Mesoscopic brain dynamics
|Hans Liljenström (2012), Scholarpedia, 7(9):4601.||doi:10.4249/scholarpedia.4601||revision #127475 [link to/cite this article]|
Mesoscopic brain dynamics usually refers to the neural activity or dynamics at intermediate scales of the nervous system, at levels between neurons and the entire brain. It is commonly considered to relate to the dynamics of cortical neural networks, typically on the spatial order of a few millimeters to centimeters, and temporally on the order of milliseconds to seconds. It is usually the type of dynamics that can be measured by methods such as ECoG (electrocorticography), EEG (electroencephalography), LFP (local field potentials) or MEG (magnetoencephalography). Indeed, the terminology can be used in relative terms, where “meso” just indicates that the scale of interest is in between the “micro” and the “macro”.
In science in general, e.g. in physics, chemistry and biology, but also in the social sciences, it is common to distinguish between two levels that may be referred to as "microscopic" and "macroscopic", respectively. Intermediate or "mesoscopic" levels are less commonly considered, but are becoming increasingly in focus (Ingber, 1992; Imry, 1997; Freeman, 2000; Haken, 2005). For example, in lasers and certain chemical reactions, spatio-temporal patterns emerge at scales much larger than the constituent atoms or molecules. The formation of such patterns, which is highly relevant to mesoscopic physics, chemistry and biology has been intensely studied by Hermann Haken and co-workers within the field of synergetics (Haken, 1983, 2002).
Mesoscopic brain dynamics is intermediate between microscopic and macroscopic neurodynamics. What is microscopic could be considered processes and systems studied with a microscope or microelectrodes. It could refer to ion channels or single neurons. The macroscopic scale, on the other hand, could be considered corresponding to the largest scales possible to measure with regard to brain activity. This would be the dynamics related to maps, or systems, such as cortico-thalamic, or cortico-cortical interactions, usually measured with PET, fMRI, or other brain imaging techniques, capturing the dynamics associated with blood flows and metabolism. Also scalp EEG may capture this type of dynamics (Bressler & Menon, 2010).
Mesoscopic brain dynamics refers typically to the dynamics of neuronal populations, networks or columns within cortical areas. It is characterized by its high complexity, often involving oscillations of different frequencies and amplitudes, perhaps interrupted by chaotic or pseudo-chaotic irregular behaviour. The mesoscopic brain dynamics is affected by the activity at other scales. For example, it is often mixed with noise, generated at a microscopic level by spontaneous activity of neurons and ion channels. It is also affected by macroscopic activity, such as slow rhythms generated by cortico-thalamic circuits or neuromodulatory influx from different brain regions.
The possibility to measure, in greater detail, the electrical part of brain activity with external electrodes was discovered and used by Berger in the early 20th century (Berger, 1929). One of the first experiments to demonstrate stimulus-induced activity in the mammalian central nervous system was made by Adrian (1942), showing oscillatory activity in the olfactory system of hedgehog.
Generation of Mesoscopic Brain Dynamics
Mesoscopic brain dynamics are partly a result of neuronal thresholds and the summed activity of a large number of neuronal elements interconnected with positive and negative feedback. This kind of neural dynamics is often characterized by oscillatory synchronous neuronal population behaviours, which underlie the rhythmical EEG waves in the cortex. Synchronization among groups of neurons were first discovered in the olfactory system (Adrian, 1942; Freeman, 1959), but has also been demonstrated in other brain structures, such as the hippocampus (Green and Arduini, 1954; Buszaki et al., 1992), thalamus (Steriade and Llinás, 1988), and the visual cortex (Eckhorn et al., 1988; Gray and Singer, 1989), where the oscillations tend to synchronize in phase. Synchronous oscillations can occur in nearby neurons, but also over considerable distances across spatially separate columns (Gray et al., 1989) and even between cortical areas (Eckhorn et al., 1988; Engel et al., 1991).
Neural oscillations may be due to intrinsic properties of certain pacemaker cells (Lllinas, 1988) or due to network effects (Traub & Miles, 1991). A population of neurons might fire together either because it responds to an afferent oscillatory input or because of cellular/synaptic interactions. An understanding for how such synchronous groups of neurons may be formed was first given by Donald Hebb (1949), who proposed that representations of sensory or motor patterns should consist of assemblies of cooperatively interacting neurons. Such assemblies could form according to a so called Hebbian synaptic modification, which depends on the co-occurrence of pre- and postsynaptic activity. The finding and analysis of cooperating neural assemblies is facilitated by triple recording from microelectrodes, which simultaneously can detect single unit spike trains, in addition to neural mass signals, such as multiple unit spike activity (MUA) and local slow-wave field potentials (LFP).
Events and processes at the microscopic level of neurons and molecules have an effect on the meso- and macroscopic levels of networks and systems, through their interactions via synaptic and non-synaptic connections. At the same time, the network or ensemble dynamics constrain the constituent neurons, engaging them in a self-organizing and coordinated activity. The higher level dynamics “enslaves” the lower levels, according to the theory of synergetics, providing an example of circular causality of complex systems (Haken, 1983, 2002).
The Olfactory Cortex as a Model System
While mesoscopic brain dynamics is observed in many brain structures, the mammalian olfactory system (primarily bulb and cortex) is often used as a model system, much due to the pioneering work of Walter Freeman and his co-workers since the 1960s (Freeman, 1959; 1975; 2000). In particular, theta and gamma rhythms are observed, as well as spatiotemporal waves of activity moving across the bulbar and cortical surfaces. Also chaotic-like behaviour has been observed and characterized (Freeman, 1987). Furthermore, the structure of this system is well characterized, and Freeman and others have successfully studied and described how structure, dynamics and function are related in this system.
Computational models have contributed to elucidate these relationships, where simulations have been able to closely mimic the dynamics, as captured by LFPs (local field potentials), ECoG, or intracranial EEG (Freeman, 1987; Li and Hopfield, 1989; Liljenström, 1991; Wilson & Bower, 1992). An intracranial EEG trace from the rat olfactory cortex (Fig. 1) is closely reproduced by a simulated EEG (Fig. 2) generated by a neural network model (Liljenstrom, 1991) of the three-layered olfactory cortex (Fig. 3). In this case, the output of several neighbouring network units, representing the average membrane potential of neuronal populations, was summed and weighted to mimic the electrical activity at an electrode located above the network surface. In Fig. 4 spatio-temporal patterns of activity, representing the neural response to an odorous input signal, is shown as color-coded positive and negative "mean membrane potentials" of the network nodes. A specific odor input results in a specific spatio-temporal pattern in the network activity, resulting in learning or recall (see below).
Transitions in Mesoscopic Brain Dynamics
Cortical neurodynamics is constantly changing, due to internal fluctuations, neuromodulation, and sensory input. Many factors influence the dynamical states, such as the excitability of neurons and the synaptic strengths between them. A number of neuromodulators affect these neural properties, including acetylcholine (ACh) and serotonin (5-HT). The concentration of these neuromodulators in the cortex seems to be directly related to the arousal or motivation of the individual (Freeman, 2000).
The state of arousal or attention may change the macro- and mesoscopic brain dynamics considerably, and even induce phase (state) transitions that could affect the functional efficiency of cognitive processes (Liljenström, 2010). Visual attention has several effects on modulating cortical dynamics, in terms of changes in firing rate (McAdams & Maunsell, 1999), as well as gamma- and beta-band coherence (Fries et al., 2001). With attention, there is a reduction in low-frequency synchronization and an increase in gamma-frequency synchronization. Generally, it is believed that lower frequency bands are generated by global circuits, whereas higher frequency bands are derived from local connections (Gu & Liljenström, 2007).
Electrical stimulation may also induce transitions in cortical dynamics. When studying the dynamical properties of the olfactory cortex, Freeman and coworkers stimulated the lateral olfactory tract (LOT) of cats and rodents with electric shock pulses of varying amplitude and duration, and recorded the neural response via intracranial EEG (Freeman, 1959; 1964). A strong pulse gives a biphasic response with a single fast wave moving across the cortical surface, whereas a weak pulse results in an oscillatory response, showing up as a series of waves with diminishing amplitude. When a short pulse is applied to the LOT input corner of the network model, waves of activity move across the model cortex, consistent with corresponding global dynamic behaviour (c.f. Fig. 4).
Another way of artificially inducing phase (state) transitions in cortical network dynamics is by using neuroactive drugs, such as certain kinds of anesthetics and anti-epileptics, which clearly can induce transitions between mental states, characterized by different oscillatory modes and frequencies (see Fig. 5). An important principle in the action of these drugs is selective blocking or activation of ion channels, which will have different neurodynamical effects, depending on the relative selectivity and the intrinsic network activity (Århem et al., 2003, 2007; Halnes et al., 2007).
Functional relevance and computational models
A fundamental question in neuroscience concerns the functional significance of mesoscopic brain dynamics, including the observed phase transitions between various oscillatory states and chaotic or noisy states. The electrical activity of the brain, as captured with EEG is considered by some to be an epiphenomenon, without any information content or functional significance, but there exists contrary evidence that mesoscopic brain dynamics at least to some degree reflects mental states and processes (Wright & Liley, 1996; Freeman, 2000).
Most cognitive and mental functions presumably involve larger “macroscopic” brain areas or even networks of interconnected cortical areas, but the mesoscopic dynamics of such an area may still reflect some aspect or part of the mental activity. For example, different conscious states, such as drowsiness, sleep or alertness may result in similar type of dynamics, such as alpha or gamma waves across several areas, and detectable at mesoscopic spatial scales. Similarly, some aspects of a “macroscopic” phenomenon such as face recognition or eating behaviour may be reflected in the “microscopic” activity of single neurons (c.f mirror neurons).
In order to elucidate the significance of mesoscopic brain dynamics, computational methods are used to supplement experimental methods. For example, there is strong computational, as well as experimental support for a population (relational) coding in cortical networks, where mesoscopic brain dynamics apparently play a functional role (Singer, 1994). Such a coding principle implies that information is contained not only in the activation level of individual neurons but also in the relations between the activities of distributed neurons.
Computer simulations with cortical neural network models support the view that complex dynamics makes neural information processing more efficient, providing a fast and accurate response to external stimuli or in associative memory tasks (Liljenström, 1995; Liljenström & Hasselmo, 1995). For example, with an initial chaotic-like state, sensitive to the input signal, the system can rapidly converge to a limit cycle attractor memory state, see Fig.6 (Wu & Liljenström, 1994). Perhaps the most direct effect of cortical oscillations could be to enhance weak signals and speed up information processing, but they may also reflect various cognitive functions, including segmentation of sensory input, learning, perception, and attention. Phase transitions in mesoscopic brain dynamics can reflect transitions between different cognitive and mental levels or states, for example corresponding to various stages of sleep, anesthesia or wake states with different levels of arousal, which in turn could affect the efficiency and rate of information processing (Liljenström, 2010).
Simulations also show that mesoscopic network dynamics can be shifted into, or out of, different oscillatory states by small changes in ion-channel densities or by changing connection strengths in a network model (Halnes et al., 2007). It is demonstrated that the blocking of specific ion channels, as a possible effect of some anesthetics, can change global brain activity from high-frequency (awake) states to low-frequency (anesthetized) states, as apparent in the recorded and simulated EEG (See Fig. 5).
It can further be demonstrated that “microscopic” noise can induce global synchronous oscillations in cortical networks and shift the system dynamics from one dynamical state to another (Liljenström & Wu, 1995; Liljenström & Århem, 1997; Basu & Liljenström, 2001). This in turn can change the efficiency of the information processing of the system, e.g. system performance can be maximized at an optimal noise level, analogous to the case of stochastic resonance (Wiesenfeld & Moss, 1995), and spontaneous activity can facilitate learning and associative memory (Liljenström, 1996).
Mesoscopic brain dynamics and consciousness
As briefly discussed above, low frequencies in mesoscopic brain dynamics correspond to low mental activity, drowsiness or sleep, whereas higher frequencies are associated with alertness and higher conscious activity. In particular, oscillations in the gamma frequency band, around 40 Hz, have long been associated with (visual) attention, initially based on experiments on cats (Eckhorn et al., 1988; Gray & Singer, 1989; Engel et al., 1991). It was this phenomenon that triggered the boost of studies on neural correlates of consciousness, as e.g. suggested by Crick & Koch (1990; Koch, 2004) and contributed to opening the field of neuroscience to consciousness studies.
The complex neurodynamics at a mesoscopic level of the brain seems significant for the macroscopic phenomena of cognition and consciousness (Århem & Liljenström, 2007). It has been related to perception, attention and associative memory, but also to volition and activity in the sensory and motor areas of the brain. Even though many details are still unknown, it is obvious that there is an interplay between the neurodynamics of the sensory and motor systems, essential for the interaction with our environment in a perception-action cycle (Cotterill, 1998; Freeman, 2000).
Associated with the perception-action cycle are the dual aspects of consciousness, attention and intention (Liljenström, 2011). Attention is primarily related to the sensory/perceptual pathways and brain areas, whereas intention is more related to the motor areas and pathways. In particular, the supplementary motor area (SMA), but also the parietal cortex, show early signs of intentional motor activity (Eccles, 1982; Libet 1985; Desmurget et al., 2009). EEG measurements from these areas reflect mesoscopic brain dynamics, apparently correlating to various conscious states and events.
Mesoscopic neurodynamics can be seen as resulting from the dynamic balance between opposing processes at several scales, from the influx and efflux of ions, inhibition and excitation etc. Such interplay between opposing processes often results in (transient or continuous) oscillatory and chaotic-like behaviour. Indeed, brain activity is constantly changing, due to neuronal information processing, intrinsic fluctuations, neuromodulation, sensory input, and internal state shifts. An essential feature of mesoscopic brain dynamics is spatio-temporal patterns of activity, appearing at the collective level of a large number of neurons. Waves of activity move across the surface of sensory cortices, with oscillations at various frequency bands. This kind of activity is often associated with mental processes and states, which can be characterized by the specific patterns involved.
A combination of mathematical analysis and computational modeling can serve as an essential complement to clinical and experimental methods in furthering our understanding of neural and mental processes. In particular, when concerning the inter-relation between structure, dynamics and function of the brain and its cognitive functions, this method may be the best way to make progress. The study of phase transitions in mesoscopic brain dynamics could be one of the most fruitful approaches in this respect (Steyn-Ross & Steyn-Ross, 2010). In fact, relating different spatial and temporal scales in the nervous system, and linking them to mental processes may be seen as one of the greatest challenges to modern neuroscience.
- Adrian E D (1942) Olfactory reactions in the brain of hedgehog. J. Physiol. 10, 459-473.
- Århem P & Johansson S (1996) Spontaneous signalling in small central neurons: Mechanisms and roles of spike-amplitude and spike-interval fluctuations. Int. J. Neural Syst. 7, 369–376.
- Århem P, Klement G & Nilsson J (2003) Mechanisms of anesthesia: Towards integrating network, cellular and molecular modeling. Neuropsycopharmacology 28, S40–S47.
- Århem P, Braun H, Huber M & Liljenström, H (2005) Non-Linear State Transitions in Neural Systems: From Ion Channels to Networks. In: Micro – Meso – Macro: Addressing Complex Systems Couplings, (H. Liljenström & U. Svedin, eds.) Singapore: World Scientific Publ. Co. pp. 37-72.
- Århem P, Klement G & Blomberg C (2006) Channel density regulation of firing patterns in a cortical neuron model. Biophys. J. 90, 4392–4404.
- Basu S & Liljenström H (2001) Spontaneously active cells induce state transitions in a model of olfactory cortex. Biosystems 63, 57–69.
- Berger H (1929) Über das elektroenkephalogramm des menschen. Arch. Psychiatr. Nervenkrankh. 87, 527–570.
- Bressler S L & Menon V (2010) Large-scale brain networks in cognition: emerging methods and principles. Trends in Cognitive Sciences 14, 277-290.
- Buszáki G, Horváth Z, Urioste R, Hetke J & Wise K (1992) High-frequency network oscillation in the hippocampus. Science 256, 1025-1027.
- Corchs S & Deco G (2002) Large-scale neural model for visual attention: Integration of experimental single-cell and fmri data. Cerebr. Cortex 12, 339–348.
- Cotterill R (1998) Enchanted Looms – Conscious Networks in Brains and Computers. Cambridge University Press.
- Crick F & Koch C. (1990) Towards a neurobiological theory of consciousness. Seminars Neurosci. 2, 263-275.
- Desmurget M, Reilly K T, Richard N, Szathmari A, Mottolese C & Sirigu A (2009) Movement intention after parietal stimulation in humans. Science 324, 811-813.
- Eccles J C (1982) The initiation of voluntary movements by the supplementary motor area. Arch. Psychiatr. Nervenkr. 231, 423-441.
- Eckhorn R, Bauer R, Jordon W, Brosch M, Kruse W, Monk M & Reitboeck H J (1988) Coherent oscillations: A mechanism of feature linking in the in the visual cortex? Biol. Cybern. 60, 121-130.
- Engel A K, Kreiter A K, König P & Singer W (1991) Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. PNAS USA 88, 6048-6052.
- Freeman W J (1959) Distribution in time and space of prepyriform electrical activity. J. Neurophysiol. 22, 644–665.
- Freeman W J (1964) Linear models of impulse inputs and linear basis functions for measuring impulse responses. Exp. Neurol. 10, 475–492.
- Freeman W J (1975) Mass Action in the Nervous System. New York: Academic Press.
- Freeman W J (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol. Cybern. 56, 139-150.
- Freeman W J (2000) Neurodynamics: An Exploration in Mesoscopic Brain Dynamics. Berlin: Springer.
- Freeman W J (2005) The necessity for mesoscopic organization to connect neural function to brain function. In: H. Liljenström, U. Svedin (eds.), Micro - Meso - Macro: Addressing Complex Systems Couplings, pp. 25–36, London: World Scientific.
- Fries P, Reynolds J H, Rorie A E & Desimone R (2001) Modulation of oscillatory neuronal synchronization by selective visual attention. Science 291, 1560–1563.
- Gray C M & Singer W (1989) Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Natl. Acad. Sci. USA 86, 1698-1702.
- Green J D & Arduini A A (1954) Hippocampal electrical activity in arousal. J. Neurophysiol. 17, 533-557.
- Gu Y & Liljenström H (2007) A neural network model of attention-modulated neurodynamics. Cognitive Neurodynamics 1, 275-285.
- Haken H (1983)Synergetics, an Introduction: Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology, New York: Springer-Verlag.
- Haken H (2002)Brain Dynamics - An Introduction to Models and Simulations, Berlin: Springer-Verlag.
- Haken H (2005) Mesoscopic levels in science - some comments. In: H. Liljenström, U. Svedin (eds.), Micro - Meso - Macro: Addressing Complex Systems Couplings, pp. 19–24, London: World Scientific.
- Halnes G, Liljenström H & Århem P (2007) Density dependent neurodynamics. BioSystems 89, 126-134.
- Hasselmo M E (1993) Acetylcholine and learning in a cortical associative memory. Neural Comp. 5, 32-44.
- Hebb D O (1949) The Organization of Behavior: A Neurophysiological Theory. New York: Wiley.
- Imry Y (1997) Introduction to Mesoscopic Physics. New York: Oxford University Press.
- Ingber L (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. Phys. Rev. A 45, R2183-2186.
- Koch C (2004) The Quest for Consciousness - A Neurobiological Approach. Greenwood Village, CO: Roberts & Co. Publ.
- Li Z & Hopfield J J (1989) Modeling the olfactory bulb and its neural oscillatory processings. Biol. Cybern. 61, 379-392.
- Libet B (1985) Unconscious cerebral initiative and the role of conscious will in voluntary action. Behav. Brain Sc. 8, 529-566.
- Liljenström H (1991) Modeling the dynamics of olfactory cortex using simplified network units and realistic architecture. Int. J. Neural Systems 2, 1-15.
- Liljenström H (1995) Autonomous learning with complex dynamics. Intl. J. Intelligent Systems 10, 119-153.
- Liljenström H (1996) Global effects of fluctuations in neural information processing. Intl. J. Neural Systems 7, 497-505.
- Liljenström H (1997) Cognition and the efficiency of neural processes In Matter Matters? On the Material Basis of the Cognitive Aspects of Mind (P Århem, H Liljenström and U Svedin, Eds.) Heidelberg: Springer, pp. 177-213.
- Liljenström H (2003) Neural stability and flexibility - A computational approach. Neuropsychopharmacology 28: S64-S73.
- Liljenström H (2010) Inducing transitions in mesoscopic brain dynamics. In: Modeling Phase Transitions in the Brain (DA Steyn-Ross & ML Steyn-Ross, eds.) New York: Springer, pp. 149-178.
- Liljenström H (2011) Intention and attention in consciousness dynamics and evolution. J. Cosmology 14, 4848-4858.
- Liljenström H & Århem P (1997) Investigating amplifying and controlling mechanisms for random events in neural systems. In Computational Neuroscience (JM Bower, Ed.) New York: Plenum Press. pp. 711-716.
- Liljenström H & Hasselmo ME (1995) Cholinergic modulation of cortical oscillatory dynamics. J. Neurophysiol. 74, 288-297.
- Liljenström H & Wu X (1995) Noise-enhanced performance in a cortical associative memory model. Int. J. Neural Systems 6, 19-29.
- Llinás R (1988) The intrinsic electrophysiological properties of mammalian neurons: Insight into central nervous system function. Science 242, 1654-1664.
- McAdams C & Maunsell J (1999) Effects of attention on orientation-tuning functions of single neurons in macaque cortical are v4. J. Neurosci. 19, 431–441.
- Singer W (1994) Putative functions of temporal correlations in neocortical processing. In: C Koch & J L Davis (eds) Large-scale neuronal theories of the brain. Cambridge, MA: The MIT Press, pp. 201-237.
- Skarda C A & Freeman W J (1987) How brains make chaos in order to make sense of the world. Behav. Brain Sci. 10, 161–195.
- Steriade M & Llinás R R (1988) The functional states of the thalamus and the associated neuronal interplay. Physiol. Rev. 68, 649-742.
- Steyn-Ross DA & Steyn-Ross ML, eds. (2010) Modeling Phase Transitions in the Brain. New York: Springer.
- Tass P A (2001) Desynchronizing double-pulse phase resetting and application to deep brain stimulation. Biol. Cybern. 85(5), 343–354.
- Traub R D & Miles R (1991) Neuronal Networks of the Hippocampus. Cambridge University Press.
- Tsuda I (1991) Chaotic Itinerancy as a Dynamical Basis of Hermeneutics in Brain and Mind. World Futures 32,167–184.
- Wiesenfeld K & Moss F (1995) Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs, Nature 373, 33-36.
- Wilson M & Bower J M (1992) Cortical oscillations and temporal interactions in a computer simulation of piriform cortex. J. Neurophysiol. 67, 981-995.
- Wright J J & Liley D T J (1996) Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behav. Brain Sci. 19, 285–320.
- Wu X & Liljenström H (1994) Regulating the nonlinear dynamics of olfactory cortex. Network: Computation in Neural Systems 5, 47-60.
Recommended reading - books
- Arbib M A, Erdi P and Szentagothai J (1998) Neural Organization - Structure, Function and Dynamics. Cambridge: MIT Press.
- Arhem P, Liljenström H & Svedin U, eds. (1997) Matter Matters? - On the Material Basis of the Cognitive Activity of Mind. Heidelberg: Springer.
- Arhem P, Blomberg, C & Liljenström H, eds. (2000) Disorder Versus Order in Brain Function. London: World Scientific.
- Freeman WJ (1975) Mass Action in the Nervous System. New York: Academic Press. © 2004: (online)
- Freeman WJ (2000) Neurodynamics - An Exploration in Mesoscopic Brain Dynamics. London: Springer.
- Haken H (2002, 2008) Brain Dynamics - An Introduction to Models and Simulations. Berlin: Springer.
- Liljenström H & Århem P (2007) Consciousness Transitions - Phylogenetic, Ontogenetic and Physiological Aspects. Amsterdam: Elsevier.
- Liljenstrom H & Svedin U, eds. (2005) Micro - Meso - Macro: Addressing Complex Systems Couplings. London: World Scientific.
- Moss F & Gielen S (2001) Neuroinformatics and Neural Modelling. Handbook of Biological Physics (ed. A J Hoff) Vol 4. Amsterdam: Elsevier.
- Perlovsky L I & Kozma R, eds. (2007) Neurodynamics of Cognition and Consciousness. Berlin: Springer.
- Steyn-Ross DA & Steyn-Ross ML, eds. (2010) Modeling Phase Transitions in the Brain. New York: Springer.