The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas

Frontiers in Physiology
Przemyslaw Waliszewski

Abstract

Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas. The global fractal capacity D 0, information D 1 and correlation D 2 dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas. Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D 0-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D 1 failed to define the same classes of equivalence. The pairs (D 0, LFD), (D 0, H), (D 0, λ), (D 1, LFD), (D 1, H), (D 1, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those me...Continue Reading

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Citations

Jan 14, 2017·Royal Society Open Science·Alan Chan, Jack A Tuszynski
Sep 8, 2019·Pharmaceutical Research·Renata Abreu-VillelaIsidoro Caraballo
Jul 4, 2020·Pathology Oncology Research : POR·Gorana AralicaPaško Konjevoda
Oct 23, 2019·Journal of Clinical Medicine·Tamara MirzapoiazovaRavi Salgia
Nov 25, 2020·Reports on Progress in Physics·Clare C YuPeter P Lee

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Methods Mentioned

BETA
surgical resection
biopsy
biopsies

Software Mentioned

Sigma Plot
Definiens Tissue Map
FracLac
Systat
Image J

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