The present report includes a population analysis which has the advantage of `borrowing' information for individual subjects from the entire group of profiles, consideration of BQL values, and simultaneously addresses issues such as the optimum structural model, the influence of covariates which might account for the variability in drug exposures among the subjects, and utilizes several statistical measures of optimum fitting and predictive performance such as visual predictive checks ().
The population analysis revealed two phases in the disposition of lithium with an initial half-life of 2.4 hours and a later half-life of 27 hours. These phases are evident in and . It is important to note that neither of these phases determines the multiple-dose accumulation of lithium. Sahin and Benet [22
] have recently pointed out that the `operational multiple-dose half-life' is a composite of various phases for drugs with absorption and polyexponential disposition and dependent on the dosing interval (τ) according to:
Multiple-dose simulations indicate that the T1/2op
for lithium is13.1 hr for the QD, 14.0 hr for the BID, and 15.1 hr for the TID (q8h) dosing regimens. The terminal phase in the single-dose profiles accounts for only a part of the dose of drug and thus does not dominate in controlling elimination of lithium. Further, the multiple dose simulations suggested that a starting dose of 300 mg twice or three times daily for youths weighing 30 kg or more and a starting dose of 300 mg once daily for those weighing less than 30 kg appear to be appropriate based on safety margins for trough concentrations (data available on request).
The pharmacokinetic parameters of lithium reflect realistic clinical conditions as the measurements were obtained at the time of first dosing in manic children and adolescent patients. Thus the variability in the time-course profiles () and the 48% CV in apparent CL () is not unexpected. These findings argue for careful selection of initial dosages of the drug based on body weights and continued practice of therapeutic drug monitoring to assure a range of effective and non-toxic drug concentrations.
The use of FFM provided the best accounting for variability in CL and volumes in these patients. Lithium is a simple ion which largely distributes into body water spaces, which helps explain these results. However, lithium is appreciably cleared by the kidneys and the lack of correlation of lithium clearance with creatinine clearance was not expected (). The reason or reasons for this are not clear. Incomplete urine collections do not account for these observations as both directly measured and calculated (from plasma values) creatinine clearances yielded such variability. The range of creatinine clearances observed in this study was limited as all patients had normal renal function. In this case observing a relationship between creatinine clearance and lithium clearance is more difficult. Also the number of patients in this study was substantially higher than in the previously published pediatric lithium study; however it is still relatively low for detecting covariate effects. The expectation of lithium clearance relating to GFR may serve best to anticipate disposition of the drug in older patients and those with renal failure.
Several studies explored lithium PK in adults [23
]. The average reported clearance was between 1.32 and 2.15 L/h and half-life between 17.1 and 27.1 h (parameters allometrically scaled to 70 kg body weight where possible). The majority of these studies were analyzed by non-compartmental analysis (NCA).
Prior to our study, lithium pharmacokinetics had only been examined in 9 children, ages ranging from 10 to 12 years, weighing between 27 and 56 kg [11
]. In this study, the average apparent lithium clearance from NCA was 1.58 L/h, which corresponds to 2.5 L/h when scaled allometrically to 70 kg body weight. Their average β-half-life from least square regression was 17.9 h. It was concluded that children had a shorter elimination half-life and greater clearance compared to adults. An NCA performed on their graphed average concentrations revealed a large extrapolated fraction of the AUC of 22%. Also the lowest measured lithium concentrations in this study were 0.03 mEq/L. NCA does not consider concentrations below the quantification limit, which might be a reason for the reported lower terminal half-life and higher clearance compared to reports from adults.
Our study also found that the terminal half-life from NCA appears shorter and the clearance scaled to 70 kg body weight higher (average 2.66 L/h) than those values previously reported in adults. The NCA provides similar results for clearance for our study and the Vitiello study [11
]. Due to truncation of the concentration-time profiles, NCA leads to biased results towards shorter elimination half-lives and higher clearances, and to the misleading conclusion that lithium clearance would be higher in children than in adults. When taking into account the concentration time profiles of all subjects simultaneously and considering concentrations below the quantification limit by population PK analysis, the allometrically scaled clearance is within the range of values reported for adults. This suggests that the differences in lithium PK parameters between children and adults can be explained by including the effect of body weight. Therefore population PK modeling was an essential tool for this analysis.
Lithium PK in plasma and urine was modeled previously by population analysis in adults, utilizing a two compartment model. The estimate for renal clearance was 1.53 L/h [25
]. In a population PK analysis in 79 adult patients [32
], a clearance of 1.36 L/h and volume of 32.8 L was reported based on a one compartment model. In this study only trough concentrations were measured, and neither data nor fittings were shown. Lean body weight and creatinine clearance were identified as covariates for lithium clearance.
In a study in obese patients [33
] a greater clearance compared to normal weight adults which correlated with total body weight but not creatinine clearance was reported. Volume of distribution correlated with fat-free mass, but volume per kg total body weight was lower in obese compared to normal weight subjects. These results agree with our conclusions that clearance and volume are correlated with total body weight and even better with fat-free mass. Our study also included obese patients (BMI greater than 24 in 12 out of 39 patients). For our study population including both lean and obese subjects, FFM explained even more of the variability than total body weight. Therefore it is important to also take into account body composition, especially in obese subjects. As obesity is commonly encountered in patients taking antipsychotic drugs, it is a useful finding that lithium clearance correlates well with fat-free mass.
Limitations of the present study are the relatively high limits of quantification of the clinical assays which lead to many samples being below the quantification limit and also the lack of measuring lithium amounts excreted in urine for determination of lithium renal clearance. Population PK analysis including the Beal M3 method for handling BQL data was applied as the most sophisticated method available in order to deal with this limitation [21
Additionally, the use of clinical laboratories, rather than a central laboratory, for lithium assay is a limitation of the present study. Despite this limitation, it was not anticipated that the results would be substantially affected, as the utilized lithium assays are standard and validated clinical methods. Similar commercial techniques for lithium assay were employed across the study sites. Specifically, all clinical laboratories used in this study analyzed the lithium samples as they were received, rather than batched for group analysis. Additionally, prior to implementation, Linearity and Precision were verified for lithium with very low coefficients of variation (typically below 6%). All clinical laboratories subscribe to College of American Pathologists (CAP) Linearity and Calibration standards. Furthermore, all clinical laboratories used in this study run quality control daily, per CAP standards, in order to ensure accuracy and precision between day and within day variation for the analyses.
In conclusion, linear elimination for lithium was found within the studied dosage regimen. Fat free mass was identified as the covariate which explained most of the variability in clearance and volume of distribution parameters. The difference in body size explains different values for the PK parameters in children compared to adults. Possible uses of the developed population pharmacokinetic model are to predict other dosage regimens, support scaling from adult to pediatric pharmacokinetics and support the design of future clinical trials.