Material properties of trabecular bone structures

The transplantation of human allograft for restoration and filling of cortical bone defects is well known. Our aim was an experimental investigation of the mechanical stability of the often used femoral head spongiosa depending on the caliber and extent of the allograft. To evaluate the orientation of the trabecular structures of the femoral head and relate this data to its mechanical properties, morphometric studies were combined with mechanical tests of cancellous bone specimens. The mechanical examination of the allograft was done following the compression test according to DIN 50106. We examined 36 human unfixed hip joint spongiosa cylinders with a height of 11 mm and a diameter of 24 mm. We took three specimens from each femoral head. We compressed the allograft at a constant velocity of 0.017 mm/sec. We calculated the maximum compression strength, the yield point and the Young's modulus. We also examined 12 parallelepipedic specimens with (17 x 17 x 51 mm) for morphometric analysis and loading in the direction of the primary compressive group (PCG), as well as perpendicular loading and at an angle of 45 degrees. We found divergent mechanical stabilities. None of the femoral heads showed comparable compressive strength. There was no position dependency of the strength of the samples. No relation between optical appearance and strength was found. We found a value for the lower compressive strength, which can be used for calculation as a basic value for safe constructions. Furthermore we tested the well known dependence of strength on the direction of the trabecular structure. We found a strong relationship between strength and load direction on the preferred direction of the trabecular structure. The sole recommendation resulting from our investigations is to rely on the lowest compressive strength for all preoperative planning. Relying on higher compressive strength by using the theoretical predicted areas of higher strength is hazardous since we found no correlation between position of sampling and strength. The size of our samples is important, because of the fact that different sizes of the samples might cause different failure mechanisms in the samples. The preparation of the femoral head spongiosa should be done according to the primary compressive group of the trabecular structure.     

Material properties of trabecular bone structures

Abstract: The transplantation of human allograft for restoration and filling of cortical bone defects is well known. Our aim was an experimental investigation of the mechanical stability of the often used femoral head spongiosa depending on the caliber and extent of the allograft. To evaluate the orientation of the trabecular structures of the femoral head and relate this data to its mechanical properties, morphometric studies were combined with mechanical tests of cancellous bone specimens. The mechanical examination of the allograft was done following the compression test according to DIN 50106. We examined 36 human unfixed hip joint spongiosa cylinders with a height of 11 mm and a diameter of 24 mm. We took three specimens from each femoral head. We compressed the allograft at a constant velocity of 0.017 mm/sec. We calculated the maximum compression strength, the yield point and the Young’s modulus. We also examined 12 parallelepipedic specimens with (17 × 17 × 51 mm) for morphometric analysis and loading in the direction of the primary compressive group (PCG), as well as perpendicular loading and at an angle of 45°. We found divergent mechanical stabilities. None of the femoral heads showed comparable compressive strength. There was no position dependency of the strength of the samples. No relation between optical appearance and strength was found. We found a value for the lower compressive strength, which can be used for calculation as a basic value for safe constructions. Furthermore we tested the well known dependence of strength on the direction of the trabecular structure. We found a strong relationship between strength and load direction on the preferred direction of the trabecular structure. The sole recommendation resulting from our investigations is to rely on the lowest compressive strength for all preoperative planning. Relying on higher compressive strength by using the theoretical predicted areas of higher strength is hazardous since we found no correlation between position of sampling and strength. The size of our samples is important, because of the fact that different sizes of the samples might cause different failure mechanisms in the samples. The preparation of the femoral head spongiosa should be done according to the primary compressive group of the trabecular structure.     

Anisotropic resolution biases estimation of fabric from 3D gray-level images

In the present paper it is investigated how anisotropic resolution, typical for clinical imaging devices like computed tomography, influences detection of principal directions of test structures. The gray-level intensity is derived as a function of position in 3D space for network-like objects under an assumption of anisotropic blurring and then three tensors of structural anisotropy are calculated for the computed gray-level image of the object. The three approaches to compute the tensor of structural anisotropy are based on zero, first and second order derivatives of the gray-level intensity. It is shown that detection of principal directions is biased under anisotropic resolution if zero and first order approaches are used. The computation of principal values is biased for all methods under anisotropic resolution. The analytical results are supported by numerical simulations. The explanation of the observed phenomenon is given. Analogies between gray-level and binary approaches to compute tensors of structural anisotropy are sketched.     

A novel method of estimating structure model index from gray-level images

According to the standard approach, estimation of the structure model index (SMI) of a trabecular bone sample has to be preceded by segmentation of the bone image and then triangulation of the trabecular surface. However, when analyzing clinical data, image segmentation should be avoided whenever possible, due to difficulties in controlling binarization artifacts. The aim of the present study is to develop a method to estimate SMI directly from gray-level images, without prior segmentation. It is shown that the standard definition of SMI can be formulated in terms of integrals of the gray-level intensity and the magnitude of the gray-level intensity gradient, computed for the analyzed image and the image eroded by an infinitesimal ball structuring element. Because in a real application the size of an eroding element is always finite, a procedure is proposed to reduce the finite size errors. The performance of the proposed method is tested for structures with known SMI. Next, based on a set of μCT images of trabecular bone from the distal radius, the proposed and the standard methods are compared. It is shown that the proposed novel approach is statistically equivalent to the standard one, if applied to high-resolution μCT data. The influence of clinically relevant factors like limited resolution and noise on the estimation of SMI is tested. It is shown that the gray-level approach is more robust against image degradation factors than the standard one.     

Acoustic emission and mechanical properties of trabecular bone

The mechanical properties of trabecular bone and a simple plug prosthetic system have been determined over a range of displacement from 0.1 to 5 mm/min. Acoustic emission, a technique which is capable of detecting dynamic processes within a material, was used to monitor the compression tests on the prosthetic system. It was found that the stiffness and strength of trabecular bone and the prosthetic system increased with increasing strain rate of testing. The acoustic emission results demonstrated that the improvement in mechanical behaviour at the fast strain rates was accompanied by a decrease in the extent of the failure of the trabeculae. The technique of activation analysis has been applied to the results in order to identify the rate controlling fracture mechanism. Finally, the strength of the prosthetic system was correlated with the shear and compressive strengths of trabecular bone.     

Prediction of mechanical properties of trabecular bone using quantitative MRI

Techniques for quantitative magnetic resonance imaging (MRI) have been developed for non-invasive estimation of the mineral density and structure of trabecular bone. The R*(2) relaxation rate (i.e. 1/T*(2)) is sensitive to bone mineral density (BMD) via susceptibility differences between trabeculae and bone marrow, and by binarizing MRI images, structural variables, such as apparent bone volume fraction, can be assessed. In the present study, trabecular bone samples of human patellae were investigated in vitro at 1.5 T to determine the ability of MRI-derived variables (R*(2) and bone volume fraction) to predict the mechanical properties (Young's modulus, yield stress and ultimate strength). Further, the MRI variables were correlated with reference measurements of volumetric BMD and bone area fraction as determined with a clinical pQCT system. The MRI variables correlated significantly (p < 0.01) with the mechanical variables (r = 0.32-0.46), BMD (r = 0.56) and bone structure (r = 0.51). A combination of R*(2) and MRI-derived bone volume fraction further improved the prediction of yield stress and ultimate strength. Although pQCT showed a trend towards better prediction of the mechanical properties, current results demonstrate the feasibility of combined MR imaging of marrow susceptibility and bone volume fraction in predicting the mechanical strength of trabecular bone and bone mineral density.     

Interrelationships between electrical properties and microstructure of human trabecular bone

Microstructural changes, such as reduction of trabecular thickness and number, are characteristic signs of osteoporosis leading to diminished bone strength. Electrical and dielectric parameters might provide diagnostically valuable information on trabecular bone microstructure not extractable from bone mineral density measurements. In this study, structural properties of human trabecular bone samples (n=26) harvested from the distal femur and proximal tibia were investigated using the computed microtomography (microCT) technique. Quantitative parameters, e.g. structural model index (SMI) or trabecular bone volume fraction (BV/TV), were calculated. In addition, the samples were examined electrically over a wide frequency range (50 Hz-5 MHz) using a two-electrode impedance spectroscopy set-up. Relative permittivity, loss factor, conductivity, phase angle, specific impedance and dissipation factor were determined. Significant linear correlations were obtained between the dissipation factor and BV/TV or SMI (|r| 0.70, p<0.01, n=26). Principal component analyses, conducted on electrical and structural parameters, revealed that the high frequency principal component of the dissipation factor was significantly related to SMI (r=0.72, p<0.01, n=26). The linear combination of high and low frequency relative permittivity predicted 73% of the variation in BV/TV. To conclude, electrical and dielectric parameters of trabecular bone, especially relative permittivity and dissipation factor, were significantly and specifically related to a trabecular microstructure as characterized with microCT. The data gathered in this study constitute a useful basis for theoretical and experimental work towards the development of impedance spectroscopy techniques for detection of bone quality in vitro or in special cases of open surgery.     

股骨近端主压力骨小梁生物力学特性

目的股骨头坏死是一种常见病,导致其发病的原因有很多,其中股骨颈骨折后股骨头坏死的原因尚不清楚,机制不明,由于其局部解剖结构特殊,根据其内部结构特点,对骨小梁结构进行研究,为解释股骨颈骨折后股骨头坏死的发生原因提供实验依据。方法对正常中国人(45～60岁)尸体股骨近端主压力骨小梁系统从上到下分成3个区,分别在Endura TEC ELF3200生物力学材料动态力学性能测试系统上,从主压力骨小梁方向及与其垂直方向上进行拉伸、压缩性能实验研究。结果得出了股骨近端主压力骨小梁系统3个区在主压力骨小梁系统方向及与其垂直方向的压缩、拉伸屈服强度、极限强度、弹性模量等测试指标的实验结果。从上到下3个区的弹性模量等生物力学性能依次递增,主压力方向的压缩生物力学性能要明显高于拉伸生物力学性能,并且生物力学性能在主压力系统方向及与其垂直方向有明显差异。结论股骨近端主压力骨小梁的主要力学性能是承受压应力,并且具有明显的各向异性。     

股骨近端主张力骨小梁生物力学特性

目的 研究股骨近端主张力骨小梁的生物力学性能,为解释股骨颈骨折后股骨头坏死的发生原因提供实验依据.方法 取8个正常国人(45 ～60岁)尸体股骨,排除畸形、骨折等病变.将近端主张力骨小梁系统从外侧到内侧分成3个区,在每个区内沿主张力小梁方向及与其垂直方向切取骨小梁试件,并分别在EnduraTEC ELF3200生物力学...     

3D打印钛合金骨小梁多孔结构的拉伸性能

文题释义：3D打印：3D打印技术开创了增材制造的生产方式,即依照3D设计蓝图可将金属粉末等原材料逐层堆积而制成最终产品,擅长构建形状结构复杂的产品与个体化定制,制作特异性假体或植入物,供植入以达到重建等目的,在骨科领域得到了广泛应用。 钛合金骨小梁：是以钛合金粉末为原材料,采用金属3D打印技术通过金属微粒逐层熔融叠加生成的一种类人体骨小梁三维空间网孔结构,其力学性能和生物学性能和人体的松质骨骨小梁极为相似,作为人工植入假体的表面结构,具有非常出色的骨长入效果。 背景：3D打印钛合金多孔结构以其良好的机械性能和生物相容性已经在骨科植入假体设计与临床应用方面得到了快速发展,与涂层假体相比,钛合金骨小梁结构具有骨长入快和骨长入好的优点。为了保证骨科植入物的安全,目前多采用实验方式确定骨小梁结构的拉伸、剪切疲劳和弯曲疲劳强度。 目的：通过力学实验和有限元数值模拟方法研究骨小梁多孔结构的力学性能。 方法：①3D打印钛合金骨小梁拉伸试件实验：设计并制备3D打印钛合金骨小梁拉伸试件,骨小梁结构的丝径为0.28-0.35 mm、孔径为0.71 mm、孔隙率为73%。检测钛合金骨小梁结构的拉伸强度,分析其失效机制,同时分析不同打印位置对骨小梁拉伸强度的影响。②数值模拟实验：利用有限元方法建立包括骨小梁理论结构的拉伸试件实体模型,模拟骨小梁试件的拉伸破坏过程。 结果与结论：①3D打印钛合金骨小梁拉伸试件的极限载荷分布在39.55-47.11 kN之间,等效极限拉伸应力分布在62.79-74.53 MPa之间,拉伸破坏的结果为网状结构断裂,说明钛合金骨小梁具有较高的拉伸强度;②3D打印钛合金骨小梁拉伸试件实验与数值模拟实验均显示,骨小梁试件受到拉伸破坏时的破坏形式为丝径断裂,不会在骨小梁与钛合金实体的结合面发生断裂;③数值模拟实验中骨小梁试件的拉伸破坏载荷低于3D打印钛合金骨小梁拉伸试件,造成该差异的原因主要为：3D打印骨小梁试件的丝径(280-350 μm之间)大于骨小梁的理论丝径(142 μm),而孔径(孔隙率75%)小于骨小梁的理论孔径(孔隙率96%)。 ORCID: 0000-0001-7000-2093(张兰) 中国组织工程研究杂志出版内容重点：生物材料;骨生物材料; 口腔生物材料; 纳米材料; 缓释材料; 材料相容性;组织工程     

Effect of human trabecular bone composition on its electrical properties

Mechanical properties of bone are determined not only by bone mineral density (BMD), but also by tissue trabecular structure and organic composition. Impedance spectroscopy has shown potential to diagnose trabecular bone BMD and strength, however, the relationships between organic composition and electrical and dielectric properties have not been systematically investigated. To investigate these issues organic composition of 26 human trabecular bone samples harvested from the distal femur and proximal tibia was determined and compared with relative permittivity, loss factor, conductivity, phase angle, specific impedance and dissipation factor measured at wide range (50 Hz to 5 MHz) of frequencies. A strong linear correlation was found between the relative permittivity at 1.2 MHz and trabecular bone fat content (r = -0.85, p<0.01, n=26). On the other hand, relative permittivity measured at 200 Hz served as a good predictor of water content (r = 0.83). Phase angle, specific impedance and especially conductivity were strongly related to the trabecular bone dry density and water content (|r| > or = 0.69). Variation in bone tissue collagen content was strongly related to the relative permittivity measured at 1.2 MHz (r = 0.64), but only moderately to other parameters. Glycosaminoglycan content showed no significant relations with any investigated electrical parameters. The present study indicates that if the trabecular bone composition is known, the relationships presented in this study could facilitate calculation of current field distribution, e.g. during electrical stimulation of osteogenesis. On the other hand, our results suggest that permittivity measured at low (<1 kHz) or high (>100 kHz) frequencies could be used, e.g. during implant surgery, for prediction of trabecular bone water or fat contents, respectively.     

Spatial variation of acoustic properties is related with mechanical properties of trabecular bone

In clinical applications, ultrasound parameters are measured as an average value over a region of interest (ROI) or as a value at a single measurement point. Due to natural adaptation to loading conditions, trabecular bone is structurally, compositionally and mechanically heterogeneous and anisotropic. Thus, spatial variation of ultrasound parameters within ROI may contain valuable information on the mechanical integrity of trabecular bone. However, this issue has not been thoroughly investigated. In the present study, we aimed at investigating the significance of the spatial variation of ultrasound parameters for the prediction of mechanical properties of human trabecular bone. For this aim, parametric maps of apparent integrated backscattering (AIB), integrated reflection coefficient (IRC), speed of sound (SOS), average attenuation (AA) and normalized broadband ultrasound attenuation (nBUA) were calculated for femoral and tibial bone cylinders (n = 19-20). Further, the effect of time window length on the AIB, variation of AIB within ROI and association between AIB and bone mechanical properties were characterized. Based on linear correlation analysis, spatial variation of AIB, assessed as standard deviation of measurements within ROI, was a strong predictor of bone ultimate strength (r = -0.82, n = 19, p < 0.01). Further, the time window length affected absolute values of AIB and strength of correlation between AIB and bone ultimate strength. Interestingly, linear combination of mean IRC and spatial variation of AIB within ROI was the strongest predictor of bone ultimate strength (r = 0.92, n = 19, p < 0.01). In conclusion, our findings suggest that the measurement of two-dimensional parametric maps of ultrasound parameters could yield information on bone status not extractable from single point measurements. This highlights the potential of parametric imaging in osteoporosis diagnostics.     

Mechanical properties of human trabecular bone lamellae quantified by nanoindentation.

Improved preventive and therapeutic strategies for skeletal diseases such as osteoporosis rely on a better understanding of the mechanical properties of trabecular bone and their influence on cell mediated adaptation processes. The mechanical properties of trabecular bone are determined by composition as well as structural (trabecular architecture), microstructural (trabecular packets) and nanostructural (lamellae) organization. Density is the major predictor of the mechanical properties of trabecular structures and has been extended to the concept of fabric to include architectural anisotropy and improve even further the power of prediction. Recent advances in QCT and MRI technologies allow for precise assessment of 3D trabecular architecture and the mechanical consequences of structural changes can be increasingly well quantified by the means of computational methods. While single trabeculae have been tested using various techniques with contrasting results, little is known about the intrinsic mechanical properties of trabecular bone lamellae on which these computational methods rely. For instance, water and mineral content have a significant effect on the elastic, viscous, yield and postyield properties of bone tissue. In addition, collagen fiber orientation affects the mechanics of single remodeling units. Variations in composition and organization determined by age, accumulated damage or disease may therefore reduce the mechanical integrity of trabecular bone and deserve more attention. The aim of this work was to utilize a nanoindentation technique to quantify elastic modulus and hardness of human trabecular bone lamellae.     

Three-dimensional image registration of MR proximal femur images for the analysis of trabecular bone parameters

This study investigated the feasibility of automatic image registration of MR high-spatial resolution proximal femur trabecular bone images as well as the effects of gray-level interpolation and volume of interest (VOI) misalignment on MR-derived trabecular bone structure parameters. For six subjects in a short-term study, a baseline scan and a follow-up scan of the proximal femur were acquired on the same day. For ten subjects in a long-term study, a follow-up scan of the proximal femur was acquired 1 year after the baseline. An automatic image registration technique, based on mutual information, utilized a baseline and a follow-up scan to compute transform parameters that aligned the two images. In the short-term study, these parameters were subsequently used to transform the follow-up image with three different gray-level interpolators. Nearest-neighbor interpolation and B-spline approximation did not significantly alter bone parameters, while linear interpolation significantly modified bone parameters (p<0.01). Improvement in image alignment due to the automatic registration for the long-term and short-term study was determined by inspecting difference images and 3D renderings. This work demonstrates the first application of automatic registration, without prior segmentation, of high-spatial resolution trabecular bone MR images of the proximal femur. Additionally, inherent heterogeneity in trabecular bone structure and imprecise positioning of the VOI along the slice (anterior-posterior) direction resulted in significant changes in bone parameters (p<0.01). Results suggest that automatic mutual information registration using B-spline approximation or nearest neighbor gray-level interpolation to transform the final image ensures VOI alignment between baseline and follow-up images and does not compromise the integrity of MR-derived trabecular bone parameters used in this study.     

Automatic analysis of trabecular bone structure from knee MRI

We investigated the feasibility of quantifying osteoarthritis (OA) by analysis of the trabecular bone structure in low-field knee MRI. Generic texture features were extracted from the images and subsequently selected by sequential floating forward selection (SFFS), following a fully automatic, uncommitted machine-learning based framework. Six different classifiers were evaluated in cross-validation schemes and the results showed that the presence of OA can be quantified by a bone structure marker. The performance of the developed marker reached a generalization area-under-the-ROC (AUC) of 0.82, which is higher than the established cartilage markers known to relate to the OA diagnosis.     

A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform

Background  

The degree of anisotropy (DA) on radiographs is related to bone structure, we present a new index to assess DA.     

Determination of the trabecular bone direction from digitised radiographs

There is increasing evidence for monitoring the bone trabecular structure to explain, in part, the mechanical properties of bone. Despite the emergence of Computed Tomography, a radiograph is the standard format as it is cheap and used for assessing implant performance. Furthermore, various image-processing techniques developed to assess the trabecular structure from radiographs have regained interest owing to improvements in imaging equipment. This study assessed the precision and accuracy of the Co-occurrence and Run-length matrix, Spatial-frequency and Minkowski-fractal techniques to infer the trabecular direction from radiographs.Ten clinical images of femoral neck regions were obtained from digitised pelvic radiographs and subsequently analysed. These data were also used to generate synthetic images where the trabecular thickness, separation and directions were controlled in order to calculate the accuracy of the techniques. Additionally, a Laplacian noise was added in order to infer the precision of the techniques. All methods assessed the trabecular direction with a high degree of accuracy in these synthetic images including a single direction and no noise. However, only the Spatial-frequency and Co-occurrence matrix methods performed well on the clinical and heavily corrupted synthetic images. This demonstrated the possibility of inferring a linear trabecular direction in clinical conditions.     

Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis

The structural integrity of vertebral trabecular bone is determined by the continuity of its trabecular network and the size of the holes comprising its marrow space, both of which determine the apparent size of the marrow spaces in a transaxial CT image. A model-independent assessment of the trabeculation pattern was determined from the lacunarity of thresholded CT images. Using test images of lumbar vertebrae from human cadavers, acquired at different slice thicknesses, we determined that both median thresholding and local adaptive thresholding (using a 7 x 7 window) successfully segmented the grey-scale images. Lacunarity analysis indicated a multifractal nature to the images, and a range of marrow space sizes with significant structure around 14-18 mm(2). Preliminary studies of in vivo images from a clinical CT scanner indicate that lacunarity analysis can follow the pattern of bone loss in osteoporosis by monitoring the homogeneity of the marrow spaces, which is related to the connectivity of the trabecular bone network and the marrow space sizes. Although the patient sample was small, derived parameters such as the maximum deviation of the lacunarity from a neutral (fractal) model, and the maximum derivative of this deviation, seem to be sufficiently sensitive to distinguish a range of bone conditions. Our results suggest that these parameters, used with bone mineral density values, may have diagnostic value in characterizing osteoporosis and predicting fracture risk.