title: Power-law hereditariness of hierarchical fractal bones.
abstract: In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law.
authors.affiliation: Center for Nonlinear Analysis and Department of Mathematical Sciences, Carnegie Mellon University, 4811 Frew Street, Pittsburgh, PA 15213-3890, U.S.A.; Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Universitá degli Studi di Trento, Via Mesiano 77, 38123 Trento, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Deseri
authors.forename: Mario
authors.initials: M
authors.lastname: Di Paola
authors.forename: Massimiliano
authors.initials: M
authors.lastname: Zingales
authors.forename: Pietro
authors.initials: P
authors.lastname: Pollaci
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena / Q000502:physiology*; D001842:Bone and Bones / Q000502:physiology*; D017709:Fractals; D008954:Models, Biological; D012212:Rheology
keywords: bone hereditariness; fractional calculus; hierarchic structure; mechanical fractance; power law