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research-article

MODAL FREQUENCIES OF LONG TIBIA BONES: HETEROGENEOUS VS. HOMOGENEOUS MATERIAL CONSIDERATIONS

[+] Author and Article Information
reem Yassine

American University of Beirut, Mechanical Engineering Deaprtment, P.O. Box 11-0236, Riad El-Solh, Beirut 1107 2020, Lebanon
ray16@mail.aub.edu

Mohammad Karim Elham

American University of Beirut, Mechanical Engineering Deaprtment, P.O. Box 11-0236, Riad El-Solh, Beirut 1107 2020, Lebanon
mohd.k.lahham@gmail.com

Samir Mustapha

American University of Beirut, Mechanical Engineering Deaprtment, P.O. Box 11-0236, Riad El-Solh, Beirut 1107 2020, Lebanon
sm154@aub.edu.lb

Ramsey Hamade

American University of Beirut, Mechanical Engineering Deaprtment, P.O. Box 11-0236, Riad El-Solh, Beirut 1107 2020, Lebanon
rh13@aub.edu.lb

1Corresponding author.

ASME doi:10.1115/1.4038448 History: Received July 04, 2017; Revised November 08, 2017

Abstract

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 (ANSYS) starting from anatomically accurate CT scans. Whole long bones are segmented into cortical and cancellous constituents based on Hounsfield (HU) values. Accurate 3-dimensional 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.

Copyright (c) 2017 by ASME
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