Differential recordings of local field potential: A genuine tool to quantify functional connectivity

Abstract

Local field potential (LFP) recording is a very useful electrophysiological method to study brain processes. However, this method is criticized for recording low frequency activity in a large area of extracellular space potentially contaminated by distal activity. Here, we theoretically and experimentally compare ground-referenced (RR) with differential recordings (DR). We analyze electrical activity in the rat cortex with these two methods. Compared with RR, DR reveals the importance of local phasic oscillatory activities and their coherence between cortical areas. Finally, we show that DR provides a more faithful assessment of functional connectivity caused by an increase in the signal to noise ratio, and of the delay in the propagation of information between two cortical structures.

Fig 1. Current source: A current in an homogenous medium yields a current source density flowing in all directions.

The current density writes: ${\displaystyle \overrightarrow{J}=\frac{I{\overrightarrow{u}}_r}{4\pi r^2}}$, where r is the distance to the current source and I the current generated at the origin. The Ohm law ($\overrightarrow{J}=\sigma \overrightarrow{E}$) leads to the potential ${\displaystyle V=\frac{I}{4\pi \sigma r}}$ created at any distance r.

Fig 2

a) Distal source: A distal source (blue ellipse) releases a density of current which gives birth to two remote potentials P₁ and P₂ respectivley located at a distance r − δr and r + δr belonging to the same brain area (red ellipse). This potential is measured by two electrodes seperated by a distance 2ε. b) Local source: A local source (blue ellipse) releases a density of current which gives birth to local potentials P₁ and P₂ respectively located at a distance r − δr and r + δr from the source and belonging to the same brain area (red ellipse), where r ∼ 2ε. This potential are measured by two electrodes sperated by a distance 2ε.

Fig 3

a) Example of potential measured in P₁ and P₂ versus distance r in normalized units. One notes the strong similitude between P₁ and P₂ when r is large in comparison with the distance shift ε of the two electrodes. Also, we oberve a strong amplitude difference between potential P₁ and P₂ when the current source is close to the electrodes pair (zoom in figure). b) Recording methods and electrodes location during the experiment.

Fig 4

a) Snippets of typical electroencephalogram (EEG) and electromyogram (EMG) recordings for the 3 vigilance states, which are wake (Wake→purple), non-rapid eye movement (NREM→red) sleep, and rapid eye movement sleep (REM→green). b) Example of hypnogram showing a temporal vigilance state dynamics.

Fig 5. Power spectrum of the two simulataneous recording modes RR (blue) and DR (red).

a) and b) respectively corresponds to NREM and REM in CA1, while c) and d) respectively corresponds to NREM and REM in PFC. In c), arrow shows sleep spindles. b) arrows shows burst activity during REM sleep in CA1. d) arrow reveals the burst of activity during REM sleep in PFC. Note that, burst activity was observed for DR in contrast with RR.

Fig 6. Coherence index between two brain regions (CA1 and PFC) during NREM a) and REM b).

Blue lines and red lines respectively correspond to RR and DR. Arrow in b) show the burst of activity during REM sleep. Note that, burst activity was observed for DR in contrast with RR.

Fig 7. Time-frequency representation of a simultaneous PFC and CA1 recordings in RR and DR mode during REM sleep, showing an occasional large frequency burst of activity common to the two brain structures located at 20s as well as a persistant oscillation at 7 Hz(θ rythm) which takes birth in CA1.

θ oscillation is a fundamental REM sleep signature in CA1. Colorbar is the normalized scale color of the time-frequency plot. We note that, θ rythm is viewable in PFC in RR mode (PFC_RR) in contrast to DR mode (PFC_DR) showing the volume conduction phenomenon. Occasional burst of activity at 20s is better identified in DR (CA1_DR) mode than RR (CA1_RR) mode.

Fig 8

a) Coherence between CA1 and PFC during REM sleep for the two recording modes RR (blue) and DR (red). Triggering source: Thin traces correspond to a trigger according to CA1, while large traces correspond to a trigger according to PFC. b) Imaginary Coherence between CA1 − PFC in RR configuration, showing the decrease of the 7 Hz peak as well as the very low frequency peak, because volume conduction is mainly represented by the real part. The 10 Hz to 15 Hz frequency band stays absent because of the poor signal to noise ratio in RR configuration. Inset: vertical zoom of the coherence index.

Fig 9

a) Individual event cross-correlation between CA1 and PFC in DR mode, showing a maximum correlation level of 0.55 at a positive lag time of 35 ms between the two regions. This positive lag indicates in our case a delay from the PFC in comparison with CA1. b) and c) are the probability density functions (blue) and cumulative probabilities (red) of the cross-correlation peak lag. A zoom on the maximum of the probility density function shows in referential mode b) a null median lag time and a fuzzy probility density function, while in differential mode c), the zoom displays a very well indentified peak and median lag time of 35 ms.

Fig 10. Coherence index vs noise to signal ratio (SNR⁻¹).

a) and b): The coherence calculations have been performed between a pure sine wave (green line) of unit amplitude vs itself added to a gaussian white noise where the magnitude has been chosen to 10 and 20 respectively for a) and b). c) The coherence index decreases rapidely with SNR⁻¹ according to a hyperbolic secant law (red line). Arrows point out the coherence level corresponding respectively to a SNR⁻¹ = 10 and 20.