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Variability of the mechanical properties of bone
1.5. Bone Tissue
Track 1. Bone Mechanics - Joint ESB Track
4760 Th, 14:30-14:45 (P42) A numerical investigation of the overall cortical bone anisotropy: contributions of material symmetry and micro-architecture Q. Grimal 1, K. Raum 2, V. Liabeuf 1, P. Laugier 1. 1Laboratoire d'imagerie param~trique, Universit~ Pierre et Marie Curie - Paris 6; CNRS UMR 7623; Paris, France, 2 Q-BAM Group, Dept. of Orthopedics, Martin Luther University, Halle, Germany Whether the overall (macroscopic) cortical bone anisotropy is mainly due to the pore distribution o r t o both the pores and the matrix intrinsic anisotropy has been debated by several authors. We propose a new model for the analysis of cortical bone overall anisotropy. Unlike existing idealized models, it takes as input realistic micro-architecture geometry (haversian canals and resorption cavities) and heterogeneous matrix elasticity. Cubic bone samples of 1 mm 3 are reconstructed from impedance 2D data obtained with a 50-MHz scanning acoustic microscope (resolution: 23~tm) [1]. After segmentation, pores are modelled as filled with compliant isotropic material. Impedance values for the bone matrix allow to derive either isotropic elastic coefficients (ISO) [1] or transverse isotropic coefficients (HEXA). Material invariance along the bone long axis is assumed. In case of HEXA, a micromechanical model of the matrix [2] is used in addition to impedance data. A procedure based on the finite element method, similar to that used in [3] was implemented to compute the overall stiffness tensor of the cubic samples [4]. Computations were done for 58 samples from one human radius. The mean anisotropy ratio is defined as AR=C33/Cll, where direction 3 is along the bone axis and direction 1 is perpendicular to it. For the ISO model AR = 1.29 (SD 0.14); for the HEXA model A R = 1.62 (SD 0.17). Comparison of model predictions with experimentally derived AR suggests that the matrix anisotropy should be accounted for to compute overall anisotropy. References [1] Raum K, et al. Phys Med Biol 2006; 51(3): 747-758. Epub 2006 Jan 19. [2] Hellmich C, UIm FJ. J Eng Mech 2002; 128(8): 898-908. [3] van Rietbergen B, et al. J Biomech 1996; 29(12): 1653-7. [4] Grimal Q, Raum K, Laugier P. In: European Conference on Computational Mechanics. 2006; Lisbon: Springer.
5857 Th, 14:45-15:00 (P42) Determination of transverse isotropic stiffness coefficients from high resolution angular acoustic impedance measurements L. Sannachi, A. Bodi, K. Raum. Q-BAM Group, Dept. of Orthopedics, Martin Luther University of Halle-Wittenberg, Germany Assessment of anisotropic elastic properties at the tissue level is still one of the major challenges in bone research. In previous studies bone sections were cut in different directions relative to a principle axis of symmetry. This causes a high preparation and measurement effort. We have developed a new acoustic scanning procedure, that allows to measure the angular dependence of the acoustic impedance of cylindrically shaped samples (diameter: 4 mm) with a single measurement. Therefore our scanning acoustic microscope (SAM200EX, Q-BAM, Halle) was equipped with a rotational stage and a scanning procedure was developed that measures the surface reflection of the rotating cylinder. It has been shown in a previous study that the acoustic impedance derived from the reflection coefficient is highly correlated with the elastic coefficient in the probing direction (Raum et al., 2006). This correlation was used to convert Z(~) to c(~). c11, c33, and c* = c13 + 2c44 were determined by fitting c(8) to an orthotropic material model. A continuum micro-mechanical open foam model (Hellmich and UIm, 2002) finally reveals the remaining elastic constants. This method was applied to the inspection of one human femur. The shaft was divided into 16 sections. From each section 4 cylinders were prepared from the anterior, posterior, medial and lateral regions. The long axis of the cylinder was always in the radial direction. The measurements were performed with a 50 MHz transducer, providing a lateral resolution of 23 ~tm. N-way ANOVA of the acoustic impedance with anatomical (A,P, M, L) and shaft positions as categorical factors showed that both factors contribute significantly to the variance of Z. The means and standard deviations of the derived elastic coefficients are: c33=32.6±4.18 GPa, Cll =28.5±13.8 GPa, c12 =6.03±0.78 GPa, c13 =7.57±1.24 GPa, c44 10.56±1.32 GPa, and c66 10.36±1.29 GPa. The correlation coefficients between the coefficients are in the range R 2 =0.7-0.9. =
=
References Hellmich, C., UIm, RJ. (2002). Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments. J. Biomech. 35:1199-1212. Raum, K., Cleveland, R.O., Peyrin, F., Laugier, R (2006). Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps. Phys. Med. Biol. 51: 747-758.
$19
5201 Th, 15:00-15:15 (P42) Apparent Young's modulus of human radius using inverse finite element method M.R. Bosisio 1, M. Talmant 2, W. Skalli 1, R Laugier 2, D. Mitton 1. 1Laboratoire
de Biom6canique ENSAM-CNRS Paris, France, 2Laboratoire d'lmagerie Param6trique Paris VI-CNRS, Paris, France The ability to assess cortical bone elastic and failure properties at the radial diaphysis has clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) have been developed to assess non invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. To date, mechanical properties of cortical bone at distal radius, (e.g., elastic modulus, yield stresses and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finiteelement method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty mm-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimenspecific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters and isotropic linear-elastic simulations. Results indicated that mean apparent Young's modulus for radial cortical bone was 16Gpa (S.D. 1.8) and yield stress was 153MPa (S.D. 33). Breaking load (12,946N, S.D. 3644), cortical thickness (2.9mm, S.D. 0.6), structural effective strain at the yield 0y = 0.0097) and failure 0u = 0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample. 4344 Variability of the mechanical properties of bone
Th, 15:15-15:30 (P42)
J. Currey. Dept Biology, University of York, York, UK Introduction: Most properties of bone cannot be compared directly, but the variability of mechanical properties, after suitable normalisation, can be. The results of such comparisons give insights into the structure-insensitivity or otherwise of different mechanical properties, and have implications for the evolutionary optimisation of bone properties. Methods: The variability of nine properties was examined: Bending strength, Young's modulus in bending, Young's modulus in tension, Tensile strength, Impact energy of slotted specimens, Ultimate strain in tension, Work of fracture, Impact energy of unslotted specimens, Work in tension. (Not all properties were measured on all specimens, of course.) The unit of investigation was the variation of properties in specimens from a single bone. The specimens used for measuring the same property were all of essentially the same size and shape. Two normalising measures of variability were used: the coefficient of variation (CV =SD/Mean), and the standard deviation of logged values. These gave essentially the same answers. A total of 1644 values of properties was determined, from bones of various vertebrate species. Estimates were made of how much of the variability was attributable to experimental error Results: The values of CV were in the same order as in the list of properties above, with work in tension being the greatest. This was four times greater than the least CV (for bending strength). Overall 'post-yield' properties were 23 more variable than 'pre-yield' properties. Experimental error was found to be very small in relation to 'inherent' variability, and in general was greater for the apparently less variable properties! Discussion: The striking finding is the considerable difference in the variability in pre-yield vs. post-yield properties. This is not completely unexpected, as yield properties tend to be less structure-sensitive than properties associated with the development and spread of cracks. These findings have implications for optimisation in bone, because the animal's 'control' over post-yield properties is much less than it is over pre-yield properties, and natural selection may shift the optimum to take account of this.
5761 Th, 16:00-16:15 (P45) Wistar rat cortical bone from growth to senescence: Correlation of mechanical, morphologic and physical chemical properties M. Vanleene 1, C. Rey 2, M.-C. Ho Ba Tho 1. 1Laboratoire de Biom6canique et g6nie Biomedical, CNRS-UMR 6600, Universit6 de Technologie de Compiegne, France, 2Centre Inter-Universitaire de Recherche et d'lng~nierie des Mat6riaux, CNRS-UMR 5085, ENSIACET-INPT, Toulouse, France The aim of our work is to investigate a model of bone properties evolution and to correlate the morphologic and physical chemical properties to the mechanical properties of bone. The relevance of Wistar rat as model for human bone is also investigated. Thus, mechanical properties (density, Young's modulus), morphologic properties (porosity percentage, pore area distribution),
Track 1. Bone Mechanics - Joint ESB Track
4760 Th, 14:30-14:45 (P42) A numerical investigation of the overall cortical bone anisotropy: contributions of material symmetry and micro-architecture Q. Grimal 1, K. Raum 2, V. Liabeuf 1, P. Laugier 1. 1Laboratoire d'imagerie param~trique, Universit~ Pierre et Marie Curie - Paris 6; CNRS UMR 7623; Paris, France, 2 Q-BAM Group, Dept. of Orthopedics, Martin Luther University, Halle, Germany Whether the overall (macroscopic) cortical bone anisotropy is mainly due to the pore distribution o r t o both the pores and the matrix intrinsic anisotropy has been debated by several authors. We propose a new model for the analysis of cortical bone overall anisotropy. Unlike existing idealized models, it takes as input realistic micro-architecture geometry (haversian canals and resorption cavities) and heterogeneous matrix elasticity. Cubic bone samples of 1 mm 3 are reconstructed from impedance 2D data obtained with a 50-MHz scanning acoustic microscope (resolution: 23~tm) [1]. After segmentation, pores are modelled as filled with compliant isotropic material. Impedance values for the bone matrix allow to derive either isotropic elastic coefficients (ISO) [1] or transverse isotropic coefficients (HEXA). Material invariance along the bone long axis is assumed. In case of HEXA, a micromechanical model of the matrix [2] is used in addition to impedance data. A procedure based on the finite element method, similar to that used in [3] was implemented to compute the overall stiffness tensor of the cubic samples [4]. Computations were done for 58 samples from one human radius. The mean anisotropy ratio is defined as AR=C33/Cll, where direction 3 is along the bone axis and direction 1 is perpendicular to it. For the ISO model AR = 1.29 (SD 0.14); for the HEXA model A R = 1.62 (SD 0.17). Comparison of model predictions with experimentally derived AR suggests that the matrix anisotropy should be accounted for to compute overall anisotropy. References [1] Raum K, et al. Phys Med Biol 2006; 51(3): 747-758. Epub 2006 Jan 19. [2] Hellmich C, UIm FJ. J Eng Mech 2002; 128(8): 898-908. [3] van Rietbergen B, et al. J Biomech 1996; 29(12): 1653-7. [4] Grimal Q, Raum K, Laugier P. In: European Conference on Computational Mechanics. 2006; Lisbon: Springer.
5857 Th, 14:45-15:00 (P42) Determination of transverse isotropic stiffness coefficients from high resolution angular acoustic impedance measurements L. Sannachi, A. Bodi, K. Raum. Q-BAM Group, Dept. of Orthopedics, Martin Luther University of Halle-Wittenberg, Germany Assessment of anisotropic elastic properties at the tissue level is still one of the major challenges in bone research. In previous studies bone sections were cut in different directions relative to a principle axis of symmetry. This causes a high preparation and measurement effort. We have developed a new acoustic scanning procedure, that allows to measure the angular dependence of the acoustic impedance of cylindrically shaped samples (diameter: 4 mm) with a single measurement. Therefore our scanning acoustic microscope (SAM200EX, Q-BAM, Halle) was equipped with a rotational stage and a scanning procedure was developed that measures the surface reflection of the rotating cylinder. It has been shown in a previous study that the acoustic impedance derived from the reflection coefficient is highly correlated with the elastic coefficient in the probing direction (Raum et al., 2006). This correlation was used to convert Z(~) to c(~). c11, c33, and c* = c13 + 2c44 were determined by fitting c(8) to an orthotropic material model. A continuum micro-mechanical open foam model (Hellmich and UIm, 2002) finally reveals the remaining elastic constants. This method was applied to the inspection of one human femur. The shaft was divided into 16 sections. From each section 4 cylinders were prepared from the anterior, posterior, medial and lateral regions. The long axis of the cylinder was always in the radial direction. The measurements were performed with a 50 MHz transducer, providing a lateral resolution of 23 ~tm. N-way ANOVA of the acoustic impedance with anatomical (A,P, M, L) and shaft positions as categorical factors showed that both factors contribute significantly to the variance of Z. The means and standard deviations of the derived elastic coefficients are: c33=32.6±4.18 GPa, Cll =28.5±13.8 GPa, c12 =6.03±0.78 GPa, c13 =7.57±1.24 GPa, c44 10.56±1.32 GPa, and c66 10.36±1.29 GPa. The correlation coefficients between the coefficients are in the range R 2 =0.7-0.9. =
=
References Hellmich, C., UIm, RJ. (2002). Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments. J. Biomech. 35:1199-1212. Raum, K., Cleveland, R.O., Peyrin, F., Laugier, R (2006). Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps. Phys. Med. Biol. 51: 747-758.
$19
5201 Th, 15:00-15:15 (P42) Apparent Young's modulus of human radius using inverse finite element method M.R. Bosisio 1, M. Talmant 2, W. Skalli 1, R Laugier 2, D. Mitton 1. 1Laboratoire
de Biom6canique ENSAM-CNRS Paris, France, 2Laboratoire d'lmagerie Param6trique Paris VI-CNRS, Paris, France The ability to assess cortical bone elastic and failure properties at the radial diaphysis has clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) have been developed to assess non invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. To date, mechanical properties of cortical bone at distal radius, (e.g., elastic modulus, yield stresses and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finiteelement method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty mm-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimenspecific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters and isotropic linear-elastic simulations. Results indicated that mean apparent Young's modulus for radial cortical bone was 16Gpa (S.D. 1.8) and yield stress was 153MPa (S.D. 33). Breaking load (12,946N, S.D. 3644), cortical thickness (2.9mm, S.D. 0.6), structural effective strain at the yield 0y = 0.0097) and failure 0u = 0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample. 4344 Variability of the mechanical properties of bone
Th, 15:15-15:30 (P42)
J. Currey. Dept Biology, University of York, York, UK Introduction: Most properties of bone cannot be compared directly, but the variability of mechanical properties, after suitable normalisation, can be. The results of such comparisons give insights into the structure-insensitivity or otherwise of different mechanical properties, and have implications for the evolutionary optimisation of bone properties. Methods: The variability of nine properties was examined: Bending strength, Young's modulus in bending, Young's modulus in tension, Tensile strength, Impact energy of slotted specimens, Ultimate strain in tension, Work of fracture, Impact energy of unslotted specimens, Work in tension. (Not all properties were measured on all specimens, of course.) The unit of investigation was the variation of properties in specimens from a single bone. The specimens used for measuring the same property were all of essentially the same size and shape. Two normalising measures of variability were used: the coefficient of variation (CV =SD/Mean), and the standard deviation of logged values. These gave essentially the same answers. A total of 1644 values of properties was determined, from bones of various vertebrate species. Estimates were made of how much of the variability was attributable to experimental error Results: The values of CV were in the same order as in the list of properties above, with work in tension being the greatest. This was four times greater than the least CV (for bending strength). Overall 'post-yield' properties were 23 more variable than 'pre-yield' properties. Experimental error was found to be very small in relation to 'inherent' variability, and in general was greater for the apparently less variable properties! Discussion: The striking finding is the considerable difference in the variability in pre-yield vs. post-yield properties. This is not completely unexpected, as yield properties tend to be less structure-sensitive than properties associated with the development and spread of cracks. These findings have implications for optimisation in bone, because the animal's 'control' over post-yield properties is much less than it is over pre-yield properties, and natural selection may shift the optimum to take account of this.
5761 Th, 16:00-16:15 (P45) Wistar rat cortical bone from growth to senescence: Correlation of mechanical, morphologic and physical chemical properties M. Vanleene 1, C. Rey 2, M.-C. Ho Ba Tho 1. 1Laboratoire de Biom6canique et g6nie Biomedical, CNRS-UMR 6600, Universit6 de Technologie de Compiegne, France, 2Centre Inter-Universitaire de Recherche et d'lng~nierie des Mat6riaux, CNRS-UMR 5085, ENSIACET-INPT, Toulouse, France The aim of our work is to investigate a model of bone properties evolution and to correlate the morphologic and physical chemical properties to the mechanical properties of bone. The relevance of Wistar rat as model for human bone is also investigated. Thus, mechanical properties (density, Young's modulus), morphologic properties (porosity percentage, pore area distribution),