Transversely isotropic and isotropic material considerations in determining the mechanical response of geometrically...

In finite element method (FEM) simulations of the mechanical response of bones, proper selection of stiffness versus density (E-ρ) formulae for bone constituents is necessary for obtaining accurate results. A considerable number of such formulae can be found in the biomechanics' literature covering both cortical and cancellous constituents. For determining the first and second modal frequencies (in both cranial-caudal and medial-lateral planes) of bovine tibia bone, this work assembled and numerically tested 22 isotropic and 21 orthotropic stiffness-density formulae combinations (cases). To accurately reproduce bone geometry, anatomical 3D models were generated from computed tomography (CT) scans. By matching the bone's digital mass to its actual mass, cortical and cancellous constituents were faithfully segmented by utilizing suitable values of three variables: (1) critical cutoff Hounsfield unit (HU) values, (2) cutoff density value, and (3) utilized number of sub-materials. Consequently, a balanced distribution of finite elements was generated with stiffness values congruent with their cancellous or cortical demarcations. Of the considered 22 isotropic formulae cases and 21 orthotropic (reduced to transversely isotropic) cases, only few yielded accurate frequency estimates. For verifying the accuracy of the solutions emanating from the various formulae, experimental vibration tests of corresponding mode frequencies and shapes (ProSig©) were conducted. When compared with the measured experimental frequency values, the most accurate isotropic formulae yielded numerical estimates of + 0.95% and + 10.65% for the first and second cranial-caudal (C-C) frequencies, respectively. The formulae yielding most accurate estimates also proved successful in estimating frequencies of a second tibia bone yielding numerical estimates within + 4.75% and + 1.88% of the said mode frequencies. For the transversely isotropic material assignment, the closest case scenario computed numerical estimates with a percentage difference of + 2.05% and + 9.36% for the first and second cranial-caudal (C-C) frequencies, respectively. Graphical abstract Mode shapes (left) 1 and (right) 2 for transversely isotropic case 15 T (Bone A): (a) cranial-caudal and (b) medial-lateral plane.