Introduction: Muscles play a critical role in supporting the spine during activities of daily living, owing, in part, to the phenomenon of short-range stiffness1,2. This property of muscle occurs in an active muscle when it is lengthened, and results in forces exceeding those predicted by the conventional force-length relationship3,4. Consequently, short-range stiffness has been proposed as a promising mechanism for imparting stability to spinal joints, because it occurs without any additional neural input5–9. However, previous investigations have only demonstrated this potential for static stability2,10,11 and there has not yet been a forward dynamic simulation to empirically demonstrate the stabilizing effect of this mechanism. In this study, we investigate whether Huxley-type muscle elements can effectively stabilize a joint while maintaining constant activation.
Methods: Our inquiry focused on assessing the stability of an inverted pendulum model (moment of inertia: 19.2 kg m2) supported by Huxley-type muscle models designed to emulate the short-range stiffness phenomenon (Figure 1A). We conducted a conventional stability analysis to determine the requisite muscle forces and stiffness that could confer adequate short-range stiffness to stabilize the system. Our simulations involved the application of a 50 ms long, 5 Nm square-wave perturbation, with numerical simulations executed using ArtiSynth12.
Results: Surprisingly, despite initial expectations of shared activation between antagonist and agonist muscles to maintain equilibrium, the inverted pendulum model exhibited instability and was unable to sustain an upright posture even with fully activated Huxley-type muscles (Figure 1B).
Figure 1: (A) Schematic diagram of the simple inverted pendulum model used in this investigation. It is supported on either side by Huxley-type muscle elements which portray this short-range stiffness phenomenon. (B) Angle over time following the 5 Nm perturbation (shaded blue region) for varying degrees of muscle activity. The dashed line indicates a stable upright equilibrium if stabilized by linear springs as is the case from static analysis.
Discussion: Our simulations have led us to conclude that muscle short-range stiffness alone may not be the sole contributor to joint stability, even in the face of modest perturbations. Instead, we propose an improved conceptual model for short-range stiffness, wherein active muscle behaves not as a simple spring but as a Maxwell element (a combination of spring and damper in series). We posit that the damping effect arising from short-range stiffness is instrumental in slowing down the mechanical response, thereby affording the central nervous system the time needed to react and stabilize the joint. Additionally, we speculate that other factors, such as residual force enhancement13, may also influence joint stability. Consequently, like other investigations14,15, we conclude that joint stability, especially in the context of spine biomechanics, appears to be complex and multifaceted, necessitating further research for a complete understanding.