Fractional model for pharmacokinetics of high dose methotrexate in children with acute lymphoblastic leukaemia

doi:10.1016/j.cnsns.2014.08.014

Communications in Nonlinear Science and Numerical Simulation

Volume 22, Issues 1–3, May 2015, Pages 451-471

https://doi.org/10.1016/j.cnsns.2014.08.014 Get rights and content

Highlights

•
Upgraded fractional model is presented for pharmacokinetics of methotrexate in children with leukaemia.
•
New parameter determination procedure is introduced.
•
Our fractional model can recognize all elimination patterns.
•
Our fractional model better fits observed non-monotonic behavior.

Abstract

The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients.

We applied two-compartment fractional model on 8 selected cases with the largest number (4–19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2–5 g/m² infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post’s and Newton’s method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC.

Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients.

A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.

Section snippets

Introduction and background

Acute lymphoblastic leukaemia (ALL) is the most common malignancy in children [1], [2], [3]. The breakthroughs in diagnostics, therapy and improvements to therapy protocols have all led to long-term curing, with an overall five-year survival rate of almost 80% in children with ALL [4], [5], [6], [7].

Methotrexate (MTX), a folic acid antagonist and the most commonly used antimetabolite in cancer therapy, has three features that contribute to its distinguished position in cancer chemotherapy: 1.

Clinical study design

This study was designed as a single-center, open-label, observational clinical trial for the investigation of the pharmacokinetics of MTX. The study protocol was in accordance with Declaration of Helsinki and was approved by the Ethic Committee of Medical Faculty, University of Novi Sad (Serbia).

Patients and treatment

A total of 43 pediatric patients with ALL were followed (121 courses, 437 concentrations). All patients were treated in Haematology and Oncology Center, Institute for children and youth health care of

Results

In this study, a total of 38 courses of MTX infusion was evaluated (1–4 courses per patient) with 217 MTX concentrations (at least 4 measured MTX concentration per patient). The longest period of MTX concentration measurement was 168 h after starting the MTX infusion. Additional blood samples were obtained in 16 courses (9 patients). Additional blood samples were obtained also in 1 course (1 patient) at 26, 28, 32 and 38 h after starting the MTX infusion. Methotrexate dose range was from 1100 to

Discussion

In the previous literature MTX pharmacokinetics is not analyzed by fractional models. It will be useful to have such data for MTX. Furthermore, by application on MTX we will obtain new useful experience with the fractional method. Also very important question is the possible clinical application. From the previous literature analyses, the control of plasma MTX concentrations is extremely important, especially in patients with renal and/or hepatic diseases, or other kind of high MTX

Conclusion

On the basis of the recorded pharmacokinetic data several MTX elimination patterns were identified. The concentrations of MTX after HDMTX infusions in children with ALL are not always in decreasing order. A special feature of the fractional model is that it can recognize and fit an observed non-monotonic behavior too. The obtained fractional system and the non-uniform sampled pharmacokinetic data related in a new developed parameter identification procedure based on the Post inversion formula

Acknowledgments

This work is supported by the:

–
Republic of Serbia, Autonomous Province of Vojvodina, Provincial secretariat for science and technological development grant No. 114-451-2048/2011-01 (JP),
–
Republic of Serbia, Ministry of Science, Grants No. 174005 (TMA), 174016 (DTS and IMM) and 174024 (SP).

The authors’ work was independent of the funders.
The excellent technical assistance and suggestions during preparation of this work of el. eng. Mrs Vesna Popović is gratefully acknowledged.

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View full text

Fractional model for pharmacokinetics of high dose methotrexate in children with acute lymphoblastic leukaemia

Highlights

Abstract

Section snippets

Introduction and background

Clinical study design

Patients and treatment

Results

Discussion

Conclusion

Acknowledgments

Mayo Clin Proc

Cancer Treat Rev

Blood

Ann Oncol

Commun Nonlinear Sci Numer Simul

Commun Nonlinear Sci Numer Simul

Biophys J

Chaos Solitons Fractals

Commun Nonlinear Sci Numer Simul

Contin Educ Anaesth Crit Care Pain

Comput Math Appl

A comparative study on the pharmacokinetics of methotrexate in a dose range of 0.5 g to 33.6 g/m2 in children with acute lymphoblastic leukemia

Cancer

Methotrexate pharmacokinetics and survival in osteosarcoma

Pediatr Blood Canc

Clinical and pharmacokinetic risk factors for high-dose methotrexate-induced toxicity in children with acute lymphoblastic leukemia

Acta Oncol

Hemostatic side effects of high-dose methotrexate in childhood acute lymphoblastic leukemia

Pediatr Haematol Oncol

Shortening infusion time for high-doe methotrexate alters antileukemic effects: a randomized prospective clinical trial

J Clin Oncol

Concept in use of high-dose methotrexate therapy

Clin Chem

Methotrexate-associated liver toxicity in a patient with breast cancer: case report and literature review

Neth J Med

Systemic methotrexate treatment in childhood psoriasis: further experience in 24 children from India

Pediatr Dermatol

Understanding and managing methotrexate nephrotoxicity

The Oncologist

Therapeutic drug monitoring of antimetabolic cytotoxic drugs

Br J Clin Pharmacol

Therapeutic drug monitoring in cancer management

Clin Chem

Continuous infusion of methotrexate in children with acute leukemia

Cancer

Population pharmacokinetics of high-dose methotrexate in children with acute lymphoblastic leukemia

Clin Pharmacokinet

High dose methotrexate population pharmacokinetics and Bayesian estimation in patients with lymphoid malignancy

Biopharm Drug Dispos

A limited sampling strategy to estimate individual pharmacokinetic parameters of methotrexate in children with acute lymphoblastic leukemia

Cancer Chemother Pharmacol

Test dose for predicting high-dose methotrexate infusions

Clin Pharmacol Ther

The importance of pharmacokinetic limited sampling models for childhood cancer drug development

Clin Can Res

Population pharmacokinetic study of methotrexate in patient with lymphoid malignancy

Cancer Chemother Pharmacol

Population pharmacokinetics of high-dose methotrexate in Japanese adult patients with malignancies: a concurrent analysis of the serum and urine concentration data

J Clin Pharm Ther

Fractional kinetics in drug absorption and disposition processes

J Pharmacokinet Pharmacodyn

A comparative study on the pharmacokinetics of methotrexate in a dose range of 0.5 g to 33.6 g/m² in children with acute lymphoblastic leukemia