Heterogeneity in chronic myeloid leukaemia dynamics during imatinib treatment: role of immune responses

Abstract

Previous studies have shown that during imatinib therapy, the decline of chronic myeloid leukaemia BCR-ABL transcript numbers involves a fast phase followed by a slow phase in averaged datasets. Drug resistance leads to regrowth. In this paper, variation of treatment responses between patients is examined. A significant positive correlation is found between slopes of the fast and the slow phase of decline. A significant negative correlation is found between slopes of the slow phase of decline and the regrowth phase. No correlation is found between slopes of the fast phase of decline and the regrowth phase. A mathematical model that is successfully fitted to diverse clinical profiles explains these correlations by invoking the immune response as a key determinant of tumour decline during treatment. Boosting immunity during drug therapy could enhance the response to treatment in patients.

Figure 1.

Average dynamics of CML during imatinib treatment, taken from Michor et al. (2005). The BCR-ABL/BCR ratios are plotted over time, averaged over many patients. Patients who relapsed during therapy were excluded. See Michor et al. (2005) for more details. A bi-phasic decline is observed, where an initial fast-decline phase is followed by a slower-decline phase. This was the first study that published such averaged time series, and similarly averaged dynamics were found in patients from the German cohort of the IRIS study (Roeder et al. 2006), not shown here.

Figure 2.

Correlations between the slopes of the fast decline, slow decline and the regrowth of BCR-ABL transcript numbers. (a) Correlations found in the clinical data from the German cohort of the IRIS study (Roeder et al. 2006). Only patients who were characterized by the presence of the relevant two slopes were included. Two significantly outlying data points were excluded. For (i) and (ii), the correlation is significant (p = 0.009 and p = 0.003, respectively). For (iii), there is no significant correlation (p = 0.59). (b) Correlations between the slopes of the fast decline, the slow decline and the regrowth, as predicted by computer simulations of the mathematical model. Simulations were run 100 times, randomly varying both the rate of specific immune proliferation, c, and the growth rate of the resistant cancer cells, r. For (i) and (ii), the correlations are significant (p < 0.0001 in each case), while for (iii) the correlation is not significant (p = 0.32). The remaining parameters of the model (chosen for illustrative purposes) were: d = 1; p = 3; b = 0.5; q = 0.01; ε = 1; η = 1 (units are yr⁻¹). x₀ = 100; y₀ = 0.001; z₀ = 0.5.

Figure 3.

Examples of individual treatment response data from the German cohort of the IRIS study, taken from Roeder et al. (2006). The dots are the actual clinical data. The line is the model fitted to the data, obtained by nonlinear least-squares regression. In (a,b), immune responses rise temporarily during therapy, contributing to the overall treatment dynamics. In (c,d), the model predicts that immune responses did not rise during therapy. Drug-resistant mutants play a role in (a) and (d), but not in (b) and (c). For further discussion, see text. Model parameter values are as follows (see electronic supplementary material for discussion of parameter values). (a) r = 2.69; c = 17.04; d = 0.58; p = 80.3; b = 8.84; q = 0.10; ε = 1; η = 1; x₀ = 35.53; y₀ = 2.73 × 10⁻⁵; z₀ = 0.06. (b) r = 0; c = 14.00; d = 1.04; p = 43.60; b = 8.97; q = 4.88 × 10⁻⁴; ε = 2.85; η = 1; x₀ = 60.76; y₀ = 0; z₀ = 0.0044. (c) r = 0; c = 0; d = 0.65; p = 0; b = 0; q = 0; ε = 0; η = 0; x₀ = 21.17; y₀ = 0; z₀ = 0. (d) r = 12.4; c = 0; d = 7.23; p = 0; b = 0; q = 0; ε = 0; η = 0; x₀ = 65.92; y₀ = 9.61 × 10⁻⁷; z₀ = 0. Units are yr⁻¹ for all models.

Figure 4.

Computer simulation of the mathematical model, which shows the possibility that during therapy, the immune response is maintained at higher levels rather than dropping to insignificant levels. In this simulation, therapy is started at time zero. As a result of maintained immunity, the initial regrowth of cancer, brought about by drug-resistant mutants, is blunted, and the number of CML cells is kept at low levels in the long term. The right panel shows the CML dynamics separately for the populations of drug-sensitive and drug-resistant cells. Parameters were chosen for illustrative purposes as follows: r = 5; c = 5; d = 0.5; p = 1; b = 0.1; q = 0.01; ε = 0.1; η = 1; x₀ = 80; y₀ = 2.7 × 10⁻⁵; z₀ = 0.06. The units of the axes are arbitrary, as the parameter set was chosen for illustrative purposes and is not based on measured parameters, which are currently unknown.