Prediction of Heptatic and Renal Clearance in Pediatric Populations : A " Bottom-Up " Approach Versus " Top-Down " Recognition of Covariates

Medications, including many that are widely used in children, are rarely tested in children. Their safety and effectiveness have not been established in children or have been established only for children of a certain ages. For example, 53 of 140 new medications were labeled for use in children when they were initially approved. Much of pediatric practice, particularly in hospitals and by specialists, has involved “offlabel” use of medications. As a consequence, about one-third of the drugs prescribed in office-based pediatric practices and about two-thirds of those prescribed to children in hospital settings are unlicensed or off-label. This proportion reaches 90% in intensive care units. Thus, accurate information about dosage in different age groups is particularly important, otherwise, children might be over or under treated. The safety of a drug in children often cannot be extrapolated from data in adults; medications may be more or less toxic in children and require specific studies. The effectiveness of a drug can be extrapolated from an adult when no relevant differences can be anticipated in disease, disease progression or exposure-effect relationships. Such data are usually supplemented with pharmacokinetic studies. Drug clearance (CL) is a principle PK parameter determining the age-dependent difference. Therefore, predicting pediatric clearance accurately is crucial for appropriate pediatric dosage regimen. Body weight normalized clearance is widely used because of its simplicity but it does not account the maturation of enzymatic and organ functions. As a result, children is often overdosed because of the over estimation of clearance, especially in neonates and young infants. Recently, anticipation of clearance is built based on more complex mathematical models, which could take a data or knowledge-driven approach by employing either observed data (top-down) or knowledge of human body (bottomup). These two approaches depend on different starting information and are likely to be used in conjunction with each other for the purposes of defining pediatric dosing guidelines. This research first focused on the bottom-up, mechanistic models for predicting age-dependent hepatic and renal elimination. The maturation of specific cytochrome P450 enzymes was modeled based the in vitro ontogeny data from hepatic microsomal studies. The age-related function then was incorporated into a well-stirred liver model with the developmental changes of other physiological factors, achieving the extrapolation from in vitro to in vivo. The model predictions using this physiologybased approach proved to be more accurate and precise than the allometric functions, in neonates and young infants less than 1 year of old for renal and hepatic enzyme eliminated drugs. In the top-down approach, population analysis is commonly used in pediatric PK studies because of heterogeneity of the study population and sparse sampling. The covariates effects such as age and size was examined in simple exponential relationships. However, these estimates, despite statistical validation in the observed population, may not suffice to predict parameters distribution and drug exposure in a new population. A more complex covariate-parameter relationship was explored to describe the maturation process and changes in physiological functions, based on the clearance values of renal and hepatic eliminated probe drugs. In these cases, the maturation information derived from metabolic probes could be used as system specific covariate models for other drugs via the same elimination routes in neonates

complex mathematical models, which could take a data or knowledge-driven approach by employing either observed data (top-down) or knowledge of human body (bottomup). These two approaches depend on different starting information and are likely to be used in conjunction with each other for the purposes of defining pediatric dosing guidelines.
This research first focused on the bottom-up, mechanistic models for predicting age-dependent hepatic and renal elimination. The maturation of specific cytochrome P450 enzymes was modeled based the in vitro ontogeny data from hepatic microsomal studies. The age-related function then was incorporated into a well-stirred liver model with the developmental changes of other physiological factors, achieving the extrapolation from in vitro to in vivo. The model predictions using this physiologybased approach proved to be more accurate and precise than the allometric functions, in neonates and young infants less than 1 year of old for renal and hepatic enzyme eliminated drugs.
In the top-down approach, population analysis is commonly used in pediatric PK studies because of heterogeneity of the study population and sparse sampling. The covariates effects such as age and size was examined in simple exponential relationships. However, these estimates, despite statistical validation in the observed population, may not suffice to predict parameters distribution and drug exposure in a new population. A more complex covariate-parameter relationship was explored to describe the maturation process and changes in physiological functions, based on the clearance values of renal and hepatic eliminated probe drugs. In these cases, the maturation information derived from metabolic probes could be used as system specific covariate models for other drugs via the same elimination routes in neonates or young infants.
vi PREFACE Manuscript Format is in use for this dissertation.

Chapter 1 (Manuscript-I)
During childhood, as the body weight and its function changes dramatically with age, drug therapy should be arranged according to age-related changes in pharmacokinetics at different age stages. Although the data on drug disposition in infants and children increased considerably over the past 2 decades, the effects of development on pharmacokinetics and pharmacodynamics remain poorly understood.
In chapter 1, the impact of developmental pharmacology on drug absorption, distribution, metabolism and elimination in infants and children are reviewed.
Absorption may be affected by difference in gastric pH and stomach emptying time.
Low plasma protein concentrations and higher body water compositions can change drug distribution. Metabolic processes are often immature at birth and this leads to reduced clearance rates and prolonged half-life for those drugs, which metabolism is a significant mechanism for elimination. Renal excretion is also reduced in neonates due to immature glomerular filtration and tubular secretion. Limited data are available on pharmacodynamics of drugs. Pharmacokinetics processes develop at different rates during the first year of life after birth, thus requiring continual modification of drug dose regimens for their safe and effective use in neonates, infants and children.

Chapter 2 (Manuscript-II)
The maturation of drug metabolizing enzymes is probably the predominant factor accounting for age associated changes. The group of drug-metabolizing enzymes most studied is the cytochrome P450 (CYP) superfamily. In chapter 2, the development of vii CYP enzymes involved in xenobiotic metabolism are reviewed from fetal through the life span. These hepatic P450s showed discrepancy in the onset of activities and develops independently. The ontogeny of individual isoform could be described in 4 groups. A first group of CYP3A7 and CYP1A1 expressed at high levels in the fetal liver but silenced in the postnatal period. A second group includes CYP2D6, CYP2E1 and CYP2C19. They surged within hours after birth although proteins could not be detected in fetal samples. A third group of P450s develops later. CYP3A4 and CYP2C9 rose during the first week after parturition and CYP1A2 is the latest isoform to be expressed in the human liver. A fourth group fourth group includes the enzymes with a relatively constant level of expression during hepatic development such as CYP3A5. Individual CYP Enzyme expression/activity data from hepatic microsomes in specific infant age groups are assembled. Tentative general mathematical functions describing the ontogeny of hepatic CYPs are elaborated from these age-specific data.
Combined with quantitative changes of other physiological factors during early life stages, these functions have permitted the development of physiological based pharmacokinetic models and the prediction of drug disposition in pediatric population.

Chapter 3 (Manuscript-III)
Drug systemic clearance mechanism matures quickly during the postnatal period and leads to rapid changes in an infant's capacity to eliminate drugs. In chapter 3, a mathematical model describing the maturation of hepatic cytochrome P450 enzymemediated clearance and renal clearance due to glomerular filtration was elaborated from developmental physiology and the ontogeny information of specific cytochrome viii P450s. The model predicts an age-and elimination pathway-specific clearance for the ontogeny of renal clearance, and metabolic clearance of CYP1A2 and CYP3A4.
The systemic clearance of 6 probe compounds was predicted using the model whose elimination is primarily mediated by a single CYP enzyme or by glomerular filtration. The model performs reasonably well for CYP3A4 substrates with predictions within 2-fold of the observed values in 87% of alfentanil and 74% of midazolam. However, poor predictions were obtained for CYP1A2 substrates caffeine and theophylline with predictions within 2-fold error less than 45%. The overall under predictions for CYP1A2 probes in infants less than 1 year of old suggested the contribution of alternative elimination pathways to the overall clearance of these drugs in neonates. For renal clearance due to glomerular filtration, the model provides reasonable predictions in neonates and young infants.
Clearance scaling is not intended to replace the clinical trials for drugs in development but it will provide a valuable guide on dosing regimens for the first-time doing in children. Furthermore, clearance scaling can greatly benefit the dose adjustment of clinical drugs used in neonates and young infants.  In pediatric population, developmental changes in clearance can be predicted by age and size (body weight or body surface area). Clearance in children is commonly scaled from adults by size using either the per kilogram, body surface area or allometric ¾ power models. But the size model does not account for the maturation process of the elimination organ and therefore may not be appropriate to scale clearance to the very young children. The physiology-based approach accounts for ix maturity but requires detailed knowledge regarding developmental changes. In chapter 4, these approaches were compared and appropriate use of these approaches is dependent on the age and clearance pathway.
A child PK database was developed and the dataset of experimentally obtained clearance values was used. Predicted clearance values in children were calculated based on the adult clearance, age and weight data using the four approaches. The ratio of predicted to observed values was graphed separately for probe substrates of three predominant clearance pathways: CYP1A2, CYP3A4 and renal clearance due to glomerular filtration. Allometric ¾ power model and body surface area approach systemically over estimated clearance in children below 1 year of old for all the compounds. Physiologybased approach accurately predicted clearance at all ages for compounds eliminated via CYP3A4. The clearance of CYP1A2 substrates within the first year were under predicted by the physiology-based approach but over estimated by the other approaches. In the case of renal clearance in children below 1 year of age, the per kilogram and physiology-based model performed similar with a few overestimations.
Physiology-based clearance scaling accurately predicted clearance in children from birth to 18 years. The allometric ¾ power and body surface area model are only accurate when the major clearance pathway is fully matured.

Chapter 5 (Manuscript-V)
Population modeling in pediatric studies often uses size and age as covariates.
Covariate-parameter correlations are described in an exponential relationship used by allometric scaling. However, extrapolations based on such parameter estimates have x limited value due to differences in the impact of developmental growth across populations. The quantitative models used to describe the clearance maturation processes across the age range may be required to improve extrapolation and predictive performance.
Previously published pharmacokinetic parameters from probe substrates of hepatic and renal elimination processes are used to develop clearance pathwayspecific maturation models. The postconceptional age (PCA) was used as the variable in the modeling practice. Clearance maturation, after standardized to a 70-kg adult, is best fitted with a Hill function. The two renal excreted compounds due to glomerular filtration, gentamicin and vancomycin, presented similar maturation half-life and Hill coefficient, suggesting a system-specific maturation function of glomerular filtration rate (GFR). Similar results were attained with CYP1A2 metabolic probes theophylline and caffeine. Midazolam and alfentanil demonstrated different clearance maturation profiles suggesting a complexity in CYP3A4 metabolism.   Table 2 Gentamicin and vancomycin maturation clearance parameter estimates .... 159 Table 3 Alfentanil and midazolam maturation clearance parameter estimates ......... 160 Table 4

Introduction
The pediatric population is very dynamic compared to the adult population. It consists of a collection of highly variable groups that span from new born babies to adolescents of 16 years old. According to the Food and Drug Administration (FDA) guidance, the pediatric population is broken down into the following age-based groups: neonates (birth to 1 month); infants (1 month to 2 years); developing children (2 to12 years); and adolescents (12 to 16 years). 1 In addition to growth in physical size, dramatic changes in body proportions, body compositions, physiology, neurologic biochemistry, and psychological development take place during the transition between infancy and childhood. Growth and development occur particularly rapidly during the first 2 years of life. Body weight typically doubles by 6 months of age and triples by the first year of life. Body surface area doubles during the first year. 2 Proportions of body water, fat and protein continuously change during infancy and childhood. Major organ systems mature in size as well as function during infancy and childhood. Additionally, the pathophysiology of some diseases and pharmacologic receptor functions change during infancy and childhood and differ from adults. For example, most cases of hypertension in children are secondary to renal disease, whereas most cases of hypertension in adults are primary or essential. This has profound effects on the design of antihypertensive drug trials with children. 3 The different sensitivity of the neuromuscular junction to d-tubocurarine (d-TC) among neonates, infants, children and adults has been determined. 4 All of the previously mentioned changes can affect the pharmacokinetics and pharmacodynamics of various drugs and other xenobiotic compounds in the infant and developing child.
Mainly due to the ethical concerns, clinical studies to investigate drug pharmacokinetics and pharmacodynamics in the pediatric population did not begin until 1970's, which is a period also accompanied by the development of sensitive and specific bioanalytical assays. Since that time, numerous studies have reported agerelated pharmacokinetic profiles, and to a lesser extent, pharmacodynamic profiles, for many therapeutic agents used in children. 5,6 Pharmacokinetic parameters including half-life, apparent volume of distribution and total plasma clearance, were shown to have substantial differences among different age groups even when normalized by body weight. 7 These findings were confirmed by population analyses in pediatric patients across broad age ranges, which indicated that in addition to body size, age is an important determinant of pharmacokinetic parameters the pediatric population. [8][9][10][11][12] Age associated developmental changes, such as body compositions, organ functions, ontogeny of drug biotransformation pathways, disease progression, pharmacological receptor functions, have all been shown to affect drug dispositions and response profoundly, especially during the first two years of life. 13 Understanding these age effects can provide a mechanistic way to identify initial doses for the pediatric population.
The purpose of this review is to summarize quantitative and qualitative developmental changes in the neonate, infant and developing child, and discuss how these changes may produce age-associated changes in the drugs' pharmacokinetics (bioavailability, volume of distribution, protein binding, hepatic and renal elimination), and pharmacodynamics. Approaches that can determine age-specific dosing regimens through a mechanistic understanding of pharmacokinetic and pharmacodynamic are discussed.

Absorption
In contrast to intravenous administration, drugs administrated extravascularly must undergo absorption to reach the systemic circulation. Absorption is frequently assumed to be a single first order process and is often quantified by absorption rate constant (k a ), the time to reach peak concentrations (t max ), and the extent of drug absorption by the fraction of the dose absorbed (F) and the value of the peak plasma concentration (C max ).
In the gastrointestinal tract, several age-related anatomic and physiological changes have been found that may affect drug absorption (Table 1.1). Gastric pH is neutral at birth but falls to pH 1-3 within 24-48 hours after birth. The pH then gradually returns to neutral again by day 8 and subsequently declines very slowly, reaching adult values only after 2 years of age. 14,15 The higher pH or relative achlorhydria in neonates and very young infants may partially explain the higher bioavailability reported for acid-labile compounds such as beta-lactam antibiotics because higher gastric pH results in their reduced degradation. 16 Bioavailability of orally administered weak acids, such as phenytoin, acetaminophen and phenobarbital, may be reduced in infants and young children due to increased ionization under achlorhydric conditions. 17,18 Gastric emptying and intestinal motility are important determinants for the rate of drug absorption in the small intestine, which is the major site of drug absorption.
Gastric emptying time during the neonatal period is prolonged relative to that of the (CYP3A4) metabolism leads to an increased oral bioavailability. 21 One study observed that intestinal biopsy specimens from young children (1-to 3-years old) had a 77% higher busulfan glutathione conjugation rate compared to older children (9-to 17-year old), which may lead to an enhanced first-pass intestinal metabolism and a reduced absorption fraction (F) in young children. 22 Gabapentin is primarily excreted in urine as unchanged drug, and its bioavailability is dose independent because the Lamino acid transporter in the GI membrane is saturated by high drug concentrations.
Oral clearance of gabapentin is 33% higher in children younger than 5 years than in older children or adults. Because renal clearance reaches adult levels at 1-2 years of age and gabapentin is not protein bound, this effect on oral clearance is not likely due to the altered clearance but decreased bioavailability caused by immature L-amino transporter activity. 23 Developmental changes also can alter the absorption of drugs by other extra vascular routes. Percutaneous absorption of drugs through skin may be high in newborns and infants owing to better hydration of the epidermis, greater perfusion of the subcutaneous layer and the larger ratio of total body surface area to body mass compared to adults. Thus, the relative exposure to steroids applied topically in newborns and infants may exceed that in adults and result in toxic effects in some instances. 24 The absorption of intramuscular administered drugs may be delayed in neonates from reduced blood flow to skeletal muscles, although it is often unpredictable in clinical practice. 25

Distribution
Independent of the route of administration, once the drug enters the blood stream; it is distributed into the vascular compartments of the body and extra vascular tissues. Plasma protein binding tends to be reduced in neonates and infants. 28 Factors that influence the drug-protein binding during infancy include: the total amount of plasma proteins such as albumin and alpha1-acid glycoprotein, the binding affinity and the presence of endogenous compounds. Reduced protein binding may result in drugs being distributed more widely and an increased apparent volume of distribution. For example, a clear link between an increased volume of distribution in neonates and the decreased protein binding has been reported for phenobarbital. 18 In addition, the decreased protein binding would alter the ratio of unbound to total plasma concentrations for the highly protein-bound antiepileptic drugs such as phenytoin, which makes the total concentrations of phenytoin difficult to interpret for therapeutic drug monitoring in neonates and young infants. 29 Finally, it is worthwhile to mention that highly bound acid drugs such as sulfonamides can compete for bilirubin-binding sites on albumin and displace bilirubin when plasma albumin level is low. This will lead to increased blood levels of unconjugated bilirubin and increase risk of kernicterus in the fetus or neonate. 30

Drug Transport
Drug transporters such P-glycoprotein (P-gp), organic anion transporting polypeptides (OATPs), organic anion transporters (OATs), cation transporters (OCTs), and breast cancer resistance protein (BCRP), may influence drug absorption, distribution and elimination. 31 Limited data in humans suggest that P-gp follows a developmental pattern. P-gp mRNA and protein were detected in human kidney and liver as early as 11 to 14 weeks of gestation but were only detected in brain and intestine in the third trimester of pregnancy. 32 A significant amount of P-gp is expressed in the intestine of neonates and infants with a large interindividual variability. 33 In human intestinal and liver tissues from individuals of different age ranging from neonatal to 85 years, P-gp expression was relatively low in the neonatal group but it increased with development and reached maximum levels in young adults (15 -38 years of age) and decreased to half the maximal levels in older individuals (67 -85 years). 34 There is differential expression of P-gp in various tissues. A study in 90 healthy volunteers aged 0 -86 years showed that P-glycoprotein activity in peripheral blood lymphocytes was highest in cord blood and progressively declined with age. 35 The clinical significance of developmental changes in transporter functions has not been systemically studied in humans.

Hepatic Metabolism
Drug metabolism can be divided into two types of reactions: phase I and phase II metabolism. Phase I metabolism involves structural alterations of drug molecules by introducing or unmasking a functional group (e.g. oxidation, reduction and hydroxylation Although glucuronidation is considerably reduced in newborns, sulfation appears to be well developed at birth. The variation in the function of the two phase II reactions can be seen with the developmental changes of acetaminophen metabolism. In early infancy, acetaminophen is primarily converted into the sulfate conjugates; but with increasing age, glucuronidation becomes the predominant form of metabolism. 13 Acetylation has also been studied and has been found to have reduced activity in the first month of life, although the effect of age appears to be less dominant than that of polymorphism of N-acetyltransferase (NAT). 50 Esterase activity is also reduced in newborn and this may partly account for the prolong effects of local anesthetics. 55 In conclusion, both phase I and II metabolic processes may be immature at birth.
These deficiencies may result in the increased risk for drug toxicity in infants and young children. An often cited example is "gray-baby" syndrome associated with the administration of chloramphenicol (substrate of UGT2B7

Renal Elimination
Excretion of drugs by the kidneys is dependent on three processes. First, glomerular filtration, a passive process whereby a drug not bound to plasma proteins is filtered into the renal tubule. Clearance by glomerular filtration is principally determined by the glomerular filtration rate (GFR) and the extent of plasma protein binding. Second, drug excretion may be augmented by the action of uptake and efflux transporters in the renal tubule epithelium of the proximal convoluted tubule. Finally, drugs may be re-absorbed from the tubule back into the blood by passive diffusion, which is determined by the physiochemical characteristics of the drug and urinary pH.
The renal clearance (CL r ) of drugs is the sum of three processes (Eq.1). Each of these processes exhibit independent rate and pattern of development.
Glomerular filtration is the major renal elimination pathway for many drugs. As shown in Figure 2, 65, 66 the glomerular filtration rate (GFR), measured by the renal mannitol clearance, is around 10-20 mL/min/m 2 at birth for a full-term newborn. This increases rapidly to 20-30 mL/min/m 2 during the first weeks of life and typically reaches adult values (70 mL/min/m 2 ) by 3-5 months. Furthermore, the increase in GFR is highly dependent on postnatal age (PNA, the chronological age since birth). Where CL r, Cr is renal creatinine clearance (ml/min/1.73m 2 ), Ht is height (cm) and SCr is serum creatinine concentration (mg/dl). K is a constant of proportionality and different for children in different age bands. K is 0.33, 0.45, 0.55, 0.55 and 0.7 for infants with low birth weight (0-12 months), full term infants (0-12 months), children (2-12 years), female adolescents (13-21 years) and male adolescents (13- Generally, for drugs principally eliminated by kidney, immature renal clearance processes result in the inefficient elimination of drugs and prolongation of their residence time in the body (e.g. the prolonged apparent half-life in the newborns for digoxin and penicillins 69 ).

Pharmacodynamics
Unlike the rapidly accumulating knowledge of the pharmacokinetic changes associated with development, little is known about receptor development and sensitivity and how maturation affects the response to the drug-receptor interaction.
Most often, the apparent developmental differences in pharmacodynamics (e.g. higher acid inhibition effect of lansoprazole in young infants) or the incidence of adverse effects (e.g., increased hepatoxicity of valproic acid in young infants) are linked with pharmacokinetic differences. 29, 70 The existence of true age-dependent differences in receptor sensitivity appears to be supported by data on certain drugs (e.g., warfarin and tubocurarine). For example, Takahashi et al. reported that the mean international normalized ratio obtained from the prepubertal patients was significantly greater than that obtained from the adult patients, despite no differences in unbound fraction of (S)warfarin observed between pediatric and adult patients. 71 This finding suggested that children might possess a greater sensitivity to warfarin than adults due to pharmacodynamic rather than pharmacokinetic differences. Marshall and Kearns reported the in vitro developmental pharmacodynamics for cyclosporine. 72 The peripheral blood monocytes of the infants showed a twofold lower mean IC 50 (peripheral blood monocyte proliferation) and sevenfold lower mean IC 90 (interleukin-2 expression) than peripheral blood monocytes from older subjects. The study provided relevant information on developmental changes in receptor binding characteristics in vitro, but this may not be reflective of the pharmacodynamic response in vivo. Future clinical research in age-related changes in the pharmacodynamic response chain is important to fully understand drug response in the pediatric population and to identify optimum therapeutic plasma concentrations in this group.

Age-related Dosing Regimen
Simple dosage formulas (normalized by body weight or body surface area) and allometric scaling may be clinically applicable in children older than 2 years of age. 73 In neonates and young infants, where age related developmental changes in drug disposition are underway, age-specific dosing regimens are needed based on observed age-related changes in bioavailability (F), volume of distribution (Vd) and overall clearance (CL). infants. The application of population pharmacokinetic-pharmacodynamic methods has been widely advocated and is described in the FDA's guidance document. 1,86 The use of physiologically based pharmacokinetic models has been recommended to help in the first time dosing in children as well as the study design. 87, 88 However there is a strong need for more research on developmental pharmacology such as the ontogeny of drug metabolizing enzymes, transporters, receptor system, and disease progress. As the gaps in knowledge are gradually filled in, the development of therapeutic pediatric dosing regimen will be enhanced, and drugs will eventually be provided to children with greater precision and safety.   Enzyme polymorphisms affect isoniazid metabolism more importantly than ontogeny -, activity or protein not detectable; +, activity or protein detectable; ++, high level of activity or protein expression

Results:
The development of CYP1A2, 2C9, 2C19, 2D6, 2E1 and 3A4 was best described by the hyperbolic function (Eq. 1) in the age range of observations. The parameter MF 0 is the enzyme activity at birth (at postnatal age of 0 day) expressed as a fraction of the adult activity. MF max is the maximal mean activity observed in the investigated samples (expressed as a fraction of the adult levels). TM 50 is the postnatal age (day) to reach 50% of the maximal enzyme activity (MF max ) observed in the investigated age range. This parameter is indicative of the development rate of each individual isoenzyme.

Equation 1
Introduction The human cytochrome P450 enzymes are a haem-containing superfamily that consists of a total 270 CYP gene families divided into 18 families and 42 subfamilies of enzymes based on converged amino acid sequences [21]. Despite the large number of CYP genes and enzymes, only the CYP1, CYP2 and CYP3 families play a major role in drug and toxicant metabolism. The remaining CYP families are more specialized enzymes involved in the synthesis and degradation of important endogenous molecules. CYP3A, CYP1A2 , CYP2C and CYP2E1 are the most abundant CYP enzymes comprising 29%, 13%, 18% and 7% of the total CYP protein content in the adult human liver, respectively [25]. When the number of known drug substrates is considered, CYP3A is the most important isozyme, metabolizing around 52% of therapeutic drugs currently on the market, followed by followed by 2D6 (31%), 2C9 (10%) and CYP1A2 (3%) [10].
In adults, a wide inter-individual variation in hepatic P450 expression and associated metabolic activity has been reported for each isoform. These variations may be the result of genetic polymorphisms and/or the induction or inhibition of enzyme activity by concomitant medications or exposure to environmental xenobiotics [20,24].
In the pediatric populations, ontogenesis, or the change of enzyme expression/activity as a function of age, is superimposed upon the genetic and or environmental factors, and adds further to variability in enzyme activity and unpredictability. The current knowledge of the ontogeny of hepatic CYP enzymes during the fetal and infant development has been reviewed in-depth [1,3,8,13,22]. It is well recognized that each individual CYP enzyme demonstrates an independent rate and pattern of development.
However the characteristic maturation patterns of each CYP enzyme have rarely been quantified as a continuous function of age from birth and the age of reaching adult level. Such enzyme maturation functions, in conjunction with other age-related physiological changes in neonates and infants, constitute the non-drug specific inputs to physiologically based pharmacokinetic (PBPK) models in pediatric studies.
Therefore, the aim of this study is to fill in a piece of knowledge gap in the developmental pharmacology. In this study, published in vitro enzyme ontogeny data on the most important hepatic CYP enzymes: CYP1A, 2B6, 2C, 2D6, 2E1 and 3A, were assembled, and the age-related changes of each CYP isoenzyme were fitted with mathematical functions.

Compilation of literature data
Computerized literature search of Medline database were conducted to find references to publications describing ontogenesis of hepatic cytochrome P450 enzymes, using search words such as CYP, human, liver or microsome or hepatocyte, fetal or infant or children or age. Additionally, bibliographies from review articles and pediatric clearance scaling papers were examined to identify relevant information.
Several methods are used to investigate the ontogeny of P450 expression in the liver. These include: including analyzing the immunoquantifiable enzyme protein levels using specific antibodies; measuring mRNA levels using nucleic acid probes; and measuring enzyme catalytic activities using probe substrates. Significant discrepancies exist between developmental profiles obtained from mRNA compared to protein expression or activity levels. As a result, the enzyme-specific ontogeny is based on in vitro literature values of age-dependent enzyme expression and activity from hepatic microsome or hepatocyte studies.
In most studies individual data were not reported. The mean values and variability were reported and stratified by age groups. The small amount of available individual data from the studies was grouped into different age bands, with variability, to reduce residual errors generated from such data. For those data reported in graphs instead of tables, an open digitizing software (Engauge Digitizer 5.1, http://digitizer.sourceforge.net/) was used to extract data by converting image files into numbers. Where developmental changes were reported for age bands, the median age was used for modeling purpose.
For each study reviewed, the in vitro enzyme expression and activity data were expressed as a ratio of adult values presented in the same study so that the absolute values/units were not an issue when comparing studies. The original enzyme protein expression and activity data compiled from published studies is summarized in Table   1.

Ontogeny modeling approach
The age-dependency for one individual enzyme isoform can be described by either protein or a probe substrate reaction. A naïve data pool approach was used to develop ontogeny models for individual isoenzymes: CYP1A2, 2C9, 2C19, 2D6, 2E1 and CYP3A4. Changes with age were evaluated by applying four different models, including hyperbolic, sigmoid (hill-type), logarithmic and mono-exponential functions [2], with minimization of residual errors (proportional error model) using nonlinear regression with NONMEM (NONMEM VI; Globomax LLC, Hanover, MD, USA).
The most parsimonious models were identified by visual inspection of fits and using the Akaike information criteria (AIC). AIC values were calculated from the following equation: AIC = NONMEM objective function value + 2 × number of parameters in each structural model.

Total hepatic cytochrome P450s
Not sure this is relevant. It is standard and you didn't personally do it. Among the studies indentified, the P450 content in adult liver varied from 0.25 to 0.5 nmol per mg microsomal protein with a mean of 0.3 nmol per mg microsomal protein. The major enzyme found in fetal livers was CYP3A7 (97 pmol per mg microsomal protein)., which accounted for about 32% of total P450 The content of CYP1A1 in fetal liver microsomes was roughly about 6 pmol per mg protein.

CYP1A1
CYP1A1 is the most abundant enzyme of CYP1A family in the adult lung tissue and is mainly involved in the biotransformation of environmental pollutants and carcinogens like benzopyrene in the lung. It is highly inducible by exposure to polycyclic aromatic hydrocarbons derived from cigarette smoking. The information regarding the ontogenesis of lung CYP1A1 is limited.
CYP1A1 does not appear to be inducible or expressed constitutively in the adult human liver. There is some evidence for the presence of CYP1A1 in human fetal liver. CYP1A1 mRNA and catalytic activity were found in human embryonic hepatic tissues at very various stages of gestation (50-60 days) [36]. Immunoreactive CYP1A1 protein has been detected in liver microsomes of human embryos at 11 to13 weeks of gestation [26]. Consistent with these reports, functional CYP1A1 may be involved in the demethylation of imipramine in human embryonic hepatic tissues at early stages of gestation (days 52-59) [5]. However, CYP1A1 mRNA and protein were not detected in the fetal liver samples in the middle or late gestation [4,11]. There are no other reports on the expression or function of CYP1A1 in fetal liver samples during the second and third trimester of gestation. The recent evidence appears to support the theory that CYP1A1 is constitutively expressed at very low levels in fetal liver during the first trimester, and then declines to nondetectable levels after the early gestation period and beyond.

CYP1A2
The reported CYP1A2 content in adult human liver accounts for about 13% of the total P450 protein expression and varies from 19 to 67 pmol per mg microsomal protein, (Rowland 2003;Zhang 2007). CYP1A2 is mainly involved in the metabolism of wide variety drugs and chemicals including theophylline, imipramine, caffeine and methoxyresorufin.
Tateishi demonstrated that CYP1A2 liver expression is about 10% of adult levels in infants younger than 1 year of age [31]. Two corroborating studies [4,28] provided convincing evidence of a maturational delay of CYP1A2 enzymatic activity. CYP1A2 protein rose in the group of infants aged 1-3 months and increased progressively to reach 50% of the adult value at one year. The ontogenic profile of the demethylation of methoxyresorufin (MEROD), a specific marker of CYP1A2, and the CYP1A2 mediated demethylation of caffeine in liver microsomes paralleled the evolution of the protein and confirmed the delayed development of CYP1A2.

CYP2A6
CYP2A6 constitutes about 4% of total P450 in the adult human liver and has a very limited role in drug metabolism [25]. CYP2A6 does not appear to be expressed in fetal liver [26].

CYP2B6
CYP2B6 is considered primarily as a hepatic enzyme and accounts for <1% of the total hepatic P450 content in adults. However, the relative abundance of CYP2B6 exhibited about a 45-fold range from 1.0 to 45 pmol per mg microsomal protein [37,38], which is much larger than that of the other cytochrome P450s. This large interindividual variability may be partially explained by the induced expression levels regulated by both the constitutive androstane (CAR) and pregnane X (PXR) receptors and their activating ligands, such as phenytoin and alcohol. CYP2B6 plays a role in the metabolism of drugs used in the pediatric population including cyclophosphamide, ifosfamide and efavirenz. CYP2B6 is highly polymorphic but null alleles are rare. CYP2B6*6 is the most clinically relevant allele associated with reduced protein expression and enzyme activity.
There is limited information about CYP2B6 expression during development. An early study found significantly low levels of CYP2B6 in 2 of 10 perinatal/infant samples [31]. In a recent study [9], detectable CYP2B6 protein was observed in 64% of the fetal samples from 10 weeks to 40 weeks gestation, which suggests it is expressed in the fetal stage.
After parturition, the percentage of samples with detectable CYP2B6 protein increased with the postnatal age from 64% in the neonatal samples to 75% in samples between 1 to 6 months, and approached 95% in samples from donors 11-17 years of age. The same trend was observed for CYP2B6 protein levels in which the median amount of CYP2B6 was 0.6 pmol/ mg microsomal protein in fetal/neonatal samples (10 weeks gestation to 30 postnatal days), and increased to 1.3 pmol/mg microsomal protein in samples after the neonatal period (>30 days to 17 years). The CYP2B6 protein levels in both groups varied 28-fold and 74-fold, respectively. The detailed developmental course for CYP2B6 expression is demonstrated in Fig. 1c based on data from a recent publication [9].
Although CYP2B6 is highly inducible, induction contributed little or none to the differences in CYP2B6 expression observed in Croom et al's study (9), suggesting that a change in constitutive CYP2B6 was involved in the age-related increase in median CYP2B6 levels not sure I understand.

CYP2C
The four members of the human CYP2C family: CYP2C8, 2C18, 2C9 and 2C19, account for 18% of the total cytochrome P450 in the adult liver [25] and metabolize about 29% of clinically used drugs [10]. CYP2C9 is the major CYP2C enzyme, followed by 2C19, 2C8 and 2C18 [19]. The CYP2C family is highly polymorphic and 11 genetic polymorphisms of CYP2C9 and 15 genetic polymorphisms of CYP2C19 have been identified. Allelic variants of CYP2C9 and 2C19 are responsible for poor metabolizer phenotypes.
Very little is known about the ontogeny of CYP2C8 and 2C18. Because many CYP2C9 and 2C19 substrates are clinically used in pediatric patients, there is considerable interest in the ontogeny of the two enzymes. CYP2C9 substrates include warfarin, phenytoin, diclofenac, ibuprofen, tolbutamide and losartan. Most proton pump inhibitors, such as omeprazole and lansoprazole are CYP2C19 substrates.
Total CYP2C proteins and RNAs were found to be very low in the fetal liver [23,26] and increased dramatically during the first week after birth. After 1 week, the level of CYP2C remained fairly stable up to age 1 year but did not exceed around 30% of the adult level. Two enzyme activities that depend on CYP2C -the hydroxylation of tolbutamide and demethylation of diazepamwere measured in these samples and were found to parallel the evolution and rise in the level of protein content after birth [33]. The bulk of the CYP2C content in this study was represented by 2C8, 2C9, 2C18 and 2C19.
A recent study from a different liver bank suggested that the ontogeny of CYP2C9 and 2C19 was different [12,16]. In fetal samples, CYP2C9-specific content and catalytic activity was about 1% of adult values during the first and second trimester, with a substantial increase (about 10% of mature values) during the third trimester. CYP2C19-specific protein and catalytic activities were detectable as early as 8 weeks of gestation, but unlike CYP2C9, CYP2C19 expression was similar throughout the prenatal period (10~20% of mature values).
The CYP2C9 and 2C19 developmental expression patterns were also quite different after birth. CYP2C9 levels increased dramatically at birth to reach about 25% of the reported adult values in the neonatal samples (first 30 days after birth). After this, CYP2C9 expression remained constant with little or no change until age 1 year. Between 1 to 2 years of postnatal age, CYP2C9 exhibited (achieved?) mature protein levels in most liver samples. In contrast, CYP2C19 expression did not change at birth and during the neonatal period, but increased about 2 fold in infants and children and by puberty achieved levels that were nearly 50% of those observed in adults. Adult CYP2C19 protein concentration and activity values were observed in samples from children after puberty.
The age-related changes in CYP2C protein and activities were presented in Fig.   1d and 1e.

CYP2D6
Although it only accounts for <2% of the human cytochrome P450 proteins, CYP2D6 is important for the oxidative metabolism of approximately 12% of therapeutic drugs. These include β-blockers, tricyclic antidepressants, antitussives drugs. Since several of these drugs are widely administered to newborns and neonates, the ontogenesis of this enzyme is important and has been investigated.
CYP2D6 is highly polymorphic with over 80 different alleles identified to date, including several complete loss-of function, reduced function, and multiple copy number alleles. A wide range of metabolic capacities result from the inheritance of different allele combinations. In the adult Caucasian population, approximately 7% of individuals are poor metabolizers. Debrisoquine, spartein, bufuralol and dextromethorphan are used as probes to evaluate 2D6 activity.
Low levels of CYP2D6 protein and activity (less than 3~5% of adult levels) were observed in the fetal liver samples [30]. In newborns, CYP2D6 protein or activity remained similar to third trimester fetal levels, but increased significantly thereafter.
This postnatal increase was independent of gestational age and appeared to be controlled by time after birth. CYP2D6 protein content was about 25% of adult levels in neonates aged 1-7 days and steadily increased to 50% in neonates of 7-28 days and reached about two-thirds the adult values in infants over 1 month to 5 years (Fig. 1f).
The rise of the CYP2D6 protein was associated with the rise in dextromethorphan Odemethylation, a sensitive and selective CYP2D6 probe reaction [34]. No significant differences in protein levels of CYP2D6 were found between infants greater than 1 year of age and less than 1 year of age, which suggests that CYP2D6 development was completed by 1 year of age [31]. Increasing CYP2D6 protein and activity was significantly associated with postnatal age for those less than 1 year old, but large interindividual variations existed.
The high degree of CYP2D6 polymorphism known to be present in children was likely to contribute to the inter-individual variability in early neonatal life. Almost 8% of Causasian children and 2% of Afirican-american children under 18 years of age were poor metabolizers. These data were consistent with known adult rates of this polymorphism (7~10% of whites and 1~2% African-Americans). Furthermore, Stevens et al. found both age and genotype to be significantly associated with increasing dextromethorphan O-demethylase activity in the postnatal age groups.

CYP2E1
CYP2E1 is an ethanol inducible enzyme and accounts for 7% of the total hepatic P450 enzymes. Despite its limited contribution to drug metabolism, CYP2E1 was considered to be toxicologically important because of its ability to convert a variety of agents, including environmental procarcinogens to reactive intermediates that can lead to organ damage and/or tumorigenesis. CYP2E1 has multiple polymorphisms identified to date, but only one variant of CYP2E1*1D has been linked to altered function.
The fetal expression of CYP2E1 was undetectable in early/mid gestation [11,26,35] but exhibited readily detectable levels in the third trimester [15]. CYP2E1 protein and its associated activity rose immediately after birth, independently of the gestational age, and increased gradually thereafter to reach the adult values by the first year of age. The detailed developmental time course of CYP2E1 is summarized in Fig.  1g based on two in vitro studies by Vieria et al. (1996) and Johnsrud et al. (2003).
Generally, Neonates up to 30 days have approximately 25% of adult levels of CYP2E1 protein, and this increases with postnatal age. Infants 31 to 90 days of age may exhibit up to 50% of adult levels. By 1 year of age, the expression approached adult values. CYP2E1*1D variant was identified with a low allelic frequency in a large pool of pediatric liver samples but it did not contributed significantly to the differences in CYP2E1 expression in different age groups.

CYP3A
The CYP3A is the most abundant and clinically important cytochrome P450 subfamily in the liver. It accounts for 33% of the total hepatic P450s and is responsible for the metabolism of almost 50% clinically used drugs. The subfamily consists of three major isoforms: CYP3A4, CYP3A5, and CYP3A7. They are structurally closely related, the amino acid sequence similarity between CYP3A4 and CYP3A5 is 84%, and it's 88% between CYP3A4 and CYP3A7. However, the isoforms differ in terms of their development with age, their tissue distributions and enzymatic properties.
CYP3A7 is the major isoenzyme expressed in the fetal liver, whereas CYP3A4 is the major isoform present in the adult liver. CYP3A5 is detectable in only 25-30% of liver microsomes of adults and is the primary CYP3A isoform expressed extrahepatically (e.g. kidney, intestine) (Wrighton 1990). Total hepatic CYP3A protein levels remain nearly constant from the early stage of gestation to adulthood [17], although the expression of specific isoforms change differently. Characterization of the developmental expression of CYP3A4, 3A5 and 3A7 has historically been difficult by the lack of CYP3A isoform-specific antibodies or marker enzyme activity.
CYP3A7 is the dominant cytochrome P450 expressed in the fetal liver, accounting for approximately 50% (30-85%) of total P450 in human fetal hepatic micrsosomes that contain only traces of CYP3A4 and CYP3A5 [17]. The CYP3A7 present in fetal liver microsomes was able to carry out the 4-hydroxylation of retinoic acid, the N-demethylation of dextromethorphan, codeine and ethylmorphine, as efficiently as those of CYP3A4/5 in adult liver microsomes [6,14,18]. CYP3A7 activity was highly detectable in human fetal microsomes as early as 8 weeks of gestation.
The 16α-hydroxylation of dehydroepiandrosterone (DHEA), a selective marker for CYP3A7-dependent activities, was actively catalyzed by the fetal liver microsomes (aged 14-40 weeks). It displayed its maximal level during the first week following birth before progressively declining to reach a very low level in adult livers (Fig. 1h).
The CYP3A7 content calculated from the amount of produced metabolite, 16αhydroxydehydroepiandrosterone (16α -OH-DHEA), also revealed an age-dependent decrease from early gestation to reach the extremely low level after1 year of age [12,29].
In contrast to the sharp decline of CYP3A7 from early gestation to infancy, CYP3A4 protein levels (based on measurements of 7β DHEA-hydroxylase activities) increased slowly with age [12,29]. The 6 β-hydroxylation of testosterone, a probe reaction for CYP3A4 activity, was extremely low in the fetal liver (less than 10% of the adult level) and began to rise after birth. The activity reached 30~40% of the adult value after 1 month of birth and approached the adult value after 1 year of age [17].
The same developmental tend was also observed based on CYP3A4 catalyzed imipramine demethylation and amprenavir oxidation [28,32], as shown in Fig. 1i.
The microsomal content of CYP3A5 was determined by immunoblotting with a selective polycolonal antibody to CYP3A5 isoform. The expression of CYP3A5 was independent of age, and remained nearly constant from the early gestational age (12 week of gestation) to adulthood. However, CYP3A5 protein expression was found highly variable and the large interindividual variability was most likely subject to the polymorphisms dictated by the frequency of CYP3A5*1/*1 or CYP3A5*3/*3 in certain age groups [29].

Ontogeny functions
The development of CYP1A2, 2C19, 2D6, 2E1 and 3A4 was best described by hyperbolic function in the age range of observations. CYP2C9 development was reasonably fitted with hyperbolic function (Eq.1).
Eq.1 Table 2 listed ontogeny parameter estimates. The individual fitting plots were summarized in Fig. 2. Parameter MF 0 was the fraction of enzyme activity at birth (at postnatal age of 0 day) against adult level, or the quantities for the postnatal onset of enzyme expressions. MF max was the maximal ratio of enzyme activity (to adult level) during the age range of investigated samples. TM 50 was the postnatal age (day) to reach 50% of the maximal enzyme activity (MF max ) observed in the investigated age range, suggesting the development rate of each individual isoenzymes to attain the maximum values. Because of the lack of data on when the adult values are reached, the ontogeny models for CYP2C9, 2C19, 2D6 and 1A2 can't be used to describe the enzymatic development beyond the specified age ranges.
The high MF 0 values for CYP2E1 suggested its fetal expression or prenatal onset, while the extremely low values of MF 0 for CYP2C9 and 1A2 suggested the two isoenzymes expression were triggered by birth effect.
CYP2C9, 2C19 and 2D6 appeared to mature faster than CYP2E1, 3A4 and CYP1A2, as shown by the short half-life values within days compared to those in months.

Conclusion
Overall, qualitative and quantitative analysis of these literature data allows the ontogeny of individual CYPs to be categorized into four groups: A first group of P450 enzymes (fetal enzymes) includes CYP3A7 and CYP1A1, which are expressed at highest level during gestation and are silenced in the postnatal period.
A second group of P450 enzymes (early neonatal enzymes) includes CYP2D6, CYP2C9 and CYP2C19, which are not expressed or expressed at low levels in the fetus but expression increases substantially within hours or days after birth.
A third group of P450 enzymes (neonatal enzymes) includes CYP3A4, CYP2E1, and CYP1A2, which expression increases slowly within months or years after birth.

Introduction
From birth onward, neonates, young infants and children develops with important age-dependent changes in body composition, in size (weight and height) and in maturation of hepatic and renal function (1). These processes all have a major impact on the pharmacokinetic (PK) profile of a drug from its absorption and distribution properties to metabolism and elimination. As a result, the developmental changes in pharmacokinetics require an age-dependent adjustment of dosing regimens in children to achieve the target systemic exposure of a drug (2), which is measured by the areaunder-the-plasma-concentration, AUC, or steady state plasma concentration, C ss . The total exposure of a drug is determined by the efficiency of the elimination processes (Eq.1). The apparent drug clearance (CL/F) is the principle PK process determining age-dependent differences in drug dosage regimens.
Simple allometric approaches can be applied to the estimation of pediatric clearance based on the adult clearance and the power function of body weight (Eq. 2).
The allometric exponent, b, typically assumes a value of 1 (the per kg model), 3/4 (the allometric ¾ power model), or 2/3 (the body surface area model) (3). These models derived from body size are simple to use in clinical practice. However, they are often failed to predict clearance in neonates and young infants because drug elimination pathways in the first year of life is not matured even after size adjustment (4,5). Hence, a mechanism-based approach considering the underlying physiological and biochemical processes that govern drug elimination has been proposed. The advantage of this approach over other size models is the ability to incorporate the ontogeny information of the various anatomical, physiological and biochemical processes in drug elimination, although a tremendous input of physiological data is required (6). Such a model has been applied to predict clearance of model drugs for different pediatric age groups using commercial software such as Simcyp or PKSim (7,8). The objective of this research is to develop a mechanistic model in R to estimate "population mean clearance value" in any age of child for selected model drugs, on the basis known compound-specific information in literature and published studies on the development physiology and enzyme ontogeny in children. For this study, the age-dependence of renal clearance via glomerular filtration and hepatic clearance via the metabolism of CYP3A4 and CYP1A2 was examined.

Selection of model drugs
Probe substrates for cytochrome P450 phase I metabolism, and renal excretion are selected according to the following criteria: The primary pathway of elimination due to one process in healthy adults was >80% of an oral dose.
Complete absorption (or >90%) from gastrointestinal tract after oral administration (po); for compounds showing incomplete absorption, only IV data were used.
Probe choice is routinely administered for clinical indications in ill neonates, infants and children.
Model drugs also need to have the established clinical use in adults and pediatric patients of all ages, the availability of published data on in vivo clearance for different age groups and, adequate published data on their in vivo absorption, distribution, metabolism and excretion (ADME) study, namely the contribution of each clearance pathway to total clearance. The list of drugs and major clearance mechanisms were shown in Table 1. Clearance mechanisms were identified from pharmacology textbook (9), a key review article (10), drug label, as well as primary literature for individual compounds as shown in the table.
The table provides an estimate of the percentage of parent compound processed by the major fate pathways. These compounds are grouped according to the primary process of clearance, which include the process of renal, CYP3A4 and CYP1A2 elimination.
Alfentanil and midazolam are metabolized by CYP3A as the primary route of disposition. Alfentanil is extensively oxidized via two major N-dealkylation pathways both of which are mediated via CYP3A4 in human liver microsomes. Human in vivo studies have shown that more than 80% of an iv dose is recovered in the urine of healthy adult volunteers as CYP3A4 metabolites (11). Midazolam metabolism is mediated by CYP3A4 to 1-hydroxy and 4-hydroxy derivative corresponds to the main metabolite and a minimum of 70% of an oral dose and 77% of an iv dose is recovered in the urine within 24 h as this metabolite (11).
N3-demthylation pathway is catalyzed by CYP1A2 with high affinity and accounts for 80% of the metabolism of caffeine in humans (12). Theophylline undergoes C-8oxidation as the major metabolite route accounting for 49.1% of the total urinary excretion, together with oxidative 1-and 3-N-demethylation (17.5% and 24.5%, respectively). These reactions are mediated by the CYP1A2 isoform at pharmacological concentrations.
Over 90% of gentamicin is predominantly excreted unchanged in urine through glomerular filtration (13). Similarly, over 80% of vancomycin is mainly eliminated into the urine as unchanged (9).

Compilation of child clearance database
Then computerized literature searches (PubMed, 1970-present) were conducted to find references or publications describing pharmacokinetics of probe substrates in children, using words such as, newborn, neonate, infant, children and crossing these with terms such as probe drug names, pharmacokinetics. Additionally, a variety of pediatric pharmacology reviews (14)(15)(16)(17)(18)(19) were examined to identify drugs for which PK datasets exists for children. Next, the primary PK studies in published literature were evaluated to extract key data including weight, gender, age, drug administration route, the number of does (single or multiple doses), the number of subjects, and PK findings such as total clearance or apparent volume of distribution. Through these sources, a database (Appendix I) of age-dependent observed clearances for 6 therapeutic probes were presented, based upon the availability of data for pertinent age groups (especially very early life stages), and being able to obtain the primary data sources (CL and body weight), having a reasonable number of subjects (at least 3 per age group).
A scan of the database shows that for these model compounds the weight normalized clearance in neonates and young infants appears different from the adults. Table 2 was extracted from the database to illustrate this pattern and to show how the data has been compiled and organized. The table shows the mean and SE of a single drug, midazolam, a CYP3A4 substrate. The observed adult clearance value was the weighted mean and only the mean adult clearance value was regarded in this study.

Physiologically based hepatic clearance scaling
The approach involves an in vitro-in vivo extrapolation of enzyme activity data determined in hepatic microsomal preparations from different pediatric age groups as well as the adult. Briefly, the adult intrinsic clearance (CL int,adult ) is back calculated from in vivo hepatic drug clearance (CL H ), the free fraction in plasma (f u ), the blood to plasma drug concentration ratio (C B /C P ), and hepatic blood flow (Q H ), using wellstirred model (Eq. 3) (20, 21). The generated adult intrinsic clearance value is then multiplied by scaling factor that represents the activity of the specific enzyme in relation to the age of the child (Eq. 4). This new child-scaled intrinsic clearance (CL int,child ) is used to generate an age-specific hepatic clearance calculated from the rearranged equation (Eq. 5) using age-specific body weight, liver weight, liver blood flow and predicted fraction unbound (scaled from adults based binding protein concentrations in blood). Figure 1A describes an overview of the process involved in scaling clearances from adult to children.
Because the elimination of midazolam and alfentanil are primarily due to CYP3A4 metabolism, their hepatic clearance is assumed to be close to their plasma clearance. The assumption was also applicable to theophylline and caffeine, which eliminations are primarily due to CYP1A2 metabolism.

Physiologically based renal clearance scaling
For renal eliminated drugs, it is well accepted that the renal clearance is proportional to glomerular filtration rate (GFR). For example, surrogate measures of GFR are often used to adjust the dosing rate in adults with impaired renal function (22). Extension of these concepts to adaption of the adult regimen for the child leads to the proposition that the renal clearance in child, expressed as a fraction of the adult values, is adjusted proportionally by GFR and free fractions in plasma (Eq. 6) (8). Where CL GFR is the compound specific renal clearance (mL/min), GFR is glomerular filtration rate (mL/min). Gentamicin and vancomycin, are used to evaluate this renal clearance model because they are excreted exclusively via filtration in the kidney and CL GFR is close to the plasma clearance.
Drug and system specific input Table 3 listed the drug specific parameters that are obtained from the literature (9,(11)(12)(13)23), such as CL adult , f u , C B /C P . The adult plasma clearance values are geometric means from different PK studies in which drugs were administered by i.v. injections.
The CL of alfentanil in healthy adult volunteers was obtained from total 241 healthy adult volunteers in 9 studies after intravenous administration and the geometric mean CL was 4.7 ml/min/kg (SD: 2.3) (11). The typical clearance of midazolam in adults was estimated from total 198 healthy adult volunteers of 4 studies, which was was 7.7 ml/min/kg (SD: 3.7) (11).
The mean clearance of caffeine in adults after iv administration was estimated from 20 subjects of 2 studies and the value was 1.97 mL/min/kg (SD: 0.92) (12). The theophylline clearance in healthy adults after iv administration was estimated from 100 subjects of 12 studies and was 1.0 mL/min/kg (SD: 0.29) (12).
The total clearance of gentamicin in healthy adults after iv administration is estimated from 219 subjects of 6 studies, which was 1.3 mL/min/kg (SD: 0.5) (13).
The total clearance of vancomycin in healthy adults after iv administration was estimated from 121 subjects of 6 studies and the mean value was 1.22 mL/min/kg (SD: 0.5) (24).
The physiological parameters such as plasma protein binding level, hepatic blood flow, liver volume and enzyme activity are variable with age. The empirical regression functions that can generate age appropriate parameters and account for the developmental differences between infants and adults are shown in Table 4. The mean physiological inputs were listed in Table 5  Where P child is the binding protein concentration in the child and P adult is the binding protein concentration in the adult.

Age-dependent physiological changes
Body weight, height and body surface area Original data on age-related changes in human body weight and height were obtained collected from reference in Appendix 2 (27). The mean weight or height changes with age in each study were pooled and fitted with the linear regression, natural spline function or polynomial functions. Polynomial equations (Table 4) best described the age-related changes in weight and height in the age band of day 1 to 18 year. Body surface area (BSA, cm 2 ) at a certain age was estimated using Dubois and Dubois function with age appropriate weight and height (Eq. 8) (28). The fitting plots of projected body weight, height and body surface area changes with age were displayed in Figure 2.
In child pharmacokinetic study database, age-associated weight or mean weight values for individual or subgroups were not always reported in each study. The missing weight values were then calculated from the known age using the regression function listed in Table 4. The height values were not reported for subjects in most studies and therefore calculated values were used.

Johnson et al. (27) studied liver volume (LV) in 5036 children and young adults
(ages from birth to 18 years) and derived a model ( Table 4). The value of liver weight (LW) can be converted from liver volume by multiplying the density of liver of 1.08 kg/L. The predicted liver weight was validated against the independent data ( Figure   2).

Cardio output and hepatic blood flow
Hepatic blood flow (Q H ) in adult was derived as the sum of the pre-portal organ blood flows, which includes the intestines, stomach, pancreas and spleen plus the arterial liver blood flow. The adult liver blood flow is scaled to children by maintaining the same percentage of cardiac output (CO) to the total sum of arterial blood flow and the portal blood flow, representing 25.5-27% for adults in the International Commission on Radiological Protection (ICRP) publication (25).

Age related change in cardiac output was modeled from Williams et al. (29) for
their investigated CO in more than 50 studies involving normotensive children, adolescents and healthy adults. For children age 0.2 to 4 y, linear regressions of CO on age seemed appropriate with r 2 =0.75. For older children (age 5 to 19 y), a nonlinear regression using body weight as the predictor is better with r 2 =0.81. The predicted cardiac output rate was validated against independent data (30). The hepatic blood flow was calculated using Equation 9 by assuming the same portion of blood flow to the liver between children and adults. The simulated changes in hepatic blood flow with age were presented in Figure 3.

Age-dependent drug metabolism
In vitro intrinsic clearance (CL int ) is determined either by drug depletion or metabolite kinetics reported for human liver microsomes. In vitro intrinsic clearance values can be scaled to the in vivo equivalent in the whole liver using average liver weight (LW; g of liver weight) with a microsomal recovery factor (MPPGL; mg of microsomal protein per g liver) (Eq. 10) (31). If the assumptions hold true that the enzyme affinity value (K m ) value for a particular enzyme isoform remains constant with adult values throughout infant development and that infants and adults express the same complement of hepatic enzymes, the in vivo intrinsic clearance for the infant is calculated using Equation 11. Thus, functional immaturity of the specific CYP enzyme and age-dependent liver growth (MPPGL and LW) explained the observed differences in CL int between the child and adult.
Ontogeny scaling factor (OSF) represents the elimination capacity of a specific enzyme in the infant relative to the adult. OSF is a unitless fraction of adult activity and is a function of both age and the particular enzyme. Liver scaling factor (LSF) represents the product of microsomal protein yield per gram liver and liver mass. Therefore, based on the age of child and the specific hepatic metabolic pathway, the prediction of intrinsic clearance in child is made based on the scaling factor for liver content and ontogenesis of a specific enzyme, in combination with the adult intrinsic clearance.
The human microsomal protein yield for adult livers is 40 mg per g liver, the most commonly used value (32) . Age was identified as a statistically significant covariate of MPPGL (33). However, the relationship between age and MP observed was difficult to be assessed. Consequently, the adult value of 40 mg microsomal protein/g of liver was used as the MPPGL recovery factor in all the age groups. The liver scaling factor (LSF) was then reduced to the ratio of liver mass between child and adult.
In vitro literature values of age-dependent CYP1A2 and CYP3A4 activity (34, 35), based on hepatic microsome studies using probe substrates or enzyme protein expression, were initially used to describe the enzyme-specific ontogeny. For each experimental study, the ratio of child to adult liver enzyme activity was sought so that absolute values and units were not an issue when comparing different studies. The functions to describe changes with age summarized in Table 4 and model fitting was displayed in Figure 4.

Age-dependent glomerular filtration rate (GFR)
The glomerular filtration value, as measured by the mannitol clearance, was reported from 63 children between the ages of 2 days and 12 years (36). A model that characterized the maturation and growth of glomerular filtration was developed by Hayton (Equation 12) (37). The predicted changes of GFR were validated against the data ( Figure 5).
Where GFR child was the calculated glomerular filtration rate in children (mL/min), BW was the body weight in kg, and age in month.

Model compilation and evaluation
The model was compiled as a function package in R (38). Clearance predictions were compared against literature values. To determine the ability of the ontogeny models to predict the observed clearances, the correlation between observed and predicted clearances for the model compounds was determined, as well as a measure of precision (the percentage of prediction values within 2-fold of the observed values).
The Person's correlation coefficient between observations and predictions were calculated with R.

Simulation
Simulations were performed using 500 virtual pediatric subjects with age ranging from birth to 18 years. The cubic spline curves of predicted clearance versus age were generated and evaluated against observed in vivo clearance values for probe substrates in children.

Results
Clearance predictions for each of the model compounds were plotted against the observations in Figure 6. For  Table 6). The overall coefficients of correlation were 0.883, 0.909 and 0.962, respectively, for CYP1A2, CYP3A4 metabolized elimination and GFR-mediated renal excretion.
The log ratio of predicted to observed clearances versus age indicated that model performance was both age and process-dependent (Figure 7). For CYP1A2 metabolic elimination, the data blow the identity line across the age range indicated the under estimation of the model for both CYP1A2 substrates. For CYP3A4 metabolic elimination, the under estimation trend for alfentanil was not changed until 2 year old of age. For GFR-mediated renal elimination, the clearances of both gentamicin and vancomycin was over estimated in children less than 1 year of old. 500 virtual pediatric subjects from born to age 18 with simulated boy weight and height were created for each of the model compounds. The simulated clearance values (normalized by weight) versus age were compared against observed in vivo clearance values for probe substrates in children (Figure 8). Most observations were within the 2-fold confidence interval.
Removal of premature data points did not improve the overall model performance. The prediction precisions of model for preterm neonate subpopulation decreased except for CYP1A2 substrates (Table 6).

Discussion
Clearance is an important pharmacokinetic concept for scaling dosage, understanding the risks of drug-drug interactions and environmental risk assessment in children. Body weight normalized clearance values often exceed those of standard adult values (39, 40). Clinicians often interpret these findings as if children had greater enzyme activities in a unit weight (or volume) of the liver than adults. This might be true if hepatic metabolic enzymes mature at birth. However, drug metabolism enzymes activity often express low at birth and develop quickly in a few months after birth, and by 1 year of old most enzymes reach the adult activity. The physiology-based scaling approach not only incorporates the ontogeny of enzymes and other physiological functions but also the growth in size. Theoretically, it should be a better model to predict the clearance across the age range from neonates to adults, especially in young infants than other methods based only on size.
Recently, the importance of age to drug clearance has been assessed by some pivotal papers from Bjorkman and Alcorn and MacNamara, and commercial software PK-sim and Simcyp. In Alcorn and McNamara's paper, an exponential growth function was used to fit the in vitro microsomal ontogeny data from birth to 6 month old and clearance was thereafter scaled for term neonates to 6 month of age (18).
Furthermore, Bjorkman used the same in vitro enzyme ontogeny function to predict clearance of alfentanil and midazolam as a function of age from birth to 20 years of age (15). Both studies suggested that additional data are required and it is critical to know at what age the enzyme activities reach the maturation level. Simcyp successfully predicted clearance for 11 drugs in children from birth to adults with inter-subject variability incorporated using a population algorithm but the software and source data are not open (7) The metabolic clearance of theophylline was under estimated in young infants <1 year of age, compared to caffeine. It could be the alternative pathways to contribute the overall clearance of theophylline or caffeine in neonates. In the adult, CYP1A2 eliminates >70% of a theophylline dose and the remaining 20% is through renal elimination, while 90% of caffeine elimination is mediated by CYP1A2 in adult with 1-1.5% excreted renally (14). The lower predicted clearance values may lie in the enhanced contribution of renal clearance to theophylline elimination in young infants, which was not considered in the model. It had been reported that renal excretion accounts for the majority of theophylline elimination in the very young infants, with limited N-demethylation by another CYP enzyme (41). In the neonate -infant group, the N-3-demethylation of caffeine was reported to correlate with CYP3A4, CYP1A2 activity, and CYP3A7. Thepresence of CYP3A7 has been detected in neonatal liver but absent in adult liver may contribute to its overall under predictions for caffeine clearance in this age group. In the current model, alternative elimination pathways are not taken into account and caused additional uncertainty in the prediction.
The interindividual variability of in vitro ontogeny observed in pediatric populations is remarkably large and is, in most cases, greater than the variability observed in adults (42). If the microsomal experiments could study a wide age range with data analyzed in small enough age groups to examine the age-related changes, especially for metabolically cleared compounds from birth to 1 year of age, the resolution of clearance prediction would be greatly improved.
There are many other parameters and assumptions in the model that require further investigation and validation. For example, it is not sure whether the amount of MPPGL is similar in pediatric and adult livers. Studies have found that microsomal recovery did not change with time. However, a recent study suggest a decrease in MPPGL with an average of 40 mg·g -1 for a 30 year old individual and 31 mg·g -1 for a 60 year old individual (33). This study has been extended using a set of pediatric samples and suggested an increase in microsomal protein content from birth to the maximum observed at approximately 30 years of age. The average neonate exhibits a microsomal protein content of only 26 mg per gram liver.
Many other enzymes exist that are responsible for drug elimination. These include many more CYPs (e.g. CYP2D6, CYP2E1 and CYP2C) and non-cytochrome P450 enzymes such as esterase, alcohol dehydrogenases. Other phase II processes include glutathione and glycine conjugation, UGT and sulfotransferase are not discussed in this study. Liver and renal transporters are not discussed either due to the lack of ontogeny data. Further experimentations to increase the ontogeny database will be needed to increase the scope of PB-based clearance scaling.

Introduction
The pharmacokinetic (PK) profiles of many drugs are different between children and adults (1,2). A principle PK parameter determining age-dependent difference is drug clearance. Predicting clearance in children based on the clearance in adult has been the topic of recent publications (3,4). Empirical approaches that focus on linear body weight (W) or body surface area (BSA) have traditionally been used. The third size model, using an exponent of weight (W 3/4 ), is termed the "allometric ¾ power model." This allometric equation can be predictive of clearance in children following a specific age (5). It becomes invalid when used below a certain age where the activities of the eliminating processes are not fully developed. This is because the size based approaches do not account for the maturation of hepatic and renal elimination (6).
A physiology-based approach has been proposed to incorporate maturation of CL for several major enzymatic (e.g. CYP3A4) and physiological (e.g. glomerular filtration) elimination processes (7)(8)(9). The drawback of this approach is that detailed knowledge about eliminating processes in adults is required and further, the ontogeny of these clearance processes is needed.
The objective of this study is to retrospectively compare the accuracy of the three size scaling approaches (linear weight, body surface area and 3/4 power model) with the physiology-based approach using compounds eliminated via various enzymatic or physiological processes (glomerular filtration). Furthermore, by using probe substrates for which the clearance process in adults is dominated (>85%) by one clearance pathway after intravenous administration, the pathway-specific age range of appropriate use for each scaling approach will be determined.

Selection of test drugs
The drugs to evaluate the prediction approaches were selected according to the following criteria: (1) The drug is routinely administered for clinical indications in ill neonates, infants and children. (2) The drug mainly binds to human serum albumin (HAS) or alpha-glycol acid protein (AGP). (3) The drug is primarily eliminated due to one process in healthy adults, which accounts >85% of an oral or i.v. dose. (4) The selected elimination processes include hepatic CYP3A4, CYP1A2 metabolism and renal excretion. (5) The drug shows complete absorption (or >90%) from gastrointestinal tract after oral administration (po). If the compound is showing incomplete absorption, only IV data are used. (6) Mean or individual clearance data for children and adults have been published.
Using the criteria described in (1)- (6), alfentanil and midazolam, theophylline and caffeine, gentamicin and vancomycin were selected separately, for CYP3A4 metabolism, for CYP1A2 metabolism and for renal clearance due to glomerular filtration.
Children PK database and age-dependent clearance dataset The pharmacokinetics of the 6 drugs has been evaluated in children to determine the appropriate dose levels for specific ages. The observed adult clearance value was the weighted mean as preciously presented (10)(11)(12) and, for vancomycin, was the adult clearance value taken from Guay et al. (13).

Physiology-based clearance scaling
This approach used information regarding clearance pathways in adults and scaled them to children. Briefly, the adult intrinsic clearance (CL int,adult ) is back calculated from in vivo hepatic drug clearance (CL H ), the free fraction in plasma (f u ), the blood to plasma drug concentration ratio (C B /C P ), and hepatic blood flow (Q H ), using the well-stirred model (Eq. 1). The generated adult intrinsic clearance value is then multiplied by scaling factors (ontogeny scaling factor [OSF] and liver scaling factor [LSF]) that represents the activity of the specific enzyme in relation to the age of the child (Eq. 2). This new child-scaled intrinsic clearance (CL int,child ) is used to generate an age-specific hepatic clearance calculated from the re-arranged equation (Eq. 3) using age-specific body weight, liver weight, liver blood flow and predicted fraction unbound (scaled from adults based binding protein concentrations in blood).
Ontogeny scaling factor (OSF) represents the elimination capacity of a specific enzyme in the infant relative to the adult; and it is a unitless fraction of adult activity with a function of both age and the particular enzyme. Liver scaling factor (LSF) represents the product of microsomal protein yield per gram liver and liver mass.
The clearance of a drug due to glomerular filtration rate in children was calculated by the following equation (Eq. 4): The age dependence of renal clearance in children by the process of glomerular filtration was studied by Hayton (14).
The age-dependent regression functions including ontogeny functions, the maturation function of glomerular filtration rate (GFR) were shown in Table 1.

Allometric scaling
In a child, the clearance can be predicted based on the known adult clearance and the power function of body weight (Eq. 4): b=1, per kg model; b= ¾, power model Where BW child is the body weight of the child and BW adult is the body weight of the adult. The mean body weight of the pediatric population from each study was used in the equation. If this value was not reported in the study, the mean weight value was taken for the mean age (or middle of the age range in some cases) using information from the International Commission on Radiological Protection (ICRP) (15). The adult body weight was set at 70 kg for all calculations. Both CL child and CL adult are given in flow units, e.g. mL/min).
The clearance in a child can also be calculated based on the adult clearance and body surface area (Eq. 5): Where BSA child is the body surface area of the child and BSA adult is the body surface area of the adult. The surface area is calculated from body weight and height using Dubios and Dubios equation (16). The mean body weight of the pediatric population from each study was used in the equation. If this value was not reported in the study, the mean weight value was taken for the mean age (or middle of the age range in some cases) using information from the International Commission on Radiological Protection (ICRP). Most pediatric studies did not report height. The height was taken for the mean age (or middle of the age range in some cases) using information from the International Commission on Radiological Protection (ICRP).The adult body surface area was set at 1.9 m 2 for all calculations.

Approach comparison
The ratios of experimentally predicted to observed clearance values (ml/min), using allometric, linear, and body surface area and physiology-based scaling, were calculated and plotted against age for each compound. The compounds were grouped according to their primary elimination pathways, which included the process of CYP3A4, CYP1A2 and renal clearance. The line of unity at which the predicted values was equal to the observed values was plotted together with the lines for where predicted clearance was either twice or half the observed clearance. To determine the age range for which allometric scaling was appropriate, and to determine if this age range depended on the process of clearance, the ratios of experimentally predicted to observed clearances (ml/min), using different scaling approaches, were calculated and plotted against age for each compound that is cleared via one prominent pathway.
To determine the ability of the defined scaling models to predict observed clearances, the correlation between observed and predicted clearances for each scaling method was determined, as well as bias and success rate (the percentage of prediction values within 2-fold of the observed values) . The bias (accuracy) was assessed by the geometric mean of the ratio of predicted and observed values or the average fold error (afe) metric using Equation 6: (under-predition=1/afe) Where N represents the number of data inputs used for the calculation. "i" in the above equations represents the age points in the age brackets defined in this study (17,18).
This approach prohibited poor overpredictions from being canceled out by equally poor underpredictions; underpredictions were of equal value to overpredictions (19). It also did not allow any single outlier prediction from biasing conclusions concerning a particular prediction method. A method that predicted all actual values perfectly would have a value of 1; one that made predictions that were on average 2-fold off (100% above or 50% below) would have a value of 2 and so forth.
In addition, the success rate was measured for each predefined age group. These groups were preterm neonates (0-30 days, <30 weeks of gestation), full term neonate (1-30 days, >=30 week of gestation), infant (1-12 months), children 1 -5 years, children 6-11 years, adolescents 12-17 years, and adults (> =18 years old). The success rate was simply the number of successful predictions using the method divided by the total number of predictions made using the method and then multiplied by 100. A prediction within an average -fold error of 2 was considered successful (19).

Results
For each elimination process, there were 2 drugs that had adequate clinical data available for assessment of prediction. For hepatic enzymes CYP3A4, physiology-based approach (method A) predicted clearance values within 2-fold of observed values for 53 of 66 data inputs ( Table 2).
The accuracy of prediction using method A was better than the other methods as indicated by the lowest geometric mean accuracy value of 2.9 ( Table 2).
For hepatic enzymes CYP1A2, the most predictive method was physiology-based method, in which 98 of 143 predictions were within 2-fold of observed, and the geometric mean prediction accuracy was 3.  Table 2). The prediction accuracy decreased in the order physiology-based > linear weight > ¾ allometric power > BSA.
In the case of renal elimination, the simplest approach, per kg body weight (method B) predicted clearance within 2-fold of observed for 101 of 135 data inputs (75%; Table 2). The geometric mean prediction accuracy value for method B was 3.0.  For hepatic enzyme metabolized drugs, there was evidence that physiology-based approach was more appropriate at young age. Physiology-based method produced little bias around the line of unity in neonates less than 1 month ( Figure 5 and 6). The 3/4 allometric power equation and BSA scaling consistently overestimated clearance in neonates. Success rates for the prediction methods by age groups were shown in Figure 7. For children greater than 1 year of age, the four prediction approaches were comparable, with values ranging from 68% to 100% success.

Physiology-based approach (method
In the case of renal elimination, the linear scaling method appeared to be the most predictive method in neonates and infants under 1 year old, in which more than 75% of predictions were within 2 fold of observed values (Figure 7). Overall, the linear scaling, 3/4 allometric power equation and BSA scaling systemically overestimated clearance in the young age groups as evidenced by the lack of data points at or below the 2-fold error line. The physiology-based approach appeared not to be biased towards either over or under estimation of clearance in neonates or infants under 1 year age. When assessed by success rate criteria, physiology-based approach appeared to be the most appropriate prediction method across the age range of neonate to 18 years.

Discussion
The body surface area model is widely used to scale drug dose in children out of infancy (16,20). This model requires the measure of height, as well as body weight, to estimate size and is usually determined from nomograms, which introduce the possibility of additional errors. Surface area can also be estimated from an allometric model with a power parameter of 2/3. However, the surface area model does not fit known observations. The body area of animals rises more slowly than the surface law would suggest, as larger animals are stockier. The surface law refers to an animal's skin. The mass of empirical evidence suggests that the appropriate scaling factor is significantly different from 0.67 and is actually 0.75 (21).
Thus, the ¾ power model has been proposed to scale metabolic and physiological processes among species based on body size, including scaling to human. This easyto-use equation presents significant improvement over the surface area model. When the clearance is calculated using the allometric surface area and compared to the ¾ power model, the two models are in close agreement for the human weight range above 20 kg (5). The surface area model overpredicts clearance by more than 10% at body weights below 20 kg (an approximate age of 5 year old child's mean weight) (6).
In our study, both body surface area model and ¾ power model tend to systemically overestimate clearance in neonates and infants under 1 year old of age, when the maturity of the process responsible for clearance are immature. This was likely because allometric scaling approaches account for development of body size but not for the ontogeny of hepatic and renal elimination pathways. Thereby, the allometric equations (BSA model and ¾ power model) are not appropriate for predicting clearance in neonates and young infants, where the intrinsic activity of the elimination process has not yet reached the activity in adults. This was also demonstrated in a study that compared the allometric approach to the physiologybased approach for the two CYP3A4 substrates, midazolam and alfentanil (22).
The per kilogram model is the poorest model but remains the most commonly used in human. In humans, an under-prediction of clearance of more than 10% occurs at bodyweights less than 47 kg compared to allometric ¾ power model. This error increases as size decreases and approaches 50% for a newborn of 3.4 kg. However, this gross under prediction is not seen for neonates and young infants in our study because of immaturity of enzyme systems or glomerular filtration (the right answer for the wrong reason!). In our study, the per kilogram model resulted in better predictions for neonates and young infants compared to allometric approaches. In the case of renal elimination, the per kg model appeared to yield more accurate predictions than physiology-based approach for neonates. The significant underpredictions of CL using per kilogram model was seen in children greater than 1 year old for renal eliminated or CYP3A4 metabolized drugs, where CYP3A4 enzyme activity and glomerular filtration has reached adult activity (23).
As demonstrated in Figure 7, the physiology-based approach, which explicitly accounts for the age dependence of hepatic enzyme activity or renal function, appears Clearance scaling is the first step towards the scaling of pharmacokinetics profiles from adults to children. The next step is to determine the age-dependent of distribution of volumes using allometric scaling or physiological approach. Together, the two parameters or a physiology-based pharmacokinetic (PBPK) simulation can lead to a reasonable prediction of a child's PK profile and decisions regarding dosing and potential therapeutic or adverse effect events can be informed.  derived CYP1A2 ontogeny scaling factor (OSF) -derived *a is the postnatal age in year **BW is body weight in kg, and age is the postnatal age in month "-" is the unitless fraction        adults >=18 year. Graph A is for CYP3A4 metabolized drugs. Graph B is for CYP1A2 metabolized drugs. Graph C is for renally eliminated drugs.

Introduction
The pharmacokinetic (PK) profiles of many drugs are different between children and adults (1). Organ maturation, body composition and ontogeny of drug elimination pathways have marked effects on pharmacokinetics parameters in the first few years of life (2). A principle PK parameter determining age-dependent difference is drug clearance. Understanding the relationship between clearance (CL) and age is useful for drug dosing.
Predicting pediatric CL of drugs used in children has been approached by using physiologically based pharmacokinetic (PBPK) simulation (3). PBPK simulation required detailed physiology data such as in vivo portions of individual elimination pathways contributed to CL, enzyme ontogeny information derived from measurements of enzyme expression and activity in postmortem livers, continuous input on age-related protein binding and physiological data into the simulation algorithm (4,5). The predicted results have been used to assist with first-time dosing in children when the complete pharmacokinetic data is absent in children (6).
An alternative approach is to use the population PK modeling to obtain ageassociated parameters when sparse drug concentration data in children is available.
Population modeling in pediatric pharmacokinetic (PK) studies often uses size and age as covariates (7). Covariate-parameter correlations are often described in simple exponential relationships used by allometric scaling (8). However, extrapolations based on such parameter estimates have limited value due to the differences in the impact of developmental growth across populations and the complexity of maturation process (9). The quantitative models that can describe the clearance maturation processes across the age range, therefore, are required to improve extrapolation and predictive performance. In this study, we collected individual or summary clearance estimates from pediatric PK studies in literature for drugs that are primarily eliminated through CYP3A4 or CYP1A2 metabolism, and renal glomerular filtration. These studies are often restricted to a particular age band e.g. neonates, infants or prepubescent children. It is possible to use CL estimates from these different age groups to develop models for the maturation of renal clearance, and hepatic clearance for CYP3A4 or CYP1A2.

Age-dependent clearance dataset
A MEDLINE (Medical Literature Analysis and Retrieval System Online) search (1976-present) were, using words such as, neonate, infant, children and crossing these with terms such as drug names, pharmacokinetics. Additionally, a variety of pediatric pharmacology reviews were examined. A database of age-dependent observed clearances (Appendix I), in neonates, young infants, children, adolescents and adults was created for therapeutic probes, which alfentanil and midazolam representing CYP3A4 metabolism, caffeine and theophylline representing CYP1A2 metabolism, gentamicin and vancomycin representing renal glomerular filtration. Table 1 was extracted from the database to illustrate this pattern and to show how the data has been compiled and organized.

Modeling CL maturation
Two developmental models were evaluated for all the six model compounds, using nonlinear regression with NONMEM VI (Globomax LLC, Hanover, MD, USA).
The first model used post conception age (PCA) as a covariate (Eq. 1). In the second model, postnatal age (PNA) was used (Eq. 2).
Where CL i is the observed clearance (mL/min) in the individual person of weight W i , CL std (mL/min/70 kg) is the typical clearance value in a standard size adult of 70 k; θ is the Hill coefficient of for clearance; βcl is a parameter estimating the fraction above or below clearance; Tcl is a parameter describing the maturation half-lives of the age-related changes of CL. These functions have been used in the developmental population PK analysis in pediatric clinical studies. Ages (PNA and PCA) were expressed in months by suing the following rules: 1 year = 12 months and 1 month = 30 days = 4.33 weeks, so that 1 year = 52 weeks. For all subjects older than age 3 months, PCA was calculated as PNA + 9.
The allometric weight scaling describes the size effect and the Hill function in this equation is used as an empirical capacity limited model for the maturation of renal function. The descriptive performance was compared between two models for all the model compounds, using visual inspection of fits and precision of estimates. The predictive performance was assessed by comparing with the observed data set to the 5 and 95 th percentiles of model-simulated data (n=500).

Results
Gentamicin and vancomycin clearance maturation was better described using PCA model (model 1) than PNA model (model 2). The descriptive performance of model 1 was slightly better than the model 2, based on evaluation of objective function, basic goodness-of-fit plots ( Figure 1) and the precision of parameter estimates ( Table 2). The predictive performance of the model using PCA sigmoidal hyperbolic model produced better prediction for alfentanil and midazolam clearance data than PNA model, according to performance plots ( Figure 3 and 4) and the precision of parameter estimates (Table 3). Alfentanil CL at birth in a term neonate was 50% of an adult value and reached the adult level by 6 month.
Midazolam clearance at birth in a term neonate was 27% of an adult, reaching 64% by 1 year of old and 80% of the matured CL at the age of 2 years. The half-life estimates (Tcl) indicated that alfentanil metabolism developed faster than midazolam metabolism.
The maturation of caffeine and theophylline clearance was better fitted using PCA sigmoidal model ( Figure 5 and 6). The parameters were presented in Table 4. In a term neonate, the caffeine clearance at birth was 8% of an adult, increasing to 50% at 6 months and by 2 years of age achieved 95% of matured activity. Theophylline clearance developed in a similar rate, reaching 50% level at 4 month of age and 95% by 2 years.

Discussion
Growth and development are two major aspects of children not seen in adults.
These aspects can be investigated by using size and age as covariates in pediatric PK studies. To identify other covariates other than body size, it is highly desirable to standardize the PK parameters to an appropriate body size measure. Once size is standardized, age or other physiological factors (i.e. GFR) can be investigated within a given dataset describing time-concentration profiles in a population. The quantitative models used to describe the maturation process vary depending on the range of the ages under investigation. An exponential age model is commonly used for population samples limited to a defined age band (10). However, this exponential function extrapolates badly beyond the range of observations. An exponential asymptotic model, similar to models based on first-order processes in biology systems, has been previously used to investigate acetaminophen age-related clearance maturation (11). A sigmoidal Emax model has been used to investigate acyclovir clearance in neonates and infants (12).
In our study, we found a sigmoidal E max model is a robust model to describe clearance maturation during infancy for different hepatic and renal elimination processes.
A plot of maturation profiles of 6 drugs representing 3 clearance processes is displayed in Figure 7. The alfentanil clearance matures more rapid, compared to the clearance of renal probes and theophylline and caffeine. The results are consistent with the in vitro development profiles of CYP3A4 and CYP1A2 enzymatic activities (13)(14)(15).
While maturation profile of midazolam in our study is similar to that predicted by Anderson et al. (16), it is slower than that observed in other drugs cleared by CYP3A4 such as alfentanil in our study and sildenafil. It has been proposed that CYP3A4 possesses three substrate binding types (Kenworthy, et al., 1999). Three CYP3A4 Renal function is influenced by physiological changes such as glomerular filtration rate (GFR) and tubular secretion/absorption processes at different stages of development. Gentamicin and vancomycin are almost entirely eliminated by kidney (17). In our study, the maturation rates of clearance values of the two antibiotics are similar. Thus, a developmental model for GFR was developed from clearance values of the two drugs throughout pediatric life until adults. It is anticipated that the renal developmental model can be used to describe maturation in clearance of other renally excreted antibiotics in neonates and infants. This approach will make a distinction between system specific and drug specific information in pediatric pharmacokinetics models (Eq. 3).
Using this approach, CL p is considered a drug specific property and is therefore estimated for each of drugs separately. The remaining information in this equation is considered system specific information that can be applied for all renally excreted drugs.
A critical question in the prediction of CL using physiology-based approach is when the activity of the applicable CYP isoforms attains adult levels.