A detailed and experimentally verified methodology is outlined on how to properly process a long tibia bone starting from computed tomography (CT) scans to finite element modeling (FEM). For pre-processing of the bone, CT scan in the form of Digital Imaging and Communications in Medicine (DICOM) files are segmented using Mimics. Next comes assigning gray value Hounsfield Units (HU) of the bone constituents into their cortical and cancellous regions. To have the FEM model arrives at the same mass of that measured experimentally, it was found that cut-off density, cut-off HU, and the utilized number of sub-materials must be considered as varying parameters. The values of these parameters had to be adjusted to properly demarcate cancellous regions from those of the cortical resulting in heterogeneous medium. Next, prior to generating the FEM mesh from the generated 3D model, volume and surface meshes had to be produced. In order to validate the methodology, the modal frequencies of a long tibia bone were experimentally measured. The FEM values of the properly processed CT scans compared favorably with those found experimentally.
Abstract:The frequency response function is a quantitative measure used in structural analysis and engineering design; hence, it is targeted for accuracy. For a large structure, a high number of substructures, also called cells, must be considered, which will lead to a high amount of computational time. In this paper, the recursive method, a finite element method, is used for computing the frequency response function, independent of the number of cells with much lesser time costs. The fundamental principle is eliminating the internal degrees of freedom that are at the interface between a cell and its succeeding one. The method is applied solely for free (no load) nodes. Based on the boundary and interior degrees of freedom, the global dynamic stiffness matrix is computed by means of products and inverses resulting with a dimension the same as that for one cell. The recursive method is demonstrated on periodic structures (cranes and buildings) under harmonic vibrations. The method yielded a satisfying time decrease with a maximum time ratio of 1 18 and a percentage difference of 19%, in comparison with the conventional finite element method. Close values were attained at low and very high frequencies; the analysis is supported for two types of materials (steel and plastic). The method maintained its efficiency with a high number of forces, excluding the case when all of the nodes are under loads.
Where heterogeneous material considerations may yield more accurate estimates of long bones' modal characteristics, homogeneous description yields faster approximate solutions. Here, modal frequencies of (bovine) long tibia bones are numerically estimated using the finite element method (FEM) (ANSYS) starting from anatomically accurate computed tomography (CT) scans. Whole long bones are segmented into cortical and cancellous constituents based on Hounsfield (HU) values. Accurate three-dimensional (3D) models are consequently developed. Bones' cortical and cancellous constituents are first treated as heterogeneous material. Relative to stiffness–density relations, stiffness values are assigned for each element yielding a stiffness-graded structure. Calculated modal frequencies are compared to those measured from dynamic experiments. Analysis was repeated where bone properties are homogenized by averaging the stiffness properties of bone constituents. Compared with experimental values of one control long bone, the heterogeneous material assumption returned good estimates of the frequency values in the cranial–caudal (CC) plane with of +0.85% for mode 1 and +10.66% for mode 2. For homogeneous material assumption, underestimates were returned with error values of −13.25% and −0.13% differences for mode 2. In the medial–lateral (ML) plane, heterogeneous material assumption returned good frequency estimates with −8.89% for mode 1 and +1.01% for mode 2. Homogeneous material assumption underestimated the frequency values with error of −20.52% for mode 1 and −7.50% for mode 2. Homogeneous simplifications yielded faster and more memory-efficient FEM runs with heterogeneous modal analysis requiring 1.5 more running time and twice the utilized memory.
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