A General Model for Scaling Basal Metabolic Rate, Glomerular Filtration Rate and Drug Clearance from Birth to Adulthood

Abstract

Understanding the maturation process of human physiology and metabolism has broad medical and pharmaceutical implications. Age and bodyweight are frequently considered as separate variables in modeling the dynamical changes of human organ functions and of drug clearance from birth to adulthood. The objective of this study is to propose a unified, continuous and bodyweight-only equation to quantify the changes of human basal metabolic rate (BMR), glomerular filtration rate (GFR) and drug clearance (CL) from infancy to adulthood. The BMR datasets were retrieved from a comprehensive historical database of male and female subjects (0.02 to 64 years). The CL datasets for 17 drugs and the GFR dataset were generated from age-incorporated maturation-and-growth models with reported parameter values. The model used in the simulation is independent of the proposed model. A statistical approach was used to simulate the model generated CL and GFR data for a hypothetical population with 26 age groups (ranging from 0 to 20 years). Besides, individual CL data for one drug, and sparse PBPK-modeled CL values for two drugs were also included for analysis. A 4-parameter, mixed-allometry equation with two power-law functions of bodyweight was proposed and evaluated as a general model using nonlinear regression and dimensionless analysis. All datasets universally reveal biphasic curves with two distinct linear segments on log-log plots. Compared with simple allometry, the biphasic model fits satisfactorily to all datasets (based on Akaikes Information Criterion and residual plots). The biphasic equation consists of two reciprocal allometric terms that asymptotically determine the overall curvature. The fitting results show a superlinear scaling phase (slope >1; ca. 1.5 - 3.5) below the characteristic bodyweight at the phase transition; and above which, a sublinear scaling phase (slope <1; ca. 0.5 - 0.7) is evident. The phase-transition bodyweight is ranging from 5 to 20 kg (corresponding to 0.5 - 9 years) and the mean value is around 10 kg ([~]2 years) for all data sets. The dimensionless analysis generalizes, and offers quantitative realization of, the maturation and growth process. In conclusion, the proposed mixed-allometry equation is a generic model that quantitatively describes the phase transition occurring in the human maturation process of BMR, GFR and drug CL.