Lorenz system in the thermodynamic modelling of leukaemia malignancy

The core idea of the proposed thermodynamic modelling of malignancy in leukaemia is entropy arising within normal haematopoiesis. 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 hypothetical model provides a description of remission and relapse in leukaemia as two hierarchical and qualitatively different states of normal haematopoiesis with their own phase spaces. Phase space transition is possible through pitchfork bifurcation, which is considered the common symmetrical scenario for relapse, induced remission and the spontaneous remission of leukaemia. Cytopenia is regarded as an adaptive reaction of haematopoiesis to an increase in entropy caused by leukaemia clones. The following predictions are formulated: a) the percentage of leukaemia cells in marrow as a criterion of remission or relapse is not necessarily constant but is a variable value; b) the probability of remission depends upon normal haematopoiesis reaching bifurcation; c) the duration of remission depends upon the eradication of leukaemia cells through induction or consolidation therapies; d) excessively high doses of chemotherapy in consolidation may induce relapse. (C) 2017 Elsevier Ltd. All rights reserved.