Elsevier

Journal of Biomechanics

Volume 33, Issue 10, October 2000, Pages 1325-1330
Journal of Biomechanics

Technical note
Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur

https://doi.org/10.1016/S0021-9290(00)00069-5Get rights and content

Abstract

Purpose: In a meta-analysis of the literature we evaluated the present knowledge of the material properties of cortical and cancellous bone to answer the question whether the available data are sufficient to realize anisotropic finite element (FE)-models of the proximal femur. Material and method: All studies that met the following criteria were analyzed: Young's modulus, tensile, compressive and torsional strengths, Poisson’s ratio, the shear modulus and the viscoelastic properties had to be determined experimentally. The experiments had to be carried out in a moist environment and at room temperature with freshly removed and untreated human cadaverous femurs. All material properties had to be determined in defined load directions (axial, transverse) and should have been correlated to apparent density (g/cm3), reflecting the individually variable and age-dependent changes of bone material properties. Results: Differences in Young's modulus of cortical [cancellous] bone at a rate of between 33% (58%) (at low apparent density) and 62% (80%) (at high apparent density), are higher in the axial than in the transverse load direction. Similar results have been seen for the compressive strength of femoral bone. For the tensile and torsional strengths, Poisson’s ratio and the shear modulus, only ultimate values have been found without a correlation to apparent density. For the viscoelastic behaviour of bone only data of cortical bone and in axial load direction have been described up to now. Conclusions: Anisotropic FE-models of the femur could be realized for most part with the summarized material properties of bone if characterized by apparent density and load directions. Because several mechanical properties have not been correlated to these main criteria, further experimental investigations will be necessary in future.

Introduction

In order to simulate the reactions of bone to physiological and non-physiological load conditions multiple computer-aided finite element models of the proximal femur have been generated since the mid-1970s (Andriacchi et al., 1976; Svensson et al., 1977; Rohlmann et al (1980), Rohlmann et al (1982), Rohlmann et al (1983); Huiskes et al., 1989). Although many previous studies had clearly demonstrated the anisotropic behaviour of bone (Dempster and Liddicoat, 1952; Bargren et al., 1974; Martens et al., 1983; Goulet et al., 1994), all FE-simulations that have been developed so far have assumed isotropic material properties without exception.

Besides the numerical problems of anisotropic simulation of bone remodelling (Beaupré et al., 1990; Jacobs et al., 1997), the main reason for this exclusive assumption of isotropic conditions in bony FE-models has been the lack of a comprehensive data bank incorporating the material properties of bone as a function of the orthotropic load directions.

Therefore, it was the aim of this study to summarize the present knowledge in the literature about the direction-dependent material properties of cortical and cancellous femoral bone. In addition, we tried to answer the question whether these data are sufficient to develop and feed anisotropic FE-models of the proximal femur.

Section snippets

Materials and methods

A survey of more than 300 published studies which investigated experimentally the following material properties of human cadaverous femurs were analyzed:

  • 1.

    Young's modulus

  • 2.

    Compressive strength, tensile strength and torsional strength

  • 3.

    Shear modulus

  • 4.

    Poisson's ratio

  • 5.

    Viscoelastic behaviour

As inclusion criteria of this evaluation all investigations had to be carried out on freshly extracted cadaverous femurs, in a moist environment and at body temperature. Additionally, studies were also accepted where

Young's modulus

The Young's modulus of cortical bone is a function of density. For this reason, cortical bone must be considered an inhomogeneous material (Rauber, 1896; Knese et al., 1956; Schmitt, 1968). Fig. 1 shows differences of Young's modulus of cortical bone between 33% (at low apparent densities; 1.5 g/cm3) and 62% (at high apparent densities; 2 g/cm3) higher in the axial than in the transverse load directions.

Similar results have been found in the case of cancellous bone (Fig. 2). Here, apparent

Discussion

Although over the last 25 years multiple investigations were performed to determine the material properties of the proximal femur, definitive statements about the real in vivo behaviour of cortical and cancellous femoral bone are still impossible. This is mainly due to restrictions in ascertaining in vivo conditions in experimental work.

For constructing finite element models of bony structures, the apparent density-dependent characterization of material properties appears to be the most

References (41)

  • A. Rohlmann et al.

    Finite-element-analysis and experimental investigation of stress in a femur

    Journal of Biomedical Engineering

    (1982)
  • A. Rohlmann et al.

    Finite-element-analysis and experimental investigation in a femur with hip endoprosthesis

    Journal of Biomechanics

    (1983)
  • D. Viano et al.

    Elastic properties of cortical bone in female human femurs

    Journal of Biomechanics

    (1976)
  • T.P. Andriacchi et al.

    A stress analysis of the femoral stem in total hip prosthesis

    Journal of Bone and Joint Surgery

    (1976)
  • G.S. Beaupré et al.

    An approach for time-dependent bone modeling and remodeling — theoretical development

    Journal of Orthpaedic Research

    (1990)
  • D. Besdo et al.

    Numerical treatment of bone as anisotropic material

    Biomedical Technology

    (1994)
  • A.H. Burstein et al.

    Aging of bone tissuemechanical properties

    Journal of Bone and Joint Surgery

    (1976)
  • D.R. Carter et al.

    Bone compressive strenghthe influence of density and strain rate

    Science

    (1976)
  • D.R. Carter et al.

    Tensile fracture of cancellous bone

    Acta Orthopaedica Scandinavica

    (1980)
  • W.T. Dempster et al.

    Compact bone as a non-isotropic material

    American Journal of Anatomy

    (1952)
  • Cited by (422)

    • Drying irreversibly affects the elastic behavior of pelvic cortical bone

      2024, Journal of the Mechanical Behavior of Biomedical Materials
    • Learned Gaussian quadrature for enriched solid finite elements

      2023, Computer Methods in Applied Mechanics and Engineering
    View all citing articles on Scopus
    View full text