Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations.

Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.

Oscillatory mechanisms in pairs of neurons connected with fast inhibitory synapses.

We study dynamical mechanisms underlying oscillatory behavior in reciprocal inhibitory pairs of neurons, using a two-dimensional cell model. We introduce one-and-two dimensional phase portraits to illustrate the behaviors, thus reducing the study of dynamical mechanisms to planar geometrical properties. We examined whether other mechanisms besides the escape and release mechanisms (Wang and Rinzel, 1992) might be needed for some cases of reciprocal inhibition, and show that, within the confines of a simple two-dimensional cell model, escape and release are sufficient for all cases. We divided the behaviors of a single cell into six different types and examined the joint behaviors arising from every combination of pairs of cells with behaviors drawn from these six types. For the case of two quiescent cells or two cells each having plateau potentials, bifurcation diagrams demonstrate the relations between synaptic threshold and synaptic strength necessary for oscillations by escape, oscillations by release, or network-generated plateau potentials. Thus we clarify the relationship between plateau potentials and oscillations in a cell. Using the two dimensional cell model we examine 1:N beating between cells and find that our simple model displays many of the essential dynamical properties displayed by more sophisticated models, some of which relate to thalamocortical spindling.

Synchronous bursting can arise from mutual excitation, even when individual cells are not endogenous bursters.

Mutual excitation between two neurons is generally thought to raise the excitation level of each neuron or, if they are both bursty, to act to synchronize their bursts. If only one is bursty, it can induce synchronized bursts in the other cell. Here we show that two nonbursty cells can be induced to burst in synchrony by mutual excitatory synaptic connections, provided the presynaptic threshold for graded synaptic transmission at each synapse is at a different level. This mechanism may operate in a recently discovered network in the lobster Homarus gammarus. By a duality between presynaptic threshold and injected current, we also show that two identical, nonbursty, mutual excitatory cells could be induced to burst in synchrony by injecting differing amounts of current in the two cells. Finally we show that differential oscillations between two mutual excitatory cells could be stopped by a slow-tailed hyperpolarizing current pulse into one cell or a slow-tailed depolarizing pulse into the other.

Synchronized action of synaptically coupled chaotic model neurons.

Experimental observations of the intracellular recorded electrical activity in individual neurons show that the temporal behavior is often chaotic. We discuss both our own observations on a cell from the stomatogastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models with chaotic neurons, building on models by Hindmarsh and Rose for bursting, spiking activity in neurons. The key feature of these simplified models of neurons is the presence of coupled slow and fast subsystems. We analyze the model neurons using the same tools employed in the analysis of our experimental data. We couple two model neurons both electrotonically and electrochemically in inhibitory and excitatory fashions. In each of these cases, we demonstrate that the model neurons can synchronize in phase and out of phase depending on the strength of the coupling. For normal synaptic coupling, we have a time delay between the action of one neuron and the response of the other. We also analyze how the synchronization depends on this delay. A rich spectrum of synchronized behaviors is possible for electrically coupled neurons and for inhibitory coupling between neurons. In synchronous neurons one typically sees chaotic motion of the coupled neurons. Excitatory coupling produces essentially periodic voltage trajectories, which are also synchronized. We display and discuss these synchronized behaviors using two "distance" measures of the synchronization.

Modeling the gastric mill central pattern generator of the lobster with a relaxation-oscillator network.

1. The gastric mill central pattern generator (CPG) controls the chewing movements of teeth in the gastric mill of the lobster. This CPG has been extensively studied, but the precise mechanism underlying pattern generation is not well understood. The goal of this research was to develop a simplified model that captures the principle, biologically significant features of this CPG. We introduce a simplified neuron model that embodies approximations of well-known membrane currents, and is able to reproduce several global characteristics of gastric mill neurons. A network built with these neurons, using graded synaptic transmission and having the synaptic connections of the biological circuit, is sufficient to explain much of the network's behavior. 2. The cell model is a generalization and extension of the Van der Pol relaxation oscillator equations. It is described by two differential equations, one for current conservation and one for slow current activation. The model has a fast current that may, by adjusting one parameter, have a region of negative resistance in its current-voltage (I-V) curve. It also has a slow current with a single gain parameter that can be regarded as the combination of slow inward and outward currents. 3. For suitable values of the fast current parameter and the slow current parameter, the isolated model neuron exhibits several different behaviors: plateau potentials, postinhibitory rebound, postburst hyperpolarization, and endogenous oscillations. When the slow current is separated into inward and outward fractions with separately adjustable gain parameters, the model neuron can fire tonically, be quiescent, or generate spontaneous voltage oscillations with varying amounts of depolarization or hyperpolarization. 4. The most common form of synaptic interaction in the gastric CPG is reciprocal inhibition. A pair of identical model cells, connected with reciprocal inhibition, oscillates in antiphase if either the isolated cells are endogenous oscillators, or they are quiescent without plateau potentials, or they have plateau potentials but the synaptic strengths are below a critical level. If the isolated cells have widely differing frequencies (or would have if the cells were made to oscillate by adjusting the fast currents), reciprocal inhibition entrains the cells to oscillate with the same frequency but with phases that are advanced or retarded relative to the phases seen when the cells have the same frequency. The frequency of the entrained pair of cells lies between the frequencies of the original cells. The relative phases can also be modified by using very unequal synaptic strengths.(ABSTRACT TRUNCATED AT 400 WORDS)