Table 1.

Maturation functions used in Eqs. (1) and (2) for the extrapolation of system-specific and combined system-specific and drug-specific model parameters in the physiology-based pharmacokinetic (PBPK) model for renal clearance from typical adults to typical pediatric individuals

System-specific parameters for Eqs. (1) and (2) (abbreviation) (units)	Maturation functions included in the pediatric PBPK model for CLR
Glomerular filtration rate (GFR) (mL/min)	$\mathrm{GFR}=112\times {\left(\frac{\mathrm{WT}}{70}\right)}^{0.63}\times \left(\frac{\mathrm{PM}{\mathrm{A}}^{3.3}}{\mathrm{PM}{\mathrm{A}}^{3.3}+{55.4}^{3.3}}\right)$
Fraction unbound (fu) (-)	[HSA ]ped/adult = 1.1287 × ln(AGE) + 33.746 ${\left[\mathrm{AGP}\right]}_{\mathrm{ped}/\text{adult}}=\frac{0.887\times {\mathrm{AGE}}^{0.38}}{{8.89}^{0.38}+{\mathrm{AGE}}^{0.38}}$ $\to {\mathrm{f}}_{\mathrm{u},\mathrm{ped}}=\frac{1}{1+\frac{\left(1-{\mathrm{f}}_{\mathrm{u},\text{adult}}\right)\times {\left[\mathrm{P}\right]}_{\mathrm{ped}}}{{\left[\mathrm{P}\right]}_{\text{adult}}\times {\mathrm{f}}_{\mathrm{u},\text{adult}}}}$
Renal blood flow (QR) (mL/min)	CO = BSA × (110 + 184 × e−0.0378 × AGE − e−0.24477 × AGE) $\mathrm{fr}=\frac{\mathrm{f}{\mathrm{r}}_{\text{males}}+\mathrm{f}{\mathrm{r}}_{\text{females}}}{2}$ $\mathrm{f}{\mathrm{r}}_{\text{males}}=4.53+\left(14.63\times \frac{\mathrm{AGE}}{0.1888+\mathrm{AGE}}\right)$ $\mathrm{f}{\mathrm{r}}_{\text{females}}=4.53+\left(13\times \frac{{\mathrm{AGE}}^{1.15}}{{0.188}^{1.15}+{\mathrm{AGE}}^{1.15}}\right)$ →QR = CO × fr
Intrinsic secretion CL (CLint,sec) (mL/min)	PTCPGK = 60 (adult value) KW = 1050 × (4.214 × WT0.823 + 4.456 × WT0.795)/1000 →CLint, sec = ontT × CLint, T × PTCPGK × KW
Blood to plasma ratio (BP) (-)	$\text{hemat}=\frac{\text{hema}{\mathrm{t}}_{\text{male}}+\text{hema}{\mathrm{t}}_{\text{female}}}{2}$ $\text{hema}{\mathrm{t}}_{\text{male}}=53-\left(\left(43\times \frac{{\mathrm{AGE}}^{1.12}}{{0.05}^{1.12}+{\mathrm{AGE}}^{1.12}}\right)\times \left(1+\left(-0.93\times \frac{{\mathrm{AGE}}^{0.25}}{{0.10}^{0.25}+{\mathrm{AGE}}^{0.25}}\right)\right)\right)$ $\text{hema}{\mathrm{t}}_{\text{female}}=53-\left(\left(37.4\times \frac{{\mathrm{AGE}}^{1.12}}{{0.05}^{1.12}+{\mathrm{AGE}}^{1.12}}\right)\times \left(1+\left(-0.80\times \frac{{\mathrm{AGE}}^{0.25}}{{0.10}^{0.25}+{\mathrm{AGE}}^{0.25}}\right)\right)\right)$ →BP = 1 + hemat × (fu × kp − 1)
Published ontogeny functions for renal transporters (ontT) (-)	$\mathrm{on}{\mathrm{t}}_{\mathrm{P}-\mathrm{gp}}=\frac{\mathrm{PN}{\mathrm{A}}^{0.73}}{\mathrm{PN}{\mathrm{A}}^{0.73}+{4.02}^{0.73}}$ $\mathrm{on}{\mathrm{t}}_{\mathrm{OA}{\mathrm{T}}_1}=\frac{\mathrm{PN}{\mathrm{A}}^{0.43}}{\mathrm{PN}{\mathrm{A}}^{0.43}+{19.71}^{0.43}}$ $\mathrm{on}{\mathrm{t}}_{\mathrm{OA}{\mathrm{T}}_3}=\frac{\mathrm{PN}{\mathrm{A}}^{0.51}}{\mathrm{PN}{\mathrm{A}}^{0.51}+{30.70}^{0.51}}$ $\mathrm{on}{\mathrm{t}}_{\mathrm{OC}{\mathrm{T}}_2}=\frac{\mathrm{PN}{\mathrm{A}}^1}{\mathrm{PN}{\mathrm{A}}^1+{4.38}^{0.51}}$ $\ast \mathrm{o}{\mathrm{n}\mathrm{t}}_{\mathrm{A}\mathrm{T}{\mathrm{S}}_{\mathrm{H}\mathrm{a}\mathrm{y}\mathrm{t}\mathrm{o}\mathrm{n}}}=\frac{(1.08\times \mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}{\mathrm{t}}^{1.04}\times {\mathrm{e}}^{-0.185\times \mathrm{a}\mathrm{g}\mathrm{e}}+1.83\times \mathrm{w}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}{\mathrm{t}}^{1.04}\times (1-{\mathrm{e}}^{-0.185\times \mathrm{a}\mathrm{g}\mathrm{e}}))}{\mathrm{o}{\mathrm{n}\mathrm{t}}_{\mathrm{A}\mathrm{T}{\mathrm{S}}_{\mathrm{H}\mathrm{a}\mathrm{y}\mathrm{t}\mathrm{o}\mathrm{n}}}\left(\mathrm{a}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{t}\right)}$ $\ast \mathrm{on}{\mathrm{t}}_{\mathrm{AT}{\mathrm{S}}_{\text{DeWoskin}}}=\frac{20.3}{79.8},\frac{14.9}{79.8},\frac{31.3}{79.8},\frac{46.5}{79.8},\frac{44.2}{79.8},\frac{66.5}{79.8},\frac{73.15}{79.8},\frac{73.15}{79.8},\frac{79.8}{79.8}$, at 1 day, 1 month, 3 months, 6 months, 1 year, 2 years, 5 years, 15 years, and adult, respectively

WT bodyweight (kg); PMA postmenstrual age (weeks); HSA human serum albumin (g/L); AGP α-acid glycoprotein (g/L); P plasma-binding protein (e.g. HSA or AGP (g/L); CO cardiac output (mL/min); hemat hematocrit; fr fraction of cardiac output directed to renal artery; BSA body surface area (m2); AGE age in (days) for the maturation of (P) and in (years) for the fraction of cardiac output and hematocrit levels; PTCPGK proximal tubule cells per gram kidney (× 106 cells); KW kidney weight (g); ontT transporters ontogeny relative to adult levels (−); CLint,T transporter-mediated active clearance (mL/min); kp blood-to-plasma partitioning coefficient of a drug; PNA postnatal age (weeks)

*Hayton et al. developed a continuous function using age in years and weight in kg, based on the data published by Rubin et al. [17]. The function covers the pediatric age range up to 12 years and values obtained at 12 years were considered mature and assigned to the typical 15-year-old and adult (ont_ATS-Hayton(adult))

*DeWoskin et al. collected literature data on tubular secretion rates and categorized it in different age groups, from neonates up to adults. For children older than 1 year and younger than 18 years, the average between the values published for children and adults was interpolated