Fractal geometry enables the objective grading of prostate cancer; Gleason 3+4 ≠ Gleason 4+3!

Przemko Waliszewski, M Tanase, Rasha Abu Eid, W Klonowski, M Pierzchalski, P Stępień, RA Stępień, G Lüdecke, F Wagenlehner, S Gattenlöhner, W Weidner

Research output: Chapter in Book/Report/Conference proceedingPublished conference contribution


Background: Tumor grading is an important prognostic criterion for prostate cancer patients. Subjective scoring according to the Gleason system is influenced by intra- and inter-observer variability in up to 80% of cases. There is a need for objective grading, which would eliminate over- or under-scoring and enable comparison of results between centers.

Methods : Fractal analysis, based upon self similarity of geometric structures, enables characterizing complex patterns by a numerical value of fractal, i.e. non-integer dimension. We compared spatial distribution of cell nuclei in prostate tissues by calculating capacity, information and correlation dimension based on the Grassberger-Procaccia algorithm as well as Higuchi dimension. We also constructed a local structural correlation diagram by a novel Java based image-transforming computer algorithm to show how some local blocks of patterns are correlated and to characterize the cell distribution by diagram size. Morphometric features of cells were investigated in 2 dimensional tissue slides after applying the colour deconvolution algorithm.

Results: Fractal structure was found in all analyzed cases. We obtained the following values of capacity, information, correlation, and Higuchi dimension: 1.451 (018), 1.521 (014), 1.986 (004) n=18 for normal prostate; 1.469 (022), 1.530 (017), 1.972 (008) n=15, 1.417 (046) n=22, Gleason 3 pattern; 1.601 (019), 1.648 (015), 1.938 (011) n=18, 1.322 (044) n=32, Gleason 4; and 1.769 (011), 1.766 (010), 1.895 (010) n=10, 1.240 (097) n=2, Gleason 5, respectively. More random distribution of cell nuclei was associated with more expanding diagram. The mean values of the diagram size were 9.5, 30.3, 41.5, 48.6, respectively. The mean diagram size for Gleason score 3+4 was lower than for Gleason score 4+3. With regard to the morphometric cell analysis, sphericity, circularity, and solidity shape were found to be statistically different between cases with Gleason score 3, and those with a score of 4 and 5 (p<0.05). Based on the cellular morphology parameters, discriminant analysis with leave one out showed that 60% of Gleason score 3 and 4 cases, 63% of Gleason score 4 and 5 cases and 62% of Gleason score 3 and 5 cases could be correctly classified.

Conclusions: This approach based upon fractal geometry allows accurate objective grading of prostate cancer and suggests the need for incorporating more objective criteria in the grading system.
Original languageEnglish
Title of host publicationProstate Cancer
Subtitle of host publication From diagnosis to managing advanced disease. Proceedings of the Global Congress on Prostate Cancer 28-30 June 2012 – Brussels, Belgium
EditorsAlex Mottrie, Bertrand Tombal, Hein Van Poppel, Gert De Meerleer
Place of PublicationLier, Belgium
Number of pages1
Publication statusPublished - Sept 2012
EventGlobal Congress on Prostate Cancer: From diagnosis to managing advanced disease - Brussels, Belgium
Duration: 28 Jun 201230 Jun 2012

Publication series

NameMirrors of Medicine
ISSN (Electronic)2034-8393


ConferenceGlobal Congress on Prostate Cancer
Internet address


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