Development of a Simple Methodology Based on Fractal Mathematics for Selective Diagnosis of Red Blood Cells Disorders

Alcides J. Leguto, Juan P. Rebechi, Manuel A. Mancilla Canales, Patricia Ponce de León, Santiago A. Bortolato, Susana Pérez, Ana M. Korol


Automatic characterization of different populations of red blood cells (RBCs) is a useful tool in Hematology and Clinical Diagnosis. In this work, we focus on different pathologies that affect hemorheological properties of humans being blood. Our main aim is to develop an analytical methodology to aid in the diagnosis of those pathologies that undergo specifically by altering RBCs membrane dynamic properties. The alterations on the RBC membranes were studied with box-counting dimension (BCD). BCDs were estimated by a standardized analysis of denoised images of RBC suspensions obtained with an optical microscope and a non-professional digital camera. The systematical denoising was carried out by the application of Wavelet Transform on the images. BCD is a fractal quantifier that has been proven to depend on the levels of RBC aggregation. Wavelet Transform denoising technique implies the decomposition of the image signals in a set of wavelets and the selection of the most significant ones through which the image can be reconstructed. In this work, we compared the BCD estimated on RBC suspensions from healthy individuals and from those affected by parasitosis (trichinosis and ascariasis), leukemia (chronic and acute) and iron-deficiency anemia. In comparison to control samples, those corresponding to patients with parasitosis and acute leukemia showed significative differences (p < 0.01) in the variances of their BCD values, while the samples corresponding to anemia and chronic leukemia showed significatively higher (p < 0.01) BCD mean values.

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