IntroductionThe issue of directionality of information flow between neural ensembles is a key question in the study of brain connectivity.

Various statistical measures have been developed during the last decade, in an effort to assess the directional connectivity and magnitude of information flow through recorded EEGs, local field potentials (LFPs) and unit spike trains. One such measure is Partial Directed Coherence (PDC), based on the frequency domain representation of linear Granger Causality.

In the present study, we have two aims:

1. To identify connectivity between medial prefrontal cortex (mPFC) and dorsal hippocampus (medial and lateral) and examine how it is modified by acute elevated neuronal activity, induced with kainic acid (KA). We address this by applying PDC on recorded local field potentials (LFPs) and processed unit spike data.

1. To compare PDC results from the different data types. The key questions are: How does processing of spike data affect PDC results? How do these relate to PDC from LFPs?

Neuronal Networks

Laboratory

Neuronal Networks

Laboratory

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84: 463-474.

2. Coomber B., O'Donoghue M. F., Mason R., 2008, Synapse, 62: 746-755.

3. Coomber B., Taxidis I., Owen M., Mason R., 2008, in preparation.

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9. Lütkepohl H., 1993, Springer.

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13. Tononi G. et al., 2006, Neuron, 52: 748-749.

AcknowledgmentsThis research was supported by the Medical Research Council, University of Nottingham and by a Marie Curie Research Training Fellowship

Discussion• In basal conditions PDC from LFPs revealed:

1. Information flow from lateral to medial hippocampus, more prominent on the alpha (α; 8-14 Hz) and beta (β; 14-30 Hz) frequency bands. This is consistent with established hippocampal neuroanatomy [8,12].

2. Information flow from mPFC to hippocampus (medial and lateral). This is inconsistent with reported monosynaptic projections from hippocampus to mPFC [6], but it seems to support recent studies showing the cortex driving the hippocampus during the Slow Oscillation state in deep sleep and anaesthesia [7,13]. So we suspect that anaesthesia is a key factor here.

• KA appeared to have a different effect on the two subjects presented here. In both cases, KA caused an increase of activity in the medial hippocampus. In case 1 activity in the lateral was also enhanced, while that in mPFC was decreased. The exact opposite happened in case 2.

• During KA activity, PDC from LFPs revealed that: 1. Information flow from mPFC to medial hippocampus was unaffected but to lateral hippocampus was significantly increased (in case 2 found only in delta (δ; 1-4),

theta (θ; 4-8) and alpha (α; 8-14) frequency bands).2. Inter-hippocampal flow was unaffected in case 2 but was completely reversed in case 1.

• In spike data the connectivity is much harder to assess and the two cases are contradictory to some extent. 1. In case 1 the most prominent feature is the great increase of information flow from medial to lateral hippocampus during KA activity. 2. On the contrary, KA in case 2 resulted in the lateral hippocampus driving both medial and mPFC (while seizing to receive information from either of them).

• KA is a well-established model of status epilepticus and spontaneous seizure in the rat. Our results confirm the particular susceptibility of the hippocampus to KA. Alterations to its functional connectivity could have implications for memory processing in epilepsy. In humans, temporal lobe seizures are associated with functional deficits, including working memory, for which the hippocampus and mPFC are both important.

• Our results further indicate that applying PDC to completely different types of neurophysiological data can yield radically different results.

• Nevertheless, PDC represents a novel technique for assessing functional brain connectivity. It could be utilised to study disruption or reversal of connectivity in conditions such as epilepsy. However, its statistical properties are still largely unexplored. Finally, the type of spike data processing appears to have very little effect on PDC, provided that parameter values are chosen carefully.

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Partial Directed Coherence• Partial Directed Coherence (PDC) [1,11] is based on the notion of Granger Causality [5]:

“An observed time series x1 “Granger-causes” another series x2, if knowledge of x1’s past significantly improves prediction of x2”.

Granger Causality is not reciprocal, i.e. x1 may Granger-cause x2 without x2 necessarily Granger-causing x1, and this yields the notion of directionality.

• In a set of N time series, Ganger Causality is detected through their multivariate autoregressive model (MAR):

where wi is white noise and p is the model order.

The coefficients Ar reflect the linear interaction of a time series’ past on another’s present [9,10].

• After Fourier-transforming the Ar’s to the frequency domain to get A(f), PDC is defined as:

PDC compares the outflow of information from xj to xi with the total outflow of information from xj to all signals.

• PDC has been shown to reveal only direct interactions [1].

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Averaged Power Spectra throughout the experiment: PC1 of firing rates (blue), MAR model with p = 30 (red).

Averaged Power Spectra throughout the experiment: PC1 of processed spikes (blue), MAR model with p = 30 (red).

Spike Trains Firing Rates PC1

Spike Trains: Firing Rates processing• Each spike train is divided into (overlapping) bins. The mean firing rate is calculated in each

bin.

• Principal Components Analysis (PCA) is performed to group the firing rates of each brain region together.

• The first principal component (PC1) of each group is kept so as to end up with one continuous function for each brain region.

• The shorter the bin length and the larger the overlap between two bins, the less information is lost in the binning.

• We set 10 msec bins and 50% overlapbetween them.

• We set the MAR model order at: p = 30 bins = 150 msec.

fN = 10Hz

fN = 100Hz

Spike Trains: Spike Times processing• We apply the French-Holden Algorithm [4] with Nyquist frequency = fN.

• Each spike (ti) in a spike train is convolved with the kernel:

Equal to filtering with a low-pass phase-less filter with cut-off frequency fN.

• The resulting continuous function is sampled with sampling rate: fS = 2fN.

• PCA is performed on the firing rates of each brain region. The first principal component (PC1) of each group is kept.

• We set fN = 60 Hz.

• We set the MAR model order at: p = 30 sample points = 250 msec.

Recordings• Electrophysiological recordings were conducted in the hippocampus and mPFC of male

isoflurane-anaesthetised Lister-hooded rats, weighing 200-350g. Multiple single-unit and LFP activity were recorded with a Plexon MAP system using micro-electrode arrays placed in each structure. Recording sites were confirmed by histology.

• Rats were administered KA (10 mg kg-1) and vehicle (5% EtOH / 5% Cremophor EL (Fluka Biochemika) / 90% saline; v/v%; n=4). After a 33 min period of basal recording, KA was administered intra-peritoneally resulting in a period of approximately 20-30 min to onset of drug-evoked responses [2,3].

• Two recording sets are presented and analysed here: Cases 1 and 2.

(a) Representation of the most medial (●) and lateral (□) dorsal hippocampal recording sites.

(b) Representation of the prelimbic mPFC (●) recording sites.

(c) Representative trace of basal activity in LFPs recorded from: mPFC, medial hippocampus and lateral hippocampus.

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LFPs: Numerical Implementation• Spike data processing, MAR/PDC calculation and plotting were performed with our

MATLAB software package which includes scripts from the toolboxes: “Biosig” (http://biosig.sourceforge.net) and “NeuroSpec” (http://www.neurospec.org).

Averaged Power Spectra throughout the experiment: LFPs (blue), MAR model with p = 70 (red).

Methods

• Model order selection criteria (Bayesian Information Criterion (BIC), Akaike Criterion) failed to yield an optimal model order (p). They kept decreasing with increasing model order.

• We set the model order to p = 70. It yields a MAR model that produces the original LFP power spectrum accurately. Much lower p gives models with bad fit. Much higher p does not particularly improve the fit.

spikes

SpikeTimes

FiringRates

LFPs

Results: Case 1• Plots of the LFPs, firing rates and spike times of the 3 brain regions from one recording. The 13 experimental epochs (3 mins duration each) occupy the horizontal axis. The gaps between them correspond to

inter-epochs periods (7 mins duration each) where no recordings were performed. • The first 4 epochs correspond to basal conditions. The effects of KA (administered during the 4th epoch) become apparent after the 7th epoch.

• PDC colour plots. The 13 experimental epochs occupy the horizontal axis. The vertical axis corresponds to the frequencies (0-50 Hz). The colour scale represents the levels of PDC.

LFPs Firing Rates Spike Times

SpikeTimes

FiringRates

LFPs

LFPs Firing Rates Spike Times

Results: Case 2• Plots of the LFPs, firing rates and spike times of the 3 brain regions from another recording.

• PDC colour plots.

Detecting Directionality of Information Flow Through Application of Partial Directed Coherence on Different Types of Neurophysiological Data

Ioannis Taxidis1, Ben Coomber2, Rob Mason2 , Markus Owen1

1School of Mathematical Sciences, 2School of Biomedical Sciences, University of Nottingham, UK

Lab web site: www.nottingham.ac.uk/neuronal-networks