Modal Frequencies of Long Tibia Bones: Heterogeneous vs Homogeneous Material Considerations

Abstract

Where heterogeneous material considerations may yield more accurate estimates of long bones’ modal characteristics, homogeneous description has the advantage for yielding faster approximate solutions. In this study, modal frequencies of (bovine) long tibia bones are numerically estimated using the finite element method (FEM) using ANSYS starting from anatomically accurate CT scans and 3D models. Whole long bones are segmented into their cortical and cancellous constituents based on Hounsfield (HU) values. 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. Modal frequencies are generated and values compared to those measured from dynamic experiments. Analysis was repeated where bone properties are homogenized by averaging the stiffness properties of bone constituents. The resulting frequencies are compared with those of the heterogeneous stiffness-graded bones. As compared with measured experimental values of one control long bone, the heterogeneous material assumption returned good estimates of the frequency values in the 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 ML plane, heterogeneous material assumption returned good estimates of the frequency values 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.