Power-law hereditariness of Hierarchical Fractal Bones

L. Deseri
Center for Nonlinear Analysis
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
and
Dipartimento di Ingegneria Civile Ambientale e Meccanica
Universitá degli Studi di Trento
Trento, Italy

M. Di Paola
Dipartimento di Ingegneria Civile Ambientale, Aerospaziale e dei Materiali (DICAM)
Universitá degli Studi di Palermo
Palermo, Italy

M. Zingales
Dipartimento di Ingegneria Civile Ambientale, Aerospaziale e dei Materiali (DICAM)
Universitá degli Studi di Palermo
Palermo, Italy
and
(BM)2-Lab
Mediterranean Center of Human Health and Advanced Biotechnologies
Universitá degli Studi di Palermo
Palermo, Italy

P. Pollaci
Dipartimento di Ingegneria Civile Ambientale e Meccanica
Universitá degli Studi di Trento
Trento, Italy

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 $\le \beta \le$ 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 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.

Get the paper in its entirety as

• 13-CNA-013.pdf

Back to CNA Publications