Lorenz System in Thermodynamical Modelling of Leukemia Malignancy

Abstract

Graphical solutions of ordinary differential equations for simplified processes of heat flow in fluids (Lorenz system) and an idea of common mathematical description are the basis for the presented thermodynamical leukemia model. The model provides description of normal hematopoiesis in leukemia as two hierarchical states corresponding to remission and relapse. Transition between them is possible through pitchfork bifurcation which is considered as the common symmetrical mechanism for the phase space changes in leukemia. This mechanism also explains phenomenon of spontaneous remission. Cytopenia is considered as an adaptive reaction of hematopoiesis to entropy increase caused by leukemic clone. The following hypotheses are formulated: a) percentage of leukemia cell in marrow for relapse or remission criterion is not strict cut-off constant but a variable value; b) Probability of getting remission depends upon reaching bifurcation; c) Length of remission depends upon degree of eradication of leukemia cells in induction.