Prediction of drug disposition in infants and children by means of physiologically based pharmacokinetic (PBPK) modelling: theophylline and midazolam as model drugs

Abstract

Aims: To create a general physiologically based pharmacokinetic (PBPK) model for drug disposition in infants and children, covering the age range from birth to adulthood, and to evaluate it with theophylline and midazolam as model drugs.

Methods: Physiological data for neonates, 0.5-, 1-, 2-, 5-, 10- and 15-year-old children, and adults, of both sexes were compiled from the literature. The data comprised body weight and surface area, organ weights, vascular and interstitial spaces, extracellular body water, organ blood flows, cardiac output and glomerular filtration rate. Tissue: plasma partition coefficients were calculated from rat data and unbound fraction (f u) of the drug in human plasma, and age-related changes in unbound intrinsic hepatic clearance were estimated from CYP1A2 and CYP2E1 (theophylline) and CYP3A4 (midazolam) activities in vitro. Volume of distribution (V dss), total and renal clearance (CL and CL R) and elimination half-life (t(1/2)) were estimated by PBPK modelling, as functions of age, and compared with literature data.

Results: The predicted V dss of theophylline was 0.4-0.6 l kg(-1) and showed only a modest change with age. The median prediction error (MPE) compared with literature data was 3.4%. Predicted total CL demonstrated the time-course generally reported in the literature. It was 20 ml h(-1) kg(-1) in the neonate, rising to 73 ml h(-1) kg(-1) at 5 years and then decreasing to 48 ml h(-1) kg(-1) in the adult. Overall, the MPE was - 4.0%. Predicted t(1/2) was 18 h in the neonate, dropping rapidly to 4.6-7.2 h from 6 months onwards, and the MPE was 24%. The predictions for midazolam were also in good agreement with literature data. V dss ranged between 1.0 and 1.7 l kg(-1) and showed only modest change with age. CL was 124 ml h(-1) kg(-1) in the neonate and peaked at 664 ml h(-1) kg(-1) at 5 years before decreasing to 425 ml h(-1) kg(-1) in the adult. Predicted t(1/2) was 6.9 h in the neonate and attained 'adult' values of 2.5-3.5 h from 1 year onwards.

Conclusions: A general PBPK model for the prediction of drug disposition over the age range neonate to young adult is presented. A reference source of physiological data was compiled and validated as far as possible. Since studies of pharmacokinetics in children present obvious practical and ethical difficulties, one aim of the work was to utilize maximally already available data. Prediction of the disposition of theophylline and midazolam, two model drugs with dissimilar physicochemical and pharmacokinetic characteristics, yielded results that generally tallied with literature data. Future use of the model may demonstrate further its strengths and weaknesses.

Figure 1

The compartmental structures of: (a) the single-tissue model used to scale k_p values from rats to humans; (b) the perfusion-limited whole-body PBPK model. BLD, Blood; LNG, lungs; BRN, brain; HRT, heart; KDN, kidneys; SKN, skin; LVR, liver; STM, stomach; GUT, intestines; PSP, pooled spleen and pancreas; MSC, muscle; FAT, adipose tissue; CRC, ‘carcass’ (rest of the body)

Figure 2

Predicted arterial concentration-time curves of theophylline in male patients after intravenous infusion of 4 mg kg⁻¹ over 5 min. Predicted concentration curves for females were similar (see t_1/2 values in Table 4). The numbers to the right of the plots denote ages (years) of the hypothetical subjects. The lowest panel shows the predicted arterial plasma concentration-time curve in a male adult after intravenous infusion of 6 mg kg⁻¹ of theophylline over 15 min, together with concentration data from St-Pierre et al.[41]. •, Dose given at 20.00 h; ○, dose given at 08.00 h. Mean values, n = 8 in both cases

Figure 3

Predicted pharmacokinetic parameters for theophylline as functions of age, together with literature data. —, Males; - - - -, females. (a) Volume of distribution at steady state (V_dss). (b) Clearance (CL). (c) Terminal half-life (t_1/2). Data sources: (▴) [50]; (▪) [51]; (•) [52]; (Δ) [53]; (□) [55]; (○) [57], mean ± SD, (actual age range 9 months to 5 years) [56], adults [41] and [43]

Figure 4

Predicted arterial concentration-time curves for midazolam in female patients after intravenous infusion of 0.2 mg kg⁻¹ over 1 min. Predicted curves for males were similar (see t_1/2 values in Table 4). The numbers to the right of the plots denote ages (years) of the hypothetical subjects. Data points in the middle panel are mean plasma concentrations in 14 patients with a mean age of 6.2 years [61], adjusted for dose (from 0.15 to 0.20 mg kg⁻¹). The model has previously been validated for middle-aged and elderly patients [18]

Figure 5

Predicted pharmacokinetic parameters for midazolam as functions of age, together with literature data. , Males; , females. (a) Volume of distribution at steady state (V_dss). (b) Clearance (CL). (c) Terminal half-life (t_1/2). Data sources: neonates [59, 60], 4.7 (± 2.6) years, 4.9 (± 2.3) years, 5.2 (± 2.5) years [58], 5.2 (± 2) years [61], adults [18][38], and [44]. Horizontal error bars (for age) are omitted for clarity