A fiber-ceramic matrix composite material model for osteonal cortical bone fracture micromechanics: Solution of arbitrary microcracks interaction

Microcracks formed in bone are due to fatigue and cyclic loading. This formation is associated with a reduction of bone resistance to fracture. However, the significance of the parameters that govern microcrack behavior is not yet fully explored. A two-dimensional micromechanical fiber-ceramic matrix composite material model of the osteonal cortical bone is presented in this paper. The solution for the edge dislocations as Green’s function, is adopted to formulate a system of singular integral equations for the general microcracks in vicinity of the osteon. The effects of microstructural morphology and heterogeneity of the bone upon the fracture behavior is investigated by computing the Stress Intensity Factor (SIF) near the microcracks tips. Analysis of microcracks interaction indicates the significance of microcracks configuration in the shape of either stress amplification or stress shielding.     

Haversian remodeling in guided bone regeneration with calcium alginate film in circular bone defect model of rabbit

The objective of this study is to investigate the effect of bioabsorbable Calcium alginate film in guided bone regeneration by the study of Haversian remodeling. Circular bone defects of 5 mm diameter were created in the corners of mandibles in 35 rabbits. The defects were covered with calcium alginate film (CAF) served as the experimental group, or collagen membrane (CM) as the control group, respectively. Healing condition was analyzed with gross, histological and immunohistochemical studies after 1, 2, 4, 6 and 8 weeks. The experimental group appeared more and earlier Haversian remodeling and osteoinductive factors leading to better bone regeneration. The control group showed more macrophages, less and later Haversian remodeling, absorbed slowly, while collected fewer osteoinductive factors in the early stage. Calcium alginate film, which is a relatively cheaper material, provides better effect than the collagen membrane in bone regeneration, Haversian remodeling and quantity of osteoinductive factors.     

Towards an analytic solution for pulsed CEST

Chemical exchange saturation transfer (CEST) is an imaging method based on magnetization exchange between solutes and water. This exchange generates changes in the measured signal after off‐resonance radiofrequency irradiation. Although the analytic solution for CEST with continuous wave (CW) irradiation has been determined, most studies are performed using pulsed irradiation. In this work, we derive an analytic solution for the CEST signal after pulsed irradiation that includes both short‐time rotation effects and long‐time saturation effects in a two‐pool system corresponding to water and a low‐concentration exchanging solute pool. Several approximations are made to balance the accuracy and simplicity of the resulting analytic form, which is tested against numerical solutions of the coupled Bloch equations and is found to be largely accurate for amides at high fields, but less accurate at the higher exchange rates, lower offsets and typically higher irradiation powers of amines.     

Ultrasonic determination of the elastic modulus of human cortical bone

The elastic modulus (C_ii) of the cortical bones of 19 individuals (14 femurs and 16 tibias, fixed in formalin) was determined ultrasonically. Elastic moduli were measured at four anatomical positions (anterior, posterior, medial and lateral) and in all three planes of orientation (transverse, longitudinal and radial). The mean tibial C_ii (34.11 GPa) was greater than that obtained for femurs (32.52 GPa). The tibial longitudinal plane C_ii (34.1 GPa) was significantly greater than the femoral longitudinal plane C_ii (32.5 GPa). C_ii was significantly higher in the tibia than the femur in both the medial and posterior anatomical positions. The anterior tibia had a significantly lower C₁₁ compared to other positions. C_ii was significantly higher in the longitudinal plane than the transverse or radial planes in both the femur and the tibia. There was no consistent difference in modulus between left and right sides. No age effects were observed. There were no significant differences between males and females, or between African Americans and European Americans.     

Estimation of the elastic modulus of child cortical bone specimens via microindentation

Purpose: Non-pathological child cortical bone (NPCCB) studies can provide clinicians with vital information and insights. However, assessing the anisotropic elastic properties of NPCCB remains a challenge for the biomechanical engineering community. For the first time, this paper provides elastic moduli values for NPCCB specimens in two perpendicular directions (longitudinal and transverse) and for two different structural components of bone tissue (osteon and interstitial lamellae).

Materials and Methods: Microindentation is one of the reference methods used to measure bone stiffness. Here, 8 adult femurs (mean age 82 ± 8.9 years), 3 child femurs (mean age 13.3 ± 2.1 years), and 16 child fibulae (mean age 10.2 ± 3.9 years) were used to assess the elastic moduli of adult and child bones by microindentation.

Results: For adult specimens, the mean moduli measured in this study are 18.1 (2.6) GPa for osteons, 21.3 (2.3) GPa for interstitial lamellae, and 13.8 (1.7) GPa in the transverse direction.

For child femur specimens, the mean modulus is 14.1 (0.8) GPa for osteons, lower than that for interstitial lamellae: 15.5 (1.5) GPa. The mean modulus is 11.8 (0.7) GPa in the transverse direction. Child fibula specimens show a higher elastic modulus for interstitial lamellae 15.8 (1.5) than for osteons 13.5 (1.6), with 10.2 (1) GPa in the transverse direction.

Conclusion: For the first time, NPCCB elastic modulus values are provided in longitudinal and transverse directions at the microscale level.     

Comparison of mechanical and ultrasound elastic modulus of ovine tibial cortical bone

Finite element models of bones can be created by deriving geometry from an X-ray CT scan. Material properties such as the elastic modulus can then be applied using either a single or set of homogeneous values, or individual elements can have local values mapped onto them. Values for the elastic modulus can be derived from the CT density values using an elasticity versus density relationship.Many elasticity–density relationships have been reported in the literature for human bone. However, while ovine in vivo models are common in orthopaedic research, no work has been done to date on creating FE models of ovine bones. To create these models and apply relevant material properties, an ovine elasticity–density relationship needs to be determined.Using fresh frozen ovine tibias the apparent density of regions of interest was determined from a clinical CT scan. The bones were the sectioned into cuboid samples of cortical bone from the regions of interest. Ultrasound was used to determine the elastic modulus in each of three directions – longitudinally, radially and tangentially. Samples then underwent traditional compression testing in each direction.The relationships between apparent density and both ultrasound, and compression modulus in each direction were determined. Ultrasound testing was found to be a highly repeatable non-destructive method of calculating the elastic modulus, particularly suited to samples of this size.The elasticity–density relationships determined in the longitudinal direction were very similar between the compression and ultrasound data over the density range examined. A clear difference was seen in the elastic modulus between the longitudinal and transverse directions of the bone samples, and a transverse elasticity–density relationship is also reported.     

Correlation between longitudinal,circumferential, and radial moduli in cortical bone: Effect of mineral content

Previous studies indicate that changes in the longitudinal elastic properties of bone due to changes in mineral content are related to the longitudinal strength of bone tissue. Changes in mineral content are expected to affect bone tissue mechanical properties along all directions, albeit to different extents. However, changes in tissue mechanical properties along the different directions are expected to be correlated to one another. In this study, we investigate if radial, circumferential, and longitudinal moduli are related in bone tissue with varying mineral content. Plexiform bovine femoral bone samples were treated in fluoride ion solutions for a period of 3 and 12 days to obtain bones with 20% and 32% lower effective mineral contents. Transmission ultrasound velocities were obtained in the radial, circumferential, and longitudinal axes of bone and combined with measured densities to obtain corresponding tensorial moduli. Results indicate that moduli decreased with fluoride ion treatments and were significantly correlated to one another ($r^2$ radial vs. longitudinal = 0.80, $r^2$ circumferential vs. longitudinal = 0.90, $r^2$ radial vs. circumferential = 0.85). Densities calculated from using ultrasound parameters, acoustic impedance and transmission velocities, were moderately correlated to those measured by the Archimedes principle ($r^2=0.54$, $p<0.01$). These results suggest that radial and circumferential ultrasound measurements could be used to determine the longitudinal properties of bone and that ultrasound may not be able to predict in vitro densities of bones containing unbonded mineral.     

Elastic moduli of untreated, demineralized and deproteinized cortical bone: validation of a theoretical model of bone as an interpenetrating composite material

A theoretical experimentally based multi-scale model of the elastic response of cortical bone is presented. It portrays the hierarchical structure of bone as a composite with interpenetrating biopolymers (collagen and non-collagenous proteins) and minerals (hydroxyapatite), together with void spaces (porosity). The model involves a bottom-up approach and employs micromechanics and classical lamination theories of composite materials. Experiments on cortical bone samples from bovine femur include completely demineralized and deproteinized bones as well as untreated bone samples. Porosity and microstructure are characterized using optical and scanning electron microscopy, and micro-computed tomography. Compression testing is used to measure longitudinal and transverse elastic moduli of all three bone types. The characterization of structure and properties of these three bone states provides a deeper understanding of the contributions of the individual components of bone to its elastic response and allows fine tuning of modeling assumptions. Very good agreement is found between theoretical modeling and compression testing results, confirming the validity of the interpretation of bone as an interpenetrating composite material.     

Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur

Experimental investigations for anatomic variation in the magnitude and anisotropy of elastic constants in human femoral cortical bone tissue have typically focused on a limited number of convenient sites near the mid-diaphysis. However, the proximal and distal ends of the diaphysis are more clinically relevant to common orthopaedic procedures and interesting mechanobiology. Therefore, the objective of this study was to measure anatomic variation in the elastic anisotropy and inhomogeneity of human cortical bone tissue along the entire length (15%–85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants) of the femoral diaphysis, using ultrasonic wave propagation in the three orthogonal specimen axes. The elastic symmetry of tissue in the distal and extreme proximal portions of the diaphysis (15%–45% and 75%–85% of the total femur length, respectively) was, at most, orthotropic. In contrast, the elastic symmetry of tissue near the mid- and proximal mid-diaphysis (50%–70% of the total femur length) was reasonably approximated as transversely isotropic. The magnitudes of elastic constants generally reached maxima near the mid- and proximal mid-diaphysis in the lateral and medial quadrants, and decreased toward the epiphyses, as well as the posterior and anterior quadrants. The elastic anisotropy ratio in the longitudinal and radial anatomic axes showed the opposite trends. These variations were significantly correlated with the apparent tissue density, as expected. In summary, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology.     

Fracture toughening mechanism of cortical bone: an experimental and numerical approach

In this investigation, the crack propagation mechanisms contributing to the toughness of cortical bone were studied using a combination of experimental and numerical approaches. Compact tension (CT) specimens were prepared from bovine cortical bones to achieve crack propagation in the longitudinal and transverse directions. Stable crack extension experiments were conducted to distinguish the crack growth resistance curves, and virtual multidimensional internal bond (VMIB) modeling was adopted to simulate the fracture responses. Results from experiments indicated that cortical bone exhibited rising resistance curves (R-curves) for crack extension parallel and perpendicular to the bone axis; the transverse fracture toughness was significantly larger, indicating that the fracture properties of cortical bone are substantially anisotropic. Microscopic observations showed that the toughening mechanisms in the longitudinal and transverse directions were different. When the crack grew in the transverse direction, the crack deflected significantly, and crack bifurcations were found at the crack wake, while, in the longitudinal direction, the crack was straight and uncracked ligaments were observed. Numerical simulations also revealed that the fracture resistance in the transverse direction was greater than that in the longitudinal direction.     

兔桡骨临界骨缺损模型的制备

背景：各种原因造成的骨折和骨缺损导致的骨不连一直是临床骨科修复的一大难题,相关产品质量的检验需要标准的骨缺损模型,然而骨缺损的临界长度至今仍无定论。 目的：建立兔桡骨骨缺损模型,以确定兔桡骨临界骨缺损长度。 方法：将18只雄性新西兰大白兔,随机分为6组,在双侧桡骨中段分别做12,13,14,15,16,17 mm的缺损,伤口缝合包扎但不固定。 结果与结论：大体标本和放射学观察显示,3个月内12,13,14,15,16 mm组的缺损均有修复完整的情况,但17 mm组无一例修复。组织学结果显示12,13,14,15,16 mm组缺损修复区有骨小梁与骨基质的形成、骨再生和再血管化、髓腔不同程度再通以及成骨细胞,17 mm组可见成骨细胞,破骨细胞,但未见骨再血管化和髓腔再通。故兔桡骨临界骨缺损长度为17 mm。     

骨组织工程三维复合支架修复兔桡骨骨缺损

背景：前期实验构建的丝素/壳聚糖/纳米羟基磷灰石复合支架具有良好的理化性质。 目的：观察丝素/壳聚糖/纳米羟基磷灰石三维复合支架修复兔桡骨大段骨缺损的效果。 方法：取新西兰大白兔36只,建立右侧桡骨长段骨缺损模型,随机均分为3组,实验组于骨缺损处植入丝素/壳聚糖/纳米羟基磷灰石复合支架,对照组于骨缺损处植入丝素/壳聚糖复合支架,空白对照组造模后不作任何处理。术后4,8,12,16周进行X射线摄片、标本大体观察、组织病理学观察。 结果与结论：术后16周,实验组缺损区X射线影像与正常骨组织无区别,骨髓腔完全再通,有明显的骨组织生成,苏木精-伊红染色可见骨小梁和较多核深染的长梭形骨细胞;对照组X射线骨密度影略低于正常骨组织,部分骨髓腔再通,苏木精-伊红染色可见骨细胞周围有不少软骨细胞,未见明显的骨小梁或骨板结构,排列较紊乱;空白对照组断端骨钙化影同正常骨组织一致,断端各自封闭形成骨不连,苏木精-伊红染色可见较多的纤维组织和少量的类骨组织。表明丝素/壳聚糖/纳米羟基磷灰石三维复合支架可较好地修复兔桡骨大段骨缺损。     

骨水泥固定桡骨远端不稳定性骨折的生物力学研究

目的：研究骨水泥髓腔内充填固定桡骨远端不稳定性骨折的可靠性。方法：用成人桡骨标本8根,先后制成桡骨远端骨折（AO：CI型）克氏针固定模型和骨水泥固定模型,分别在ZWD－10生物力学试验机上纵向加载,测试抗压强度,同时用非接触引伸测量系统收集图像数据,结果：骨水泥且平均抗压强度为克氏针组的27倍,P＜0．01,有显著差异,结论：骨水泥充填固定桡骨远端不稳定性骨折的抗压强度优于克氏针固定。     

Calibration of a constitutive model for the post-yield behaviour of cortical bone

In this work, the post-yield behaviour of cortical bone is investigated using finite element modelling, nanoindentation and atomic force microscopy. Based on recent investigations, it is proposed that, since pressure dependent deformation mechanisms may contribute to yielding in bone, constitutive models attempting to capture its post-yield behaviour should also incorporate pressure dependence. Nanoindentation testing is performed using a spheroconical indenter tip, and subsequent atomic force microscopy at the indented site shows that bone does not exhibit surface pile-up. By simulating the nanoindentation test, it is found that a Mises based constitutive law cannot simultaneously capture the deformations and load–displacement curve produced during nanoindentation. However, an extended Drucker–Prager model can capture the post-yield behaviour of bone accurately, since it accounts for pressure dependent yield. This suggests that frictional mechanisms are central to the post-yield behaviour of bone. In this work, the extended Drucker–Prager model is calibrated and validated using further simulations.     

Static magnetic field effects on bone formation of rats with an ischemic bone model

Effects of a static magnetic field were studied on bone formation using an ischemic rat femur model. Metal rods were prepared from magnetized and unmagnetized samariun cobalt to have tapered structure, both with the same geometrical dimension, and were implanted transcortically into the middle diaphysis of 88 rat femurs. Both sides of the rat femoral artery were ligated to create an ischemic bone model, followed by implantation of the tapered rod to the femur. The bone mineral density (BMD) and weight of the femurs were measured at 1st and 3rd week after implantation.The result at the 3rd week post-implantation revealed that the BMD and weight of the ischemic bone model rats were significantly reduced, compared with that of non-operated femur. It was also found that the magnetized group had significantly higher bone weights than the unmagnetized (p<0.05). The BMD of the rats implanted with the magnetized rods were similar to those of the non-operated (p>0.05). This enhancement of the femoral bone formation of the ischemic rat model by the static magnetic field seems to be due to the improved blood circulation of the femur.     

Cost-analysis of PCR-guided pre-emptive antibiotic treatment of Staphylococcus aureus infections: an analytic decision model

The aim of this study is to examine whether rapid polymerase chain reaction (PCR)-based screening is a cost-efficient tool to optimize pre-emptive antibiotic therapy of methicillin-resistant and methicillin-sensitive Staphylococcus aureus (MRSA and MSSA, respectively) infections. A decision analytic cost model was developed, based on data from the peer-reviewed literature. Sensitivity analyses were undertaken to investigate the impact of variation in the MRSA rate, cost ratio of the cost of inappropriate antibiotic therapy to the cost of appropriate antibiotic therapy, PCR test cost, and total hospital costs per case. At a current MRSA rate of 24.5?% in Germany, PCR-guided treatment regimens are cost-efficient compared to empirical strategies. The costs of alternative treatment strategies differ, on average, up to 1,780 € per case. An empirical MRSA treatment strategy is least costly when the cost ratio is less than 1.06. When the total hospital cost per MRSA case is increased, pre-emptive MSSA treatment with PCR tests achieves the lowest average cost. Early verification and adaptation of an initial pre-emptive antibiotic treatment of S. aureus infections using PCR-based tests are advantageous in Germany and other European countries. PCR tests, accordingly, should be considered as elements in antimicrobial stewardship programs.     

幼龄兔及成年兔桡骨骨缺损模型中骨缺损大小的对比研究

目的 探讨不同月龄新西兰兔建立桡骨骨缺损模型时骨缺损大小的选择。方法 选取3月龄(幼龄兔)及6月龄(成年兔)健康雄性新西兰兔各20只,根据兔龄分为A组(3月龄)和B组(6月龄),每组兔前肢采用数字表法随机分为2亚组制备桡骨骨缺损模型,每组20侧。其中A1组、B1组桡骨骨缺损长度为15 mm,A2组、B2组骨缺损长度为20 mm。分别于模型制备术后第4、8、12周行X线检查,并应用X线Lane-Sandhu评分标准评估骨愈合情况。术后12周处死所有实验动物,取桡骨标本进行大体及组织学观察,分析骨愈合情况。结果 制备骨缺损模型术后,所有实验兔均存活。X线检查显示:术后第8周A1组骨缺损基本愈合,至第12周新生骨塑形完全,与正常桡骨形态类似;其余3组至第12周骨缺损均未完全修复,断端及邻近尺侧有少量新骨生成,髓腔封闭。术后各时间点X线Lane-Sandhu评分结果示:组内比较,A1组评分均高于A2组,差异均有统计学意义(P值均<0.05);B1组与B2组评分比较,差异均无统计学意义(P值均>0.05)。组间缺损尺寸相同的亚组间比较:A1组、A2组评分分别高于B1组、B2组,差异均有统计学意义(P值均<0.05)。术后12周标本大体观察显示:A1组断端形成骨性桥接,新生骨塑形良好,其余3组断端髓腔封闭,缺损区由纤维组织填充。组织学结果示A1组修复完全,新生骨骨板排列规则;其余3组缺损空腔可见纤维组织填充。结论 兔龄和骨缺损大小对于术后骨缺损愈合情况有重要影响,在构建兔桡骨骨缺损模型的动物实验中,幼龄兔(3月龄)骨缺损长度宜选择20 mm,成年兔(6月龄)宜选择15 mm。