Theoretical implications of the biomechanical fracture threshold

Abstract

Because of the dichotomous nature of a bone fracture, when Phi, the ratio of the applied impact force to the bone strength, is greater than a critical value--the biomechanical fracture threshold--fracture should occur. We sought to elucidate the conceptual implications of this biomechanical fracture threshold with application to hip fracture. We used data from the PaTH study, a 2-yr clinical trial in postmenopausal women treated with alendronate, PTH, or their combination. Outcomes included the force applied to the hip in a sideways fall as estimated from subject height and weight; femoral strength as determined by QCT-based finite element analysis; the load-to-strength ratio Phi; and total hip areal BMD from DXA. Results indicated that those with "very low" femoral strength (<2000 N) invariably had load-to-strength ratio Phi values well above the theoretical biomechanical fracture threshold (Phi = 1), but those with "moderately low" femoral strength (2000-4000 N) displayed Phi values both above and below the theoretical biomechanical fracture threshold. This finding implies that the risk of a hip fracture can be high in those with only moderately low BMD because femoral strength can be low relative to fall impact forces. The observed weak correlation between areal BMD and the load-to-strength ratio Phi (r2 = 0.14) suggests that consideration of the biomechanical fracture threshold may improve fracture risk assessment, particularly for those in the osteopenic range. Regarding treatment effects, only those subjects having load-to-strength ratio Phi values within a relatively narrow "transition zone" of +/- 20% of the assumed biomechanical fracture threshold at baseline were predicted to change fracture status during the trial. In theory, outcomes of fracture trials may be dominated by the responses of those within the "transition zone" at baseline, and treatment benefits in terms of fracture efficacy may depend the patient's baseline status with respect to the biomechanical fracture threshold. We conclude that consideration of the theoretical implications of the biomechanical fracture threshold may lead to new insights and advances in the assessment and treatment of osteoporosis.

FIG. 1

Baseline values of the load-to-strength ratio Φ plotted against femoral strength for a simulated fall to the side of the hip (n = 166). The moderate degree of scatter and the nonlinear nature of the relation indicates that subjects with “very low” bone strength (<2000 N) are highly likely to be above the theoretical fracture threshold (dashed line) but that subjects with “moderately low” bone strength (2000–4000 N) can fall above or below the fracture threshold.

FIG. 2

The weak but significant (r ² = 0.14, p < 0.001) relation between Φ at baseline and areal BMD (total hip) at baseline (n = 166). The dashed line shows the theoretical biomechanical fracture threshold (Φ = 1). The solid lines separate categories of osteoporotic (T-score < −2.5; n = 23), osteopenic (−2.5 < T-score < −1.0, n = 121), and normal (T-score > −1.0, n = 22) patients, based on the T-score values of the total hip areal BMD values. Most individuals (∼75%) in this cohort were above the theoretical biomechanical fracture threshold.

FIG. 3

QCT-based FE-calculated strength of the femur for a sideways fall versus total hip areal BMD by DXA (n = 166).

FIG. 4

Plot of Φ at baseline vs. Φ at 24-mo follow-up (n = 166). Data from the PaTH cohort, all treatments pooled, simulated fall to the side of the hip. Values below the Y = X line show a positive benefit of treatment on bone strength. During the course of the trail, subjects in the indicated boxes moved either below or above the theoretical biomechanical fracture threshold (assumed value Φ = 1.0 shown with dashed lines). All such subjects had baseline Φ values within a “transition zone” range of about 0.8–1.2. Altogether, there were 77 subjects within the transition zone at baseline.