Design of new therapy strategies for cyclical neutropenia using a delay differential equations model

• Main Author: Foley, Catherine, 1980-
• Format: Others
• Language: en
• Published: McGill University 2004
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82229

Cyclical neutropenia (CN) is a rare hematological disorder characterized by oscillations in the circulating neutrophil count. The treatment for this disease uses granulocyte colony stimulating factor (G-CSF) on a daily basis. Cyclical neutropenia has been extensively modelled due to its interesting dynamics. However, there has been no attempt to use these dynamical features in order to improve existing treatments. A computer simulated study proposing three non-standard treatment protocols to achieve good results with smaller G-CSF dosing and/or fewer days of administration is presented. If the results of this modelling are borne out clinically, it will entail considerable financial savings. The results are based on a two-compartment mathematical model of the white blood cell regulatory system which has eleven parameters, including two delays (Bernard et al. (2003a)). A complete stability analysis of this two dimensional delay differential equations system is provided, in order to characterize the different features of the model. In particular, an interesting bistability was found for certain relevant parameter values, suggesting that the oscillations seen in CN could be stopped by appropriately perturbing the system.