Fractal Analysis in Human Pathology

Luzi, Pietro; Bianciardi, Giorgio; Miracco, Clelia; Santi, Maria Margherita De; Vecchio, Maria Teresa Del; ALIA, Lutfi; Tosi, Piero

doi:10.1111/j.1749-6632.1999.tb10428.x

Cited by 23 publications

(16 citation statements)

References 9 publications

(20 reference statements)

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“…The use of fractal analysis is a known technique in clinical science and particularly in pathology. [13][14][15][16][17][18] The important possibility of diagnosis before the rise of real objective or clinical symptom is of paramount interest in the medical field. The precise use of fractal analysis in neuroimaging is a moving field with a very promising future.…”

Section: Resultsmentioning

confidence: 99%

Fractal Approach to Understand Pfo and DCS in Sport Divers

Jayalalitha

Uthayakumar

2010

Fractals

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The prevalence of Patent Foramen Ovale (PFO) is an increasing risk factor for paradoxical cerebral embolism. Decompression Sickness (DCS) results from gas coming out of solution in the bodily fluids and tissues when a diver ascends too quickly. This occurs because decreasing pressure lowers the solubility of gas in liquid. Also, the expansion of gas in the lungs may lead to alveolar rupture which may, in turn, result in Arterial Gas Embolism (AGE). The amount of nitrogen that diffuses into the bodily tissues during a dive depends on the depth of the dive and the duration of exposure. PFO acquires significance in various congenital heart diseases leading to right to left shunt and thus to paradoxical embolism. The presence of asymptomatic brain lesion like "spots" has been investigated in a randomized population of diving individuals. The partial pressure of the gas can be calculated by Henry's Law and the pressure of the blood stream can be calculated by Poiseuille's Law. The statistical comparison of the fractal dimension was obtained by means of Box Counting Method with slope analysis. We observe that PFO plays a significant role in the occurrence of unexplained cerebral DCS and white spots in the brain.

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Section: Resultsmentioning

confidence: 99%

Fractal Approach to Understand Pfo and DCS in Sport Divers

Jayalalitha

Uthayakumar

2010

Fractals

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“…Diferentes estudios se han enfocado hacia la descripción morfológica de distintos tipos de cáncer (11,12), para la identificación del sitio primario de cáncer en metástasis ósea (26) y en imágenes diagnósticas utilizadas para tamizaje como la mamografía (18). También se ha aplicado al estudio de diferentes fenómenos, tales como la morfología cardiovascular, permitiendo la diferenciación de arterias coronarias normales de las reestenosadas (27), metodología que fue generalizada posteriormente hallando el número total de posibles prototipos arteriales en proceso de reestenosis (28).…”

Section: Discussionunclassified

Fractales: ayuda diagnóstica para células preneoplásicas y cancerígenas del epitelio escamoso cervical confirmación de aplicabilidad clínica

et al. 2016

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ResumenAntecedentes: Se desarrolló un método diagnóstico fractal para evaluar células del cuello uterino utilizando el concepto de Armonía Matemática Intrínseca (AMI) y variabilidad celular, el cual diferencia matemáticamente células normales de células L-SIL y H-SIL, haciendo innecesario el diagnóstico de células ASCUS.Objetivo: confirmar la capacidad diagnóstica de la metodología desarrollada mediante un estudio ciego de comparación con el Gold Standard.Método: se tomaron fotografías digitales de 50 preparaciones citológicas de mujeres entre 20 y 55 años: 5 con diagnóstico de citología normal y 45 con diferentes grados de lesión hasta carcinoma, incluyendo 5 ASCUS. Se calculó la dimensión fractal de tres objetos matemáticos: núcleo, citoplasma y totalidad, a partir de la superposición de cinco rejillas. Además, se evaluó su dimensión fractal mediante el concepto de AMI y variabilidad celular. Los resultados obtenidos se compararon con el diagnóstico citopatológico convencional determinando su sensibilidad, especificidad y coeficiente kappa.Resultados: La sensibilidad y especificidad fue del 100%, y el coeficiente Kappa de 1.Conclusiones: Los resultados en una población diferente a la inicial son una evidencia de la capacidad de esta metodología para diagnosticar objetiva y cuantitativamente células normales, L-SIL y H-SIL, así como aclarar el diagnósti-co de las células ASCUS con base en la dimensión fractal y el concepto de AMI y variabilidad.Palabras Clave: Cáncer, Cuello uterino, Fractal, Citología, Diagnóstico.

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“…Some studies that apply fractal methodologies to the study of neoplastic structures have been developed, and some analyses of mammograms [12] [13], to the cells of the oral mucosa [14], in bladder invasive cancer [15], and in ocular tissue [16], among others [17] [18] [19], have also been applied. Recently, applications of fractal geometry to the analysis of the nucleus and cytoplasm of cervical cells have been developed [20] [21], which permit to differentiate normality of Low Grade Squamous Intraepithelial Lesions (LGSIL) and High Grade Squamous Intraepithelial Lesions (HGSIL), determining, moreover, mathematical relations of the ASCUS cells (Squamous Atypia of Undetermined Significance) which associate them to an state of normality or lesion.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Evaluation of Cervical Cells. Fractal and Euclidean Diagnostic Methodology of Clinical Application

Velásquez¹,

Cárdenas²,

Arroyave³

et al. 2018

JBM

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Background: The concomitant use of fractal and Euclidian measurements has led to the development of new methodologies of cell evaluation, including a diagnosis of cervical cells that set up differences between normality and various degrees of lesion, to carcinoma. Aim: To confirm the diagnostic capacity of the methodology based on fractal and Euclidian geometry for the mathematical diagnosis through a blind study of normal cells and with different types of lesion, as atypia of undetermined significance (ASCUS), low grade squamous intra-epithelial lesion (LGSIL) and high grade squamous intra-epithelial lesion (HGSIL). Methods: 100 cells of Papanicolaou tests were analyzed and divided into 4 groups according to conventional parameters: 25 normal, 25 ASCUS, 25 LGSIL and 25 HGSIL. By means of the Box-counting Fractal Space, we calculated the fractal dimension and occupying spaces of the border and surface in pixels of the cell nucleus and cytoplasm. The diagnostic parameters of the previously developed methodology were applied and compared with the conventional diagnosis, setting up sensibility, specificity, negative likelihood ratio and Kappa coefficient. Results: The values of the occupation of the border and surface of the cell nucleus and cytoplasm were consistent with the values found by the diagnostic methodology previously found. The subtraction of the nucleus and cytoplasm frontiers presented values between: 189 and 482 for normality; 159

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Fractal Analysis in Human Pathology

Cited by 23 publications

References 9 publications

Fractal Approach to Understand Pfo and DCS in Sport Divers

Fractal Approach to Understand Pfo and DCS in Sport Divers

Fractales: ayuda diagnóstica para células preneoplásicas y cancerígenas del epitelio escamoso cervical confirmación de aplicabilidad clínica

Geometrical Evaluation of Cervical Cells. Fractal and Euclidean Diagnostic Methodology of Clinical Application

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