Elsevier

Bone

Volume 33, Issue 4, October 2003, Pages 744-750
Bone

Original article
Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography

https://doi.org/10.1016/S8756-3282(03)00210-2Get rights and content

Abstract

The correlation between bone mineral density and vertebral strength is not based on mechanical principles and thus the method cannot reflect the effects of subtle geometric features and densitometric inhomogeneities that may substantially affect vertebral strength. Finite element models derived from quantitative computed tomography (QCT) scans overcome such limitations. The overall goal of this study was to establish that QCT-based “voxel” finite element models are better predictors of vertebral compressive strength than QCT measures of bone mineral density with or without measures of cross-sectional area. QCT scans were taken of 13 vertebral bodies excised from 13 cadavers (L1–L4; age: 37–87 years; M = 6, F = 7) and used to calculate bone mineral density (BMDQCT). The QCT voxel data were converted into linearly elastic finite element models of each vertebra, from which measures of vertebral stiffness and strength were computed. The vertebrae were biomechanically tested in compression to measure strength. Vertebral strength was positively correlated with the finite element measures of strength (r2 = 0.86, P < 0.0001) and stiffness (r2 = 0.82, P < 0.0001), the product of BMDQCT and vertebral minimum cross-sectional area (r2 = 0.65, P = 0.0008), and BMDQCT alone (r2 = 0.53, P = 0.005). These results demonstrate that highly automated “voxel” finite element models are superior to correlation-based QCT methods in predicting vertebral compressive strength and therefore offer great promise for improvement of clinical fracture risk assessment.

Introduction

Noninvasive measurements of bone mineral density are central to the diagnosis and management of osteoporosis. However, quantitative computed tomography (QCT)-based estimates of bone mineral density have generally only shown modest correlations (r2 = 0.49–0.69) to in vitro measurements of vertebral strength [1], [2], [3]. Not surprisingly, vertebral bone mineral density alone is limited in differentiating between patients with and without vertebral fractures [4]. These limitations necessitate that clinical studies enroll hundreds and sometimes thousands of patients and follow them for many years to develop sufficient statistical power for analyses of disease and treatment effects [5], [6]. More accurate metrics should improve diagnosis and management of osteoporosis and may provide a more sensitive and therefore more timely measure of the effects of therapeutic interventions.

Although a wealth of literature exists on correlations between bone mineral density and vertebral strength [1], [2], [3], [7], [8], [9], [10], [11], [12], several theoretical considerations undermine the use of bone mineral density alone as a surrogate for vertebral strength. Bone mineral density is an integral value of material content and therefore cannot reflect the potentially important effects of subtle geometric and structural differences [9], [13] and densitometric inhomogeneities [14], [15] on vertebral strength. Studies that directly compared dual energy x-ray absorptiometry (DXA) and QCT found that both techniques were similarly correlated with the fracture strength of vertebral bodies (r2 = 0.49–0.74) [1], [2], [3]. However, other studies found that QCT is better than DXA in clinically assessing bone loss [16], [17] and fracture risk [16], [17], [18]. All these techniques possess limited generality because of their empirical nature.

Finite element models derived from QCT scans may improve predictions of vertebral strength because they mechanically integrate all the geometrical and material property data within the scans. Such QCT-based finite element models have found successful use in strength prediction of the proximal femur [19], [20], [21], and for the spine they have been used to investigate the theoretical effects of vertebroplasty [22], disc degeneration [23], and bone density [23], [24] on fracture risk. While one study found that geometry-based finite element models (r2 = 0.79) were a better predictor of vertebral strength than CT-derived estimates of density (r2 = 0.67) [25], an important consideration for clinical implementation is the extent to which the model generation can be automated from clinical QCT scans. The so-called voxel method [20], [23], [24], in which QCT voxels are converted directly into finite elements, is most attractive in this respect. Voxel-based finite element models of vertebrae [23], [24] have not been validated by any in vitro experiments and thus their advantage over QCT-derived bone mineral density is unclear.

The goal of this study was to establish that voxel-based finite element models predict vertebral compressive strength better than measures of QCT-derived bone mineral density and geometry. We used QCT scans to develop clinical measures of bone mineral density and patient-specific finite element models of a series of cadaveric thoracolumbar vertebrae. We then compared predictions of the strength of the vertebrae generated from the finite element models and those derived from analysis of the QCT scans alone against the in vitro measurements of the vertebral compressive strength.

Section snippets

QCT scanning

Data from 17 isolated vertebrae taken from 17 cadavers (T11–L4; age: 20–87 years; males = 8, females = 9) were used from a previous experiment [26]. In those experiments, the intervertebral disc material was removed from both endplates, and the posterior elements were removed by sectioning through the pedicles with an autopsy saw. Quantitative computed tomography scans were taken of the vertebral bodies using a clinical scanner (GE 9800; General Electric, Milwaukee, WI, USA: 140 kV, 70 mA, 1.5

Results

The finite element model-derived regression variables (FFE and KFE) showed better correlations with compressive strength than either the product of BMDQCT and Amin or BMDQCT alone (Table 1 and Fig. 4 ). All of the explanatory variables and fracture strength were positively correlated with one another (P < 0.005) to varying degrees (0.71 < r < 0.95; Table 2). The explanatory variables had a significant effect on the absolute value of the regression residual (P = 0.01). The mean of the absolute

Discussion

These results demonstrate that voxel-based finite element model-derived estimates of strength are better predictors of in vitro vertebral compressive strength than clinical measures of bone density derived from QCT with or without geometry. While BMDQCT is well correlated (r2 = 0.91) with the elastic modulus of machined specimens of vertebral trabecular bone [31], (volumetric) bone mineral density by itself does not reflect any structural information of the whole vertebra. Finite element models

Acknowledgements

Funding was provided by grants from the National Institutes of Health (AR41481) and the National Science Foundation (BES-9625030). The National Disease Research Interchange (NDRI) and the Willed Body Program of UCSF provided the human tissue used in these experiments. The authors would like to acknowledge Dr. Peter Bacchetti for his guidance on statistical issues, Dr. David Kopperdahl for his work in the QCT scanning and mechanical testing of the vertebrae, and Mr. Jesse Lanzon for his

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