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PEDIATRICS |
From Aster-Cephac, Saint-Benoit, France (Dr Gregoire, Dr Gualano, Ms Geneteau, Dr Millerioux, Ms Brault, Dr Mignot) and the Department of Neonatology, University Hospital of Nantes, France (Dr Roze).
Address for reprints: Nicolas Gregoire, Aster-Cephac 90 avenue des Hauts de la Chaume BP28 86281, Saint-Benoit, France.
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Key Words: Ibuprofen enantiomers • premature neonates • pharmacokinetics
In premature infants delivered before 28 weeks' gestation, Narayanan et al4 performed a historical comparison of the prophylactic administration (n = 130) of indomethacin versus the curative approach of PDA (n = 170). They showed that the former resulted in a decreased need for secondary treatment; particularly, the incidence of surgical ligations decreased from 41% to 21%. Other controlled trials have demonstrated that prophylactic treatment with indomethacin reduced the incidence of PDA as well as of intraventricular hemorrhage. However, renal side effects such as oliguria, anuria, and transient renal failure were encountered.5,6 Significant cerebral vasoconstriction and alteration of cerebral perfusion were also reported, which raised serious concerns about the decrease in oxygen availability and cellular oxygenation while using indomethacin.7,8
A number of clinical studies have been performed in the premature newborn to test intravenous ibuprofen in the curative treatment and in the prophylaxis of PDA. In premature infants younger than 33 weeks' gestational age (GA), ibuprofen has been shown to be as effective as indomethacin in the curative treatment of PDA, with significantly fewer renal side effects.9-11 Prophylactic administration of ibuprofen in premature infants younger than 32 weeks' GA (mean = 28 weeks' GA) was shown to reduce the incidence of PDA, with a trend in lowering the incidence of intraventricular hemorrhage.12,13 More recently, open studies have confirmed the beneficial effect of this prophylactic approach on the incidences of PDA and of secondary surgical ligation.14,15
Ibuprofen is a nonsteroidal anti-inflammatory drug of the 2 arylpropionic acid class, which has, as a common structural feature, a tetrahedral chiral carbon atom within the propionic acid side chain moiety, with the S(+)-enantiomer possessing most of the beneficial activity.16 In adults, ibuprofen demonstrates marked stereoselectivity in its pharmacokinetics, with substantial unidirectional inversion of the R(-)- to the S(+)-enantiomers.17 The ductus arteriosus is endowed with cyclooxygenase, which synthesizes prostaglandins; some of these mediators, such as prostaglandin E2, are responsible for the patency of the ductus.18 Therefore, inhibition of the cyclooxygenase by ibuprofen is believed to be its main mechanism of action in the treatment of PDA.
After intravenous administration of 10 mg/kg ibuprofen within the 3 first hours of life in 21 premature newborns of 22 to 31 weeks' GA,19 kinetic parameters were estimated as follows: t1/2ß = 30.5 ± 4.2 h, Vd = 62 ± 4 mL/kg, and CL = 2 ± 0.3 mL/kg/h. Another study has recently been reported in 27 premature infants (mean = 28.6 weeks' GA) treated from the third day of life20: peak serum concentrations 1 hour after the first and third doses were 33.3 ± 8.5 and 28.4 ± 9.2 mg/L, respectively, and the total body clearance and the elimination rate constant increased significantly between days 3 and 5. In patients with closed ductus arteriosus after treatment, the ibuprofen serum concentration was higher compared with patients with persistent ductus arteriosus after treatment.
These pharmacokinetic studies used a full sampling approach and considered only the ibuprofen racemate. The objective of the present study was to evaluate the pharmacokinetic parameters for both S(+)- and R(-)ibuprofen enantiomers in very premature neonates (strictly inferior to 28 weeks) and possible relationships between the pharmacokinetic parameters and various covariates. Moreover, a minimal impact on the premature neonates was obtained by applying a sparse sampling approach and a population pharmacokinetic analysis. The clinical trial was prematurely terminated because of 3 cases of severe hypoxemia after ibuprofen administration.21 Complete clinical outcomes of the present study will be described in a separate publication. The objective of the present pharmacokinetic analysis was to evaluate the pharmacokinetic parameters for both S- and R-ibuprofen enantiomers in very premature neonates (gestational age strictly inferior to 28 weeks) and possible relationships between the pharmacokinetic parameters and various covariates.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Premature newborn infants (gestational age strictly less than 28 weeks) aged strictly less than 6 hours were selected for study. Newborns meeting the inclusion criteria were randomized according to a balanced 1:1 ratio design to receive either prophylactic active medication (i.e., ibuprofen) or placebo. The study consisted of 2 successive periods of treatment (i.e., a prophylactic period followed by a curative period when necessary).
Intravenous ibuprofen (PEDEA®) was provided by the sponsor (Orphan Europe, immeuble "Le Guillaumet" 60 avenue du Général de Gaulle 92046 Paris-La Défense, France). It was a ready-to-use solution in 2-mL ampoules containing 10 mg of ibuprofen. The intravenous line was flushed with 1.5 mL of 0.9% sodium chloride following injection to ensure that all of the drug was actually administered. The placebo solutions contained 0.9% sodium chloride. Prophylactic ibuprofen or placebo was administered as 3 successive IV doses at 24-hour intervals. The initial dose of ibuprofen was 10 mg/kg, and the 2 next doses were 5 mg/kg. The first injection was administered within the first 6 hours of life; the time of this first administration represents time 0 of the study for a given infant. The second and third injections were administered at 24 and 48 hours. If a PDA was diagnosed on any echographic evaluation from T72 (ie, 24 hours after the last injection of prophylactic medication), a curative treatment was administered.
The curative treatment was not blinded and consisted of a course of ibuprofen, using the same dose regimen as for prophylactic treatment. A sparse sampling strategy was used: 1 sample was taken just after the third injection of prophylactic medication, and 1 sample was taken 48 hours after the third injection of prophylactic medication. In addition, in the case of curative treatment, another sample was taken after the third curative injection according to a randomized timing, which was defined as either just after administration or 24 hours after administration.
Individual subject characteristics included gestational age, gender, birth weight, weight at day 3 (day 3 corresponds to the third administration day), serum creatinine at birthday and at day 3, any maternal treatment with glucocorticoids and/or indomethacin prior to delivery, and the type of treatment (prophylactic or curative).
Analytical Method
Each sample required a volume of 0.2 mL of total blood and was centrifuged within 2 hours. Plasma was transferred to tubes, which were stored promptly in an upright position at approximately -25°C until transferred to analytical laboratories for analysis.
The analysis of the study samples was performed at CEPHAC (90 avenue des Hauts de la Chaume, 86281 St Benoit Cedex, France).
Plasma samples (100 µL) were extracted with 4 mL of an ether/hexane mixture (20/80) after the addition of ethanol (10 µL), the internal standard (S-ketoprofen), and 2N hydrochloric acid (200 µL). The organic phase (3.8 mL) was shaken and centrifuged for 5 minutes at 2600g (approximately 4°C) after addition of pH2 Titrisol buffer (1 mL). Afterwards, the organic phase (3.3 mL) was evaporated to dryness under a gentle stream of nitrogen at approximately 35°C. The residue was reconstituted with 200 µL of mobile phase. The mobile phase was prepared by adding 17.4 g of dipotassium hydrogen phosphate (K2HPO4), 100 mL of water, 10 mL of 2-propanol, and 2 mL of triethylamine, then completing with water up to 2000 mL. The pH of the mobile phase was adjusted to approximately 6.9, with orthophosphoric acid at 85% (2.6 mL). The LC system comprised a Waters 600 pump, a WISP717plus automatic injector (Waters), and an UV/visible detector 2487 (Waters) operating at 220 nm. The column was a Chiral-AGP 100 x 4.0 mm (Interchim), and the flow rate was 0.5 mL/min. The analytical procedure for the determination of R-ibuprofen and S-ibuprofen was validated in terms of linearity, recovery, intrabatch and interbatch precision and inaccuracy, specificity, stability of the extracts, dilution process, stability after 3 freeze-thaw cycles, stability after 4 hours of storage at ambient temperature, and long-term stability at approximately -25°C (3 months). The analytical procedure in human plasma was shown to be linear from 0.100 to 10.000 µg/mL, and the limit of quantification was validated at 0.100 µg/mL. Within each batch of study samples, at least 5 out of 6 nondiluted quality control (QC) samples were within 15% of their respective nominal value, and all diluted QC samples were within 15% of their respective nominal value. For each quality control concentration level, the imprecision (expressed as coefficient of variation) and the inaccuracy (expressed as a percentage of the difference of the mean) were lower than 5% and 8%, respectively, for R-ibuprofen and 5% and 7%, respectively, for S-ibuprofen. Therefore, the inaccuracy and imprecision of the analysis of the study samples were found acceptable.
Pharmacokinetic Model Development
Pharmacokinetic analysis was performed with a population pharmacokinetics approach by using NONMEM (Version V, Level 1.1) and Compaq Visual Fortran (standard edition, Version 6.6) as a compiler.
Although the duration of injection was not documented, the administration of ibuprofen was considered as an instantaneous IV bolus.
A first-order (FO) method for estimation was used to fit the models. Determination of the final model was conducted in 3 main steps. In the first step, a base model was determined to fit the data. In the second step, the influence of several covariates was tested. Finally, relevant covariates were added to the base model to define the final model.
The model used for pharmacokinetic analysis took into account the hypothesis of the unidirectional transformation of the R-enantiomer into the S-enantiomer established in adults. Because there were only 2 sampling times, monocompartmental modeling was admitted for both R- and S-ibuprofen. A proportional model of variance was used to describe the interindividual variability of the pharmacokinetic parameters and the residual variability.
The available covariates—gestational age, postnatal age, gender, birth weight, weight at day 3 (day 3 corresponds to the third administration day), serum creatinine at birthday and at day 3, any maternal treatment with glucocorticoids and/or indomethacin prior to delivery, and type of treatment (prophylactic or curative)—were analyzed by regression against model parameter estimates. To reduce the statistical risk of detecting an effect that does not exist, we tested only biologically plausible models of covariates. The likelihood ratio test was used to test the effect of the inclusion of covariates. An a priori level of significance of P < 0.01 was chosen. At this significance level, a fall in objective function (which is a global measure of the goodness of fit) of 6.6 or more when a single new covariate was introduced indicated that this covariate had substantially improved the overall goodness of fit. Covariates defined as relevant during this previous step were added cumulatively into the model. Afterwards, the model was evaluated by a backward elimination procedure: covariates were removed one after the other (the weakest first), and a new objective function (OF) was checked against those of the previous model. An increase in OF greater than 7.9 (P < 0.005) was required to keep the covariate in the final model. This step was repeated until each covariate had been tested.
Model Validation
The robustness of the final population model was assessed using a bootstrap method.22,23 A bootstrap sample was generated by repeated random sampling, with replacement, from the original data set. The bootstrap sampling was performed with Wings for Nonmem—software that uses the public-domain text-processing program AWK. Each bootstrap sample was run through NONMEM to obtain parameter estimates. The mean parameter estimates obtained from the overall bootstrap replicates of data were compared with those obtained with the final model. Confidence intervals for mean parameter estimates were also calculated from the bootstrap replicates.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Individual Concentration Data
Ten R-ibuprofen concentrations and 2 S-ibuprofen concentrations were measured below the limit of concentration (BLQ). To extract some information from these samples, we substituted BLQ concentrations by half the limit of quantification. Mean and percent coefficient of variation (CV%) plasma concentrations of R- and S-ibuprofen observed after either 3 prophylactic or 3 curative IV doses of ibuprofen racemate at 24-hour intervals are presented in Table II. The mean concentration of S-ibuprofen, measured just after the third prophylactic administration (34.98 µg/mL), was comparable with the mean concentration measured just after the third curative administration (32.50 µg/mL). The same held true for R-ibuprofen (7.51 and 7.90 µg/mL, respectively). Overall, the mean concentration of S-ibuprofen just after dosing was about 4.5-fold higher than the mean concentration of R-ibuprofen, irrespective of the treatment period (prophylactic or curative). Afterwards, the relative proportion of S-ibuprofen to R-ibuprofen increased, reaching an S-to-R ratio of 38 at 48 hours after the third prophylactic injection and 115 at 24 hours after the third curative injection.
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Base Model
The base model is shown schematically in Figure 1. The modeling was performed using systems of differential equations with an ADVAN 8 subroutine of NONMEM. This model takes into account the unidirectional inversion of the R(-)- to S(+)-enantiomers (K21 constant). The estimation of 2 different elimination rate constants (Kel) and 2 different volumes of distribution (V) for R- and S-ibuprofen did not improve the fitting. Therefore, Kel and V were estimated as equal for R- and S-ibuprofen.
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Population Pharmacokinetic Model
After covariate selection, the final model described an increasing elimination with increasing gestational age and 2 different rates of R- to S-ibuprofen transformation (K21), depending on whether the subject received a prophylactic or a curative treatment. The effect of gestational age on the elimination constant (Kel) was expressed as follows: Kel = 
1 x e(Age-26.6)x2, where 1 corresponds to the typical value of Kel for neonates with a gestational age of 26.6 weeks, and 2 corresponds to a multiplicative factor. Among the covariates tested, the gestational age, the birth weight, and the weight on the third administration day had an effect on the volume of distribution. However, these effects were redundant with the effect of the gestational age on Kel; therefore, they were not kept in the final model. Previous treatment of the mother with glucocorticoids or indomethacin seemed to influence Kel, but this effect could not be estimated because of rounding error during the minimization process. Moreover, the volume of distribution of ibuprofen in neonates with a closed ductus or an open ductus was comparable on the day of the last prophylactic administration.
The final model, including gestational age and the 2 different K21, depending on whether the treatment was prophylactic or curative, significantly improved the fitting compared with the base model because the decrease of objective function was 107.
Mean pharmacokinetic parameters and interindividual variability of R- and S-ibuprofen, obtained from the final model after 3 prophylactic IV doses of ibuprofen racemate at 24-hour intervals, are presented in Table III. The mean volume of distribution, which was the same for both R- and S-ibuprofen, was about 183 mL. The mean clearance of S-ibuprofen (CLS =5.0 mL/h) was about 2.5-fold lower than that of R-ibuprofen (CLR = 12.7 mL/h). Consistently, the mean half-life of S-ibuprofen (t1/2,S = 25.5 hours) was 2.5-fold greater than that of R-ibuprofen (t1/2,R = 10.0 hours). A rather high interindividual variability was attached to the pharmacokinetic parameters (e.g., 101%, 109%, and 60% for the volume of distribution, Kel, and K21, respectively). The mean proportion of R-ibuprofen transformed into S-ibuprofen (R) was about 61% (calculated as
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Overall, the precision obtained on all mean parameters was good, as indicated by the narrow 95% confidence interval. By contrast, confidence intervals on interindividual variability were large.
According to the equation of Kel, mean clearances of R- and S-ibuprofen increase about 1.4-fold and 2.6-fold, respectively, between 25 and 28 weeks' GA. Moreover, the mean clearance of R-ibuprofen was about 2.75-fold greater after curative treatment than after prophylactic treatment (35.0 mL/h vs 12.7 mL/h, respectively). Consistently, the mean half-life of R-ibuprofen after curative treatment (3.6 hours) was about 2.75-fold lower than that after prophylactic treatment (10.0 hours). In addition, the mean proportion of R-ibuprofen transformed into S-ibuprofen (R) was about 1.4-fold higher after curative treatment (0.86) than after prophylactic treatment (0.61).
Model Validation
Observed plasma concentrations and the mean prediction of the S-ibuprofen concentration-time profile, obtained from the final model after 3 IV doses of an ibuprofen racemate at 24-hour intervals, are presented in Figure 2. Observed plasma concentrations and the mean prediction of the R-ibuprofen concentration-time profile, obtained from the final model after 3 IV doses of an ibuprofen racemate at 24-hour intervals, are presented in Figure 3.
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Visual inspection of observed and predicted concentrations of R-ibuprofen indicated an overprediction of the concentrations observed just after dosing. After review of the individual values, it appeared that 1 neonate had a very high concentration of R-ibuprofen just after drug administration (49.52 µg/mL), which may partly explain the overprediction mentioned above. Stability of population parameters and interindividual variability obtained with the final model were evaluated by comparison with mean estimates obtained from 1174 bootstrap samples of the original data. The parameter values obtained from the bootstrap analysis (Table IV) agreed reasonably with those obtained from the final model, which indicates that the estimates obtained with the final model are robust. Overall, the final model overestimated the concentrations of R-ibuprofen observed just after the third prophylactic administration.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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The final population model obtained in this study was monocompartmental for both R- and S-ibuprofen. This model included a unilateral chiral transformation from R- to S-enantiomers and an effect of gestational age on the elimination rate. The mean proportion of R-ibuprofen transformed into S-ibuprofen was about 61% after prophylactic treatment, which is close to proportions already reported in adults administered with an ibuprofen racemate (between 52% and 69%).24
This final model overestimated R-ibuprofen concentrations measured just after the third administration. This bias may be due to the variability of the injection rate. Indeed, the administration was considered as an instantaneous IV bolus because the duration of injection was not documented. However, although the IV injection was rapid, it may be that it was performed with some variability. As drug concentrations decline rapidly just after dosing, a variation in the duration of injection may lead to noticeable changes in early drug concentrations. Although they did not report t1/2ß values, Van Overmeire et al20 described a distribution phase of ibuprofen preterm infants following a 15-minute intravenous infusion. This suggests that in our study, despite the small volume of distribution of ibuprofen, it may be that the distribution of ibuprofen was not complete at the early time of sampling (ie, just after dosing). Moreover, R- and S-ibuprofen bind extensively to serum albumin (about 95% in neonates vs 99% in adults) but with a binding constant 2.3-fold greater for R-ibuprofen.19,24 The relative fraction bound to plasma proteins influences activity and distribution of R- and S-ibuprofen. Thus, a bicompartmental model with 2 different distribution kinetics for R- and S-ibuprofen might be better to fit the data than the monocompartmental model we used. However, the sampling schedule of the present study did not allow such an approach.
The half-lives of R- and S-ibuprofen in healthy adult volunteers are reported to be between 1 and 3 hours.24 Values of half-lives and clearance reported in the present study indicate that the elimination of both R- and S-ibuprofen turns out to be markedly prolonged in preterm newborns compared to adults. This prolonged elimination is consistent with results previously reported for racemic ibuprofen in premature neonates: Aranda et al19 reported an elimination half-life for racemic ibuprofen of 30.5 ± 4.2 hours in premature infants receiving ibuprofen within the first 12 hours of life. Van Overmeire et al20 reported different half-lives on the third (43 ± 7.8 hours) and fifth days (26.8 ± 6.5 hours) after birth. Ibuprofen is cleared by hepatic metabolism, mainly through cytochrome P450 2C9 and 2C8. In addition, the activity of CYP 2C9 is known to be low at birth.20 Therefore, the prolonged half-life of ibuprofen in the preterm newborn could be partly explained by a reduced cytochrome P450 activity. However, a low glucuronic conjugation capability and/or a reduced renal elimination of ibuprofen or metabolites may also explain the prolonged half-life of ibuprofen in the preterm newborn.
This study also showed that after the third administration of an ibuprofen racemate, plasma concentrations of S-ibuprofen are markedly higher than plasma concentrations of R-ibuprofen in very premature neonates. Overall, the difference between R- and S-ibuprofen concentrations observed after the third administration was consistent with the accumulation related to the 2 different half-lives estimated by the model for R- and S-ibuprofen. Based on the structural final model used in this study, this difference of half-life was attributed to the chiral transformation from R- to S-ibuprofen. It is established that after administration of an ibuprofen racemate in healthy volunteers, R-ibuprofen undergoes a unidirectional metabolic inversion to S-ibuprofen.17 However, it is not clearly established that R- and S-ibuprofen half-lives are different after racemate administration in healthy adults. Several investigators have found that R-ibuprofen is eliminated from plasma more rapidly than S-ibuprofen, whereas others have reported similar t1/2ß for both enantiomers.24 In children, results are also disparate: Kelley et al25 suggested that in febrile children (11 months to 11.5 years), the plasma half-life of the S-enantiomer is longer (139 minutes) relative to the R-enantiomer (88 minutes). In contrast, Rey et al26 found (in 6- to 18-month-old children) mean half-lives of 1.6 and 1.5 hours for S- and R-ibuprofen, respectively. The results we obtained in very premature neonates elicit a marked difference between the half-life of enantiomers, with the R-ibuprofen half-life being 2.5-fold shorter than the S-ibuprofen half-life after IV injection of a racemate, which is consistent with the results of Kelley et al. However, modeling alone cannot establish that the large difference between the half-life of R- and S-enantiomers is due to interconversion in neonates.
Mean clearances of R- and S-ibuprofen obtained from the final model were increased 1.4-fold and 2.6- fold, respectively, in neonates 28 weeks' GA compared with those 25 weeks' GA. In contrast, Aranda et al19 found no influence of gestational age (newborns between 22.7 and 31.5 weeks' GA) on drug elimination. Differences in data analysis methods (population methodology vs the standard 2-stage approach, as used by Aranda et al) and differences of sample size of the 2 studies (21 patients in the Aranda et al study vs 62 subjects in the present analysis) may explain the discrepancy mentioned above. Overall, our results suggest that elimination capabilities of R- and S-ibuprofen increase with gestational age (between 24.0 and 27.9 weeks' GA) and probably in relation with hepatic or renal maturity.
R-ibuprofen clearance was about 2.75-fold greater after curative treatment than after prophylactic treatment. Assuming that data actually follow a biexponential model instead of the monocompartmental model used in the present analysis, the shorter half-life observed following curative treatment could be partly due to the fact that the data points were obtained at 24 hours instead of 48 hours. However, R-ibuprofen concentrations were markedly lower after curative treatment than after prophylactic treatment, suggesting an actual difference of clearances. These differences of R-ibuprofen clearance might be due to differences in postnatal age because newborns received prophylactic ibuprofen within the first 6 hours of life or curative ibuprofen between 3 and 8 days after birth. Therefore, for neonates who received curative treatment, metabolic capabilities are deemed to have increased with postnatal age. It is also possible that this difference may reflect a difference in volume of distribution for the enantiomers, but the sparse data collected did not allow differentiating the distribution of R- and S-ibuprofen. Beforehand, the presence of hemodynamically significant patent ductus arteriosus was also likely to have altered drug disposition by causing hypoperfusion of drug-eliminating organs (liver and kidney).20 During the present study, on the day of the last prophylactic administration, of the 52 neonates who were treated with ibuprofen, 11 had an opened ductus and 41 had a closing ductus. Neonates with a closing ductus had a mean volume of distribution of 163 mL (IC95%: [108; 218]), whereas neonates with an opened ductus had a mean volume of distribution of 171 mL (IC95% [116; 226]). Therefore, no obvious difference in the volume of distribution between neonates with a closing or an opened ductus was elicited on the day of the last prophylactic administration.
A preliminary pharmacokinetic/pharmacodynamic (PK/PD) analysis was performed to estimate the potential relationship between individual R- or S-ibuprofen pharmacokinetics and safety/efficacy outcomes. Mean parameters (dose, concentrations, AUC) were compared between subjects who presented 1 particular safety/efficacy outcome and subjects who did not present this outcome. No relationship was elicited (P < 0.01) between individual ibuprofen pharmacokinetics and safety/efficacy outcomes. Overall, the power of the statistical comparisons was weak because of the large interindividual variability and the small group sizes for each safety/efficacy outcome.
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CONCLUSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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In the study conditions, a model was defined that indicates a large discrepancy overall between R- and S-ibuprofen pharmacokinetics in very premature infants and an increase of the clearance of both enantiomers with the gestational age. This should be considered to assess PK/PD relationships of ibuprofen in premature neonates and subsequently to understand and refine the use of ibuprofen in managing PDA, either as prophylactic or curative treatment. A preliminary PK/PD analysis did not elicit any relationship between individual R- or S-ibuprofen pharmacokinetics and safety/efficacy outcomes. However, further investigations with larger groups would be necessary to be conclusive, and because the unbound drug is the active form, the determination of the unbound fraction of R- and S-ibuprofen might be helpful for PK/PD assessment.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Submitted for publication April 17, 2004; Revised version accepted June 17, 2004.
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REFERENCES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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