Zeno's paradox in ancient times held that for an arrow to reach its target it had to cover half the distance first, and half of that first, and so forth. By infinite regression it was inferred never to be able to start at all. This paradox was resolved in the 17th Century with the invention by Leibniz and Newton of the calculus of infinitesimals. As the distance of travel decreased so also did the time needed to cross it. In the limit, as the distance and time increments both approached zero, their ratio approached a finite value, the velocity. Thereupon the modern view of dynamics came into being, replacing the ancient world of static physics.
The acceptance and success of this new way of thinking was not based on philosophical considerations. It was solidly grounded in the new mathematics of precise description and prediction. The modeling of the solar system and the tides was followed by a host of applications, first in military hardware and mechanical devices, which supported the industrial revolution, then in thermodynamics, electrical power networks, electromagnetic and radiological devices, nuclear power systems, aircraft, computers, and so on. Descriptive metaphors for the study of change also found their way into many other fields, such as drama, literature and psychodynamics, but significantly without the support of descriptive equations. Such reasonings remained analogies with little disprovability or predictive power.
Early on the brain was seen as a physical dynamical system,
and the new concepts were almost immediately applied in attempts
to explain its processes, beginning with Descartes, who conceived
the pineal as a kind of valve used by the soul to regulate the
pumping of spiritual fluid into the muscles, an idea that was
quickly disproven by Borelli using a plethysmograph. There followed
the analogies of clockworks, telegraph and telephone systems,
thermodynamics (which underlay Freudian theory), digital computers,
and holographs. None of these likenesses is adequately supported
by reference to measurements of brain activity made during its
normal functioning, nor is the brain "like" any man-made
machine. If anything, it is "like" a natural, self-organizing
process such as a star or a hurricane. With the guidance of genes
it creates and maintains its structure, and it exchanges matter
and energy with its surround. Yet it is unique, in that it moves
itself through its surround and incorporates facets of its environment
for its own purposes, to flourish and prevail. Its dynamical processes
are in time scales of fractions of a second, and its distance
scales are in millimeters. It is these intrinsic processes that
we must describe mathematically, which means to construct, solve,
and evaluate sets of descriptive differential equations. Only
then can we say that we know and understand brain dynamics.
As a dynamical system seen from the outside, the brain takes inputs in the form of stimuli and gives outputs in the form of responses. We should not begin with the whole but with the smallest part that will suffice. For many purposes that is the neuron. We measure its input, such as a volley of afferent action potentials, and its output, such as a postsynaptic potential (PSP), and we use the ratio of output to input to specify an input-output (I-O) pair. We repeat this test ad nauseam under varying conditions, until there are no more surprises. The collection of I-O pairs constitutes the experimental data base.
We examine these pairs and devise a model, which consists of a differential equation that, when solved for the input and the initial conditions at the start of the input, yield a curve that can be fitted to the observed output. We can call this equation an operator that transforms the input into the output. For example, a nerve impulse is transformed by an axodendritic synapse into an exponentially decaying PSP, and a model consisting of a differential equation suffices to describe this operation. From this simple beginning, which forms a main foundation of modern cellular neurophysiology and more recently of the new field of neural networks, we generalize to arrays of interconnected neurons and to trains of impulses in an unlimited variety of network configurations.
Herein lies a kind of pathology of modeling. In the minds of modelers these networks grow in lucubratory complexity and in fascination, independently of their original intent to explain the brain. In order to keep onto the track of that goal, it is essential to refer constantly to I-O pairs from brains that are active in the pursuit of their own goals during the time of recording and measurement. Models of behavior, such as those of Freud, Pavlov, Hull, Skinner, Grossberg, and others are not brain models, because they are not concerned with and immediately tested against the brain activity that underlies and accompanies goal-directed behavior. My intent here is to demonstrate an experimental pathway to the realization of dynamic brain models, which are testable with electrophysiological and neuropharmacological tools.
For reasons that I will discuss the electroencephalogram
(EEG) will be especially important in the coming "Decade
of the Brain", but in ways that have not been generally foreseen.
A Task Force of the American Psychiatric Association has recently
completed a list and assessment of the current and potential uses
of quantitative EEG ("qEEG") in psychiatry (Luchins
1990). The list includes temporal spectral analysis, visual imaging
of color coded brain activity maps, and multiple discriminant
analysis of EEGs and evoked potentials from groups of subjects.
Regrettably the Task Force failed to perceive the uses of "qEEGs"
as data bases for modeling brain dynamics, which supports my main
contention here, that perception is 95% expectation and 5% sensory
input.
My own work has been focussed on the olfactory system in small laboratory animals, because this is the simplest and phylogenetically oldest sensory system, and because it is the most important of the senses for cats, rabbits and rats. Of the roughly 35 years that I have devoted to this study, the first 30 were spent in learning what questions to ask. Only in the past few years have some answers been forthcoming.
The crucial experiments are simple in conception, although it took over a decade to do them successfully for the first time. Rabbits were implanted with an array of 64 electrodes in an 8 x 8 grid placed onto the surface of the olfactory bulb. They were trained to respond by licking to one odorant, such as amyl acetate that was accompanied by a reward (water), and merely to sniff in response to another odorant (such as butyric acid) as an unrewarded stimulus. On each trial a set of 64 EEG traces was recorded for 6 sec, that included a control period and a test period. Brief EEG segments lasting 0.1 msec were selected during the times of inhalation of the background, control air or either of the two odorants presented on randomly interspersed trials. Sets of several hundred of these EEG segments were analyzed for each animal. We knew which of the 3 states each segment came from. The crucial question was, what aspect or aspects of the segments would enable us to classify the segments correctly in respect to the antecedent conditions?
The hypotheses were that, between the time of inhalation and the performance of a correct response, odorant information existed in the bulb as a pattern of neural activity, on the basis of which the animal made the discrimination, and that this information would be detectable in some as yet to be determined properties of the EEGs. Our results showed that the information we sought was indeed manifested in the EEGs. It was identified as a spatial pattern of oscillation in the high frequency range of 40- 80 Hz that we termed the "gamma" range, in analogy to the high end of the x-ray spectrum. A common wave form was found in each segment, and the spatial pattern of its amplitude tended to converge toward a reproducible shape each time that the background or an odorant was present. In principle this form of information is quite simple. It is like a frame in a black-and-white movie, in which the carrier wave is the light, and the shape is formed by the highs and lows of the amplitude or intensity of the light.
The finding that the central "code" for olfaction is spatial is not surprising. This was predicted by Adrian (1950) on the basis of his pioneering studies in the hedgehog. After all, the role of the receptors forming a sheet of neurons in the nasal cavity is to transform an incident chemical species into a spatial pattern of action potentials, much as a retinal pattern of light is transformed to a pattern of ganglion cell activity. This spatial pattern of receptor activity is transmitted to the bulb by unbranched axons that have some degree of topographic order, so that a new spatial pattern can be predicted to be generated in the bulb for each new odorant. Evidence for its existence has been presented by several groups using metabolic labeling techniques (e.g. Lancet et al. 1982). And it is not surprising that the information should exist in the induced burst of activity accompanying each inhalation, which rises above the background activity during inhalation, because it is well known that detection of odors takes place on inhalation. But there are five aspects that are very surprising.
First, the information is uniformly distributed over the entire olfactory bulb for every odorant. By inference every neuron participates in every discrimination, even if and perhaps especially if it does not fire, because a spatial pattern requires both black and white. This fact has been demonstrated by repeating the classification test while deleting randomly selected groups of channels. No channel is any more or less important than any other channel in effecting correct classifications. Furthermore, we and many other investigators have attempted to demonstrate odorant specificity in the discharge rates of action potentials from single neurons. These attempts have never succeeded. In view of the facts that the minimal number of channels for correct classification of EEG segments is 8 to 16, and that each segment reflects the activity of many thousands of neurons, we have concluded that the information relating to odorants is carried by assemblies of millions of neurons, and it is not detectable in the activity of the handful of neurons that can be simultaneously accessed by multiple microelectrode recording.
This finding establishes the significance of the EEGs as experimental variables. These electrical potentials result from the synaptic currents of neurons that flow between the cells, where they sum over the contributions of large numbers of neurons (Freeman 1975, 1991). Thereby the EEGs give direct access to the amplitudes of synaptic activity of populations of neurons. This is the hierarchical level, I believe, which the goal-oriented behavior is being elaborated.
Second, we find that the bulbar information does not relate to the stimulus directly but instead to the meaning of the stimulus. This has been shown in several ways. The simplest way is to switch a reward between two odorants, so that the previously rewarded stimulus is no longer reinforced and vice versa. Both spatial patterns change, though the two odorants do not. So also does the spatial pattern for the control segments in background air. So also do all pre-existing patterns change when a new odorant is added to the repertoire. We infer that the patterns for all odorants that can be discriminated by a subject change whenever there is a change in the odorant environment. Furthermore, we trained rabbits serially to odorants A, B, C, D, and then back to A, and found that the original pattern did not recur, but a new one appeared. This property is to be expected in a true associative memory, because the context is no longer the same.
The point here is that the brain does not process "information" in the commonly used sense of the word. It processes meaning. When we scan a photograph or an abstract, we take in its import, not its number of pixels or bits. The regularities that we should seek and find in patterns of central neural activity have no immediate or direct relations to the patterns of sensory stimuli that induce the cortical activity but instead to the perceptions and goals of the subjects.
Third, the carrier wave is aperiodic. That is, it does not show oscillations at single frequencies, but instead has wave forms that are erratic and unpredictable in each segment, nor is it ever the same in any two segments, irrespective of odorant condition. Yet the same wave form appears on all the channels, although of course at different amplitudes. Moreover, during exhalation and prior to each inhalation there is persisting background activity, which is highly irregular, with its energy broadly distributed over the gamma range of the spectrum. Odorant segments in many instances show no increase or even a decrease in overall EEG amplitude from this basal state, yet always display a remarkable commonality of wave form across channels.
The possibility that this seemingly random wave form could occur by chance almost simultaneously on all channels is vanishingly small. We sought a mechanism by which a common activity might be imposed in this gamma spectral range onto the whole bulb, either by receptors or by centrifugal pathways from the forebrain and brainstem. We found firm evidence that no external driving can produce the observed commonality of wave form. Indeed, a substantial aperiodic basal activity persists after the bulb and olfactory cortex are surgically de-afferented and isolated as a unit from the rest of the brain.
These findings have led to the insight, already reached independently by other investigators (e.g. Babloyantz and Destexhe 1986), that the brain activity is characteristically. More specifically, many parts of the physicochemical brain are capable of generating controlled but locally unpredictable activity that looks like noise but is not. This is significant in two respects. The lesser is that it directs us to search for carrier wave forms that are aperiodic and not for oscillations at specific frequencies such as the alpha or the "40 Hz". The greater significance attaches to the property of chaotic systems in their ability to jump suddenly and completely from one global activity pattern to another, just as, for example, we jump from one word to the next in the rapid flow of speech and from one gait to another in walking, jogging and running. Our EEGs are showing us sequences of patterns, each of which is carried by a chaotic wave form and not by a wave at a single frequency, as previous EEG studies had led us to expect.
Fourth, we find that a surgical, pharmacological, or cryogenic inactivation of the main pathway from the bulb to the olfactory cortex causes the cortical activity to go silent both in respect to action potentials and to EEGs, and the bulbar activity to display nearly periodic oscillation with each inhalation (Freeman 1975; Gray and Skinner 1988). On recovery from the interruption of the pathway, the normal action potentials and EEGs return. These findings demonstrate that the background unit and EEG activity between inhalations as well as the induced impulse and wave activity during inhalations are global properties of the entire olfactory system. The mechanism includes interaction between the bulb and the olfactory cortex, meaning that activity is transmitted not only from the bulb to the cortex by surface pathways but in the reverse direction by deep pathways.
These findings mean that the chaotic activity that is produced by the bulb and the olfactory cortex is a global property of the entire central system. The irregular activity is not the local sum of the noise of idle neurons. It is the controlled and directed product of the whole. Further, the background state is not a silent equilibrium that is perturbed by noise. It is a chaotic state that keeps the system in constant readiness to jump to any desired perceptual state at any time.
Fifth, we found that pattern formation can be chemically controlled. Modification in the spatial EEG patterns in the olfactory bulb with conditioning requires the participation of other parts of the brain by means of centrifugal pathways (Gray, Freeman & Skinner, 1986). We prepared rabbits with an array implanted onto one bulb to measure EEG patterns and with cannulas placed in both bulbs, in order to inject a beta blocker, propanolol, so as to prevent the action of norepinephrine in the bulb. This is normally released into the bulb by the locus coeruleus following an unconditioned stimulus (a mild electric shock) that accompanies an odorant, and normally a new spatial pattern of EEG activity appears as an animal acquires a conditioned response to the odorant. But when the bulbs were both perfused with propanolol, the spatial patterns of the EEG did not change during the training, nor did the rabbits acquire a conditioned response to the odorant. When we presented the rabbits with an odorant without reinforcement but with injection of norepinephrine directly into the bulb, there were dramatic changes in spatial pattern. Such changes do not occur when no reinforcement is presented, or when it is presented in conjunction with a visual or auditory cue but not with an odorant.
This set of findings gives important clues to
the roles of the many centrifugal pathways into the olfactory
system. It appears likely that these pathways do not carry detailed
information in the form of highly specific and structured activity
patterns. Instead, they carry global modulations that constitute
generic commands, such as "turn on", "turn off",
"imprint", "habituate", bifurcate", and
so forth. I conclude that the connections to and from the forebrain
into the olfactory system are essential for its operation, and
that the modulations are implemented by well known transmitters
and neuromodulators, including the monoamines, acetylcholine,
and probably various neuropeptides.
These surprising results pose major challenges for development of descriptive models, but they also give us several key insights into the dynamical processes to be modeled. First, we are assured that the proper element for our model is the local population and not the single neuron. Perhaps paradoxically this provides an enormous simplification, because the dendrites of neurons in a local neighborhood can be modeled as a simple integrator. The amplitude of output is transformed to the frequency of pulses, but the relationship is not shown by a straight line (linear) as it is for single neurons (reviewed by Freeman 1975). Instead it has the form of an S-shaped curve between the axonal thresholds and maximal firing frequencies for the population. Most of the complexities of the single neuron remain at the hierarchical level of the neuron.
Oscillations arise when an excitatory population is coupled into a loop with an inhibitory population to form a negative feedback loop. The oscillations are periodic in a model of the bulb, as we find to be the case in the experimentally isolated bulb. Chaos in the model arises when the bulbar loop is interconnected with the olfactory cortical loop, so that each excites the other. Each has its own characteristic period, but they differ and cannot agree. Neither can escape the other, so that perennial aperiodic oscillation results. If the two parts are disconnected, the chaos in the model disappears, as it does in the experimental animals.
The bulb and the cortex are each simulated by an array of local oscillators, that are interconnected between the excitatory elements by simulated synapses, so that they excite each other. These connections couple the oscillators into a layer, and they ensure that the whole array oscillates with a common wave form. There are large numbers of input an output connections, essentially one pair for each local oscillator. The mutually excitatory synapses between the oscillators are selectively strengthened during learning to "identify" and "odorant" by presentation of examples of a class of stimuli, leading to the formation of a Hebbian nerve cell assembly or groups of local oscillators that are co-excited by the stimuli. A global command is required in the model to "form an assembly", which is equivalent to the release of norepinephrine into the bulb by the locus coeruleus in response to reinforcement by an unconditioned stimulus. Two or more classes of stimuli are formed in sequential "training" sessions, leading to formation of multiple "nerve cell assemblies" that are separated by simulated "habituation".
The end result is that the array of coupled oscillators generates a reproducible spatial pattern of amplitude of a common chaotic wave form whenever an example of a learned class of stimuli is presented to the model. That pattern serves to identify and classify the stimulus presented. We say that for each learned class of stimuli the model has a chaotic attractor with a basin of attraction. In dynamical parlance this means that the olfactory system (and its model) has certain preferred patterns of activity, any one of which it naturally falls into if given the opportunity. That opportunity is provided by the presence of any stimulus in a class that it has learned to respond to, whether or not the example was included in the original training set. A stimulus of this class provides the input and starting conditions that are needed to place the system into the basin of attraction, so named in analogy to a bowl in which a ball will roll to the bottom and stay there. I infer that there is a learned chaotic attractor and attendant basin of attraction for each class of odorant that a subject can discriminate, and that its basin defines the range of generalization for identification of a stimulus of that class.
Our dynamical model classifies industrial objects such as bolts and screws in the same way, I believe, that the bulb classifies odorants (Freeman, Yao and Burke 1988; Yao et al. 1991). We present it with a few examples of each class of object that it is to identify and train it by increasing the synaptic weights between pairs of local oscillators that are co-activated by the inputs. This sets up the equivalent of nerve cell assemblies. Thereafter, with each test input the system jumps from a basal chaotic state to the basin of an appropriate chaotic attractor, and the output is expressed as a spatial pattern of amplitude of a common chaotic wave form, in the same way that the olfactory bulb jumps to a distinctive spatial pattern of chaotic activity when the nasal receptors are presented with a familiar odorant.
Evidence for this dynamical process of perception
has now been accumulated for the olfactory system in rabbits,
rats and cats; for the visual system in monkey (Freeman and van
Dijk 1987), cat (Eckhorn et al. 1988; Gray et al. 1989) and human
(Schippers 1990); and quite tentatively for the somatosensory
system in human (Freeman and Maurer 1989). Our chaotic dynamical
model derived and implemented according to these principles has
been shown to solve classification problems that other neural
networks cannot.
These experimental data and descriptive dynamic models have profound consequences for understanding how sensory cortexes work at the interface between the brain and the outside world. The crucial point is made by tracing the course of a stimulus into the receptor layer, where it is transduced into a pattern of action potentials, and then into the cerebral cortex, through the thalamus for other systems but directly for olfactory input. What happens in the bulb is a sudden destabilization of the bulbar system, so that it makes an explosive jump from a pre-existing state, expressed in a spatial pattern of activity, to a new state that is expressed in a different spatial pattern. The pattern is selected by the stimulus, and, if reinforcement is provided, there is further slight modification of the pattern, but in the main the pattern is determined by prior experience with this class of stimulus. The pattern expresses the nature of the class and the meaning for the subject rather than the pattern of the particular stimulus. The identity of the receptors that are activated is irrelevant and is not retained, because the activated receptors belong in a class of equivalent receptors. The output does not express the identity of a chemical material but a collection of experiences that the subject has had with the material. The sensory data serve to trigger the formation of the action pattern that then replaces them.
The need for this process can be comprehended by noting that the olfactory environment is infinitely rich in odorant substances, only a small portion of which ever come to the attention of a subject or form the basis for action. That portion is different for every subject, because it depends in part on genetic determinants of the system but mostly on previous experience with selected odorants and the contexts of reinforcement. In a word, the flow of information from the environment is infinitely dimensioned. Any system for information processing must reduce such a flow to a finite rate, lest it be confused or overwhelmed. Man-made systems do this by means of filters, which are designed by observers to accept the portions that are desired by the observers. Brains have no homunculi to specify their goals and desired inputs, and they rely instead on chaotic processes to generate activity patterns that are finite dimensioned. The commonly used sobriquet "self-organizing" connotes the feature that chaotic systems can create information as well as destroy it. I think that chaotic neurodynamics of the kind we have modeled is the origin of novel behavior as diverse as learning by insight or trial and error, invention, recollection both accurate and faulty, and outright confabulation. In brief, perception and memory recall form a unitary dynamical process by which meaning is created.
Because each chaotic pattern is created from within and not imposed from outside, I infer that there is no instance in which raw sense data are incorporated and stored in the cortex as whole patterns or episodic representations. There is only the modification of synaptic weights among populations of neurons, such that after some train of experience there is an appurtenant pattern of neural activity and of behavior in follow up to the presentation, by stimulation or recall, of an example of a learned class of stimuli. The experimentally documented process of "mapping" from each input to each output of the olfactory bulb invokes a fundamental epistemological issue raised most effectively by Immanuel Kant (1781) of the relationship between an event or object and the perception of it. The perceptual process that I have sketched here allows the brain to "know" only its own experience of the object and not the "reality". If we can generalize to the other senses, as I think we must, then all of our individual knowledge is created and organized by chaotic processes, that are shaped by receptor input but cannot ever capture the actualities of the matter and energy that impinge on the receptors. We cannot know the Ding-an-sich (thing-in-itself), only our self-organized patterns that stem from it.
This conclusion is not new, and it is perhaps not even surprising to many philosophers and psychologists, who are already aware that a perception is in the mind of the beholder, and that memory is a creative process rather than a look-up table of imprinted data. But the critical question I am addressing here is: what new evidence can experimental brain science bring to drive home this conclusion? The discovery of meaningful spatial patterns in EEGs is not in itself convincing, because two kinds of spatially patterned activity co-exist in the bulb with each inhalation concurrently. One consists of _the global spatial pattern of cooperative bulbar activity that expresses the meanings of a stimulus. The other kind is stimulus-evoked activity, which has the differing form of spatial patterns of pulse firings in sparse networks of interconnected neurons, and which expresses the properties of the stimulus. Both kinds of patterns can be observed and measured only in part, but they can be inferred to exist in their entirety, the global pattern by spatial ensemble averaging and the pulse pattern by time ensemble averaging (Freeman 1987). How can we know which of these patterns is accepted and acted upon by the olfactory cortex to which the bulb transmits?
It is immediately clear that the global pattern
that is transmitted from the bulb is accepted by the cortex, because
the EEGs of the olfactory cortex are usually highly correlated
with those of the bulb in the gamma range of frequencies at which
the bulb is driving the cortex (Bressler 1988). But what happens
to the stimulus-evoked activity pattern after it is transmitted
from the bulb. My answer is based on the structure of the transmission
pathway and the functional properties of the cortical neurons
that receive the bulbar output. Each bulbar axon branches and
distributes its output broadly over the cortex. Conversely each
cortical neuron receives input from many thousands of widely distributed
bulbar neurons, and its dendrites sum that input continually over
time. I have demonstrated both experimentally and mathematically
that the only portion of the input from the bulb to the cortex
that survives this operation of space-time integration is the
common wave form, which is the product of the global cooperativity
between the bulb and cortex. The stimulus-evoked pulse pattern
is localized spatially, and it is poorly coordinated temporally,
so that even though it is transmitted to the cortex, as recordings
from the pathway have demonstrated, it is expunged by the smoothing
process of integration in the receiving neurons. Hence experimental
evidence from contemporary electrophysiology supports Kant's insight,
that objects in the "real world" are unknowable. The
model asserts that their traces are removed by a "laundering"
operation in the second stage of the synthesizing processes of
perception. Yet the model also asserts that the traces continue
to exist in the bulbar messages, and that if some aspect of an
object is made significant by further reinforcement, the cortex
can modify its sensitivity and accept that aspect, although not
by any sequence of steps "the whole thing". This appears
to be how more complex discriminations are achieved, particularly
by humans using language (Rabin and Cain 1984), but that is another
story.
There are two main extrapolations from this epistemological lesson to be dealt with. First, brain dynamics is largely a study of the self-organization of patterns along an evolving trajectory, and, second, changes take place by sudden jumps from each pattern to the next. What I have modeled thus far are merely the first two steps in the perceptual pathway for olfaction, and then only for one frame at a time in what is clearly a life-long sequence of frames or steps. The models thus far constitute the barest threshold of brain dynamics. Yet despite the enormity of the task ahead, it is possible to speculate heuristically on what might be some of the principles in accordance with which the whole brain takes short steps and creates its own path into the future.
I will focus on the perceptual step that follows identification and classification of a stimulus, which is the estimation of its intensity in the goal-directed behavior of searching. In regard to a scent of predator or prey, its meaning resides not merely in its class but also in its concentration, most importantly with respect to the recent past: is it getting stronger or weaker? But this sequence from two or more sniffs has no value unless the subject can remember where it was and what it did in conjunction with each previous frame, so as to plot its next move toward or away from the inferred source. Three kinds of information are required for assembly of a concentration estimate: the sequence of perceptual samples from the bulb; a record of the sequence of motor commands that instigated the taking of samples, which consists of reafferent messages to the sensory cortex; and proprioceptive data from the musculoskeletal system on whether and how the intended actions were taken. These diverse kinds of neural data must be stored and combined over time periods ranging upward from fractions of a second to the limits of the attention span for the species.
We have no models for how this is done. However, we can say with assurance that it must be done for each sensory modality. Either there is a separate short term memory for synthesizing exteroceptive and proprioceptive inputs for each modality, or the inputs from the several modalities are first combined, including the proprioceptive, and there is a single storage. Brain anatomy clearly indicates that the brain is organized around the latter principle, because all sensory systems feed into the entorhinal cortex, and this is the primary source of input to the hippocampus. In turn the largest projection of the hippocampus is back to the entorhinal cortex, which itself projects back to all of the sensory cortexes from which it received messages. I would suppose that an act of perception may arise in the limbic system and be expressed through the entorhinal cortex as reafferent messages to the sensory cortexes and as motor commands to look, listen and sniff. The EEG evidence from the olfactory system shows that a wave of excitation sweeps over the bulb with the resulting inhalation, and that a state change occurs yielding a burst of oscillation in the gamma range having a spatial pattern of amplitude that constitutes the desired perceptual message. This is transmitted among other places to the entorhinal cortex. From my own and others' observations on other sensory cortical EEGs, I infer that similar explosive jumps take place in those cortexes, with transmission by successive stages of perceptual messages, perhaps in a time frame coinciding with that for the olfactory message. When combined and transmitted to the hippocampus, these may shape the activity in that structure, which by recursive action re-shapes the entorhinal activity pattern in accordance with the recent past. The basis is thereby laid for a next step in a cycle of command, reafference, sample, and integrate, that evolves into the simplest sequence of behavior along a goal-oriented search trajectory.
It is obvious that higher order trajectories involving selection among competing and time-varying goals must involve the frontal cortex, and indeed the entire forebrain and the neuromodulatory systems of the brainstem as well. However, in modeling dynamical systems it is important not to go beyond the data, and at present we do not know with sufficient assurance whether neocortical sensory systems share a common central "code" with each other and with the paleocortex or have radically different forms of expression of meanings. Furthermore, I reiterate that my speculation is unsupported by models, that is, by descriptive sets of coupled differential equations that have been evaluated by fitting the curves comprising their solutions to data points from the measurements of brain activity during goal-directed behavior. But in principle it could be supported or at least tested and disproven, if the data and the models were in hand. To achieve that end we need arrays of EEG data from each of these cortical structures along with measurements of the concomitant behavior.
It should not be supposed that these EEG data might provide a means for reading the thoughts of subjects. An attempt to do so would stem from a serious misconception of what is being proposed in dynamical modeling. The focus of interest should lie not in contents but in processes of organization, through which the brain structures itself by creating its own patterns within its own frames of reference. Among the principle concerns of psychologists and psychiatrists are disorders in organization, such as compulsions, obsessions, anorexias, bulimias, acute anxieties, panic states, Tourette syndromes, attentional deficits, amnesias, autisms, hallucinations, fugues, hypnotic states, multiple personalities, and so forth. These maladaptive behaviors have some of the stigmata of dynamical systems gone pathologically awry in the brain, in that they are commonly seen as sudden and episodic jumps from one global pattern to another of subjective and objective behavior, each episode having a course of its own, often stereotypic although never twice identical, unaffected by voluntary efforts at control, and characterized by hyperstability and loss of adaptiveness. They are not likely to be explicable in terms of mental stress, poor diet, improper mental hygiene, unbalanced chemistry, unhappy childhood, etc. No organic pathology in a contemporary sense can be attached to these conditions, nor should that be expected, if they are disturbances in some basic processes of self-organization by the brain.
One example of disorderly brain dynamics must suffice, for at present it is the only one I have. An experimental partial complex seizure can be reliably induced in the olfactory system by brief supramaximal electrical stimulation of the lateral olfactory tract. It is characterized by a 3/sec spike-wave complex similar to the pattern of classic petit mal epilepsy in humans. Each spike is followed in 30 msec by an ipsilateral twitch of the lips and eyelids. The episode lasts for less than a minute, during which there is loss of normal behavior corresponding to a clinically defined state of absence. The seizure ends abruptly with the return to normal EEG activity and near-normal behavior, although any learning in the preceding few minutes is not retained. The induction involves no chemical or anatomical lesion, and it does not result in kindling or persisting pathology if it is not repeated regularly.
The onset of the seizure spike train coincides with a collapse of the monosynaptically evoked bulbar and cortical synaptic responses to the electrical stimuli, which appears to be due to transmitter depletion in the axon terminals of the stimulated pathway. Upon the consequent abrupt withdrawal of further excitatory input to the system that has been driven to an unusually high level of activity, an instability appears in that the entire system jumps to the stereotypic repetitive discharge. In effect the synaptic disconnection results in a catastrophic collapse of the entire system, rendering it incapable of participating in normal behavior. This pattern of operation has been simulated with the same dynamic model that is used to replicate the chaotic EEG wave forms and pattern classification operations of the olfactory system, by reducing to 15% the strength of the connection representing the lateral olfactory tract (Freeman, 1986). The prediction has been physiologically verified that the instability results from runaway discharge of the inhibitory interneurons in the olfactory cortex.
I conjecture that this pathological process may not be unique to the olfactory system but may be prone to occur in any similarly organized cortical system in the forebrain. It provides a prototypical experiment for a new field of experimental neuropathodynamics that is devoted to exploring the ways in which large assemblies of interactive neuronal populations can be made to abandon the normal domain of flexible and adaptive behavior and fall into the basin of attraction of a low dimensioned chaotic attractor, giving a stereotypic neural activity pattern from which the brain cannot easily escape.
Participation by biologists and behavioral scientists in this endeavor is essential, in part to keep the focus of the enterprise on behavior and to gain the powerful perspectives on normal behavior that studies of pathological behavior yield, but still more usefully to bring to bear an understanding of the pharmacology and behavioral effects of neuroactive drugs. In my experience this is a valuable two-way exchange. The synaptic actions of neurotransmitters are the means by which neurons cooperate and form ensembles, and their strengths of action are expressed as the gain coefficients in the dynamic models. The changes that are effected by neuromodulators at synapses and by mimetics and blocking agents are expressed by changing the values of selected coefficients. A principle value of the dynamic models lies in using it to predict the effects of a drug on a complex interactive neural system incorporating nonlinear feedback. For instance, the role of acetylcholine at a neuromuscular synapse is well understood, because its action is unidirectionally forward, and the relationship between input and output can be specified by a gain coefficient, but its actions on cerebral cortex are unclear. A change in the strength of one or more types of synapse in a system with multiple loops can cause a complex configuration of change in its output for even the simplest input such as an afferent electrical stimulus. A dynamic model of cortex serves as a vehicle for testing hypotheses not only about synaptic modulation with a drug but also about the model itself.
An example is from our study of carnosine as a putative transmitter for the excitatory action of the primary olfactory nerve from the olfactory receptors to the bulb (Gonzalez and Freeman 1980). Biochemical evidence had shown that the nerve contains this dipeptide and the enzymes that make and degrade it (Margolis 1974), but recordings of the activity of the recipient mitral cells had shown that its action was usually inhibitory. Our model showed that the mitral cells are subject to excitation from the nerve and from each other and to inhibition from interneurons, the granule cells. Depending on the relative strengths of the several synaptic actions, the level of mitral activity during application of carnosine might be above, at or below the prestimulus control level, but that in all cases the granule cells must show a sustained increase in activity. This prediction was verified experimentally by recording the sustained output of the granule cells as a steady transbulbar DC potential. This effect does not require direct excitation of granule cells by the nerve, which does not occur in any case.
Comparable neuropharmacological studies conjointly
with dynamic modeling have been done for barbiturates and other
anesthetics (Freeman 1975), norepinephrine (Gray et al. 1986),
acetylcholine (Seyal 1976), and GABA (Rhoades, 1991). Considering
that a substantial part of neurobiology rests on studies of neuroactive
drugs, which are understood at the molecular, cellular and behavioral
levels but not at the neural system level, the study and modeling
of their effects on brain dynamics should have a high priority.
Surely the brain is no longer interpretable as a hierarchy of reflexes or instincts, nor as a thermodynamic or chemical engine. It is a self-organization of neurons and neuronal pools that is dominated by synaptic interactions and modulations. Only in the past decade have the necessary mathematical and technical tools become available for precise description and prediction of the macroscopic properties of the assemblage. Not every behavioral scientist needs to know and use these tools, but somebody must. It is unlikely to be a mathematician or engineer and more likely to be a versatile medical student or resident in the mental health field. Fortunately, a beginning requires not a profound knowledge of either mathematics or engineering but an understanding of brain and behavior and access to an unlimited supply of new data. The aim should be kept clearly in mind of understanding brain dynamics, not finding new methods of diagnosis and treatment. Expecting these would be like asking William Harvey to treat pulmonary edema or myocardial infarction
All of these new insights have come from study of the spatial patterns of brain activity in waking subjects. Four techniques are now at hand to provide these data: recording of electrical fields of potential (EEG); magnetoencephalography (MEG); multiple unit recording with intracerebral microelectrodes; and visual display of voltage sensitive optical dyes that are impregnated into an area of cortex. The spatial mapping procedures based on metabolic uptake and blood flow (e.g. PET, SPECT, 2-DOG, etc.) are slow too slow, and they measure secondary effects of activity, although they should prove very useful as adjuncts, to determine where and when to apply fine-grained arrays and in conjunction with which behavior. Among these techniques the EEG is at present the most useful, because it has the least noise and can be used without time ensemble averaging to access the background and foreground activity patterns on single trials. EEGs can be accessed non-invasively and non-destructively from the scalp with minimal restrictions on head movement for periods of hours to days, which is essential for studies of learning and memory. The technique is the most inexpensive and reliable, and the equipment needed is widely available, including the required computer software. For these reasons I have chosen to emphasize the EEG in my experimental work and in this collection of reprinted research reports.
A new tool requires controlled testing and calibration.
Elsewhere I have predicted (Freeman 1991) that, when a human subject
is asked to gaze at an ambiguous visual figure such as a Neckar
cube, the spatial pattern of gamma activity from a closely spaced
array placed on the scalp over the visual cortex will be found
to alternate between two spatial patterns with each reversal of
the image. If the prediction is upheld, this experiment might
serve for calibration. The approach can provide access to perceptual
data directly from the brain during behavior, which are the raw
materials from which meaning can be extracted by the creation
of dynamical models to explain them. In its own way this approach
is self-organizing, chaotic, and unpredictable, and it defies
prescription by symbol-manipulating rules. It is characterized
by the delights of an ultimate freedom to explore a new and largely
unknown domain of neuroscience, in which untold numbers of discoveries
wait to be made.
The selection of reprints in this volume is
intended to recount the major turning points that I have encountered
over the past three decades in reaching the point of view that
I have sketched in this introduction. They begin with a study
of the volume distribution of the fields of EEG and evoked potential
in the olfactory cortex, and with an exhaustive study of the behavioral
correlates of these potentials in the cat. They include essays
on techniques for measurement, for building models with piece-wise
linear differential equations, and then address crucial insights
into the nonlinearities and the synaptic modifications in the
cortex that mediate learning. They conclude with descriptions
of the central information management by chaotic dynamics that
underlies the acts of perception, by which animals and humans
come to terms with their ever-changing and not fully predictable
environments. In the course of this pilgrimage the crucial insights
that constituted the turning of corners in a labyrinth in retrospect
now can be seen to have an intelligible structure. This labyrinth
will be entered and explored by another new generation of behavioral
scientists and neurobiologists. These essays may constitute a
provisional map for them.
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