TY - JOUR
T1 - Mechanisms underlying rhythmic locomotion: interactions between activation, tension and body curvature waves
JF - The Journal of Experimental Biology
JO - J. Exp. Biol.
SP - 211
LP - 219
DO - 10.1242/jeb.058669
VL - 215
IS - 2
AU - Chen, Jun
AU - Friesen, W. Otto
AU - Iwasaki, Tetsuya
Y1 - 2012/01/15
UR - http://jeb.biologists.org/content/215/2/211.abstract
N2 - Undulatory 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 speed ≈0.84), 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. a(f)activation factor for leech musclead(t)time course of activation factor of dorsal muscleai(t)activation factor at the ith body segmentav(t)time course of activation factor of ventral muscleadcolumn vector of discretized ad(t)avcolumn vector of discretized av(t)a*column vector of discretized ad(t) or av(t)CPGcentral pattern generatorDE-3dorsal excitatory motoneuron 3DE-5dorsal excitatory motoneuron 5EMGelectromyographicfmotoneuron spike frequencyfdnet spike frequency of MN activating the dorsal musclefvnet spike frequency of MN activating the ventral muscleh(x)strain factor in tension modelhd(t)time course of strain factor of dorsal muscle tensionhi(t)strain factor at the ith body segmenthv(t)time course of strain factor of ventral muscle tensionhdcolumn vector of discretized hd(t)hvcolumn vector of discretized hv(t)h*column vector of discretized hd(t) or hv(t)H*diagonal matrix with diagonal being h*LMIlinear matrix inequalityMNmotoneuronP(s)transfer function in muscle activation modelrhalf of body thicknessri, θiamplitude and phase of the fundamental harmonic component of the product of hi(t)ai(t)sLaplace variableTtension of leech body wallTd(t)time course of tension of dorsal muscleTv(t)time course of tension of ventral muscleTdcolumn vector of discretized Td(t)Tvcolumn vector of discretized Tv(t)T*column vector of discretized Td(t) or Tv(t)u(t)time course of muscle torqueucolumn vector of discretized u(t)xmuscle strainxdstrain of dorsal musclexvstrain of ventral muscleαstatic gain of the transfer function for muscle activationαi, βi, γiamplitude, phase and bias of activation factor in the tension model at the ith jointamplitude, phase and bias of strain factor in the tension model at the ith jointδphase difference between ai(t) and hi(t)εsmall perturbation parameterηlength constant of tension modelμpassive (tonus) tension at nominal swim length (i.e. x=0)ρratio of normalized amplitudes of ai(t) and hi(t)τ1time constant in muscle activationτ2time delay in muscle activationωoscillation frequency*representing dorsal or ventral muscle
ER -