A coupled oscillator model of disordered interlimb coordination in patients with Parkinson’s disease
Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan.Biological Cybernetics (Impact Factor: 1.71). 03/2003; 88(2):152-62. DOI: 10.1007/s00422-002-0371-9
Coordination between the left and right limbs during cyclic movements, which can be characterized by the amplitude of each limb's oscillatory movement and relative phase, is impaired in patients with Parkinson's disease (PD). A pedaling exercise on an ergometer in a recent clinical study revealed several types of coordination disorder in PD patients. These include an irregular and burst-like amplitude modulation with intermittent changes in its relative phase, a typical sign of chaotic behavior in nonlinear dynamical systems. This clinical observation leads us to hypothesize that emergence of the rhythmic motor behaviors might be concerned with nonlinearity of an underlying dynamical system. In order to gain insight into this hypothesis, we consider a simple hard-wired central pattern generator model consisting of two identical oscillators connected by reciprocal inhibition. In the model, each oscillator acts as a neural half-center controlling movement of a single limb, either left or right, and receives a control input modeling a flow of descending signals from higher motor centers. When these two control inputs are tonic-constant and identical, the model has left-right symmetry and basically exhibits ordered coordination with an alternating periodic oscillation. We show that, depending on the intensities of these two control inputs and on the difference between them that introduces asymmetry into the model, the model can reproduce several behaviors observed in the clinical study. Bifurcation analysis of the model clarifies two possible mechanisms for the generation of disordered coordination in the model: one is the spontaneous symmetry-breaking bifurcation in the model with the left-right symmetry. The other is related to the degree of asymmetry reflecting the difference between the two control inputs. Finally, clinical implications by the model's dynamics are briefly discussed.
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- "However, indices used for summarizing gait alterations in a quantitative manner have usually been found poorly correlated with the severity of disease (Yogev et al., 2007; Plotnik and Hausdorff, 2008). This discrepancy is likely due to the complex and probably non-linear neural networks that are involved in generating and maintaining rhythmic, symmetric, and coordinated walking (Plotnik and Hausdorff, 2008), including higher motor centers, such as the basal ganglia, spinal central pattern generators, and reflexes that are related to ground contact (Grillner and Wallén, 1985; Asai et al., 2003). Alternatively, this finding might be attributed to difficulties in mathematically modeling the clinical loss of gait ―kinetic melody‖ in patients with PD. "
ABSTRACT: Objective: Recently, an intrinsic fractal harmonic structure was found underlying the rhythm of physiological walking, but it has not yet been investigated in subjects with a neurological disease. The aim of this study was to determine if and how this harmonic structure is altered in patients with Parkinson's Disease. Methods: Gait analysis of 70 patients with Parkinson's Disease in pharmacological phase on was performed, the findings of which we compared with reference data of age-matched healthy subjects. Fifteen patients were retested after a washout period of 12h. Results: Alterations in all spatio-temporal gait parameters and gait indices with regard to symmetry, coordination, and harmony were noted, but after correction for multicollinearity bias, only the latter correlated significantly with Unified Parkinson's Disease Rating Scale motor score (p=0.001). The fractal gait structure underwent even more extensive alterations in pharmacological off phase (p<0.05). Conclusions: The intrinsic gait harmony was altered in patients with Parkinson's Disease and significantly correlated to motor severity. It could be partially recovered by assumption of L-dopa. Significance: Loss of harmony is a quantitatively assessable gait benchmark in Parkinson's Disease. It seems to be dependent on dopaminergic but also on non-dopaminergic networks.
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- "In addition, neurophysiological modeling studies have shown that salient stability-related phenomena in interlimb coordination (e.g., in-phase being more stable than antiphase; frequency-induced transitions between movement patterns) can arise in a system of two coupled neural oscillators in the absence of afferent feedback, yielding a dynamical account of integrated timing (Asai et al. 2003; Grossberg et al. 1997). However, afference-based interlimb interactions have also been demonstrated, e.g., in the form of effects of passive limb movements on the stability of rhythmic interlimb coordination (Serrien et al. 2001; Stinear and Byblow 2001; Swinnen et al. 1995). "
ABSTRACT: Three sources of interlimb interactions have been postulated to underlie the stability characteristics of bimanual coordination but have never been evaluated in conjunction: integrated timing of feedforward control signals, phase entrainment by contralateral afference, and timing corrections based on the perceived error of relative phase. In this study, the relative contributions of these interactions were discerned through systematic comparisons of five tasks involving rhythmic flexion-extension movements about the wrist, performed bimanually (in-phase and antiphase coordination) or unimanually with or without comparable passive movements of the contralateral hand. The main findings were the following. 1) Contralateral passive movements during unimanual active movements induced phase entrainment to interlimb phasing of either 0 degrees (in-phase) or 180 degrees (antiphase). 2) Entrainment strength increased with the passive movements' amplitude, but was similar for in-phase and antiphase movements. 3) Coordination of unimanual active movements with passive movements of the contralateral hand (kinesthetic tracking) was characterized by similar bilateral EMG activity as observed in active bimanual coordination. 4) During kinesthetic tracking the timing of the movements of the active hand was modulated by afference-based error corrections, which were more pronounced during in-phase coordination. 5) Indications of in-phase coordination being more stable than antiphase coordination were most prominent during active bimanual coordination and marginal during kinesthetic tracking. Together the results indicated that phase entrainment by contralateral afference contributed equally to the stability of in-phase and antiphase coordination, and that differential stability of these patterns depended predominantly on integrated timing of feedforward signals, with only a minor role for afference-based error corrections.
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ABSTRACT: In our recent reports motor coordination of human lower limbs has been investigated during pedaling a special kind of ergometer which allows its left and right pedals to rotate independently. In particular, relative phase between left and right rotational-velocity waveforms of the pedals and their amplitude modulation have been analyzed for patients with Parkinson's disease (PD). Several patients showed peculiar interlimb coordination different from the regular anti-phase pattern of normal subjects. We have reported that these disordered patterns could be classified into four groups. Moreover, it has been demonstrated that a mathematical model could reproduce most of the disordered patterns. Such a model includes a schematization of the central pattern generator with two identical half-centers mutually coupled and two tonic control signals from higher motor centers, each of which inputs to one of the half-centers. Depending on the intensities of the tonic signals and on the differences between them, the model could generate a range of dynamics comparable to the clinically observed disordered patterns. In this paper, we explore the dynamics of the model by varying the intensities of the tonic signals in the model. Using the same method used for classifying the clinical data, the dynamics of the model are classified into several groups. The classified groups for the simulated data are compared with those for the clinical data to look at qualitative correspondence. Our systematic exploration of the model's dynamics in a wide range of the parameter space has revealed global organization of the bifurcations including Hopf bifurcations and cascades of period-doubling bifurcations among others, suggesting that the bifurcations, induced by instability of stable dynamics of the human motor control system, are responsible for the emergence of the disordered coordination in PD patients.
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