Lymphoma and Leukemia Cells Possess Fractal Dimensions That Correlate with Their Biological Features

Background: Living cells can be viewed as complex adaptive systems that exhibit non-linear dynamics and fractal features. We investigated the fractal qualities of normal and malignant hematological cells and their potential as a tool for characterizing cell phenotype and clinical behavior. Methods: A mathematical algorithm and an optic tool for fractal analysis of nuclei were developed. A total of 4,713 lymphoid cells derived from 66 patients of five distinct diagnostic groups (normal and reactive lymphocytes, low-grade lymphomas and an aggressive lymphoma) were assessed for their fractal dimension. In addition, in 19 patients fractal analysis of leukemia cells was compared to clinical endpoints. Results: After validating our method, hematological cells possessed fractal dimensions corresponding to their clinical entity. There was a highly significant overall difference in fractal dimensions between various types of hematological malignancies. A preliminary correlation was found between the fractal dimension and the clinical outcome of leukemia patients. Conclusions: Hematological cells possess fractal dimensions that correlate with their biological properties. Measurement of fractal dimension seems to be a sensitive method to assess the hematological cell phenotype and to define a clinical group. This tool may be potentially useful for the evaluation of clinical behavior of hematological diseases.

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