Abstract
Background: The clinical management of lytic
tumors of the spine is currently based on geometric measurements
of the defect. However, the mechanical behavior of a structure depends
on both its material and its geometric properties. Quantitative
computed tomography and dual-energy x-ray absorptiometry were investigated
as noninvasive tools for measuring the material and geometric properties of
vertebrae with a simulated lytic defect. From these measures, yield
loads were predicted with use of composite beam theory.
Methods: Thirty-four fresh-frozen cadaveric
spines were segmented into functional spinal units of three vertebral
bodies with two intervertebral discs at the thoracic and lumbar
levels. Lytic defects of equal size were created in one of three
locations: the anterior, lateral, or posterior region of the vertebra. Each
spinal unit was scanned with use of computed tomography and dual-energy
x-ray absorptiometry, and axial and bending rigidities were calculated
from the image data. Each specimen was brought to failure under
combined compression and forward flexion, and the axial load and bending
moment at yield were recorded.
Results: Although the relative defect size was
nearly constant, measured yield loads had a large dispersion, suggesting
that defect size alone was a poor predictor of failure. However,
image-derived measures of structural rigidity correlated moderately well
with measured yield loads. Furthermore, with use of composite beam
theory with quantitative computed tomography-derived rigidities,
vertebral yield loads were predicted on a one-to-one basis (concordance,
rc = 0.74).
Conclusions: Although current clinical guidelines
for predicting fracture risk are based on geometric measurements
of the defect, we have shown that the relative size of the defect
alone does not account for the variation in vertebral yield loads.
However, composite beam theory analysis with quantitative computed
tomography-derived measures of rigidity can be used to prospectively
predict the yield loads of vertebrae with lytic defects.
Clinical Relevance: Image-predicted vertebral
yield loads and analytical models that approximate loads applied
to the spine during activities of daily living can be used to calculate
a factor of fracture risk that can be employed by physicians to
plan appropriate treatment or intervention.
More than one million new cases of cancer are diagnosed every
year in the United States3. Of
the patients who die of cancer, more than 80 percent have evidence
of skeletal metastases at the time of autopsy30,35,
with the spine being the most common site of such metastases irrespective
of the primary tumor site37. Lymphoma,
melanoma, and carcinoma of the breast, prostate, kidney, and thyroid
account for 75 percent of the spinal metastases. Carcinomas of the
breast and lung most often metastasize to the thoracic vertebrae;
carcinoma of the prostate most often metastasizes to the lumbar
vertebrae and sacrum14.
Signs and symptoms of spinal metastases include pain, vertebral
fracture, and mechanical instability that can lead to progressive
neurological deficits, severely compromising a patient's quality
of life. Approximately 30 percent of bone metastases lead to fracture
or produce hypercalcemia that necessitates medical treatment38. Surgical decompression and stabilization
may be indicated for the treatment of impending fracture, progressive
spinal deformity, and progressive neurological compromise9,18.
Definitive guidelines for surgical intervention have not been
determined. Current clinical criteria, based on conventional radiographs,
include a 50 percent decrease in vertebral height9,
50 percent kyphotic deformity32,
or 70 percent destruction4. However,
these radiographic criteria often apply only after the onset of
debilitating symptoms. Moreover, studies have shown that geometric measures
alone do not reliably predict a vertebral fracture threshold1,5,10,24,33. Also, Taneichi et al.36 showed that while, in general, vertebrae
with a small defect have little increased risk of fracture and vertebrae
with a large defect have a markedly increased risk, the risk of
fracture for vertebrae with an intermediate-sized defect (affecting
25 to 45 percent of the cross-sectional area) was variable and depended
on the location of the defect.
The effect of density on mechanical behavior has been extensively
investigated6,20,21,31. Quantitative
computed tomography has often been used to measure bone density
and has also been proven to be a useful tool in the prediction of vertebral
strength5,24,27. Bone mineral
density as measured with dual-energy x-ray absorptiometry has also
been shown to correlate with the failure load of intact vertebrae2,7,26, and dual-energy x-ray absorptiometry
deserves further investigation as an alternative to computed tomography
because of its low cost, increasing accessibility, and low radiation
exposure. However, the usefulness of either method to predict fracture in
vertebrae with a lytic defect is currently unknown.
The mechanical behavior of a structure is a function of both
its material and its geometric properties. Therefore, any method
of predicting fracture risk must be able to measure changes in both
bone material behavior (such as by monitoring apparent bone density)
and bone structural geometry (such as by measuring cross-sectional
area and moment of inertia). Composite beam theory is an analytical theory
that accounts for both the material properties of the individual
elements that make up the structure and the overall geometry of
the structure itself. In previous studies7,23,24,26,27,
the effect of either material or geometric properties alone on vertebral
fracture was investigated. In our study, however, we attempted to
predict vertebral failure using beam theory by measuring structural
rigidity. Structural rigidity is a property defined by the product
of the material modulus and cross-sectional geometry of the structure,
and it is equivalent to the slope of the linear portion of the load-deformation
curve.
Although bones have complex material behaviors and irregular
geometries, previous investigations have demonstrated that beam-theory
calculations based on image-derived rigidity measurements correlate
well with experimental results17,39.
Applying beam theory to cylindrical rods of trabecular bone with
simulated lytic defects, Hong et al.17 found
that axial, bending, and torsional rigidities, calculated with quantitative
computed tomography and dual-energy x-ray absorptiometry, correlated
well with uniaxial tensile, bending, and torsional failure loads,
respectively (r2 > 0.84). Applying beam
theory to whole bones, Windhagen et al.39 found
that axial rigidity, calculated with quantitative computed tomography,
was highly correlated with the overall applied load at failure (r2 =
0.85) for thoracic and lumbar vertebral bodies with simulated defects
of variable size (5 to 20 percent by volume) contained within the
vertebral body centrum.
In our study, we further examined whether we could use composite
beam theory with image-derived structural rigidities to predict
the failure load of whole vertebrae with a simulated osteolytic
defect of intermediate size, created in one of three clinically
relevant locations of the vertebrae. We tested the hypotheses that
structural rigidities calculated from quantitative computed tomographic and
dual-energy x-ray absorptiometric measurements correlate with measured
failure load, that correlations between calculated rigidity and failure
load are independent of defect location and vertebral type, and
that composite beam theory can be used to predict the measured failure
load of vertebrae with a simulated lytic defect of intermediate size.
Specimens
Thirty-four fresh-frozen spines from the cadavera of eighteen
female and eleven male individuals and five individuals of unknown
gender were obtained. The mean age at the time of death was 74.2 years
(range, thirty-seven to 102 years). Radiographs of each specimen
were reviewed by the senior author (B. D. S.) to confirm the absence
of lytic or blastic bone defects, fractures, or major deformity.
The surrounding soft tissues were removed, preserving the facet
capsules, intervertebral discs, ligaments (ligamentum flavum and
anterior longitudinal, posterior longitudinal, supraspinous, and
interspinous ligaments) and rib head attachments. The spines were
segmented into functional spinal units (segments of three vertebral
bodies with two intervertebral discs). Two spinal levels commonly
affected by metastatic carcinoma were investigated. Eighteen spinal
units containing the seventh, eighth, and ninth thoracic vertebrae
and sixteen spinal units containing the first, second, and third
lumbar vertebrae were used.
A simulated lytic defect involving approximately 30 percent of
the cross-sectional area was created in the middle vertebra of each
functional spinal unit. This intermediate size was chosen because the
fracture risk associated with these defects is the most clinically
confounding36. The relative size
of the defect (the area of the defect divided by the area of the
vertebral body) was measured with transverse computed tomography scans.
The defects were created in one of three clinically representative36 locations (Fig. 1): the anterior,
lateral, or posterior region of the vertebra. A contained defect
in the anterior region of the vertebral body centrum was created
in eleven specimens; an uncontained defect in the lateral region
of the vertebral body centrum was created in twelve specimens; and
an uncontained defect in the posterior third of the vertebrae with
destruction of a costovertebral joint in thoracic vertebrae, and destruction
of a pedicle in lumbar vertebrae, was created in eleven specimens.
The anterior defects were created with an expanding reamer39 inserted through a small anterior
pilot hole at a vascular foramen. The lytic defects were filled with
an agarose gel to simulate tumor tissue.
Quantitative Computed Tomography
Specimens were thawed overnight at 4 degrees Celsius and were
encased in vacuum-degassed acrylic tubes filled with saline solution.
A high-speed helical computed tomographic scanner (Advantage; General
Electric Medical Systems, Milwaukee, Wisconsin) was used to image consecutive
transverse cross sections that were one millimeter thick and one
millimeter apart. A calcium hydroxyapatite phantom (CIRS, Norfolk, Virginia)
consisting of six chambers containing bone-ash densities ranging
from zero to 1.5 grams per cubic centimeter was imaged with the
specimens and was used to convert image gray-scale data (Hounsfield
units) to apparent bone density13.
Although bone is composed of mineral, organic matrix, and water,
computed tomography primarily images bone mineral. Therefore, the
density measured by quantitative computed tomography approximates
the density of the mineral phase, or the ash density, ?ash. In order
to use the density-to-modulus relationships empirically derived
by previous investigators31,34,
the density must be adjusted by the mass ash fraction to convert
to apparent bone density, ?app (the density of the combined mineral
and organic phases of bone):
where the ash fraction, fash, is 0.66, as reported by Cowin8.
The elastic modulus is the intrinsic stiffness of a material
and is defined by the slope of the linear region of the stress-strain
curve. The elastic modulus of each pixel in the image was calculated from
apparent density with use of empirical relationships31,34. For trabecular bone, the elastic
modulus was calculated in gigapascals with a squared power law function
of density, where density is in grams per cubic centimeter31:
For apparent bone densities of more than 1.123 grams per cubic
centimeter (cortical bone), a linear relationship with density34 was used:
Structural analysis was performed with use of custom computation
algorithms coded into commercial image-analysis software (AVS; Advanced Visual
Systems, Waltham, Massachusetts). The entire vertebral cross section,
including both the vertebral body and the posterior structures,
was analyzed. For every cross section of each vertebra, the algorithm
calculated the equivalent bone density of each pixel in the region
of interest, converted the density to elastic modulus (as described
in Equations 2 and 3), and then calculated the cross-sectional axial
and bending rigidities by adding the rigidity contribution to the
cross section of each individual pixel (Fig. 2). Bending rigidity was calculated
about the modulus-weighted centroidal axis:
where E(?app) is the elastic modulus as a function of apparent
density (as calculated in Equations 2 and 3), da is
an incremental area element with pixel dimensions determined with
the resolution of the computed tomographic image, EA is
the axial rigidity as calculated in Equation 4, and
x¯
is the coordinate of the modulus-weighted centroid calculated from
the first moment:
Dual-Energy X-Ray Absorptiometry
Specimens were thawed overnight at 4 degrees Celsius, immersed
in a bath of saline solution, and scanned on a QDR 2000+ bone densitometer
(Hologic, Waltham, Massachusetts) from the inferior to the superior
end plate along the transverse plane in the anteroposterior and
lateral projections.
Vertebral structural geometry was calculated with methods similar
to those derived by Martin and Burr25.
X-ray attenuation profiles of bone mineral density, BMD, in grams
per square centimeter for transverse cross sections through the
vertebrae were generated (Fig. 3). The cross-sectional area occupied
by bone mineral was calculated from the area under this curve:
where ?tiss is an assumed constant tissue density (1.94 grams
per cubic centimeter, as reported by Cowin8)
and dx is an incremental length element determined by the resolution
of the bone densitometer machine. The cross-sectional mass moment
of inertia was calculated relative to the centroid and perpendicular
to the scan direction, x:
where A is the cross-sectional area (as calculated
in Equation 7) and =x
is the coordinate of the
centroid calculated from the first moment:
Assuming that only the bone mineral attenuates the x-ray, the
calculated cross-sectional area represents the area of the cross
section that is occupied by bone mineral, not the total bone area.
Similarly, the calculated mass moment of inertia represents the
distribution of bone mineral about the centroidal axis, not the
distribution of total bone area. Therefore, geometric properties
calculated from dual-energy x-ray absorptiometry were effectively weighted
by the amount of bone mineral, a material property of the structure.
For this reason, cross-sectional area and mass moment of inertia
measured with dual-energy x-ray absorptiometry were considered analogs
of axial and bending rigidity, respectively.
Mechanical Testing
The superior and inferior vertebral bodies of each spinal unit
were partially embedded in polymethylmethacrylate, such that the
potted ends were parallel to one another and perpendicular to the longitudinal
axis of the spine. The specimens were tested to failure under combined
axial compression and forward flexion with use of a custom hydraulic
testing system (Fig. 4)39.
Physiologically relevant anterior and posterior compressive loads
were applied by two hydraulic actuators of equal cross-sectional
area at a distance ratio of four to three relative to the posterior
margin of the vertebral body and at a loading rate of 133 newtons
per second, simulating a scenario of forward bending and lifting.
These hydraulic actuators were powered by a common pressure source under
load control. The applied loads were assumed to be entirely in the
sagittal plane.
For the intact vertebrae, the forward bending moment was linearly
related to the applied axial load (Fig. 4):
After failure occurred, the relationship between the moment arms, a and b,
changed as the neutral axis and instantaneous center of rotation
shifted. Therefore, failure was defined as the yield load at which
the relationship between applied axial load and forward flexion moment
deviated from linearity.
Loads and moments along three mutually orthogonal axes were measured
at the superior vertebral body with a six-degrees-of-freedom load-cell
(Advanced Medical Technology, Newton, Massachusetts). Displacements
were measured with an infrared optical system (MacReflex; Qulisys, Glastonbury,
Connecticut) whereby reflective markers were attached to the superior
and inferior end plates of the middle vertebrae anteriorly and posteriorly
and the relative positions of the markers were tracked to calculate
the axial and rotational deformation of the vertebrae. The load
data and coordinates of the reflective markers were collected simultaneously
with use of a synchronization system (MP100WSW; Biopac Systems,
Santa Barbara, California). The entire mechanical test was scanned
in real time with fluoroscopy (Mini 6600 digital mobile c-arm; OEC
Medical Systems, Salt Lake City, Utah) to observe the compressive fracture
patterns, which were classified as anterior wedge, vertical compression,
or burst fractures as reported by McAfee et al.22,
Ferguson and Allen12, and Holdsworth16, respectively.
Theory
The axial and bending rigidities calculated from computed tomographic
images (Equations 4 and 5) were combined with use of composite beam
theory (Equation 11) to predict the failure load of every cross
section in each vertebra's computed tomographic scan. For each vertebra,
the cross section with the minimum predicted failure load was assumed
to be the site of failure initiation.
We assumed that the elastic behavior of whole bones correlates
with the behavior of bone tissue at yield and that bone on the material
level fails at a constant strain independent of density. The axial compressive
yield load in combined compression and bending was thus predicted
from the cross-sectional geometric and material properties of the bone
structure:
where e is the yield strain (1 percent for trabecular bone in
compression19), Fz
is the axial compressive yield load, EA is the
axial rigidity of the cross section with the minimum predicted failure
load, My is the applied bending moment at yield
(which is a function of Fz, derived empirically), c is
the distance from the neutral axis to the outer perimeter of bone
in the cross section, and EI is the bending rigidity
of the cross section with the minimum predicted failure load11. The axial and bending rigidities
were calculated with use of quantitative computed tomography as described
above.
Statistical Analysis
In order to test the hypothesis that structural properties correlate
with measured failure loads, linear regression analyses were performed
to determine the coefficient of determination (r2)
for each structural parameter versus the measured failure load for
each imaging modality. The equality of correlation coefficients
(r) among the structural parameters and image modalities was tested
by chi-square analysis. A Fisher's z transformation and t test were
performed to test the equality of correlation coefficients between
imaging modalities for each structural parameter. If the test of
equality among correlation coefficients within each group was negative,
a Tukey-type test for multiple comparisons was performed to determine
which individual members of the group differed40.
To test the hypothesis that the correlations between structural
properties and measured failure load are independent of defect location
and vertebral type, an analysis of covariance was used to determine
the equality of the slopes of the regressions for the three different
defect locations and two different vertebral types. The grouping covariates
were defect location and vertebral type, the independent variable
was each structural parameter, and the dependent variable was measured failure
load.
To test the hypothesis that composite beam theory can be used
to predict the actual measured failure loads, a concordance correlation
was performed to determine how well the failure loads calculated with
use of composite beam theory matched one-to-one with the measured
failure loads (deviation from the line y = x).
Post-test analyses were performed to determine whether sufficient
statistical power (b £ 0.2) existed to test for significant differences
between groups at a = 0.05.
Specimen information, observed fracture patterns, image-derived
material and structural properties, and mechanically measured failure
loads are shown in Table I for the thoracic and lumbar spinal
segments. The contribution to the failure load from the bending term
in Equation 10 was found to be, on the average, three times greater
than that of the axial compressive term.
Fracture Patterns
The fracture patterns observed were comparable with those found
clinically12,16,22. Although vertebral
failure (yield) was measured from the load-deformation data, simultaneous real-time
fluoroscopy revealed that this mechanically measured failure was
approximately coincidental with the observed event of fracture.
Effect of Defect Size on Failure Load
Although the relative cross-sectional area of the anterior and
lateral defects was nearly constant at 30 percent of the vertebral
body cross-sectional area (coefficient of variation, 18 percent),
the measured failure loads for these specimens had a large dispersion
(coefficient of variation, 63 percent). Therefore, defect size alone
was not predictive of vertebral failure.
Regression Analysis
Bone density, structural rigidity, and calculated failure load
correlated with the measured failure load (Table II). Comparisons
were made among the measured structural parameters for each of the
imaging modalities. Within the power of the analysis (b £ 0.2), significant
differences could not be detected among correlations between quantitative
computed tomography-derived parameters and measured failure load.
For the dual-energy x-ray absorptiometry-derived parameters, correlations
between measured failure load and density and between failure load
and axial rigidity analog were better than the correlation between
measured failure load and bending rigidity analog (Tukey test).
Within the power of the analysis (p £ 0.2), significant differences
could not be detected between the two imaging modalities for correlations
between the measured structural parameters and the measured failure
loads.
Both vertebral type and defect location affected the regressions
between the structural properties and the measured failure load.
For both computed tomography (p = 0.001) and dual-energy x-ray absorptiometry
(p = 0.006), the slope of the regression between axial rigidity
and measured failure load was dependent on vertebral type (Table III). For both
computed tomography (p = 0.006) and dual-energy x-ray absorptiometry
(p = 0.010), the slope of the regression between bending rigidity and
measured bending moment at failure was dependent on defect location
(Table IV).
Similarly, the slope of the regression between the computed tomography-predicted
failure load and the measured failure load was dependent on defect
location (p = 0.023) (Fig. 5).
Concordance Correlations
A concordance correlation was performed to determine how well
the failure load calculated with use of composite beam theory and
quantitative computed tomography-derived measures of rigidity predicted
the measured failure load on a one-to-one basis (Fig. 6). There was
a good correlation (rc = 0.74) with the line y = x.
The results of our study showed that the measures of structural
rigidity derived from both quantitative computed tomography and
dual-energy x-ray absorptiometry correlated with the measured vertebral
failure loads. However, these correlations were affected by defect
location and vertebral type. Perhaps more importantly, with the
use of composite beam theory with quantitative computed tomography-derived
measures of structural rigidity, the vertebral failure load was
predicted on a one-to-one basis.
Other investigators have attempted to use both quantitative computed
tomography and dual-energy x-ray absorptiometry to measure structural properties
of bones with a simulated lytic defect and to correlate these measures
with failure load17,39. The results
of such studies were promising but were limited in scope. Hong et
al.17 studied the idealized case
using cylindrical rods of trabecular bone with a regularly shaped
geometric defect. They demonstrated that axial, bending, and torsional
rigidities measured with both imaging modalities were highly correlated
with failure in compression, bending, and torsion, respectively. Windhagen
et al.39 studied human vertebrae
with a simulated defect entirely contained within the vertebral
body centrum. In their study, the cross section with the greatest
relative area of bone removed was imaged and the posterior elements
were excluded from the analysis. Axial rigidity was highly correlated
with failure load, although the mechanical test consisted of both
axial compression and forward bending.
In our study, we attempted to expand upon these preliminary investigations
by testing a model closer to clinical reality. Whole vertebral functional spinal
units at levels frequently affected by metastatic cancer were studied,
relevant soft-tissue connections were preserved, the entire vertebra was
considered in the structural analysis, and a more physiological
loading scenario was modeled. We hypothesized that vertebral failure
through a lytic defect is a function of both the material and the
cross-sectional geometric properties of the bone at and around the
defect and therefore that failure depends on the structural rigidity
of the whole bone construct. Failure load was predicted at sequential
transverse cross sections through the entire vertebra with use of
quantitative computed tomography-derived measures of axial and bending
rigidity in beam theory for combined bending and axial compression.
We assumed that bone tissue yielded in compression at the cross
section through the bone with the minimum predicted failure load.
The hypothesis that composite beam theory can be used in the analysis
of vertebral failure was confirmed by a high concordance correlation between
the measured and predicted failure loads independent of the effect
of vertebral type or defect location. Moreover, to the best of our
knowledge, the present study is the first to go beyond retrospective
correlation, to prospective prediction of the failure load of vertebrae
with a simulated lytic defect.
The specimens used in our study were mostly from the cadavera
of elderly and osteoporotic individuals. Although the relative cross-sectional
area of the defect was nearly constant, there was a large dispersion
(coefficient of variation, 63 percent) in the measured failure loads.
This finding suggests that, at least for vertebrae with a lytic
defect of intermediate size, relative defect size alone accounts for
little of the variation in the measured failure loads. Evaluation
of defect geometry alone ignores the important contribution of the
material properties of the surrounding bone. Structural analysis
takes into account the effect of bone quality on the material properties
through the density-dependent modulus term. The results of structural
analysis demonstrate that noninvasively derived measures of structural
rigidity correlate moderately well with measured failure load, explaining much
of the variance in the load-carrying capacity of whole bones.
There are some important limitations to our experimental methods.
Composite beam theory, which was derived to explain the mechanical
behavior of long, slender, axisymmetrical beams of heterogeneous
elastic material, was extrapolated in our study to describe the
behavior of an irregularly shaped short column of heterogeneous
material. However, this theory was chosen because of its simplicity
and potential ease of application to patient-specific analyses.
We tested the applicability of composite beam theory to the physiologically relevant
loading scenario of combined compression and forward bending of
the spine as an alternative to more sophisticated methods, such
as finite element analysis, which are labor intensive and computationally
expensive for patient-specific analyses. Given the limits of the
theory, the good correlation between rigidity and failure load and
the reasonable accuracy of the predicted failure load are all the
more notable.
All ex vivo experiments have some limitations
when extrapolated to in vivo results. For example,
although the intervertebral discs are known to dissipate forces
in the spine, our cadaveric spine model may not have retained the
same in vivo characteristics, especially after
the freezing process. Moreover, the disc degeneration in our elderly
population may have been more extensive than it is in middle-aged
patients with metastatic carcinoma. However, the integrity of the
specimens was maintained as well as possible by retaining all of
the important soft-tissue attachments and by keeping the specimens
wrapped in gauze soaked in saline solution, both in and out of the
freezer. In addition, the observed fracture patterns that resulted
from the mechanical test were similar to those observed clinically12,16,22, indicating that the transmitted
load distribution through the intervertebral discs was comparable with
the in vivo situation.
Although the metastatic tumor mass itself was modeled by an agarose
gel filling the defects, the actual material properties of tumors
are largely unknown. Only one study, conducted by Hipp et al.15, attempted to measure the material
properties of lytic breast metastases. Significant reductions in the
stiffness of the bone-tumor composite were measured. However, it
is unclear how well the agarose gel-bone composite mimicked their
limited findings.
The specimens were tested with the soft tissues intact; however,
computed tomography and dual-energy x-ray absorptiometry image bone
only and do not account for the role of soft tissues in load transmission
and failure mechanics. The supraspinous and interspinous ligaments,
ligamentum flavum, facet joint capsules, and posterior longitudinal
ligament together act as a tension band when the spine is in forward
flexion, effectively counterbalancing the anterior compressive force
and bending moment on the vertebral body. The effects of this tension
band are ignored in the calculation of the neutral bending axis.
This analysis is applicable only to lytic metastases. Osteoblastic
metastases attenuate x-rays, but the relationship between the amount
of x-ray attenuation and the stiffness (modulus) of the blastic
tumor is unknown and cannot be accounted for at this time. Composite
beam theory, however, can reflect multiple material properties and,
once the appropriate x-ray attenuation-modulus relationships are
clarified for osteoblastic tissue, this analysis can be extended
to include osteoblastic metastases as well.
The mechanical testing apparatus introduced out-of-plane parasitic
loads and moments that may have confounded the measured failure
load. However, the magnitudes of these parasitic loads and moments
at failure, as measured by the six-channel load-cell, were small
compared with the applied loads in the sagittal plane. The apparatus
also confined the motion of the spine to the sagittal plane, while in
vivo failure might occur due to motion in any plane. Theoretically,
failure due to bending should occur about the axis of the minimum
principal moment of inertia. However, while the principal moments and
corresponding axes were calculated, they were not considered in
the analysis since loads were imposed along the anatomical axes
and not the principal directions.
Despite these limitations, the results of our study confirm those
of previous investigators. Like Biggemann et al.1,
Brinckmann et al.5, and Dimar
et al.10, we found that the combination
of material and geometric properties was more predictive of vertebral
failure than was defect area alone. The measured failure loads and
axial rigidity values obtained from quantitative computed tomography were
comparable with those found by Windhagen et al.39.
Moreover, like Taneichi et al.36,
we found that vertebral fracture risk may depend on defect location
and vertebral type.
Of the two imaging techniques, only quantitative computed tomography
could be used to prospectively predict the failure load of vertebrae
with use of composite beam theory. The failure loads calculated
with use of composite beam theory, with structural rigidities measured
with quantitative computed tomography, could not be shown to correlate
with measured failure load better than these measures of rigidity
alone. However, this result may be a consequence of the loading
configuration, which was dominated by the axial compressive load;
the fact that the axial and bending rigidities are interrelated
(r2 = 0.58) for these vertebral specimens
of similar shape; and the limited distribution of defect size, shape,
and location.
Dual-energy x-ray absorptiometry was investigated as an alternative
to quantitative computed tomography because the former is inexpensive,
is readily accessible, and exposes the patient to lower levels of
radiation, making serial evaluations feasible to assess a patient's
response to cancer treatments. Both bone mineral density and dual-energy x-ray
absorptiometry-derived axial rigidity analogs correlated well with
measured failure load. However, dual-energy x-ray absorptiometry
cannot be used to measure the modulus-weighted, cross-sectional
properties necessary to calculate the failure load with use of composite
beam theory. Other investigators who have proposed methods to calculate
cross-sectional area and moment of inertia from dual-energy x-ray
absorptiometry attenuation data22,28 have
also acknowledged that these measurements are not directly equivalent
to standard cross-sectional geometric properties because this imaging modality
measures the spatial distribution of bone mineral only. Although
bone mineral density was highly correlative with vertebral failure
load, dual-energy x-ray absorptiometry cannot be used as a universal
tool for predicting the failure of all bones because the linear
regression coefficients are dependent on the geometry of the specific
bone in question and the particular loading scenario being evaluated.
We were motivated to reform our study by the clinical need to
better identify which patients are at substantial fracture risk
so that appropriate intervention can be initiated before catastrophic
failure occurs. Currently, there is no proven sensitive or specific
method for predicting pathological fracture of the spine. Decisions
regarding the management of lytic vertebral metastases are currently based
on geometric measurements of the bone or the defect, or both. We
demonstrated that defect size alone does not account for the variation
in vertebral failure load. The results of our study suggest that
better treatment plans can be made by predicting failure (and, by
extension, by predicting fracture, as shown by coincidental yield
and fluoroscopy data) with use of quantitative computed tomography-derived
structural properties coupled with composite beam theory. Although
the specific load scenario that results in pathological fracture
will always be unknown, with an analytical spine model29it is possible to estimate the load
applied to the spine during an index activity commonly incurred during
daily living that may be associated with pathological fracture.
The predicted failure load calculated with use of quantitative computed tomography-derived
rigidities and composite beam theory could be compared with the
anticipated load to which the vertebra would be subjected during
the index activity (such as forward bending to lift a heavy object
off the ground). If the anticipated load exceeded the load-carrying
capacity of the involved vertebra, failure and subsequent fracture
would be expected to occur. In this way, an appropriate fracture
risk index could be determined that would serve as a guideline for
clinicians to use when recommending a course of treatment.
Note: The authors thank OEC Medical Systems for the use of their
Mini 6600 digital mobile c-arm fluoroscope in our testing; Sara
E. Wilson, M.S., for the use of her spine models in determining
applied vertebral loads; and the Whitaker Foundation, the National
Institutes of Health, and the Children's Orthopaedic Surgery Foundation
for funding this research.
Biggemann, M.; Hilweg, D.; and Brinckmann, P.: Prediction of the compressive strength of vertebral bodies
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