The extracellular record is typically biphasic and is interpreted as an indication that the recording tip is near the cell body (Frank 1955; Terzuolo and Araki 1961). Direct demonstration of the relationship between the action potential and extracellular "unit" activity derives from simultaneous recording of the intra- and extracellular signals from the same cell (Fig. 2.1). It is quite obvious from the recordings that there are differences between the forms of the intracellular and extracellular signals. First, the amplitude of the extracellular signal is one or two orders of magnitude smaller. Second, the duration of the extracellular spike is significantly shorter than that of the action potential recorded intracellularly. Third, the overall shape of the extracellular signal is quite different than the intracellular one. Nevertheless, it is of utmost importance that the intracellularly and extracellularly measured parameters of the action potentials quite reliably correlate, indicating that some of the intracellular changes may be inferred from a proper quantitative analysis of the extracellular signal. One such promising possibility is that the post-spike part of the extracellular unit may be used to assess e. g., spike afterhyperpolarization and GABAA-mediated recurrent inhibition.

Due to the low-pass filtering property of the extracellular space, the amplitude of the extracellularly recorded unit activity attenuates quite rapidly. Although the neuron-electrode distance for efficient recording of unit activity varies substantially from cell to cell (see below), certain generalizations can be made from measurements made on neocortical pyramidal cells (Fig. 2.3A). A silicon probe with a diamond-shaped recording site configuration ("tetrode") was used to map the isopotential contours around a spontaneously active pyramidal cell in the anesthetized rat. The probe was advanced in small steps in the vicinity of a single neuron and the amplitudes of the successively recorded spikes were measured. These data-generated plots were then compared with contour maps generated by calculating the action-potential generated voltage by a model neuron (Fig. 2.3B). These early experiments with multiple-site probes suggested that a) imaging the location of the action potential generation site is feasible using three or more recording sites with adequate signal-to-noise ratio, b) the site spacings for simultaneous recordings from the same cell should preferably be less than 50 µm for cortical pyramidal cells and c) temporal coherency of both unit potentials and low-frequency noise between adjacent recordings sites can be employed in signal l processing algorithms to improve single-unit sorting and signal-to-noise ratios. The use of multiple recording possibilities from the same neuron provided new methods for improving single unit sorting based on the temporal coherence of spikes from closely-spaced recording sites (Drake et al., 1988; McNaughton et al., 1983; Reece and O'Keefe, 1989).

Neurons are not point sources of extraces of extracellular current generation but complex three-dimensional structures. Consequently, the somata of neurons cannot be regarded as the sole source of action potentials. Supporting previous suggestions (Llinas and Nicholson, 1971), recent in vitro work provided evidence that the dendritic membrane can exhibit electroresponsive properties and actively support propagation of action potentials in dendritic compartments (Huguenard et al., 1989; Regehr et al., 1993; Stuart and Sakman, 1994; Spruston et al., 1995; Magee and Johnston, 1995). Specifically, simultaneous recordings from the soma and dendrites of neocortical and hippocampal pyramidal cells and substantia nigra neurons in vitro suggest that sodium spikes, initiated in the axon initial segment, actively backpropagate into the distal dendrites (Stuart and Sakman, 1994; Spruston et al., 1995; Häusser et al., 1995). The in vitro measurements are also supported by experiments carried out in the freely moving rats. Simultaneous measurements from both soma and dendrites in hippocampal and neocortical pyramidal cells show that the action potential triggered at the action initiation site below the soma (putative axon initial segment) and travels back to the dendrites at 0.5 to 2 m/sec (Fig. 2.2; Buzsáki et al., 1996). These observations have important implications for the extracellular measurement and selection of unit activity. Importantly, dendritic sodium conductances may be affected by both the intrinsic activity of the recorded neuron and interneuron-mediated inhibition of the dendrites. The attenuation or failure of the active dendritic propagation of the action potential, in turn will reduce the size of the extracellularly recorded unit activity. Briefly, a simple two-dimensional neuron model with a strong current sink representing the soma and a current source representing a single dendritic branch imposes limitations on the accuracy of unit sorting algorithms based on stationary models of spike generation. This difficulty poses problems for multiunit spike separation, especially for bursting neurons.

Repetitive spikes with decrementing amplitude occur spontaneously during consummatory behaviors and slow wave sleep in hippocampal pyramidal cells and are termed "complex-spike" bursts (Ranck, 1973). A possible mechanism for the generation of the decrementing amplitude units during the burst is illustrated in Fig. 2.4. Linear arrays of silicon probes (see below) with 25-µm recording intervals were closely positioned to CA1 or CA3 pyramidal neurons, so that sodium spikes could be recorded from the same cell(s) at 4 recording sites. The amplitude decrement of spikes during a complex-spike burst was frequency-dependent (Ranck, 1973); spikes occurring at shorter intervals were attenuated more than spikes with h longer interspike intervals. However, the degree of spike amplitude attenuation strongly depended on the recording site. Close to the cell body, only a moderate amplitude decrement was observed within a complex-spike burst (Fig. 2.2, site 4). At the same time, the amplitude attenuation at more distal recording sites (dendritic locations) was often substantial (Fig. 2.2, sites 2 and 3). Late occurring action potentials at dendritic recording sites were sometimes buried in the background noise. An interpretation of this observation is that "complex-spikes" in the extracellular field emerge because the extracellular electrode integrates electrical activity over a large segment of the somadendritic surface and because spikes occurring in fast succession may fail to invade the dendrites equally (Buzsáki et al., 1996). An important practical implication of these experiments is that the magnitude of the amplitude decrement during a complex-spike burst depends on the relative distance of the recording electrode from the soma of the neuron. The closer the electrode to the neuron the larger the amplitude dectement is. Thus, the amplitude ratio between the two recording electrodes will be biased toward the more distant electrode. The consequence of all this is that spike sorting algorithms based on spatial localization of the spike may regard the successive spikes of a complex-spike series as separate neurons.

Of the many parameters that may influence the amplitude and waveform of the extracellular unit response, properties of the neuron membrane, the three-dimensional structure of the cell and the extracellular milieu appear most important. It follows that the strategies of extracellular recordings should be adapted both to the anatomical region and to the neuron type in question.

The lipid bilayer of the neuronal membrane functions as a series capacitance between the intracellular signal and the extracellular recording electrode. This capacitance is believed to determine the primary shape of the extracellular potential. A strong support for the hypothesis of capacitive differentiation comes from thcomes from the observation that the first derivative of the intracellular action potential is very similar to the extracellularly recorded (wide band) unit (Fig. 2.1). Given this reliable correlation, the rise and fall time of the action potential can be predicted from the extracellular trace. It is also noteworthy from these simultaneous recordings that other parameters, such as the spike after-hyperpolarization may also be inferred from the extracellular record.

The capacitive differentiation by the lipid membrane should also affect the amplitude of the extracellular unit potential. Faster rising-falling action potentials should generate larger amplitude extracellular units than wide action potentials. This hypothesis has yet to be verified. However, this prediction is supported by the significantly larger amplitude derivatives of the action potentials of the majority of hippocampal interneurons (Fig. 2.5). In general, the duration of the action potential is considerably shorter in cortical interneurons than in pyramidal cells, and this distinction is often used as a criteria for the extracellular identification of interneurons (Buzsáki and Eidelberg, 1982). Unfortunately, this criterion is not absolute, since the action potential duration of basket cells and hippocampal pyramidal neurons may be quite similar. Therefore, although short duration extracellular units may positivively identify several interneuronal types, this criterion alone is not sufficient for all types (Freund and Buzsáki, 1996).

The momentary polarization level of the cell membrane has a significant effect on the amplitude of the action potential. When a neuron discharges from a relatively more depolarized membrane potential, the action potential is proportionally smaller. Such an amplitude rn amplitude reduction is also reflected by the extracellularly recorded units. The amplitude reduction may be substantial when e. g., a pyramidal cell fires a high-threshold calcium spike crowned with fast, sodium spikes. A large "ramp-like" depolarization of the neuron will have a similar effect. For example, hippocampal pyramidal cells increase their discharge rate several-fold when the rat crosses the "spatial field" of the neuron. As shown experimentally, the amplitude decrement of the unit shows a predictive relationship with behavior. The amplitude of the spatial unit is smaller in the center than at the periphery of the spatial field (Wilson, personal communication). A reasonable interpretation of the amplitude decrease is that the neuron is maximally depolarized in the center of the spatial field.

Conversely, hyperpolarization of the membrane results in an increase of the amplitude of the extracellular units. Amplitude histograms of multiple unit activity from the ventrolateral nucleus of the thalamus revealed larger amplitude units during slow wave sleep than in the awake state. Recording from putative single units with sharp tungsten electrodes (> 5 MOhm) showed a consistent amplitude increase during sleep (our unpublished findings). A likely interpretation of these observation is that during sleep spindles thalamocortical cells are rhythmically hyperpolarized by the inhihibitory reticular nucleus neurons and discharge low threshold calcium spikes (Steriade and Llinas, 1988; Sawyer et al., 1994), whereas in the awake animal they typically discharge single or repetitive "simple" sodium spikes, initiated above the resting membrane potential.

This variable is perhaps the most important for the design of the recording electrode configuration. As discussed above, the voltage sensed by the extracellular electrode depends strongly on the direction and density of current flow. Consequently, neurons with parallel dendrites should generate larger amplitude currents in the extracellular space than cells with radially running dendrites. Although this relationship has long been tacitly acknowledged, formal experiments comparing extracellular activity recorded from different cell types by the same recording electrode are rare. Cortical pyramidal cells and cerebellar Purkinje neurons have a large apical dendrite and therefore a very large part of the current flow in the perisomatic region points to the same direction. The result is a large and dense extracellular current flow, an optimal condition for extracellular recording. The unidirectional dendritic architecture of cortical pyramidal cells is the explanation why juxtadendritic action potentials ials can be recorded several hundred µm from the cell body (Fig. 2.2). Parvalbumin-immunoreactive basket cells and chandelier cells in the hippocampus are similar in shape to pyramidal cells (Li et al., 1992; Gulyas et al., 1993; Buhl et al., 1994; Sik et al., 1995). Although, in contrast to pyramidal cells, several apical dendrites emanate from the soma, they run in the same direction and therefore the currents generated by the traveling action potentials in the different dendrites sum linearly in the extracellular space. This allows for simultaneous recording of relatively large amplitude units from both soma and dendrites of these neurons (Fig. 2.6).

Many neurons, however, possess radially projecting dendrites. Consequently, the action potential, emanated from the soma, travels into various directions. The small amplitude multiple dipoles, created by the action potentials traveling somatofugally in the various dendrites, therefore tend to diminish, rather than enhance, each other in the extracellular space. The result is a small amplitude extracellular unit due to the "closed" field generated by the radially running currents. This has two consequences for extracellular recordings. First, smaller amplitude action potentials will be generated by these neurons and therefore the recording electrode should be placed closer to the cell body during the experiment. Second, less number of neurons can be recorded by the same size electrode than, for example, in the pyramidal layers of the neocortex or hippocampus. Figure 7 illustrates these assumptions. In this experiment the same kind of sili silicon probe as used in Figs. 4 and 5 was placed in the hilar region of the hippocampal dentate gyrus. Despite of close spacing of the recording sites (25 µm), each site recorded a different neuron. This physiological observation is congruent with the non-pyramidal shape of these cells (Amaral, 1978). Another illustration is shown in Fig. 2.8. In this experiment the recording probe was placed into the dorsal part of the thalamus for simultaneous monitoring of the GABAergic neurons of the reticular nucleus and thalamocortical cells. Again, each of the four recording sites selected different cells with virtually no coherent action potentials at neighboring sites. Both reticular and thalamocortical cells have radially projecting dendrites (Fig. 2.8B), supporting the hypothesis that the small electrical fields generated by these neurons may be explained by their anatomical architecture.

A further difficulty that may be encountered during a physiological experiment is that the action potential initiation site may vary in the same neuron (Llinas and Nicholson, 1971; Traub and Miles, 1995). Although this is believed to happen only during pathological states in cortical principal cells, it appears that at least in some interneuron types in the cortex the action potential may emerge from one of the dendrites. Moreover, the action potential may emanate from various dendrites in an unpredictable fashion and it may not propagate equally to same set of dendrites from the different trigger sites. Therefore, the same interneuron can produce extracellular unit activity with varying shape, amplitude and spatial features (Fig. 2.9). The multiple site generation of action potentials throughout the dendritic arbor may also explain why the amplitude variability of extracellularly recorded interneurons sometimes exceeds 80% (our unpublished findings). Overall, these observations suggest that the methods and criteria worked out for unit sorting of pyramidal neurons may ns may not always apply to cortical interneurons. In effect, the currently available unit sorting methods based on spike shape differentiation will treat the different modes of firing of the same neuron as different cell clusters. The opposite technical problem may arise if neighboring neurons are electrically coupled or their action potentials temporally coincide. In this case, activity of several units may be falsely represented as a single unit cluster.

A frequently used physiological method to identify units is to examine its evoked response properties. For example, neurons which project to known anatomical targets may be differentiated from those which do not by antidromic stimulation. Interneurons often fire repetitive spikes, whereas principal cells typically discharge only a single spike due to orthodromic stimulation. While these methods are quite reliable when a single cell is well-isolated, they are not foolproof when multiple unit activity is recorded by the electrode. Orthodromically evoked units are often much smaller in amplitude than "spontaneously" occurring units. The reason is that stimulation recruits strong feed-forward inhibition, which in turn, may shunt the dendritic membrane and attenuate the somadendritic backpropagation of the action potential (Fal (Fig. 2.10; Buzsáki et al., 1996), resulting in smaller amplitude extracellular unit. Synchronous activation of a large number of excitatory afferents by the simulation may also induce "ectopic" dendritic spike generation (Turner and Richardson, 1991), therefore the "spatial location" of the evoked and spontaneous units may be classified differently by the spike sorting algorithm. A useful method to circumvent these problems is to test each recognized units with an antidromic collision test. Albeit this approach may be time-consuming, it is perhaps the best on-line tool to separate projection and local circuit neurons. Unfortunately, the collision test is not particularly useful when neighboring neurons, such as hippocampal pyramidal cells, possess strongly overlapping targets.

Changes in the extracellular milieu may also affect several parameters of the action potential. Ischemia, anoxia or epileptic activity change dramatically the Na⁺/K⁺ exchanger mechanism and build-up of extracellular K+ and glutamate may affect spike repolarization, afterhyperpolarization as well as the site of action potential generation (Fig. 2.11). Importantly in the present context, the spike initiation site of the action potential may migrate and extracellularly recorded spike shapes and spike locations will change accordingly. In short, modification of these factors may result in false identification of the altered spikes as new sets of neurons.

Most knowledMost knowledge about the physiological function of the brain is based on studies of sequentially analyzed single site recordings. Although it has long been recognized that the computational power of complex neuronal networks cannot be fully recognized by studying the properties of single cells or activity of a few, selected sites, experimental access to the emergent properties of cooperating neurons has largely been impossible until quite recently. Direct investigation of the temporal dynamics of neuronal populations can only be based on simultaneous observation of large neuronal aggregates (Buzsáki et al., 1992; Wilson and McNaughton, 1993). The two critical requirements towards this goal are 1) placing a large number of recording electrodes in a small amount of tissue at the submillimeter range and 2) doing this without a significant tissue damage. These major requirements put constraints on wire electrodes due to the limited number of recording sites. Additional constraints are the number of lead wires, preamplifiers and the size of the head connector which could be carried by a behaving animal. Progress in this field has been accelerated by the development of silicon microtechnology-based multichannel recording devices (Kuperstein and Eichenbaum, 1985; Wise and Najafi, 1991).

In such silicon devices, the number of thin-film recording sites are defined lithographically usining the technology of integrated circuits (Fig. 2.12). The supporting silicon substrate is shaped using micromachining and a diffused boron etch-stop (Najafi, et al., 1985). The probe thicknesses are 10-15 µm with shank widths as narrow as 25 µm. Thus, these structures are capable of dimensions similar to those of a single cell. The tissue displacement for a single shank is typically less than for a single wire electrode even today, and each shank can carry many isolated sites. All dimensions (e.g., shank widths, thicknesses, site positions) can be controlled within ±1 µm or less.

Parallel with the development of recording and storage methods, various computational algorithms have been devised for the decomposition of multiple unit data into single neuron events. Numerous spike recognition/sorting programs are available commercially, as well. Despite of major efforts in numerous laboratories, none of the currently available methods is sufficiently reliable. Typically, two types of errors are generated by both on-line and post-hoc methods: false identification and omission ernd omission errors. False unit identification error is inherent in methods based on amplitude and spike-shape recognition, since similar neurons equidistant from the recording site may generate spikes of identical amplitude and shape. This type of error is especially high when recordings are made from areas of high density of identical neurons, such as the pyramidal and granule cell layers of the hippocampus or the different neocortical layers. One efficient method to decrease false identification error is to use only the unit with the largest amplitude from each electrode. Although this selection increases single cell identification, it can occur only at the expense of drastically reducing the number of units for further analysis. Spike omission errors arise from the variability of the extracellularly recorded spike amplitude and shape of the same neuron, as discussed above. Spike omission errors therefore increase substantially with bursting cells and interneurons.

Current strategies for cell sorting of multiple unit data fall into two major categories. The first approach (amplitude/wave-shape recognition methods) is based on the presumption that different types of neurons generate different wave forms of spikes (Abeles and Goldstein, 1977). While this is true in general, neurons recorded by a single electrode are typically of the same type therefore have very similar shapes. The sececond approach requires simultaneous recordings from the same cells. The rationale behind this "spatial" method is that neurons which are at different distances from the recording sites will have different spike amplitude ratios when recorded from two or more sites simultaneously (McNaughton et al., 1983). Although two-channel recording enhances accuracy of unit separation, a more complete determination of point-like sources in Euclidean space requires at least four, preferably non-coplanar recording sites (Drake et al., 1988; Recce and O'Keefe, 1989). An obvious problem with the spatial method is that extracellularly recorded units reflect currents generated by both soma and dendrites and the variation of the dendritic spike amplitude modifies the virtual, extracellularly determined "site" of action potential generation (Fig. 2.4). Thus, both waveform recognition and spatial approaches have virtues and shortcomings. A combination of these approaches along with post-hoc tests (see below) may improve the accuracy of neuronal isolation.

To date, no reliability indices have yet been worked out for the quantitative assessment of false identification and omission errors generated by the different methods. Although independent measures are not available for matching the classified unit clusters with individual cells, it would nevertheless be important to examine how similarar or dissimilar clusters are generated by the methods used in different laboratories from the same database. Below, I will describe a spike sorting method which takes advantage of the metric spacing of the recordings sites of silicon probes. The reliability of the developed algorithm was examined by the spatially distinct field potentials generated by different afferents, prior to using the program for unit sorting.

Before testing the spatial localization method on single neurons, I examined the reliability of the method with field potentials. This approach was used to provide an independent test for the reliability of spatial localization. In the hippocampus, three major intermittent field events, generated by the activity of separate afferents can be recognized: sharp waves (SPW) and two types of dentate spikes (DS1 and DS2; Buzsáki et al., 1983; Bragin et al., 1995). Previous current-source density analysis of these events revealed large sinks corresponding to the concerted activity of the Schaffer collaterals on CA1 pyramidal cells and of the medial and lateral perforant path fibers on the granule cells, respectively.

On the basis of the afferent projections to pyr to pyramidal cells and granule cells one can assume an invariant relationship between the anatomical sites and the calculated location of the physiological events in the Cartesian space. The amplitudes of these events recorded from each site of the probe can be represented by an amplitude vector. Each component of this amplitude vector reflects the field momentum for that channel. Assuming the homogeneity of the extracellular medium, the average of these field momentums covaries with the location of the field generation. Two functions, the "center of field" and "interpolated field position" have been devised to project the field momentums to an Euclidean coordinate system where one dimension corresponds to the spatial location of the field event and the other dimension indicates the average amplitude. In such a projection, each event is represented by a point in the location-amplitude space. A cluster of superimposed points of such a projection is assumed to be specific for the afferents involved in the generation of a particular field spike sequence.

Center of field: Analogous to the term of 'center of mass', the 'center of field' is estimatedated by the mean of the weighted amplitudes. First, peak-to-peak amplitudes are calculated for each channel and stored along with the times of their occurrence. The amplitude of the event at each recording site is weighed by a factor determined by the interelectrode distance and the order of the recording site (e. g., 1 to 16) as the first moment. The mean of weighted amplitudes are then plotted as a function of the sum of the amplitudes (Fig. 2.13). The xy coordinates were given by the functions:

and

Interpolated field position: Since electrical events propagate passively in the extracellular space, their amplitude correlates inversely with the distance of the source from the electrode. With multiple recording sites, the source of the event can be estimated by using interpolation. Assuming that the field potential changes nonlinearly in the extracellular space, a cubic-spline interpolation of the measured amplitudes recorded at each site is used. Interpolation of the simultaneously registered amplitude values (y) allows to locate the real amplitude peak between electrode sites (Fig. 2.13). The position of this peak (z )on a continuous scale is assumed to reflect the relative location of the field source. I use sample values where refers to the location of the jth recording site. The peak position is defined as:

at a point where

The interpolation of y is based on the amplitude at the discrete points:

and

The cubic spline interpolation (5-6) is taking into account of the first and second derivatives of a given point in order to provide a polynomial function which is smooth in the first derivative, and continuous in the second derivative (Press et al., 1992). Since the first and last channels last channels have to be included when the derivatives of the first and last points are calculated, I appended two additional channels as channel 0 and channel n+1 with 0 amplitude of signal. The position of the amplitude peak relative to the electrode sites provides an estimate for the location of electrical source. Plots of peak positions are expected to form clusters.

Spontaneous field events were recorded simultaneously at 16 sites along the CA1-dentate gyrus axis. The recording sites were spaced at 100 µm. The 16-channel amplitude vectors and "the center of field" were calculated for each successively identified field event. The distribution of the detected events was grouped by K-means clustering where K (the number of clusters) was varied. The K at which F was maximal was considered the be the optimal partitioning. The "center of field" versus amplitude plots revealed three well-separated clusters (Fig. 2.14). The amplitude variance of the sharp waves was almost three-fold that of DS1 and more than six fold that of DS2. sharp waves formed a clear cluster between sites 2 and 4 on the virtually continuous scale of the multisite electrode (virtual axis from 1 to 16) and without an overlap with DS1 or DS2. The estimated field generators of DS1 and DS2 were located between 10 and 13 on the virtual axis and were much closer to each other than to sharp waves. Yet, clustering of multiplple-site recorded data clearly separated DS1 and DS2 events. Classification was significantly improved when the cluster of sharp waves was removed from the data base. The clustering method positively identified each sharp wave, 92% of DS1 and 68% of DS2 detected by visual inspection of each event.

Having established our ability to reliably detect field events by "spatial" methods, I used a similar approach for unit-cell separation. Since parts of the method are similar to spike separation developed for "wire-tetrode electrodes", only the differences are emphasized here. These differences take advantage of the linear arrangement of the recordings sites of silicon probes.

The first step is the conversion of simultaneous recorded spike events into a spatial domain. Briefly, spike events are plotted in a 3-dimensional space using the "center of field", the "interpolated field position" measures and amplitude as x, y and z coordinates (Figs. 13 and 15). The second step attempts to separate the events (units) into functionally meaningful clusters (Fig. 2.15).