Assessing Granger Causality in Electrophysiological Data: Removing the Adverse Effects of Common Signals via Bipolar Derivations

Abstract

Multielectrode voltage data are usually recorded against a common reference. Such data are frequently used without further treatment to assess patterns of functional connectivity between neuronal populations and between brain areas. It is important to note from the outset that such an approach is valid only when the reference electrode is nearly electrically silent. In practice, however, the reference electrode is generally not electrically silent, thereby adding a common signal to the recorded data. Volume conduction further complicates the problem. In this study we demonstrate the adverse effects of common signals on the estimation of Granger causality, which is a statistical measure used to infer synaptic transmission and information flow in neural circuits from multielectrode data. We further test the hypothesis that the problem can be overcome by utilizing bipolar derivations where the difference between two nearby electrodes is taken and treated as a representation of local neural activity. Simulated data generated by a neuronal network model where the connectivity pattern is known were considered first. This was followed by analyzing data from three experimental preparations where a priori predictions regarding the patterns of causal interactions can be made: (1) laminar recordings from the hippocampus of an anesthetized rat during theta rhythm, (2) laminar recordings from V4 of an awake-behaving macaque monkey during alpha rhythm, and (3) ECoG recordings from electrode arrays implanted in the middle temporal lobe and prefrontal cortex of an epilepsy patient during fixation. For both simulation and experimental analysis the results show that bipolar derivations yield the expected connectivity patterns whereas the untreated data (referred to as unipolar signals) do not. In addition, current source density signals, where applicable, yield results that are close to the expected connectivity patterns, whereas the commonly practiced average re-reference method leads to erroneous results.

Keywords: ECoG; Granger causality; V4; bipolar signals; hippocampus; unipolar signals.

Figure 1

Simulation model. (A) Coupling scheme. (B) Granger causality spectra using bipolar signals which are in agreement with ground truth. (C) Granger causality spectra using unipolar signals which are not in agreement with ground truth. (D) Analysis of the unipolar Granger causality UV → XY as a function of the signal to reference ratio (SRR) (green curve). Black horizontal lines in (B–D) represents the level of statistical significance (p < 0.05).

Figure 2

Laminar recording from rat hippocampus. (A) Schematic of the multielectrode with 16 equally spaced (100 μm) contacts and theta generators as identified by phase realigned and averaged (PRAT) CSD (color-coded) and LFPs (smooth traces, blue). Granger causality spectral analysis using (B) bipolar data, (C) unipolar data, (D) CSD data, and (E) average re-referenced data. (F) Comparison of unipolar LFPs from CA1 and average reference signals. (G) Schematic summarizing the Granger causality results where “OTHER” includes unipolar data, average re-referenced data and CSD data. Bipolar results are in agreement with ground truth. Black horizontal lines in (B–E) represents the level of statistical significance (p < 0.05).

Figure 3

Laminar recording from monkey V4. (A) Schematic of the multielectrode with 14 equally spaced (200 μm) contacts and alpha generators as identified by phase realigned and averaged (PRAT) CSD (color-coded) and LFPs (smooth traces, blue). Granger causality spectral analysis using (B) bipolar data, (C) unipolar data, (D) CSD data, and (E) average re-referenced data. (F) Comparison of unipolar LFPs from granular layer and average reference signals. (G) Schematic summarizing the Granger causality results where “OTHER” includes unipolar data, average re-referenced data and CSD data. Bipolar results are in agreement with ground truth. Black horizontal lines in (B–E) represents the level of statistical significance (p < 0.05).

Figure 4

ECoG recording from epilepsy patient. (A) Placement of electrode arrays. (B) Granger causality spectra using bipolar data. (C) Granger causality spectra using unipolar data. (D,E) Schematic summarizing the Granger causality results where the thickness of the arrows is proportional to the corresponding Granger causality values.