G. Pfister

Most effective stimulation site in subthalamic deep brain stimulation for Parkinson's disease

The optimal stimulation site in subthalamic deep brain stimulation (STN‐DBS) was evaluated by correlation of the stereotactic position of the stimulation electrode with the electrophysiologically specified dorsal STN border. In a series of 25 electrodes, best clinical results with least energy consumption were found in contacts located in the dorsolateral border zone, whereas contacts within the subthalamic white matter, e.g., zona incerta, were significantly less effective. We suggest that the dorsolateral STN border should be covered by STN‐DBS.

Multiple oscillators are causing parkinsonian and essential tremor

The tremors of Parkinsons disease (PD) and essential tremor (ET) are traditionally considered to depend on a central oscillator producing rhythmic activation of the motoneurones of all extremities. To test this hypothesis, we have compared electromyographic tremor activity in different muscles of the affected limbs using cross spectral analysis, including coherence and phase. Surface electromyographic recordings from both arms, legs, and the neck were analyzed in 22 patients with PD and 28 patients with ET. Volume conduction between neighboring muscles producing artificial “coherence” has been found to be an important methodologic problem. We have developed a mathematical test to exclude data that could distort the results. According to this test, 10% or 25% of muscle combinations from the same limb had to be excluded from further analysis in PD or ET, respectively. In both, patients with PD and ET, we found a considerable number of muscle combinations oscillating at virtually the same frequency (▵ frequency <0.4 Hz) without showing a significant coherence. Thus, the frequency difference between different muscles is not sufficient to measure the correlation between two muscles. Significant coherencies between muscles within the same arm or leg were found in 70% or 90% of patients with PD or ET, respectively, whereas only one patient with PD and not a single patient with ET showed significant coherencies between muscles from different limbs. The phase between coherent muscles of the same arm of patients with PD showed a preference of either a reciprocal alternating pattern for antagonistic muscles in forearm flexor and upper arm extensor as opposed to a co‐contraction pattern between the hand flexors and the triceps brachii. In patients with ET such clear differences were lacking. We conclude that multiple oscillators are responsible for the tremor in different extremities of patients with PD and ET. Differences between PD and ET concerning the phase relation within the arm may either be related to the topography within the basal ganglia or to differently involvedspinal pathways.

Extracting model equations from experimental data

This letter wants to present a general data-driven method for formulating suitable model equations for nonlinear complex systems. The method is validated in a quantitative way by its application to experimentally found data of a chaotic electric circuit. Furthermore, the results of an analysis of tremor data from patients suffering from Parkinsons disease, from essential tremor, and from normal subjects with physiological tremor are presented, discussed and compared. They allow a distinction between the different forms of tremor.

Bifurcation phenomena in Taylor-Couette flow in a very short annulus

We present the results of an experimental and numerical investigation into Taylor-Couette flow with gap-length to width ratios (Γ = l / d ) ranging from 0.3 to 1.4. Laser-Doppler-velocimetry is used to obtain quantitative information on the bifurcation set experimentally, and novel flow phenomena are uncovered. These results are compared with those obtained using numerical bifurcation techniques applied to a finite-element discretization of the Navier-Stokes equations. In general, the agreement is good and most of the observations are satisfactorily explained.

Optimal Reconstruction of Strange Attractors from Purely Geometrical Arguments

A method to obtain the best delay time for the reconstruction of chaotic attractors in phase space is presented. The procedure uses purely geometrical considerations and guarantees a maximum distance of trajectories. This is tested with numerical (Duffing oscillator) and experimental (Taylor-Couette flow) systems by calculating correlation dimensions and Lyapunov spectra.

Space-dependent order parameter in circular couette flow transitions

Abstract We show that in circular Couette flow (i) for the transition to steady Taylor-vortex flow and (ii) for the transition to time-dependent wavy-vortex flow a space-dependent order parameter obeys a Ginzburg-Landau-type equation. Our measurements allow extrapolation of the critical Reynolds numbers to infinitely long cylinders.

End effects on the transition to time‐dependent motion in the Taylor experiment

Laser‐Doppler velocimetry has been used to measure the critical Reynolds number for the onset of time‐dependent motion and its characteristic features in Taylor‐Couette flow. For moderate values of the aspect ratio Γ the critical Reynolds number is observed to be extremely sensitive to length effects, and the form of oscillation arising at the stability limit is found to change in neighboring ranges of Γ. At even higher Reynolds number the oscillation type may change and hysteresis phenomena are observed. These new features are beyond the reach of any available theory and they highlight the need for caution when transition to turbulence observations are interpreted.

Flow in a small annulus between concentric cylinders

Rotationally symmetric vortex flows between concentric cylinders with the inner one rotating and the outer one at rest have been investigated by numerical simulation and by laser-Doppler velocimetry for an annulus of aspect ratio Γ = 1.05 with a radius ratio η = 0.5066. Stationary states and relaxation towards them were explored close to the transition from the primary flow, which is mirror symmetric with respect to the midplane of the annulus, to a flow which gradually loses the symmetry. Detailed comparison of numerically simulated and measured velocity fields is made.

Delay estimation for cortico-peripheral relations.

In neurophysiology, time delays between concurrently measured time series are usually estimated from the slope of a straight line fitted to the phase spectrum. We point out that this estimate is valid only in the case in which, one signal is a mere time-delayed copy of the other one. We present a procedure for delay estimation that applies to a much wider class of systems with nontrivial phase spectrum like for example lowpass filters. The procedure is based on the Hilbert transform relation between the phase of a linear system and its log gain. The Hilbert transform relation is nonlocal in frequency space, a fact that limits its applicability to experimental data. We explore these limits, and demonstrate that the method is applicable to neurophysiological time series. We present the successful application of the Hilbert transform behavior method to concurrently recorded epicortical brain activity and peripheral tremor. We point out and explain physiologically unreasonable delay estimates given by the traditional method. Finally, we discuss the assumptions underlying the applicability of the Hilbert transform method in the neuroscience context.

Mutual information and global strange attractors in Taylor-Couette flow

Abstract We apply a new method for the estimation of the mutual information M to experimental time series from different locations in weakly turbulent Taylor-Couette flow. We observe a dependence of M on the partition scale e and find M (e) ∞ DM log (1/e) for small e and sufficient embedding dimension m. Our results confirm, that the overall dynamics of the Taylor-Couette flow is dominated by a global strange attractor of fractal information dimension D 1 = D M at moderate Reynolds numbers. The dimension estimates obtained by our method are found to be more reliable than results from dimension algorithms based on single measurements alone, a fact which makes our method most attractive for dimension analysis in extended systems.