Dynamic assessment and FEM modeling of the modal frequencies and shapes of bovine tibia bone.

Abstract

Frequency response function (FRF) and Complex Mode Indicator Function (CMIF) techniques were used to experimentally measure the modal frequencies for several long (bovine) tibia bones. CMIF has an advantage of detecting closely spaced modes by excluding misinterpreted peaks. It was found that the difference between the two methods did not exceed 2.98 percent. CMIF data was more consistent when varying impact location. Effect of bone’s geometrical attributes on modal frequencies was statistically scrutinized and highly correlated parameters were identified. Bone length exhibited high correspondence to frequencies (p 0.05) for practically all modes. Also, four simple equations were developed, relating modes 1 and 2 in the cranial-caudal (C-C) and medial-lateral (M-L) planes to the characteristic length of the bone. Starting from anatomically accurate computed tomography (CT) scans, the finite elements method (FEM) using ANSYS was employed to numerically estimate the modal frequencies of the same experimentally-characterized long (bovine) tibia bones. Accurate results require the proper selection of stiffness versus density (E-ρ) formulae for both cortical and cancellous bone constituents. This work uncovered and tested 22 literature-reported formulae to assign elemental stiffness relative to stiffness–density relations. Bones are segmented into their cortical and cancellous constituents according to found suitable values of three variables: 1) critical cut-off Hounsfield (HU), 2) cut-off density, and 3) utilized number of materials. These variables were found by replicating the bone actual mass. Numerically estimated modal frequencies are compared to those measured from our dynamic experiments. Out of the 22 literature-reported formulae considered, the most accurate formulae yielded numerical estimates with errors (percentage difference between experimental data and FEM solution) of 0.95percent and 10.65percent for 1st and 2nd cranial-caudal (C-C) frequencies, respectively.