Mathematical model of acute myeloblastic leukaemia: an investigation of the relevant kinetic parameters

A simple model of acute myeloblastic leukaemia (AML) development is introduced, explicitly including cell growth, cell differentiation and cell-cell interaction. Each of these processes is described by a single model parameter. It is hypothesized that the leukaemic cell is characterized by an alteration of only one of these processes. The kinetic behaviour of the AML system is examined separately for possible alterations of each of the three parameters describing the three processes involved. It is shown that, on the basis of the existing data on AML kinetics, the alteration of the growth and cell-cell interaction parameters can be eliminated as a possible source of AML. Thus kinetic data support the modification of the differentiation process as the origin of the AML state. Further, the growth characteristics of normal and leukaemic cells in the presence of each other are analysed. It is shown how the initial growth of leukaemic cells depends on the difference in the differentiation of normal and leukaemic cells and how the same difference determines the decay of normal cells in the presence of the predominantly leukaemic population. Correlations between the kinetic parameters of the normal and leukaemic populations are suggested to characterize the leukaemic state.