System approach to modeling metabolite formation from parent drug: a working example with methotrexate

The aim of this methodological study was to present and exemplify a system-approach-based technology in modeling the formation of the metabolite from the parent drug. To represent this process, the parent-metabolite dynamic system was defined in such a way that the concentration-time profile of the parent drug was considered the input, while the concentration-time profile of the metabolite the output, of this system. The system-approach-based modeling technology was used to determine the model of the parent-metabolite dynamic system and to obtain the model-based estimates of the rate of metabolite formation, the rate of metabolic ratio and the mean time of metabolite formation. The technology was applied to concentration data for methotrexate and 7-hydroxymethotrexate in patients with psoriasis after a single oral methotrexate dose. Third-order linear models were selected as optimal to approximate the parent-metabolite dynamic systems representing the formation of 7-hydroxymethotrexate from methotrexate of these patients. The model-based estimates of the metabolic ratios ranged from 0.53 to 0.95. The model-based estimates of the mean times of formation of 7-hydroxymethotrexate from methotrexate ranged from 9.13 to 25.13 h. The model-based estimates of the rates of formation of 7-hydroxymethotrexate from methotrexate reached peak values (ranging from 0.03 to 0.11 h-1) in the time interval 1.5-4.5 h after administration of methotraxate. This study does not only introduce the method that may be useful in gaining insight into metabolite formation, but also presents a new example of the methodological, conceptual and computational uniformity of the system-approach-based technology in modeling various biomedical systems.