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Noninvasive Imaging Predicts Failure Load of the Spine with Simulated Osteolytic Defects*

Kelli M. Whealan, M.S., S. Daniel Kwak, Ph.D., John R. Tedrow, M.Eng., Kaoru Inoue, Ph.D.# and Brian D. Snyder, M.D., Ph.D.**

Investigation performed at the Orthopedic Biomechanics Laboratory, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts
*No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. Funds were received in total or partial support of the research or clinical study presented in this article. The funding sources were the Whitaker Foundation, National Institutes of Health Grant CA 40211-11, and the Children's Orthopaedic Surgery Foundation.
Read in part at the Annual Meeting of the Orthopaedic Research Society, Anaheim, California, February 3, 1999, and the Summer Bioengineering Conference of the American Society of Mechanical Engineers, Big Sky, Montana, 1999.
NuVasive, 10065 Old Grove Road, San Diego, California 92131.
Orthopedic Biomechanics Laboratory, Beth Israel Deaconess Medical Center, 330 Brookline Avenue, RN 115, Boston, Massachusetts 02215.
#Department of Occupational Therapy, College of Medical Technology, Hokkaido University, 060-0812 Sapporo, Japan.
**Department of Orthopaedic Surgery, Children's Hospital, Hunnewell 2, 300 Longwood Avenue, Boston, Massachusetts 02115. E-mail address: snyder_b{at}a1.tch.harvard.edu

	Abstract

Top Abstract Introduction Materials and Methods Results Discussion References

 
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.

	Introduction

Top Abstract Introduction Materials and Methods Results Discussion References

 
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 autopsy^30,35, 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 compromise^9,18.

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 threshold^1,5,10,24,33. 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 investigated^6,20,21,31. 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 strength^5,24,27. Bone mineral density as measured with dual-energy x-ray absorptiometry has also been shown to correlate with the failure load of intact vertebrae^2,7,26, 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 studies^{7,23,24,26,27}, 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 results^17,39. 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.

	Materials and Methods

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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.

View larger version (71K): [in this window] [in a new window]   Fig. 1: Computed tomography images showing the locations of the simulated defects. Anterior and lateral defects involved approximately 30 percent of the cross-sectional area of the vertebral body. Posterior defects involved pedicle destruction in lumbar vertebrae and costovertebral joint destruction in thoracic vertebrae.

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 investigators^31,34, 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, f_ash, 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 relationships^31,34. 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:

View larger version (85K): [in this window] [in a new window]   Fig. 2: Pixel-mapping algorithms. , are the coordinates of the modulus-weighted centroid, and da represents a single pixel with dimensions determined by the resolution of the computed tomography image. The density of each pixel was converted to elastic modulus from empirical relationships31,34, and the modulus-weighted pixels were summed with geometric measures to calculate rigidity (Equations 4, 5, and 6).

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 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:

View larger version (26K): [in this window] [in a new window]   Fig. 3: Dual-energy x-ray absorptiometry cross-sectional attenuation profile. The x-ray attenuation at each point along the scan path depends on the length and distribution of bone at x. BMD = bone mineral density, and dx = incremental element length.

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 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.

View larger version (50K): [in this window] [in a new window]   Fig. 4: Illustration of the hydraulic spine testing system39. The system applies combined forward flexion and axial compression simulating the action of bending to lift a heavy object. For the intact vertebrae, the instantaneous center of rotation is located along the posterior margin of the middle vertebral body. After failure occurred, the instantaneous center of rotation changed. Failure was defined as the load at which the relationship between axial load and forward flexion moment deviated from linearity. d.o.f. = degrees of freedom, and F = force.

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 is the yield strain (1 percent for trabecular bone in compression¹⁹), F_z is the axial compressive yield load, EA is the axial rigidity of the cross section with the minimum predicted failure load, M_y is the applied bending moment at yield (which is a function of F_z, 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 Ł 0.2) existed to test for significant differences between groups at a = 0.05.

	Results

Top Abstract Introduction Materials and Methods Results Discussion References

 
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.

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 Ł 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 Ł 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.

View larger version (19K): [in this window] [in a new window]   Fig. 5: The slope of the regression line for the correlation between the quantitative computed tomography (QCT)-predicted and the measured failure loads (Fz) was dependent on defect location (p = 0.023). Although the overall regression was good (r2 = 0.69), the correlative fit can be improved if confounding variables are considered.

View larger version (14K): [in this window] [in a new window]   Fig. 6: Concordance of predicted failure load by quantitative computed tomography (QCT) and measured failure load (Fz) about the y = x line (rc = 0.74).

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

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 load^17,39. 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 clinically^12,16,22, 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 data^22,28 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 model²⁹ it 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.

	References

Top Abstract Introduction Materials and Methods Results Discussion References

 

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