A coupled oscillator model of disordered interlimb coordination in patients with Parkinson's disease.
ABSTRACT 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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ABSTRACT: Complex-valued Hopfield network is used to model the dynamics of a network of limit cycle oscillators, each of which emerges via Hopf bifurcation, to investigate the dependency of the network dynamics on a bifurcation parameter. As an application, a network of two complex-valued neurons is used as a central pattern generator model for a biped locomotion. A bifurcation parameter is a constant input from higher motor centers. Numerical calculations show the system successfully expresses some characteristic behaviors, which were obtained by more complicated Fitzhugh-Nagumo oscillator model, and which were found in clinical data of disordered interlimb coordination caused by Parkinson's disease. The observed results of symmetric anti -phase synchronization, asymmetric synchronization, and breakdown of the synchronization can be explained by the existence condition of the energy function of the complex-valued neural network, and by the synchronization condition of a coupled system of phase oscillators.Neural Networks, 2007. IJCNN 2007. International Joint Conference on; 09/2007
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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.Biosystems 09/2003; 71(1-2):11-21. · 1.58 Impact Factor
- The Japanese Journal of Rehabilitation Medicine 01/2006; 43(5):315-321.