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TECHNICAL PAPERS: Bone/Orthopedic

Subject-Specific Finite Element Model of the Pelvis: Development, Validation and Sensitivity Studies

[+] Author and Article Information
Andrew E. Anderson, Benjamin D. Tuttle

Department of Bioengineering, University of Utah, 50 South Central Campus Drive, Room 2480, Salt Lake City, UT

Christopher L. Peters

Department of Orthopedics, University of Utah Medical Center, Salt Lake City, UT

Jeffrey A. Weiss1

Department of Bioengineering, University of Utah, 50 South Central Campus Drive, Room 2480, Salt Lake City, UT and Department of Orthopedics, University of Utah Medical Center, Salt Lake City, UTjeff.weiss@utah.edu

1

To whom correspondence should be addressed.

J Biomech Eng 127(3), 364-373 (Feb 04, 2005) (10 pages) doi:10.1115/1.1894148 History: Received January 12, 2004; Revised January 25, 2005; Accepted February 04, 2005

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x(experimental strains=FEpredicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of fixture for loading the pelvis via a femoral implant component. (a) actuator, (b) load cell, (c) ball joint, (d) femoral component, (e) pelvis, (f) mounting pan for embedding pelvis, and (g) lockable X-Y translation table.

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Figure 2

Left—CT image slice at the level of the ilium, showing the registration block (arrow) and the distinct boundary between cortical and trabecular bone. Middle—the original polygonal surface representing the cortical bone was reconstructed by Delaunay triangulation of the points composing the segmented contours. Right—polygonal surface after decimation to reduce the number of polygons and smoothing to reduce high-frequency digitizing artifact. A—anterior, P—posterior, M—medial, L—lateral, I—inferior, S—superior.

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Figure 3

Left—FE mesh of the pelvis, composed of 190,000 tetrahedral elements and 31,000 shell elements. Right—close-up view of the mesh at the acetabulum.

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Figure 4

Schematics illustrating the special cases considered in determination of cortical thickness. Both the distance between the surfaces and the angle of the dot product between the normal vector (n) with that of the vector created by subtracting the trabecular and cortical node coordinates were considered. Nodes on the cortical surface are represented as open circles, while nodes on the trabecular surface are shown as filled circles. Case A—the smallest angle of the dot product between the cortical node and nearest trabecular node neighbor yields the desired thickness measurement. Case B—the smallest distance between nodes provides the desired thickness measurement. Case C—the normal vector (n) from the cortical node does not intersect the trabecular surface. For cases B and C, a weighting scheme was applied such that the smallest distance between the nodes was taken as the cortical thickness when the originally reported thickness value exceeded 1.5 X the smallest distance between nodes on the two surfaces.

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Figure 5

Left—tissue equivalent phantom containing 10 aluminum tubes used to simulate cortical bone with varying thickness. The phantom was scanned with a CT scanner and manually segmented to determine the accuracy of cortical bone reconstruction. Right—cross-sectional CT image of the cortical bone phantom. Changes in thickness can be seen for the thicker tubes but become less apparent as the tube wall thickness decreases.

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Figure 6

Left—schematic showing the length measurements that were obtained from the cadaveric pelvis with an electromagnetic digitizer. Measurements were based on identifiable anatomical features of the iliac wing, ischium, obturator foramen, pubis, and acetabulum. Right—excellent agreement was observed between experimental measurements and the FE mesh dimensions, yielding a total error of less than 3%.

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Figure 7

Contours of position dependent cortical bone thickness with rectangles indicating the locations of the ten strain gauges used during experimental loading. Left panel—anterior view, right panel—medial view. Cortical thickness was highest along the iliac crest, the ascending pubis ramus, at the gluteal surface and around the acetabular rim. Areas of thin cortical bone were located at the acetabular cup, the ischial tuberosity, the iliac fossa, and the area surrounding the pubic tubercle. Cortical thickness beneath the surface of the strain gauges was similar to the average model thickness of 1.41 mm but deviated less.

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Figure 8

Distribution of von Mises stress at 1 X body weight. Left panel—anterior view, right panel—medial view. Areas of greatest stress were near the pubis-symphasis joint, superior acetabular rim, and on the ilium just superior to the acetabulum.

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Figure 9

FE predicted versus experimental cortical bone principal strains. Top panel—subject specific, middle panel—constant trabecular modulus, bottom panel—constant cortical thickness. For the subject-specific model there was strong correlation between FE predicted strains with those that were measured experimentally with a best-fit line that did not differ significantly from the line y=x(experimental strains=FEpredicted strains). Changes to the trabecular modulus did not have as significant of an effect on the resulting cortical bone strains as did changes to cortical bone thickness.

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