Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two‐dimensional complexity

• DOI: 10.1002/path.970
• Publication Date: 2002-08-25T21:20:09Z
• Authors: Daniel Chappard; Erick Legrand; Bénédicte Haettich; Gérard Chalès; Bernard Auvinet; Jean‐Paul Eschard; Jean‐Pierre Hamelin; Michel‐Félix Baslé; Maurice Audran
• Keywords: Lacunarity; Box counting; Star (game theory)

Abstract Trabecular bone has been reported as having two‐dimensional (2‐D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several dimensions ( D ) are known and computational ways to obtain them vary considerably. This study compared three algorithms on same series of biopsies, Kolmogorov, Minkowski–Bouligand, mass‐radius dimensions. The relationships histomorphometric descriptors 2‐D trabecular architecture were investigated. Bone biopsies obtained from 148 osteoporotic male patients. volume (BV/TV), (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces trabeculae), inter‐connectivity index, Euler–Poincaré number computed. box‐counting method was used Kolmogorov dimension k ), dilatation for Minkowski–Bouligand MB sandbox MR lacunarity L ). Logarithmic observed between BV/TV best correlation lowest . Lacunarity marrow cavities (ICI, volume, Tb.Sp). Linear among techniques which appeared highly correlated. A cluster analysis all parameters provided tree groups descriptors: trabeculae (Tb.Th, strut); (Euler, ICI, ); complexity network (Tb.N 's). sole cannot be instead classic architecture; rather reflects branching trabeculae. Computation time is also an important determinant when choosing one these methods. Copyright © 2001 John Wiley & Sons, Ltd.