6533b858fe1ef96bd12b61a7
RESEARCH PRODUCT
Power-law hereditariness of hierarchical fractal bones
Mario Di PaolaPietro PollaciMassimiliano ZingalesLuca DeseriLuca Deserisubject
Quantitative Biology::Tissues and OrgansApplied MathematicsMathematical analysisBiomedical EngineeringPower lawFractional calculusSuperposition principleFractalComputational Theory and MathematicsModeling and SimulationHausdorff dimensionStress relaxationExponentRelaxation (approximation)Molecular BiologySoftwareMathematicsdescription
SUMMARY 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. Copyright © 2013 John Wiley & Sons, Ltd.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-07-08 | International Journal for Numerical Methods in Biomedical Engineering |