Anisotropy Of Cortical Bone Research Articles

Frequency-Driven Crack Propagation in Ultrasonically-Assisted Bone Cutting

Ultrasonically-assisted bone cutting with high precision has manyadvantagesfororthopedic surgeries. However, irregular crack propagation, large fractured chips, and surface damagemay occurduring the cutting processdue to the brittleness and anisotropy of cortical bone. These can be minimized by optimizing the operating parameters of the cutting tool; cutting frequency, amplitude, speed, depth, and temperature, inconsideration of the toughening mechanism of bone. Therefore, the current study is motivated to investigate the effect of varying frequencyon crack propagation in ultrasonically-assisted bone cutting through the means of finite element analysis. The pattern of crack propagation in relation to the variation of frequencieswas investigated using the extended finite element method (XFEM) in consideration of the bone microstructures. The results showed that crack propagation is effectively controlled when the tool isoperated at higher frequencies, but an up-forward crack propagation following the trajectory of tool vibration is only apparent at frequencies higher than 800 Hz. Neglecting the operating outputsat2400 Hz, the induced force and stress are observed to decrease proportionallywith increasing frequency.

Effect of saturation on the elastic properties and anisotropy of cortical bone

This paper focuses on the modeling of the effect of saturation on the overall elastic properties of cortical bone. We first use micromechanical model of Salguero, Saadat & Sevostianov (2014) to model anisotropic effective elastic stiffness of drained cortical bone and then apply replacement relations (see review of Sevostianov, 2020) to evaluate effect of the saturation. The model is verified by comparison with the experimental data of Granke et al. (2011). It is shown that accounting for the saturation makes the model consistent with the experiment data. We also compared the extents of anisotropy of the saturated and drained bones and show that presence of the biological fluid in pores reduces the overall anisotropy.

Improvements of material removal in cortical bone via impact cutting method

Bone cutting with high efficiency as well as low levels of forces and damage has a great significance for orthopaedic surgeries. Due to the brittleness and anisotropy of cortical bone, a conventional cutting process can cause irregular crack propagation and fractured bone chip, affecting the tissue removal process and postoperative recovery. In this paper, a high-frequency impact cutting method is investigated, and its effect on fracture propagation, chip formation and cutting forces is studied for orthogonal cutting. Experimental results show that cracks are deflected by cement lines in conventional cutting, forming fractured blocks or split chips. In impact cutting, the cutting-induced fractures expand along a main shear direction, generating small pieces of triangular segmented chips. Cutting forces are significantly reduced with vibration-induced impacts; especially, the main cutting force is nearly 70% lower than that in the conventional cutting. The main reason for this is much higher strain rates in high-frequency impact cutting than in a conventional process, and direct penetration of fractures across the osteonal matrix without deflections along the cement lines. This results in a straighter path along the main shear plane and totally different chip morphology; so, a lower consumption of cutting energy in the main shear direction reduces the macroscopic cutting force. The results of this study have an important theoretical and practical value for revealing the mechanism of impact cutting, improving the efficiency of osteotomy and supporting the innovation in bone surgical instruments.

In vivo ultrasound imaging of the bone cortex

Current clinical ultrasound scanners cannot be used to image the interior morphology of bones because these scanners fail to address the complicated physics involved for exact image reconstruction. Here, we show that if the physics is properly addressed, bone cortex can be imaged using a conventional transducer array and a programmable ultrasound scanner. We provide in vivo proof for this technique by scanning the radius and tibia of two healthy volunteers and comparing the thickness of the radius bone with high-resolution peripheral x-ray computed tomography. Our method assumes a medium that is composed of different homogeneous layers with unique elastic anisotropy and ultrasonic wave-speed values. The applicable values of these layers are found by optimizing image sharpness and intensity over a range of relevant values. In the algorithm of image reconstruction we take wave refraction between the layers into account using a ray-tracing technique. The estimated values of the ultrasonic wave-speed and anisotropy in cortical bone are in agreement with ex vivo studies reported in the literature. These parameters are of interest since they were proposed as biomarkers for cortical bone quality. In this paper we discuss the physics involved with ultrasound imaging of bone and provide an algorithm to successfully image the first segment of cortical bone.

The preliminary evaluation of a 1 MHz ultrasound probe for measuring the elastic anisotropy of human cortical bone

Our objective is to evaluate an ultrasound probe for measurements of velocity and anisotropy in human cortical bone (tibia). The anisotropy of cortical bone is a known and mechanically relevant property in the context of osteoporotic fracture risk. Current in vivo quantitative ultrasound devices measuring the velocity of ultrasound in long bones can only be applied in the axial direction. For anisotropy measurements a second direction for velocity measurements preferably perpendicular to the axial direction is necessary. We developed a new ultrasound probe which permits axial transmission measurements with a simultaneous second perpendicular direction (tangential). Anisotropy measurements were performed on isotropic and anisotropic phantoms and two excised human female tibiae (age 63 and 82). Anisotropy ratios (AI; ratio of squared ultrasound velocities in the two directions) were for the isotropic phantom 1.06±0.01 and for the anisotropic phantom 1.14±0.03 (mean±standard deviation). AI was 1.83±0.29 in the tibia from the older donor and 1.37±0.18 in the tibia from the younger donor. The AIs were in the expected range and differed significantly (p<0.05, t-test) between the tibiae. Measured sound velocities were reproducible (mean standard deviation of short time precision of both channels for phantom measurements 31m/s) and in agreement with reported velocities of the phantom material. Our results document the feasibility of anisotropy measurements at long bones using a single probe. Further improvements in the design of the probe and tests in vivo are warranted. If this approach can be evaluated in vivo an additional tool for assessing the bone status is available for clinical use.

Vascular Structure and Elastic Anisotropy in Cortical Bone

Elastic properties define the relationship in cortical bone between loading and deformation. Our investigations show the considerable variations in 3D elastic properties in the craniofacial skeleton, in particular, the variations in anisotropy as indicated by the ratio of elastic modulus between the axes of minimum and maximum stiffness within the cortical plane. These variations are an important but generally overlooked aspect of bone quality. Continuing studies are testing whether variations in cortical elastic anisotropy correlate with variations in 3D osteonal structure. A positive correlation would lend support to the claim that 3D osteonal structure is influenced by the orientation of mechanical loads in cortical bone. In the majority of midfacial cortical bone specimens, average osteon orientation weighted by osteon length is within 15 degrees of the direction of maximum stiffness. The anisotropy ratios are moderately correlated with the standard deviation of osteon orientation with R values of about 0.50. Results suggest that osteon orientation is a structural correlate of cortical anisotropy. However, the moderate correlations suggest that other factors, such as collagen orientation, or the quantity and structure of primary bone, are likely also important in determining cortical bone anisotropy at a supraosteonal or bulk level of organization. Supported by NSF BCS‐0240865.

Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models.

The ultrasonic axial transmission technique, used to assess cortical shells of long bones, is investigated using numerical simulations based on a three-dimensional (3D) finite difference code. We focus our interest on the effects of 3D cortical bone geometry (curvature, cortical thickness), anisotropy, and microporosity on speed of sound (SOS) measurements for different frequencies in the MHz range. We first show that SOS values measured on tubular cortical shells are identical to those measured on cortical plates of equal thickness. Anisotropy of cortical bone is then shown to have a major impact on SOS measurement as a function of cortical thickness. The range of SOS values measured on anisotropic bone is half the range found when bone is considered isotropic. Dependence of thickness occurs for cortical shell thinner than 0.5 x lambda(bone) in anisotropic bone (lambda(bone): wavelength in bone), whereas it occurs for cortical shell thinner than lambda(bone) when anisotropy is neglected. Sensitivity of SOS along the bone axis to intracortical microporosity is shown to be approximately -20 m s(-1) per percent of porosity. Using homogenized porous bone, we finally show that the cortical depth that contributes to lateral wave SOS measurement is approximately 1-1.5 mm for frequencies ranging from 500 kHz to 2 MHz under classical in vivo measurement conditions.

Applications of an anisotropic parameter to cortical bone.

An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anisotropic parametric equations (eta(sigma) and eta(epsilon)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (eta(sigma) = eta(epsilon) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p < 0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanical levels of anisotropy within other tissues and materials of interest.

Elastic properties and masticatory bone stress in the macaque mandible.

One important limitation of mechanical analyses with strain gages is the difficulty in directly estimating patterns of stress or loading in skeletal elements from strain measurements. Because of the inherent anisotropy in cortical bone, orientation of principal strains and stresses do not necessarily coincide, and it has been demonstrated theoretically that such differences may be as great as 45 degrees (Cowin and Hart, 1990). Likewise, relative proportions of stress and strain magnitudes may differ. This investigation measured the elastic properties of a region of cortical bone on both the buccal and lingual surfaces of the lower border of the macaque mandible. The elastic property data was then combined with macaque mandibular strain data from published and a new in vivo strain gage experiment to determine directions and magnitudes of maximum and minimum principal stresses. The goal was to compare the stresses and strains and assess the differences in orientation and relative magnitude between them. The main question was whether these differences might lead to different interpretations of mandibular function. Elastic and shear moduli, and Poisson's ratios were measured using an ultrasonic technique from buccal and lingual cortical surfaces in 12 macaque mandibles. Mandibular strain gage data were taken from a published set of experiments (Hylander, 1979), and from a new experiment in which rosette strain gauges were fixed to the buccal and lingual cortices of the mandibular corpus of an adult female Macaca fascicularis, after which bone strain was recorded during mastication. Averaged elastic properties were combined with strain data to calculate an estimate of stresses in the mandibular corpus. The elastic properties were similar to those of the human mandibular cortex. Near its lower border, the macaque mandible was most stiff in a longitudinal direction, less stiff in an inferosuperior direction, and least stiff in a direction normal to the bone's surface. The lingual aspect of the mandible was slightly stiffer than the buccal aspect. Magnitudes of stresses calculated from average strains ranged from a compressive stress of -16.00 GPa to a tensile stress of 8.84 GPa. The orientation of the principal stresses depended on whether the strain gage site was on the working or balancing side. On the balancing side of the mandibles, maximum principal stresses were oriented nearly perpendicular to the lower border of the mandible. On the working side of the mandibles, the orientation of the maximum principal stresses was more variable than on the balancing side, indicating a larger range of possible mechanisms of loading. Near the lower border of the mandible, differences between the orientation of stresses and strains were 12 degrees or less. Compared to ratios between maximum and minimum strains, ratios between maximum and minimum stresses were more divergent from a ratio of 1.0. Results did not provide any major reinterpretations of mandibular function in macaques, but rather confirmed and extended existing work. The differences between stresses and strains on the balancing side of the mandible generally supported the view that during the power stroke the mandible was bent and slightly twisted both during mastication and transducer biting. The calculated stresses served to de-emphasize the relative importance of torsion. On the working side, the greater range of variability in the stress analysis compared to the strain analysis suggested that a more detailed examination of loadings and stress patterns in each individual experiment would be useful to interpret the results. Torsion was evident on the working side; but in a number of experiments, further information was needed to interpret other superimposed regional loading patterns, which may have included parasagittal bending and reverse parasagittal bending.