Fractal dimension analysis a supplementary mathematical method for bone defect regeneration measurement

Abstract Aim or purpose The geometry of a bone defect is very complex. Its shape is too complicated to measure or compare with other bone defects using only traditional measuring methods Traditional measuring techniques based on the histomorphometric analysis of a bone specimen require supplementary measuring. For the fractal dimension analysis (FDA) mathematic formulas are used to describe complicated and chaotic shapes. The FDA offers a possibility of a comparison between complicated and complex shapes such as a histological image of a bone defect. The aim of this study was to evaluate the FDA of bone defects as a supplementary method for a defect regeneration assessment. Materials and methods For the purpose of this study, microscopic photographs of bone specimens stained with hematoxylin and eosin obtained during a block biopsy were used. The bone blocks used in this study were obtained during a rat animal model study. Specimens were collected from 36 Wistar rats where a cranial defect was created and augmented with five different novel biomaterials and compared to the unfilled defect in the control group. New bone formation in every specimen was histomorphometrically measured by two independent operators and compared to FDA measurements. Results Both traditional and FDA techniques have shown statistically significant differences between bone formation in test groups compared to the control one; on the other hand, no statistically significant difference was found between other groups. The Pearson’s r-test was conducted to measure the linear dependence (correlation) between standard measurements and the FDA, and a positive linear correlation was found −r = 0.94. Conclusions The FDA can be used as a supplementary method for bone regeneration measurements.