Grzegorz Kokot

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties.

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Image-based finite element modeling of the three-point bending test of cortical bone

The numerical simulation of the response of bone tissue to loading is a very common method in the biomedical engineering. The high diversity of bone quality, fractures and metabolic diseases, requires different approaches to numerical simulation. The main aim of this study was image-based finite element modeling (FEM) of the three-point bending tests of cortical bone. The results from the simulation performed based on own materials can be then used to non-destructive prediction of the bone mechanical strength. The samples were scanned by X-ray microcomputed tomography (XMT). Grey values of the imaged phantom were calibrated to known values of the phantom densities. It enabled estimation of the calibration curve for mineral level in bone, that was further applied to the calculation of bone density and the estimation of the material parameters in the FE model. In one example, the finite element analysis gives the deflection y=0.7 mm that match results from experiments where deflection was equal to y =0,69mm. The reported studies delivered useful data for future prediction of the mechanical parameters based on only imaging data.

The Topology Optimization Using Evolutionary Algorithms

The coupling of modern, alternative optimization methods such as evolutionary algorithms with the effective tool for analysis of mechanical structures - BEM, gives a new optimization method, which allows to perform the generalized shape optimization (a simultaneous shape and topology optimization) for elastic mechanical structures. This new evolutionary method is free from typical limitations connected with classical optimization methods. In the paper results of researches on the application of evolutionary methods in the domain of mechanics are presented. Numerical examples for some topology optimization problems are presented, too.

Microscale’s relationship between Young’s modulus and tissue density. Prediction of displacements

Abstract The study presents an experimental verification of Wagner et al.’s relationship in microscale and proposes a modification of this relationship. For this purpose, 11 cubic specimens were microcomputed tomography scanned and mechanically tested with the displacement full-field measurements using a digital image correlation system. Then, numerical simulations of the compression tests were performed using a finite elements method. The Young’s modulus distributions assigned to the finite elements models were calculated using both of Wagner et al.’s relationships: original and modified. Comparison of the experimental and numerical results indicated the accuracy of numerical solutions for both relationships.

Digital Image Correlation and nanoindentationin evaluation of material parametersof cancellous bone microstructure

Purpose: Purpose of this paper is to present the possibilities of the application of the two methods: Digital Image Correlation and nanoindentation in porous bone tissues testing. Firstly, as a tool in the evaluation process of material parameters for porous microstructures, such as bone tissues or other foams and, secondly, as validation and verification tools for finite element analysis of bone or foams structures. Those methods are helpful when the high accuracy of the mechanical parameters of porous microstructures is required. Design/methodology/approach: Two methods: Digital Image Correlation (DIC) and nanoindentation are used as an efficient approach in the evaluation process of material parameters or constitutive relationship of porous structures like bone tissues. Digital image correlation enlarges the accuracy of classical mechanical tests and the nanoindentation allows to look inside the microstructure. Findings: The proposed methods were found to be effective in experimental testing and material parameters evaluation process of some special materials. Among them are porous structures, such as bone tissue. Additionally, the DIC is an excellent tool for finite element model validation and results verification. Practical implications: The presented method based on the combination of the Digital Image Correlation and nanoindentation presents new possibilities in material testing fields, material behavior and parameters evaluation. They have great advantages, among others, in the field of testing of porous bone structure or determining the mechanical parameters of bone tissue. Originality/value: The paper presents methods for testing the complicated porous bone structures: evaluating mechanical behavior of the whole structure and evaluating mechanical properties of the single element of the structure. The mechanical parameters of human cancellous bone structures are presented as the preliminary research results.