Torsional stiffness and strength of the proximal tibia are better predicted by finite element models than DXA or QCT

Abstract

Individuals with spinal cord injury experience a rapid loss of bone mineral below the neurological lesion. The clinical consequence of this bone loss is a high rate of fracture around regions of the knee. The ability to predict the mechanical competence of bones at this location may serve as an important clinical tool to assess fracture risk in the spinal cord injury population. The purpose of this study was to develop, and statistically compare, non-invasive methods to predict torsional stiffness (K) and strength (Tult) of the proximal tibia. Twenty-two human tibiae were assigned to either a "training set" or a "test set" (11 specimens each) and mechanically loaded to failure. The training set was used to develop subject-specific finite element (FE) models, and statistical models based on dual energy x-ray absorptiometry (DXA) and quantitative computed tomography (QCT), to predict K and Tult; the test set was used for cross-validation. Mechanical testing produced clinically relevant spiral fractures in all specimens. All methods were accurate and reliable predictors of K (cross-validation r(2)≥0.91; error≤13%), however FE models explained an additional 15% of the variance in measured Tult and illustrated 12-16% less error than DXA and QCT models. Given the strong correlations between measured and FE predicted K (cross-validation r(2)=0.95; error=10%) and Tult (cross-validation r(2)=0.91; error=9%), we believe the FE modeling procedure has reached a level of accuracy necessary to answer clinically relevant questions.

Figure 1

A frontal plane cut-through view of the QCT regions (Epi, Met, Dia) of interest for a representative specimen. Yellow pixels superimposed on the image correspond to integral, trabecular and cortical regions of bone.

Figure 2

(a) Proximal tibia being loaded in internal rotation using the linear actuated torsional device. (b) Lateral view of a proximal tibia illustrating a spiral fracture pattern (see arrows).

Figure 3

Representative torque-rotation curve (solid line) illustrating the linear elastic projection (dashed line) used to calculate stiffness K, and the point on the curve corresponding to ultimate strength T_ult.

Figure 4

Anteriomedial view of a representative FE model illustrating the distribution of axial moduli E₃ on the surface (left) and internal (right) elements.

Figure 5

Anteriomedial views of a representative FE model illustrating maximum principal strain and progression of surface element failure (i.e., ε_max>1.41%). The FE predicted T_ult corresponded to the torque at which 10% of the surface elements had failed.

Figure 6

The predicted torsional stiffness K and strength T_ult for the training set (open circles) and test set (closed circles) plotted against the actual measured values. Regression equations and coefficients of variation are for the test set. All slopes and intercepts were not significantly different from unity and zero, respectively (p<0.05).

Figure 7

Measured (solid line) and FE predicted (dashed) torque-rotation curves for representative specimens illustrating relatively good fits (left) and relatively poor fits (right). The point of predicted fracture is labeled with an X.