Satoshi Yamada

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).

Residual Stress Around the Cortical Surface in Bovine Femoral Diaphysis

Residual stress in living tissue plays an important role in mechanical strength. We have reported that residual stress exists in the bone tissue of a rabbits tibiofibula. The purpose of this study is to measure the residual stress around the outer cortical region of bovine femoral diaphysis and to discuss the distribution of the stress. This work proposed the sin(2) psi method of X-ray diffraction to the measurement of residual stresses in bone tissue. In this method, residual stress can be estimated from the variation in the interplanar spacings orientated to a number of directions without the lattice strain in the stress direction. Four-point bending tests of strip specimens taken from bovine femoral diaphysis were carried out during X-ray irradiation in advance. In the proximal, middle, and distal sections of bovine femoral diaphyses, the residual stresses at the cortical surface were measured using characteristic Mo-Kalpha X-rays. The bending tests of strip specimens with X-ray irradiation showed that the method could reliably estimate residual stresses in the bone tissue. The residual stress of the bone axial direction was larger than that of the circumferential direction. The stresses in the middle part of five diaphyses along the bone axial direction were tensile. The maximum stress was 162 MPa at the lateral position and the minimum was 78 MPa at the posterior position. The residual stress in the bone axial direction varies around the circumferential region. In addition, the bone axial distributions of residual stresses were different in the proximal, middle, and distal sections of the individual femur. Furthermore, it was confirmed that residual stress in the bone tissue was released by the cutting out of the specimen. The residual stresses in bone tissue could be measured by this method. The results show that residual stress in the bone axial direction at the cortical surface in bovine femoral diaphysis is tensile and varies around the circumferential region.

Influence of osteon area fraction and degree of orientation of HAp crystals on mechanical properties in bovine femur

Cortical bone has a hierarchical structure, spanning from the macrostructure at several millimeters or whole bone level, the microstructure at several hundred micrometers level, to the nanostructure at hydroxyapatite (HAp) crystals and collagen fibrils levels. The aim of the study is to understand the relationship between the HAp crystal orientation and the elastic modulus and the relationship between the osteon area fraction and the deformation behavior of HAp crystals in cortical bone. In the experiments, five strip specimens (40×2×1mm(3)) aligned with the bone axis were taken from the cortical bone of a bovine femur. The degree of c-axis orientation of HAp crystals in the specimens was measured with the X-ray diffraction technique with the imaging plate. To measure the deformation behavior of HAp crystals in the specimens, tensile tests under X-ray irradiation were conducted. The specimens were cut at the X-ray measurement positions and osteon area fraction and porosity at the transverse cross-sections were observed. Further, the volume fraction of HAp of the specimens was measured. Results showed the degree of c-axis orientation of HAp crystals was positively correlated with the elastic modulus of the specimens (r=0.94). The volume fraction of HAp and the porosity showed no statistical correlation with the elastic modulus and the tensile strength. The HAp crystal strain ε(H) increased linearly with the bone tissue strain ε. The average value of ε(H)/ε was 0.69±0.13 and there was no correlation between the osteon area fraction and ε(H)/ε (r=-0.27, p=0.33). The results suggest that the degree of c-axis orientation of HAp crystals affects the elastic modulus and the magnitude of HAp crystal strain does not depend on the osteon area fraction.

Effects of growth on residual stress distribution along the radial depth of cortical cylinders from bovine femurs

Residual stress is defined as the stress that remains in bone tissue without any external forces. This study investigated the effects of growth on residual stress distributions from the surface to deeper regions of cortical cylinders obtained from less-than-one-month-old (Group Y) and two-year-old (Group M) bovine femurs. In these experiments, five diaphysis specimens from each group were used. Residual stress was measured using a high-energy synchrotron white X-ray beam to penetrate X-rays into the deeper region of the bone specimens. The measurements in the cortical cylinders from Groups Y and M were performed at 0.5- and 1-mm intervals, respectively, from the outer surface to the deeper region of the diaphysis specimens at four positions: anterior, posterior, lateral, and medial. The residual stress was calculated on the basis of variation in the interplanar spacing of hydroxyapatite crystals in the bone tissue. According to the results, the diaphysis specimens from Group Y were not subjected to large residual stresses (average -1.2 MPa and 2.4 MPa at the surface region and 1.5mm depth, respectively). In Group M, the surface region of the diaphysis specimens was subjected to tensile residual stresses (average 6.7 MPa) and the deeper region was subjected to compressive stresses (average -8.2 MPa at 3mm depth). There was a strong significant difference between both these regions. The value of residual stresses at the surface region of the diaphysis specimens in both the groups had a positive statistical correlation with the cortical thickness at the measured locations.

Nanostructure and elastic modulus of single trabecula in bovine cancellous bone

We aimed to investigate the elastic modulus of trabeculae using tensile tests and assess the effects of nanostructure at the hydroxyapatite (HAp) crystal scale on the elastic modulus. In the experiments, 18 trabeculae that were at least 3mm in length in the proximal epiphysis of three adult bovine femurs were used. Tensile tests were conducted using a small tensile testing device coupled with microscopy under air-dried condition. The c-axis orientation of HAp crystals and the degree of orientation were measured by X-ray diffraction. To observe the deformation behavior of HAp crystals under tensile loading, the same tensile tests were conducted in X-ray diffraction measurements. The mineral content of specimens was evaluated using energy dispersive X-ray spectrometry. The elastic modulus of a single trabecula varied from 4.5 to 23.6 GPa, and the average was 11.5 ± 5.0 GPa. The c-axis of HAp crystals was aligned with the trabecular axis and the crystals were lineally deformed under tensile loading. The ratio of the HAp crystal strain to the tissue strain (strain ratio) had a significant correlation with the elastic modulus (r=0.79; P<0.001). However, the mineral content and the degree of orientation did not vary widely and did not correlate with the elastic modulus in this study. It suggests that the strain ratio may represent the nanostructure of a single trabecula and would determine the elastic modulus as well as mineral content and orientation.

Micro-cantilever bending for elastic modulus measurements of a single trabecula in cancellous bone

Mechanical tests performed on small bone specimens such a single trabecula remain challenging because their isolation, fixation, and precise loading are complicated. Hence, we describe a novel experimental method to measure the elastic properties of a single trabecula using micro-cantilever bending (MCB) testing. The method does not require specimens to be completely separated from the cancellous bone, and the specimen can be easily fixed during the test. In total, 10 trabecular specimens taken from the proximal epiphysis of an adult bovine femur were used in the present study. Measurements were conducted using a small testing device comprising a 1-axial stage, load cell, optical microscope, and small plate with a taper bore for applying load at the edge of the specimen. Each specimen was positioned at the edge of the bore and was deformed by displacing the stage. The deflection of the specimen was observed by optical microscopy. The elastic modulus of the specimen was calculated on the basis of the force-deflection relationship, assuming that the shape of the specimen was a vertical circular cylinder. As a result, an average elastic modulus of 9.1±5.4GPa was obtained for a single trabecula, including the values in literature. Thus, the MCB test is a novel simple method for biomechanical analysis of a single trabecula.

Age-Related Residual Stresses at Diaphyseal Surface of Bovine Femur Measured by XRD-IP System

The presence of residual stress in the diaphysis of quadrupedal extremities has been reported. Residual stress is defined as the stress that remains in bone tissue without any external forces. It is one of the stresses applied to bone tissue, as well as static stresses due to the body weight and dynamic stresses due to the movement. The bone residual stress can be measured from the deformation state of hydroxyapatite (HAp) crystals in bone tissue using X-ray diffraction. The authors proposed a sin2.. method for detecting residual stress at the diaphyseal surface of extremities. However, the previous system requires a complicated experimental setup, long irradiation time, and limitations of the sample size. Here, X-ray imaging plate (IP) can detect the two dimensional distribution of the diffracted X-rays from the HAp crystals in one irradiation. The aim of the study was to establish a simple measurement system using an X-ray diffraction technique with IP (XRD-IP) for obtaining the residual stress at the diaphyseal surface of extremities and to apply this system to residual stress measurements of young and mature bovine femurs. In the experiments, the mid-diaphysis part of femurs taken from a lessthan- 1-month-old and a 23-month-old bovine were used. The diaphysis specimens were irradiated with characteristic Mo- K.. X-rays, and the X-ray diffraction pattern was detected by an IP. A part of Debye ring of the (211) planes of HAp crystals was obtained in the pattern and the residual stress in the bone axis was calculated from the deformation state of the ring. The magnitude of residual stresses in the mature bone corresponded approximately to the results of the previous method. Further, it was demonstrated that the residual stresses at diaphyseal surface varied with age and location.

Structural strength of cancellous specimens from bovine femur under cyclic compression

The incidence of osteoporotic fractures was estimated as nine million worldwide in 2000, with particular occurrence at the proximity of joints rich in cancellous bone. Although most of these fractures spontaneously heal, some fractures progressively collapse during the early post-fracture period. Prediction of bone fragility during progressive collapse following initial fracture is clinically important. However, the mechanism of collapse, especially the gradual loss of the height in the cancellous bone region, is not clearly proved. The strength of cancellous bone after yield stress is difficult to predict since structural and mechanical strength cannot be determined a priori. The purpose of this study was to identify whether the baseline structure and volume of cancellous bone contributed to the change in cancellous bone strength under cyclic loading. A total of fifteen cubic cancellous bone specimens were obtained from two 2-year-old bovines and divided into three groups by collection regions: femoral head, neck, and proximal metaphysis. Structural indices of each 5-mm cubic specimen were determined using micro-computed tomography. Specimens were then subjected to five cycles of uniaxial compressive loading at 0.05 mm/min with initial 20 N loading, 0.3 mm displacement, and then unloading to 0.2 mm with 0.1 mm displacement for five successive cycles. Elastic modulus and yield stress of cancellous bone decreased exponentially during five loading cycles. The decrease ratio of yield stress from baseline to fifth cycle was strongly correlated with bone volume fraction (BV/TV, r = 0.96, p < 0.01) and structural model index (SMI, r = − 0.81, p < 0.01). The decrease ratio of elastic modulus from baseline to fifth cycle was also correlated with BV/TV (r = 0.80, p < 0.01) and SMI (r = − 0.78, p < 0.01). These data indicate that structural deterioration of cancellous bone is associated with bone strength after yield stress. This study suggests that baseline cancellous bone structure estimated from adjacent non-fractured bone contributes to the cancellous bone strength during collapse.

Residual Stress and Structural Anisotropy of Cortical Bone

The concept of residual stress and strain does not have long history for biological tissues. In the case of cortical bone, during remodeling process the old tissue is replaced by the new tissue with construction of osteons. Since the new tissue is generated under in vivo loadings as a non-deformed state, an indeterminate structure may be generated as a result of difference between the deformations of the old and new phases. Further, the mechanical properties (e.g. elastic modulus) are also different in these phases. Because of such non-uniform structures in cortical bone, residual stress/strain will remain in the replaced region even without external loading being applied. Tadano and co-workers initiated efforts to estimate residual stress/strain in cortical bone. In a very few applications with bone, the authors have successfully applied X-ray diffraction to quantify residual stresses at the bone surface. In this work, site-specific residual strain characteristics in relation with the mineral crystal orientation were studied and the sin2 ψ method was applied to measure residual stresses in bovine and rabbit extremities. The relationship between residual stress and osteon population density on the respective sites has also been obtained. Thus the knowledge about residual stress/strain in cortical bone, related with mineral crystal distribution and osteon population density, might play an important role in the biomechanical aspects of bone healing and remodeling.

Irradiation conditions for fiber laser bonding of HAp-glass ceramics with bovine cortical bone

Orthopedic implants are widely used to repair bones and to replace articulating joint surfaces. It is important to develop an instantaneous technique for the direct bonding of bone and implant materials. The aim of this study was to develop a technique for the laser bonding of bone with an implant material like ceramics. Ceramic specimens (10 mm diameter and 1 mm thickness) were sintered with hydroxyapatite and MgO-Al2O3-SiO2 glass powders mixed in 40:60 wt% proportions. A small hole was bored at the center of a ceramic specimen. The ceramic specimen was positioned onto a bovine bone specimen and a 5 mm diameter area of the ceramic specimen was irradiated using a fiber laser beam (1070-1080 nm wavelength). As a result, the bone and the ceramic specimens bonded strongly under the irradiation conditions of a 400 W laser power and a 1.0 s exposure time. The maximum shear strength was 5.3 ± 2.3 N. A bonding substance that penetrated deeply into the bone specimen was generated around the hole in the ceramic specimen. On using the fiber laser, the ceramic specimen instantaneously bonded to the bone specimen. Further, the irradiation conditions required for the bonding were investigated.