PD Dr Georg Hempel, Institut für Pharmazeutische und Medizinische Chemie – Klinische Pharmazie-, Hittorfstr. 58-62, 48149 Münster, Germany. E-mail: firstname.lastname@example.org
We analysed 1221 serum activity measurements in 168 children from the Berlin-Frankfürt-Münster acute lymphoblastic leukaemia studies, ALL-BFM (Berlin-Frankfürt-Münster) 95 and ALL-BFM REZ, in order to develop a pharmacokinetic model describing the activity-time course of pegylated (PEG)-asparaginase for all dose levels. Patients received 500, 750, 1000 or 2500 U/m2 PEG-asparaginase on up to nine occasions. Serum samples were analysed for asparaginase activity and data analysis was done using nonlinear mixed effects modelling (NONMEM Vers. VI, Globomax, Hanouet, MD, USA). Different linear and nonlinear models were tested. The best model applicable to all dosing groups was a one-compartmental model with clearance (Cl) increasing with time according to the formula: Cl=Cli *e(0·0793 *t) where Cli = initial clearance and t = time after dose. The parameters found were: volume of distribution (V) 1·02 ± 26% l/m2, Cli 59·9 ± 59% ml/d per m2 (mean ± interindividual variability). Interoccasion variability was substantial with 0·183 l/m2 for V and 44·7 ml/d per m2 for Cl, respectively. A subgroup of the patients showed a high clearance, probably due to the development of inactivating antibodies. This is the first model able to predict the activity-time course of PEG-asparaginase at different dosing levels and can therefore be used for developing new dosing regimens.
Asparaginase is an important part of many treatment protocols for acute lymphoblastic leukaemia (ALL) with proven therapeutic efficacy (Hill et al, 1967). Pegylated (PEG)-asparaginase is an enzyme derived from Escherichia coli and conjugated to polyethylene glycol. This chemical derivatisation causes a reduced clearance of the enzyme, which has practical advantages compared to the native forms (Asselin et al, 1993). All asparaginases cause a wide spectrum of side-effects, such as hepatic dysfunction, pancreatitis and severe allergic reactions (Muller & Boos, 1998). With PEG-asparaginase an anaphylactic shock appears to be less frequent but the phenomenon of rapid decline of asparaginase activity without clinical symptoms called ‘silent inactivation’ is a complication possibly affecting therapeutic outcome (Muller et al, 2000). Therefore, asparaginase activity is controlled in many centres of the German ALL-BFM (Berlin-Frankfürt-Münster) group after administration of PEG-asparaginase.
The pharmacokinetic behaviour of PEG-asparaginase is characterized by a slow elimination and a low volume of distribution. Notably, increasing the dose does not result in a longer duration of activity above a threshold value of 100 international units (U)/l (Vieira Pinheiro et al, 2002; Avramis & Panosyan, 2005). This observation cannot be described by a linear model or by Michaelis–Menten kinetics. Investigations with other asparaginase formulations indicate that the activity in serum should be maintained above this threshold level of 100 U/l for more than 20 d (Riccardi et al, 1981; Ahlke et al, 1997). In order to predict the activity-time course of the enzyme in certain patient groups a population pharmacokinetic model would be very useful. Population pharmacokinetics allows the identification of covariates which can explain the variability in the pharmacokinetic parameters. Based on these covariates in a pharmacokinetic model, precise dosing recommendations can be developed. Attempts to develop such a model were described using first-order kinetics or a Michaelis–Menten model (Avramis et al, 2002; Muller et al, 2002). However, the one-compartment model with first order kinetics cannot describe the curve shape of the plasma activity time courses when plotting on a half-logarithmic scale.
The present investigation retrospectively analysed the routinely collected serum samples from ALL-BFM studies (ALL-BFM 95 and ALL-BFM REZ) after the administration of different doses of PEG-asparaginase to build a population pharmacokinetic model that describes the pharmacokinetics of PEG-asparaginase sufficiently for all available dosing levels.
Patients and methods
Data were obtained from 168 patients with ALL or non-Hodgkin lymphoma (NHL) from 27 centres in Germany during induction and/or relapse treatment according to the ALL/NHL-BFM 95 and ALL/NHL-BFM REZ protocols. Patients were treated between August 1997 and December 2000. Data regarding induction and relapse treatment were available for six patients. The main patients’ characteristics are shown in Table I. PEG-asparaginase was administered at 1000 or 2500 U/m2 on day 8 during reinduction in protocol II, replacing the four administrations of 10 000 U/m2E. coli asparaginase (Asparaginase medac®, medac GmbH, Wedel, Germany). Patients receiving 500 or 750 U/m2 PEG-asparaginase were treated according to individual treatment decisions. The absolute dose administered ranged from 200 to 5000 U corresponding to four main dosing levels of 500, 750, 1000 and 2500 U/m2. Administration was performed intravenously over approximately 2 h. Co-medication included daily dexamethasone 10 mg/m2, vincristine 1·5 mg/m2 and doxorubicin 30 mg/m2 on days 8, 15, 22 and 29.
Table I. Patient’ characteristics.
BSA, body surface area.
*Blood samples from six patients were available from both induction and relapse.
Blood samples for the determination of asparaginase activity were collected between day 1 and day 36 as part of standard clinical blood sampling in the morning. Immediately after withdrawal, the samples were centrifuged and the serum was sent to the laboratory for measurement without freezing.
Pegylated-asparaginase activities were measured as part of the clinical routine according to the l-aspartic β-hydroxamate (AHA) assay (Lanvers et al, 2002). Briefly, patient serum was incubated with an excess of AHA at 37°C. PEG-asparaginase hydrolyses AHA to l-aspartic acid and hydroxylamine, which condenses with 8-hydroxyquinoline and oxidizes to indooxine. The product was quantified by photometric detection at 710 nm. The method has a lower limit of quantification of 5 U/l. Samples collected before July 1999 were measured with the method described by Boos et al (1995) based on the release of ammonia using Nesslers’ reagent for derivatisation and photometric detection at 450 nm, which has a quantification limit of 20 U/l. Samples with activity below the limit of quantification were set to a value of 10 U/l for the pharmacokinetic analysis.
Pharmacokinetic analysis and statistics
Data were analysed using nonlinear mixed effects modelling (NONMEM, version VI). Different structural models were tested, such as linear one and two-compartment models and one-compartment models with non-linear elimination. To account for non-linear elimination, Michaelis–Menten Elimination (MM-Elimination) and time-dependent Clearance (Cl) were tested according to the formula:
where TAD is time after dose, i.e. the time from starting the last drug administration, Θ1 is the typical initial clearance and Θ2 the factor for the exponential increase of clearance with TAD. An exponential model was used for inter-patient variability. To account for the residual error the additive, proportional and combination error model were evaluated. Data were analysed using the first order estimation method (FO). Individual pharmacokinetic parameters were obtained by Bayesian estimation using the posthoc option.
Covariates available were: body surface area (BSA), age, sex, primary disease/relapse and previous allergic reaction to conventional asparaginase medac®. Weight and height were not available for 44 patients and could therefore not be included in the analysis. The influence of the available continuous and categorical covariates was tested in different ways. The corresponding objective function values (OFVs) were compared to values of the model without the respective covariate by the chi-square test of difference. A decrease of the interindividual variability (IIV) estimate was considered in order to assess the impact of each covariate. In general, a decrease in the OFV of more than 6·6 was considered a significant improvement of the model (Hill et al, 1969; Chatelut et al, 1996).
Interoccasion variability (IOV) was tested as additive factors analogous to an algorithm proposed by Karlsson and Sheiner (1993). The first four occasions were used for the IOV quantification which included almost 98% of all activities sampled.
A total of 1221 PEG-asparaginase activities were collected at different days from day 0 to day 35 following 258 administrations. The distribution of the samples versus the day after the last dose is shown in Fig 1. Half of the PEG-asparaginase activities were withdrawn within 8 d after administration and 75% within 14 d after administration. Most of the samples available for the analysis were drawn after the first administration (80%) and 10%, 5% and 3% of the samples were drawn after the second, third and fourth administration, respectively. From 36 patients, activities from more than one administration were obtained for up to nine occasions. After the first administration, activities ranged from 5 U/l (limit of quantification, LOQ) to 4053 U/l.
Structural pharmacokinetic and residual error model
The combined error model for residual variability was superior to all other models tested and was therefore used in the following comparisons. The model development process is shown in Table II. A one-compartment model was sufficient to describe the distribution of PEG-asparaginase (Model 1). The addition of a second compartment did not result in a drop in the objective function (OF) and provided no useful parameter estimates (data not shown). Therefore, we attempted to further improve the one-compartment model.
Table II. Development of the pharmacokinetic model.
Volume of distribution
Interindivid. variability (%)
Interindivid. variability (%)
*Vmax 280 U/l d, Km 1570 U/l.
†IOVCl 44·7 ml/d per m2, IOVV 0·183 l/m2.
Clearance increasing with time Cl = Θ1*e(Θ2 *TAD)
Model 3 with BSA as a covariate
Θ1:64·9 ml/d per m2 Θ2:0·0762
Model 3a with interoccasion variability for Cl and V†
Θ1:59·9 ml/d per m2 Θ2:0·0793
Comparing the linear model to the nonlinear models (model 2, 3, 3a and 3b), a significant decrease in OF was observed. The OF decreased by 178 for the model with Michelis–Menten-elimination (Model 2), and even by 459 for the model with clearance increasing with time after dose (Model 3). Acceptable residual errors were seen for model 3 with an additive error of 25 U/l and a proportional error of 26·3% compared to 51 U/l and 37·8% for the linear model.
Covariates and interoccassion variability were evaluated based on model 3. No influence of sex on V and Cl was seen. Inclusion of BSA or age alone showed a positive influence on OFV and IIV. However, redundancy of both covariates became apparent when they were included at the same time. In general, decreases in the OF were greater with BSA than with age as a covariate and, therefore, BSA was kept as the sole covariate for V and Cl in the final model. Within the algorithms mentioned above, inclusion of
gave the best results regarding OF, residual error and interindividual variability (model 3a).
Inclusion of IOV on V and Cl was associated with a remarkable decrease in the OF (−281, model 3b). It also decreased the IIV values and unexplained residual errors, indicating that some of these were due to interoccasion variability. Therefore, the one-compartment model with time-dependent clearance including BSA as a covariate and IOV was the final model.
According to this model, the mean initial half-life was 11·8 d and this decreased to 1·93 d (46·3 h) on day 21. Figure 2 shows the goodness-of-fit-plots for this model, demonstrating an equalized dispersion except for a subgroup with poorer predicted activities in the lower range of 10–200 U/l. Figure 3 shows the PEG-asparaginase activity-time-curves of representative patients at different dosing levels, demonstrating a sufficient fit of the model.
Analysis of the individual Bayesian posthoc estimates of the pharmacokinetic parameters showed that the clearance during relapse was significantly increased in comparison to induction therapy (median clearance 0·0931 in relapse vs. 0·0524 l/h per m2 induction, P < 0·001 Mann–Whitney Rank Sum Test). Plotting the posthoc estimates of the volume of distribution per square metre (V/BSA) versus the age of the patients, a trend towards higher V/BSA was observed (Fig 4).
To our knowledge, this is the first population pharmacokinetic model for PEG-asparaginase describing data from different dosing schedules simultaneously. We found that a one-compartment-model with time-dependent clearance performed well and was better than a model with Michaelis–Menten elimination, as proposed in earlier investigations (Avramis et al, 2002).
The observation of a constant time above the threshold value of 100 U/l with different doses (Avramis & Panosyan, 2005) did not correspond with any linear or Michaelis–Menten model. Therefore, other models, such as polynomial or multi-compartmental models etc., were tested to describe this phenomenon. The applied one-compartment-model with time-dependent clearance described here is able to predict the activity-time course of PEG-asparaginase.
With a time-dependent clearance, the corresponding half-life also changed with time after dose. On average, the half-life decreased from 11·8 d on day 1 to 2·4 d on day 20 after administration. In the literature, the reported half-life for PEG-asparaginase of 5·5 d in children (Avramis et al, 2002) is somewhat misleading, as it implies first-order kinetics.
Notably, in this and other pharmacokinetic investigations with asparaginase, the estimated volume of distribution was very low, indicating that asparaginase is distributed in no other compartments than plasma (Ho et al, 1986; Avramis et al, 2002). Raes et al (2006) presented results of measurements for the total blood volume in children by radioactive iodine quantification. They reported a plasma volume of 1·5 ± 0·28 l/m2 for 42 boys and 1·38 l/m2 for 35 girls aged 9·8 ± 4·6 years. These reported plasma volumes were higher than the volume of distribution of 1·02 l/m2 for PEG-asparaginase in our population analysis. A confounding factor could be that all assays for the measurement of asparaginase activity in serum do not necessarily provide values that correspond to the activity provided by the manufacturer. One has to consider that asparaginase activity is highly dependent on experimental conditions, such as pH and ion concentration. As a consequence, deviations between the nominal activity given to the patient and the measured serum activity can occur. However, our assay was standardized to the pharmaceutical preparation applied to the patients.
A higher volume of distribution – when normalized to BSA – was reported for PEG-asparaginase in adults (Avramis & Spence, 2007). We also found a trend towards higher volumes of distribution in the older patients (Fig 4). However, including age into the model as a covariate for the volume of distribution did not reduce the interindividual variability (26% vs. 26%). Analysing serum activities from both adults and children together will provide a better insight into the age-dependent pharmacokinetics.
Our findings support the observation that increasing the dose of PEG-asparaginase does not necessarily result in a longer time with serum activities above the threshold value of 100 U/l supposed to be necessary for antileukaemic activity (Riccardi et al, 1981; Ahlke et al, 1997). Therefore, our pharmacokinetic model does not provide a rationale for escalating the dose of PEG-asparaginase.
The predictability of the model presented here is, however, limited due to the development of antibodies binding to asparaginase, resulting in a fast decline of asparaginase activity. This can be seen in Fig 2A, with deviations for the samples with low asparaginase activity. With PEG-asparaginase the phenomenon of silent inactivation is known to be associated with a rapid decline in activity without clinical signals of an allergic reaction (Wenner et al, 2005). In addition, we have recently shown that antibodies binding to polyethylene glycol can also affect asparaginase activity (Armstrong et al, 2007). With the availability of antibody measurements – asparaginase and polyethylene glycol – the model could be substantially improved.
We would expect that the higher clearance of PEG-asparaginase found in relapse in comparison to patients in induction therapy is due to the development of antibodies. Therefore, instead of including relapse versus induction in the model, we are confident that antibody results will improve the model. Unfortunately, the antibody results were not available for the samples analysed here. With the antibody measurements available, the intra-individual variability in the clearance of 44·7 ml/d per m2 could be markedly reduced.
The best way to control asparaginase therapy would therefore be the measurement of both types of antibodies before therapy. Including the antibody data into the population pharmacokinetic model should enable us to predict the activity-time course more precisely.