Self-organization of brain function

• Hermann Haken, Institute for Theoretical Physics I, Center of Synergetics, University of Stuttgart, Germany

Self-organization phenomena can be found everywhere in the inanimate and animate world. Self-organization of brain function is a particularly interesting example.

Figure 1: Transition of parallel movement of index fingers to antiparallel, symmetric movement.

Self-organization and the brain

Self-organization is defined as a process by which systems that are in general composed of many parts spontaneously acquire their structure or function without specific interference from an agent that is not part of the system. Examples are provided by the growth of plants and animals. A counter example is the creation of a sculpture by an artist.

The concept of self-organization was discussed in ancient Greek philosophy (see F. Paslack 1991). In more modern times, self-organization was discussed by the German philosopher Immanuel Kant (cf. Paslack 1991), who in particular dealt with the formation of the planetary system, as well as by the German philosopher Schelling (cf. Paslack 1991), whose discussion remains rather weak, however. In more modern times, self-organization was discussed by Heinz von Foerster (1992) within his "Cybernetics of second order". A systematic study of self-organization phenomena is performed in the interdisciplinary field of synergetics (Haken 2004) that is concerned with a profound mathematical basis of self-organization as well as with experimental studies of these phenomena.

Self-organization phenomena can be found everywhere in the inanimate and animate world. Here we provide a particularly interesting example, namely self-organization phenomena of the human brain. The human brain is the most complex system we know in the world. It is composed of up to 100 billions neurons (and glia cells) which are strongly interconnected. For instance, a single neuron can have more than 10,000 connections to other neurons. The central question is: who or what steers the numerous neurons so that they can produce macroscopic phenomena such as the coherent steering of muscles in locomotion, grasping, vision i.e. in particular pattern recognition, decision making etc. An early proposal that the brain acts as a self-organizing system according to the laws revealed by synergetics was made by H. Haken in 1983, e.g., gait transitions of horses were conceived as non-equilibrium phase transitions studied in synergetics that provides an explicit example of self-organizing phenomena. A similar suggestion was made in the context of dissipative structures by Kugler, Kelso and Turvey (1980).

Movement

In movement and cognitive neuroscience, the experiments by Kelso (1981; 1984; for review see Kelso, 1995) and their theoretical modelling by Haken, Kelso and Bunz (1985; called the HKB model in the literature, Figure 2; for review, see Haken, 1996) have become a paradigm for self-organization in biological systems. Kelso informed subjects to move their index fingers in parallel and then to increase the movement speed. At a critical value of speed an entirely involuntary spontaneous transition to symmetric finger movement took place ( Figure 1). Using the concepts of control parameters and order parameters it was predicted that there must be phenomena known from the theory of non-equilibrium phase transitions, namely hysteresis, critical slowing down and critical fluctuations ( Figure 2). The experiments by Kelso and co-workers clearly showed the existence of these phenomena which ruled out especially the notion of the brain acting as a computer. Subsequent experiments using a high density SQuID array to measure the magnetoencephalographic activity of the sensorimotor cortex revealed a spontaneous transition between different brain activities close to the transition point (Kelso, et al., 1992). Detailed analysis due to Fuchs, Kelso and Haken (1992) and theoretical modelling by Jirsa et al. (1994; see also Jirsa, Fuchs and Kelso, 1998) revealed the existence and action of order parameters. i.e. it appears as if close to the transition point the system is governed by few order parameters.

Figure 2: The frequency of the index finger movement can be interpreted as control parameter, whereas the relative phase between the fingers as order parameter. The dynamics of the order parameter can be visualized as the overdamped motion of a ball in a hilly landscape whose valleys define the stable states. In the case of the finger movement, the landscape is drawn in this figure for increasing speed (from upper left to right lower corner). The upper valley is connected with the parallel finger movement, whereas the lower valley is connected with the anti-parallel movement. Close to a critical value of the control parameter (the finger speed), the upper valley becomes very flat. That allows critical fluctuations and critical slowing down. When the valley disappears, a transition occurs. If the sequence of control parameter values is reversed, the upper valley appears again, but the ball will not spontaneously jump from the lower to the upper level (hysteresis) (Haken-Kelso-Bunz model).

Figure 3: The pedalo on which a person can move by appropriate movements of his/her legs.

The phenomenon of self-organization becomes also manifest in experiments in which a subject has to learn to move on a pedalo ( Figure 3). The detailed analysis shows that during the learning period, the number of degrees of freedom used is more and more reduced and finally the system is governed by one complex order parameter. Again, fluctuations can clearly be seen. The experiments were performed by Körndle and the theoretically analysis by Haas and Haken (see Haken 1996).

Visual perception

Figure 4: Example of bistability of vision: a face or just fruit and vegetables? (Painting by the middle age painter Arcimboldo).

A further manifestation of self-organization can be found in vision. Typical phenomena are bistability of vision, where the same picture causes quite different percepts (Figure 4) and hysteresis (Figure 5) where the percept seen depends on previous experience. A large class of phenomena consists of the perception of ambiguous patterns i.e. vase/face (Figure 6), Necker-cube, old woman/young woman etc. where the percepts oscillate back and forth between two or more different interpretations. All these phenomena can be modelled as self-organization processes in terms of synergetics (cf. Haken 2004b).

Typical examples of self-organization can also be observed when local electric fields of the brain are measured, experiments mainly done on cats and monkeys. When an anaesthetized cat sits in front of a screen on which two bars are moving in the same direction and at the same speed, then the firing of two groups of neurons at different locations in the visual cortex becomes correlated (Gray and Singer 1987, Eckhorn et al. 1988). On the other hand, this correlation effect breaks down when the bars move in opposite directions. For a survey see for instance Engel et al. (1992) and for theoretical approaches see Gerstner and Kistler (2002) and Haken (2007) with further references).

The experiments and their theoretical modeling mentioned above are only a small section out of a huge variety of other approaches which aim at demonstrating that the human brain or, more generally speaking, any brain, acts by means of self-organization. Here self-organization was studied in the context of cognitive function. Self-Organization can also be observed in the growth of brains which would require, however, another article.

Figure 5: Hysteresis in perception: start from the left upper corner, follow the first row and then proceed the same way along the lower row. You will notice a jump from the perception of a man's face to that of a woman. Do the same observations in the reverse direction: the transition from woman to man's face occurs at a later point than before.

Figure 6: In case of two order parameters, oscillations are possible. This figure shows an ambiguous picture in which our perception oscillates back and forth between the percepts vase and face.

Relevance to the mind-body problem

All these studies are intimately and even unavoidably connected with the mind-body problem including the question of free will. One general remark should suffice here, though the field is extremely wide. Within the framework of theoretical modelling by means of the concepts of synergetics, the following picture evolves at least with respect to pattern recognition. As we know, neurons act at time scales of milliseconds, whereas percepts evolve in times of half a second to few seconds. Thus we have a typical timescale separation which plays a fundamental role in synergetics. According to it, at the long-time scale, order parameters are acting while at short-time scales the individual parts act and are enslaved by the order parameters. This leads to the concept of circular causality which holds for many self-organizing systems. Close to a transition point collective variables, i.e. order parameters come into existence by means of the cooperation of the individual parts. On the other hand, the order parameters determine (and enslave) the individual parts. This leads to the concept of circular causality: order parameters, individual parts, order parameters etc.. We may start this circle with the individual parts, go one way round and then observe that the individual parts find their coherent action by themselves. Or we start from the order parameters, go the circle around and find that the order parameters determine their behaviour. In this case, an enormous information reduction takes place, because only little information is needed to describe the order parameters. Such a picture in which purely mathematical relations (compare the article on synergetics) are used, allows different philosophical interpretations. A materialist will say that the primary agent is provided by the individual parts, i.e. the neurons. In idealism one may say that the functioning is governed by an immaterial agent, namely the order parameters. Finally one may adopt also the idea that both are just two sides of the same coin as expressed by Spinoza. Evidently, ontology comes in, when brain function is dealt with.

References

• Eckhorn, R., et al. Coherent Oscillations: A Mechanism of Feature Linking in the Visual Cortex? Multiple electrode and correlation analyses in the cat (Biol. Cybern 60, 121-130, 1988)

• Engel, A.K., König, P., Schillen, T.B. Why Does the Cortex Oscillate? (Current Biology 2, 332-334, 1992)

• Fuchs, A., Kelso, J.A.S., Haken, H. Phase Transitions in the Human Brain: Spatial Mode Dynamics (International Journal of Bifurcation and Chaos 2, 917-939, 1992)

• Gerstner, W., Kistler W.M. Spiking Neuron Models (Cambridge University Press, Aug. 2002)

• Gray, C.M., Singer, W. Stimulus-Dependent Neuronal Oscillations in the Cat Visual Cortex Area (17. IBRO Abstr. Neuroscience Letters Suppl. 22, 1301, 1987)

• Haken, H. Synergetics, Introduction and Advanced Topics (Springer, Berlin, 2004a)

• Haken, H. Synopsis and Introduction. In Başar, E., Flohr, H., Haken, H., Mandell, A.J. (eds.), Synergetics of the Brain (Springer, Berlin, 1983, 3-25)

• Haken, H. Principles of Brain Functioning (Springer, Berlin, 1996) with further references

• Haken, H. Brain Dynamics. Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise (Springer, Berlin, 2002, 2007)

• Haken, H. Synergetic Computers and Cognition (2nd ed., Springer, Berlin, 2004b)

• Jirsa, V.K., Friedrich, R., Haken, H., Kelso, J.A.S. A Theoretical Model of Phase Transitions in the Human Brain (Biological Cybernetics, Springer, 1994, Vol. 71, 27-35)

• Jirsa, V. K., Fuchs, A., & Kelso, J.A.S. (1998) Connecting cortical and behavioral dynamics: Bimanual coordination. Neural Computation, 10, 2019-2045.

• Kelso, J.A.S. (1981) On the oscillatory basis of movement. Bulletin of the Psychonomic Society, 18, 63.

• Kelso, J.A.S. (1984) Phase transitions and critical behavior in human bimanual coordination. American Journal of Physiology: Regulatory, Integrative and Comparative, 15, R1000-R1004.

• Kelso, J.A.S. Dynamic Patterns: The Self-Organization of Brain and Behavior (MIT Press, Cambridge, MA 1995) with further references

• Kelso, J.A.S., Bressler, S.L., Buchanan, S., DeGuzman, G.C., Ding, M., Fuchs, A. & Holroyd, T. (1992) A phase transition in human brain and behavior. Physics Letters A, 169, 134 144.

• Kugler, P.N., Kelso, J.A.S., & Turvey, M.T. (1980) Coordinative structures as dissipative structures I. Theoretical lines of convergence. In G.E. Stelmach & J. Requin (Eds.), Tutorials in motor behavior. Amsterdam: North Holland.

• Paslack, F. (1991) Urgeschichte der Selbstorganisation (Vieweg, Braunschweig)

• von Foerster, Heinz. Cybernetics. In: The Encyclopedia of Artificial Intelligence. 2nd edition, S.C. Skapiro (ed.) (John Wiley and Sons, New York, 1992, 309-312)

Internal references

• Valentino Braitenberg (2007) Brain. Scholarpedia, 2(11):2918.

• Jeff Moehlis, Kresimir Josic, Eric T. Shea-Brown (2006) Periodic orbit. Scholarpedia, 1(7):1358.

• Hermann Haken (2007) Synergetics. Scholarpedia, 2(1):1400.

See Also

Self-Organization, Haken-Kelso-Bunz Model, Coordination Dynamics

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Reviewed by: Anonymous

Accepted on: 2007-03-27 12:11:40 GMT