Freeman's mass action

From Scholarpedia

Author: Dr. Walter J. Freeman, University of California, Berkeley, California
Author: Dr. Robert Kozma, Computational NeuroDynamics Lab, University of Memphis, TN

Freeman's Mass Action (FMA) denotes the collective synaptic actions that neurons in vast numbers in cortex exert on each other, thereby synchronizing their firing of action potentials. In the aggregate it is a powerful force that creates bursts of cortical electrical activity resembling tornados and hurricanes. FMA instantly and repetitively retrieves memories and binds them with sensory information into percepts that express the meaning of the information. FMA is observed indirectly by measuring extracellular action potentials and dendritic potentials observed in brain waves. It must not be confused with these epiphenomena.

Introduction: The percept in FMA: the door to perception

Everyone has experienced the hunger triggered by the odor of a favorite food, the cascade of associations on glimpsing a familiar face, the surge of dread or delight on recognizing a familiar voice, and so on. That is perception: “the meaningful impression of any object obtained by use of the senses” (Webster). We ask the question: How do brains perceive the meanings of stimuli in a flash of recognition?

To answer the question question we placed electrodes inside the skull and recorded brain waves (the electrocorticogram, ECoG)^[1], which we examined for structures that we identified as the neural correlates of perception in the stages before consciousness. We recorded the ECoG directly from the surfaces of sensory cortices in animals that we trained to perceive conditioned stimuli (CS). We know that many neurons fire simultaneously and synchronously, though we cannot say precisely how many neurons^[2] with how much synchrony. We have shown that the mean rates of firing are correlated with the wave amplitudes.^[3] We know that the action potentials relayed from sensory receptors to sensory cortex excite pyramidal cells, which excite each other and the inhibitory interneurons. And we know that by negative feedback among pyramidal cells and interneurons, FMA causes ECoG oscillations at frequencies in the beta and gamma ranges (20-80 Hz). We infer that the impact of a CS on a sensory cortex begins the construction of a percept by FMA, which we believe happens upon the emergence of a recognizable spatiotemporal pattern in the ECoG.

In these patterns we identify four characteristic features, which we use to describe pre-conscious percepts and deduce how they form. We focus our essay on the features, because one cannot understand FMA theory without knowing the phenomena on which the theory is based. We describe FMA theory elsewhere.^[4] We begin with illustrations from the olfactory ECoGs (Figs. 1, 2), because olfaction is the simplest sensory system, and proceed to the visual, auditory and somatic ECoGs (Figs. 3-6).

[[Box: Mesoscopic versus Microscopic Neurodynamics: A paradigm shift. We believe that FMA involves a paradigm shift, because the theory encompasses new techniques, exemplary experiments, and rules of evidence. A comparable shift occurred in the 19th century, when electricity and magnetism were conceived in Newtonian terms as forces exerted by point charges acting at a distance instantaneously on other point charges. Michael Faraday reconceived the forces as fields, and James Clark Maxwell devised new mathematics, which led to discovery of the electromagnetic spectrum [Arianrhod, 2003]. Most artificial neural networks are Newtonian models, to the extent that they treat microscopic neural pulses as point processes at trigger zones and synapses, often instantaneous with zero lag. FMA requires a Maxwellian approach by conceiving mesoscopic neural activity as a continuum of energy density with finite transmission velocities. Just as the Maxwellian paradigm subsumes the Newtonian laws of Coulomb and Oersted, field neurodynamics [Freeman, 2000] incorporates neural operations at the microscopic level, most specifically at the sites of entry of microscopic activity into mesoscopic domains and exit from those domains to the microscopic level. ]]

The beta-gamma burst, resembling a tone burst

Figure 1: The ECoG from the olfactory cortex illustrates (i) the ubiquitous background spontaneous activity of cortex; (ii) the increase in power with arousal following a sniff of fish (arrows); and (iii) the intermittency of bursts of oscillation (frames). Reprinted from Fig. 7.1 on p. 404 in Freeman (1975).

We isolated a hungry cat that a sound-tight box with a steady inflow of clean air. When it had settled awake to rest, we gave it a brief, faint odor of fish. The cat sniffed, meowed, and scratched, searching for fish. An hour later after feeding to satiety, it ignored the stimulus.

The olfactory ECoG (Fig. 1) illustrates three important properties of the beta-gamma response. First, normal cortex at rest always has spontaneous activity that is almost completely devoid of structure. It is self-regulated noise. The noise is sustained by mutual excitation among cortical neurons, and it is stabilized by refractory periods.^[5] Second, the activity transmitted by receptors to cortex signaling a CS is far weaker than that in the cortical response. Cortex amplifies the input. It also increases its background activity in proportion to the degree of arousal (Fig. 1), and it reorganizes the background into nonrandom patterns, the gamma bursts. Third, repeated sniffs induce a sequence of bursts but with random variation in burst latencies. That variation implies that the onset of a percept depends not just on the sniff. Onset requires a spontaneous break, a discontinuity in the background activity that “jitters” the precise time of burst onset.^[6] In Section 4 we claim that the random event that precipitates percept formation is a null spike.

Figure 2: Left: The 8x8 signals are from a 3.5x3.5 mm square grid of electrodes (spacing 0.5 mm) on the olfactory bulb. Right: The amplitudes of the mean AM patterns are displayed in contour plots. The difference between those in Trial Set 1 reflects formation of neural assembly during training. The pattern differences from Set 1 to Set 2 with the same control and stimulus inputs reflect permanent changes in memory with consolidation. The lack of AM pattern invariance with invariant stimuli shows that AM patterns are retrieved from memory and modified by input. They are not representations of sensory stimuli; they are creations by sensory cortex. Reprinted from Fig. 12, p. 73 in Freeman (2001a).

The spatial AM pattern, resembling an interference pattern

We use an 8x8 electrode array fixed on the cortical surface to sample the ECoG at 64 points. The waveform of the gamma oscillation is similar at all 64 points, differing slightly in frequency and phase but mainly in amplitude (Fig. 2). The wave carries the percept, and the spatial pattern of amplitude modulation (AM) expresses the content. We display the AM pattern with the 64 amplitudes of the carrier wave as a contour plot. When a subject has learned to perceive and respond selectively to a CS, the spatial AM pattern corresponding to the CS appears whenever the subject perceives the CS.^[7]

We infer that the early change in AM pattern (e.g., from “Air” to “Amyl” in Trial Set 1, Fig. 2) is due to strengthening of synapses between only those pairs of pyramidal cells that are simultaneously excited by the CS in reinforcement learning (responding to rewards and punishments). This inference is based on Hebb’s Rule: “Neurons that fire together wire together.” Such an assembly of mutually excitatory neurons is thought to ignite entirely when a CS excites any part. The assembly sensitizes the cortex to the CS, amplifies the impact, and it averages over variations in CS from trial to trial, so it enables inductive generalization of the CS to a category. We infer that a new assembly forms when a subject learns a new CS, which explains the initial formation of a new AM pattern.

The AM pattern is not a transcription or representation of a stimulus, because it changes overnight and for days afterward during consolidation. It also changes when the same stimulus is given a different context. For example, if the reward is switched from one stimulus to another, so that the subject stops responding to the first and starts responding to the second, both AM patterns change. In brief, the AM pattern manifests the contextual meaning and significance of the CS. The knowledge is stored in very widespread synaptic changes. We know this because all pre-existing AM patterns change, whenever cortex creates a new one, which demonstrates a broad, associative, structural memory. The modified synapses determine the active memory, the remembrance. The AM pattern combines the retrieved memory with the current CS and context. These properties are clearly required for a percept.^[8]

Figure 3: Extraction of the dynamic structures reflecting FMA from ECoG requires high resolution in time, space and spectrum. A. Measurement of the instantaneous power and frequency begins with narrow band filtering (optimally 5 Hz) in search for the carrier wave. B. Search for frames is by display of bursts of oscillation centered at the peak frequency and demarcated by the beats. C. An AM pattern in a frame is revealed in the stable distribution of analytic power over the surface. Null spikes in log₁₀ power demarcate burst start and end. D. The carrier is shown by its minimal spatial and temporal variations in the instantaneous frequency.

The null spike, resembling a tornado

The carrier amplitude is also modulated in time. When the excitatory pyramidal cells and inhibitory interneurons interact, a sensory volley causes the cortex to ring like a struck bell. The evoked oscillation is not directly seen, because it is submerged in the background noise, and the mean frequency varies randomly from each burst to the next. The spectral peaks that we can see in short time windows (0.1 s, Fig. 3, A) blend into a near-linear spectral slope in longer windows (6 s). The problem is that the evoked ringing can suddenly transit into an endogenous burst without warning. We solve the problem by filtering the ECoG with a narrow pass band (optimally 5 Hz) that includes the carrier frequency of a burst. We find the carrier frequency by searching for a peak in the spectrum.

This filter reveals beats: waxing and waning of the amplitude. We distinguish a beta-gamma burst that carries an AM pattern (Fig. 3, B) from background activity by the wide variation of amplitude, which we square to represent power in the signals from the array. This example shows beta power ranging 100-fold from least to greatest in the 64 signals.

Between bursts the power may approach zero. The log₁₀ power of each signal (Fig. 3, C) shows that the duration of down spikes is shorter than the digitizing interval (here 2 ms). For this reason, and because the frequency is never truly fixed, we have to calculate the instantaneous power and instantaneous frequency (Fig. 3, D) at each sampled point in time and space. The instantaneous power is similar to the mean square amplitude of the filtered ECoG. The instantaneous frequency shows how rapidly the power is changing. ^[9] As we show in (Fig. 3, D), the frequency is nearly constant in time through the burst, so that the temporal variation is negligible. However, the spatial variation in frequency is significant, because spatial standard deviation of frequency tells us the width of the pass band. The interactive neurons do not and cannot enter into complete synchrony. The width of the spectral distribution of frequencies determines the interval between beats. The narrower is the pass band, the longer is the burst duration in the filtered ECoG.^[10]

The spatial display of the null spike shows it is extremely localized (Fig. 4, A). The spike location differs from each AM pattern to the next without relation to the CS. The shape of the funnel of log₁₀ power (Fig. 4, B) has the narrow width that is consistent with a highly localized area of dendrites, in which the power in the ECoG has momentarily vanished in that pass band. At that time step and place the instantaneous frequency is undefined. Comparison of the center frequencies before and after the null spike reveals a discontinuity in the phase as the cortex jumps to a new center frequency (Fig. 4, C).

Figure 4: The fine structure of the instantaneous amplitude and phase from the Hilbert transform of the narrow band pass filtered ECoG is revealed by short digitizing steps in time (here 2 ms) and space (here 0.79 mm in an 8x8 electrode grid on the visual cortex of a rabbit). A. Color-coded contour plot of analytic power (square of amplitude). B. Perspective view of a null spike. C. Color-coded contour plot of analytic phase showing a discontinuity at the location of the null spike. D. Perspective view of a phase cone (12 ms later) showing its apex near the site of the null spike and its downward slope from the apex (negative phase gradient) showing an explosion.

The spatial PM pattern, resembling a hurricane

Each beta-gamma burst also carries a spatial pattern of phase modulation (PM) (Fig. 4, D) that can be fitted with a cone. We think this means that the burst starts at a point that will become the apex and spreads rapidly over the cortical surface. In half the events it resembles the wave from a stone dropped in water (explosive), but in the other half it is like nothing we have seen before (implosive). In both cases the rate of spread is equal to the conduction velocity of the axons carrying the event across the cortex. In theory we predict that the apex of the cone should coincide with the location of the preceding null spike, and this does occur, but the relation is usually obscured by the overlap of multiple phase cones at different frequencies. The spread continues until the cumulative phase lag is so great that the shared power decreases below 50%, giving what is called a soft boundary condition.

The extremely localized nature of the null spike is illustrated in successive frames of movies (Fig. 5). The direction of the extreme phase at the apex (+ lead or - lag) varies randomly from each burst to the next. Cinematographic display (Fig. 6) of the spatial patterns of the recorded amplitude (not the instantaneous amplitude) of the band pass filtered ECoG often show either explosion (repeated outward thrusts with each half cycle) or implosion (inward thrusts). Some displays also show prominent rotation, either clockwise or counter-clockwise, in the form of a vortex. The field of the percept has at each point both amplitude and rates of change in time and space. From this finding we infer that FMA is a continuous vector field, unlike the electric potential of the ECoG, which is a scalar field, and unlike the pulse activity in neuron assemblies and related networks, which Sherrington (“Man on His Nature”, 1940, pp. 177-178) described as “myriads of trains of moving lights” in an “enchanted loom” – not a mesoscopic field but a collection of microscopic point processes (illustrated by Izhikevich and Edelman, 2008). This difference has deep significance for brain theory; it succinctly denotes the difference between a self-organizing, evolving medium and a passive storage medium – a dynamic vs. static memory. This difference is profound, and it leads on several paths to the frontier of brain theory.

The phase transition: a neural mechanism creating percepts starting well before consciousness

These four features provide a hypothesis on how percepts form in cortex. We propose that the background noise condenses into an AM pattern, similarly to the way water vapor congeals into a raindrop. Hence we call it a cortical phase transition. The pre-stimulus background FMA contains all frequencies of oscillation, randomly dispersed but still constraining all the neurons in a group discipline. A volley of action potentials relayed from sensory receptors evokes a gamma oscillation by unbalancing the background excitation and inhibition by excess excitation. The narrow band of the evoked oscillation leads to interference that, sooner or later, briefly cancels FMA interactions. Like a tornado, the null spike destroys existing order, which opens an opportunity for cortex to build anew. If the volley carries information from a CS, it ignites a neural assembly that generalizes the input to a category. The simultaneous firings in the assembly direct the cortex into a stereotypic pattern. The pattern is selected by the input, but it is determined by the synaptic connections shaped by learning. Thereby the input activates a memory that is expressed in an AM pattern.^[11] The CS also provides new information with which cortex updates the synaptic memory storage and the dynamic remembrance.

The loss of FMA during the null spike breaks the spontaneous background activity. In that moment the neurons are released from self-imposed order. They are susceptible to capture by the next memory that is elicited by the CS or input from the brain. The event spreads across the cortex at the velocity of long connections, which is revealed in the slope of the phase cone. The resulting AM pattern is broadcast from the entire sensory cortex throughout the forebrain as a basis for multisensory integration and decision-making by the whole brain. Therefore, we regard the null spike as the ultimate marker for the onset of each new percept; it shows the beat of the perceptual clock that enables each sensory cortex to follow rapid changes in the world and the brain. The new structure emerges by the condensation of neural activity into an AM pattern. The process resembles the change from a gas to a liquid, so we call it a phase transition of cortex from a receiving phase to a transmitting phase.

In theory the locations of the null spike, the conic apex, and the center of the vortex should coincide. In practice they seldom do. We propose three reasons. First, the spatiotemporal resolution of our measurements is marginal. For future recording the digitizing step should be decreased from 2 ms to 0.2 ms in order to sample the high frequency gamma oscillations, and the interelectrode distance should be decreased below 0.8 mm with increased number of electrodes in order to improve the movies in scope and resolution. Second, the signal processing methods must be improved. Decomposition of ECoG by Fourier, Hilbert and wavelet transforms fails to take advantage of our new knowledge about the intrinsic features of percepts by using them as basis functions. Third, the present theory is largely borrowed from physics and mathematics and does not yet stand on its own. Brain science is still in adolescence; the next decade will surely bring explosive growth with stronger union of brain theory and experimental science.

References

Recommended Reading

• Baars BJ, Gage NM (2007) Cognition, Brain, and Consciousness: Introduction to Cognitive Neuroscience. New York: Academic Press.
• Freeman WJ (1991) The physiology of perception. Scientific American 264: 78-85.
• Freeman WJ (2001a) How Brains Make Up Their Minds. New York: Columbia UP.

Scholarpedia References

• Freeman Intentionality, Scholarpedia, 2(2):1337.
• Freeman Hilbert transform for brain waves, Scholarpedia, 2(1):1338.
• Freeman and Erwin Freeman K-set, Scholarpedia, 3(2):3238.
• Freeman and Breakspear Scale-free neocortical dynamics, Scholarpedia, 2(2):1357.
• Freund and Kali Interneurons, Scholarpedia, 3(9):4720.
• Kozma Neuropercolation, 2(8):1360.
• Liljenstrom Mesoscopic Brain Dynamics, in preparation.
• Nunez PL, Srinivasan R (2007) Electroencephalogram. Scholarpedia, 2(2):1348.
• Pikovsky A, Rosenblum M (2007) Synchronization. Scholarpedia, 2(12):1459.
• Pribram K (2007) Holonomic brain theory. Scholarpedia, 2(5):2735.
• Tang and Wiesenfeld Self-organized Criticality, in preparation.

References for background on intracranial ECoG

• Braitenberg V, Schüz A (1998) Cortex: Statistics and Geometry of Neuronal Connectivity, 2nd ed. Berlin: Springer-Verlag.
• Freeman WJ (2001b) The olfactory system: odor detection and classification. Chapter in: Frontiers in Biology, Volume 3. Intelligent Systems. Part II Brain Components as Elements of Intelligent Function. Pages 509-526. New York: Academic Press. http://repositories.cdlib.org/postprints/1006/
• Freeman W.J. (2004a) Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude. Clin Neurophysiol 115: 2077-2088. http://repositories.cdlib.org/postprints/1006
• Freeman W.J. (2004b) Origin, structure, and role of background EEG activity. Part 2. Analytic phase. Clin Neurophysiol 115: 2089-2107. http://repositories.cdlib.org/postprints/987.
• Freeman W.J. (2005) Origin, structure, and role of background EEG activity. Part 3. Neural frame classification. Clin Neurophysiol 116 (5): 1118-1129. http://repositories.cdlib.org/postprints/2134/
• Freeman WJ (2006) Origin, structure, and role of background EEG activity. Part 4. Neural frame simulation. Clin Neurophysiol 117: 572-589.
• Freeman WJ (2009) Deep analysis of perception through dynamic structures that emerge in cortical activity from self-regulated noise. Cognitive Neurodyn 3(1): 105-116. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s11571-009-9075-3
• Freeman WJ, Holmes MD, West GA, Vanhatalo S (2006) Fine spatiotemporal structure of phase in human intracranial EEG. Clin Neurophysiol 117(6): 1228-1243.
• Izhikevich EM, Edelman GM. (2008) Large-scale model of mammalian thalamocortical systems, PNAS 105 (9): 3593-3598.
• Jensen HJ (1998) Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. New York: Cambridge University Press, 1998.
• Kozma R, Freeman WJ (2008) Intermittent spatio-temporal de-synchronization and sequenced synchrony in ECoG signals. Special Issue: Synchronization in Complex Networks, Suykens J, Osipov G (eds). Chaos 18, 037131. http://link.aip.org/link/?CHA/18/037131
• Schüz A, Miller R (eds.) (2002) Cortical Areas: Unity and Diversity. New York: Taylor and Francis.
• Tallon-Baudry C, Bertrand O, Peronnet F, Pernier J. Induced gamma-band activity during the delay of a visual short-term memory task in humans. J. Neurosci. 1998, 18: 4244-4254.

References for applications to scalp EEG

• Freeman WJ, Rogers LJ, Holmes MD, Silbergeld DL (2000) Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands. J Neurosci Methods 95: 111-121.
• Freeman WJ, Burke BC, Holmes MD (2003) Aperiodic phase re-setting in scalp EEG of beta-gamma oscillations by state transitions at alpha-theta rates. Human Brain Mapping 19(4):248-272. http://repositories.cdlib.org/postprints/3347
• Pockett S, Bold GEJ, Freeman WJ (2009) EEG synchrony during a perceptual-cognitive task: Widespread phase synchrony at all frequencies. Clin Neurophysiol 120: 695-708.
• Ruiz Y, Li G, Freeman WF, Gonzalez E. (2009) Detecting stable phase structures on EEG signals to classify brain activity amplitude patterns. J Zhejiang Univ 10(10):1483-1491.
• Ramon C, Freeman WJ, Holmes MD, Ishimaru A, Haueisen J, Schimpf PH, Resvanian E (2009) Similarities between simulated spatial spectra of scalp EEG, MEG and structural MRI. Brain Topography, in press

References for FMA theory

• Arianrhod R (2003) Einsteins’s Heroes. Imagining the World through the Language of Mathematics. Oxford UK: Oxford UP.
• Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends Cogn Sci 5: 2-36.
• Freeman WJ (1975) Mass Action in the Nervous System. New York: Academic Press. © 2004: http://sulcus.berkeley.edu/MANSWWW/MANSWWW.html
• Freeman WJ (2000) Neurodynamics. An Exploration of Mesoscopic Brain Dynamics. London: Springer. http://sulcus.berkeley.edu/*Freeman WJ (2008) A pseudo-equilibrium thermodynamic model of information processing in nonlinear brain dynamics. Neural Networks 21: 257-265. http://repositories.cdlib.org/postprints/2781
• Freeman WJ, Kozma R. Appendix: Bollobás B, Ballister P (2009) Chapter 7. Scale-free cortical planar networks. Handbook Large-Scale Random Networks. Series: Bolyai Mathematical Studies, Bollobás B, Kozma R, Miklos D (eds.), New York: Springer., pp. 277-324. http://www.springer.com/math/numbers/book/978-3-540-69394-9
• Freeman WJ, Vitiello G (2006) Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics. Physics of Life Reviews 3: 93-118. http://repositories.cdlib.org/postprints/1515
• Freeman WJ, Vitiello G (2009) Dissipative neurodynamics in perception forms cortical patterns that are stabilized by vortices. J Physics Conf Series 174 (2009) 012011. http://www.iop.org/EJ/toc/1742-6596/174/1
• Freeman WJ, Zhai J (2009) Simulated power spectral density (PSD) of background electrocorticogram (ECoG). Cognitive Neurodynamics 3(1): 97-103. http://dx.doi.org/10.1007/s11571-008-9064-y.
• Freyer F, Aquino K, Robinson PA, Ritter P, Breakspear M (2009) Bistability and non-Gaussian fluctuations in spontaneous cortical activity. J Neurosci 29(26): 8512-8524.
• Rice SO (1950) Mathematical Analysis of Random Noise. Tech Publ Monograph B-1589. New York: Bell Telephone Labs Inc. http://en.wikipedia.org/wiki/Rice_distribution
• Tsuda I (2001) Toward an interpretation of dynamics neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24: 793-847.

External Links

http://sulcus.berkeley.edu/Null_Spikes_Movies

Footnotes

Dr. Robert Kozma, Computational NeuroDynamics Lab, University of Memphis, TN, was invited on 27 January 2009.