Research Papers

Heterogeneous Versus Homogeneous Material Considerations in Determining the Modal Frequencies of Long Tibia Bones

[+] Author and Article Information
Reem A. Yassine

Mechanical Engineering Department,
American University of Beirut,
P.O. Box: 11-0236, Riad El-Solh,
Beirut 1107 2020, Lebanon

Mohammad Karim Elham, Samir Mustapha, Ramsey F. Hamade

Mechanical Engineering Department,
American University of Beirut,
P.O. Box: 11-0236, Riad El-Solh,
Beirut 1107 2020, Lebanon

1Corresponding author.

Manuscript received July 4, 2017; final manuscript received November 8, 2017; published online January 5, 2018. Assoc. Editor: Xiaoning Jiang.

ASME J of Medical Diagnostics 1(2), 021001 (Jan 05, 2018) (5 pages) Paper No: JESMDT-17-2014; doi: 10.1115/1.4038448 History: Received July 04, 2017; Revised November 08, 2017

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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Grahic Jump Location
Fig. 2

Variation of the modulus of elasticity (MPa) as a function of radius (shown for case III): (top) heterogeneous material and (bottom) homogeneous material

Grahic Jump Location
Fig. 3

Frequency values for numerical and experimental results for heterogeneous and homogeneous scenarios: (top) CC plane and (bottom) ML plane using cases I, II, and III

Grahic Jump Location
Fig. 4

Frequency results upon varying the mesh (for case III; Table 1)




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