Application of a feedback optimal control algorithm to a population pharmacokinetic-pharmacodynamic model of cytarabine-derived and lenograstim-reduced myelosuppression in acute myeloid leukemia
Felix Jost (1), Enrico Schalk (2), Daniela Weber (3), Hartmut Döhner (3), Thomas Fischer (2) and Sebastian Sager (1)
(1) Institute of Mathematical Optimization, Faculty of Mathematics, Otto-von-Guericke University Magdeburg, Germany, (2)Department of Hematology and Oncology, Medical Faculty, Otto-von-Guericke University Magdeburg, Germany, (3) Department of Internal Medicine III, University Hospital Ulm, Germany
Objectives:
The aim of this work was the development of a population pharmacokinetic-pharmacodynamic (PK/PD) model describing the dynamics of white blood cells (WBC) of acute myeloid leukemia (AML) patients treated with cytotoxic cytarabine (Ara-C) and support of lenograstim (G-CSF, granulocyte-colony stimulating factor) during consolidation therapy. Further, we investigated a computational approach which proposes individually optimized treatment schedules of Ara-C and lenograstim together with optimal WBC measurement time points from optimal experimental designs. The efficacy of the optimized treatment schedules is quantified by the consideration of leukemic cells within the model.
Methods:
The second priority consolidation arm of the AMLSG 12-09 study [1] was provided by the Department of Internal Medicine III, University Hospital Ulm, Ulm, Germany and used for model development, validation and calibration. The dataset includes WBC count measurements (6-16 per cycle) from 86 consolidation Ara-C cycles (CCs), partitioned in one, two, and three consecutive CCs from 20, 6, and 18 AML patients (median 65 years, 19 (43%) male) from 2010 and 2012 which were treated with high- or intermediate-dosage of Ara-C at days 1,2 and 3. The treatment schedule intended daily 263μg lenograstim administrations starting 9 days after the start of Ara-C treatment until hematological recovery, i.e. neutrophil count >0.5G/L, was achieved. We linked and extended the myelosuppression model considering endogenous G-CSF [2] with a PK model for Ara-C [3] and lenograstim [4]. As no endogenous G-CSF measurements were observed, the modeling process, especially the linkage of endogenous and exogenous G-CSF, was guided by the observed G-CSF concentrations shown in Figures 1 and 2 from [4,5]. The PK/PD model was fitted to the WBC count measurements using nonlinear mixed-effects modeling implemented in NONMEM 7.4. To obtain a clinical impact from mathematically optimized treatment schedules, cytokine-dependent leukemic cells were incorporated to the PK/PD model via a two compartment model presented by Stiehl et al. [5]. The interaction between WBCs and leukemic cells occurs through competition for G-CSF. Then, the feedback optimal control algorithm from [6] was applied to the novel PK/PD model as follows: For one exemplary patient the first two CCs were used for model personalization. Then, the treatment plan and the measurement time points of the third CC were optimized and compared to the actual CC. For this we minimized the amount of leukemic cells with respect to a lower bound of 1G/L on the WBC count dynamics and a total administered amount of high-dosage Ara-C, currently being the standard treatment in one CC for patients aged 60 years and younger [7]. As initial condition of the leukemic cell dynamics we assumed a relative amount of 5% compared to the healthy cells.
Results:
The WBC concentration-time data were best described by the extended myelosuppression model considering a parametrized secondary PD effect of Ara-C on the proliferation speed. The lenograstim administration was modelled by an additional depot compartment. The absorption rate constant was fixed to a value such that the simulated G-CSF concentrations qualitatively coincided with published concentration-time profiles. The linkage between the central compartment of the PK model and the endogenous G-CSF compartment of the PD model was modelled by a first-order process using the absorption rate constant of the depot compartment. We used the same constant as no observed G-CSF concentrations were available to identify a parametrized version of the model. Regarding the obtained optimal treatment plan from the feedback algorithm, the optimization suggests two consecutive CCs leading to nadir values close to 1G/L compared to the actual third CC with a measured nadir value of 0.5G/L.
Conclusions:
We present a PK/PD model for predicting leukopenia during consolidation therapy of AML patients treated with Ara-C and lenograstim. In a case study we demonstrate a computational approach minimizing the number of leukemic cells through optimized treatment schedules and thereby satisfying clinically important constraints such as a WBC count threshold of 1G/L.
References:
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