Power-law hereditariness of hierarchical fractal bones

Luca Deseri, Mario Di Paola, Massimiliano Zingales, Pietro Pollaci

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1338-1360
Number of pages23
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number12
StatePublished - Dec 2013


  • Bone hereditariness
  • Fractional calculus
  • Hierarchic structure
  • Mechanical fractance
  • Power law

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Software
  • Applied Mathematics
  • Modeling and Simulation
  • Biomedical Engineering
  • Molecular Biology


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