Krzysztof Nowicki

Microarchitecture Parameters Describe Bone Structure and Its Strength Better Than BMD

Introduction and Hypothesis. Some papers have shown that bone mineral density (BMD) may not be accurate in predicting fracture risk. Recently microarchitecture parameters have been reported to give information on bone characteristics. The aim of this study was to find out if the values of volume, fractal dimension, and bone mineral density are correlated with bone strength. Methods. Forty-two human bone samples harvested during total hip replacement surgery were cut to cylindrical samples. The geometrical mesh of layers of bone mass obtained from microCT investigation and the volumes of each layer and fractal dimension were calculated. The finite element method was applied to calculate the compression force F causing ε = 0.8% strain. Results. There were stronger correlations for microarchitecture parameters with strength than those for bone mineral density. The values of determination coefficient R 2 for mean volume and force were 0.88 and 0.90 for mean fractal dimension and force, while for BMD and force the value was 0.53. The samples with bigger mean bone volume of layers and bigger mean fractal dimension of layers (more complex structure) presented higher strength. Conclusion. The volumetric and fractal dimension parameters better describe bone structure and strength than BMD.

Study of the behavior of the trabecular bone under cyclic compression with stepwise increasing amplitude

This paper presents the results of a study of 61 trabecular bone samples exposed to a cyclic (1 Hz) compression load. The load was increased stepwise. Characteristic patterns of the hysteresis loop for the middle cycles of successive steps of load and for respective steps of load are presented. Characteristic patterns of secant modulus were also determined. The fatigue life results recorded were compared with the indices of bone architecture determined using micro-CT. Using Pearsons correlation, the best relationship between fatigue life and bone volume ratio (BV/TV) and the maximum load for which there was also reported a maximal value secant stiffness were identified. Based on these findings, it was determined that it is possible to use stepwise increasing load for analysis of the fatigue behavior of trabecular bone.

The Relationship between Trabecular Bone Structure Modeling Methods and the Elastic Modulus as Calculated by FEM

Trabecular bone cores were collected from the femoral head at the time of surgery (hip arthroplasty). Investigated were 42 specimens, from patients with osteoporosis and coxarthrosis. The cores were scanned used computer microtomography (microCT) system at an isotropic spatial resolution of 36 microns. Image stacks were converted to finite element models via a bone voxel-to-element algorithm. The apparent modulus was calculated based on the assumptions that for the elastic properties, E = 10 MPa and ν = 0.3. The compressive deformation as calculated by finite elements (FE) analysis was 0.8%. The models were coarsened to effectively change the resolution or voxel size (from 72 microns to 288 microns or from 72 microns to 1080 microns). The aim of our study is to determine how an increase in the distance between scans changes the elastic properties as calculated by FE models. We tried to find a border value voxel size at which the module values were possible to calculate. As the voxel size increased, the mean voxel volume increased and the FEA-derived apparent modulus decreased. The slope of voxel size versus modulus relationship correlated with several architectural indices of trabecular bone.

Fatigue Energy Dissipation in Trabecular Bone Samples with Stepwise-Increasing Amplitude Loading*

Abstract The research method proposed in the paper assumes multi-level loads of trabecular bone, which are similar to the real ones and demonstrate a step-wise amplitude increase. Throughout the study, such loadings were applied to bone structures sampled from 61 donors. The samples were obtained after hip arthroplasty from the neck fragment of femur heads. All the samples were scanned with a desktop microtomographer. The fatigue damage of the sample structures throughout the experiments was seen in changes in the form of the hysteresis loop recorded in the stress-strain system. The dissipation energy, which is calculated based on the hysteresis loop, is present in the fatigue life function. A three-stage sample fatigue damage pattern was demonstrated. The sum of the dissipation energies was calculated for all the hysteresis loops, and thus we obtain the accumulated dissipation energy, which is referred to as the total fatigue life for all the samples. The calculation results were determined to have an exponential-like curve and reported a high value of the coefficient of determinacy. The accumulated dissipation energy is also related to the value of the compressive stress levels applied. Referring the calculated results of the accumulated energy to the structure index BV/TV, we identified the existence of a strong relationship between the quantities.

Trabecular Bone Microstructural FEM Analysis for Out-Of Plane Resolution Change

The paper presents comparison of two methods of voxel defining for trabecular bone structure modelling. Regular cubic voxels were considered, the size of which changed uniformly in three mutually perpendicular directions depending on the adopted resolution. Also elongated rectangular voxels were proposed, characterized with fixed in-plane resolution and variable length along out-of plane direction. For both types of voxels a number of analyses were performed using finite element method with structures of varied BV/TV values. It was stated that voxel dimension change in out-of plane direction allows for decreasing of a number of scans required for correct reflect of the modelled structure stiffness for the needs of numerical analyses.

Verification of selected hypotheses attempting to explain the effect of fatigue damage build-up in trabecular bones

This paper presents results of verification computations done for selected hypotheses attempting to explain the effect of fatigue damage buildup, performed for loads with gradually increasing amplitude applied to trabecular bone samples. The study tested 42 trabecular bone samples of 10 mm diameter and 8.5 mm height cut out from human femoral heads along the axis of symmetry of the bone’s neck. A value for the damage function D was determined for each sample based on the Palmgren-Miner hypothesis and a non-linear variant of the hypothesis. The two hypotheses were based on a fatigue diagram parameterized in accordance with literature references and on an area exposed to fatigue proposed by the authors: σ-BV/TV-log10Nf. The outcomes are insufficient for making a recommendation on application of fatigue damage buildup hypotheses. Instead, the results suggest that the hypotheses should be used very carefully.

Performance of Bone Modelling Techniques in the Assessment of Bone Fragility

This paper describes the effect of different radiation-reducing methods of bone modelling on the volume of bone models and structural differences between individual models. Careful analysis of data has enabled to determine which of these methods are the best from a structural point of view. The next step is to compare different methods of bone modelling with regard to potential similarities in strength behaviours of bone models.

Accuracy of Analytical-Experimental Method for Determining the Fatigue Characteristics in a Limited Life Region

The study discusses the issue of determining the accuracy of fatigue characteristics in a high-cycle fatigue range using analytical-experimental methods. The analytical-experimental methods are defined as a characteristic curve obtained using an analytical method and additional experiment aimed to increase its accuracy. The higher the amount of data the higher the characteristic curve accuracy. The study aims to address the question “what values should be determined experimentally to obtain an S-N curve in a high-cycle fatigue range with a satisfactory estimation of the fatigue life.

Applying a Stepwise Load for Calculation of the S-N Curve for Trabecular Bone Based on the Linear Hypothesis for Fatigue Damage Accumulation

In this work were presented calculated fatigue curves based on fatigue tests of trabecular bone under stepwise load with the application of a linear hypothesis accumulation of fatigue damage. The investigation was performed on 61 cylindrical bone samples obtained from the neck of different femur heads. The bone sample fatigue tests were carried out under compression with stepwise increases of the applied load. The fatigue calculation assumed the Palmgren-Miner (P-M) linear hypothesis accumulation of fatigue damage and the associated modified formulae. The obtained mean fatigue curves were based on the modified stress σ/E0 (E0 – initial stiffnes) for the assumed rule-determined slope or y-intercept. The highest agreement with the literature was obtained for Σn/N=10.

Method of Determining the Initial Stiffness Modulus for Trabecular Bone under Stepwise Load

In this work was presented method of initial stiffness modulus E0 calculation based on fatigue tests of trabecular bone under stepwise load. The investigation was performed on 61 cylindrical bone samples obtained from the neck of different femur heads. The bone sample fatigue tests were carried out under compression with stepwise increases of the applied load. The obtained values of the initial stiffness modulus E0 were consistent with literature data and can be used to determine the S-N curve for trabecular bone using the hypotheses of fatigue damage accumulation. It was also an unsuccessful attempt to find a statistical relationship between the values of the initial stiffness modulus E0 and indices of bone structure.