Mechanisms underlying rhythmic locomotion: interactions between activation, tension and body curvature waves

Abstract

SUMMARYUndulatory animal locomotion arises from three closely related propagating waves that sweep rostrocaudally along the body: activation of segmental muscles by motoneurons (MNs), strain of the body wall, and muscle tension induced by activation and strain. Neuromechanical models that predict the relative propagation speeds of neural/muscle activation, muscle tension and body curvature can reveal crucial underlying control features of the central nervous system and the power-generating mechanisms of the muscle. We provide an analytical explanation of the relative speeds of these three waves based on a model of neuromuscular activation and a model of the body-fluid interactions for leech anguilliform-like swimming. First, we deduced the motoneuron spike frequencies that activate the muscle and the resulting muscle tension during swimming in intact leeches from muscle bending moments. Muscle bending moments were derived from our video-recorded kinematic motion data by our body-fluid interaction model. The phase relationships of neural activation and muscle tension in the strain cycle were then calculated. Our study predicts that the MN activation and body curvature waves have roughly the same speed (the ratio of curvature to MN activation speedϷ0.84), whereas the tension wave travels about twice as fast. The high speed of the tension wave resulting from slow MN activation is explained by the multiplicative effects of MN activation and muscle strain on tension development. That is, the product of two slower waves (activation and strain) with appropriate amplitude, bias and phase can generate a tension wave with twice the propagation speed of the factors. Our study predicts that (1) the bending moment required for swimming is achieved by minimal MN spike frequency, rather than by minimal muscle tension; (2) MN activity is greater in the mid-body than in the head and tail regions; (3) inhibitory MNs not only accelerate the muscle relaxation but also reduce the intrinsic tonus tension during one sector of the swim cycle; and (4) movements of the caudal end are passive during swimming. These predictions await verification or rejection through further experiments on swimming animals.

Biological clockwork underlying adaptive rhythmic movements

“…It takes about one cycle for the crests of the body curvature to travel from head to tail (indicated by an arrow), resulting in one full wave in each snapshot. The speed of the traveling waves is roughly the same for the intersegmental progression of CPG membrane potentials but is much greater for the bending moment, consistent with the prediction previously derived from analysis of muscle, body, and fluid mechanics (37). The speed difference sets the timing of the moment and curvature in-phase near head, antiphase near tail, and 90°apart in the middle.…”

“…The instantaneous muscle power is proportional to the product of the moment and the rate of change of curvature, and hence the average power is roughly equal to zero near head and tail and is positive in the midbody. Consequently, the energy for swimming is mainly supplied by midbody muscles, and the tail end oscillates almost passively (37).…”

Using Computational and Mechanical Models to Study Animal Locomotion

“…4 In a computational swimmer with no sensory feedback, the neuromechanical phase lag changes with mechanical parameters (A) and frequency of tailbeat (B) and has an impact on swimming performance (C and D). revealed an anterior-to-posterior traveling wave of muscle activation that traveled faster than the kinematic wave, similar to organisms swimming in Newtonian fluids (Wardle et al 1995;Tytell et al 2010;Chen et al 2012). This ratio was independent of the volume fraction of the granular bed.…”

“…The local membrane potential is used to trigger the contraction of the cardiac muscle which drives the motion of the fluid. Chen et al (2011Chen et al ( , 2012 have developed a complete model of a swimming leech, including muscle activation, passive body tension, and fluid dynamics. Tytell et al (2010) performed similar immersed boundary simulations in which the activation of muscle fibers is used to propel a virtual lamprey through a fluid (discussed below).…”

Analytical insights into optimality and resonance in fish swimming

“…The muscle bending moments consist of active and passive components [20]. The active component (u 1 , u 2 ) results from the difference in antagonistic left/right muscle tensions and is directly controlled through motoneuron activation.…”