Age- and direction-related adaptations of lumbar vertebral trabecular bone with respect to apparent stiffness and tissue level stress distribution

The objective of this study was to study the age-related adaptation of lumbar vertebral trabecular bone at the apparent level, as well as the tissue level in three orthogonal directions. Ninety trabecular specimens were obtained from six normal L4 vertebral bodies of six male cadavers in two age groups, three aged 62 years and three aged 69 years, and were scanned using a high-resolution micro-computed tomography （micro-CT） system, then converted to micro- finite element models to do micro-finite element analyses. The relationship between apparent stiffness and bone volume fraction, and the tissue level yon Mises stress distribution for each trabecular specimen when compressed separately in the longitudinal direction, medial-lateral and anterior-posterior directions （transverse directions） were derived and compared between two age groups. The results showed that at the apparent level, trabecular bones from 69-year group had stiffer bone structure relative to their volume fractions in all three directions, and in both age groups, changes in bone volume fraction could explain more variations in apparent stiffness in the longitudinal direction than the transverse directions; at the tissue level, aging had little effect on the tissue von Mises stress distributions for the compressions in all the three directions. The novelty of the present study was that it provided quantitative assessments on the age and direction- related adaptation of Chinese male lumbar vertebral trabecular bone from two different levels： stiffness at the apparent level and stress distribution at the tissue level. It may help to understand the failure mechanisms and fracture risks of vertebral body associated with aging and direction for the prevention of fracture risks in elder individuals.     

Optimal internal architectures of femoral bone based on relaxation by homogenization and isotropic material design

The influence of the loading conditions on the trabecular architecture of a femur is investigated by using topology optimization methods. The response of the bone to physiological loads results in changes of the internal architecture of bone, reflected by a modification of internal effective density and mechanical properties. The homogenization based optimization model is developed for predicting optimal bone density distribution, wherein bone tissue is assumed to be a composite material consisting of a mixture of material and void. The homogenization scheme treats the geometric parameters of the microstructures and their orientation as design variables and homogenizes the properties in that microstructure, which is generally anisotropic. The penalization of the optimal material density then leads to a classical optimal structure which consists of regions with bone material and regions without bone material. The IMD (Isotropic Material Design) approach is next applied to determine the optimal elasticity tensor in terms of the bulk and shear moduli for the present loading applied to the femoral bone sample. IMD is able to provide both the external shape and topology together with the optimal layout of the isotropic moduli. Both topology optimization methods appear to be complementary. Simulations of the internal bone architecture of the human proximal femur results in a density distribution pattern with good consistency with that of the real bone.     

Tissue level microstructure and mechanical properties of the femoral head in the proximal femur of fracture patients

This study aims to investigate the regional variations of trabecular morphological parameters and mechanical parameters of the femoral head,as well as to determine the relationship between trabecular morphological and mechanical parameters.Seven femoral heads from patients with fractured proximal femur were scanned using a micro-CT system.Each femoral head was divided into 12 sub-regions according to the trabecular orientation.One 125 mm~3 trabecular cubic model was reconstructed from each sub-region.A total of 81 trabecular models were reconstructed,except three destroyed sub-regions from two femoral heads during the surgery.Trabecular morphological parameters,i.e.trabecular separation(Tb.Sp),trabecular thickness(Tb.Th),specific bone surface(BS/B V),bone volume fraction(BV/TV),structural model index(SMI),and degree of anisotropy(DA) were measured.Micro-finite element analyses were performed for each cube to obtain the apparent Young's modulus and tissue level von Mises stress distribution under 1%compressive strain along three orthogonal directions,respectively.Results revealed significant regional variations in the morphological parameters(P0.05).Young's moduli along the trabecular orientation were significantly higher than those along the other two directions.In general,trabecular mechanical properties in the medial region were lower than those in the lateral region.Trabecular mechanical parameters along the trabecular orientation were significantly correlated with BS/BV,BV/TV,Tb.Th,and DA.In this study,regional variations of microstructural features and mechanical properties in the femoral head of patients with proximal femur fracture were thoroughly investigated at the tissue level.The results of this study will help to elucidate the mechanism of femoral head fracture for reducing fracture risk and developing treatment strategies for the elderly.     

A fully anisotropic hierarchical hybrid cellular automaton algorithm to simulate bone remodeling

Computational models of the bone remodeling process have been utilized to further our understanding of the adaptation of bone architecture to changes in its mechanical environment. The hierarchical hybrid cellular automata (HHCA) algorithm is a multi-scale approach for the simulation of the adaptation of bone. Currently, this remodeling algorithm utilizes the apparent material properties of the trabecular architecture. The objective of this work is to increase the fidelity of the HHCA algorithm by incorporating the local anisotropic properties of these structures. Preliminary analyses display improved efficiency and a more consistent material distribution when incorporating anisotropic properties into the HHCA methodology.     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.     

Effect of Compressive Straining on Nanoindentation Elastic Modulus of Trabecular Bone

Trabecular bone with its porous structure is an important compressive load bearing member. Different structural factors such as porosity, non-homogeneous deformation, varying trabeculae thickness, connectivity, and nanoscale (10 nm to 1 μm) to macroscale (~0.1 mm to 10 mm) composition hierarchy determine the failure properties of trabecular bone. While the above factors have important bearing on bone properties, an understanding of how the local nanoscale properties change at different macroscale compressive strain levels can be important to develop an understanding of how bone fails. In the present work, such analyses are performed on bovine femoral trabecular bone samples derived from a single animal. Analyses focus on measuring nanoindentation elastic moduli at three distinct levels of compressive strains in the bone samples: (1) when the samples are not loaded; (2) after the samples have been loaded to a strain level just before apparent yielding and the macroscale compression test is stopped; and (3) after the samples have been compressed to a strain level after apparent yielding and the macroscale compression test is stopped. Nanoindentation elastic modulus values are two orders of magnitude higher than the macroscale compressive elastic modulus values of all samples. A high variability in macroscale compressive elastic modulus values is observed because of porous architecture and small sample size. Nanoindentation elastic modulus values show a progressive reduction with increase in the extent of macroscale compressive deformation. Apparent yielding has a significant effect on this trend. The decrease in nanoindentation modulus value for all samples accelerates from approximately 20% before yielding to approximately 60% after yielding in comparison to the nanoindentation modulus values at 0% strain level. The level of variation in the predicted nanoindentation modulus values is the lowest for uncompressed samples (~16–18%). However, with increase in the extent of compression, the level of variation increases. It varied between 50% and 90% for the samples tested after yielding showing a widespread heterogeneity in local nanoscale structural order after apparent yielding. Scanning electron microscope (SEM) observations suggest that apparent yielding significantly destroys local nanoscale structural order. However, quantitative results suggest that a significant residual nanoscale stiffness varying from 5 GPa to 8 GPa among different samples still remains for possible repair facilitation.     

Equivalent Fracture Network Permeability of Multilayer-Complex Naturally Fractured Reservoirs

Modeling naturally fractured reservoirs (NFRs) requires an accurate representation of fracture network permeability (FNP). Conventionally, logs, cores, seismic, and pressure transient tests are used as a data base for this. Our previous attempts showed that a strong correlation exists between the fractal parameters of 2-D fracture networks and their permeability (Jafari and Babadagli, SPE 113618, Western Regional and Pacific Section AAPG joint meeting, 2008; Jafari and Babadagli, SPE Reserv Eval Eng 12(3):455–469, 2009a). We also showed that 1-D well (cores-logs) and 3-D reservoir data (well test) may not be sufficient in FNP mapping and that 2-D (outcrop) characteristics are needed (Jafari and Babadagli, SPE 124077, SPE/EAGE reservoir characterization and simulation conference, 2009b). This paper is an extension of those studies, where only 2-D (single-layer, uniform fracture characteristics in z direction) representations were used. In this paper, we considered a more complex and realistic 3-D network system. Two-dimensional random fractures with known fractal and statistical characteristics were distributed in the x- and y directions. A variation of fracture network characteristics in the z direction was presented by a multilayer system representing three different facieses with different fracture properties. Wells were placed in different locations of the model to collect 1-D fracture density and pressure transient data. In addition, five different fractal and statistical properties of the network of each layer were measured. The equivalent FNP was calculated using a commercial software package as the base case. Using available 1-D, 2-D, and 3-D data, multivariable regression analyses were performed to obtain equivalent FNP correlations for many different fracture network realizations. The derived equations were validated against a new set of synthetic fracture networks, and the conditions at which 1-D, 2-D and 3-D data are sufficient to map FNP were determined. The importance of the inclusion of each data type, i.e., 1-D, 2-D and 3-D, in the correlations was discussed. It was shown that using only 3-D data are insufficient to predict the FNP due to wide spatial heterogeneity of the fracture properties in the reservoir, which cannot be captured from single-well tests. Incorporating all types of data (1-D, 2-D, and 3-D) would result in better prediction. Also, it is recommended that the 2-D data of the most conductive layer in reservoir, which has longer fractures with a higher density, should be incorporated in the correlations.     

Fluid Flow Analysis of Integrated Porous Bone Scaffold and Cancellous Bone at Different Skeletal Sites: In Silico Study

The dynamic characteristic of bone is its ability to remodel itself through mechanobiological responses. Bone regeneration is triggered by mechanical cues from physiological activities that generate structural strain and cause bone marrow movement. This phenomenon is crucial for bone scaffold when implanted in the cancellous bone as host tissue. Often, the fluid movement of bone scaffold and cancellous bone is studied separately, which does not represent the actual environment once implanted. In the present study, the fluid flow analysis properties of bone scaffold integrated into the cancellous bone at different skeletal sites are investigated. Three types of porous bone scaffolds categorized based on pore size configurations: 1 mm, 0.8 mm and hybrid (0.8 mm interlaced with 0.5 mm) were used. Three different skeletal sites of femoral bone were selected: neck, lateral condyle and medial condyle. Computational fluid dynamics was utilized to analyze the fluid flow properties of bone scaffold integrated cancellous bone. The results of this study reveal that the localization and maximum value of shear stress in an independent bone scaffold are significantly different compared to the bone scaffold integrated with cancellous bone by about 160% to 448% percentage difference. Low shear stress and high permeability were found across models that have higher Tb.Sp (trabecular separation). Specimen C and femoral lateral condyle showed the highest permeability in their respective category.

     

THE EFFECTS OF COD BONE GELATIN ON TRABECULAR MICROSTRUCTURE AND MECHANICAL PROPERTIES OF CANCELLOUS BONE

Osteoporosis is a common clinical complication of post-menopausal women and the elderly and can significantly complicate the severity of bone fragility. The purpose of this study is to investigate how cod bone gelatin administration influences trabecular biomechanical properties after ovariectomy. Both biomechanical properties and trabecular microarchitectures were evaluated for cancellous bone samples from female ovariectomized rats, which were either shamoperated or treated with marine peptide(0.75, 1.5, 3.0, 6.0 g/kg body weight) for 90 days. The results have confirmed that cod bone gelatin treatment is effective in the prevention of mechanical property loss by preserving bone mass and trabecular architecture.     

Identification of a constitutive law for trabecular bone samples under remodeling in the framework of irreversible thermodynamics

We construct in the present paper constitutive models for bone remodeling based on micromechanical analyses at the scale of a representative unit cell (RUC) including a porous trabecular microstructure. The time evolution of the microstructure is simulated as a surface remodeling process by relating the surface growth remodeling velocity to a surface driving force incorporating a (surface) Eshelby tensor. Adopting the framework of irreversible thermodynamics, a 2D constitutive model based on the setting up of the free energy density and a dissipation potential is identified from FE simulations performed over a unit cell representative of the trabecular architecture obtained from real bone microstructures. The static and evolutive effective properties of bone at the scale of the RUC are obtained by combining a methodology for the evaluation of the average kinematic and static variables over a prototype unit cell and numerical simulations with controlled imposed first gradient rates. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae within the RUC is of viscoplastic type and relates the average growth strain rate to the homogenized stress tensor. The postulated model includes a power law function of an effective stress chosen to depend on the first and second stress invariants. The model coefficients are calibrated from a set of virtual testing performed over the RUC subjected to a sequence of loadings. Numerical simulations show that overall bone growth does not show any growth kinematic hardening. The obtained results quantify the strength and importance of different types of external loads (uniaxial tension, simple shear, and biaxial loading) on the overall remodeling process and the development of elastic deformations within the RUC.     

二氧化碳在砂岩透镜体中充注封存的盖层岩石抗断裂性能分析

把CO2这一主要的温室气体注入到地下深处具有适当封闭条件的地层中进行封存和隔离,已被公认为是有效减少CO2排放量的一种比较安全的技术途径。砂岩透镜体油气藏具有良好的圈闭构造和储层物性,油气濒临枯竭的砂岩透镜体是较理想的CO2地质封存箱。基于币形裂纹模型和水力致裂原理,将纵向厚度和横向展布长度均远小于盖层岩石尺度的水平产状砂岩透镜体简化为盖层岩石中的I型币形裂纹,从岩石断裂力学角度分析封存箱盖层岩石的抗断裂性能。采用叠加原理给出了盖层岩石币形裂纹尖端（砂岩透镜体尖灭部位）应力强度因子的计算公式,在此基础上提出了断裂力学判别准则（K=KIC）和临界有效压应力判别准则（P=PC）,从岩石断裂力学角度为砂岩透镜体封存箱盖层岩石抗断裂性能分析和评价提供了一种新的研究思路。     

A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus

A bone cell population dynamics model for cortical bone remodeling under mechanical stimulus is developed in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these experimental results such as the increase percentage of final values of bone mineral content (BMC) and bone fracture energy (BFE) among different loading schemes (which proves the validity of the model), but also predict the realtime development pattern of BMC and BFE, as well as the dynamics of osteoblasts (OBA), osteoclasts (OCA), nitric oxide (NO) and prostaglandin E₂ (PGE₂) for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an insight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechanical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foundation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimulus can be investigated. The to-be identified control mechanism will help to develop effective drugs and combined nonpharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering.     

Numerical simulation on the adaptation of forms in trabecular bone to mechanical disuse and basic multi-cellular unit activation threshold at menopause

The objective of this paper is to identify the effects of mechanical disuse and basic multi-cellular unit （BMU） activation threshold on the form of trabecular bone during menopause. A bone adaptation model with mechanical- biological factors at BMU level was integrated with finite element analysis to simulate the changes of trabecular bone structure during menopause. Mechanical disuse and changes in the BMU activation threshold were applied to the model for the period from 4 years before to 4 years after menopause. The changes in bone volume fraction, trabecular thickness and fractal dimension of the trabecular structures were used to quantify the changes of trabecular bone in three different cases associated with mechanical disuse and BMU activation threshold. It was found that the changes in the simulated bone volume fraction were highly correlated and consistent with clinical data, and that the trabecular thickness reduced signi-ficantly during menopause and was highly linearly correlated with the bone volume fraction, and that the change trend of fractal dimension of the simulated trabecular structure was in correspondence with clinical observations. The numerical simulation in this paper may help to better understand the relationship between the bone morphology and the mecha-nical, as well as biological environment; and can provide a quantitative computational model and methodology for the numerical simulation of the bone structural morphological changes caused by the mechanical environment, and/or the biological environment.     

Aging in the cortical bone: a constitutive law and its application

It is well known that the material behavior of human cortical bone changes from ductile to more brittle due to aging. This process is accompanied by a decrease of the maximum specific deformation energy. Numerous mechanical tests of specimens have shown a relationship between the mechanical behavior, age and microstructure, especially the porosity, mineralization and fraction of the secondary osteonal area. But up to now, this relationship is not explicitly considered in a constitutive law. Measured stress–strain curves, taken from the literature, from one-dimensional mechanical experiments in tension (McCalden et al. in J Bone Joint Surg Am 75(8):1193–1205, 1993) have been characterized by Young’s modulus, elastic, plastic and fracture energy, fracture stress and strain. The specimens have been harvested from the femora of 46 deceased individuals. Based on this data, we set up a system of equations taking into account the microstructure of the bone material by analogy to common procedures in fracture and damage mechanics. Solving this system for all measured experimental data leads to the determination of the independent damage parameters for each individual person. It turned out that some characteristic mechanical values and one independent damage parameter are statistically significant dependent on age and microstructure. We receive a constitutive law, which describes the mechanical behavior up to fracture by measurable parameters for the microstructure and the individual age and gender only. In turn, we calculate the individual tolerable load for bending, using a nonlinear stress–strain curve, and postulate an age-dependent fracture load for healthy bone by means of the statistical regression. Deviation from the standard is an indication for a bone disease in particular for osteoporosis.     

松质骨弹性模量计算的均匀化方法

对松质骨建立了六种单胞微观结构模型，采用均匀化方法和有限元方法计算松质骨的宏观等效弹性模量。给出了六种单胞模型的松质骨弹性模量与材料密度(体分比）的关系，与实验数据进行了对比，分析了不同微观结构模型在不同骨骼中的应用。结果表明，本文方法及六种单胞模型可以对松质骨微观结构和材料性能进行有效的模拟计算。同时本文又着重对松质骨的宏观等效弹性模量与体分比的指数关系进行了探讨。     

Influence of Storage Duration on Retention of Original Fracture Toughness

Accurate knowledge of bone properties is central in the prediction of failure and the development of injury treatment protocols. Often when bone properties are measured experimentally, bone specimens have to be chemically preserved prior to or during testing. Understanding the effect of the bone preservation method on the material properties is important. Degradation of properties due to preservation methods may lead to incorrect reporting of values of the bone properties. A salient question is, therefore, whether the preservation of bovine cortical bone in ethanol for extended periods of time affects fracture toughness; and if so, whether that affect is reversible. To answer these questions, a three-point bending test set-up was constructed to perform experiments over a period of 9 weeks. A total of 109 specimens of cortical bone of the same orientation were manufactured from the mid-diaphysis of the femur. These specimens were separated into three groups based on location in the femur; namely, medial, lateral, and posterior. The specimens were preserved in ethanol. At the end of each week, a sample of specimens was selected for testing, with the last sample tested after 9 weeks of preservation. It was shown that after 9 weeks of preservation in ethanol, followed by rehydration with physiological saline, the fracture toughness of the specimen was unchanged from that of the control specimen. Omission of rehydration in saline resulted in to an increased fracture toughness of up to 17%.     

Evaluation of X-ray sources for quantitative two- and three-dimensional imaging of liquid mass distribution in atomizing sprays

Quantitative measurement of liquid mass distribution is demonstrated in an impinging-jet atomizing spray using a broadband, ∼80 keV X-ray tube source for 2-D radiography and 3-D computed tomography (CT). The accuracy, precision, and sensitivity of these data are evaluated using narrowband, ∼10 keV, synchrotron radiation from the Argonne National Laboratory Advanced Photon Source (APS) at the same flow conditions. It is found that the broadband X-ray tube source can be used for 2-D measurement of the equivalent path length (EPL) and 3-D CT imaging of liquid mass distribution with typical error of 5–10%. Data are compared for cases with and without the use of potassium iodide (KI), which at 15% concentration by mass increases the attenuation coefficient eightfold and enables 2-D and 3-D measurement of EPL with a signal-to-noise ratio (SNR) of 5:1 down to 15 μm. At this concentration, the effects of energy-dependent attenuation (i.e., spectral beam hardening) are negligible for EPL up to 5 mm. Hence, the use of broadband X-ray tube sources is feasible for many practical engineering sprays with a dynamic range in EPL of ∼330:1. The advantages and limitations of using broadband and narrowband X-ray sources are discussed, and recommendations for improving performance are presented.     

A stochastic homogenization approach to estimate bone elastic properties

The mechanical properties of bone tissue depend on its hierarchical structure spanning many length scales, from the organ down to the nanoscale. Multiscale models allow estimating bone mechanical properties at the macroscale based on information on bone organization and composition at the lower scales. However, the reliability of these estimates can be questioned in view of the many uncertainties affecting the information which they are based on. In this paper, a new methodology is proposed, coupling probabilistic modeling and micromechanical homogenization to estimate the material properties of bone while taking into account the uncertainties on the bone micro- and nanostructure. Elastic coefficients of bone solid matrix are computed using a three-scale micromechanical homogenization method. A probabilistic model of the uncertain parameters allows propagating the uncertainties affecting their actual values into the estimated material properties of bone. The probability density functions of the random variables are constructed using the Maximum Entropy principle. Numerical simulations are used to show the relevance of this approach.     

Microstructures and properties of cancellous bone of avascular necrosis of femoral heads

The aim of this study is to investigate microscopic structure and characterize cancellous bone of avascular necrosis of the femoral head （ANFH）. The rabbit model of the ANFH is established. The histopathologic features are studied successfully. The differences between the steroidinjection group （S.G.） and the controlled group （C.G.） are examined, including the weight of rabbits, the hematological examination and the three-dimensional stnactures. It is found that the plasma levels of cholesterol （CHO）, high-density lipoprotein （HDL） and low-density lipoprotein （LDL） in S.G. are lower than those in C.G. when the triglyceride （TG） increased in the S.G.; but the bone mineral content （BMC） and the structural model index （SMI） of the organ and tissue decreased significantly in S.G. Three-dimensional structures of the femoral head are obtained using micro-computed tomography （CT） scanning and the mechanical model is established to analyze the influences of these structural changes on the mechanical properties of the cancellous bone.     

Synthesis and surface modification of nanophosphorous-based flame retardant agent by continuous flow hydrothermal synthesis

Nanoparticles can provide flame retardance to hosting polymers and act as nano fire extinguishers. Hydroxyapatite (Ca₅(OH)(PO₄)₃) (HA) is not hygroscopic, and is thermally stable up to 800 °C, with 18.5 wt% phosphorous content. It is this high phosphorous content that can provide HA with flame retardant properties. In this paper, we report on the continuous synthesis of ultrafine HA using a hydrothermal synthesis technique. The HA surface properties were changed from hydrophilic to hydrophobic by post-synthesis surface modification. The ratio of the HA nanoparticles and an intumescent agent known as Exolit AP750 was investigated to yield a self-extinguishing multi-component epoxy nanocomposite for extended application under extreme fire conditions. The HA/AP750/epoxy nanocomposite was able to resist a flame at 1700 °C and self-extinguish after the flame had been removed. The nanocomposite showed an enhanced flammability performance in standard cone calorimetry testing and formed a compact and cohesive protective char layer with a 50% decrease in peak heat released compared with virgin epoxy. Our aim was to establish the use of HA as an effective nanofiller with phosphorous-based flame retardant properties. The surface of this nano fire extinguisher was modified effectively with different surfactants for enhanced compatibility with different polymeric matrices.