Tangential Algorithm for Calculation of the Fractal Dimension of Kidney Tubuli Sections Algoritmo de Tangencialización para el Cálculo de la Dimensión Fractal de Túbulos Renales Seccionados

SUMMARY: We have developed a new algorithm to calculate the fractal dimension of dog kidney proximal convoluted tubulesection. This algorithm is intermediate between box-counting and perimeter-stepping algorithms. The result of this new algorithm andcorrelations found between fractal dimensions and other Euclidian values of these tubuli, suggest that this algorithm is adequate tocalculate fractal dimensions by points. KEY WORDS: Fractal; Kidney; Proximal convoluted tubuli. INTRODUCTION An object is fractal if it has got fractal dimension(Mandelbrot, 1985).The nephron is the structural unit responsible for themain functions of the kidneys. The nephron has twocomponents, the glomerulus and the renal tubule. Renaltubule has several components, one of which is the proximalconvoluted tubule (Fig. 1).To know if proximal convoluted tubuli are fractalsopens the possibility of being able to characterize them bymeans a unique and objective value (Mandelbrot; Gil et al .,1992), that probably could have some taxonomic value.We developed a new algorithm to calculate the fractaldimension of convoluted objects, like the outline images ofa serially sectioned proximal convoluted tubule. The resultingalgorithm is intermediate between box-counting andperimeter-stepping algorithms (Cross, 1994).