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*Corresponding author, Phone:＋81-25–227–0677, Fax:＋81-25–227–0821, E-mail: tnakada＠bri.niigata-u.ac.jp

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Magnetic Resonance in Medical Sciences, Vol. 3, No. 2, p. 51–63, 2004

SPECIAL CONTRIBUTION

Brain Chip: A Hypothesis

Tsutomu NAKADA*

Center for Integrated Human Brain Science, Brain Research Institute, University of Niigata1 Asahimachi, Niigata 951-8585, Japan

(Received March 25, 2004; Accepted July 7, 2004)

This article is the English version of the Brain Chip hypothesis previously presented inthe books ``Brain Equation One Plus One (Kinokuniya, 2001)'' and ``Plus Alpha(Kinokuniya, 2002).'' The concept in this article has been translated into English by theauthor himself in response to an overwhelming number of requests from colleagues outsideJapan.

Keywords: cerebellar chip, neural net, aquaporin-4, radial glial ˆber

Introduction

There is no doubt of the essential role of discreteneuronal networks in brain function. Nevertheless,models of brain function based on neuronalnetworks alone fail to answer the various fun-damental questions of how the brain works, suchas, ``What is the neuronal substrate of conscious-ness?'', or ``Why do anesthetic eŠects diminish athigher atmospheric pressure?'', or ``How canpurely endogenous processes be initiated?'' Theseare but a few examples of as yet unsatisfactorilyaddressed questions. In spite of concerted eŠort bypreeminent neuroscientists, no single complete the-ory of brain function explaining these phenomenol-ogies has been oŠered. This void strongly suggeststhat there is a missing link in the current fundamen-tal concept of how the brain works.

This apparent impasse in neuroscience hasrecently been surmounted by the Vortex Theory,which eŠectively links all important phenomenol-ogies into a single fundamental concept of thebrain's functional organization.1 The theory isˆrmly based on biological and anatomical reality,essential considerations for any biological hypothe-sis. This manuscript is an introduction to thefundamental architectural unit of the associationcortex in the Vortex Theory, namely, the brainchip.

Developments

PhysiologyResearch on synaptic plasticity in the cerebellum

has dramatically advanced the concept of brainfunction. The discovery of learning neuronsconˆrmed the existence of the biological counter-part of Perceptron, an artiˆcial neuron in the ˆeldof neural net and, in turn, provided virtual prooffor the concept that, similar to artiˆcial neural net,diverse functionality of the brain can be construct-ed based on a single functional unit. The conceptof cerebellar learning was further reˆned by theidentiˆcation of a physiologic biological functionalunit, namely, the cerebellar chip.2

A simpliˆed representation of the cerebellar chipis given in Fig. 1. The chip is organized around asingle output neuron, the Purkinje cell. Informa-tion reaching the cerebellum is ˆrst processed bymany, so termed, pre-processing neurons such asgranular cells. The output of these pre-processingneurons reaches the Purkinje cells via the parallelˆbers which form synaptic connections withdendrites of the Purkinje cells. Transmission e‹-cacy of the synapses between parallel ˆbers andthe Purkinje cells is modiˆable, forming the basisof synaptic plasticity, and provides the biologicsubstrate of cerebellar learning processes. The roleof transmission e‹cacy in the learning process isanalogous to the variable weights in the learningprocess of the McCulloch and Pitts neuron(Fig. 2).3 Patterns of ensemble ˆring of Purkinjecells represent the result of learning, and aŠectsperformance of a given behavior, such as eyemovements. If a resultant behavior deviates fromthe original expectation, feedback signals will reach

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Fig. 1. Cerebellar ChipFunctionally, the cerebellum is now considered to be an organ collectivelyformed by identical functional units. The individual unit is referred to as``cerebellar chip'', in analogy to a computer chip. Each cerebellar chip has asingle output neuron, the Purkinje cell. Information to the cerebellum is ˆrstprocessed by numerous preprocessing neurons, such as the granular cells, andeventually reaches the Purkinje cells via parallel ˆber (PF) input. The transmis-sion e‹cacy of the synapses between parallel ˆbers and Purkinje cells ismodiˆable, forming the basis of synaptic plasticity, and provides the substrateof the cerebellar learning process. The outcome of cerebellar system output isexamined in other systems, and error signals are fed back to each Purkinje cell ifthe outcome is undesirable. These error signals are carried by the climbing ˆbersand provide the learning trigger for the corresponding Purkinje cells. Once adesirable outcome is achieved, the error signals will cease, and the learningprocess will be put on hold similar to the situation where the hold command isgiven to the McCulloch and Pitts neuron.

Fig. 2. McCulloch-Pitts classical linear model of theneuronAt given time t input signals xi(t ) reach the synapses.Each input is transmitted through the synapse to theneuron after each has been modiˆed by weight wi. Whenthe sum of the inputs reaches threshold u, the output ofthe neuron at time t＋1, y(t＋1), will become 1.

y(t＋1)＝

1 if Si

wixi(t )Æu

0 if Si

wixi(t )ºu

Fig. 3. Starting point of the Brain ChipSimilar to the cerebellum, the cerebrum consists of numerous outputneurons, the pyramidal cells. Their synapses, which receive various inputsignals from preprocessing neurons in the cortex through intracorticalˆbers, are highly plastic. A high degree of plasticity is observed even inthe primary cortices, including the primary visual cortex. Should thefunctional unit of the cerebrum be organized similar to the cerebellarchip, such a functional unit, referred to here as ``Brain Chip'', is expect-ed to have a similar conˆguration. However, in comparison to thecerebellar chip, it is apparent that the cerebral cortex lacks climbingˆbers. In this conˆguration, the learning trigger is missing in the cerebralcortex.

Fig. 4. Neuroblast delivery systemLeft: Schematic presentation of the process ofneuroblast migration. RGF: radial glial ˆber. GM:germinal matrix. CP: cortical plate.Right: Scanning electron-microscope picturedepicting actual neuroblast migration. (Courtesy ofY. Ikuta (Professor Emeritus, University of Niigata).

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†1A brief description of this simulation study is given in the Appendix.†2NO has been implicated as one of the determining factor of brain development.

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the corresponding cerebellar chips and eŠectchanges in transmission e‹cacy, i.e. the learningprocess. The outcome of the cerebellar systemoutput is examined in other systems, and errorsignals are fed back to each Purkinje cell if theoutcome is undesirable. These error signals arecarried by the climbing ˆbers and provide thelearning trigger for the corresponding Purkinjecells. Once the desirable outcome is achieved, errorsignals will cease and the learning process will beput on hold, similar to the situation of the holdcommand given to the McCulloch and Pittsneuron.

Evolution is the result of inevitable events basedon principles of nature. In this context, it is highlyplausible that the basic organization of the cerebralcortex consists of single functional units analogousto the cerebellar cortex. Should such a unit,referred to here as brain chip, exist, it is likely tohave evolved as an improved version of itspredecessor, the cerebellar chip. It is thereforeuseful to examine carefully the basic anatomicalarchitecture of the cerebral cortex in context of thecerebellar chip.

The cerebral cortex exhibits a basic neuralarchitecture similar to the cerebellum. The logicalcerebral counterpart of cerebellar Purkinje cells isthe pyramidal cells. There are numerous pre-processing neurons in the cerebral cortex whichrepresent the counterpart of the granular cells inthe cerebellum. Similar to the parallel ˆbers, axonsof the small neurons in the cerebral cortex formsynaptic connections with dendrites of the pyrami-dal cells, the transmission e‹cacy of which, even inthe primary visual cortex, is highly plastic. Onecomponent missing in the cerebral cortex in thecontext of chip conˆguration is the equivalentstructure to the cerebellar climbing ˆbers (Fig. 3).

OntogenyOntogenetic development of the cerebral cortex

is phenomenologically well described. The cellswhich eventually form the six-layered cortexmigrate from the surface of the lateral ventricle, thegerminal matrix, following guiding tracts providedby the radial glial ˆbers (Fig. 4). Each migratingcell reaches the surface of the cortex after ˆrstpassing through all the previously migrated andsettled cells, as if a six-story building were con-structed beginning from the ˆrst story upward tothe sixth (Fig. 5). It is readily apparent that thisprocess will not deˆne the gross shape of the brain.

Instead, the determining factor of the gross shapeof the brain is the pattern of growth of the radialglial ˆbers (Fig. 6).4

In nature, structural formation almost alwaysfollows the principal role of self-organization inMarkovian fashion. Recently, I have providedvirtual proof that the brain self-organizes based onthe rule of free convection†1. To follow the basicprinciples of heat convection, radial glial ˆbers areonly required to advance the tip of the ˆber in thedirection of convective heat ‰ow.5 This process canbe accomplished by the emission of small amountsof a gaseous substrate, such as nitric oxide (NO)†2

(Fig. 7). The process can be seen as following atransparent blueprint drawn precisely to actualsize. Each ˆber tip advances to its destination byfollowing the principal rule of heat convectiongoverning the particular space in which the tip islocated. Advancement of radial glial ˆbers, step-by-step, has been given previously.

BiologyRecent work has unambiguously shown that

astrocytes are a cousin of neurons and derive fromidentical stem cells. The work provides impetus forthe rigorous re-examination of astrocyte function.From the histological standpoint, there are twostructures associated with astrocytes, the assemblyand the electron dense layer. The role of thesestructures has long been enigmatic and poorlyunderstood. Since nature seldom creates a structurewithout a speciˆc corresponding function, it isprudent to analyze these structures for theirpotential role in brain function in regards tolearningWinformation processing (Fig. 8).

The assembly is a protein structure foundabundantly throughout the astrocyte cytoplasmicmembrane. Recent studies indicate that this struc-ture is identical to the water channel, aquaporin-4,found in great abundance in the collecting tubulesof the kidney.6 These ˆndings strongly indicate: (1)that one of the speciˆc functions of astrocytes isrelated to the regulation of water contents in thebrain; and (2) that the brain has compartments withdiŠerential water contents.

There is no doubt that the primary role ofastrocytes is the physical support of neurons. Theorganizational characteristic of the astrocyte ismatrix formation, which is an eŠective means ofestablishing compartments with diŠerent contentscharacteristics. This, together with the presence ofwater channels (aquaporin), make it highly plausi-

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Fig. 5. Six-story building analogyThe process of cerebral cortex formation is analogous toconstructing a six-story building. First, a constructionelevator is set up. The material for each ‰oor is fabricatedelsewhere, and is delivered to each ‰oor by elevator. Uponcompletion of a ‰oor, construction moves to the next levelup. Once all six-stories are completed, the constructionelevator is removed, leaving a space in the center of thebuilding. In the brain, the radial glial ˆbers play the role ofconstruction elevator. Following completion of brainformation, the radial glial ˆbers will disappear, leaving aspace in the center of each cortical column.

Fig. 6. Schema for gross shape formationThe gross shape of the brain is determined by how the glial ˆbers grow. In thisschema, each ˆber grows straight out from the center, forming a half-sphere.

Fig. 7. Schema showing advancement of radial glial ˆbersSchematic presentation of the proposed growth pattern of a radial glial ˆberusing nitric oxide (NO) as example. The tip of the growing radial glial ˆberemits a gaseous substrate (NO in this ˆgure), which ‰ows based on the heatconvection schema. The radial glial ˆber grows in the direction of NO ‰ow.GM: germinal matrix. RGF: radial glial ˆber. RGC: radial glial cell.

Fig. 8. Astrocytes and Aquaporin-4Left: Schematic presentation of an astrocyteand its principal processes. Modiˆed andredrawn based on the ˆgures from Hirano,1999 and Sasaki, 1999. Astrocytes possessall the structural signiˆcance necessary foranatomical realization of the hypothesis. Thekey elements include: (1) electron rich layerformed by the principal processes just beneaththe pia mater; (2) two compartments ofextracellular spaces segregated by principalprocesses; and (3) assembly. ``D'' indicates``dry area'', the second extracellular space.See text for details. a: astrocyte, b: neuron, c:axon bundle, d: vessel, e: neighboringastrocyte, f: electron rich layer, g: assembly.Right: Electron-microscopic picture depictingaquaporin-4 rich astrocyte processes. Upper:glia limitans: Lower: perivascular area.(Courtesy of J. Neeley. (Johns HopkinsUniversity)).

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ble that astrocytes maintain two diŠerent types ofextracellular compartments in the brain. Theconventional extracellular space is ˆlled withextracellular ‰uid, and indeed exists in certainstructures where astrocytes eŠectively seal oŠ anarea in order to maintain a conventional extracellu-lar ‰uid environment, e.g., the surroundings of thesynaptic areas and the nodes of Ranvier. Thesecond extracellular space, therefore, likely con-stitutes a dryer environment of lower watercontents than conventional extracellular space(Fig. 8).

Given that the astrocyte matrix is indeedcomposed of relatively dry components, the matrixcan be conceptualized to represent biologicalStyrofoam. In other words, the astrocyte matrixhas the perfect properties to function as moldingmaterial for protecting neuron networks.

Proposals

Synaptic Equivalence: ELDERThe term ``electron-dense'' originally came from

transmission electron-microscope observations thatcertain portions of membrane exhibited higherdensity. The ˆnding implied that compared to otherareas of the membrane, the electron densemembrane contained a much higher number ofmolecular elements that blocked the electron beam.Histologically, this layer (glia limitans) is formedby the footlike processes of the short ˆbers ofˆbrous atrocytes (marginal glia). Similar to perivas-cular regions, glia limitans is aquaporin rich.Therefore, it is highly plausible that glia limitans iseŠectively separated from brain parenchyma byrelatively dry space (Fig. 8). Although the precisecellular characteristics of marginal glia and glialimitans are not understood, these observationspoint to one conclusion. Under the condition whereintense dynamic electrical activities take place, forexample, the cortex in live animals, the layer islikely to be charged because of the dielectric eŠectof the dry area. This implies that the ``electron-dense layer'', originally coined as an electronmicroscopy term, is literally electron dense in lifefunctioning brain and can play the role of electrondonor.

The electron dense layer faces layer I of thecortex (molecular layer), which contains virtuallyall the terminal dendrites of the pyramidal cellsregardless of location of their cell bodies. Theprincipal role of dendrites is to receive signals. Theconventionally known means of signal transmissionis synaptic transmission, which involves theconversion of chemical signals to electrical signals

by receptors on dendrites. As a synthesis of theavailable information, I propose there is a synapse-like structure at the surface of Layer I (molecularlayer), which I term ELDER (electron-dense layerand dendritic ramiˆcation). While the electrondense layer plays the role of synaptic button, thedendritic ramiˆcations represent the receptors. Thespace in between these two structures, the ELDERgap, is a compartment the water contents of whichis regulated by the assembly (Fig. 9). Transmissionin the ELDER system occurs as a function ofpermittivity changes of the ELDER gap based ontransient water condensation to be discussed below.

Synaptic Transmission Equivalent: Vortex-EntropyWaves

As shown by the analogy to the six-story building(Fig. 5), the cortex is built from the bottom up byadding layer on top of completed layer. The radialglial ˆbers play the role of ``elevator'' whichtransports necessary materials (neuroblasts) to thetop of the completed ‰oor. To optimize e‹ciency,it is highly conceivable that each building unit usesa single elevator located at the center of thebuilding to be built. In brain development, a singleradial glial ˆber is known to be responsible for asingle cortical column and is located at the center ofthe column.

Radial glial ˆbers disappear following comple-tion of cortical development, leaving a hollow,tract-like structure in the center of each corticalcolumn (Fig. 10). This tube-like space is proposedbe part of the second, dry extracellular space. Thiscenter structure, which is referred to as CEO(climbing-ˆber equivalence organon), has the idealconˆguration to serve as conduit for dissipation ofthe tremendous amount of heat generated by theneuron networks, a biological air-cooling system. Itwill be recalled that the formation of CEO is basedon the heat convention schema (see Appendix I).

Within CEO, there is a steady air ‰ow driven bya steady state transfer of heat. When surfeit heat isgenerated by neuronal processing, an intriguingphenomenon will occur (Fig. 11): the production oftwo waves, namely, an entropy-vortex wave and asound wave (Appendix II). Since these waves aregenerated under subsonic conditions, the soundwaves propagate radially in three dimensions. Theentropy-vortex waves, however, move along theoriginal ‰ow, i.e., they travel within CEO towardsthe surface of the brain (Fig. 12). Upon reachingthe surface, these entropy-vortex waves meet theELDER containing space at the center of thecolumn, I term LGS (lattice gas shell) (Fig. 13).

At steady state, LGS has a steady ‰ow. With the

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Fig. 9. ELDERSchematic presentation of the ELDER system. Withthe permittivity lower than threshold (left), there isno current (rest). The higher water density within theELDER space increases permittivity. Once thresholdis reached (right), current will be introduced (excita-tion). ERL: electron rich layer, just beneath of thepia matter, formed by astrocyte processes. Bluearrow: ELDER gap.

Fig. 10. Schema of CEORadial glial ˆbers disappear following completion of cortical development, leaving a hollow, tract-likestructure in the center of each cortical column (Fig. 10). This tube-like space is conceived to be part of thesecond extracellular space, namely, dry space. This structure, which is referred to as CEO (climbing-ˆberequivalence organon), possesses the ideal conˆguration to serve as conduit for the dissipation of thetremendous amount of heat generated by the neuron networks, a biological air-cooling system. Note, theformation of CEO is based on the heat convention schema (see Appendix).

Fig. 11. Vortex and Sound wavesMinor perturbation results in the formation of oneentropy-vortex wave and one sound wave. Theformer travels in the direction identical to theoriginal ‰ow, whereas the latter radially in alldirections. The entropy-vortex wave carries newlyprocessed information (ds»0), while the sound wavedoes not (ds＝0). See Appendix II.

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arrival of entropy-vortex waves, signiˆcant wavespropagate outward from the center (Fig. 14). Thetransient passage of these waves increases the watercontents within the ELDER gaps su‹ciently forelectron transmission to occur, and results in theactivation of a group pyramidal cells simultaneous-ly. A certain type of Aquaporin channel may beactivated by water (or CO2) density alteration andgenerate active release of water akin to convention-al neurotransmitter release. In either case, waterfunctions as a neurotransmitter. Since waves decayas a function of distance, activation will beweighted based on the distance of pyramidal cellswith respect to the center of the column (Fig. 15).The process eŠectively provides a learning kernel

equivalent to Kohonen's map (Appendix III).

Discussion

Brain Chip: Biological Kohonen's ChipThe human brain contains more than one

hundred billion neurons and 1014 synapses. Evenwithout regard to the size of the genome, it can beeasily concluded that a deterministic blueprint forconnectivity of such an enormous number ofnetworks is unrealistic. Therefore, as in the case ofstructure formation, self-organizing processes mustplay a signiˆcant role in developing functionalconnectivity of neurons.

Among the many algorithms in neural netmodels, the concept generally referred to asKohonen's self-organizing map, provides the mostplausible self-organization processes for creating

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Fig. 12. Vortex Wave and CEOWLGSSchematic view of vortex wave formation by neuralinput within CEO. Minor perturbation of the steady‰ow due to arrival of a neural impulse results in vortexwave formation (right). The vortex wave travels in thedirection identical to the original ‰ow, namely, withinthe CEO, and towards LGS. See Fig. 14 for schematicview of the area indicated by white arrow as seen fromthe ventral aspect of the brain.

Fig. 13. Simpliˆed view of the brainSchematic presentation of the dual processing shellsystem. a: lattice-gas shell, b: neural network shell, c:white matter and other deep structures Fig. 14. Ripple vs. Vortex wave

Under steady state, the dry space of LGS, whichcontains the ELDER space, shows non-organizedripples (left). With the arrival of a vortex wave to thecenter of a column, signiˆcantly organized waves willpropagate outward from the center (right).

Fig. 15. Brain ChipThe brain chip is a two-dimensional cerebellar chip where multiple pyramidal cells receive learning triggerssimultaneously. In this schema two sets of six pyramidal cells are considered to form a single brain chip.Arrival of a vortex wave generates an organized wave propagating outward from the center, whichactivates multiple pyramidal cells simultaneously through ELDER activation. Since a wave decays as afunction of distance, activation is weighted based on the distance of pyramidal cells from the center of thecolumn.

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associative memories, the conˆguration of which isvirtually identical to that found in neurophysiologi-cal studies.7

The CEO-LGS system ˆlls the missing role of theclimbing ˆbers equivalent in the cerebral cortex.The single column unit CEO, as schematicallydepicted in Fig. 16, has the conˆguration of a twodimensional cerebellar chip. Instead of one to oneactivation of a Purkinje cell by a linearly connectedclimbing ˆber as in the cerebellar chip, spatiallygraded activation through the ELDER system of agroup of pyramidal cells within a single brain chipcan be eŠectively achieved by the CEO-LGSsystem. This conˆguration is highly compatiblewith the self-organizing neural net of Kohonen typefor eŠectively creating associative memory, theconˆguration of which has been repeatedly vali-dated by neurophysiological studies.

The Legacy of Linus C. PaulingDouble Nobel Price laureate (Chemistry and

Peace), Linus Carl Pauling, was deeply intriguedby the fact that the inert gas, Xenon, was anexcellent general anesthetic. He concluded that theonly property common to all anesthetic agents,including Xenon, was their eŠect on water crystalli-zation.8 The hydrate-microcrystal (aqueous-phase)theory did not receive signiˆcant attention.Nevertheless, as Pauling himself stated,9 ``thehydrate-microcrystal idea should be an importantpart of the accepted theory of general anesthesiawhen the theory is ˆnally formulated.'' One of themain reasons why the hydrate-microcrystal theorydid not receive the nod of approval from thescientiˆc society was because Pauling incorrectlyimplied the eŠect of water condensation on neu-ronal membrane potentials. Had Pauling knownthe Vortex Model and brain chip theory, he wouldimmediately have realized that water condensationwithin CEO and ELDER to be the critical factor.

Under the Vortex TheoryWBrain Chip concept,consciousness can be deˆned as the steady, ran-dom, spontaneous discharges of cortical pyram-idal cells through ELDER mediated electron ‰owtriggered by the steady ‰ow of the CEO-LGSsystem. Establishment of a steady state within theLGS of the brain requires a certain thermodynamicsteady state or homeostasis. The thermal gradientsrequired to produce a convective force are depend-ent on the presence of an appropriately heated solidbody core. In the context of the free convectiveself-organization schema, the reticular activationsystem (RAS), or reticular formation, and itsconnectivity within the thalamus likely play theprimary role of a solid body with steady tempera-

ture for generating convective ‰ow. The state ofconsciousness is dependent on the establishment ofthe requisite thermodynamics, and, resultantestablishment of steady state cortical activitiesthrough the ELDER system.

A highly plausible explanation for the basicmechanism of anesthetic agents is, as Paulinganticipated, their eŠect on the kinetic viscosity(Reynold's number) of a ‰uid or gas involved inpropagating an essential steady ‰ow because ofwater microcrystal formation.10 Such an alterationin kinetic viscosity produces alteration in thekinetics of the steady ‰ow and, hence, ELDERactivities. Pauling's microcrystal theory also pro-vides an answer to the long unsolved mystery inanesthesia: Why anesthetic eŠect is enhanced whenthe subject is placed in an environment of loweratmospheric pressure. Pauling had shown thathydrate microcrystal formation due to admixturewith anesthetic agents, including alcohol, is de-pendent on atmospheric pressure. At lower at-mospheric pressure, the identical concentrationof an anesthetic agent results in more readymicrocrystal formation.

Implication for functional MRI: Aquaporin as amediator of autoregulation

One of the regional phenomena known to occurin association with brain activities is the phenome-non generally referred to as autoregulation, themainfeature of which is an increase in regional blood‰ow.11 Although the exact controlling mechanismsof autoregulation are not known, there have beenmany unambiguous observations of the coupling ofphysiological increase in regional blood ‰ow andregional brain activities. In 1961 SokoloŠ in-troduced autoradiograpic images of the primaryvisual cortex exhibiting an increase in regionalblood ‰ow well corresponding to retinal stimula-tion.12 This observation became the world ˆrst``functional image'', and established the concept ofbrain activation study. The revolutionary advancesin computer technology made possible for au-toregulation based functional imaging, pioneeredby SokoloŠ, to be performed routinely in humansnon-invasively. The ˆrst representative technologywas positron emission tomography (PET), especial-ly the one based on infusion of O15 labeled water(H2O15-PET).

Widely adopted fMRI methodologies detectpixels which show a statistically signiˆcant increase(not decrease) in signal intensity on T2* weightedimages. In other words, the technique detects adecline in relative deoxy-Hb concentrations in agiven voxel. Since an increase in oxygen consump-

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Fig. 16. Brain Chip as biological Kohonen's mapVortex waves in the brain chip play the equivalentrole of climbing ˆbers in the cerebellar chip with onenotable diŠerence. The physics of a wave gives thebrain chip a two dimensional property. At the sametime, the vortex wave fulˆlls the condition necessaryfor the distance dependent learning weighting ofKohonen's map.

Fig. 17. Schematic presentation of the ``oxygenoversupply'' hypothesisThis simpliˆed hypothesis states that oxygen supplyin relation to an increase in activation-inducedperfusion (‰ow in Figure) exceeds oxygen consump-tion associated with neuronal activities. As a result,regional deoxy-Hb levels paradoxically decrease inassociation with neuronal activities (brain activa-tion). However, that regional deoxy-Hb declineassociated with increase in regional blood ‰ow cansimply be explained by the well-known Munro-Kelliedoctrine without additionally introducing the con-cept of oxygen consumption (see Fig. 18). Accord-ingly, fMRI should be considered to be a blood ‰owbased functional imaging method virtually identicalto H2O15-PET.

Fig. 18. Munro-Kellie doctrine and functional imagingThe Munro-Kellie doctrine dictates the relative volume ratioamong three components of the adult brain, the volume of whichcan acutely be altered, namely, arterial blood (A), venous blood(V), and cerebrospinal ‰uid (F). Since the total volume of the brainin the adult is ˆxed by the skull, any acute change in any of thesecomponents must be accommodated by the others. It is wellknown that, within a region of activated cortex, arterial blood ‰owincreases, resulting in an increase in cerebral blood volume in thearterial blood component. Under the condition where cerebrospi-nal ‰uid cannot be reduced signiˆcantly, as in the case of normalbrain, compensation occurs through reduction of venous volume(bottom ˆgure). While H2O15-PET directly measures in‰ow, fMRIrelies on indirect signal alteration associated with secondaryreduction of venous volume through deoxyhemoglobin inducedsusceptibility eŠects.

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tion associated with regional neural activitiesresults in an increase in deoxy-Hb concentrationsand, hence, a decline in signal intensity on T2

weighted images, fMRI in fact detects a phenom-enon totally opposite to that predicted basedon oxygen consumption. The reverse observed

phenomenon is generally attributed to an ``over-supply of oxygen'' brought about by an increase inregional blood ‰ow (Fig. 17).13 Therefore, the

majority of, if not all, fMRI studies detect regionalbrain activities based on regional blood ‰ow. It iswell known that an increase in regional blood ‰ow

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Fig. 19. Typical time series of an activated pixel in the primary motor cortexRed: raw data. Blue: boxcar type model function. Note the delay in activationsignal changes compared to actual task performance.

Fig. 20. Subdivision of primary motor cortexRepresentative independent component fMRI images within the right primary sensorimotor cortex(SMI) obtained by independent component-cross correlation-sequential epoch (ICS) analysis. Theentire right SMI was covered by two consecutive 5 mm thick axial slices placed 2.5 mm apart. ICSanalysis identiˆes functionally independent, spatially discrete components (independent componentfMRI images). Activated areas are quantitatively color-coded according to the magnitude ofactivation using a diŠerential color schema for each functionally discrete independent component.Red graphs indicate representative time series of independent components corresponding to theaccompanying fMRI image. Blue lines represent the 6 second delayed boxcar model function appliedto cross correlation analysis. The abscissa indicates time in seconds and the ordinate indicatespercent mean intensity changes. MI-4a, 4 anterior area of the primary motor cortex; MI-4p, 4posterior area of the primary motor cortex; 3a, 3a area of the primary sensory cortex; SI, the``classical'' primary sensory cortex (Brodmann areas 1, 2 and 3b).To provide better visualization of the three dimensional (3D) relationship, part of the activation mapof slice 1 is placed over that of slice 2 (upper left). The schematic gray block (upper right) shows the3D spatial position of SMI and the localization of the independent areas of activation. CS: centralsulcus. MI-4a, 4 anterior area of the primary motor cortex; MI-4p, 4 posterior area of the primarymotor cortex; 3a, 3a area of the primary sensory cortex; SI, the ``classical'' primary sensory cortex(Brodmann areas 1, 2 and 3b).

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Fig. 21. Champagne and bubble cuterWomen often carried a bubble cutter for drinkingchampagne at social functions in order to be sparedthe embarrassment of eructating, or burping, inpublic.

Fig. 22. Similar to the release of bubbles into theair eŠected by stirring champagne using a bubble cut-ter, an entropy-vortex wave (solid arrow) can releaseCO2 (red) from extracellular ‰uid where CO2 is undernear saturation. While the entropy-vortex waveintroduces activation of ELDER, CO2 can also aŠectaquaporin channels of surrounding vessels, therebyeŠectively producing coupling of neural activities andblood ‰ow with spatial as well as temporal concor-dance.

†3Readers are reminded that this discussion is for regional blood ‰ow, not for regional blood volume.†4There are several reasons to believe that CO2 would be the primary gas within the dry area. High concentrations of

carbonic anhydrase in oligodendroglia may indeed re‰ect this functionality.

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results in spontaneous reduction in venous bloodvolume in accordance with the Munro-Kelliedoctrine (Fig. 18).14 It is clear that a decline inrelative deoxy-Hb concentrations in a given voxel,the basis of fMRI, is readily explainable as a phys-iological epiphenomenon accompanying increasein regional blood ‰ow, without the need to in-voke changes in blood oxygenation. Like its sistermethods, such as H2O15-PET, fMRI is another

functional imaging method based on regionalblood ‰ow.

What is the mechanism of neural activitiesassociated increase in regional blood ‰ow? Again,the vortex theory gives a highly plausible hypothe-sis of the molecular mechanisms of autoregulation,namely, temporal and spatial coupling of neuralactivity and blood ‰ow. It is well known that theresponse in regional blood ‰ow corresponding toneural activities shows a delay of four to sixseconds (Fig. 19). Nevertheless, once activated,increases in blood ‰ow has a relatively low timeconstant consonant with ‰ow changes associatedwith caliber changes in blood vessels. This indicatesthat the molecular mechanisms responsible forblood ‰ow change possess at least two cascades ofprocesses the ˆnal result of which is an increase invessel caliber†3. Vessels within the region of cortexwhich is the target of this discussion do not possessa muscular layer that controls vessel caliber.Therefore, theoretically, vessel caliber change canbe accomplished by either: 1) increase in in‰owcontrolled by the proximal arterial componentresulting in increase vessel caliber due to passivechanges in the ‰exible vessel walls; or 2) physicalstructure, as yet to be deˆned. One's intuition mayaccept the former. Several studies, however,indicate that regional ‰ow changes coupled withgiven neural activities occur in the order of lessthan 1 mm3 (Fig. 20), clearly indicating that theformer possibility is not the case. Accordingly, onehas to accept the latter, requiring identiˆcation ofnon-muscular structures responsible for caliberchanges. The best candidate is aquaporin-4(assembly) regulated water contents of the struc-tures surrounding vessels. Such a structure isastrocyte feet (Fig. 8).

According to the Vortex Theory,1 one of themain constituents of the ‰uid ‰owing within theCOE and LGS is likely to be CO2

†4 (REF). Follow-ing arrival of input, an entropy-vortex wave iscreated and travels along the CEO (Fig. 12). If CO2

content within the ‰uid is at near saturation, thisperturbation results in release of CO2 from the ‰uidanalogous to champagne stirred by a bubble cutter(Fig. 21). How aquaporin-4 (assembly) will beactivated is not totally understood at this point.Nevertheless, accumulating data suggest two poten-tial candidates, namely, water molecules and CO2.

Carbon dioxide (CO2), rather than oxygen (O2),is believed to have an important role in regional

62

Fig. 24. Kohonen's map

Fig. 23. Heat convection and brain shapeA representative example of simulation results basedon free convection. Due to imperfection of theselected initial conditions, the simulated image(simulation) is not wholly identical to an actual brain(Schematic). Nevertheless, the striking similarities instructural detail are demonstrated, strongly indicat-ing that brain organization indeed follows the self-organization schema of free convection.

62 T. Nakada

Magnetic Resonance in Medical Sciences

blood ‰ow alteration.11,15 Should aquaporin-4surrounding vessels indeed be regulated by CO2, thephysical pressure imposed on vessels by astrocytefeet could be reduced resulting in increased blood‰ow (Fig. 22). This can eŠectively explain theobserved spatial and temporal coupling of neuralactivities and blood ‰ow (autoregulation).

Acknowledgements

The work is supported by grants from theMinistry of Education, Culture, Sports, Science,and Technology (Japan). The manuscript ispresented in part at the Center of Excellence (COE)Hearing, National Council of Science (Japan),June 2000 and the 32nd Annual Meeting of theSociety for Neuroscience, Orlando, FL, 2002.

Appendix IHeat Convection Schema and Brain Shape

Three-dimensional simulation of free convectionwas performed using an SGI Origin-2000, 64 CPUsystem. The governing equations in Eulerian formare given as:

&&t

r＋:･(rv)＝0

&&t

(rv)＋:･(rv)v＋:p＝F

&&t

(re)＋:･(rev)＋:(pv)＝G＋rv･F

where e＝v･v2＋

(g－1)－1pr

where e is the total speciˆc energy, r, mass density,p, pressure, F and G, momentum source andenergy source, respectively, and, g, the ratio ofspeciˆc heats. Representative examples of two-dimensional ``slice'' images of consecutive steps ofthe simulation are sampled and shown in Fig. 23.Details of the process are reported previously.5

Appendix IIEntropy-Vortex Wave

Euler's equation is given by:

&dv&t＋(v･:)dv＋

1r :dp＝0

where dv and dp

represent small perturbations invelocity and pressure, respectively.

Similarly, conservation of entropy and theequation of continuity give:

&ds&t＋v･:ds＝0

&dp&t＋v･:dp＋rc2:･dv＝0

where dr＝dpc 2＋Ø&r

&s »pds and c represent sound

velocity.

For a perturbation having the form exp [ik･r－ivt ], one gets:

(v･k－v)ds＝0

(v･k－v)dv＋k dpr＝0

(v･k－v)dp＋rc2k･dv＝0

This result prescribes that there will be two typesof perturbations, namely, entropy-vortex wave andsound wave, as deˆned below.

Entropy-Vortex Wave

v＝v･k

ds»0

dp＝0

6363Brain Chip: A Hypothesis

Vol. 3 No. 2, 2004

dr＝Ødrds »p

ds

k･dv＝0

:×dv＝ik×dv»0

Sound Wave

(v－v･k)2＝c2k2

ds＝0

dp＝c2dr

(v－v･k)dp＝rc2k･dv

k×dv＝0

For the purpose of brain modeling, the followingpoints are emphasized: (1) for entropy-vortexwave, ds»0 and v＝v･k; and (2) for sound wave,ds＝0. These conditions predict that a perturbationcan produce entropy changes (ds»0) and, hence,information processing, and create entropy-vortexwaves. The fact, v＝v･k, ensures that an entropy-vortex wave, which carries newly processedinformation, travels only in the direction identicalto the original ‰ow.10

Appendix IIIKohonen's Self-organizing Map

One of the most successful neural net applica-tions for the creation of associative memoriessimilar to that observed in brain, in vivo, is theself-organizing map (SOM) initially introduced byKohonen, a non-linear method based on unsuper-vised learning processes.

A schematic presentation of SOM is shown inFig. 24. Any point on the two dimensionally spreadneural lattice can be excited.

For each input x, the learning processes areconˆned to a local group of neurons centered atsite s, where maximum adaptation occurs. Theadaptive changes will decay according to theirdistance from the center (Neighborhood kernel) inGaussian fashion.

hrs＝exp Ø－¿r－s¿2

s 2 »Assuming active, non-linear forgetting, e,

occurs, the learning rule of each synapse can begiven as:

w r(new)＝(1－e･hrs)w r

(old )＋e･hrs･x.

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