The fractal dimension of nuclear chromatin as a prognostic factor in acute precursor B lymphoblastic leukemia

The fractal nature of the DNA arrangement has been postulated to be a common feature of all cell nuclei. We investigated the prognostic importance of the fractal dimension (FD) of chromatin in blasts of patients with acute precursor B lymphoblastic leukemia (B-ALL). In 28 patients, gray scale transformed pseudo-3D images of 100 nuclei (May-Grünwald-Giemsa stained bone marrow smears) were analyzed. FD was determined by the Minkowski-Bouligand method extended to three dimensions. Goodness-of-fit of FD was estimated by the R2 values in the log-log plots. Whereas FD presented no prognostic relevance, patients with higher R2 values showed a prolonged survival. White blood cell count (WBC), age and mean fluorescence intensity of CD45 (MFICD45) were all unfavorable prognostic factors in univariate analyses. In a multivariate Cox-regression, R2, WBC, and MFICD45, entered the final model, which showed to be stable in a bootstrap resampling study. Blasts with lower R2 values, equivalent to accentuated "coarseness" of the chromatin pattern, which may reflect profound changes of the DNA methylation, indicated a poor prognosis. In conclusion the goodness-of-fit of the Minkowski-Bouligand dimension of chromatin can be regarded as a new and biologically relevant prognostic factor for patients with B-ALL.