NEURAL NETWORKS: FROM BIOLOGY TO HARDWARE IMPLEMENTATIONS,
CHIA (CAGLIARI), ITALY, SEPTEMBER 23-27, 1996.

EXTRACELLULAR RECORDING FROM MULTIPLE NEIGHBORING CELLS IN PRIMATE CORTEX

M. Sahani, J. S. Pezaris, R. A. Andersen

Division of Biology
Computation and Neural Systems
Caltech, Pasadena, CA 91125, USA

panel 1: introduction

In this poster we describe our efforts to record and interpret signals from neighboring cells in the posterior parietal cortex of the macaque. We focus primarily on the technical issues raised in this project, and include data from one recording site as an illustration. The collection and analysis of data is ongoing.

unravelling dynamical microcircuits

• Computation within a single cortical area is likely to be a dynamic process, involving local recurrent circuitry.

• Anatomical studies suggest that cells within a single column, or even closer, have the connectivity necessary to form recurrent microcircuits.

• To understand the computations carried out by these microcircuits, and the functional relevance of the connections within them, we need to be able to record simultaneously in a behaving animal from the cells that comprise them.

concerted signaling

• Nearby cells in cortex tend to be both anatomically connected and functionally related.

• Thus both the opportunity and the motive for concerted signaling by neighboring neurons is present.

panel 2: tetrodes

The cartoon above illustrates the principle underlying tetrode operation.

• Tetrodes are extracellular micro-electrodes made from a bundle of four insulated wires, twisted and glued together.

• The tip is cut and each exposed conductor plated for about 10 microamp-seconds in AuCl₄.

• Action potentials from each cell close to the tip generate detectable waveforms on each wire. As in quadraphonic sound, the four-channel signature of each cell is determined both by the source field generated by the spike as well as the cell's spatial relationship to the electrode.

• In the diagram, the magenta and cyan cells are each close to one wire tip, while the red and green ones are distant.

• We have been able to record and recognize up to 7 cells within an estimated 100 micron diameter volume.

panel 3: photomicrograph

Photomicrograph detail of a tetrode tip superimposed on a Nissl stained cortical slice showing the relative sizes of the tetrode wires and cell bodies.

panel 4: spike recognition

two stages

• Identify the family of spike shapes associated with each detectable cell. This stage corresponds to the familiar ``spike clustering'' operation.

• Identify the times when action potentials from each cell occurred. In general this is performed by a filter-like algorithm.

filtering is important

• Event detection schemes to provide candidate spike shapes for clustering are dependent on the shapes of the events in the data. In the extreme case of a simple threshold, clusters that lie close to the threshold will be incompletely detected. More sophisticated general template techniques can be improved by knowing the precise templates to search for.

• Overlapped spikes generally defeat clustering algorithms. We are particularly interested in spikes that arrive within 2ms of each other, where the probability of overlap is large. Filtering techniques, particularly if linear, can resolve such cases accurately.

• Clustering algorithms are generally worse than O(n), and require multiple iterations over the entire data set. Greater efficiency is possible by clustering a small group of events and converting to filters to detect subsequent spikes.

panel 5: signal processing

analog signal

• The signals are amplified with a two-stage gain of 80-100 dB (custom).

• They are then low-pass filtered (9-pole analog Bessel) at 6.4 kHz to prevent aliasing (Tucker Davis Technologies, Gainsville, Florida).

• They are digitized at 12.8 kHz on each channel by a 16 bit instrumentation A/D (TDT).

• Finally, they are high-pass filtered using a 32-tap digital Hamming windowed FIR filter with the 3dB point at 640Hz.

event detection

• Events are detected by threshold crossing, with the threshold set to 4 to 6 times the RMS of the filtered signal. See the panel above for comments on this process.

• Event waveforms are reconstructed with Fourier techniques, and the events are resampled to align the sampling frame with the reconstructed peak. See below for a discussion of the significance of this.

panel 6: clustering - subspace

choosing the subspace

• Events are stored as 64-sample vectors (16 samples per channel) with the reconstructed peak at sample number 8.

• Clustering simply on peak height (that is, sample number 8) seems to be remarkably effective. This exploits the quadraphonic amplitude effect of the tetrode.

• Non-linear transformations (such as peak width) might, in principle, be useful. We have not seen remarkable improvements, however.

• Linear transformations of the vector (such as PCA) should only be useful for dimensionality reduction. If a clustering algorithm can run in the higher dimensional space it should perform as well as on the transformed space. In particular, we have had little success with PCA since we often see noise or burst variation dominating inter-cluster variation, as in the example below.

panel 7: clustering - noise

choosing the noise model

• Electrical noise and noise due to the superposition of sub-threshold neural events (``background noise'') may be taken to be gaussian.

• Noise due to sample frame shifts is uniform and unequal at points along the waveform (it is proportional to the local derivative). At points near the waveform peak at our sample rate it can approach one quarter the magnitude of the signal. At twice our sampling rate the SNR is still 8. This noise source may dominate gaussian sources and must be removed prior to gaussian model fitting.
  

  
  

• Intrinsic spike variability is also non-gaussian and anisotropic. This is not easily removed (although a predictive burst model involving a mean waveform varying with time since the last spike could be combined with a gaussian noise assumption). We follow Fee et al (1996) in fitting more clusters that expected and then ``merging'' clusters so as to describe a single cell by multiple centers. However we use a mixture of gaussians with general (i.e. non-isotropic) covariance matrices for the initial fitting, and thus frequently capture bursting variability in the first stage. We are therefore relatively successful with far fewer initial models than used by Fee et al.

panel 8: em mathematics

• We are given observations d_i that are presumed to have arisen from the mixture
  

  Here m_k represents the probability density function, theta_k the parameters, and pi(k) the mixture probability, of the kth model. We would like to ``fit'' this mixture model to the data, that is we want theta_k and pi(k) for all k, such that p(d_i) is maximized.

• If we knew which model the ith data point came from, that is, if we had the labels {k_i}, this problem would be easy (at least for gaussian mixtures). We could simply fit each model m_k(d_i;theta_k) to maximize the probability of those d_i labeled to come from that model.

• The EM (Estimation Maximization) algorithm iterates the following two steps:
  • Estimate a probability distribution for the missing data. In the mixture case these are the labels {k_i}. We make the distribution for k_i proportional to the likelihood of the data point d_i under the k_ith model from the previous iteration, i.e.
    

  • Maximize the likelihood of the observed and estimated data. In this case we fit the models to the labeled data weighted by the probabilities r_i(k):
    

panel 9: em results

• These plots show peak heights on the 4 channels (in volts at digitization) of about 1/10 of the events recorded at one site. The clusters have been identified by EM fitting a mixture of gaussians with unconstrained covariance matrices to the 4-element peak vector. Assignment to gaussians is done by greatest likelihood.

• Pay special attention to the magenta cluster. It would be quite difficult to identify this group by hand.

panel 10: filtering

optimal linear filtering

• Roberts and Hartline (1975), and Gozani and Miller (1994) have suggested the following straightforward procedure. The center of each cluster m_k(t) and the typical noise waveform eta(t) are identified, and an optimal matched filter (method due to Wiener) is generated for each template
  

  Where tilde indicates Fourier transformation to the frequency domain. A frequency dependent prefactor may also be introduced.

• The filter is optimal in the sense that the response to the distractors (m_j(t) and eta(t)) is minimized under the constraint that the response to m_k(t) is unity. Informally, the filter modifies the simplest matched filter, which is just the spike template itself, by deemphasizing frequency channels where the template shares power with the distractors.

• If such filters can be constructed, overlap resolution will be automatic. The response of each filter to the overlap will be the sum of the responses to the spikes in the overlap, which will be 1 if and only if the corresponding template is present. A simple threshold on the output of the filter should therefore suffice.

• In practice spike waveforms are sufficiently similar that orthogonalization of the filters is not possible.

panel 11: more filtering

• The figure below shows the output of filters based on the three prominent clusters in the cluster diagram above.
  

• It is clear that while filter for the red cell is well orthogonalized to the distractor templates, the other two filters are quite poor.

nonlinear filtering

• While more work is necessary to resolve overlaps, nonlinear filtering techniques may be useful. Recently Chandra and Optican (1996) have implemented a two-layer network architecture to sort signals from a single electrode. We continue to examine this and other possibilities.

panel 12: example data

The data used to demonstrate the sorting process above was taken from a site at a depth of about 3mm in the posterior parietal cortex of a behaving macaque. Closer examination of these data proves to be instructive.

task

• The monkey is performing the delayed saccade task. He fixates a point of light on a dark screen while a peripheral target light is flashed. He must remember the location of the target, and when the fixation point is extinguished make a direct saccade to it. Once his eye has stopped in the correct area the target is re-illuminated to provide feedback (which usually results in another, corrective, saccade).

cells

• We shall examine the three relatively frequently firing cells, colored red, green and blue in the cluster diagrams.

panel 13: cell responses

• These diagrams show PST histograms and rasters for the cells detected at our example site. The eight histograms are aligned on the fixation offset (cue to saccade). Each subpanel collects trials for a target in a single peripheral location. The direction is indicated by the position of the subpanel relative to the center of the group. The locations were 15 degrees from fixation.

• The crosses indicate the times of behavioral events during the trial as follows: green, fixation acquisition; magenta, target presentation; cyan, fixation offset; red, target acquisition.

• Note that the red cell responds strongly after both saccades (coming on to fixation and moving to the target). It also exhibits a sharp sensory response to targets flashed directly above or below fixation.

• The green and blue cells fire throughout active fixation periods. They are pre-saccadically suppressed and rebound after the saccade. Presumably they are involved in maintenance of active fixation, or have foveal sensory receptive fields.

panel 14: correlations

long time scale

• The green cell seems to trail both red and blue. This is somewhat consistent with the PSTHs and is probably stimulus induced (these correlograms are not corrected for stimulus effects).

short time scale

• Here the green cell leads the other two with a time delay consistent with monosynaptic transmission. We believe this to reflect the underlying connectivity. Note that because the analysis used to create these correlations did not fully handle overlapped events, the actual counts in the zero-delay bins are likely higher than reported.

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Maneesh Sahani, 216-76 Caltech, Pasadena, CA 91125, USA, maneesh@caltech.edu, 5 October 1996