Anna Gebhard (1), Patrick Lilienthal (1), Markus Metzler (2), Manfred Rauh (2), Sebastian Sager (1), Kjeld Schmiegelow (3, 4), Linea Natalie Toksvang (3), Jakob Zierk (2)
(1) MathOpt group, Institute of Mathematical Optimization, Faculty of Mathematics, Otto von Guericke University Magdeburg, Magdeburg, Germany, (2) Department of Pediatrics and Adolescent Medicine, University Hospital Erlangen, Erlangen, Germany, (3) Department of Pediatrics and Adolescent Medicine, University Hospital Rigshospitalet, Copenhagen, Denmark, (4) Institute of Clinical Medicine, Faculty of Medicine, University of Copenhagen, Copenhagen, Denmark
Introduction:
Acute lymphoblastic leukemia (ALL) is one of the most common pediatric malignancies [1] and is treated with initial high-dose chemotherapy followed by oral maintenance therapy with 6-mercaptopurine (6MP) and low-dose methotrexate (MTX). While the survival rates of pediatric ALL have reached approximately 90% [1], the dose-response relationships during maintenance therapy vary widely between patients and necessitate further research of the corresponding dynamics. Currently, the doses of 6MP and MTX are adjusted according to the patients‘ white blood cell count (WBC) or the absolute neutrophil count (ANC) [2]. This is where a comprehensive pharmacokinetic–pharmacodynamic (PKPD) model would allow for extensive treatment simulation, a comparison of different dosing strategies, and individualised target ranges accounting for the natural variation of WBC [2]. The modeling part of this abstract is based on and largely follows [3], where the process and the resulting PKPD model are described.
Objectives:
Existing pharmacokinetic (PK) and pharmacodynamic (PD) models of 6MP and MTX [4, 5, 6, 7, 8, 9, 10] either were not developed for children with ALL, used doses in different ranges than necessary for maintenance therapy or relied mainly on values taken from the literature. We build on the model by Jost et al. [8] with a data set containing not only observations of the ANC, but also measurements of thioguanine nucleotides and MTX in the red blood cells (E-TGN and E-MTX), allowing for the estimation of PK parameters.
In this work, we aim to (i) construct a PKPD model of the treatment effect of 6MP and MTX on the ANC during maintenance therapy, (ii) evaluate the impact of additional measurements of drug concentrations in the red blood cells and (iii) simulate and compare different dosing strategies.
Methods:
We used a subset of the data set described in Schmiegelow et al. [11] to develop PK models for E-TGN and E-MTX as well as a PKPD model capable of predicting individual ANC trajectories. The data set consists of 452 patients with 4624 E-TGN, 4192 E-MTX, and 9808 ANC observations, making it one of the most detailed data sets available for model development for pediatric ALL.
For the PK of E-MTX, we relied on the models [4, 5, 6, 7] as a starting point and analysed 20 model variants with fixed plasma-PK based on various literature sources [4, 6, 12, 13] and linear or Michaelis-Menten kinetics for the influx of MTX into the red blood cells. We modeled the PK of E-TGN similar to models [9, 10], again fixing the plasma-PK to values from the literature [14] and comparing linear and Michaelis-Menten kinetics for the influx into the red blood cells, leading to six model variants. The PKPD model was then constructed by linking the two resulting PK models and the state-of-the-art myelosuppression model by Friberg et al. [15] with a linear effect function. We cross-validated the results of the modeling process with a data set containing 50% of each individual patient’s observations, and performed a sensitivity analysis for all fixed parameters of the PKPD model.
The PKPD model was then used to simulate different treatment strategies, using dosing schedules either independent of patients‘ individual parameters or exploiting the model dynamics. We compared steady dosing with 6MP doses of 5, 25, 50, 75, 100, 125 and 150 mg/m2 to a treatment strategy that takes the delay by the transit compartments in the Friberg model [15] as well as the individual base ANC level of the patients into account. The latter strategy is based on computing the expected time-shifted ANC and using this for the dosing decisions, and offers the opportunity to individualise the target range.
Results:
We show that for the E-MTX PK, a model with linear kinetics, a dose-adjusted bioavailability and the influx into the red blood cells based on the peripheral compartment works well enough in the low-dose MTX regime and is more robust when estimating with the cross-validation data set. The E-TGN PK are best represented by either linear kinetics or Michaelis-Menten kinetics without interindividual variability for the influx into the red blood cells.
When linking these PK models to the Friberg et al. [15] model, we show that the best-performing model has Michaelis-Menten kinetics in the E-TGN PK submodel and an effect function solely based on E-TGN, leaving out the MTX PK submodel completely. While our results seem similar to the ones based on the simpler model by Jost et al. [8], who were not able to include observations of E-TGN in their modeling process, we show our model to outperform it when data availability is limited: the newly developed PKPD model improves the root-mean-square (RMSE) and the mean-absolute errors (MAE) of the population predictions of the ANC compared to those of the Jost et al. [8] model by almost 50%, indicating that with no prior knowledge, our model performs better. When comparing the individual predictions of the cross-validation, the Jost et al. [8] model leads to more than twice as high standard deviations of the individual RMSE and MAE, suggesting more extreme deviations of the predicted ANC values from the observed ANC values.
The sensitivity analysis for the fixed parameters of the PKPD model led to a maximal absolute distance of 0.49 for the absorption rate, and smaller maximal absolute distances for all other fixed parameters, indicating no considerable influence on the resulting ANC trajectories.
Simulating steady treatment for different 6MP doses led to, unsurprisingly, decreasing ANC values for increasing doses. As the PK of E-TGN are modeled by Michaelis-Menten kinetics, we expected the differences between the effects of two doses to decrease for increasing doses, which was also evident in the simulation results with the ANC levels differing only marginally between doses of 75, 100, 125 and 150 mg/m2. Taking the delay by the transit compartments and the individual base ANC level of the patients into account when making a dosing decision steers the ANC levels to the base ANC level for each patient, leading to fewer oscillations of the ANC and fewer minimal ANC values below 0.5 G/L, indicating less risk for neutropenia.
Conclusions:
The newly developed PKPD model predicts the effect of maintenance therapy of childhood ALL on the patient-specific ANC dynamics. We show that the data set with metabolite observations in the red blood cells leads to a PKPD model with improved results when less data is available as is often the case in clinical practice, but that model predictions are comparable to those of a model with fixed PK when data availability is not limited, indicating that this model structure is the most promising for ALL maintenance therapy. Taking the model dynamics and individual patient parameters into account when simulating allows for suggesting a novel treatment strategy possibly lowering the risk of neutropenia during maintenance therapy.
References:
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[15] Friberg, L. E., Henningsson, A., Maas, H., Nguyen, L., & Karlsson, M. O. (2002). Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. Journal of clinical oncology, 20(24), 4713-4721.
Reference: PAGE 32 (2024) Abstr 10919 [www.page-meeting.org/?abstract=10919]
Poster: Drug/Disease Modelling - Oncology