Elastic anisotropy and off-axis ultrasonic velocity distribution in human cortical bone

Abstract

Elastic structure in cortical bone is usually simplified as orthotropic or transversely isotropic, which allows estimates of three-dimensional technical constants from ultrasonic and density measurements. These elastic property estimates can then be used to study phenotypic changes in cortical bone structure and function, and to create finite element models of skeletal structures for studies of organismal variation and functional adaptation. This study examines assumptions of orthotropic or transversely isotropic material structure in cortical bone through the investigation of off-axis ultrasonic velocities in the cortical plane in 10 samples each from a human femur, mandible and cranium. Longitudinal ultrasonic velocities were measured twice through each bone sample by rotating the perimeter of each sample in 1°angular intervals between two ultrasonic transducers. The data were fit to sine curves f(x) = (A · sin(x + B) + C) and the goodness of fit was examined. All the data from the femur fit closely with the ideal sine curve model, and all three coefficients were similar among specimens, indicating similar elastic properties, anisotropies and orientations of the axes of maximum stiffness. Off-axis ultrasonic velocities in the mandible largely fit the sine curve model, although there were regional variations in the coefficients. Off-axis ultrasonic velocities from the cranial vault conformed to the sine curve model in some regions but not in others, which shows an irregular and complex pattern. We hypothesize that these variations in ultrasonic velocities reflect variations in the underlying bulk microstructure of the cortical bone, especially in the three-dimensional patterns of osteonal orientation and structure. Elastic property estimates made with ultrasonic techniques are likely valid in the femur and mandible; errors in estimates from cranial bone need to be evaluated regionally. Approximate orthotropic structure in bulk cortical bone specimens should be assessed if ultrasound is used to estimate three-dimensional elastic properties.

Tensile Mechanical Properties of Swine Cortical Mandibular Bone

“…Obviously, such a large specimen size cannot be obtained from the limited ALV bone, making this test inappropriate for evaluating the anisotropy of this zone. Schwartz-Dabney and Dechow (2003) [22] and Chung and Dechow (2011) [2] used an ultrasonic technique on 10-mm-diameter specimens and found that human mandibles have the highest stiffness values mainly parallel to the occlusal plane. Rapoff et al, [2008] [24] performed microindentation tests on one M. fascicularis mandible and also found a higher modulus in the antero-posterior direction compared to either the lateral or the OG direction.…”

“…Bones have structure-function relationship. For example, the bones of the lower limb that are loaded extensively during locomotion have superior mechanical properties along their longitudinal axis compared to the lateral axis [1] – [2] . The mandible is a unique bone that differs from long bones in that it has a U-shaped geometry and is connected to the skull bilaterally.…”

Sensitivity and ex vivo validation of finite element models of the domestic pig cranium

“…2000; Zapata et al. 2010; Chung & Dechow, 2011). As material properties vary throughout the skull, and may not be aligned with a standard anatomical axis (Peterson & Dechow, 2003; Wang & Dechow, 2006; Dechow et al.…”

“…Orthotropy is well known from long bones and the mandible across several taxa, and has been demonstrated to be present in the cranium to varying degrees as well (O'Mahony et al 2000;Zapata et al 2010;Chung & Dechow, 2011). As material properties vary throughout the skull, and may not be aligned with a standard anatomical axis (Peterson & Dechow, 2003;Wang & Dechow, 2006;Dechow et al 2010), defining cranial orthotropy in an FE model is considerably difficult, even with detailed measurements of material properties (which were unavailable for this study).…”

Food mechanical properties and dietary ecology

“…In addition, these properties can either be homogeneous (locationally independent) or heterogeneous (locationally dependent) within the material. Most biological tissues are anisotropic and heterogeneous, but some can be treated as orthotropic, transversely isotropic, isotropic and/or homogeneous (Currey and Butler, ; Ashman, ; Rho et al, ; Peterson and Dechow, ; Dumont et al, ; Peterson et al, ; Wang et al, ; Currey, ; Dechow et al, ; Chung and Dechow, ; Davis et al, ). Assuming a material is isotropic and homogeneous is convenient, as many of the equations from materials science (and, in particular, fracture mechanics) are based on these assumptions (Wang, ; Roylance, ; Callister, ).…”