Transmission of force in the lumbosacral spine during backward falls

Abstract

Study design: Mathematical model, combined with and verified using human subject data.

Objective: (1) To develop and verify a lumped-parameter mathematical model for prediction of spine forces during backward falls; (2) to use this model to evaluate the effect of floor stiffness on spine forces during falls; and (3) to compare predicted impact forces with forces previously measured to fracture the spine.

Summary of background data: Vertebral fractures are the most common osteoporotic fractures and commonly result from falls from standing height. Compliant flooring reduces the force at the ground during a backward fall from standing; however, the effect on spine forces is unknown.

Methods: A 6-df model of the body was developed and verified using data from 10 human subjects falling from standing onto 3 types of compliant floors (soft: 59 kN/m, medium: 67 kN/m, and firm: 95 kN/m). The simulated ground forces were compared with those measured experimentally. The model was also used to assess the effect of floor stiffness on spine forces at various intervertebral levels.

Results: There was less than 14% difference between model predictions and experimentally measured peak ground reaction forces, when averaged over all floor conditions. When compared with the rigid floor, average peak spine force attenuations of 46%, 43%, and 41% were achieved with the soft, medium, and firm floors, respectively (3.7, 3.9, 4.1 kN vs. 6.9 kN at L4/L5). Spine forces were lower than those at the ground and decreased cranially (4.9, 3.9, 3.7, 3.5 kN at the ground, L5/S1, L4/L5, and L3/L4, respectively, for the soft floor).

Conclusion: Lowering the floor stiffness (from 400 to 59 kN/m) can attenuate peak lumbosacral spine forces in a backward fall onto the buttocks from standing by 46% (average peak from 6.9 to 3.7 kN at L4/L5) to values closer to the average tolerance of the spine to fracture (3.4 kN).

Figure 1

Schematic of the lumped-parameter model used to calculate spine forces during a backward fall onto the buttocks. The upper body, L4, L5, sacrum, pelvis, and skin overlying the ischial tuberosities were modeled as masses separated by linear springs and dampers, which represented the L3/L4, L4/L5, L5/S1, sacroiliac joints, and the soft tissue overlying the ischial tuberosities (buttocks). The floor was represented as a linear spring.

Figure 2

Sample graph of the experimental ground force versus time for a typical trial (subject 4 falling onto the firm floor, stiffness of 95 kN/m, trial 2) showing key points for buttock stiffness and damping co-efficient calculations (first peak, second peak, and the valley between the first 2 peaks are shown with a circle, triangle, and square, respectively). The inset diagram shows the model used to determine buttock stiffness and damping (m: body mass, k: buttock stiffness coefficient, c: buttock damping coefficient). The simulated ground force for this trial is also shown (only the first peak in ground force was simulated, which was created with the 6-df model shown in Figure 1, not the single df model shown in the inset diagram).

Figure 3

Sample-simulated ground reaction and spine forces for a subject (number 4) falling with a velocity of 3.5 m/s onto floors with stiffnesses of 59 kN/m (soft) A, 67 kN/m (medium) B, 95 kN/m (firm) C, and 400 kN/m (rigid) D.

Figure 4

Average peak simulated ground and spine forces for 10 subjects falling at 3.5 m/s onto floors of 4 different stiffnesses. Standard deviations are shown with error bars. Experimentally measured average peak ground forces are also shown, which correspond to impact velocities between 2.5 and 4.1 m/s. The average tolerance (+/− 1 SD, shown with the shaded area) of the lumbosacral spine for a compression velocity of 0.2 m/s is also shown, which was extrapolated between tolerance values for compression velocities between 0.01 and 2.5 m/s.