Lorenz System in Thermodynamical Modelling of Leukemia

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 proposed thermodynamical leukemia model. The model provides description of remission and relapse in leukemia as two hierarchical states of normal hematopoiesis. Transition between them is possible through a pitchfork bifurcation which is considered as the common symmetrical mechanism for the phase space changes in leukemia and 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 a strict cut-off constant but a variable value; b) Probability of getting remission depends upon reaching bifurcation; c) Duration of remission depends upon degree of eradication of leukemia cells in induction.