Tangential Algorithm for Calculation of the Fractal Dimension of Kidney Tubuli Sections

Gil, Joaquín Navarro; Gimeno, Miguel; Laborda, Jesús; Nuviala, Javier; Belanche, Ignacio

doi:10.4067/s0717-95022006000100006

Cited by 4 publications

(7 citation statements)

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“…Finally, we found that the fractal complexity of tubules (measured by the fractal dimension) had excellent correlation with the eGFR in hypertensive patients. Previous work already showed the application of fractal analysis of kidney sections, limited to normal subjects [ 13 ]. Moreover, there has been an attempt to make a semiautomatic measurement of chronic renal damage by recognizing texture modification of tubule-interstitial structures in kidney biopsies [ 14 ].…”

Section: Discussionmentioning

confidence: 99%

A cross-sectional study on the relationship between hematological data and quantitative morphological indices from kidney biopsies in different glomerular diseases

et al. 2018

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BackgroundThe classical approach to the analysis of kidney biopsies is based on semi-quantitative scores of the amount of sclerosis, inflammatory infiltrate, fibrosis and vascular damage. However, advanced renal lesions may be accompanied by a paucity of clinical features and, conversely, important clinical abnormalities may be accompanied by minimal histopathological changes. The objective of this study is to correlate new, semiautomatic, quantitative features of kidney biopsies (e.g. fractal analysis) with clinical and hematological parameters using a cross-sectional design.MethodsWhole slide images from sixty-seven biopsies of patients diagnosed for diabetic nephropathy, hypertensive nephropathy, focal segmental glomerulosclerosis (FSGS) or IgA nephropathy have been used. The images have been semi-automatically quantified in the ImageJ environment, in order to derive the glomerular density, the tubular density, the number of tubules per glomerulus and the fractal dimension of the tubular lumen in the cortex (an index of complexity of the tubular lumen). For each patient, hemato-chemical data have been retrieved, including the uric acid level and the creatinine-based eGFR.ResultsA linear relationship between eGFR and glomerular density was observed in hypertension and FSGS, but not in diabetic nephropathy. Conversely, the eGFR correlated with the tubular density across different glomerular conditions. Moreover, the tubular density was linearly correlated with uric acid levels in different pathological conditions. The fractal dimension of tubular lumen was correlated with the eGFR but only in hypertensive patients. Finally, blood pressure was not correlated to any of the morphological indices tested.ConclusionsWe propose the use of the fractal dimension as a new morphological descriptor of the nephron integrity.

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Section: Discussionmentioning

confidence: 99%

A cross-sectional study on the relationship between hematological data and quantitative morphological indices from kidney biopsies in different glomerular diseases

et al. 2018

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“…Consequently, we can have a single quantitative measure to discriminate each of these two dog kidney components by mean automatic tools. Also this dimension value is different from the linear fractal dimension we obtained (Gil et al, 2006), logic because we used different measure unit. We think this work method is easy to use and more sure to obtain results.…”

Section: Discussionmentioning

confidence: 89%

“…Para ello, hemos obtenido la dimensión fractal de los túbulos contorneados proximales del riñón de perro, mediante la técnica de recuento de cajas. El valor fractal obtenido es una dimensión de superficie, diferente de la dimensión fractal lineal que calculamos previamente (Gil et al, 2006). De esta forma, desde imágenes microscópicas, nos es posible obtener una medida simple y cuantitativa para diferenciar estos compontes del riñón de perro.…”

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“…It could be an attractive idea, for instance to automate its recognition by mean a computer. In the kidney, calculation of the fractal dimension may open this way (Gil et al, 1992, Gil et al, 2006.…”

Section: Introductionmentioning

confidence: 99%

“…We know the proximal convoluted tubule has a fractal lineal geometry (Gil et al, 2006), but is it the only one possible?…”

Section: Introductionmentioning

confidence: 99%

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Fractal Dimension of Dog Kidney Proximal Convoluted Tubuli Sections by Mean Box-Counting Algorithm

Gil¹,

Gimeno²,

Laborda³

et al. 2006

Int. J. Morphol.

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The possibility of characterizing the proximal convoluted tubuli of the dog kidney by means of a unique and objective value, is an attractive idea in order to automate its recognition in anatomy and patology. For this, we obtained a fractal dimension of the proximal convoluted tubuli in the dog kidney by mean box-counting method. The fractal value we obtained is a flat dimension, and it is different than the line fractal dimension of the dog kidney arterial pattern, which was previously calculated by us (Gil et al., 2006). Thus, from optical microscopy images, we are able to obtain a single quantitative measure to discriminate these dog kidney components. This measures can use to automate its recognition. Fractal geometry provides many advantages when examining the complex microscopical images of natural objects.

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The Convoluted Tubules of the Nephron Must Be Considered Elliptical, and Not Circular, in Stereological Studies of the Kidney

Ortega‐Martínez

Gutiérrez‐Dávila

Gutiérrez-Arenas

et al. 2021

Kidney Blood Press Res

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Introduction: The diameter and area of the proximal convoluted tubule (PCT) and the distal convoluted tubule (DCT) are of the main parameters analyzed in stereological studies of the kidney. However, there is no consensus about if the PCT and DCT should be considered circular or elliptical in shape. Objective: To analyze if there are significant differences in the diameter and area of the PCT and DCT, depending on whether they are considered circular or elliptical. Methods: Paraffin-embedded sections of kidneys from CD1 mice were stained with hematoxylin and eosin and examined using a light microscope. Images were captured using a camera linked to image analysis software. A short diameter (d) and a long diameter (D) were measured in both PCT and DCT. A small circular area (SCA), a large circular area (LCA), and an elliptical area (EA) were calculated with mathematical formulas that incorporate d and D values, while a program area (PA) was provided by the software. Results: There was a significant difference between d and D in both PCT (F = 1.354, Sig = 0.000) and DCT (F = 4.989, Sig = 0.000). Also, there were significant differences in the tubular areas in both PCT (F = 34.843, Sig = 0.000) and DCT (F = 22.390, Sig = 0.000); circular areas were different from elliptical areas (SCA and LCA vs. EA and PA). Conclusion: The convoluted tubules of the nephron must not be considered circular, but rather elliptical; care should be taken every time the tubules are analyzed in stereological studies of the kidney, especially when evaluating their diameters and areas.

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Tangential Algorithm for Calculation of the Fractal Dimension of Kidney Tubuli Sections

Cited by 4 publications

References 4 publications

A cross-sectional study on the relationship between hematological data and quantitative morphological indices from kidney biopsies in different glomerular diseases

A cross-sectional study on the relationship between hematological data and quantitative morphological indices from kidney biopsies in different glomerular diseases

Fractal Dimension of Dog Kidney Proximal Convoluted Tubuli Sections by Mean Box-Counting Algorithm

The Convoluted Tubules of the Nephron Must Be Considered Elliptical, and Not Circular, in Stereological Studies of the Kidney

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