a train of 40 Gaussian pulses (peak amplitude 0.11 ng, σ = 20 ms, AUC = 5.5 ng) delivered at 8.3 Hz, resulting in a burst duration of ∼5 s, consistent with the reported burst‐firing time course of oxytocinergic neurons (Yaguchi et al., 2023) (Fig. 5A , oxytocin release). Oxytocin was then rapidly transported to the venous pool via cerebral blood flow (Fig. 5A , C _oxt, venous), resulting in a concentration peak of 88 pg·mL⁻¹. The sudden increase in oxytocin in the venous circulation resulted in a transiently higher venous concentration than arterial, lasting approximately 2.5 s. Subsequently continuous drug removal led to higher oxytocin concentrations in the maternal arterial circulation than in the venous circulation. The systemic oxytocin clearance rate was 5.09 L·min⁻¹, yielding a half‐life of about 2.04 min. Oxytocin then undergoes arteriovenous exchange through the cardiopulmonary circulation and is subsequently delivered via arterial blood to the myometrium (Fig. 5A , C _{oxt, myo}), achieving a peak myometrial concentration of ∼7 pg·mL⁻¹ with a time delay of 7.5 s. This latter is consistent with the predicted myometrial concentration in myometrium of ∼9 pg·mL⁻¹ for a venous peak of 88 pg·mL⁻¹ (partition coefficient: 0.256 and $f_{\mathrm{u},\mathrm{p}}$: 0.4). Overall the predicted systemic pharmacokinetic metrics (distribution volume, clearance, half‐life and venous concentration range), together with key downstream outputs (fetal umbilical concentrations, cytosolic Ca²⁺, membrane potential, peak stress, excitation duration and EC₅₀), are in line with previously reported values. A quantitative comparison between model predictions and literature‐reported ranges is summarized in Table 2, demonstrating that the simulated outputs fall within, or closely match, the corresponding experimental ranges across multiple scales.

Figure 5. Simulation results of oxytocin‐induced uterine smooth muscle excitability.

A, oxytocin release from the hypothalamus (oxytocin release), oxytocin concentration in the myometrium (C _{oxt, myo}), oxytocin concentration in the blood (C _{oxt, blood}), oxytocin concentration in the arterial blood (C _{oxt, a}) and oxytocin concentration in the venous blood (C _{oxt, v}); B, concentration of oxytocin–oxytocin receptor complexes (C _oxtrc) and inositol trisphosphate (IP₃); C, calcium release flux (J _rel), SERCA pump‐mediated calcium uptake flux (J _up), cytosolic calcium concentration (ca _i ), active stress (stress) and membrane potential (V _m).

Oxytocin rapidly binds to free OXTRs to form OXTR complexes (Fig. 5B , C _oxtrc) (Dubey et al., 2024), which in turn stimulate the generation of IP₃ with oscillations ranging from 35 to 60 nm (Fig. 5B , IP₃). The increase in IP₃ thereby triggers calcium release from the SR. Calcium flux is governed primarily by two processes: calcium efflux from the SR into the cytosol (Fig. 5C , J _rel) and calcium uptake into the SR mediated by the SERCA pump (Fig. 5C , J _up) (Testrow et al., 2018). The combined effects of these fluxes determine the net calcium current in the SR. Changes in intracellular ion concentrations cause mild membrane depolarization, which activates voltage‐dependent calcium channels, allowing further calcium influx into the cytosol. As a result cytosolic calcium concentration (Berridge, 2008) (Fig. 5C , ca _i ) rises from 0.1 to 0.4 µM. The increase in cytosolic calcium induces burst APs in USMC (Fig. 5C , Vm), with amplitudes ranging from −50 to 5 mV and a resting potential of −50 mV. Concurrently the increase in cytosolic calcium induces mechanical contraction of USMC, leading to a rise in active stress (Fig. 5C , stress), which reaches approximately 75 mmHg. These results indicate that the model can recapitulate oxytocin‐induced USMC excitability and its key physiological features. Furthermore the simulated membrane potential waveform closely matched experimental data, characterized by periodic APs with an individual duration of approximately 36.4 s.

Figure 6 shows how contraction duration and MVU change with increasing total oxytocin released. As the release amount increases, both contraction duration and MVU rise accordingly. Within the physiological contraction range MVU can reach up to ∼300 MVU; when contraction duration falls within 20–60 s, the model yields MVU values of approximately 150–250 MVU (Hauth et al., 1986).

Figure 6. Effects of total oxytocin release on contraction duration and uterine activity quantified by MVU.

A, uterus contraction duration. B, MVU.

To identify the key drivers of model output we performed a one‐at‐a‐time (OAT) sensitivity analysis and quantified parameter influence using the absolute |NSC|. Table 3 summarizes the sensitive parameters (|NSC|≥ 0.25; Mi et al., 2024) together with their |NSC| values and rankings, sorted in descending order of |NSC|. Overall the most sensitive parameters were predominantly associated with the OXTR signalling module. In contrast parameters in the P‐PBPK module generally exhibited moderate sensitivity. Among elimination‐related parameters, both the CAP‐mediated Michaelis–Menten kinetics and hepatic clearance exhibited sensitivity. Specifically the |NSC| values of $V_{\max }$ and $K_{\mathrm{m}}$ for CAPI were higher than those of hepatic clearance, whereas the corresponding CAPII parameters were less sensitive than hepatic clearance but still exceeded the sensitivity threshold and remained influential. Overall these findings are consistent with reports that enzymatic degradation is a highly efficient elimination route for oxytocin and that the liver is one of the major eliminating organs (Lozic & Ludwig, 2022).

Table 3.

Comparison between simulated and measured results

Parameter	Definition	|NSC|
$v_{\mathrm{I}{\mathrm{P}}_3\mathrm{R}}$	Rate of IP3 binding to IP3R	5.721
$P$	Oxytocin release period	5.534
$k_{\mathrm{des}}$	OXTRC degradation rate	5.39
$k_5^{\mathrm{I}{\mathrm{P}}_3}$	The binding constant governing IP3 dephosphorylation by 5‐phosphatase	5.376
$v_{\mathrm{SERCA}}$	The maximum uptake rate of SERCA channel	5.368
$v_5$	The maximal rate of IP3 dephosphorylation catalysed by IP3 5‐phosphatase	5.346
$k_{\mathrm{SR}\_\mathrm{leak}}$	Rate constant for calcium leakage	5.307
$C_{\mathrm{oxtrc}}$	OXTR concentration	5.23
$K_{\mathrm{m},\mathrm{CAPI}}$	Michaelis constant of CAPI	5.219
$V_{\max ,\mathrm{CAPI}}$	The maximum reaction rate of CAPI	5.192
$\mathrm{C}{\mathrm{a}}_u$	The calcium ions concentration in SR	5.127
$k_{\mathrm{on}}$	The association rate constant	5.114
$k_{\mathrm{cat}}$	The rate of PIP2 turnover by PLC	5.108
$\mathrm{PLC}{\beta }_{\mathrm{total}}$	Total PLCβ3 protein concentration	5.107
$A$	Amount of oxytocin release	5.096
$d_4$	Constant related to IP3 receptor activation	5.07
$d5$	Dissociation constant of the Ca2+ activation site on IP3R	3.924
$d_2$	Scaling factor controlling	3.841
$d_1$	Dissociation constant of the IP3‐binding site on IP3R	3.053
$d_3$	IP3‐related dissociation constant appearing	2.52
$\mathrm{GA}$	Gestational weeks	1.287
$k_{\mathrm{SERCA}}$	The rate constant for calcium uptake via SERCA channel	1.171
$K_{\mathrm{d}}^{\mathrm{PLC}\beta }$	Dissociation constant between OXTRC and PLCβ	0.999
${\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{m}}$	The clearance rate of oxytocin by maternal liver	0.689
$K_{\mathrm{m},\mathrm{CAPII}}$	Michaelis constant of CAPII	0.363
$V_{\max ,\mathrm{CAPII}}$	The maximum reaction rate of CAPII	0.387
$f_{u,p}$	The fraction of the substance that is unbound in the plasma	0.303
$\sigma$	Pulse width	0.282

Figure 7 shows the plateau type AP generated by increasing pituitary oxytocin release, and a balanced inward and backward current through $K_{\mathrm{m},\mathrm{caL}}$ and $K\circ$. The plateau type AP was characterized by a prominent initial spike followed by a sustained depolarized plateau, during which the membrane potential remained between approximately −35 and −30 mV (Parkington et al., 2025).

Figure 7. Simulation results of oxytocin‐induced plateau type action potentials using pituitary oxytocin release = 7 ng, ${\mathit{K}}_{\mathbf{m},\mathbf{caL}}$= 0.6 µm, $K\circ$= 5.4 mm .

From top to bottom, the panels show the pituitary oxytocin release rate (oxytocin release), maternal blood oxytocin concentrations (C _{oxt, blood}), where C _{oxt, v} and C _{oxt, a} represent the maternal venous and arterial oxytocin concentrations, respectively, cytosolic Ca^{2 +} concentration (ca _i ) and membrane potential (V _m).

Discussion

Multiscale PBPK‐PD model

In this work we propose a novel mechanistic framework to describe oxytocin‐induced uterine excitation and contraction. The model integrates a maternal–fetal PBPK framework to characterize oxytocin distribution and clearance across organs with OXTR activation and the resulting IP₃ generation, which triggers calcium release from the SR and ultimately leads to uterine excitation and contraction. This model reproduces not only the long bursting phenotype but also the plateau type AP characterized by a prominent initial spike followed by a sustained depolarized phase (Inoue et al., 1990; Kawarabayashi et al., 1990; Nakao et al., 1997; Parkington et al., 2025). Key model predictions included a plasma half‐life of 2.04 min (Knox et al., 2024), a systemic clearance of 5.09 L·min⁻¹ (Thornton et al., 1990), a peak maternal plasma oxytocin concentration of 88 pg·mL⁻¹, umbilical arterial and venous oxytocin concentrations of 15.8 and 1.8 pg·mL⁻¹ (Buckley et al., 2023; Nathan et al., 2021), respectively, a contraction duration of 36.4 s (Rhomadona et al., 2019), and an MVU of 219 mmHg (Cahill et al., 2024); all were within reported ranges in the literature.

Several mathematical and computational models have been developed to describe different aspects of oxytocin physiology, although these efforts remain largely fragmented across scales. Pharmacokinetic models, typically formulated as one or two compartment systems, have been used to characterize oxytocin clearance, half‐life and plasma concentration profiles during labour induction and postpartum administration (Fuchs, 1983; Robinson et al., 2003). More recently limited pregnancy PBPK frameworks have incorporated hormonal dynamics, but explicit maternal–fetal oxytocin PBPK models remain scarce. At the neuroendocrine level computational models of hypothalamic oxytocin neuron networks have described burst firing, synchronization and pulsatile hormone release, particularly in the context of lactation and parturition (Douglas et al., 2001; Leng & Brown, 1997; Wang & Hatton, 2005). At the cellular level receptor‐mediated Gq/PLC/IP₃/Ca²⁺ signalling cascades have been modelled in smooth muscle and myometrial cells to investigate calcium oscillations and contractile activation, although these models are typically generic GPCR frameworks rather than oxytocin‐specific systems (Dupont et al., 2011; Keizer & Levine, 1996). Finally uterine electrophysiology and biomechanical models have been developed to simulate myometrial electrical activity and contractile force generation, often using phenomenological calcium inputs rather than mechanistic endocrine coupling. To date an integrated multiscale framework linking neuroendocrine secretion, systemic maternal–fetal PK, intracellular signalling and uterine biomechanics has not been reported (Rihana et al., 2009; Young, 1997).

Based on organ‐specific tissue composition, we estimated partition coefficients and clearance parameters that were consistent with reported systemic clearance rates and plasma half‐life of oxytocin. Using reported posterior pituitary oxytocin secretion characteristics (magnitude, firing rate and duration), the model reliably reproduced typical maternal venous concentration peaks (∼88 pg·mL^{− 1}) and umbilical venous and arterial concentrations. Both resting and contraction‐induced IP₃ levels were consistent with existing experimental data. Simulated uterine contraction duration, burst frequency (≈1 spike·s⁻¹) and generated stress fell within physiological ranges.

Organ‐specific tissue composition was used to estimate partition coefficients and clearance parameters, reproducing reported systemic clearance and plasma half‐life. Using literature‐derived posterior pituitary secretion profiles (magnitude, firing rate and duration), the model accurately predicted maternal venous concentration peak (∼88 pg·mL^{− 1}), which has been shown to range from 20 to 700 pg·mL^{− 1} (Uvnäs‐Moberg et al., 2019). Reported umbilical artery oxytocin concentrations (29.8 ± 7.5 pg·mL^{− 1}) and umbilical vein concentrations (16.1 ± 5.9 pg·mL^{− 1}) in caesarean non‐labour women, as well as the broader reported ranges (15–40 pg·mL^{− 1}(Buckley et al., 2023; Nathan et al., 2021) in the umbilical artery and 4–12 (Buckley et al., 2023; Nathan et al., 2021) pg·mL^{− 1} in the umbilical vein), were successfully reproduced by the model, with deviations of approximately 14 pg·mL^{− 1}, falling within the reported variability (0–20 pg·mL^{− 1}; Buckley et al., 2023; Nathan et al., 2021). The higher umbilical artery concentration relative to umbilical vein concentration suggests placental uptake and transport as a potential pathway from fetal to maternal circulation. Both resting and contraction‐induced IP₃ levels were consistent with existing experimental data. Simulated uterine contraction duration, burst frequency (≈1 spike·s^{− 1}) and generated stress as well MVU fell within physiological ranges. The model is configurable, with key biological and pharmacological parameters – including OXTR expression, receptor affinity and pulsatile oxytocin release – readily parameterized to support scenario‐based simulations under diverse physiological and therapeutic conditions.

We found that the model is highly sensitive to the oxytocin association rate and OXTR concentration. Both parameters may shift the dose–response curve leftward, giving rise to enhanced excitability. Literature showed a great variability, with k _on ranging from 6.8·10⁵ M⁻¹·min⁻¹ to 4·10⁷ M⁻¹·min⁻¹, with upper limits reaching 10⁸–10⁹ M⁻¹·min⁻¹, it may approach its physiological upper limit during labour (Pliska & Jutz, 2018). The literature shows that myometrial OXTR expression is markedly upregulated during pregnancy and exhibits substantial inter‐individual variability, increasing from a relatively low level in early pregnancy (629 fmol·mg⁻¹ protein) to late pregnancy (1510 fmol·mg⁻¹ protein), and reaching an even higher upper limit in some individuals (3673 fmol·mg⁻¹ protein) (Fuchs, 1983). This increased OXTR concentration is also related to enhanced uterine contractility as labour approaches. In addition OXTR distribution is heterogeneous, meaning that not all regions have the same probability of initiating uterine excitation and contraction, although this hypothesis still needs to be experimentally validated.

Limitations of the study and future works

This study developed a multiscale dynamic PBPK‐PD model. It captures the full process from endogenous oxytocin release to USMC excitation. The model is used to systematically characterize oxytocin distribution in the body and its mechanisms of action on USMCs. However several limitations remain. The model does not account for dynamic changes in ion channel expression and conductivity during pregnancy, which are known to play key roles in regulating uterine excitability throughout gestation (Sims et al., 1982). Unfortunately such data are currently unavailable. If dynamic changes in ion channel expression and tissue conductivity across pregnancy could be systematically incorporated within a 3D model, this would facilitate the development of a gestational age‐dependent model that could be more fully translated into clinical practice.

In addition although the pulsatile release of pituitary oxytocin falls within a physiologically reasonable range, its parameters may be influenced by multiple interacting factors, such as prostaglandins, oestrogen and progesterone withdrawal (Aguilar & Mitchell, 2010). It is also important to note that oxytocin is typically administered intravenously in clinical settings for labour induction or augmentation (Buckley et al., 2023; Uvnäs‐Moberg, 2024). However the primary aim of the present model is to characterize the physiological mechanisms by which endogenous circulating oxytocin regulates uterine excitation and contraction in vivo; therefore exogenous oxytocin administration has not yet been incorporated.

Another limitation of the present model is that it does not explicitly incorporate local oxytocin production from intrauterine tissues. Previous studies have shown that human amnion, chorion and decidual tissues can express oxytocin mRNA (Blanks et al., 2003; Chibbar et al., 1993). However prior reports have indicated that oxytocin concentrations in the amniochorion and placental decidua are relatively low (Chibbar et al., 1993; Mauri et al., 1995), suggesting that this local oxytocin system may contribute to labour activation mainly through interactions with prostaglandin related pathways (Chibbar et al., 1993). In contrast the PBPK‐PD framework developed in this study primarily focuses on circulating oxytocin exposure, namely oxytocin input associated with neurohypophyseal release and systemic distribution, and its effects on OXTR mediated USMC excitation contraction coupling. Therefore in the current model, the contribution of local intrauterine oxytocin production was expected to be limited and was not included as an independent source term.

Despite these limitations the model proposed in this study provides a systematic quantitative framework for understanding oxytocin distribution during pregnancy and its downstream effects on uterine electrophysiology and contraction. This framework also provides a foundation for future investigations into the mechanisms underlying preterm uterine contractions and for the development of tocolytic strategies. Future work should further extend the current pregnancy PBPK‐PD framework by explicitly modelling exogenous oxytocin administration, which may support individualized dose optimization and improve the model's clinical utility. In addition the amnion, chorion and decidua could be incorporated as local oxytocin‐producing compartments to further evaluate their contributions to the timing and amplification of labour‐associated uterine contractions. Furthermore coupling the current framework with a three‐dimensional tissue‐ or organ‐scale model would allow spatial heterogeneity in OXTR expression and uterine myocyte excitability to be represented, thereby enabling future investigation of uterine electrical activation and the emergence of pacemaker regions.

Conclusion

We developed and validated a multiscale PBPK‐PD model of oxytocin‐induced uterine excitation and contraction in term‐pregnant women, integrating systemic PK with OXTR signalling to mechanistically link oxytocin exposure to USMC excitability and contractile activation. The model precisely captures oxytocin dynamics, from its release from the posterior pituitary and distribution across organs (with partition coefficients and clearance rates accurately estimated), to receptor binding and complex formation with internalization and recycling, and finally to IP₃‐mediated calcium release from the SR, which drives the initiation and modulation of uterine electromechanical activity. It reliably reproduces key physiological parameters reported in the literature, including systemic clearance, oxytocin half‐life, venous and arteriovenous peak concentrations, and IP₃ levels, resulting in membrane APs that closely match observed amplitude and morphology. This framework provides mechanistic insight into abnormal preterm contractions and uterine atony and lays the foundation for optimizing oxytocin dosing during labour induction, as well as for developing novel models to assess the efficacy of tocolytic drugs, ultimately supporting improved maternal and fetal outcomes.

Competing interests

The authors declare no conflict of interest.

Author contributions

Y.Y.: Conceptualization, methodology, software, formal analysis, investigation, visualization, writing – original draft. C.B.: Methodology, software, validation, writing – review and editing. X.Z.: Formal analysis, investigation, visualization, writing – review and editing. A.C.: Conceptualization, methodology, supervision, writing – review and editing. M.G.: Investigation, data curation, validation. G.L.: Resources, funding acquisition. L.Y.: Investigation, validation, writing – review and editing. R.M.‐O.: Methodology, software, validation, writing – review and editing. Y.M.: Investigation, resources, project administration. D.H.: Conceptualization, supervision, project administration, funding acquisition, writing – review and editing. Y.Y.‐L.: Conceptualization, methodology, supervision, project administration, funding acquisition, writing – review and editing.

Funding

This work was supported by the National Natural Science Foundation of China (12402350, U20A20388), the Beijing Natural Science Foundation (1262001), the National Foreign Experts Program (H20240220), the Spanish Ministry of Science and Innovation and the European Regional Development Fund, State Plan for Scientific, Technical and Innovation Research 2021–2023 (PID2021‐124038OB‐I00) and 2024–2027 (PID2024‐159119OB‐I00) and INBIO2025 (AP2025‐01), and the Beijing Postdoctoral Science Foundation (2025‐ZZ‐18) and the Fundamental Research Funds for Beijing Municipal Universities (312000546325001).

Generative AI statement

OpenAI ChatGPT was used solely to assist with English language polishing, grammatical correction and literature searches. All AI assisted text was reviewed and revised by the authors, and all retrieved references and related scientific information were independently verified against the original sources. The authors take full responsibility for the accuracy and integrity of the manuscript.

Supporting information

Peer Review History

Biography

Yongxiu Yang is a PhD student in biomedical engineering at Beijing University of Technology, China, under the supervision of Prof. Dongmei Hao and Prof. Yiyao Ye‐Lin. With a background in computer engineering she developed a strong interest in computational physiology and maternal health research during her doctoral training. Her research focuses on multiscale uterine electrophysiology, PBPK‐PD modelling and electrophysiological signal analysis.

A $K_{\mathrm{p},\mathrm{u}}$ calculations

Oxytocin is a cyclic nonapeptide. It has both basic and acidic residues. It has multiple ionizable groups and no single dominant pKa. Its net ionization depends on pH. At physiological pH (7.0–7.4), its net charge is near zero. It is neither a strong acid nor a strong base. Thus electrostatic interactions with acidic phospholipids or extracellular proteins are limited. Its tissue distribution is driven mainly by peptide transport, receptor binding and enzymatic degradation. Acid–base partitioning is not the main factor. Oxytocin has a molecular weight of ∼1007 Da and a logP of about −3 to −4, and so it is highly hydrophilic. Passive transmembrane diffusion is unlikely, and so the drug distribution is governed by the distribution of extracellular fluid. Due to the high hydrophilicity and low lipophilicity of oxytocin, we made the following assumptions in the main text:

1. Intracellular accumulation of oxytocin is negligible. Oxytocin is mainly distributed in the interstitial fluid, with no significant partition into cells, organelles or membrane lipids.

2. Trans‐epithelial active transport of oxytocin is negligible. Unbound oxytocin rapidly equilibrates between interstitial fluid and plasma, and the unbound concentrations in these two spaces are approximately equal.

3. Only the binding of oxytocin to soluble proteins in plasma and interstitial fluid is considered. Binding to membrane components and other tissue structures is ignored.

Under the extracellular‐fluid–dominated distribution assumption, a tissue is divided into three parts: the plasma volume fraction $f_{\mathrm{p}}$, the interstitial fluid fraction $f_{\mathrm{ISF}}$ and the intracellular fluid fraction f _ICF.

$$f_{\mathrm{p}}+f_{\mathrm{ISF}}+f_{\mathrm{ICF}}=1$$ (A1)

In each tissue compartment, we define three concentrations: protein‐bound, unbound (free) and total. The total concentration equals the sum of bound and unbound concentrations. Because the substance is assumed not to cross the cell membrane, both bound and unbound concentrations in the intracellular part are zero. Thus the concentrations of interest are: $C_{\mathrm{p}}$ and $C_{\mathrm{p},\mathrm{u}}$: total and unbound concentrations in plasma. $C_{\mathrm{ISF}}$ and $C_{\mathrm{ISF},u}$: total and unbound concentrations in interstitial fluid. $C_{\mathrm{t}}$ and $C_{\mathrm{t},\mathrm{u}}$: total and unbound concentrations in the whole tissue.

Because, under Assumption 2, intracellular concentrations are zero, the tissue concentrations depend only on the plasma and interstitial components. Then:

$$C_{\mathrm{t}}=f_{\mathrm{ISF}}·C_{\mathrm{ISF}}$$ (A2)

$$C_{\mathrm{t},\mathrm{u}}=f_{\mathrm{ISF}}·C_{\mathrm{ISF},\mathrm{u}}$$ (A3)

And:

$${\mathrm{C}}_{\mathrm{ISF},\mathrm{u}}\approx C_{\mathrm{p},\mathrm{u}}$$ (A4)

Based on these concentrations, we define the unbound fraction of the substance.

$$f_{\mathrm{u},\mathrm{p}}=\frac{C_{\mathrm{p},\mathrm{u}}}{C_{\mathrm{p}}}$$ (A5)

$$f_{\mathrm{u},\mathrm{ISF}}=\frac{C_{\mathrm{ISF},\mathrm{u}}}{C_{\mathrm{ISF}}}$$ (A6)

that is

$$C_{\mathrm{p}}=\frac{C_{\mathrm{p},\mathrm{u}}}{f_{\mathrm{u},\mathrm{p}}}$$ (A7)

$$C_{\mathrm{ISF}}=\frac{C_{\mathrm{ISF},\mathrm{u}}}{f_{\mathrm{u},\mathrm{ISF}}}$$ (A8)

Here $f_{\mathrm{u},\mathrm{p}}$ denotes the unbound fraction of the substance in plasma, and $f_{\mathrm{u},\mathrm{ISF}}$ denotes the unbound fraction in interstitial fluid. According to the definition of the tissue‐to‐plasma partition coefficient ($K_{\mathrm{p}}$), tissue‐to‐unbound plasma partition coefficient ($K_{\mathrm{p},\mathrm{u}}$) and unbound tissue‐to‐unbound plasma partition coefficient ($K_{\mathrm{p},\mathrm{uu}}$) (Poulin & Theil, 2000), we can obtain:

$$K_{\mathrm{p}}=\frac{C_{\mathrm{t}}}{C_{\mathrm{p}}}$$ (A9)

$$K_{\mathrm{p},\mathrm{u}}=\frac{C_{\mathrm{t}}}{C_{\mathrm{p},\mathrm{u}}}=\frac{C_{\mathrm{t}}}{C_{\mathrm{p}}·f_{\mathrm{u},\mathrm{p}}}=\frac{K_{\mathrm{p}}}{f_{\mathrm{u},\mathrm{p}}}$$ (A10)

$$K_{\mathrm{p},\mathrm{uu}}=\frac{C_{\mathrm{t},\mathrm{u}}}{C_{\mathrm{p},\mathrm{u}}}=\frac{f_{\mathrm{ISF}}·C_{\mathrm{ISF},\mathrm{u}}}{C_{\mathrm{p},\mathrm{u}}}\approx f_{\mathrm{ISF}}$$ (A11)

By substituting into  eqns (A2), (A7) and (A8), we obtain:

$$\begin{array}{ccc}\hfill K_{\mathrm{p}}& =& \frac{C_{\mathrm{t}}}{C_{\mathrm{p}}}=\frac{f_{\mathrm{ISF}}·C_{\mathrm{ISF}}}{C_{\mathrm{p}}}=f_{\mathrm{ISF}}·\frac{\frac{C_{\mathrm{ISF},\mathrm{u}}}{f_{\mathrm{u},\mathrm{ISF}}}}{\frac{C_{\mathrm{p},\mathrm{u}}}{f_{\mathrm{u},\mathrm{p}}}}\hfill \\ & =& f_{\mathrm{ISF}}·\frac{f_{\mathrm{u},\mathrm{p}}}{f_{\mathrm{u},\mathrm{ISF}}}·\frac{C_{\mathrm{ISF},\mathrm{u}}}{C_{\mathrm{p},\mathrm{u}}}\hfill \end{array}$$ (A12)

By substituting into  eqn (A4)

$$K_{\mathrm{p}}\approx f_{\mathrm{ISF}}·\frac{f_{\mathrm{u},\mathrm{p}}}{f_{\mathrm{u},\mathrm{ISF}}}$$ (A13)

According to McNamara (1983) and Bruno (2016):

$$f_{\mathrm{u},\mathrm{ISF}}=\frac{1}{1+\mathrm{I}:\mathrm{P}·\frac{1-f_{\mathrm{u},\mathrm{p}}}{f_{\mathrm{u},\mathrm{p}}}}$$ (A14)

where I:P is the interstitial to plasma protein ratio.

By substituting  eqn (A11) into  eqn (A12), the $K_{\mathrm{p}}$ value is obtained as:

$$K_{\mathrm{p}}=f_{\mathrm{ISF}}·\frac{f_{\mathrm{u},\mathrm{p}}}{f_{\mathrm{u},\mathrm{ISF}}}=f_{\mathrm{ISF}}·\left(f_{\mathrm{u},\mathrm{p}}+\mathrm{I}:\mathrm{P}\left(1-f_{\mathrm{u},\mathrm{p}}\right)\right)$$ (A15)

For ‘Other’ compartment:

$$K_{\mathrm{p}\mathrm{other}}=\frac{V_{\mathrm{d}}-V_{\mathrm{p}}-{\sum }_i{V}_i·K_{pi}}{V_{\mathrm{other}}}$$ (A16)

Here $V_{\mathrm{d}}$ is the total volume of distribution, $V_{\mathrm{p}}$ is the plasma volume and $V_{\mathrm{other}}$ is the volume of the ‘other’ compartment. $V_i$ and ${K_{\mathrm{p}}}_i$ represent the volume and partition coefficient of each compartment i (excluding arterial and venous compartments). According to the literature (Dawood et al., 1980), the volume of distribution of oxytocin is 15 L (Nielsen et al., 2017).

According to  eqn (A9):

$$K_{\mathrm{p},\mathrm{u}}=\frac{K_{\mathrm{p}}}{f_{\mathrm{u},\mathrm{p}}}=\frac{f_{\mathrm{ISF}}·\left(f_{\mathrm{u},\mathrm{p}}+\mathrm{I}:\mathrm{P}\left(1-f_{\mathrm{u},\mathrm{p}}\right)\right)}{f_{\mathrm{u},\mathrm{p}}}$$ (A17)

B m‐PBPK model

From eqn (1) of Kapraun et al (2019). the mass of an average pregnant woman is given by

$$\begin{array}{ccc}\hfill M^{\mathrm{m}}\left(\mathrm{GA}\right)& =& 61103.0-10.614·\mathrm{GA}+29.161·\mathrm{G}{\mathrm{A}}^2\hfill \\ & & -0.50203·\mathrm{G}{\mathrm{A}}^3\hfill \end{array}$$ (B.1)

where $M^{\mathrm{m}}(\mathrm{GA})$ is the maternal mass (in g) and GA is the gestational age (in weeks).

The volume of an average pregnant woman is thus given by

$$V^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{M^{\mathrm{m}}\left(\mathrm{GA}\right)}{{\rho }^{\mathrm{m}}}$$ (B.2)

where $V^{\mathrm{m}}(\mathrm{GA})$ is the maternal volume (in mL) and ${\rho }^{\mathrm{m}}$ is the maternal reference density of 1.04 g·mL^−1.

B.1 Blood compartment in m‐PBPK

From eqn (5) of Kapraun et al (2019), the maternal plasma volume is given by

$$V_{\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)=2495.8+\frac{1240.6}{1.0+e^{-0.33138\left(\mathrm{GA}-17.813\right)}}$$ (B1.1)

where $V_{\mathrm{p}}^{\mathrm{m}}(\mathrm{GA})$ is maternal plasma volume (in mL).

From eqn (6) of Kapraun et al (2019) the maternal RBC volume is given by

$$V_{\mathrm{rbc}}^{\mathrm{m}}\left(\mathrm{GA}\right)=1516.9+\frac{327.04}{1.0+e^{-0.62555\left(\mathrm{GA}-21.452\right)}}$$ (B1.2)

where $V_{\mathrm{rbc}}^{\mathrm{m}}(\mathrm{GA})$ is maternal red blood cell volume (in mL).

Combining  eqns (B1.1) and (B1.2) gives,

$$V_{\mathrm{blood}}^{\mathrm{m}}\left(\mathrm{GA}\right)=V_{\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)+V_{\mathrm{rbc}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B1.3)

where $V_{\mathrm{blood}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal blood volume (in mL).

The haematocrit is thus given by eqn (24) of Kapraun et al. (2019), that is

$$H^{\mathrm{m}}\left(\mathrm{GA}\right)=39.192-0.10562,\mathrm{GA}-0.00071045,\mathrm{G}{\mathrm{A}}^2$$ (B.1.4)

where $H^{\mathrm{m}}(\mathrm{GA})$ is the maternal haematocrit as a percentage.

Now from Table 1 of Gaohua et al. (2012) we have

$$V_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{0.0205}{0.0205+0.0411}·V_{\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B1.5)

$$V_{\mathrm{ven}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{0.0411}{0.0205+0.0411}·V_{\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B1.6)

where $V_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial plasma volume (in mL) and $V_{\mathrm{ven}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal venous plasma volume (in mL).

From eqn (13) of Kapraun et al. (2019) the maternal cardiac output is given by

$$\begin{array}{ccc}\hfill Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& \frac{301.78}{3600.0}+\frac{3.2512}{3600.0}·\mathrm{GA}\frac{0.15947}{3600.0}\hfill \\ & & ·\mathrm{G}{\mathrm{A}}^2-\frac{0.0047059}{3600.0}·\mathrm{G}{\mathrm{A}}^3\hfill \end{array}$$ (B1.7)

where $Q_{\mathrm{co}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal cardiac output (in mL·ms⁻¹).

We also have

$$Q_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B1.8)

$$Q_{\mathrm{ven}}^{\mathrm{m}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B1.9)

where $Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial flow rate (in mL·ms⁻¹) and $Q_{\mathrm{ven}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal venous flow rate (in mL·ms⁻¹).

The oxytocin concentration in venous is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{ven}}^m\left(t\right)}{\mathrm{dt}}=\frac{{\sum }_i{Q}_i^m·C_{v_i}^m\left(t\right)-Q_{\mathrm{ven}}^m\left(\mathrm{GA}\right)·C_{\mathrm{ven}}^m\left(t\right)+R_{\mathrm{pituitary}}^m\left(\mathrm{GA},t\right)}{V_{\mathrm{ven}}^m\left(\mathrm{GA}\right)}\\ -\frac{C{L}_{\mathrm{ven}}^m\left(\mathrm{GA},t\right)·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{ven}}^m\left(t\right)}{V_{\mathrm{ven}}^m\left(\mathrm{GA}\right)}\end{array}$$ (B1.10)

where $Q_i^{\mathrm{m}}$ is the blood flow rate for organ $i\in$ {brain, fat, kidney, liver, heart, myometrium, placenta, other}; $C_{{\mathrm{v}}_i}^{\mathrm{m}}$ is the concentration of the substance in the maternal venous blood leaving organ i, as defined in eqn (5) of the main text; $C_{\mathrm{ven}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in maternal venous plasma and ${\mathrm{CL}}_{\mathrm{ven}}^{\mathrm{m}}(\mathrm{GA},t)$ is the clearance rate of oxytocin in the venous plasma calculated in section 2.1.3 of the main text. $R_{\mathrm{pituitary}}^{\mathrm{m}}(GA,t)$ represents the pituitary oxytocin release rate (section 2.1.2 in the main text).

The oxytocin concentration in arterial plasma is given by:

$$\frac{d{C}_{\mathrm{art}}^{\mathrm{m}}\left(t\right)}{dt}=\frac{Q_{\mathrm{aorta}}^{\mathrm{m}}·C_{v_{\mathrm{heart},\mathrm{l}}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-{\mathrm{CL}}_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA},t\right)·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)}$$ (B1.11)

where $Q_{\mathrm{aorta}}^{\mathrm{m}}$ is the blood flow rate for the maternal aorta, $C_{v_{\mathrm{heart},\mathrm{l}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the left heart (main text eqn 5), $C_{\mathrm{art}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in maternal arterial plasma and ${\mathrm{CL}}_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA},t)$ is the clearance rate of oxytocin in the arterial plasma as calculated in section 2.1.3.

B.2 Brain compartment in m‐PBPK

The maternal brain volume does not vary as a function of gestational age. To allow for scaling based on maternal body size we have used Tables 8 and 13 of Kapraun et al. (2019) that the maternal brain volume is given by

$$V_{\mathrm{brain}}^{\mathrm{m}}=\frac{1274.9·{\rho }_{\mathrm{brain}}^{\mathrm{m}}·V^{\mathrm{m}}\left(0\right)}{M^{\mathrm{m}}\left(0\right)}$$ (B2.1)

where $V_{\mathrm{brain}}^{\mathrm{m}}$ is the maternal brain volume (mL), and ${\rho }_{\mathrm{brain}}^{\mathrm{m}}$ = 1.04 g·mL⁻¹ is the brain tissue density. $V^{\mathrm{m}}(0)$ is the reference maternal volume at gestational week 0 (calculated from eqn (B.2) in mL). $M^{\mathrm{m}}(0)$ is the reference maternal body mass at gestational week 0 (calculated from  eqn (B.1) in g).

From eqn (15) of Kapraun et al. (2019) the maternal brain blood flow rate is given by

$$Q_{\mathrm{brain}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{17.0+\frac{\left(16.6-17.0\right)}{40.0}·\mathrm{GA}}{100.0}·Q_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B2.2)

where $Q_{\mathrm{brain}}^{\mathrm{m}}(\mathrm{GA})$ is maternal brain blood flow rate in mL·ms⁻¹, and $Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial flow rate given by  eqn (B1.8).

The oxytocin concentration in the brain compartment is given by:

$$\frac{d{C}_{\mathrm{brain}}^{\mathrm{m}}\left(t\right)}{dt}=\frac{Q_{\mathrm{brain}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{brain}}^{\mathrm{m}}·C_{v_{\mathrm{brain}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{brain}}^{\mathrm{m}}}$$ (B2.3)

where $C_{\mathrm{brain}}^{\mathrm{m}}(t)$ represents the oxytocin concentration in the maternal brain, and $C_{v_{\mathrm{brain}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the brain (main text eqn 5).

B.3 Fat compartment in m‐PBPK

From eqn (3) of Kapraun et al. (2019) the maternal fat mass is given by

$$M_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)=17067.0+149.37·\mathrm{GA}$$ (B3.1)

From eqn (4) of Kapraun et al. (2019) the maternal fat volume is given by

$$V_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{fat}}^{\mathrm{m}}}$$ (B3.2)

Here ${\rho }_{\mathrm{fat}}^{\mathrm{m}}$ = 0.950 g·mL⁻¹ is the fat tissue density.

From eqn (14) of Kapraun et al. (2019) the maternal fat blood flow rate is given by

$$Q_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{8.5+\frac{7.8-8.5}{40.0}·\mathrm{GA}}{100.0}·Q_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B3.3)

where $Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial flow rate given by  eqn (B1.8).

The oxytocin concentration in the fat compartment is given by:

$$\frac{d{C}_{\mathrm{fat}}^{\mathrm{m}}\left(t\right)}{dt}=\frac{Q_{\mathrm{fat}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{fat}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)}$$ (B3.4)

where$C_{\mathrm{fat}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in maternal fat, and $C_{{\mathrm{v}}_{\mathrm{fat}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving fat (main text eqn 5).

1. B.4 Gut compartment in m‐PBPK

The maternal gut volume does not vary as a function of gestational age. To allow for scaling based on maternal body size we have used Tables 8 and 13 of Kapraun et al. (2019) and the maternal gut volume is given by

$$V_{\mathrm{gut}}^{\mathrm{m}}=\frac{1111.0·{\rho }_{\mathrm{gut}}^{\mathrm{m}}·V^{\mathrm{m}}\left(0\right)}{M^{\mathrm{m}}\left(0\right)}$$ (B4.1)

where $V_{\mathrm{gut}}^{\mathrm{m}}$ is the maternal gut volume in mL, ${\rho }_{\mathrm{gut}}^{\mathrm{m}}$ = 1.045 g·mL⁻¹ is the maternal gut density, $V^{\mathrm{m}}(0)$ is the reference maternal body volume 0 weeks gestational age, in mL, given by eqn (1.68), and $M^{\mathrm{m}}(0)$ is the reference maternal body mass 0 weeks gestational age (in g), given by  eqn (B.1).

From eqn (18) of Kapraun et al. (2019) the maternal gut blood flow rate is given by

$$Q_{\mathrm{gut}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{17.0+\frac{12.5-17.0}{40.0}·\mathrm{GA}}{100.0}·Q_{\mathrm{art}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B4.2)

where $Q_{\mathrm{gut}}^{\mathrm{m}}(\mathrm{GA})$ is maternal gut blood flow rate (in mL·ms⁻¹), and $Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial flow rate given by  eqn (B1.8).

The oxytocin concentration in the gut compartment is given by:

$$\frac{d{C}_{\mathrm{gut}}^{\mathrm{m}}\left(t\right)}{dt}=\frac{Q_{\mathrm{gut}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{gut}}^{\mathrm{m}}·C_{v_{\mathrm{gut}}}^{\mathrm{m}}\left(t\right)}{V_{gut}^m}$$ (B4.3)

where $C_{\mathrm{gut}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in the maternal gut, and $C_{v_{\mathrm{gut}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the gut (main text eqn 5).

2. B.5 Kidney compartment in m‐PBPK

Maternal kidney volume does not vary with gestational age. To allow for scaling based on maternal body size we have from Tables 8 and 13 of Kapraun et al. (2019) that the maternal kidney volume is given by:

$$V_{\mathrm{kidney}}^{\mathrm{m}}=\frac{265.53·{\rho }_{\mathrm{kidney}}^{\mathrm{m}}·V^{\mathrm{m}}\left(0\right)}{M^{\mathrm{m}}\left(0\right)}$$ (B5.1)

where $V_{\mathrm{kidney}}^{\mathrm{m}}$ is the maternal Kidney volume in mL, ${\rho }_{\mathrm{kidney}}^{\mathrm{m}}$= 1.05 g·mL⁻¹ is the maternal kidney density, $V^{\mathrm{m}}(0)$ is the reference maternal body volume 0 weeks gestational age (in mL) given by  eqn (B.2) and $M^{\mathrm{m}}(0)$ is the reference maternal body mass 0 weeks gestational age (in g) given by  eqn (B.1).

From eqn (17) of Kapraun et al. (2019) the maternal kidney blood flow rate is given by

$$\begin{array}{ccc}\hfill Q_{\mathrm{kidney}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& \frac{53.248}{3600.0}+\frac{3.6447}{3600.0}·\mathrm{GA}-\frac{0.15357}{3600.0}\hfill \\ & & ·\mathrm{G}{\mathrm{A}}^2+\frac{0.0016968}{3600.0}·\mathrm{G}{\mathrm{A}}^3\hfill \end{array}$$ (B5.2)

where $Q_{\mathrm{kidney}}^{\mathrm{m}}(\mathrm{GA})$ is the kidney blood flow rate.

The oxytocin concentration in the kidney compartment is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{kidney}}^{\mathrm{m}}\left(t\right)}{\mathrm{dt}}=\frac{Q_{\mathrm{kidney}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{kidney}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{kidney}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{kidney}}^{\mathrm{m}}}\\ -\frac{{\mathrm{CL}}_{\mathrm{kidney}}^{\mathrm{m}}·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{kidney}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{kidney}}^{\mathrm{m}}}\end{array}$$ (B5.3)

where $C_{\mathrm{kidney}}^{\mathrm{m}}(t)$ denotes the oxytocin concentration in the maternal kidney, ${\mathrm{CL}}_{\mathrm{kidney}}^{\mathrm{m}}$ represents the clearance rate of oxytocin by the maternal kidney, calculated in section 2.1.3, and $C_{{\mathrm{v}}_{\mathrm{kidney}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the kidney (main text eqn 5).

B.6 Liver compartment in m‐PBPK

The maternal liver volume does not vary as a function of gestational age. To allow for scaling based on maternal body size we have from Tables 8 and 13 of Kapraun et al. (2019) that the maternal liver volume is given by

$$V_{\mathrm{liver}}^{\mathrm{m}}=\frac{1355.9·{\rho }_{\mathrm{liver}}^{\mathrm{m}}·V^{\mathrm{m}}\left(0\right)}{M^{\mathrm{m}}\left(0\right)}$$ (B6.1)

where $V_{\mathrm{liver}}^{\mathrm{m}}$ is the maternal liver volume in mL, ${\rho }_{\mathrm{liver}}^{\mathrm{m}}$ = 1.05 g·mL⁻¹ is the maternal liver density, $V^{\mathrm{m}}(0)$ is the reference maternal body volume 0 weeks gestational age (in mL) given by  eqn (B.2) and $M^{\mathrm{m}}(0)$ is the reference maternal body mass 0 weeks gestational age (in g) given by  eqn (B.1).

From eqn (17) of Kapraun et al. (2019), the maternal liver blood flow rate is given by $\begin{array}{c}{Q}_{\mathrm{liver}}^{\mathrm{m}}(\mathrm{GA})=\frac{27+\frac{20-27}{40.0}·\mathrm{GA}}{100.0}·Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})\end{array}$ (B6.2)where $Q_{\mathrm{liver}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal liver blood flow rate, and $Q_{\mathrm{art}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal arterial flow rate given by  eqn (B1.8).

The oxytocin concentration in the liver compartment is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{liver}}^{\mathrm{m}}\left(t\right)}{\mathrm{dt}}=\frac{Q_{\mathrm{iver}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-\left(Q_{\mathrm{liver}}^{\mathrm{m}}\left(\mathrm{GA}\right)+Q_{\mathrm{gut}}^{\mathrm{m}}\left(\mathrm{GA}\right)\right)·C_{{\mathrm{v}}_{\mathrm{liver}}}^{\mathrm{m}}}{V_{\mathrm{liver}}^{\mathrm{m}}}\\ -\frac{{\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{m}}·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{liver}}^{\mathrm{m}}\left(t\right)+Q_{\mathrm{gut}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{gut}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{liver}}^{\mathrm{m}}}\end{array}$$ (B6.3)

where $C_{\mathrm{liver}}^{\mathrm{m}}(t)$ is the oxytocin concentration in the maternal liver, and ${\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{m}}$ indicates the clearance rate of oxytocin by the maternal liver, calculated in section 2.1.3 of the main text. $C_{{\mathrm{v}}_{\mathrm{liver}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the liver (main text eqn 5).

B.7 Heart compartment in m‐PBPK

According to Table 1 in Levitt and Schnider (2005), heart tissue weight accounts for 4.7% of total body weight, and heart tissue blood flow accounts for 4.72% of total blood flow. Accordingly the heart tissue volume and perfusion flow were defined as:

$$M_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)=0.047·M^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B7.1)

$$V_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{{\rho }^{\mathrm{m}}}$$ (B7.2)

$$Q_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)=0.0472·Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B7.3)

Here $M_{\mathrm{heart}}^{\mathrm{m}}(\mathrm{GA})$ is the weight of the heart, $M^{\mathrm{m}}(\mathrm{GA})$ is maternal mass, $V_{\mathrm{heart}}^{\mathrm{m}}(\mathrm{GA})$ is the volume of the heart and $Q_{co}^{\mathrm{m}}(\mathrm{GA})$ is the maternal cardiac output.

The oxytocin concentration in the heart compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{heart}}^{\mathrm{m}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{heart}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{heart}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{heart}}^{\mathrm{m}}}\hfill \end{array}$$ (B7.4)

where $C_{\mathrm{heart}}^{\mathrm{m}}(t)$ is the oxytocin concentration in the maternal heart, and $C_{{\mathrm{v}}_{\mathrm{heart}}}^{\mathrm{m}}$ is the concentration of the substance in the venous blood leaving the heart (main text eqn 5).

B.8 Lung compartment in m‐PBPK

The maternal lung volume does not vary as a function of gestational age. To allow for scaling based on maternal body size, we have from Tables 8 and 13 of Kapraun et al. (2019) that the maternal lung volume is given by

$$V_{\mathrm{lung}}^{\mathrm{m}}=\frac{919.45·{\rho }_{\mathrm{lung}}^{\mathrm{m}}·V^{\mathrm{m}}\left(0\right)}{M^{\mathrm{m}}\left(0\right)}$$ (B8.1)

where $V_{\mathrm{lung}}^{\mathrm{m}}$ is the maternal lung volume (in mL), ${\rho }_{\mathrm{lung}}^{\mathrm{m}}$= 1.05g·mL⁻¹ is the maternal lung density, $V^{\mathrm{m}}(0)$ is the reference maternal body volume 0 weeks gestational age (in mL) given by  eqn (B.2) and $M^{\mathrm{m}}(0)$ is the reference maternal body mass 0 weeks gestational age (in g) given by  eqn (B.1).

The oxytocin concentration in the lung compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{lung}}^{\mathrm{m}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{co}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{ven}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{lung}}^{\mathrm{m}}}\hfill \end{array}$$ (B8.2)

where $C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{m}}$ is the concentration of the substance in the venous blood leaving the lung (main text eqn 5).

B.9 Placenta compartment in m‐PBPK

From eqn (8) of Kapraun et al. (2019) the placental volume is given by

$$V_{\mathrm{placenta}}\left(\mathrm{GA}\right)=\left\{\begin{array}{c}-1.7646·GA+0.91775·\mathrm{G}{\mathrm{A}}^2-0.011543·\mathrm{G}{\mathrm{A}}^3,\mathrm{GA}\ge 2\\ 0,\mathrm{GA}<2\end{array}\right.$$ (B9.1)

where $V_{\mathrm{placenta}}^{\mathrm{m}}(\mathrm{GA})$ is the placental volume in mL. To avoid negative volumes it is assumed that the placenta does not appear until 2 weeks of gestation.

From Dallmann et al. (2017) approximately 52.5% of the placenta is maternal tissue. Thus defining

$$F{V}_{\mathrm{placenta}}^{\mathrm{m}}=0.525$$ (B9.2)

$$V_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)=F{V}_{\mathrm{placenta}}^{\mathrm{m}}·V_{\mathrm{placenta}}\left(\mathrm{GA}\right)$$ (B9.3)

The placental mass $M_{\mathrm{pla}}^{\mathrm{m}}(\mathrm{GA})$ is:

$$M_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)=V_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)·{\rho }_{\mathrm{pla}}^{\mathrm{m}}$$ (B9.4)

From eqn (22) of Kapraun et al. (2019), the blood flow to the maternal placenta is

$$Q_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\left\{\begin{array}{c}0,\mathrm{GA}\le 3.6\\ \frac{0.8}{36.4}·\left(\mathrm{GA}-3.6\right)·0.01·\left(0.4+\frac{11.6}{40}·\mathrm{GA}\right)·Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right),\mathrm{otherwise}\end{array}\right.$$ (B9.5)

where $Q_{\mathrm{pla}}^{\mathrm{m}}(\mathrm{GA})$ is the blood flow to the maternal placenta, and $Q_{\mathrm{co}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal cardiac output.

The oxytocin concentration in the placenta compartment is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{pla}}^{\mathrm{m}}\left(t\right)}{\mathrm{dt}}=\frac{Q_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{pla}}}^{\mathrm{m}}\left(t\right)-k_{\mathrm{mf}}·C_{\mathrm{pla}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)}\\ +\frac{k_{\mathrm{fm}}·C_{\mathrm{pla}}^{\mathrm{f}}\left(t\right)-C{\mathrm{L}}_{\mathrm{pla}}^{\mathrm{m}}·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{pla}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)}\end{array}$$ (B9.6)

where $C_{\mathrm{pla}}^{\mathrm{m}}(t)$ is the oxytocin concentration in the maternal placenta, ${\mathrm{CL}}_{\mathrm{pla}}^{\mathrm{m}}$ is the clearance rate of oxytocin by the maternal placenta calculated in section 2.1.3 of the main text, $C_{{\mathrm{v}}_{\mathrm{pla}}}^{\mathrm{m}}$ is the concentration of the substance in the venous blood leaving the maternal placenta (main text eqn 5), $k_{mf}=15.17$ µL·min⁻¹·g⁻¹, reported in Malek et al. (1996), represents the rate of placental transfer of oxytocin from the mother to the fetus, $k_{\mathrm{fm}}=11.79$ µL·min⁻¹·g⁻¹, reported in Malek et al. (1996), represents the rate of placental transfer of oxytocin from the fetus to the mother.

B.10 Myometrium compartment in m‐PBPK

We divided the myometrium into two parts for modelling: the region in contact with the placenta (p) and not in contact with the placenta (np). Therefore we need to know the fraction of the myometrium that is covered by the placenta.

As well as the uterine wall (which contains the myometrium and endometrium) the uterus contains the ‘products of conception’, namely, the placenta, the fetus and the amniotic fluid.

From eqn (9) of Kapraun et al. (2019) the average volume of amniotic fluid in the uterus is

$$V_{\mathrm{amniotic}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{822.34}{1+{\mathrm{e}}^{-0.26988\left(\mathrm{GA}-20.150\right)}}$$ (B10.1)

where $V_{\mathrm{amniotic}}^{\mathrm{m}}(\mathrm{GA})$ is the amniotic fluid volume (in mL).

The mass of the amniotic fluid is thus given by

$$M_{\mathrm{amniotic}}^{\mathrm{m}}\left(\mathrm{GA}\right)={\rho }_{\mathrm{amniotic}}^{\mathrm{m}}·V_{\mathrm{amniotic}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B10.2)

where $M_{\mathrm{amniotic}}^{\mathrm{m}}(\mathrm{GA})$ is the amniotic fluid mass (in g), and ${\rho }_{\mathrm{amniotic}}^{\mathrm{m}}$= 1.01g·mL⁻¹ is the amniotic density.

The total internal volume of the uterus is given by

$$\begin{array}{ccc}\hfill V_{\mathrm{uterus}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& V_{\mathrm{placenta}}^{\mathrm{f}}\left(\mathrm{GA}\right)+V^f\left(\mathrm{GA}\right)\hfill \\ & & +V_{\mathrm{amniotic}}^{\mathrm{m}}\left(\mathrm{GA}\right)\hfill \end{array}$$ (B10.3)

where $V_{\mathrm{uterus}}^{\mathrm{m}}(\mathrm{GA})$ is the uterine volume in mL, and $V_{\mathrm{placenta}}^{\mathrm{f}}(\mathrm{GA})$ and $V^{\mathrm{f}}(\mathrm{GA})$ are the placenta and fetal volumes given in eqns (C7.2) and (C.2), respectively.

To compute relative volumes and areas, consider the volume of an ellipsoid in a box of size 2a, 2b and 2c is given by

$$V=\frac{4\pi abc}{3}$$ (B10.4)

If we now assume that the ellipsoid is a prolate spheroid [i.e. (a = b)], then the surface area is

$$S=2\pi a^2\left(1+\frac{c}{ae}{\sin }^{-1}\left(e\right)\right)$$ (B10.5)

where

$$e=\sqrt{1-\frac{a^2}{c^2}}$$ (B10.6)

Now Louwagie et al. (2021) measured the dimensions of the uterus as a function of gestational age. They found that the long axis increases by approximately (9.0 mm·week⁻¹), that is

$$L\left(\mathrm{GA}\right)=\left\{\begin{array}{cc}-24.865+8.976·\mathrm{GA}& \mathrm{GA}\ge 5\\ 20.015,& \mathrm{GA}<5\end{array}\right.$$ (B10.7)

where $L(\mathrm{GA})$ is the length of the long axis of the uterus (in mm). To avoid problems with negative numbers it is assumed that the uterus begins to grow only after 5 weeks of gestation.

The uterine ‘long’ radius is thus given by

$$c\left(\mathrm{GA}\right)=\frac{L\left(\mathrm{GA}\right)}{2}$$ (B10.8)

where $c(\mathrm{GA})$ is the uterine long radius (in mm) as a function of gestational age, and $L(\mathrm{GA})$ is the uterine length given by  eqn (B10.7).

If we assume that the uterus can be approximated as a prolate spheroid, then the short radius (a) can be determined by substituting  eqns (B10.3) and (B10.8) into  eqn (B10.4) and rearranging to give

$$a\left(\mathrm{GA}\right)=\sqrt{\frac{3·V_{\mathrm{uterus}}^{\mathrm{m}}\left(\mathrm{GA}\right)·1000}{4·\pi ·c\left(\mathrm{GA}\right)}}$$ (B10.9)

where $a(\mathrm{GA})$ is the uterine short radius (in mm) as a function of gestational age; the factor of 1000 converts from mL to mm³.

Once the uterine radius is known, then the uterine surface area can be determined from  eqns (B10.5) and (B10.6), that is

$$\begin{array}{ccc}\hfill S_{\mathrm{uterus}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& 2\pi a^2\left(\mathrm{GA}\right)\hfill \\ & & \left(1+\frac{c\left(\mathrm{GA}\right)}{a\left(\mathrm{GA}\right),\mathrm{e}\left(\mathrm{GA}\right)}{\sin }^{-1}\left(\mathrm{e}\left(\mathrm{GA}\right)\right)\right)\hfill \end{array}$$ (B10.10)

where

$$e\left(\mathrm{GA}\right)=\sqrt{1-\frac{a^2\left(\mathrm{GA}\right)}{c^2\left(\mathrm{GA}\right)}}$$ (B10.11)

In addition the placental area must be calculated. To compute the area covered by the placenta we can approximate it as a circular disk. A common assumption is that the thickness of the placenta (in mm) is approximately equal to the gestational age (in weeks). This has been confirmed (to a first approximation) by a more detailed measurement study by Karthikeyan et al. (2012). Thus we have

$$t_{\mathrm{placenta}}\left(\mathrm{GA}\right)=\mathrm{GA}$$ (B10.12)

And

$$S_{\mathrm{placenta}}\left(\mathrm{GA}\right)=\frac{1000·V_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{t_{\mathrm{placenta}}\left(\mathrm{GA}\right)}$$ (B10.13)

where $S_{\mathrm{placenta}}(\mathrm{GA})$ is the placental surface area in mm² and $V_{\mathrm{pla}}^{\mathrm{m}}(\mathrm{GA})$ are given in  eqn (B9.3), and the factor of 1000.0 is to convert from mL to mm³.

To compute the proportion of the uterus covered by the placenta, we use the relative areas of the placenta and the uterine wall. The fraction of the uterus covered by the placenta is to be calculated from

$$F{S}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{S_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{S_{\mathrm{uterus}}^{\mathrm{m}}\left(\mathrm{GA}\right)}$$ (B10.14)

According to Table 1 proposed by Abduljalil et al. (2012), the uterine mass can be obtained as follows:

$$M_{\mathrm{uterus}}^{\mathrm{m}}\left(GA\right)=80+8.293·\mathrm{GA}+0.3546·\mathrm{G}{\mathrm{A}}^2$$

We approximate the myometrial mass by this value. For the whole myometrium its volume is equal to its mass divided by its density, that is

$$V_{\mathrm{myo}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{uterus}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{{\rho }^{\mathrm{m}}}$$ (B10.15)

Here ${\rho }^{\mathrm{m}}$ is the average maternal density during pregnancy.

According to  eqn (B10.14) we can therefore define the volumes of the P and nP as follows:

$$V_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)=F{S}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)·V_{\mathrm{myo}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B10.16)

$$V_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\left(1-F{S}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)\right)·V_{\mathrm{myo}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B10.17)

From eqn (64) of Dallmann et al. (2017) the blood flow through the uterine arteries is

$$Q_{\mathrm{UA}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{0.0159}{1+21.8{\mathrm{e}}^{-0.159\mathrm{GA}}}-0.0003283$$ (B10.18)

where $Q_{UA}^m(\mathrm{GA})$ is the flow through the uterine arteries (in mL·ms⁻¹) as a function of gestational age.

Thus we define the uterine blood flow fraction as follows:

$$F{Q}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{Q_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{Q_{\mathrm{UA}}^{\mathrm{m}}\left(\mathrm{GA}\right)}$$ (B10.19)

Thus the blood flows to the P and nP are defined as follows:

$$Q_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)=Q_{\mathrm{pla}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B10.20)

$$Q_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\left(1-F{Q}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)\right)·Q_{\mathrm{UA}}^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B10.21)

The oxytocin concentration in the p and np is given by:

$$\begin{array}{ccc}\hfill \frac{d{C}_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(t\right)}{\mathrm{dt}}& =& \frac{Q_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}·C_{v_{\mathrm{myo},\mathrm{p}}}^{\mathrm{m}}\left(t\right)-{\mathrm{CL}}_{\mathrm{myo}}^{\mathrm{m}}·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}}\hfill \\ & & \frac{-{k_{\mathrm{p}}}_{\mathrm{np}}·C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(t\right)+{k_{\mathrm{np}}}_{\mathrm{p}}·C_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}}\hfill \end{array}$$ (B10.22)

$$\begin{array}{ccc}\hfill \frac{d{C}_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(t\right)}{\mathrm{dt}}& =& \frac{Q_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}·C_{{\mathrm{v}}_{\mathrm{myo},\mathrm{np}}}^{\mathrm{m}}\left(t\right)-{k_{\mathrm{np}}}_p·C_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}}\hfill \\ & & \frac{+{k_{\mathrm{p}}}_{\mathrm{np}}·C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}}\hfill \end{array}$$ (B10.23)

where $C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}(t)$ represents the maternal myometrium oxytocin concentration in P. $C_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}(t)$ represents the maternal myometrium oxytocin concentration in nP, ${\mathrm{CL}}_{\mathrm{myo}}^{\mathrm{m}}$ is the clearance rate of oxytocin by the maternal myometrium calculated in section 2.1.3 of the main text, $C_{{\mathrm{v}}_{\mathrm{myo},\mathrm{p}}}^{\mathrm{m}}(t)$ and $C_{{\mathrm{v}}_{\mathrm{myo},\mathrm{np}}}^{\mathrm{m}}(t)$ are the concentrations of the substance in the venous blood leaving P and nP, and ${k_p}_{\mathrm{np}}$ and $k{n_p}_{\mathrm{p}}$ denote the bidirectional inter‐regional transfer rate constant for oxytocin between P and the nP; it was set to 5.0 × 10⁻⁵ ms⁻¹ as an estimated parameter to represent slow exchange between the two regions.

The overall maternal myometrial concentration is the weighted average of the concentrations in the P and nP, weighted by the placental coverage fraction:

$$\begin{array}{ccc}\hfill C_{\mathrm{myo}}^{\mathrm{m}}\left(t\right)& =& F{S}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)·C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}\left(t\right)\hfill \\ & & +\left(1-F{S}_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)\right)·C_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}\left(t\right)\hfill \end{array}$$ (B10.24)

B.11 Other compartment in m‐PBPK

The other compartment contains all other body components that are not explicitly modelled.

From eqn 10 of Kapraun et al. (2019), the fat‐free mass excluding the products of conception (see subsubsection A.10), $M_{\mathrm{ffmx}}^{\mathrm{m}}(\mathrm{GA})$ (in g) is given by

$$\begin{array}{ccc}\hfill M_{\mathrm{ffmx}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& M^{\mathrm{m}}\left(\mathrm{GA}\right)-M_{\mathrm{fat}}^{\mathrm{m}}\left(\mathrm{GA}\right)-M^{\mathrm{f}}\left(\mathrm{GA}\right)\hfill \\ & & -M_{\mathrm{placenta}}^{\mathrm{m}}\left(\mathrm{GA}\right)-M_{\mathrm{amniotic}}^{\mathrm{m}}\left(\mathrm{GA}\right)\hfill \end{array}$$ (B11.1)

where $M_{\mathrm{fat}}^{\mathrm{m}}(\mathrm{GA})$ is the total maternal mass, $M_{\mathrm{fat}}^{\mathrm{m}}(\mathrm{GA})$ is the fat mass, $M^{\mathrm{f}}(\mathrm{GA})$ is the fetal mass, $M_{\mathrm{placenta}}^{\mathrm{m}}(\mathrm{GA})$ is the placental mass and $M_{\mathrm{amniotic}}^{\mathrm{m}}(\mathrm{GA})$ is the amniotic fluid mass.

The fat‐free volume excluding the products of conception is thus given by

$$V_{\mathrm{ffmx}}^{\mathrm{m}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{ffmx}}^{\mathrm{m}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{ffmx}}^{\mathrm{m}}}$$ (B11.2)

where $V_{\mathrm{ffmx}}^{\mathrm{m}}(\mathrm{GA})$ is the fat‐free volume excluding the products of conception (in mL), ${\rho }_{\mathrm{ffmx}}^{\mathrm{m}}$ = 1.1g·mL⁻¹ is the fat‐free density excluding the products of conception and $M_{\mathrm{ffmx}}^{\mathrm{m}}(\mathrm{GA})$ is the fat‐free mass excluding the products of conception given in eqn (B11.1).

From eqns (11) and (12) of Kapraun et al. (2019), the volume of the other compartment is thus given by

$$\begin{array}{ccc}\hfill V_{\mathrm{other}}^{\mathrm{m}}\left(\mathrm{GA}\right)& =& V_{\mathrm{ffmx}}^{\mathrm{m}}\left(\mathrm{GA}\right)-V_{\mathrm{p}}^{\mathrm{m}}\left(\mathrm{GA}\right)-V_{\mathrm{rbc}}^{\mathrm{m}}\left(\mathrm{GA}\right)\hfill \\ & & -\sum _i{V}_i^{\mathrm{m}}\left(\mathrm{GA}\right)\hfill \end{array}$$ (B11.3)

where $V_{\mathrm{other}}^{\mathrm{m}}(\mathrm{GA})$ is the maternal other volume (in mL), and $V_{\mathrm{p}}^{\mathrm{m}}(\mathrm{GA})$ denotes the maternal plasma volume defined by equation (B1.1). $V_{\mathrm{rbc}}^{\mathrm{m}}(\mathrm{GA})$ denotes the maternal red blood cell volume defined by equation (B1.2). $V_{\mathrm{i}}^{\mathrm{m}}(\mathrm{GA})$ denotes the volume of compartment $i$ in m‐PBPK where $i\in \{\mathrm{brain},\mathrm{gut},\mathrm{kidney},\mathrm{liver},\mathrm{lung},\mathrm{myometrium}\}$.

From eqn (23) of Kapraun et al. (2019), the blood flow rate of the other compartment is given by

$$Q_{\mathrm{other}}^{\mathrm{m}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{m}}\left(\mathrm{GA}\right)-\sum _i{Q}_i^{\mathrm{m}}\left(\mathrm{GA}\right)$$ (B11.4)

where $Q_{\mathrm{other}}^{\mathrm{m}}(\mathrm{GA})$ is the other blood flow rate in mL·ms⁻¹, $Q_{\mathrm{co}}^{\mathrm{m}}(\mathrm{GA})$ is the total maternal cardiac output given in  eqn (B1.7) and $Q_{\mathrm{i}}^{\mathrm{m}}(\mathrm{GA})$ denotes the blood flow rate to compartment $i$ in m‐PBPK, where $i\in [\mathrm{brain},\mathrm{fat},\mathrm{gut},\mathrm{kidney},\mathrm{liver},\mathrm{lung},\mathrm{myometrium},\mathrm{placenta}]$.

The oxytocin concentration in the other compartment is given by:

$$\frac{d{C}_{\mathrm{other}}^{\mathrm{m}}\left(t\right)}{dt}=\frac{Q_{\mathrm{other}}^{\mathrm{m}}·C_{\mathrm{art}}^{\mathrm{m}}\left(t\right)-Q_{\mathrm{other}}^{\mathrm{m}}·C_{{\mathrm{v}}_{\mathrm{other}}}^{\mathrm{m}}\left(t\right)}{V_{\mathrm{other}}^{\mathrm{m}}}$$ (B11.5)

where $C_{\mathrm{other}}^{\mathrm{m}}(t)$ is the oxytocin concentration in maternal other organs, and $C_{{\mathrm{v}}_{\mathrm{other}}}^{\mathrm{m}}(t)$ is the concentration of the substance in the venous blood leaving the other compartment (main text eqn 5).

C f‐PBPK model

From eqn (2) of Kapraun et al. (2019) the mass of an average fetus is given by

$$\begin{array}{ccc}\hfill M^{\mathrm{f}}\left(\mathrm{GA}\right)& =& 0.0018282\hfill \\ & & \times \exp ·\frac{1.1735}{0.077577}\left(1-e^{-0.077577,\mathrm{GA}}\right)\hfill \end{array}$$ (C.1)

where $M^{\mathrm{f}}(\mathrm{GA})$ is the fetal mass (in g) and GA is the gestational age (in weeks).

The volume of an average fetus is thus given by

$$V^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }^{\mathrm{f}}}$$ (C.2)

where $V^{\mathrm{f}}(\mathrm{GA})$ is the fetal volume (in mL) and ${\rho }^{\mathrm{f}}$ is the fetal reference density of 1.0 g·mL⁻¹.

C.1 Blood compartment in f‐PBPK

From Fig. 2 of Nicolaides et al. (1987) the fetal blood volume per unit fetal mass is given by

$${\rho }_{\mathrm{blood}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.13783-0.00149\mathrm{GA}$$ (C1.1)

where ${\rho }_{\mathrm{blood}}^{\mathrm{f}}(\mathrm{GA})$ is fetal blood volume per unit fetal mass (in mL·g⁻¹).

The fetal blood volume is thus given by

$$V_{\mathrm{blood}}^{\mathrm{f}}\left(\mathrm{GA}\right)={\rho }_{\mathrm{blood}}^{\mathrm{f}}\left(\mathrm{GA}\right)·M^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.2)

where ${\rho }_{\mathrm{blood}}^{\mathrm{f}}(\mathrm{GA})$ is fetal blood volume per unit fetal mass (in mL·g⁻¹).

The fetal haematocrit is given by eqn (59) of Kapraun et al. (2019), that is

$$\begin{array}{ccc}\hfill H^{\mathrm{f}}\left(\mathrm{GA}\right)& =& 4.5061\mathrm{GA}-0.18487\mathrm{G}{\mathrm{A}}^2\hfill \\ & & +0.0026766\mathrm{G}{\mathrm{A}}^3\hfill \end{array}$$ (C1.3)

where ${\mathrm{H}}^f(\mathrm{GA})$ is the fetal haematocrit (as a percentage).

The fetal RBC volume is thus given by

$$V_{\mathrm{rbc}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{H^{\mathrm{f}}\left(\mathrm{GA}\right)}{100}·V_{\mathrm{blood}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.4)

where $V_{\mathrm{rbc}}^{\mathrm{f}}(\mathrm{GA})$ is fetal red blood cell volume (in mL), and the fetal plasma volume is given by

$$V_{\mathrm{p}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\left(1-\frac{H^f\left(\mathrm{GA}\right)}{100}\right)·V_{\mathrm{blood}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.5)

where $V_{\mathrm{p}}^{\mathrm{f}}(\mathrm{GA})$ is fetal plasma volume (in mL).

Now assuming similar ratios to those of the mother, we have from Table 1 of Gaohua et al. (2012) the fetal arterial and venous volumes, that is

$$V_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.0205}{0.0205+0.0411}·V_{\mathrm{p}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.6)

$$V_{\mathrm{ven}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.0411}{0.0205+0.0411}·V_{\mathrm{p}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.7)

where $V_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial plasma volume (in mL) and $V_{\mathrm{ven}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal venous plasma volume (in mL).

Due to the fetus getting oxygenated blood from the mother via the placenta, the fetal cardiopulmonary system is more complicated due to several ducts. As shown in Fig. 1 in the main text, the fetal right and left atria are linked via the foramen ovale and the right ventricle and aorta are linked via the ductus arteriosus.

From eqn (44) of Kapraun et al. (2019) the fetal right ventricular output is given by

$$Q_{\mathrm{rvent}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.041108}{1+{\mathrm{e}}^{-0.14837\left(\mathrm{GA}-43.108\right)}}$$ (C1.8)

where $Q_{\mathrm{rvent}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal right ventricular output (in mL·ms⁻¹).

From eqn (45) of Kapraun et al. (2019) the fetal left ventricular output is given by

$$Q_{\mathrm{lvent}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.008438}{1+{\mathrm{e}}^{-0.21916\left(\mathrm{GA}-30.231\right)}}$$ (C1.9)

where $Q_{\mathrm{lvent}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal left ventricular output (in mL·ms⁻¹).

We also have from eqn (46) of Kapraun et al. (2019) the fetal ductus arteriosus flow is given by

$$Q_{\mathrm{da}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.018755}{1+{\mathrm{e}}^{-0.18031\left(\mathrm{GA}-35.939\right)}}$$ (C1.10)

where $Q_{\mathrm{da}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal ductus arteriosus flow (in mL·ms⁻¹).

From Fig. 1 in the main text and eqn 47 of Kapraun et al. (2019), the fetal cardiac output is given by

$$Q_{\mathrm{co}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{lvent}}^{\mathrm{f}}\left(\mathrm{GA}\right)+Q_{\mathrm{da}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.11)

where $Q_{\mathrm{co}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal cardiac output (in mL·ms⁻¹).

We also have

$$Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.12)

$$Q_{\mathrm{ven}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C1.13)

where $Q_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial flow rate (in mL·ms⁻¹) and $Q_{\mathrm{ven}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal venous flow rate (in mL·ms⁻¹).

The oxytocin concentration in the fetal venous plasma is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{ven}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{{\sum }_i{Q}_i^{\mathrm{f}}·C_{{\mathrm{v}}_i}^{\mathrm{f}}\left(t\right)+Q_{\mathrm{dv}}^{\mathrm{f}}·C_{\mathrm{uven}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{ven}}^{\mathrm{f}}\left(GA\right)·C_{\mathrm{ven}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{ven}}^{\mathrm{f}}\left(GA\right)}\hfill \end{array}$$ (C1.14)

where $Q_i^{\mathrm{f}}$ represents the blood flow rate returning from each fetal organ to the fetal venous compartment, and $C_{{\mathrm{v}}_i}^{\mathrm{f}}(t)$ represents the concentration of the substance in the venous blood leaving each fetal organ (eqn (5) in the main text), with $i\in \{\mathrm{brain},\mathrm{kidney},\mathrm{liver},\mathrm{other}\}$; $Q_{\mathrm{dv}}^{\mathrm{f}}$ represents the blood flow rate through the fetal ductus venosus (eqn C7.6), $C_{\mathrm{uven}}^{\mathrm{f}}(t)$ is the oxytocin concentration in the fetal umbilical vein and $C_{\mathrm{ven}}^{\mathrm{f}}(t)$ is the oxytocin concentration in the fetal venous plasma.

The oxytocin concentration in the fetal arterial plasma is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{art}}^f\left(t\right)}{\mathrm{dt}}=\frac{\left(Q_{\mathrm{da}}^{\mathrm{f}}\left(\mathrm{GA}\right)+Q_{\mathrm{lvent}}^{\mathrm{f}}\left(\mathrm{GA}\right)\right))·C_{\mathrm{ven}}^{\mathrm{f}}\left(t\right)+Q_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\\ -\frac{Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\end{array}$$ (C1.15)

where $Q_{\mathrm{lung}}^{\mathrm{f}}(\mathrm{GA})$ is the blood flow rate in the fetal lung, $C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{f}}(t)$ is the venous‐equivalent oxytocin concentration in the fetal lung (eqn (5) in the main text) and $C_{\mathrm{art}}^{\mathrm{f}}(t)$ is the oxytocin concentration in the fetal aorta.

Because the oxytocinase activity in fetal blood is very low and comparable to that in non‐pregnant women (Oya et al., 1974), we did not model oxytocinase‐mediated clearance in the fetal circulation in this study. This aspect will be further explored in our future research.

C.2 Brain compartment in f‐PBPK

$$M_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.01574·{\mathrm{e}}^{\frac{0.70707}{0.064827}\left(1-{\mathrm{e}}^{-0.048276\mathrm{GA}}\right)}$$ (C2.1)

where $M_{\mathrm{brain}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal brain mass (in g).

The fetal brain volume is thus given by eqn 30 of Kapraun et al. (2019), that is

$$V_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{brain}}^{\mathrm{f}}}$$ (C2.2)

where $V_{\mathrm{brain}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal brain volume (in mL) and ${\rho }_{\mathrm{brain}}^{\mathrm{f}}$ is the fetal brain density of $1.04$ g·mL⁻¹.

From eqn (54) of Kapraun et al. (2019) the fetal brain blood flow rate is given by

$$Q_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{14.3}{75}\left(1-\frac{Q_{\mathrm{placenta}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{Q_{\mathrm{A}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\right)Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C2.3)

where $Q_{\mathrm{brain}}^{\mathrm{f}}(\mathrm{GA})$ is fetal brain blood flow rate (in mL·ms⁻¹), $Q_{\mathrm{pla}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal placental flow rate and $Q_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial flow rate.

The oxytocin concentration in the fetal brain compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{brain}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{brain}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{brain}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{brain}}^{\mathrm{f}}}\hfill \end{array}$$ (C2.4)

where, $C_{\mathrm{brain}}^{\mathrm{f}}(t)$ denotes the oxytocin concentration in fetal brain, and $C_{{\mathrm{v}}_{\mathrm{brain}}}^{\mathrm{f}}(t)$ is the concentration of the substance in the venous blood leaving the brain (eqn (5) in the main text).

C.3 Gut compartment in f‐PBPK

From eqn (42) of Kapraun et al. (2019) the fetal gut mass is given by

$$M_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.00081828·{\mathrm{e}}^{\frac{0.65028}{0.047724}\left(1-{\mathrm{e}}^{-0.047724\mathrm{GA}}\right)}$$ (C3.1)

where $M_{\mathrm{gut}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal gut mass (in g).

The fetal gut volume is thus given by eqn (42) of Kapraun et al. (2019), that is

$$V_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{gut}}^{\mathrm{f}}}$$ (C3.2)

where $V_{\mathrm{gut}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal gut volume (in mL), and ${\rho }_{\mathrm{gut}}^{\mathrm{f}}$ is the fetal gut density of 1.045 g·mL⁻¹.

From eqn (52) of Kapraun et al. (2019) the fetal gut blood flow rate is given by

$$Q_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{6.8}{75}\left(1-\frac{Q_{\mathrm{placenta}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\right)Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C3.3)

where $Q_{\mathrm{gut}}^{\mathrm{f}}(\mathrm{GA})$ is fetal gut blood flow rate (in mL·ms⁻¹), $Q_{\mathrm{placenta}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal placental flow rate given by  eqn (C7.3) and $Q_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial flow rate given by  eqn (C1.12).

The oxytocin concentration in the fetal gut compartment is given by:

$$\frac{d{C}_{\mathrm{gut}}^{\mathrm{f}}\left(t\right)}{dt}=\frac{Q_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{gut}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)}$$ (C3.4)

where $C_{\mathrm{gut}}^{\mathrm{f}}(t)$ denotes the oxytocin concentration in the fetal gut and $C_{{\mathrm{v}}_{\mathrm{gut}}}^{\mathrm{f}}(t)$ is the concentration of the substance in the venous blood leaving the gut (eqn 5) in the main text).

C.4 Kidney compartment in f‐PBPK

From eqn (34) of Kapraun et al. (2019) the fetal kidney mass is given by

$$M_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.016011·M^{\mathrm{f}}{\left(\mathrm{GA}\right)}^{0.87512}$$ (C4.1)

where $M_{\mathrm{kidney}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal kidney mass (in g).

The fetal kidney volume is thus given by eqn 36 of Kapraun et al. (2019), that is

$$V_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{kidney}}^{\mathrm{f}}}$$ (C4.2)

where $V_{\mathrm{kidney}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal kidney volume (in mL) and ${\rho }_{\mathrm{kidney}}^{\mathrm{f}}$ is the fetal kidney density of $1.05$ g·mL⁻¹.

From eqn (53) of Kapraun et al. (2019) the fetal kidney blood flow rate is given by

$$Q_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{5.4}{75}\left(1-\frac{Q_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\right)Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C4.3)

where $Q_{\mathrm{kidney}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal kidney blood flow rate (in mL·ms⁻¹), $Q_{\mathrm{pla}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal placental flow rate given by  eqn (C7.3) and $Q_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial flow rate given by  eqn (C1.12).

The oxytocin concentration in the fetal kidney compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{kidney}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{kidney}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{kidney}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C4.4)

where $C_{\mathrm{kidney}}^{\mathrm{f}}(t)$ denotes the oxytocin concentration in the fetal kidney, and $C_{{\mathrm{v}}_{\mathrm{kidney}}}^{\mathrm{f}}(t)$ is concentration of the substance in the venous blood leaving kidney (eqn 5) in the main text).

1. C.5 Liver compartment in f‐PBPK

From eqn (32) of Kapraun et al. (2019) the fetal liver mass is given by

$$M_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.0074774·{\mathrm{e}}^{\frac{0.65856}{0.061662}\left(1-{\mathrm{e}}^{-0.061662\mathrm{GA}}\right)}$$ (C5.1)

where $M_{\mathrm{liver}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal liver mass (in g).

$$M_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.0074774·{\mathrm{e}}^{\frac{0.65856}{0.061662}\left(1-{\mathrm{e}}^{-0.061662\mathrm{GA}}\right)}$$ (C5.2)

The fetal liver volume is thus given by eqn (22) of Kapraun et al. (2019), that is

$$V_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{liver}}^{\mathrm{f}}}$$ (C5.3)

where $V_{\mathrm{liver}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal liver volume (in mL) and ${\rho }_{\mathrm{liver}}^{\mathrm{f}}$ is the fetal liver density of 1.05 g·mL⁻¹.

$$V_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{liver}}^{\mathrm{f}}}$$ (C5.4)

From eqn (55) of Kapraun et al. (2019) the fetal liver blood flow rate is given by

$$\begin{array}{ccc}\hfill Q_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)& =& \frac{6.5}{54}\left(1-\frac{26.5}{75}\right)\left(1-\frac{Q_{\mathrm{placenta}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{Q_{\mathrm{A}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\right)\hfill \\ & & Q_{\mathrm{art}}^{\mathrm{f}}\left(\mathrm{GA}\right)\hfill \end{array}$$ (C5.5)

where $Q_{\mathrm{liver}}^{\mathrm{f}}(\mathrm{GA})$ is fetal liver blood flow rate (in mL·ms⁻¹), ${\mathrm{Q}}_{\mathrm{placenta}}^f$ is the fetal placental flow rate given by  eqn (C7.3) and $Q_{\mathrm{art}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal arterial flow rate given by  eqn (C1.12).

The oxytocin concentration in the fetal liver compartment is given by:

$$\begin{array}{ccc}\hfill \frac{d{C}_{l\mathrm{iver}}^{\mathrm{f}}\left(t\right)}{\mathrm{dt}}& =& \frac{Q_{\mathrm{ps}}^{\mathrm{f}}·C_{\mathrm{uven}}^{\mathrm{f}}\left(t\right)+Q_{\mathrm{gut}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{gut}}}^{\mathrm{f}}\left(t\right)-\left(Q_{\mathrm{ps}}^{\mathrm{f}}+Q_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)+Q_{\mathrm{gut}}^{\mathrm{f}}\right)·C_{{\mathrm{v}}_{\mathrm{liver}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \\ & & -\frac{{\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{f}}·f_{\mathrm{u},\mathrm{p}}·C_{\mathrm{liver}}^f\left(t\right)+Q_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{liver}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C5.6)

where $C_{\mathrm{liver}}^{\mathrm{f}}(t)$ is the oxytocin concentration in the fetal liver, $Q_{\mathrm{ps}}^{\mathrm{f}}$ is the blood flow rate from the umbilical vein to the portal vein [eqn (C7.7)], $C_{{\mathrm{v}}_{\mathrm{liver}}}^{\mathrm{f}}(t)$ is the venous equivalent oxytocin concentration in the fetal liver (eqn (5) in the main text) and ${\mathrm{CL}}_{\mathrm{liver}}^{\mathrm{f}}$ is the fetal liver oxytocin clearance rate, the value reported in section 2.1.3 of the main text.

C.6 Lung compartment in f‐PBPK

Because the fetal component has only a minor impact on oxytocin concentration profiles in the whole PBPK system. For that we did not model the heart as a separate compartment; instead, we represented mass exchange between the arterial and venous pools via the lungs and the fetal ductus venosus.

From eqn (37) of Kapraun et al. (2019) the fetal lung mass is given by

$$M_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.000030454·{\mathrm{e}}^{\frac{1.0627}{0.084004}\left(1-{\mathrm{e}}^{-0.084004\mathrm{GA}}\right)}$$ (C6.1)

where $M_{\mathrm{lung}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal Lung mass (in g).

The fetal lung volume is thus given by eqn 38 of Kapraun et al. (2019), that is

$$V_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{M_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)}{{\rho }_{\mathrm{lung}}^{\mathrm{f}}}$$ (C6.2)

where $V_{\mathrm{lung}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal lung volume (in mL) and ${\rho }_{\mathrm{lung}}^{\mathrm{f}}=1.05$ g·mL⁻¹ is the fetal lung density.

From eqn (48) of Kapraun et al. (2019) the fetal flow to the lung is given by

$$Q_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{rvent}}^{\mathrm{f}}\left(\mathrm{GA}\right)-Q_{\mathrm{da}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C6.3)

where $Q_{\mathrm{lung}}^{\mathrm{f}}$ is fetal lung blood flow rate (in mL·ms⁻¹), $Q_{\mathrm{rvent}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal right ventricular rate given by  eqn (C1.8) and $Q_{\mathrm{da}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal ductus arteriosus flow rate given by  eqn (C1.10).

The oxytocin concentration in the fetal lung compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{lung}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{ven}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{lung}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C6.4)

where $C_{\mathrm{lung}}^{\mathrm{f}}(t)$ denotes the oxytocin concentration in the fetal lung compartment. $C_{{\mathrm{v}}_{\mathrm{lung}}}^{\mathrm{f}}(t)$ is the venous equivalent oxytocin concentration in the fetal lung (eqn 5 in main text).

C.7 Placenta compartment in f‐PBPK

From Dallmann et al. (2017) approximately 52.5% of the placenta is maternal tissue, the rest fetal, thus defining

$$F{V}_{\mathrm{placenta}}^{\mathrm{f}}=1.0-F{V}_{\mathrm{placenta}}^{\mathrm{m}}$$ (C7.1)

We have

$$V_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)=F{V}_{\mathrm{placenta}}^{\mathrm{f}}·V_{\mathrm{placenta}}\left(\mathrm{GA}\right)$$ (C7.2)

where $F{V}_{\mathrm{placenta}}^{\mathrm{m}}$ is the maternal placental fraction and is given in  eqn (B9.2), and $V_{\mathrm{placenta}}(\mathrm{GA})$ is the total placental volume, given by  eqn (B9.1).

Blood enters the fetal placenta via the umbilical arteries. From eqn 50 of Kapraun et al. (2019) the placental blood flow rate into the placenta is given by

$$Q_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)=\frac{0.00437}{1+{\mathrm{e}}^{-0.22183·\left(\mathrm{GA}-28.784\right)}}$$ (C7.3)

where $Q_{\mathrm{pla}}^{\mathrm{f}}(\mathrm{GA})$ is the placental blood flow rate (in mL·ms⁻¹).

According to the principle of mass conservation, the flow entering the umbilical artery must equal the flow entering the placenta, the flow exiting the placenta and the flow in the umbilical vein, that is:

$$Q_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C7.4)

$$Q_{\mathrm{VenCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C7.5)

According to Dallmann et al. (2017) the geometric parameters of the umbilical cord vary with gestational age ($GA$, in weeks) and are used to model the total volume of umbilical cord blood. The umbilical cord length ($cor{d}_l(GA)$ in cm) is defined as:

$$\mathrm{cor}{\mathrm{d}}_{\mathrm{l}}\left(\mathrm{GA}\right)=84.3·{\mathrm{e}}^{-{\mathrm{e}}^{-1.36·\log \left(\mathrm{GA}\right)+3.94}}$$ (C7.6)

The umbilical cord diameter (in cm) is defined as:

$$\begin{array}{ccc}\hfill \mathrm{cor}{\mathrm{d}}_{\mathrm{d}}\left(\mathrm{GA}\right)& =& -0.00000168·\mathrm{G}{\mathrm{A}}^4+0.0000238·\mathrm{G}{\mathrm{A}}^3\hfill \\ & & +0.00205·\mathrm{G}{\mathrm{A}}^2+0.0187·\mathrm{GA}\hfill \end{array}$$ (C7.7)

Under the assumption that the umbilical cord can be approximated as a cylinder (Dallmann et al., 2017), the total cord volume (i.e. the geometric volume), when $\mathrm{cor}{\mathrm{d}}_l$ and $\mathrm{cor}{\mathrm{d}}_d$ are expressed in cm (approximately 73.6 mL at 40 gestation weeks, in cm^3 = mL), is estimated as:

$$V_{\mathrm{cord}}\left(\mathrm{GA}\right)=\pi ·{\left(\frac{\mathrm{cor}{\mathrm{d}}_{\mathrm{d}}\left(\mathrm{GA}\right)}{2}\right)}^2·\mathrm{cor}{\mathrm{d}}_{\mathrm{l}}\left(\mathrm{GA}\right)$$ (C7.8)

According to Dallmann et al. (2017) the volumes of the umbilical venous and arterial blood are defined as fixed fractions of the total umbilical cord volume, given by:

$$V_{\mathrm{VenCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.267·V_{\mathrm{cord}}\left(\mathrm{GA}\right)$$ (C7.9)

$$V_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)=0.0639·V_{\mathrm{cord}}\left(\mathrm{GA}\right)$$ (C7.10)

where $V_{\mathrm{VenCord}}^{\mathrm{f}}(\mathrm{GA})$ is the umbilical arterial volume and $V_{\mathrm{ArtCord}}^{\mathrm{f}}(\mathrm{GA})$ is the umbilical venous volume.

The blood flow out of the fetal placenta is via the umbilical vein, which then splits into two parts. The first part carries blood to the fetal liver via the portal sinus. The second part, the ductus venosus, bypasses the fetal liver and carries blood from the umbilical vein to the inferior vena cava. From eqn 51 of Kapraun et al. (2019) the ductus venosus blood flow rate is given by

$$Q_{\mathrm{dv}}^{\mathrm{f}}\left(\mathrm{GA}\right)=3.15333·{10}^{-5}·{\mathrm{e}}^{\frac{0.098249}{0.0064374}\left(1-{\mathrm{e}}^{-0.0064374,\mathrm{GA}}\right)}$$ (C7.11)

where $Q_{\mathrm{dv}}^{\mathrm{f}}(\mathrm{GA})$ is the ductus venosus blood flow rate (in mL·ms⁻¹).

The flow into the liver via the portal sinus is thus given by

$$Q_{\mathrm{ps}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{uven}}^{\mathrm{f}}\left(\mathrm{GA}\right)-Q_{\mathrm{dv}}^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C7.12)

where $Q_{\mathrm{ps}}^{\mathrm{f}}(\mathrm{GA})$ is the portal sinus blood flow rate (in mL·ms⁻¹).

Although the umbilical cord primarily serves as a transport pathway in oxytocin kinetics and contributes only minimally to the overall distribution of oxytocin within the maternal–fetal system, several studies have reported oxytocin concentrations in both the umbilical vein and the umbilical artery, with an observed concentration difference typically around 0–20 pg·mL⁻¹ (Nathan et al., 2021; Buckley et al., 2023). Therefore the umbilical artery and umbilical vein were explicitly modelled in this study.

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{ArtCord}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{ArtCord}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C7.13)

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{VenCord}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{VenCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{pla}}^{\mathrm{f}}\left(t\right)-\left(Q_{\mathrm{ps}}^{\mathrm{f}}\left(\mathrm{GA}\right)+Q_{\mathrm{dv}}^{\mathrm{f}}\left(\mathrm{GA}\right)\right)·C_{\mathrm{VenCord}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{VenCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C7.14)

The oxytocin concentration in the fetal placenta compartment is given by:

$$\begin{array}{c}\frac{d{C}_{\mathrm{pla}}^{\mathrm{f}}\left(t\right)}{\mathrm{dt}}=\frac{Q_{\mathrm{ArtCord}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-\left(Q_{\mathrm{dv}}^{\mathrm{f}}\left(\mathrm{GA}\right)+Q_{\mathrm{ps}}^{\mathrm{f}}\left(\mathrm{GA}\right)\right)·C_{{\mathrm{v}}_{\mathrm{pla}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\\ +\frac{k_{\mathrm{mf}}·C_{\mathrm{pla}}^{\mathrm{m}}\left(t\right)-k_{\mathrm{fm}}·C_{\mathrm{pla}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{pla}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\end{array}$$ (C7.15)

where $C_{\mathrm{pla}}^{\mathrm{f}}(t)$ is the oxytocin concentration on the fetal side of the placenta, and $C_{{\mathrm{v}}_{\mathrm{pla}}}^{\mathrm{f}}(t)$ denotes the venous‐equivalent oxytocin concentration on the fetal side of the placenta (eqn (5) in the main text).

C.8 Other compartment in f‐PBPK

The volume of the fetal other compartment is given by

$$\begin{array}{ccc}\hfill V_{\mathrm{other}}^{\mathrm{f}}\left(\mathrm{GA}\right)& =& V^{\mathrm{f}}\left(\mathrm{GA}\right)-V_{\mathrm{p}}^{\mathrm{f}}\left(\mathrm{GA}\right)-V_{\mathrm{rbc}}^{\mathrm{f}}\left(\mathrm{GA}\right)\hfill \\ & & -\sum _i{\mathrm{V}}_i^{\mathrm{f}}\left(\mathrm{GA}\right)\hfill \end{array}$$ (C8.1)

where $V_{\mathrm{other}}^{\mathrm{f}}(\mathrm{GA})$ is the volume of the fetal other compartment (in mL), $V^{\mathrm{f}}(\mathrm{GA})$ is the fetal volume, $V_{\mathrm{p}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal plasma volume, $V_{\mathrm{rbc}}^{\mathrm{f}}(\mathrm{GA})$ the fetal RBC volume and $V_{\mathrm{i}}^{\mathrm{f}}(\mathrm{GA})$ denotes the volume of compartment $i$ in f‐PBPK, where $i\in \{\mathrm{brain},\mathrm{gut},\mathrm{kidney},\mathrm{liver},\mathrm{lung}\}$.

The blood flow into the fetal other component is given by

$$Q_{\mathrm{other}}^{\mathrm{f}}\left(\mathrm{GA}\right)=Q_{\mathrm{co}}^{\mathrm{f}}\left(\mathrm{GA}\right)-\sum _i{Q}_i^{\mathrm{f}}\left(\mathrm{GA}\right)$$ (C8.2)

where $Q_{\mathrm{other}}^{\mathrm{f}}(\mathrm{GA})$ is the blood flow into the fetal other compartment (in mL·ms⁻¹), $Q_{\mathrm{co}}^{\mathrm{f}}(\mathrm{GA})$ is the fetal cardiac output and $Q_{\mathrm{i}}^{\mathrm{f}}(\mathrm{GA})$ denotes the blood flow rate to compartment $i$, in f‐PBPK where $i\in \{\mathrm{brain},,\mathrm{gut},\mathrm{kidney},\mathrm{liver},\mathrm{lung},\}$.

The oxytocin concentration in the fetal placenta compartment is given by:

$$\begin{array}{ccc}& & \frac{d{C}_{\mathrm{other}}^{\mathrm{f}}\left(t\right)}{dt}\hfill \\ & & =\frac{Q_{\mathrm{other}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{\mathrm{art}}^{\mathrm{f}}\left(t\right)-Q_{\mathrm{other}}^{\mathrm{f}}\left(\mathrm{GA}\right)·C_{{\mathrm{v}}_{\mathrm{other}}}^{\mathrm{f}}\left(t\right)}{V_{\mathrm{other}}^{\mathrm{f}}\left(\mathrm{GA}\right)}\hfill \end{array}$$ (C8.3)

where $C_{\mathrm{other}}^{\mathrm{f}}(t)$ is the oxytocin concentration in fetal other organs, and $C_{{\mathrm{v}}_{\mathrm{other}}}^{\mathrm{f}}(t)$ is the concentration of the substance in the venous blood leaving the other compartment (eqn (5) in the main text).

1. D oxytocin receptor signalling parameters

Tables A1, A2, A3, A4.

Table A1.

Parameters for oxytocin binding

Parameter	Value	Unit	Definition	Ref.
$\mathrm{Kin}{\mathrm{t}}_{\max }$	1.67e−05	ms−1	Maximum rate of receptor internalization	Kim et al. (2024)
$k_{\mathrm{phos}}$	4e−05	mM	Rate for receptor phosphorylation	Kim et al. (2024)
$k_{\mathrm{des}}$	4.01e−05	ms−1	Rate of degradation of oxytocin–oxytocin receptor complex	Willets et al. (2009)
$k_{\mathrm{on}}$	4e7	L·mol−1·ms−1	Rate of oxytocin with oxytocin receptors binding	Pliska and Jutz (2018)
$k_{\mathrm{off}}$	0.0224	ms−1	Rate of oxytocin with oxytocin receptors dissociation	/
$\gamma$	0.475	/	Parameter for calculation of initial oxytocin receptor concentration	/

Table A2.

Parameters of IP₃ production

Parameter	Value	Unit	Definition	Ref.
$\mathrm{PLC}{\beta }_{\mathrm{total}}$	133.33	nM	Total PLCβ3 protein concentration	Yang and Jafri (2015)
$K_{\mathrm{d}}^{\mathrm{PLC}\beta }$	100	nM	Dissociation constant between OXTRC and PLCβ	Yang and Jafri (2015)
$k_{\mathrm{cat}}$	0.0569	pmol·mL−1·ms−1	pmol·mL−1·ms−1	Yang and Jafri (2015)
$v_5$	0.625	pmol·mL−1·ms−1	pmol·mL−1·ms−1	Yang and Jafri (2015)
$k_5^{\mathrm{I}{\mathrm{P}}_3}$	25,000	pmol·mL−1	pmol·mL−1·ms−1	Yang and Jafri (2015)
$v_6$	0.625	pmol·mL−1·ms−1	The maximal rate of IP3 phosphorylation to IP4 catalysed by IP3 3‐kinase	Yang and Jafri (2015)
$k_6^{\mathrm{I}{\mathrm{P}}_3}$	25,000	pmol·mL−1·ms−1	the IP3 binding constant for the 3‐kinase mediated IP3 to IP4 phosphorylation term	Yang and Jafri (2015)
$k_7^{\mathrm{I}{\mathrm{P}}_3}$	200	pmol·mL−1·ms−1	The Ca2+ binding constant parameter that determines how intracellular Ca2+ enhances the 3‐kinase phosphorylation rate.	Yang and Jafri (2015)

Table A3.

Parameters of SR Ca²⁺ channels

Parameter	Value	Unit	Definition	Ref.
$v_{\mathrm{I}{\mathrm{P}}_3\mathrm{R}}$	1.95e−06	mM·ms−1	Rate of IP3 binding to IP3 receptors	/
$d_1$	0.00105	mM·ms−1	Dissociation constant of the IP3‐binding site on IP3R	Shuai and Jung (2003)
$d_2$	0.0005	mM·ms−1	Scaling factor controlling	Shuai and Jung (2003)
$d_3$	0.0003	mM·ms−1	IP3‐related dissociation constant appearing	Shuai and Jung (2003)
$d_4$	0.00013	mM·ms−1	Constant related to IP3 receptor activation	Shuai and Jung (2003)
$d_5$	0.00008	Mm	Dissociation constant of the Ca2+ activation site on IP3R	Shuai and Jung (2003)
$\mathrm{C}{\mathrm{a}}_u$	0.015	mM	The calcium ions concentration in sarcoplasmic reticulum	Shuai and Jung (2003)
$v_{\mathrm{SERCA}}$	0.5e−06	mM·ms−1	Maximum uptake rate of SERCA channel	Shuai and Jung (2003)
$k_{\mathrm{SERCA}}$	0.0001	mM	The rate constant for calcium uptake via SERCA channel	Shuai and Jung (2003)
$k_{\mathrm{SR}\_\mathrm{leak}}$	1e−08	ms−1	Rate constant for calcium leakage	/
$z_{\mathrm{ca}}$	2	/	Charge number of calcium ions	Tong et al. (2014)
$F$	96,485.0	C·mol−1	Faraday constant	Tong et al. (2014)
$\mathrm{Av}$	4	cm2·µL−1	Volume‐to‐membrane area ratio	Tong et al. (2014)
$C_{\mathrm{m}}$	10	µF·cm2 −1	Membrane capacitance	Tong et al. (2014)
$\mathrm{buff}$	0.015	/	Buffering coefficient	Tong et al. (2014)

Table A4.

Parameters of integrating with original tong model

$\mathrm{MLC}{\mathrm{K}}_{\max }$	0.84	/	Maximum fraction of MLCK	Testrow et al. (2018)
$K_{\mathrm{MLCK}}$	0.000721746	mM	Half‐activation of MLCK	Testrow et al. (2018)
$K_{\mathrm{CaMLCK}}$	0.00108	mM	Half‐activation of MLCK set by calcium ion concentration	Testrow et al. (2018)
$\mathrm{nm}$	8.7613	/	Hill coefficient for $k_1$	Testrow et al. (2018)
$k_2$	0.4e‐3	mM·ms−1	Rate of conversion from $M\mathrm{p}$ to $M$	Testrow et al. (2018)
$k_7$	4.5e‐5	mM·ms−1	Rate of conversion from AM to M	Testrow et al. (2018)
$k_4$	0.1e‐3	mM·ms−1	Rate of conversion from $\mathrm{AMp}$ to $M\mathrm{p}$	Testrow et al. (2018)
$k_3$	1.8e‐3	mM·ms−1	Rate of conversion from $M\mathrm{p}$ to $\mathrm{AMp}$	Testrow et al. (2018)
$k_5$	0.4e‐3	mM·ms−1	Rate of conversion from $\mathrm{AMp}$ to $\mathrm{AM}$	Testrow et al. (2018)
$\sigma$	14,000	Pascal	Convert the phosphorylation level inside the cell into cellular stress	Vila Pouca et al. (2019)
$\lambda$	$0.00750062$	/	Unit conversion from Pascal to mmHg	/

E initial values

The initial conditions of our model (including the initial oxytocin concentrations in all compartments of the P‐PBPK module and the initial state variables in the OXTR signalling module) were taken from the same steady‐state simulation snapshot (Table A5).

Table A5.

Initial values

	State variable	Initial values	Unit
m‐PBPK	$C_{\mathrm{ven}}^{\mathrm{m}}(t)$	0.0150	pmol·mL−1
	$C_{\mathrm{art}}^{\mathrm{m}}(t)$	0.0147	pmol·mL−1
	$C_{\mathrm{brain}}^{\mathrm{m}}(t)$	3.74×10−7	pmol·mL−1
	$C_{\mathrm{fat}}^{\mathrm{m}}(t)$	0.0009	pmol·mL−1
	$C_{\mathrm{gut}}^{\mathrm{m}}(t)$	0.00132	pmol·mL−1
	$C_{\mathrm{kidney}}^{\mathrm{m}}(t)$	0.0010	pmol·mL−1
	$C_{\mathrm{liver}}^{\mathrm{m}}(t)$	0.0008	pmol·mL−1
	$C_{\mathrm{heart},\mathrm{r}}^{\mathrm{m}}(t)$	0.00148	pmol·mL−1
	$C_{\mathrm{heart},\mathrm{l}}^{\mathrm{m}}(t)$	0.00149	pmol·mL−1
	$C_{\mathrm{lung}}^{\mathrm{m}}(t)$	0.0013	pmol·mL−1
	$C_{\mathrm{pla}}^{\mathrm{m}}(t)$	0.0018	pmol·mL−1
	$C_{\mathrm{myo},\mathrm{p}}^{\mathrm{m}}(t)$	0.0023	pmol·mL−1
	$C_{\mathrm{myo},\mathrm{np}}^{\mathrm{m}}(t)$	0.0175	pmol·mL−1
	$C_{\mathrm{other}}^{\mathrm{m}}(t)$	0.0055	pmol·mL−1
f‐PBPK	$C_{\mathrm{ven}}^{\mathrm{f}}(t)$	0.0158	pmol·mL−1
	$C_{\mathrm{art}}^{\mathrm{f}}(t)$	0.0175	pmol·mL−1
	$C_{\mathrm{brain}}^{\mathrm{f}}(t)$	5.31×10−7	pmol·mL−1
	$C_{\mathrm{gut}}^{\mathrm{f}}(t)$	0.0046	pmol·mL−1
	$C_{\mathrm{kidney}}^{\mathrm{f}}(t)$	0.0036	pmol·mL−1
	$C_{\mathrm{liver}}^{\mathrm{f}}(t)$	0.0015	pmol·mL−1
	$C_{\mathrm{lung}}^{\mathrm{f}}(t)$	0.005	pmol·mL−1
	$C_{\mathrm{ArtCord}}^{\mathrm{f}}(t)$	0.0158	pmol·mL−1
	$C_{\mathrm{VenCord}}^{\mathrm{f}}(t)$	0.00174	pmol·mL−1
	$C_{\mathrm{pla}}^{\mathrm{f}}(t)$	0.0017	pmol·mL−1
	$C_{\mathrm{other}}^{\mathrm{f}}(t)$	0.0104	pmol·mL−1
Oxytocin receptor signalling	$C_{\mathrm{oxtr}}$	216	pmol·mL−1
	$C_{\mathrm{oxtrc}}$	0.0111	pmol·mL−1
	$C_{\mathrm{oxtrc},\mathrm{int}}$	0.0272	pmol·mL−1
	$\mathrm{I}{\mathrm{P}}_3$	4.359	pmol·mL−1
	cai	0.0002	mM
	$V$	−49	mM
	$M$	0.957	mM
	$M_{\mathrm{p}}$	0.0004	mM
	$\mathrm{AM}$	0.0409	mM
	$\mathrm{A}{\mathrm{M}}_{\mathrm{p}}$	0.00174	mM

The only exception is the OXTR concentration, which is not constant during pregnancy but increases progressively with gestational age (GA). Using the OXTR data reported by Kimura et al. (1996), we fitted an exponential growth function and defined the fold increase of OXTR during pregnancy as:

$$\mathrm{oxt}{\mathrm{r}}_{\mathrm{growth}}=2·{\mathrm{e}}^{0.13·\mathrm{GA}}$$ (D.1)

where $\mathrm{GA}$ denotes gestational weeks and $\mathrm{oxt}{\mathrm{r}}_{\mathrm{growth}}$ is a dimensionless scaling factor relative to the non‐pregnant baseline. Accordingly the $\mathrm{GA}$‐specific initial OXTR concentration on myometrial cell membranes was defined as:

$$C_{\mathrm{oxtr},\mathrm{init}}\left(\mathrm{GA}\right)=C_{\mathrm{oxtr},\mathrm{early}}·\mathrm{oxt}{\mathrm{r}}_{\mathrm{growth}}$$ (D.2)

Here ${\mathrm{C}}_{oxtr,early}$ is the baseline receptor concentration in the non‐pregnant state. To estimate ${\mathrm{C}}_{oxtr,early}$ we used the late‐pregnancy ($\mathrm{GA}$ = 40 weeks) OXTR levels reported by Fuchs et al. (approximately 2000 fmol·mg⁻¹ protein; Fuchs, 1983) and back‐calculated the baseline value using eqns (26) and (28), yielding ${\mathrm{C}}_{oxtr,early}$ = 0.597 pmol·mL⁻¹. In this calculation literature values in fmol·mg⁻¹ protein were converted to pmol·mL⁻¹ as:

$$\left[\mathrm{OXTR}\right]=\mathrm{OXT}{\mathrm{R}}_{\mathrm{lit}}·U_{\mathrm{fmol}\to \mathrm{pmol}}·f_{\mathrm{prot}}·\rho$$ (D.3)

where $\mathrm{OXT}{\mathrm{R}}_{\mathrm{lit}}=2077$ fmol·mg⁻¹ protein is the oxytocin concentration reported in Fuchs et al. (1983), $U_{\mathrm{fmol}\to \mathrm{pmol}}=0.001$ is the unit‐conversion factor, $f_{prot}=0.1$ (Gam et al., 2017) is the proportion of tissue protein per milligram of wet tissue and $\rho =1.04$ g·mL⁻¹ (Kapraun et al., 2019) represents the average body density of pregnant women.

Data availability statement

The simulation data generated and analysed during this study are available from the corresponding author upon reasonable request. The computational model code used to generate the results of this study is available from the corresponding author upon reasonable request.