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

Jovan K. Popovic
Organization: University of Novi Sad
Dragan T. Spasic
Organization: University of Novi Sad
Jela Tošic
Organization: University of Novi Sad
Jovanka L. Kolarovic
Organization: University of Novi Sad
Rachid Malti
Organization: University of Novi Sad
Igor M. Mitic
Organization: University of Novi Sad
Stevan Pilipovic
Organization: University of Novi Sad
Teodor M. Atanackovic
Organization: University of Novi Sad
Journal / Anthology

Communications in Nonlinear Science and Numerical Simulation
Year: 2015
Volume: 22
Page range: 451–471

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. Weapplied two-compartment fractionalmodel 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 inMathematica 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 newparameter determination procedure can be successfully used.

*Applied Mathematics