Lorenz System in Thermodynamical Modelling of Leukemia Malignancy

Entropy rising within normal hematopoiesis is the core idea of the proposed thermodynamical model of malignancy in leukemia. Mathematically its description is supposed to be similar to the Lorenz system of ordinary differential equations for simplified processes of heat flow in fluids. The model provides description of remission and relapse in leukemia as two hierarchical and qualitatively different states of normal hematopoiesis with their own phase spaces. Phase space transition is possible through pitchfork bifurcation, which is considered as the common symmetrical scenario for relapse, induced remission and spontaneous remission of leukemia. Cytopenia is regarded as an adaptive reaction of hematopoiesis to entropy increase caused by leukemia clone. The following hypotheses are formulated: a) Percentage of leukemia cells in marrow as criterion of remission or relapse is not necessarily constant but a variable value; b) Probability of getting remission depends upon normal hematopoiesis reaching bifurcation; c) Duration of remission depends upon eradication of leukemia cells in induction or consolidation therapies; d) Excessively high doses of chemotherapy in consolidation might induce relapse.