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Journal of Biomechanical Engineering | Volume 129 | Issue 3 | TECHNICAL PAPERS
TECHNICAL PAPERS: Bone/Orthopedic

A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments

[+] Author and Article Information
Zohar Yosibash1

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israelzohary@bgu.ac.il

Royi Padan

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Leo Joskowicz

School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Charles Milgrom

Department of Orthopaedics, Hadassah University Hospital, Jerusalem 91120, Israel

1

Corresponding author.

J Biomech Eng 129(3), 297-309 (Nov 14, 2006) (13 pages) doi:10.1115/1.2720906 History: Received March 07, 2006; Revised November 14, 2006
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The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young’s modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.
Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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+Resultant force [N] due to head displacement of 1mm for 0deg inclination angle: convergence of FEA resultant force according to several E(ρapp) relations
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Resultant force [N] due to head displacement of 1mm for 0deg inclination angle: convergence of FEA resultant force according to several E(ρapp) relations
Figure 14

Resultant force [N] due to head displacement of 1mm for 0deg inclination angle: convergence of FEA resultant force according to several E(ρapp) relations

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+von Mises stress (MPa) for a 1500N load in the bone at 0deg inclination angle
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von Mises stress (MPa) for a 1500N load in the bone at 0deg inclination angle
Figure 15

von Mises stress (MPa) for a 1500N load in the bone at 0deg inclination angle

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+FEA results using Cody relations compared to experimental observations: Femur head displacement at 1500N compression at several inclination angles (error bars indicate min. and max. measured values)
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FEA results using Cody relations compared to experimental observations: Femur head displacement at 1500N compression at several inclination angles (error bars indicate min. and max. measured values)
Figure 16

FEA results using Cody relations compared to experimental observations: Femur head displacement at 1500N compression at several inclination angles (error bars indicate min. and max. measured values)

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+Four regions of the fresh-frozen bone model. The trabecular region was divided into three subregions, low trabecular, trochanter, and head, each with a different spatial field for the Young’s modulus. In the right we show the location at which the head was trimmed to mimic the applied load in the experiment.
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Four regions of the fresh-frozen bone model. The trabecular region was divided into three subregions, low trabecular, trochanter, and head, each with a different spatial field for the Young’s modulus. In the right we show the location at which the head was trimmed to mimic the applied load in the experiment.
Figure 1

Four regions of the fresh-frozen bone model. The trabecular region was divided into three subregions, low trabecular, trochanter, and head, each with a different spatial field for the Young’s modulus. In the right we show the location at which the head was trimmed to mimic the applied load in the experiment.

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+The steps for generating the p-FE model: (a) outer surface border points; (b) approximated smooth surface; (c) solid body having a cortical/trabecular separating surface; and (d) meshed model with two different mesh regions
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The steps for generating the p-FE model: (a) outer surface border points; (b) approximated smooth surface; (c) solid body having a cortical/trabecular separating surface; and (d) meshed model with two different mesh regions
Figure 2

The steps for generating the p-FE model: (a) outer surface border points; (b) approximated smooth surface; (c) solid body having a cortical/trabecular separating surface; and (d) meshed model with two different mesh regions

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+Fresh-frozen femur shows insensitive behavior to different strain rates (at 7deg inclination): head’s displacement vis. load (top) and neck superior strain vis. load (bottom)
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Fresh-frozen femur shows insensitive behavior to different strain rates (at 7deg inclination): head’s displacement vis. load (top) and neck superior strain vis. load (bottom)
Figure 11

Fresh-frozen femur shows insensitive behavior to different strain rates (at 7deg inclination): head’s displacement vis. load (top) and neck superior strain vis. load (bottom)

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+Inclination angle influence on strains at neck superior (top) and inferior (bottom)
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Inclination angle influence on strains at neck superior (top) and inferior (bottom)
Figure 12

Inclination angle influence on strains at neck superior (top) and inferior (bottom)

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+Resultant force (Fz) versus degree of freedom (DOF) under head displacement of 1mm(0deg tilt): (top) influence of different FE meshes and (bottom) moving average box sizes
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Resultant force (Fz) versus degree of freedom (DOF) under head displacement of 1mm(0deg tilt): (top) influence of different FE meshes and (bottom) moving average box sizes
Figure 13

Resultant force (Fz) versus degree of freedom (DOF) under head displacement of 1mm(0deg tilt): (top) influence of different FE meshes and (bottom) moving average box sizes

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+Apparent density on one of the “worse approximated” slices of the investigated bone: (a)ρapp computed from HU; (b)ρapp distribution after moving average; (c)ρappLMS represented by the LMS function
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Apparent density on one of the “worse approximated” slices of the investigated bone: (a)ρapp computed from HU; (b)ρapp distribution after moving average; (c)ρappLMS represented by the LMS function
Figure 3

Apparent density on one of the “worse approximated” slices of the investigated bone: (a)ρapp computed from HU; (b)ρapp distribution after moving average; (c)ρappLMS represented by the LMS function

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+Relations between Young’s modulus and apparent density as reported in past publications for the trabecular (top) and cortical (bottom) bone
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Relations between Young’s modulus and apparent density as reported in past publications for the trabecular (top) and cortical (bottom) bone
Figure 4

Relations between Young’s modulus and apparent density as reported in past publications for the trabecular (top) and cortical (bottom) bone

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+Femur under load and representing FE model. Load is applied at an angle of 20deg to the shaft axis.
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Femur under load and representing FE model. Load is applied at an angle of 20deg to the shaft axis.
Figure 5

Femur under load and representing FE model. Load is applied at an angle of 20deg to the shaft axis.

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+Bone mounting jig (dimensions in mm): (1) slider - controls the bone’s inclination angle; (2) steel cylinder (3) 4× M6 bolts (4) base and rail (5) stopper. Load and displacements measurements (embalmed bone): Load cell, ball, and socket joint for load transmission and the LVDT.
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Bone mounting jig (dimensions in mm): (1) slider - controls the bone’s inclination angle; (2) steel cylinder (3) 4× M6 bolts (4) base and rail (5) stopper. Load and displacements measurements (embalmed bone): Load cell, ball, and socket joint for load transmission and the LVDT.
Figure 6

Bone mounting jig (dimensions in mm): (1) slider - controls the bone’s inclination angle; (2) steel cylinder (3) 4× M6 bolts (4) base and rail (5) stopper. Load and displacements measurements (embalmed bone): Load cell, ball, and socket joint for load transmission and the LVDT.

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+Strain gauges locations: (A) neck superior, (B) neck inferior, (C) shaft medial, and (D) shaft lateral
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Strain gauges locations: (A) neck superior, (B) neck inferior, (C) shaft medial, and (D) shaft lateral
Figure 7

Strain gauges locations: (A) neck superior, (B) neck inferior, (C) shaft medial, and (D) shaft lateral

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+Experiments on fresh–frozen bone at different inclination angles (from left to right): 0deg, 7deg, 15deg, 20deg
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Experiments on fresh–frozen bone at different inclination angles (from left to right): 0deg, 7deg, 15deg, 20deg
Figure 8

Experiments on fresh–frozen bone at different inclination angles (from left to right): 0deg, 7deg, 15deg, 20deg

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+Fresh-frozen bone at 7deg inclination under 1500N load: (top) Different strain gauges versus load; (bottom) strain (neck superior) versus load at neck inferior
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Fresh-frozen bone at 7deg inclination under 1500N load: (top) Different strain gauges versus load; (bottom) strain (neck superior) versus load at neck inferior
Figure 9

Fresh-frozen bone at 7deg inclination under 1500N load: (top) Different strain gauges versus load; (bottom) strain (neck superior) versus load at neck inferior

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+Fresh-frozen load vis. time response for 1500N load at 15deg inclination. Linear response is noticed after 200N preload.
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Fresh-frozen load vis. time response for 1500N load at 15deg inclination. Linear response is noticed after 200N preload.
Figure 10

Fresh-frozen load vis. time response for 1500N load at 15deg inclination. Linear response is noticed after 200N preload.

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