Biomechanics of vertebral level, geometry, and transcortical tumors in the metastatic spine

Article Outline

• Abstract
• 1. Introduction
• 2. Materials and methods
• 3. Results
  • 3.1. Model optimization and validation
  • 3.2. Vertebral geometry
  • 3.3. Transcortical tumors
• 4. Discussion
  • 4.1. Vertebral geometry
  • 4.2. Transcortical tumors
• Acknowledgements
• References
• Copyright

Abstract 

Metastatic involvement can disrupt the mechanical integrity of the spine, rendering vertebrae susceptible to burst fracture and neurologic damage. Fracture risk assessment for patients with spinal metastases is important in considering prophylactic treatment options. Stability of thoracic vertebrae affected by metastatic disease has been shown to be dependent on tumor size and bone density, but additional structural and geometric factors may also play a role in fracture risk assessment. The objective of this study was to use parametric finite element modeling to determine the effects of vertebral level, geometry, and metastatic compromise to the cortical shell on the risk of burst fracture in the thoracic spine. Analysis of vertebral level and geometry was assessed by investigation of seven scenarios ranging in geometry from T2–T4 to T10–T12. The effects of cortical shell compromised were assessed by comparison of four transcortical scenarios to a fully contained central vertebral body tumor scenario. Results demonstrated that upper thoracic vertebrae are at greater risk of burst fracture and that kyphotic motion segments are at decreased risk of burst fracture. Vertebrae with transcortical lesions are up to 30% less likely to lead to burst fracture initiation. The findings of this study are important for improving the understanding of burst fracture mechanics in metastatically involved vertebrae and guiding future modeling efforts.

Keywords: Spine, Metastases, Geometry, Kyphosis, Burst fracture, Finite element

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1. Introduction 

Metastatic involvement to the spine occurs in as many as one-third of all cancer patients (Wong, 1990). When cancer cells migrate to the spine, the mechanical integrity of the vertebral bone is compromised, rendering the vertebra susceptible to fracture. In metastatically involved vertebrae, a common pattern of failure is burst fracture, which is commonly characterized by destruction of the posterior wall of the vertebral body with potential for retropulsion of bone or tumor fragments into the spinal canal. This type of fracture can lead to severe and often irreversible neurologic complications due to the proximity to the spinal cord and nerve roots. Therefore, fracture risk assessment of metastatically compromised vertebrae may be useful in directing prophylactic treatment and maintaining optimum quality of life for patients affected by spinal metastases.

The anatomy of the thoracic spine varies considerably between subsequent levels. Anatomic variability associated with changes in thoracic level arises from changes in vertebral size and shape, endplate angles, disc height, kyphotic angle, and articular facet joint orientation. Previous work has indicated that failure load is decreased for vertebrae in the upper thoracic spine (Messerer, 1880; White and Panjabi, 1992). However, this work did not examine the mechanics of pathologic burst fracture. Patient-specific differences seen in morphology within a specific vertebral level may also affect burst fracture risk. With improved understanding of the effects of vertebral geometry, the risk of burst fracture in patients with spinal anomalies may be better understood.

Metastatic disease may also involve compromise of the vertebral cortical shell. Previous works have investigated the effect of transcortical lesions on failure load (Silva et al., 1993; Taneichi et al., 1997), indicating that increased cortical shell disruption decreases failure load in metastatic vertebrae. However, direct comparisons of failure loads of transcortical lesions to fully contained tumors and the specific effect of cortical shell destruction on burst fracture risk have not been investigated.

The objective of this study was two-fold:

The hypothesis of this work is that vertebral geometry/level and metastatic compromise of the cortical shell will be important factors impacting the risk of burst fracture initiation in the metastatic spine.

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2. Materials and methods 

A three-dimensional parametric model of a metastatically involved spinal motion segment was developed and analyzed using commercial software (Truegrid 2.1.5, XYZ Scientific Applications, Livermore, CA, I-DEAs 8m3, UGS, Plano, TX, ABAQUS/Standard 6.3.1, ABAQUS Inc., Pawtucket, RI). Previous studies have demonstrated the importance of modeling the spine using poroelasticity in order to represent the mechanics of burst fracture in the metastatic spine (Whyne et al., 2001). Accordingly, all materials, excluding the posterior elements, were represented biphasically with the fluid phase defined as incompressible with the properties of water (Bryant et al., 1989; Hong et al., 1998) (Table 1). The posterior elements were not modeled biphasically as they are relatively nonporous in comparison to the anterior column (Argoubi and Shirazi-Adl, 1996). Vertebral body trabecular bone was modeled as transversely isotropic (Kopperdahl and Keaveny, 1998; Mosekilde et al., 1987; Silva et al., 1997). The intervertebral disc consisted of the nucleus pulposus and annulus fibrosis, modeled as elastic and hyperelastic materials (Duncan and Lotz, 1998). Finally, the collagen fibers in the annulus were modeled as hypoelastic rebar reinforcement (Shirazi-Adl et al., 1986).

Table 1. Finite element model material properties

Anisotropic elastic
Material	Elastic modulus (MPa)	Poisson's ratio	Shear modulus (MPa)	Permeability (mm/s)
Trabecular bone—low density	33.3, 33.3, 100	0.1, 0.1, 0.1	15.14, 30.28, 30.28	100
Isotropic elastic
Material	Elastic modulus (MPa)	Poisson's ratio	Permeability (mm/s)
Cortical bone	1000	0.3	9.97E−14
Cartilaginous endplate	25	0.1	6.98E−09
Nucleus pulposus	1	0.499	1.00E−09
Posterior elements	1000	0.3	na
Isotropic hyperelastic
Material	Method of definition	Permeability (mm/s)
Tumor	Mooney-Rivlin strain energy	5.88E−06
Annulus fibrosis	Polynomial strain energy function	2.50E−09
Hypoelastic rebar
Material	Method of definition
Collagen	Tangent modulus matrix
Ligaments
Material	Elastic modulus (MPa)	Poisson's ratio	Cross-sect. area (mm2)
Anterior longitudinal	20	0.3	38
Posterior longitudinal	70	0.3	20
Ligamenal flavum	50	0.3	60
Intertransverse ligament	50	0.3	10
Supraspinous ligament	28	0.3	35.5

Silva et al. (1997), Kopperdahl and Keaveny (1998), Mosekilde et al. (1987), Nauman et al. (1999), Hong et al. (1998), Bryant et al. (1989), Brown and Vrahas (1984), Argoubi and Shirazi-Adl (1996), Lotz et al. (1995), Simon et al. (1985), Whyne et al. (2000), Duncan and Lotz (1998), Shirazi-Adl et al. (1986).

Mesh density optimization and validation were conducted by parametrically adjusting the model to represent L1 in order to allow comparisons to experimental data available for this level (Whyne et al., 2003a, Whyne et al., 2003b). The experimental work tested 12 cadaveric spinal motion segments, consisting of an entire L1 vertebra, adjacent intervertebral discs with simulated metastases, under axial loads of 800 and 1200N applied at a rate of 16,000N/s (Whyne et al., 2003a, Whyne et al., 2003b). Average tumor volume in the cadaveric specimens was 17.9% vertebral body volume. Accordingly, the finite element model was analyzed with 17.9% tumor volume and parameters were adjusted to the average dimensions of those measured for the specimens. Boundary conditions were applied such that the model constraints were equivalent to that of the experimental protocol. Load-induced canal narrowing (LICN) was used to compare the model results to the experimental data (Whyne et al., 2003a, Whyne et al., 2003b). Mesh density was varied systematically to determine the required density to ensure repeatability of the outcome parameters.

To analyze the effect of thoracic level on risk of burst fracture initiation, the parametric model was analyzed with geometric scenarios representing motion segments from T2–T4 to T10–T12. Vertebral geometry was defined based on average dimensions available in the literature (Fig. 1, Table 2) (Berry et al., 1987; Panjabi et al., 1991, Panjabi et al., 1993; Pooni et al., 1986). For all scenarios, a serrated central tumor was defined as 24% vertebral body volume, which has been clinically identified as an approximate threshold for burst fracture initiation (Roth et al., 2004).

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• Fig. 1. 

  Selected thoracic vertebral parametric dimensions. SCD, spinal canal depth; SCW, spinal canal width; SPD, spinous process depth; TVPW, transverse process width; TVPD, transverse process depth; TVPHt, transverse process height; VBHt, vertebral body height; VBW, vertebral body width; VBD, vertebral body depth; PHt, pedicle height; PW, pedicle width; MVBW, mid-vertebral body width; IVBW, inferior vertebral body width; IVBD, inferior vertebral body depth; IPA, inferior process angle; SPA, superior process angle.

Table 2. Quantitative three-dimensional vertebral morphology applied to finite element model

SuPAs, superior process sagittal angle; SCD, spinal canal depth; IPAs, inferior process sagittal plane angle; IVBD, inferior vertebral body depth; MVBD, mid-vertebral body depth; load, axial compressive load; IPAt, inferior process transverse plane angle; VBD, vertebral body depth; SuPHt, superior process height; VBHt, vertebral body height; IVBW, inferior vertebral body width; VBW, vertebral body width; IPHt, inferior process height; TVPW, transverse process width; MVBW, mid-vertebral body width; IPW, inferior process width; PHt, pedicle height; SuPAt, superior process transeverse plane angle; PW, pedicle width; SuPW, superior process width; SCW, spinal canal width; and SpPD, spinous process depth. All units are in mm unless otherwise described. ¹Panjabi et al. (1991), ²Panjabi et al. (1993), ³Berry et al. (1987).

Average vertebral endplate angles are approximately 2° (Panjabi et al., 1991). The model was analyzed with endplate angles in this range and compared to zero endplate angle. The normal kyphotic angle of the thoracic spine is 35° and is distributed over approximately seven vertebra (White and Panjabi, 1992), averaging 5° per vertebra. Consequently, the kyphotic angle between sequential vertebrae was set to 5° to investigate the effect of kyphosis (in addition to endplates angle of 2°) on burst fracture risk and compared to the model incorporating parallel endplates and discs. Since kyphotic angle is larger for upper thoracic vertebrae, vertebral angles were applied to the T3 motion segment (Fig. 2). Axial loads were applied based on the approximation that the load due to bodyweight on successive thoracolumbar vertebrae increases in the inferior direction by 2.4% for each level (Schultz et al., 1982).

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• Fig. 2. 

  Finite element mesh of T3 with applied vertebral angles. Endplate angles (EPAs) ranged from 0° to 2° and kyphotic angle (KA) ranged from 0° to 5°.

Transcortical tumor scenarios were analyzed with metastatic lesions in lateral, anterior, anterolateral, and posterolateral locations of a T7 motion segment (Fig. 3). Disruption of the cortical shell was represented by modifying material properties of the cortical shell elements to cartilaginous properties at the outer portion of the metastatic neoplasm (Whyne et al., 2003a). These scenarios were compared to a central tumor scenario to determine the effects of cortical shell disruption on vertebral stability. Axial loads of 691N were applied at a rate of 16,000N/s, which is the approximate load at T7 from lifting of 3.83kg with outstretched arms (Schultz et al., 1982).

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• Fig. 3. 

  Transverse cross-section of tumor location scenarios modeled in this study. Each tumor volume was defined as 24% vertebral body volume.

Risk of burst fracture initiation was assessed by vertebral bulge (VB) and LICN. VB is a measure of the change in length of the vertebral body along the intersection of sagittal and transverse planes to assess relative motion between the anterior and posterior vertebral body walls. LICN is a similar measure of the decrease in anterior–posterior length of the canal to assess posterior wall motion relative to posterior elements. These parameters, particularly VB, have been found to be excellent predictors of burst fracture risk in a retrospective clinical study by Roth et al. (2004). To normalize for vertebral size differences, VB and LICN were also expressed as a ratio of VB to vertebral depth (nVB) and LICN as a ratio of canal depth (nLICN). For parametric analysis, correlation coefficients were calculated for all vertebral parameters with respect to VB and LICN. In considering transcortical tumors, risk assessment was also based on posterior wall tensile hoop strain (PWTHS) and vertebral body trabecular bone pore pressure (POR), which have demonstrated correlation to VB and LICN (Whyne et al., 2003a, Whyne et al., 2003b).

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3. Results 

3.1. Model optimization and validation 

Mesh density optimization was conducted from 6172 to 19,540 continuum elements. Repeatability errors were less than 0.6% for all scenarios with a mesh density of 9672 elements or greater. Consequently, the final mesh selected for computational analyses was equivalent to the density of the L1 model with 10,612 elements. The final mesh of the thoracic spinal motion segment comprised 19,712 20-noded hexahedral elements, 13 truss elements, and 92,189 nodes. In comparing model results to previously reported experimental data, values for canal narrowing were within ranges seen in the axially loaded cavaderic specimens. Differences in canal narrowing of the finite element model for 1200 and 800N loads were within 1.23% of the averaged experimental data.

3.2. Vertebral geometry 

T3 exhibited the largest VB and LICN (0.469 and 0.242mm, respectively). The smallest VB resulted from loading of T5 and T7 (0.359 and 0.386mm, respectively). In comparison to T3, T5 and T7 scenarios also exhibited 30.0% and 31.4% decreases in LICN, respectively. An increase in 2° in endplate angles of T3 led to a 6.59% decrease in VB and a 2.38% decrease in LICN in comparison to the parallel endplate and disc scenario. An increase in 5° in kyphotic angle and 2° in endplate angle yielded decreases in VB and LICN of 7.29% and 4.34% in comparison to scenarios with changes in endplate angles alone. Normalized VB decreased inferiorly for each vertebral segment. Normalized LICN was only noticeably different for T3, which yielded 27.8% greater nLICN than any other level (Table 3).

Table 3. Effects of vertebral level on vertebral bulge (VB) and load-induced canal narrowing (LICN)

VB and LICN were normalized for vertebral size by the vertebral body depth (nVB) and spinal canal depth (nLICN), respectively. The effects of 2° endplate angle (EPA) and 5° kyphotic angle (KA) were reported using geometry of the T3 motion segment.

Vertebral dimensions were correlated to VB and LICN to investigate the effects of specific vertebral geometry on burst fracture risk (Table 4). Highest positive correlations to VB were exhibited with spinous process depth, spinal canal width, superior process width, and applied pressure load, while largest negative correlations were exhibited with superior process sagittal angle, spinal canal depth, inferior process sagittal angle, and inferior vertebral body depth.

Table 4. Correlation coefficients for vertebral dimensions relative to VB and LICN

Acronyms are consistent with Table 5.2.1. FLOAD and PLOAD refer to applied force and applied pressure respectively. VB vol refers to vertebral body volume and Disc Ht refers to average intervertebral disc height of the spinal motion segment.

3.3. Transcortical tumors 

The central tumor scenario led to the largest PWTHS (1.06E-02). Transcortical tumor scenarios led to an average decrease in PWTHS of 25.8% in comparison to PWTHS exhibited from the central tumor scenario. The area of cortical destruction was largest with the posterolateral transcortical tumor scenario (range 131–294mm²). For transcortical tumor scenarios, cross-sectional area of cortical shell destruction was negatively correlated with PWTHS (correlation ).

All scenarios simulating metastatic tumors resulted in increased VB (range 0.283–2.06mm). All scenarios also led to increased LICN (range 0.034–0.166mm); however, transcortical tumors were associated with an average decrease in LICN of 66.8% (range 42.8–79.3%) in comparison to a central tumor scenario. With destruction of the cortical shell, trabecular bone POR decreased by an average of 68.0% in the metastatically involved vertebra (range 53.6–77.4%) (Table 5).

Table 5. Effects of transcortical tumors on VB, LICN, and PWTHS

Vol depicts the volume of the tumor as a percent of the vertebral body volume. Trans area is a measure of the area of cortical shell destroyed by metastatic tumor. POR is a measure of the maximum nodal pore pressure of the trabecular bone of the metastatically involved vertebra.

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4. Discussion 

4.1. Vertebral geometry 

The first objective of this study was to quantify the effects of vertebral geometry in the thoracic spine on the risk of burst fracture initiation. The results indicate that T3 is at the greatest risk of pathologic burst fracture initiation amongst all levels analyzed in this study. Resulting normalized VB decreased from upper thoracic to lower thoracic, even with increased applied loads for lower vertebrae. This indicates that upper vertebrae are at greater risk of burst fracture initiation than lower segments. Previous findings of the intact spine have also indicated that lower thoracic vertebrae exhibit increased failure load and that T3 exhibits the smallest failure load in the thoracic spine (Messerer, 1880; White and Panjabi, 1992). This may be better understood with consideration to specific parametric differences between vertebrae.

The relation between specific vertebral parameters may be useful in assessment of patients with anatomical spinal anomalies. Correlation studies indicated that vertebrae with increased spinal canal width were associated with increased VB. Conversely, vertebrae with increased spinal canal depth exhibited decreased VB. This may be a consequence of the increase in moment of inertia associated with the increase in spinal canal depth. This is analogous to the increased strength of an ellipsoidal strut along its larger radius. LICN exhibited the same correlation trend as VB with lower magnitude.

During the analyses performed in this study, numerous parameters were varied concurrently to represent geometric differences corresponding to a change in vertebral level. Thus, effects exhibited by certain parameters may not necessarily be reflective of their individual geometric impact on VB or LICN, but be confounded by their relation to other parameters changing simultaneously. This may explain the findings of several parameters, such as the spinous process depth and facet angles, which exhibited strong correlations to VB and LICN, but have no obvious mechanical explanation. Relatively strong correlations for some quantities may motivate more specific studies. Analyses with a single parameter manipulation are required to confirm whether these specific effects are causal or a result from a combination of other parametric changes with vertebral level.

The results of the current study indicated the increased thoracic kyphotic angle is associated with decreased VB and LICN. This may be due to the change in loading mechanism for curved segments. Alteration of kyphotic angle changes the direction of the force vector with respect to the restrained inferior face, creating a moment about the bottom of the motion segment. The results in this study demonstrated that axial loading was the principle load type contributing to burst fracture initiation. Consequently, alteration of load type caused by increase in kyphotic angle may explain the decrease in VB exhibited in the kyphotic spinal motion segment.

The results of this study indicate that spinal segment scenarios with nonparallel endplates lead to a decrease in VB and LICN. Increasing the endplate angle led to a consequent decrease in vertebral body volume since these parameters are mutually dependent. Modest negative correlation to VB and LICN was found for vertebral body volume (correlation coefficients were −0.168 and −0.381, respectively). Therefore, consequent vertebral body volume changes with increased endplate angles do not appear to be affecting the results in VB. A similar mutual dependence exists between kyphotic angle and average disc height between vertebrae. Increases in kyphotic angles led to consequent decreases in average disc height. Small negative correlations were found for disc height with respect to VB and LICN (correlation coefficients were −0.041 and −0.205, respectively). Therefore, the effects of kyphotic angle on VB are not likely affected by changes in disc height.

Several previous finite element models of the spine have been created assuming parallel endplates (Lu et al., 1996; Kim, 2001; Whyne et al., 2003a; Wilcox et al., 2004; Tschirhart et al., 2004). The results of this study provide a quantitative value of this approximation, which may be useful in directing future modeling efforts. Consequently, future finite element analyses of spine models may not require specific incorporation of vertebral angles, which can be a labor-intensive task, but rather use the results of the current study to assess the impact of the assumption.

The results of this study also have considerable clinical importance in that patients affected by spinal metastases in T3 may be at greater risk of burst fracture. It is recognized, however, that burst fracture may not necessarily lead to neurological deficit, particularly if the capacity of the canal is larger relative to the size of the spinal cord. At T3, this is the case relative to T9 (which has the least reserve). The results indicate that the anatomical parameters in comparing T3 to T9, compensate for the increased burst fracture risk at T3, due to vertebral geometry, which provides increased spinal canal reserve. The risk of burst fracture may be greater, but the risk of neurological consequence may be less.

4.2. Transcortical tumors 

The second objective of these analyses was to quantify the effects of transcortical lytic lesions on burst fracture initiation in comparison to a central tumor volume contained within the vertebral body. Depending on tumor location, radial displacement is affected by displacement of the uncontained tumor through the disrupted cortical shell. For example, VB is very large with anterior transcortical tumor placement due to compromise of the anterior shell, however this is not likely indicative of increased prospect for burst fracture initiation since the majority of motion is through the anterior wall. Consequently, risk of burst fracture was assessed by PWTHS and LICN, which are the least biased quantifiable measures for evaluation of burst fracture initiation with cortical shell compromise.

Reduced PWTHSs were demonstrated for the uncontained tumor scenarios as compared to the central scenario. Similarly, transcortical tumor scenarios exhibited decreased LICN in comparison to the contained tumor scenario. This would indicate that the prospect for developing pain due to canal narrowing is decreased for patients with noncontained tumors. Cortical shell destruction by tumor tissue led to a decrease in pressurization within the vertebral body under load. The disrupted cortical shell allows the reduction of pressure as the tumor bulges from the vertebral body. There was also an increase in PWTHS exhibited by the anterolateral tumor scenario in comparison to other transcortical scenarios, which may be explained by the lesser amount of transcortical destruction in this scenario.

Previous studies have investigated the effects of tumor location on fracture risk. Silva et al. (1993) tested vertebra with void defects and similar cortical shell disruption in anterior, posterior, and lateral vertebral body locations and compared these findings to lesions within the pedicle. Vertebral strength reductions were similar for all vertebral body lesions, however lesions within the pedicle led to less strength reduction. Silva et al. (1993) also reported that relative strength reduction decreased with increased size of the cortical defect, which contrasts the findings of the current study. However, correlations were weak in comparison to the current study ( vs. ) and no consideration was given to mechanism of failure. In addition, cortical shell disruption was not independent of defect size and no comparison was made to fully contained vertebral body lesions.

Whealan et al. (2000) analyzed the effects of tumors in contained anterior locations and transcortical lateral locations in an in vitro study. The results of this study indicated a similar prospect for burst fracture with transcortical lateral lesions; however, simulation of contained lesions involved compromise of the cortical shell with injection of simulated tumor tissue. Consequently, there was a pressure loss from the vertebral body for all simulated tumor scenarios, thus decreasing the prospect for pathologic burst fracture due to increased vertebral body pressurization.

Tschirhart et al. (2004) reported that tumor location affected burst fracture initiation, as posterior vertebral body tumors were associated with approximately 30% increased VB in comparison to central tumors. However, no scenarios were investigated with disruption of the cortical shell. The results of the current study indicate that tumor location is not as significant once the cortical shell has been compromised. Rather, the risk of burst fracture initiation is dependent on the amount of cortical shell disruption due to changes in POR within the vertebral body. Increased cortical shell disruption actually decreases the prospect for burst fracture initiation. It appears that transcortical involvement is protective for the burst fracture, but is significant for the risk of mechanical instability and consequent pain. Treatment would be indicated for this as opposed to the additional need to address neurological compromise.

Finite element modeling of transcortical tumors is more complex and computationally expensive than analyzing contained tumor volumes. However, understanding the mechanics of both types of tumor scenarios is important since both occur clinically and can lead to burst fracture.

This study was focused on the pre-failure biomechanical stability of the metastatically involved spine. Consequently, the results describe the events only leading up to the initiation of, but not including, the actual fracture. Finite element techniques used previously to predict the failure behavior of bones have demonstrated that models incorporating material and geometric nonlinearities can facilitate accurate assessment of fracture loads and fracture patterns (Lotz et al., 1991). Thus, while the analysis in this study is appropriate for studying factors that influence the risk of fracture initiation, this approach cannot be used to address issues pertaining to the subsequent fracture itself.

In summary, the results of this study provide quantitative assessment of the effects of vertebral level, geometry, ribcage, and transcortical tumors. Upper thoracic vertebrae were found to be at increased risk of burst fracture with metastatic involvement in comparison to lower thoracic vertebral levels. Increased kyphotic angles exhibited decreased risk of pathologic burst fracture initiation. The ribcage provided reduction in risk of burst fracture initiation. Finally, transcortical tumor scenarios investigated in this study resulted in decreased risk in initiation of burst fracture. These findings are important in facilitating improved understanding of burst fracture mechanics of the thoracic spine, and motivating more informed clinical decision-making regarding treatment of patients with spinal metastases.

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Acknowledgements 

Support for this work was provided by Natural Sciences and Engineering Research Council of Canada (NSERC).

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References 

1. Argoubi M, Shirazi-Adl A. Poroelastic creep response analysis of a lumbar motion segment in compression. Journal of Biomechanics. 1996;29(10):1331–1339
   • View In Article
   • Abstract
   • Full-Text PDF (1234 KB)
   • CrossRef
2. Berry JL, Moran JM, Berg WS, Steffee AD. A morphometric study of human lumbar and selected thoracic vertebrae. Spine. 1987;12(4):362–367
   • View In Article
   • MEDLINE
   • CrossRef
3. Brown TD, Vrahas MS. The apparent elastic modulus of the juxtarticular subchondral bone of the femoral head. Journal of Orthopaedic Research. 1984;2(1):32–38
   • View In Article
4. Bryant JD, David T, Gaskell PH, King S, Lond G. Rheology of bovine bone marrow. Proceedings of the Institution of Mechanical Engineers. 1989;203:71–75
   • View In Article
5. Duncan NA, Lotz JC. Experimental validation of a porohyperelastic finite element model of the annulus fibrosis. Computer Methods in Biomechanics and Biomedical Engineering—2. London: Gordon and Breach Science Publishers; 1998;pp. 527–534
   • View In Article
6. Hong JH, Ah JH, Lim TH, An HS. Correlation among permeability, apparent density, and porosity of human lumbar vertebral trabecular bone. New Orleans: Transactions of the 44th Annual Meeting: Orthopaedic Research Society; 1998;
   • View In Article
7. Kim Y. Prediction of mechanical behaviors at interfaces between bone and two interbody cages of lumbar spine segments. Spine. 2001;26(13):1437–1442
   • View In Article
   • MEDLINE
   • CrossRef
8. Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. Journal of Biomechanics. 1998;31(7):601–608
   • View In Article
   • Abstract
   • Full Text
   • Full-Text PDF (139 KB)
   • CrossRef
9. Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models: part I—linear analysis. Journal of Biomechanical Engineering. 1991;113(4):353–360
   • View In Article
   • MEDLINE
   • CrossRef
10. Lotz JC, Glazer PA, Gryler EC. Tensile properties of the human vertebral endplate. Helsinki, Finland: The 22nd Annual Symposium of the International Society for the Study of the Lumbar Spine; 1995;
    • View In Article
11. Lu YM, Hutton WC, Gharpuray VM. Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse?. A viscoelastic finite element model. Spine. 1996;21(22):2570–2579
    • View In Article
12. Messerer O. Uber elasticitat und festig kei der Meuschhichen knoclion. Buchhandling: Stutgart, J.G. Cattaschen; 1880;
    • View In Article
13. Mosekilde L, Mosekilde L, Danielsen CC. Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone. 1987;8(2):79–85
    • View In Article
    • MEDLINE
    • CrossRef
14. Nauman EA, Fong KE, Keaveny TM. Dependence of intertrabecular permeability on flow direction and anatomic site. Annals of Biomedical Engineering. 1999;27(4):517–524
    • View In Article
    • MEDLINE
    • CrossRef
15. Panjabi MM, Takata K, Goel V, Federico D, Oxland T, Duranceau J, et al. Thoracic human vertebrae. Quantitative three-dimensional anatomy. Spine. 1991;16(8):888–901
    • View In Article
    • MEDLINE
    • CrossRef
16. Panjabi MM, Oxland T, Takata K, Goel V, Duranceau J, Krag M. Articular facets of the human spine. Quantitative three-dimensional anatomy. Spine. 1993;18(10):1298–1310
    • View In Article
    • MEDLINE
    • CrossRef
17. Pooni JS, Hukins DWL, Harris PF, Hilton RC, Davies KE. Comparison of the structure of human intervertebral discs in the cervical, thoracic, and lumbar regions of the spine. Surgical-Radiologic Anatomy. 1986;8(3):175–182
    • View In Article
18. Roth SE, Mousavi P, Finkelstein J, Chow E, Kreder H, Whyne CM. Metastatic burst fracture risk prediction using biomechanically based equations. Clinical Orthopaedics and Related Research. 2004;419:83–90
    • View In Article
    • CrossRef
19. Schultz A, Andersson G, Ortengren R, Haderspeck K, Nachemson A. Loads on the lumbar spine. Validation of a biomechanical analysis by measurements of intradiscal pressures and myoelectric signals. Journal of Bone and Joint Surgery—American Volume. 1982;64(5):713–720
    • View In Article
20. Shirazi-Adl A, Ahmed AM, Shrivastava SC. A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. Journal of Biomechanics. 1986;19(4):331–350
    • View In Article
    • MEDLINE
    • CrossRef
21. Silva MJ, Hipp JA, McGowan DP, Takenchi T, Hayes WC. Strength reductions of throracic vertebra in the presence of transcortical osseous defects: effect of defect location, pedicle disruption, and defect size. European Spine Journal. 1993;2:118–125
    • View In Article
22. Silva MJ, Keaveny TM, Hayes WC. Load sharing between the shell and centrum in the lumbar vertebral body. Spine. 1997;22(2):140–150
    • View In Article
    • MEDLINE
    • CrossRef
23. Simon BR, Wu JSS, Carlton MW, Kazarian LE, France EP, Evans JH, et al. Poroelastic dynamic structural models of rhesus spinal motion segments. Spine. 1985;10(6):494–507
    • View In Article
    • MEDLINE
    • CrossRef
24. Taneichi H, Kaneda K, Takeda N, Abumi K, Satoh S. Risk factors and probability of vertebral body collapse in metastases of the thoracic and lumbar spine. Spine. 1997;22(3):239–245
    • View In Article
    • MEDLINE
    • CrossRef
25. Tschirhart CE, Nagpurkar A, Whyne CM. Effects of tumour location, shape and surface serration on burst fracture risk in the metastatic spine. Journal of Biomechanics. 2004;37(5):653–660
    • View In Article
    • Abstract
    • Full Text
    • Full-Text PDF (633 KB)
    • CrossRef
26. Whealan KM, Kwak SD, Tedrow JR, Inoue K, Snyder BD. Noninvasive imaging predicts failure load of the spine with simulated osteolytic defects. Journal of Bone and Joint Surgery—American Volume. 2000;82(9):1240–1251
    • View In Article
27. White AA, Panjabi MM. Clinical Biomechanics of the Spine. second ed. Philadelphia, PA: JB Lippincott Company; 1992;
    • View In Article
28. Whyne CM, Hu SS, Workman KL, Lotz JC. Biphasic material properties of lytic bone metastases. Annals of Biomedical Engineering. 2000;28(9):1154–1158
    • View In Article
    • MEDLINE
    • CrossRef
29. Whyne CM, Hu SS, Lotz JC. Parametric finite element analysis of vertebral bodies affected by tumors. Journal of Biomechanics. 2001;34(10):1317–1324
    • View In Article
    • Abstract
    • Full Text
    • Full-Text PDF (292 KB)
    • CrossRef
30. Whyne CM, Hu SS, Lotz JC. Biomechanically derived guideline equations for burst fracture risk prediction in the metastatically involved spine. Journal of Spinal Disorders & Techniques. 2003;16(2):180–185
    • View In Article
    • MEDLINE
    • CrossRef
31. Whyne CM, Hu SS, Lotz JC. Burst fracture in the metastatically involved spine: development, validation, and parametric analysis of a three-dimensional poroelastic finite-element model. Spine. 2003;28(7):652–660
    • View In Article
    • CrossRef
32. Wilcox RK, Allen DJ, Hall RM, Limb D, Barton DC, Dickson RA. A dynamic investigation of the burst fracture process using a combined experimental and finite element approach. European Spine Journal. 2004;13:481–488
    • View In Article
33. Wong DA, Fornasier VL, MacNab I. Spinal metastases: the obvious, the occult, and the impostors. Spine. 1990;15(1):1–4
    • View In Article
    • MEDLINE
    • CrossRef