The causal relationship between subcortical local field potential oscillations and Parkinsonian resting tremor

Abstract

To study the dynamical mechanism which generates Parkinsonian resting tremor, we apply coupling directionality analysis to local field potentials (LFP) and accelerometer signals recorded in an ensemble of 48 tremor epochs in four Parkinsonian patients with depth electrodes implanted in the ventro-intermediate nucleus of the thalamus (VIM) or the subthalmic nucleus (STN). Apart from the traditional linear Granger causality method we use two nonlinear techniques: phase dynamics modelling and nonlinear Granger causality. We detect a bidirectional coupling between the subcortical (VIM or STN) oscillation and the tremor, in the theta range (around 5 Hz) as well as broadband (>2 Hz). In particular, we show that the theta band LFP oscillations definitely play an efferent role in tremor generation, while beta band LFP oscillations might additionally contribute. The brain-->tremor driving is a complex, nonlinear mechanism, which is reliably detected with the two nonlinear techniques only. In contrast, the tremor-->brain driving is detected with any of the techniques including the linear one, though the latter is less sensitive. The phase dynamics modelling (applied to theta band oscillations) consistently reveals a long delay in the order of 1-2 mean tremor periods for the brain-->tremor driving and a small delay, compatible with the neural transmission time, for the proprioceptive feedback. Granger causality estimation (applied to broadband signals) does not provide reliable estimates of the delay times, but is even more sensitive to detect the brain-->tremor influence than the phase dynamics modelling.

Granger causality with signal-dependent noise

“…When the tremor occurs, both AR and AR-BEKK models identify the causal influence from brain to tremor. However, the AR-BEKK model also detects a feedback from tremor to brain which has been broadly reported in the literatures (Smirnov et al, 2008;Tass et al, 2010). A significant influence from brain to tremor at around 4 Hz is spotted which is also consistent with the previous findings (Wu et al, 2008).…”

Suppression of spontaneous oscillations in high-frequency stimulated neuron models

“…Tremor-related theta band oscillations are typically no pronounced feature in LFP recordings, presumably since different neuronal subpopulations belonging to different limbs oscillate with time varying phase and frequency relationships [41,43,44]. Nevertheless, with nonlinear data analysis tools it was shown that theta band (3-7 Hz) LFP oscillations drive the peripheral tremor [45].…”

Method of estimation of synchronization strength between low-frequency oscillations in heart rate variability and photoplethysmographic waveform variability

“…Instantaneous phases of oscillating systems appear to be most sensitive to appearance of weak coupling between systems [44,45,[60][61][62]. In this case, with coupling increasing the first changes in system dynamics take place in the phases and only afterwards they can be detected in the amplitudes.…”