Multifractal structure of acini immunoreactive to cytokeratin 18 in normal and pathologic prostate
1 Department of Anatomy, Histology, and Neuroscience. School of Medicine, Autonomous University of Madrid. C/Arzobispo Morcillo 2, 28029-Madrid, Spain.
2 Department of Anaesthesiology. Hospital Ramón y Cajal, Madrid, Spain.
3 Department of Surgery (Urology). Hospital de La Princesa, School of Medicine, Autonomous University of Madrid, Spain.
Research Article
Open Access Research Journal of Life Sciences, 2026, 11(01), 009-033.
Article DOI: 10.53022/oarjls.2026.11.1.0036
Publication history:
Received on 31 December 2025; revised on 07 February 2026; accepted on 09 February 2026
Abstract:
As with other biological textures, the complexity of the distribution of acini from the prostate could be characterized by fractal geometry. In the present study the fractality of prostatic acini immunoreactive for cytokeratin 18 (ck18) in normal prostate (CTR), benign prostatic hyperplasia (BPH), and adenocarcinoma (CA) will be analyzed to detect fractal changes in BPH and CA about CTR. Other texture parameters such as lacunarity (Λ) and the local connected fractal dimension (LCFD) were also estimated. Specimens from all the groups were immunostained to ck18 and studied by multifractal analysis, calculating the multifractal spectrum f(α), and the generalized dimension DQ. LCFD and Λ were estimated to assess the heterogeneity of acinar distribution. To find out if the random distribution of immunostaining for ck18 produces changes in the fractality of the cases studied, the same analysis methods were applied to the surrogate data obtained from the real data. Principal Components Analysis (PCA) was used to find patterns or groupings of the CTR, BPH, and CA cases. The results suggest that the acinar distribution shows a multifractal structure in both normal and pathological prostate. The degree of multifractality in CA is significantly higher than in CTR and BPH. It is also observed that the heterogeneity of the acinar structure of the CA is greater than in CTR and BPH, as indicated by lacunarity and LCFD. The variables introduced in the PCA discriminate the CA group from the CTR and BPH groups.
Keywords:
Prostate Cancer; Benign Prostate Hyperplasia; Multifractals; Generalized Fractal Dimension; Lacunarity; Surrogate Data
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