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Cellular Oncology
Volume 28 (2006), Issue 1-2, Pages 55-59

The Fractal Dimension of Nuclear Chromatin as a Prognostic Factor in Acute Precursor B Lymphoblastic Leukemia

Randall L. Adam,1 Rosana C. Silva,2 Fernanda G. Pereira,2 Neucimar J. Leite,3 Irene Lorand-Metze,2 and Konradin Metze1

1Department of Pathology, Faculty of Medicine, State University of Campinas, Brazil
2Department of Clinical Medicine, Faculty of Medicine, State University of Campinas, Brazil
3Institute of Computing, State University of Campinas, BR 13081-970 Campinas - SP, Brazil

Copyright © 2006 Hindawi Publishing Corporation and the authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.