Evaluation of the Phase-Dependent Rhythm Control of Human Walking Using Phase Response Curves

Abstract

Humans and animals control their walking rhythms to maintain motion in a variable environment. The neural mechanism for controlling rhythm has been investigated in many studies using mechanical and electrical stimulation. However, quantitative evaluation of rhythm variation in response to perturbation at various timings has rarely been investigated. Such a characteristic of rhythm is described by the phase response curve (PRC). Dynamical simulations of human skeletal models with changing walking rhythms (phase reset) described a relation between the effective phase reset on stability and PRC, and phase reset around touch-down was shown to improve stability. A PRC of human walking was estimated by pulling the swing leg, but such perturbations hardly influenced the stance leg, so the relation between the PRC and walking events was difficult to discuss. This research thus examines human response to variations in floor velocity. Such perturbation yields another problem, in that the swing leg is indirectly (and weakly) perturbed, so the precision of PRC decreases. To solve this problem, this research adopts the weighted spike-triggered average (WSTA) method. In the WSTA method, a sequential pulsed perturbation is used for stimulation. This is in contrast with the conventional impulse method, which applies an intermittent impulsive perturbation. The WSTA method can be used to analyze responses to a large number of perturbations for each sequence. In the experiment, perturbations are applied to walking subjects by rapidly accelerating and decelerating a treadmill belt, and measured data are analyzed by the WSTA and impulse methods. The PRC obtained by the WSTA method had clear and stable waveforms with a higher temporal resolution than those obtained by the impulse method. By investigation of the rhythm transition for each phase of walking using the obtained PRC, a rhythm change that extends the touch-down and mid-single support phases is found to occur.

Exercise Promotes Neurite Extensions from Grafted Dopaminergic Neurons in the Direction of the Dorsolateral Striatum in Parkinson’s Disease Model Rats

“…Treadmill training started 7 days after the transplantation, 30 min per day, 5 days per week for 5 continuous weeks. According to some reports, the effect of treadmill training depends on the running velocity [23]. In the present study, the velocity was changed four times during the 30 min-treadmill training (15 cm/s for 10 min, 20 cm/s for 10 min 15 cm/s for 5 min, and 20 cm/s for 5 min) ( Fig.…”

Interaction mechanisms quantified from dynamical features of frog choruses

“…Here we use four datasets of the audio data in which all the frogs stably called more than 1400 times in four hours, allowing us to precisely estimate a phase oscillator model by utilizing the large sample size of call timing. [20][21][22][23] including alternating chorus patterns of male Japanese tree frogs [13][14][15]19]. In this study, we first calculate a phase φ n (t i ) (n = 1, 2, 3) with discrete time t i for the nth frog from the separated audio data according to Eq.…”

Data-driven spectral analysis for coordinative structures in periodic systems with unknown and redundant dynamics

“…We adopted this approach with the assumption that there are underlying dynamical systems or limit cycles behind the segmental angles during locomotion. In limit cycles, phase description has been developed for locomotion such as using local joint angles [47,48,49,13] or right heel-contact cycle as global description [50]. Compared with these studies, we extracted global phases at the gait frequency and at additional harmonic frequencies in a data-driven manner.…”

“…Second is related to our assumption that the walking dynamics is on a limit cycle. Actually, walking is sometimes not an ideal cyclic motion; thus we need a method adapting to rhythm shift and perturbation (observed as a phase reset in [47,50,48] and a phase locking in [49]). Our approach can theoretically describe an asymptotic phase in asymptotically stable dynamical systems [38,36]; therefore, it will be possible to apply it to the perturbed or more complicated locomotion [62,63].…”

“…In this study, we confirmed that the theoretical requirements are satisfied for locomotion data from the viewpoint of the convergence of estimation error. Although other locomotion studies obtained phase descriptions using local joint angles [47,48,49,13] or a global one [50], in this study, we obtain global phase descriptions with various frequencies from locomotion data at various speeds. Furthermore, we examine the difference and similarity between the conventional and our approaches by investigating the extracted dynamical information on the conventional coordinative structures.…”