The micro-mechanics of cortical shell removal in the human vertebral body

Abstract

An improved understanding of the biomechanical role of the vertebral cortical shell with respect to the trabecular bone may improve diagnosis of osteoporosis and provide insight into the effects of disease, aging, and drug treatments. In this study, we present results from finite element simulations of removal of the shell from the vertebral body and the associated mechanical effects in terms of overall change in vertebral structural stiffness and of the tissue-level stresses. Specimen-specific micro-mechanical finite element models of thirteen vertebrae were generated from micro-CT scans with 60-μm voxel size. An algorithm was developed to automatically isolate the thin (and discontinuous) shell and the images were converted into finite element models by mapping each image voxel into a finite element. After removal of the endplates, compressive loading conditions were applied and linear elastic analyses were run for three cases – with and without the shell, and shell-only models. The models contained up to 13.6 million elements and were solved using a maximum of 144 CPUs in parallel, 300 GB memory, and a custom code with a parallel mesh partitioner and algebraic multigrid solver. Results indicated that the shell was on average, 0.38 ± 0.06 mm thick, accounted for 21–39% of the overall bone mass, but accounted for 38–68% of the overall vertebral stiffness. Examination of the tissue-level stresses indicated that this disproportionately large mechanical effect of shell removal was due in part to unloading of the remaining peripheral trabeculae adjacent to the shell. Stress paths were also preferentially within vertically-aligned bone: the cortical shell and vertically-aligned trabeculae. Taken together, these results demonstrate two important roles of the thin vertebral cortical shell: it can carry significant load by virtue of representing a large proportion of the vertically-aligned bone tissue within the vertebra, and, as a shell, it also maximizes the load carrying capacity of the trabecular centrum, particularly around the periphery.

Full text

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THE MICROMECHANICS OF CORTICAL SHELL REMOVAL
IN THE HUMAN VERTEBRAL BODY
Senthil K. Eswaran 1, 2
Harun H. Bayraktar 1, 2, 3
Mark F. Adams 4
Atul Gupta 1
Paul F. Hoffmann 1, 2
David C. Lee 1
Panayiotis Papadopoulos 2, 3
Tony M. Keaveny 1, 2, 5
(1) Orthopaedic Biomechanics Laboratory, 2166 Etcheverry Hall, University of California,
Berkeley, CA 94720
(2) Department of Mechanical Engineering, University of California, Berkeley, CA 94720
(3) Computational Solid Mechanics Laboratory, University of California, Berkeley, CA 94720
(4) Department of Applied Physics and Applied Mathematics, Columbia University, New York,
NY 10027, USA
(5) Department of Bioengineering, University of California, Berkeley, CA 94720
Original Article
For submission to Computer Methods in Applied Mechanics and Engineering
December 9, 2005
Running title: Micromechanics of the vertebral body
Corresponding author:
Senthil K. Eswaran
2166 Etcheverry Hall
University of California
Berkeley, CA 94720-1740
USA
(510) 642-3787, fax (510) 642-6163
senthilk@me.berkeley.edu

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Please address all reprint requests to:
Tony M. Keaveny
6175 Etcheverry Hall
Department of Mechanical Engineering
University of California
Berkeley, CA 94720-1740
USA
(510) 643-8017, fax (510) 642-6163
tmk@me.berkeley.edu

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Keywords
1. Spine biomechanics
2. Micromechanics
3. Cortical shell
4. Finite element analysis
5. Vertebral body
6. Trabecular bone

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1
Abstract
An improved understanding of the biomechanical role of the vertebral cortical shell with
respect to the trabecular bone may improve diagnosis of osteoporosis and provide insight into the
effects of disease, aging, and drug treatments. In this study, we present results from finite
element simulations of removal of the shell from the vertebral body and its mechanical effects in
terms of overall change in vertebral structural stiffness and of the tissue-level stresses. Specimen-
specific micro-mechanical finite element models of thirteen vertebrae were generated from 30-
micron resolution micro-CT scans. An algorithm was developed to automatically isolate the thin
(and discontinuous) shell and the images were converted into finite element models by mapping
each image voxel into a finite element. Compressive loading conditions were applied and linear
elastic analyses were run for three cases — with and without the shell, and shell-only models.
The models contained up to 13.6 million elements and were solved using a maximum of 144
CPUs in parallel and 300 GB memory, and a custom code with a parallel mesh partitioner and
algebraic multigrid solver. Results indicated that the shell was on average, 0.38 ± 0.06 mm thick,
accounted for 21–39% of the overall bone mass, but accounted for 38–68% of the overall
vertebral stiffness. Examination of the tissue level stresses indicated that this disproportionately
large mechanical effect of shell removal was due in part to unloading of the remaining peripheral
trabeculae adjacent to the shell. Stress paths were also preferentially within vertically aligned
bone: the cortical shell and vertically aligned trabeculae. Taken together, these results
demonstrate two important roles of the thin vertebral cortical shell: it can carry significant load
by virtue of representing a large proportion of the vertically aligned bone tissue within the
vertebra, and, as a shell, it also maximizes the load carrying capacity of the trabecular centrum,
particularly around the periphery.

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Introduction
The human lumbar and thoracic vertebrae are major load-bearing bones within the spinal
column that consist primarily of highly porous trabecular bone, surrounded by a thin cortical
shell. The mechanical integrity of the vertebra is a critical factor in the etiology of age-related
osteoporotic fractures and in the support structure for a variety of orthopaedic implants such as
pedicle screws and intervertebral disc replacements. An improved understanding of the
biomechanical role of the vertebral cortical shell with respect to the trabecular bone may improve
diagnosis of osteoporosis and provide insight into the effects of disease, aging, and drug
treatments. It may also provide a basis for mechanistic validation of finite element models used
for fracture risk prediction (7, 11, 14, 16) and for improved design of spinal implants.
Since the cortical shell is a thin, discontinuous and porous structure, it has been difficult
to characterize its mechanical contribution to the overall strength of the vertebral body. While
some experimental studies have concluded that the cortical shell takes over 40% of the load (14,
23, 31), others have concluded that it takes less than 15% (17, 26). The major shortcoming of the
experimental studies is controlling the removal process of the shell: if too much is removed, it
may induce damage to the trabecular centrum, if too little is removed, the effect of the shell is
underestimated. Since the shell is on the order of 0.25 to 0.4 mm thick (9, 22, 25, 30), it is
difficult to remove it in a precise fashion. Continuum level finite element models (7, 11, 14, 16)
suffer from a simplistic modeling of the shell and its interaction with the trabecular centrum,
although these analyses have provided unique insight. For example, it has been shown that the
load taken by the shell depends on the location along the superior-inferior axis (5, 26), as well as
the applied boundary conditions (14).