Directional Dependence of Experimental Trunk Stiffness: Role of Muscle-Stiffness Variation of Nonneural Origin

Abstract

Trunk stiffness is an important parameter for trunk stability analysis and needs to be evaluated accurately. Discrepancies regarding the dependence of trunk stiffness on the direction of movement in the sagittal plane suggest inherent sources of error that require explanation. In contrast to the common assumption that the muscle stiffness remains constant prior to the induction of a reflex during position perturbations, it is postulated that muscle-stiffness changes of nonneural origin occur and alter the experimental trunk stiffness, causing it to depend on the sagittal direction. This is confirmed through reinterpretation of existing test data for a healthy subject, numerical simulation, and sensitivity analysis using a biomechanical model. The trunk stiffness is determined through a static approach (in forward and backward directions) and compared with the model stiffness for assumed scenarios involving deactivated muscles. The difference in stiffness between the opposite directions reaches 17.5% without a preload and decreases when a moderate vertical preload is applied. The increased muscle activation induced by preloads or electrical stimuli explains the apparent discrepancies observed in previous studies. The experimental stiffness invariably remains between low and high model-stiffness estimates based on extreme scenarios of the postulated losses of muscle activation, thereby confirming our hypothesis.

Numerical Identification of Deep Muscle Residual Tensions (Tones) Based on Multi-Directional Trunk Stiffness Data

“…The data consist of the experimental trunk stiffness measured along different directions for the sample population who participated in the original work [18]. A numerical biomechanical model [10] of the trunk is used to calculate the trunk stiffnesses depending on the muscle tones taken as input parameters. The identification procedure solves the boundaries of the domain of feasible tone values by matching the tone-dependent model stiffness with the experimental stiffness taken as a reference.…”

“…Details on the experimental protocol relative to the multidirectional trunk test, and the relevant ethical and safety considerations, are given in [18]. A numerical musculoskeletal trunk model [10] is used to calculate the upper and lower bounds of the trunk flexural stiffnesses in five different directions. The domain of possible tone values, or equivalent RMTTs, is narrowed down by locating the experimental trunk stiffness [18] relative to those bounds.…”

“…The vertebrae, the intervertebral discs, the sternum, and the ribs are represented by beam elements and the ligaments are modeled as linear springs. Each muscle is represented by its tensile force and stiffness while taking into account the unilateral behavior of the muscle-tendon complex [10]. The maximum active force of a muscle is evaluated proportionally to its largest physiological cross-sectional area (PCSA).…”

“…On the other hand, muscle tone levels influence the behavior of the trunk. Through a sensitivity analysis, [2,10] showed the model trunk flexural stiffness to be significantly influenced by the muscle tones, treated as model parameters. This finding suggests that accurate estimation of muscle tone is helpful for a better assessment of trunk behavior.…”

“…For the deep muscles, unlike traditional intrusive means of tone measurement, this method is painless and safe for the subject. The identification procedure is intended to capture the properties of the hardly accessible deep muscles, through the association of experimental trunk stiffness data with numerical simulation of the biomechanical trunk system behavior [10].…”