Parkinsonian Tremor and Simplification in Network Dynamics

Abstract

We explore the behavior of richly connected inhibitory neural networks under parameter changes that correspond to weakening of synaptic efficacies between network units, and show that transitions from irregular to periodic dynamics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnecting loops of the brain's motor circuitry, which involve many inhibitory connections, exhibit such transitions. Normal physiological tremor is irregular while other forms of tremor show more regular oscillations. Tremor in Parkinson's disease, for example, stems from weakened synaptic efficacies of dopaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in Parkinson's disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in the network models are suggestive of akinesia in Parkinson's disease. This model is consistent with the view that normal physiological systems can be regulated by robust and richly connected feedback networks with complex dynamics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior.

Understanding Parkinsonian Handwriting Through a Computational Model of Basal Ganglia

“…Under dopaminedeficient conditions, the output of the network changes from a fixedpoint attractor state to a periodic, tremulous state resembling Parkinsonian tremor. Edwards, Beuter, and Glass (1999) presented a network model of Parkinsonian tremor that can exhibit transition from irregular tremor to regular oscillations. A preliminary model of BG-related movement disorders was proposed by Mitchel, Brotchie, and Crossman (1991).…”

Modeling the Parkinson's tremor and its treatments

“…There are a few computational simulations, done by other researchers concerned with the main symptoms of PD (Fukumoto 1986;Asai et al, 2003;Edwards and Beuter, 1999;Titcombe et al, 2001). Fukumoto assumes that fatigue of intrafusal fibers, which results from chronic stimulation by the gamma system, is the main cause of Parkinsonian tremor and presents a mathematical model based on this assumption.…”

“…There are a few computational simulations, concerned with the main symptoms as tremor (Titcombe et al, 2001;Edwards and Beuter, 1999;Asai et al, 2003). Titcombe et al have designed a Hopf bifurcation model which had a response similar to tremor behavior under DBS.…”

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