Populations and ensemble averages
The basic anatomy and physiology of neurons is familiar in terms of the Neuron Doctrine, which holds that the element of neural function is the individual neuron. Complementary to this doctrine is the concept of the cooperative neural mass, that exists through synaptic connections among participating neurons (Figure 3). In this hierarchical view the population activity co-exists with the trains of action potentials from individual neurons in the form of shared spatially distributed patterns of activity occupying large areas of cortex, having sudden onsets and offsets, and lasting small fractions of a second. These wave packets have only recently become available for measurement with large arrays of electrodes and amplifiers. They form the foundation of this new approach.
The concept of coexisting "microscopic" and "macroscopic" activity is familiar. Each person as an individual speaks with one voice, but each participates in families, committees and economic units. Those larger participations become apparent only in the aggregate, such as committee reports, vote tallies or economic indices. Similarly, each animal is also part of a species, a food chain, and an ecological system. A water molecule is simultaneously part of a hailstone, a cloud and a weather front. The challenge of applying this concept to brain function is not theoretical. It is experimental. How can one observe the activity of a neural mass? And how can one determine that what one sees relates to behavioral brain function? The collective activity must be observed as a sum or an average of the activity of members of the population. Like a census taker one must collect data from individuals, make averages over samples, and then find the behavioral correlates of the results, which have no meaning unless and until they are related to what the brain is doing.
One must choose between two methods of averaging. A single amplifier suffices for recording a trace of activity from one neuron in a mass or from a local group of neurons acting in concert (Figure 2). The recorded trace typically lasts merely a few seconds or even a fraction of a second. On repeated stimulation one can collect and store an ensemble of traces over time. If one aligns these stored traces using the stimulus time marker, one can compute an average trace called an ensemble time average, also known as an averaged evoked potential or event related response (Basar, 1980). With many electrodes in a spatial matrix one can simultaneously obtain an ensemble of traces each time the stimulus is presented (Figure 4). However, by using the stimulus time marker to align successive evoked potentials from serial stimuli, one can also compute a spatial ensemble average for the single stimulus presentation on every channel (Figure 5). In this example it is computed from the collection of averaged evoked potentials instead of from the unaveraged time traces.
Profound differences exist between these two averages. For example, suppose that a chorus sings a musical phrase under the baton of a conductor. The listener hears a spatial ensemble average from the singers, who also hear and respond to each other interactively. Now suppose that the conductor were to ask each member to sing the phrase solo while the sound is taped, using a tap of the baton to start each singer. The conductor could make a time ensemble average by aligning the tape segments at the tap and summing the sounds to reconstitute the chorale. The reason this method cannot give the same result as simultaneous singing is that the singers do not have the necessary precision of pitch and timing unless they can interact to form a population as they sing.
Time ensemble averaging works well for neuronal events that are solidly time-locked to stimuli, but it does not work on population events, because each collective cortical event is internally generated. The onset time of each event is related but not bound to the stimulus and variable in latency. Endogenous events typically consist of brief fluctuations that vary in their frequency both within particular events and over successive events (Figure 2). These variations cause destructive time ensemble averaging. A spatial ensemble average of a collection of traces that are recorded simultaneously, in contrast, tends to wash out local detail but to emphasize the common wave form of the population.
Time ensemble averaging can be used to display the impulse response of cortex to its sensory input, and spatial ensemble averaging can be used to derive an estimate of its perceptual output. This is shown by comparing two forms of electrical field potentials recorded from the olfactory bulb. First, an electrical stimulus delivered to the afferent pathway leads to a characteristic damped oscillation. This can be recorded with an array of 64 electrodes. When the stimulus is low intensity, the response of the bulb is an oscillation at 40 - 60 Hz like the ringing of a bell when it is struck (Figure 4). The response is restricted to a part of the bulb to which the stimulated axons carry the input. It has the same frequency of oscillation everywhere over its duration, and its amplitude pattern reflects accurately the spatial pattern of the input (Freeman, 1991). In other words, this is a stimulus-bound response of the bulb. Because the oscillation occurs only when the input intensity is low, it is obscured by the ongoing EEG, so it must be extracted by repeated stimulation and time ensemble averaging at each of the 64 channels. Measurement of the spatial pattern of phase of the 64 damped cosines reveals a time lag of the oscillation corresponding to the direction and speed of propagation of the afferent axons that carry the electrically evoked action potentials (Figure 5). The contributions of the EEG are removed by this approach, along with the amplitude and phase patterns of the endogenous bursts, because the times of onset of the bursts and their frequencies of oscillation vary unpredictably from one burst to the next without precise relation to the times of onset of the electrical stimulus.
In contrast, the normal input is from olfactory receptors that are activated by inhalation, which induces a burst of oscillation in the EEG (Figure 2). The burst involves the entire bulb (Bressler, 1984). It is observed through the same array of 64 electrodes placed on the bulbar surface, serving as a 4x4 mm window. A typical burst with one inhalation has a duration of about 100 msec with 4-6 cycles of oscillation at typical frequencies of 40 - 60 Hz. There is a common wave form distributed over the entire bulb, which is derived by statistical analysis, and it is found to have a spatial pattern of amplitude modulation (Figure 6). Furthermore, perceptual information is carried in this spatial AM pattern.
This burst is not evoked by the input. It is induced, because the input makes the bulbar populations unstable. The instability is manifested when the bulb jumps to a new state and creates a new spatial AM pattern of activity. The evidence for this state change is found in the spatial pattern of the phase of the common oscillation. This has the form of a cone, which implies that each transition starts at one point, called a site of nucleation, and spreads uniformly in all directions at rates near 2 m/sec, the velocity of axon collaterals in the bulb (Freeman & Baird, 1987). The location of the apex of the cone is a random variable between successive bursts, and can be found anywhere on the bulbar surface unrelated to the odorant stimuli that select the spatial AM pattern (Figure 7). The polarity of the apex (maximal phase lead or lag) is also a random variable, so that the point cannot serve to "locate" a "pacemaker" neuron. Hence the phase pattern proves that the bursts are endogenous or "self-organized".