A review of morphology–elasticity relationships in human trabecular bone: theories and experiments

Raccoons Reveal Hidden Diversity in Trabecular Bone Development

Trabecular bone, and its ability to rapidly modify its structure in response to strain exerted on skeletal elements, has garnered increased attention from researchers with the advancement of CT technology that allows for the analysis of its complex lattice-like framework. Much of this research has focused on adults of select taxa, but analysis into trabecular development across ontogeny remains limited. In this paper, we explore the shift in several trabecular characteristics in the articular head of the humerus and femur in Procyon lotor across the entirely of the species' lifespan. Our results show that while body mass plays a role in determining trabecular structure, other elements such as bone growth, increased activity, and puberty result in trends not observed in the interspecific analysis of adults. Furthermore, differences in the trabeculae of the humerus and femur suggest combining distinct boney elements in meta-analysis may obfuscate the variety in the structures. Finally, rates at which fore and hindlimb trabeculae orient themselves early in life differ enough to warrant further exploration to identify the currently unknown causes for their variation.

A review of the current status and future prospects of the bone remodeling process: Biological and mathematical perspectives

This review dives into the complex dynamics of bone remodeling, combining biological insights with mathematical perspectives to better understand this fundamental aspect of skeletal health. Bone, being a crucial part of our body, constantly renews itself, and with the growing number of individuals facing bone-related issues, research in this field is vital. In this review, we categorized and classified most common mathematical models used to simulate the mechanical behavior of bone under different loading and health conditions, shedding light on the evolving landscape of bone biology. While current models have effectively captured the essence of healthy bone remodeling, the ever-expanding knowledge in bone biology suggests an update in mathematical methods. Knowing the role of the skeleton in whole-body physiology, and looking at the recent discoveries about activities of bone cells emphasize the urgency of refining our mathematical descriptions of the bone remodeling process. The underexplored impact of bone diseases like osteoporosis, Paget's disease, or breast cancer on bone remodeling also points to the need for intensified research into diverse disease types and their unique effects on bone health. By reviewing a range of bone remodeling models, we show the necessity for tailor-made mathematical models to decipher their roots and enhance patient treatment strategies. Collaboration among scientists from various domains is pivotal to surmount these challenges, ensuring improved accuracy and applicability of mathematical models. Ultimately, this effort aims to deepen our understanding of bone remodeling processes and their broader implications for diverse health conditions.

Trabecular architecture of the distal femur in extant hominids

Extant great apes are characterized by a wide range of locomotor, postural and manipulative behaviours that each require the limbs to be used in different ways. In addition to external bone morphology, comparative investigation of trabecular bone, which (re-)models to reflect loads incurred during life, can provide novel insights into bone functional adaptation. Here, we use canonical holistic morphometric analysis (cHMA) to analyse the trabecular morphology in the distal femoral epiphysis of Homo sapiens (n = 26), Gorilla gorilla (n = 14), Pan troglodytes (n = 15) and Pongo sp. (n = 9). We test two predictions: (1) that differing locomotor behaviours will be reflected in differing trabecular architecture of the distal femur across Homo, Pan, Gorilla and Pongo; (2) that trabecular architecture will significantly differ between male and female Gorilla due to their different levels of arboreality but not between male and female Pan or Homo based on previous studies of locomotor behaviours. Results indicate that trabecular architecture differs among extant great apes based on their locomotor repertoires. The relative bone volume and degree of anisotropy patterns found reflect habitual use of extended knee postures during bipedalism in Homo, and habitual use of flexed knee posture during terrestrial and arboreal locomotion in Pan and Gorilla. Trabecular architecture in Pongo is consistent with a highly mobile knee joint that may vary in posture from extension to full flexion. Within Gorilla, trabecular architecture suggests a different loading of knee in extension/flexion between females and males, but no sex differences were found in Pan or Homo, supporting our predictions. Inter- and intra-specific variation in trabecular architecture of distal femur provides a comparative context to interpret knee postures and, in turn, locomotor behaviours in fossil hominins.

Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

BACKGROUND

Numerous prior studies hypothesized a power-law relationship (E∝ρ^α) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.

METHODS

This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f_min), organic (f_org) and water (f_wat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.

FINDINGS

Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.

INTERPRETATION

This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database "Osteoporotic Virtual Physiological Human Project." To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

Biomechanical properties and clinical significance of cancellous bone in proximal femur: A review

Trabecular bone plays an important role in the load-bearing capacity of the femur. Understanding the structural characteristics, biomechanics, and mechanical conduction of the trabecular bone is of great value in studying the mechanism of fractures and formulating surgical plans. The past decade has witnessed unprecedented progress in imaging, biomechanics and finite element analysis techniques, translating into a better understanding of trabecular bone. This article reviews the research progress achieved over the years regarding femoral trabecular bone, especially on factors influencing the strength of the proximal femoral cancellous bone and cancellous bone microfractures and provides a comprehensive overview of the latest findings on proximal femoral trabecular bone and their clinical significance.

Effect of radiation-induced damage of trabecular bone tissue evaluated using indentation and digital volume correlation

Exposure to X-ray radiation for an extended amount of time can cause damage to the bone tissue and therefore affect its mechanical properties. Specifically, high-resolution X-ray Computed Tomography (XCT), in both synchrotron and lab-based systems, has been employed extensively for evaluating bone micro-to-nano architecture. However, to date, it is still unclear how long exposures to X-ray radiation affect the mechanical properties of trabecular bone, particularly in relation to lab-XCT systems. Indentation has been widely used to identify local mechanical properties such as hardness and elastic modulus of bone and other biological tissues. The purpose of this study is therefore, to use indentation and XCT-based investigative tools such as digital volume correlation (DVC) to assess the microdamage induced by long exposure of trabecular bone tissue to X-ray radiation and how this affects its local mechanical properties. Trabecular bone specimens were indented before and after X-ray exposures of 33 and 66 h, where variation of elastic modulus was evaluated at every stage. The resulting elastic modulus was decreased, and micro-cracks appeared in the specimens after the first long X-ray exposure and crack formation increased after the second exposure. High strain concentration around the damaged tissue exceeding 1% was also observed from DVC analysis. The outcomes of this study show the importance of designing appropriate XCT-based experiments in lab systems to avoid degradation of the bone tissue mechanical properties due to radiation and these results will help to inform future studies that require long X-ray exposure for in situ experiments or generation of reliable subject-specific computational models.

Experimentally characterizing the spatially varying anisotropic mechanical property of cancellous bone via a Bayesian calibration method

Traditional experimental tests for characterizing bone's mechanical properties usually hypothesize a uniaxial stress condition without quantitatively evaluating the influence of spatially varying principal material orientations, which cannot accurately predict the mechanical properties distribution of bones in vivo environment. In this study, a Bayesian calibrating procedure was developed using quantified multiaxial stress to investigate cancellous bone's local anisotropic elastic performance around joints as the spatial variation of main bearing orientations. First, the bone cube specimens from the distal femur of sheep are prepared using traditional anatomical axes. The multiaxial stress state of each bone specimen is calibrated using the actual principal material orientations derived from fabric tensor at different anatomical locations. Based on the calibrated multiaxial stress state, the process of identifying mechanical properties is described as an inverse problem. Then, a Bayesian calibration procedure based on a surrogate constitutive model was developed via multiaxial stress correction to identify the anisotropic material parameters. Finally, a comparison between the experiment and simulation results is discussed by applying the optimal model parameters obtained from the Bayesian probability distribution. Compared to traditional uniaxial methods, our results prove that the calibration based on the spatial variation of the main bearing orientations can significantly improve the accuracy of characterizing regional anisotropic mechanical responses. Moreover, we determine that the actual mechanical property distribution is influenced by complicated mechanical stimulation. This study provides a novel method to evaluate the spatially varying mechanical properties of bone tissues enduring complex mechanical loading accurately and effectively. It is expected to provide more realistic mechanical design targets in vivo for a personalized artificial bone prosthesis in clinical treatment.

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

Predicting the trabecular bone apparent stiffness tensor with spherical convolutional neural networks

The apparent stiffness tensor is relevant for characterizing trabecular bone quality. Previous studies have used morphology-stiffness relationships for estimating the apparent stiffness tensor. In this paper, we propose to train spherical convolutional neural networks (SphCNNs) to estimate this tensor. Information of the edges, trabecular thickness, and spacing are summarized in functions on the unitary sphere used as inputs for the SphCNNs. The concomitant dimensionality reduction makes it possible to train neural networks on relatively small datasets. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (μFE), which was considered as the gold standard, and models based on fourth-order fabric tensors. Combining edges and trabecular thickness yields significant improvements in the accuracy compared to the methods based on fourth-order fabric tensors. From the results, SphCNNs are promising for replacing the more expensive μFE stiffness estimations.

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Characteristic stiffness tensors are derived from trabecular bone micro-CT samples.

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Previous approximation methods fall short on heterogeneous data-sets.

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The gradient, trabecular thickness and spacing are mapped to a spherical domain.

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Spherical convolutional neural networks are used for the prediction.

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The prediction error is significantly reduced compared to the state-of-the-art.

Growth and development of trabecular structure in the calcaneus of Japanese macaques (Macaca fuscata) reflects locomotor behavior, life history, and neuromuscular development

Bone structure dynamically adapts to its mechanical environment throughout ontogeny by altering the structure of trabecular bone, the three-dimensional mesh-like structure found underneath joint surfaces. Trabecular structure, then, can provide a record of variation in loading directions and magnitude; and in ontogenetic samples, it can potentially be used to track developmental shifts in limb posture. We aim to broaden the analysis of trabecular bone ontogeny by incorporating interactions between ontogenetic variation in locomotor repertoire, neuromuscular maturation, and life history. We examine the associations between these variables and age-related variation in trabecular structure in the calcaneus of Japanese macaques (Macaca fuscata). We used high-resolution micro-computed tomography scanning to image the calcaneus in a cross-sectional sample of 34 juvenile M. fuscata aged between 0 and 7 years old at the Primate Research Institute, Japan. We calculated whole bone averages of standard trabecular properties and generated whole-bone morphometric maps of bone volume fraction and Young's modulus. Trabecular structure becomes increasingly heterogeneous in older individuals. Bone volume fraction (BV/total volume [TV]) decreases during the first month of life and increases afterward, coinciding with the onset of independent locomotion in M. fuscata. At birth, primary Young's modulus is oriented orthogonal to the ossification center, but after locomotor onset bone structure becomes stiffest in the direction of joint surfaces and muscle attachments. Age-related variation in bone volume fraction is best predicted by an interaction between the estimated percentage of adult brain size, body mass, and locomotor onset. To explain our findings, we propose a model where interactions between age-related increases in body weight and maturation of the neuromuscular system alter the loading environment of the calcaneus, to which the internal trabecular structure dynamically adapts. This model cannot be directly tested based on our cross-sectional data. However, confirmation of the model by longitudinal experiments and in multiple species would show that trabecular structure can be used both to infer behavior from fossil morphology and serve as a valuable proxy for neuromuscular maturation and life history events like locomotor onset and the achievement of an adult-like gait. This approach could significantly expand our knowledge of the biology and behavior of fossil species.

Limit analysis of human proximal femur

A limit analysis numerical approach oriented to predict the peak/collapse load of human proximal femur, under two different loading conditions, is presented. A yield criterion of Tsai-Hu-type, expressed in principal stress space, is used to model the orthotropic bone tissues. A simplified human femur 3D model is envisaged to carry on numerical simulation of in-vitro tests borrowed from the relevant literature and to reproduce their findings. A critical discussion, together with possible future developments, is presented.

Can DXA image-based deep learning model predict the anisotropic elastic behavior of trabecular bone?

3D image-based finite element (FE) and bone volume fraction (BV/TV)/fabric tensor modeling techniques are currently used to determine the apparent stiffness tensor of trabecular bone for assessing its anisotropic elastic behavior. Inspired by the recent success of deep learning (DL) techniques, we hypothesized that DL modeling techniques could be used to predict the apparent stiffness tensor of trabecular bone directly using dual-energy X-ray absorptiometry (DXA) images. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the apparent stiffness tensor of trabecular bone cubes using their DXA images. Trabecular bone cubes obtained from human cadaver proximal femurs were used to obtain simulated DXA images as input, and the apparent stiffness tensor of the trabecular cubes determined by using micro-CT based FE simulations was used as output (ground truth) to train the DL model. The prediction accuracy of the DL model was evaluated by comparing it with the micro-CT based FE models, histomorphometric parameter based multiple linear regression models, and BV/TV/fabric tensor based multiple linear regression models. The results showed that DXA image-based DL model achieved high fidelity in predicting the apparent stiffness tensor of trabecular bone cubes (R² = 0.905-0.973), comparable to or better than the histomorphometric parameter based multiple linear regression and BV/TV/fabric tensor based multiple linear regression models, thus supporting the hypothesis of this study. The outcome of this study could be used to help develop DXA image-based DL techniques for clinical assessment of bone fracture risk.

Mechanical Properties of Compact Bone Defined by the Stress-Strain Curve Measured Using Uniaxial Tensile Test: A Concise Review and Practical Guide

Mechanical properties are crucial parameters for scaffold design for bone tissue engineering; therefore, it is important to understand the definitions of the mechanical properties of bones and relevant analysis methods, such that tissue engineers can use this information to properly design the mechanical properties of scaffolds for bone tissue engineering. The main purpose of this article is to provide a review and practical guide to understand and analyze the mechanical properties of compact bone that can be defined and extracted from the stress-strain curve measured using uniaxial tensile test until failure. The typical stress-strain curve of compact bone measured using uniaxial tensile test until failure is a bilinear, monotonically increasing curve. The associated mechanical properties can be obtained by analyzing this bilinear stress-strain curve. In this article, a computer programming code for analyzing the bilinear stress-strain curve of compact bone for quantifying the associated mechanical properties is provided, such that the readers can use this computer code to perform the analysis directly. In addition to being applied to compact bone, the information provided by this article can also be applied to quantify the mechanical properties of any material having a bilinear stress-strain curve, such as a whole bone, some metals and biomaterials. The information provided by this article can be applied by tissue engineers, such that they can have a reference to properly design the mechanical properties of scaffolds for bone tissue engineering. The information can also be applied by researchers in biomechanics and orthopedics to compare the mechanical properties of bones in different physiological or pathological conditions.

Identification of effective elastic modulus using modal analysis; application to canine cancellous bone

Mechanical properties of cancellous bone is of increasing interest due to its involvement in aging pathologies and oncology. Characterization of fragile bone tissue is challenging and available methodologies include quasi-static compressive tests of small size specimens, ultrasound and indentation techniques. We hypothesized that modal analysis of flexure beams could be a complementary methodology to obtain Young modulus. The sampling methodology was adapted such that the uniqueness of the linear dynamic response was available to determine the elastic modulus from natural frequencies and mode shapes. In a first step, the methodology was validated using a synthetic bone model as control. Then, water-jet cutting allowed collecting fourteen small beam-like specimens in canine distal femurs. X-ray microtomography confirmed the microarchitecture preservation, the homogeneity and the isotropy at the specimen scale to derive effective properties. The first natural frequency in clamped-free boundary conditions was used to obtain mean values of Young modulus, which ranged from 210 MPa to 280 MPa depending on the specimen collection site. Experimental tests were rapid and reproducible and our preliminary results were in good agreement with literature data. In conclusion, beam modal analysis could be considered for exploring mechanical properties of fragile and scarce biological tissues.

Empirical relationships between bone density and ultimate strength: A literature review

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Neither cortical nor trabecular: An unusual type of bone in the heavy-load-bearing lower pharyngeal jaw of the black drum (Pogonias cromis)

Durophagous fish consume a diet based primarily on hard-shelled animals, mainly mollusks. In order to successfully perform this task, they are equipped with an extra set of jaws located in their throat called pharyngeal jaws. Here we present the results of a study of the structure of the bony material of the exceptionally powerful lower pharyngeal jaws (LPJs) of the black drum Pogonias cromis which generate the highest biting forces documented in bony fishes. In particular, we studied the two long and slender struts that support the entire dental plate and teeth of the LPJ, in order to determine how this structure withstands the huge stresses it encounters repetitively and for long periods of time. We describe the hierarchical structure of the struts of lower pharyngeal jaw of P. cromis at a wide range of length scales, and show how it is adapted to successfully achieve its high mechanical performance. In particular, we show that the bone material of the strut is neither cortical nor cancellous, and although it is highly porous, its complex and layered three-dimensional arrangement of thick lamellae sheets, which are inter-connected by thin plates, is perfectly tailored to withstand extremely large but directionally-consistent forces. STATEMENT OF SIGNIFICANCE: The diet of some fish consists of hard food, like mollusks and shells. In order to accomplish the task of cracking this type of food, they have an extra set of bony jaws located in their throat, called pharyngeal jaws. Here we describe the hierarchical structural elements of these jaws which allow them to withstand huge forces repeatedly over long periods of time. Surprisingly, the structure is very porous, but its architectural design is superbly adapted to handle consistently-oriented forces. This structural motif defines a new bony material which is neither cortical nor cancellous.

Effect of loading frequency on deformations at the bone-implant interface

This study considers the time-dependent behaviour of bone in the context of loosening of metal implants, which is one of the typical complications of joint replacement and fracture-fixation surgeries. We employed viscoelastic properties developed from our previous experimental studies for trabecular bone in a representative bone-implant construct, which was subjected to cyclic loading at varying loading frequencies. We found that the separation between the bone and the implant is a function of loading frequency and increases with number of loading cycles applied. Our analysis shows that at the start of cyclic loading, a higher frequency results in a lower displacement response of bone at the bone-implant interface; however, after the bone-implant system has been subjected to a large number of cycles (>500 cycles in this study), higher interfacial displacements are observed at higher loading frequencies. In other words, higher loading frequencies will not result in bone-implant separation if limited number of cycles are applied. In all cases, interfacial displacements increase as bone volume ratio decreases. This simple approach can be used to evaluate the mechanical environment in bone-implant systems due to cyclic loading which commonly used time-independent models that are unable to simulate. The approach can also be used to evaluate implant loosening due to cyclic loading.

Microstructure-based numerical computational method for the insertion torque of dental implant

The bone quality has a significant effect on the insertion torque of dental implant. In most clinical studies, bone density is used as a gold standard in predicting insertion torque. By contrast, trabecular microstructure is ignored. In this study, a microstructure-based numerical computational method with high accuracy and efficiency for the insertion torque of dental implant was proposed by introducing two microscopic variables, namely, volume fraction and fabric tensor. First, two kinds of 3D microstructural solid models with same volume fraction and fabric tensor were established on the basis of the microstructural topology of six reference specimens. Second, a new numerical simulation method based on homogenous theory was used to explore the material models of these 3D microstructural solid models at the microscopic scale. Then, the anisotropic material models of specimens were developed on the basis of the mixture rule. Thereafter, a numerical simulation based on the anisotropic finite element (FE) model was carried out to acquire the insertion torque. To demonstrate the efficiency and accuracy of the simulation based on the anisotropic FE model, numerical simulations based on isotropic FE model and micro-computer tomography (micro-CT) FE models were also implemented as comparisons. Comparison of the simulated peak insertion torques of the anisotropic, isotropic, and micro-CT FE models with insertion experiments demonstrated the feasibility and potential of the proposed method. The anisotropic FE model reduced the time consumption by 91.85% and enhanced the accuracy by 11.82% compared with the micro-CT and isotropic FE models, respectively.

The risk of loosening of extramedullary fracture fixation devices

Extramedullary devices that use screws, pins or wires are used extensively to treat fractures in normal and diseased bone. A common failure mode is implant loosening at the bone-screw/pin/wire interface before fracture healing occurs. This review first considers the fundamental mechanics of the bone-fixator construct with focus on interfacial strains that result in loosening. It then evaluates the time-independent and time-dependent material models of bone that have been used to simulate and predict loosening. It is shown that the recently developed time-dependent models are capable of predicting loosening due to cyclic loads in bone of varying quality.

Patellar bone strain after total knee arthroplasty is correlated with bone mineral density and body mass index

Patella-related complications after total knee arthroplasty (TKA) remain a major clinical concern. Previous studies have suggested that increased postoperative patellar bone strain could be related to such complications, but there is limited knowledge on patellar strain after TKA. The objective of this study was to predict patellar bone strain after TKA and evaluate correlations with various preoperative data. Fourteen TKA patients with a minimum follow-up of one year were included in this study. Using preoperative CT datasets, preoperative planning, and postoperative X-rays, a method is presented to generate patient-specific finite element models after virtual TKA. Patellar kinematics and forces were predicted during a squat movement, and patellar bone strain was evaluated at 60° of knee flexion. Strain varied greatly among patients, but was strongly negatively correlated (r = -0.85, p < 0.001) with bone mineral density (BMD) and moderately positively (r  = 0.54, p  =  0.05) with body mass index (BMI). The BMI/BMD ratio explained 87% of strain, and should be further investigated as a potential risk factor for clinical complications. This study represents a preliminary step towards the identification of patients at risk of patellar complications after TKA.

Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity

With ageing and various diseases, the vascular pore volume fraction (porosity) in cortical bone increases, and the morphology of the pore network is altered. Cortical bone elasticity is known to decrease with increasing porosity, but the effect of the microstructure is largely unknown, while it has been thoroughly studied for trabecular bone. Also, popular micromechanical models have disregarded several micro-architectural features, idealizing pores as cylinders aligned with the axis of the diaphysis. The aim of this paper is to quantify the relative effects on cortical bone anisotropic elasticity of porosity and other descriptors of the pore network micro-architecture associated with pore number, size and shape. The five stiffness constants of bone assumed to be a transversely isotropic material were measured with resonant ultrasound spectroscopy in 55 specimens from the femoral diaphysis of 29 donors. The pore network, imaged with synchrotron radiation X-ray micro-computed tomography, was used to derive the pore descriptors and to build a homogenization model using the fast Fourier transform (FFT) method. The model was calibrated using experimental elasticity. A detailed analysis of the computed effective elasticity revealed in particular that porosity explains most of the variations of the five stiffness constants and that the effects of other micro-architectural features are small compared to usual experimental errors. We also have evidence that modelling the pore network as an ensemble of cylinders yields biased elasticity values compared to predictions based on the real micro-architecture. The FFT homogenization method is shown to be particularly efficient to model cortical bone.

Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems

Aims

Loosening is a well-known complication in the fixation of fractures using devices such as locking plates or unilateral fixators. It is believed that high strains in the bone at the bone-screw interface can initiate loosening, which can result in infection, and further loosening. Here, we present a new theory of loosening of implants. The time-dependent response of bone subjected to loads results in interfacial deformations in the bone which accumulate with cyclical loading and thus accentuates loosening.

Methods

We used an 'ideal' bone-screw system, in which the screw is subjected to cyclical lateral loads and trabecular bone is modelled as non-linear viscoelastic and non-linear viscoelastic-viscoplastic material, based on recent experiments, which we conducted.

Results

We found that the interfacial deformation in the bone increases with the number of cycles, and the use of a non-linear viscoelastic-viscoplastic model results in larger deformations, some of which are irrecoverable. There is an apparent trend in which interfacial deformations increase with increasing porosity of bone.

Conclusion

The developed time-dependent model of the mechanical behaviour of bone permits prediction of loosening due to cyclical loads, which has not been possible previously. Application of this model shows that implant loosening will be accentuated by cyclical loading due to physiological activities, and the risks of loosening are greater in osteoporotic patients.Cite this article: S. Xie, K. Manda, P. Pankaj. Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems. Bone Joint Res 2018;7:580-586. DOI: 10.1302/2046-3758.710.BJR-2018-0085.R1.

Trabecular bone patterning across the human hand

Hand bone morphology is regularly used to link particular hominin species with behaviors relevant to cognitive/technological progress. Debates about the functional significance of differing hominin hand bone morphologies tend to rely on establishing phylogenetic relationships and/or inferring behavior from epigenetic variation arising from mechanical loading and adaptive bone modeling. Most research focuses on variation in cortical bone structure, but additional information about hand function may be provided through the analysis of internal trabecular structure. While primate hand bone trabecular structure is known to vary in ways that are consistent with expected joint loading differences during manipulation and locomotion, no study exists that has documented this variation across the numerous bones of the hand. We quantify the trabecular structure in 22 bones of the human hand (early/extant modern Homo sapiens) and compare structural variation between two groups associated with post-agricultural/industrial (post-Neolithic) and foraging/hunter-gatherer (forager) subsistence strategies. We (1) establish trabecular bone volume fraction (BV/TV), modulus (E), degree of anisotropy (DA), mean trabecular thickness (Tb.Th) and spacing (Tb.Sp); (2) visualize the average distribution of site-specific BV/TV for each bone; and (3) examine if the variation in trabecular structure is consistent with expected joint loading differences among the regions of the hand and between the groups. Results indicate similar distributions of trabecular bone in both groups, with those of the forager sample presenting higher BV/TV, E, and lower DA, suggesting greater and more variable loading during manipulation. We find indications of higher loading along the ulnar side of the forager sample hand, with high site-specific BV/TV distributions among the carpals that are suggestive of high loading while the wrist moves through the 'dart-thrower's' motion. These results support the use of trabecular structure to infer behavior and have direct implications for refining our understanding of human hand evolution and fossil hominin hand use.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone

Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.

From Tension to Compression: Asymmetric Mechanical Behaviour of Trabecular Bone's Organic Phase

Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases with their content ratio known to change with age. Therefore, the contribution of bone constituents on bone's mechanical behaviour, in tension and compression, at varying load levels and with changing porosity (which increases with age) is of great interest, but remains unknown. We investigated the mechanical response of demineralised bone by subjecting a set of bone samples to fully reversed cyclic tension-compression loads with varying magnitudes. We show that the tension to compression response of the organic phase of trabecular bone is asymmetric; it stiffens in tension and undergoes stiffness reduction in compression. Our results indicate that demineralised trabecular bone struts experience inelastic buckling under compression which causes irreversible damage, while irreversible strains due to microcracking are less visible in tension. We also identified that the values of this asymmetric mechanical response is associated to the original bone volume ratio (BV/TV).

Setting Directions: Anisotropy in Hierarchically Organized Porous Silica

Structural hierarchy, porosity, and isotropy/anisotropy are highly relevant factors for mechanical properties and thereby the functionality of porous materials. However, even though anisotropic and hierarchically organized, porous materials are well known in nature, such as bone or wood, producing the synthetic counterparts in the laboratory is difficult. We report for the first time a straightforward combination of sol-gel processing and shear-induced alignment to create hierarchical silica monoliths exhibiting anisotropy on the levels of both, meso- and macropores. The resulting material consists of an anisotropic macroporous network of struts comprising 2D hexagonally organized cylindrical mesopores. While the anisotropy of the mesopores is an inherent feature of the pores formed by liquid crystal templating, the anisotropy of the macropores is induced by shearing of the network. Scanning electron microscopy and small-angle X-ray scattering show that the majority of network forming struts is oriented towards the shearing direction; a quantitative analysis of scattering data confirms that roughly 40% of the strut volume exhibits a preferred orientation. The anisotropy of the material's macroporosity is also reflected in its mechanical properties; i.e., the Young's modulus differs by nearly a factor of 2 between the directions of shear application and perpendicular to it. Unexpectedly, the adsorption-induced strain of the material exhibits little to no anisotropy.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

μCT-based trabecular anisotropy can be reproducibly computed from HR-pQCT scans using the triangulated bone surface

The trabecular structure can be assessed at the wrist or tibia via high-resolution peripheral quantitative computed tomography (HR-pQCT). Yet on this modality, the performance of the existing methods, evaluating trabecular anisotropy is usually overlooked, especially in terms of reproducibility. We thus proposed to compare the TRI routine used by SCANCO Medical AG (Brüttisellen, Switzerland), the classical mean intercept length (MIL), and the grey-level structure tensor (GST) to the mean surface length (MSL), a new method for evaluating a second-order fabric tensor based on the triangulation of the bone surface. The distal radius of 24 fresh-frozen human forearms was scanned three times via HR-pQCT protocols (61μm, 82μm nominal voxel size), dissected, and imaged via micro computed tomography (μCT) at 16μm nominal voxel size. After registering the scans, we compared for each resolution the fabric tensors, determined by the mentioned techniques for 182 trabecular regions of interest. We then evaluated the reproducibility of the fabric information measured by HR-pQCT via precision errors. On μCT, TRI and GST were respectively the best and worst surrogates for MIL_μCT (MIL computed on μCT) in terms of eigenvalues and main direction of anisotropy. On HR-pQCT, however, MSL provided the best approximation of MIL_μCT. Surprisingly, surface-based approaches (TRI, MSL) also proved to be more precise than both MIL and GST. Our findings confirm that MSL can reproducibly estimate MIL_μCT, the current gold standard. MSL thus enables the direct mapping of the fabric-dependent material properties required in homogenised HR-pQCT-based finite element models.

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

Trabecular architecture in the thumb of Pan and Homo: implications for investigating hand use, loading, and hand preference in the fossil record

OBJECTIVES

Humans display an 85-95% cross-cultural right-hand bias in skilled tasks, which is considered a derived behavior because such a high frequency is not reported in wild non-human primates. Handedness is generally considered to be an evolutionary byproduct of selection for manual dexterity and augmented visuo-cognitive capabilities within the context of complex stone tool manufacture/use. Testing this hypothesis requires an understanding of when appreciable levels of right dominant behavior entered the fossil record. Because bone remodels in vivo, skeletal asymmetries are thought to reflect greater mechanical loading on the dominant side, but incomplete preservation of external morphology and ambiguities about past loading environments complicate interpretations. We test if internal trabecular bone is capable of providing additional information by analyzing the thumb of Homo sapiens and Pan.

MATERIALS AND METHODS

We assess trabecular structure at the distal head and proximal base of paired (left/right) first metacarpals using micro-CT scans of Homo sapiens (n = 14) and Pan (n = 9). Throughout each epiphysis we quantify average and local bone volume fraction (BV/TV), degree of anisotropy (DA), and elastic modulus (E) to address bone volume patterning and directional asymmetry.

RESULTS

We find a right directional asymmetry in H. sapiens consistent with population-level handedness, but also report a left directional asymmetry in Pan that may be the result of postural and/or locomotor loading.

CONCLUSION

We conclude that trabecular bone is capable of detecting right/left directional asymmetry, but suggest coupling studies of internal structure with analyses of other skeletal elements and cortical bone prior to applications in the fossil record.

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{n}\,{=}\,13$$\end{document}n=13) at loads corresponding to physiological strain level of 2000 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu }{\upvarepsilon }$$\end{document}με. We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r^2\,{=}\,0.73,\ p\,{<}\,0.001$$\end{document}r2=0.73,p<0.001) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.

On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution

Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.

A patient-specific model of total knee arthroplasty to estimate patellar strain: A case study

BACKGROUND

Inappropriate patellar cut during total knee arthroplasty can lead to patellar complications due to increased bone strain. In this study, we evaluated patellar bone strain of a patient who had a deeper patellar cut than the recommended.

METHODS

A patient-specific model based on patient preoperative data was created. The model was decoupled into two levels: knee and patella. The knee model predicted kinematics and forces on the patella during squat movement. The patella model used these values to predict bone strain after total knee arthroplasty. Mechanical properties of the patellar bone were identified with micro-finite element modeling testing of cadaveric samples. The model was validated with a robotic knee simulator and postoperative X-rays. For this patient, we compared the deeper patellar cut depth to the recommended one, and evaluated patellar bone volume with octahedral shear strain above 1%.

FINDINGS

Model predictions were consistent with experimental measurements of the robotic knee simulator and postoperative X-rays. Compared to the recommended cut, the deeper cut increased the critical strain bone volume, but by less than 3% of total patellar volume.

INTERPRETATION

We thus conclude that the predicted increase in patellar strain should be within an acceptable range, since this patient had no complaints 8 months after surgery. This validated patient-specific model will later be used to address other questions on groups of patients, to eventually improve surgical planning and outcome of total knee arthroplasty.

Comparison of mixed and kinematic uniform boundary conditions in homogenized elasticity of femoral trabecular bone using microfinite element analyses

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (lFE) analysis allows computing the apparent elastic properties of trabecular bone for use in homogenized FE (hFE) analysis,but the results depend unfortunately on the type of applied boundary conditions(BCs). In this study, 167 human femoral trabecular cubic regions with a side length of 5.3mm were extracted from three proximal femora and analyzed using lFE analysis to compare systematically their stiffness with kinematic uniform BCs (KUBCs) and periodicity-compatible mixed uniform BCs (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset–Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length (MIL). Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset–Curnier model fitted the apparent elastic constants successfully in both cases with adjusted coefficients of determination (r2adj) of 0.986 for KUBCs and 0.975 for PMUBCs. The proper use of these BCs for hFE analysis of whole bones will need to be investigated in future work.

Quantitative description of collagen fibre network on trabecular bone surfaces based on AFM imaging

The collagen fibre network is an important part of extracellular matrix (ECM) on trabecular bone surface. The geometry features of the network can provide us insights into its physical and physiological properties. However, previous researches have not focused on the geometry and the quantitative description of the collagen fibre network on trabecular bone surface. In this study,we developed a procedure to quantitatively describe the network and verified the validity of the procedure. The experiment proceeds as follow. Atomic force microscopy (AFM) was used to acquire submicron resolution images of the trabecular surface. Then, an image analysing procedure was built to extract important parameters, including, fibre orientation, fibre density, fibre width, fibre crossing numbers, the number of holes formed by fibre s, and the area of holes from AFM images. In order to verify the validity of the parameters extracted by image analysing methods, we adopted two other methods, which are statistical geometry model and computer simulation, to calculate those same parameters and check the consistency of the three methods' results. Statistical tests indicate that there is no significant difference between three groups. We conclude that, (a) the ECM on trabecular surface mainly consists of random collagen fibre network with oriented fibres; (b) our method based on image analysing can be used to characterize quantitative geometry features of the collagen fibre network effectively. This method may provide a basis for quantitative investigating the architecture and function of collagen fibre network.