Load-relaxation properties of the human trunk in response to prolonged flexion: measuring and modeling the effect of flexion angle

Abstract

Experimental studies suggest that prolonged trunk flexion reduces passive support of the spine. To understand alterations of the synergy between active and passive tissues following such loadings, several studies have assessed the time-dependent behavior of passive tissues including those within spinal motion segments and muscles. Yet, there remain limitations regarding load-relaxation of the lumbar spine in response to flexion exposures and the influence of different flexion angles. Ten healthy participants were exposed for 16 min to each of five magnitudes of lumbar flexion specified relative to individual flexion-relaxation angles (i.e., 30, 40, 60, 80, and 100%), during which lumbar flexion angle and trunk moment were recorded. Outcome measures were initial trunk moment, moment drop, parameters of four viscoelastic models (i.e., Standard Linear Solid model, the Prony Series, Schapery's Theory, and the Modified Superposition Method), and changes in neutral zone and viscoelastic state following exposure. There were significant effects of flexion angle on initial moment, moment drop, changes in normalized neutral zone, and some parameters of the Standard Linear Solid model. Initial moment, moment drop, and changes in normalized neutral zone increased exponentially with flexion angle. Kelvin-solid models produced better predictions of temporal behaviors. Observed responses to trunk flexion suggest nonlinearity in viscoelastic properties, and which likely reflected viscoelastic behaviors of spinal (lumbar) motion segments. Flexion-induced changes in viscous properties and neutral zone imply an increase in internal loads and perhaps increased risk of low back disorders. Kelvin-solid models, especially the Prony Series model appeared to be more effective at modeling load-relaxation of the trunk.

Figure 1. Experimental setup for load-relaxation test (60% FR angle condition illustrated).

Figure 2. Illustration of a hysteresis loop.

The highlighted area (ΔE) denotes the dissipated energy; NZ in flexion (extension) is the distance between point A (point B) and the neutral posture. Target lumbar flexion angle = 30, 40, 60, 80, or 100% FR.

Figure 3. Illustration of two Kelvin-solid models: (a) SLS model (b) Prony Series model.

Each spring and damper in series represents a Maxwell model. For clarity, linear rather than rotational components are illustrated.

Figure 4. Effects of lumbar flexion angles on direct outcome measures: (a) initial moment, (b) moment drop, and (c) percentage change in normalized NZ.

Post-hoc groupings are indicated by brackets and letters, and best-fit exponential relationships are provided.

Figure 5. Mean measures of viscoelastic model prediction quality: (a) R ² and (b): root-mean-square errors (RMSE).

Figure 6. Effects of lumbar flexion angle on SLS model parameters: (a): stiffness of Maxwell component = K₁, (b): parallel stiffness = K₂, (c): relaxation time constant = T, and (d): instantaneous stiffness = K₁+K₂.

Post-hoc groupings are indicated by brackets and letters, and best-fit relationships (linear or exponential) are provided.

Figure 7. Fast and slow phases of moment drop during the load-relaxation period.

Representative data are shown, and which indicate the advantage of the Prony Series over the SLS model for predicting measured behaviors. Results are for a 100% FR exposure.