arXiv:0808.1135v1 [q-bio.NC] 7 Aug 2008 ae nfntoa rdet hog h otxadsca- and cortex the dynamics through gradients of develo- functional aspects on some author based of The model functional [19]. as a literature case ped the Schn. in much-discussed reported others the the and explain hand to first cere- author of of the cases allowed interpretation This the dynamic localizations. a of bral propose “central”syndrome to called and author charac- cortex, to the the led in what features injury terize Civil special brain and Spanish with selec- zone the them parieto-occipital hundred from of Twelve one injuries (1936-39). brain about War with studied patients author ted This (1910-1986)[16, 18]. Gonzalo Justo 17, of research pioneering the references and [15] func- also (see of therein). [1] component organization inherent brain a mul-tional include as to interactions revised be tisensory aut- to notions need some longstanding organization that to cortical suggest of According findings level. these all and oxygen hors, tomography blood of emission magnetic analysis positron functional by imaging, revealed resonance multisensory been these of have to Some interactions cortex 14]. visual 13, of [11, it contribution only the as tactile in referring “unimodal”, example cor- as 12] for in occurs regarded 11, activity traditionally 10, found affect regions was 9, can tical It 8, interactions others). 7, many cross-modal 6, among that works 5, recent 4, some 3, to processes 2, cerebral [1, integrative in (e.g., effects cross-modal and nti re fies ercl ntepeetwork present the in recall we ideas, of order this In multisensory on reported works many years, recent In itilso,vsa ytm ri yais cln laws scaling dynamics, brain system, visual illusion, tilt e words: analysi Key the restrict We networks. approxim neural follow to biological sensory found of is The laws nerv facilitation proposed. the multisensory was by in functions or sensory ac reduction higher allometricaly scale to affected lower a being qualities as d is sensory interpreted cortex different the is of syndrome specificity uni the This which and continuity in integrat proposed functional integrati was a incomplete scheme multisensory suggest by that of dynamics facilitation stage brain or a stimulus w as mass as higher neural appears vision tilted the stimulus, or on Inverted minimum excitability. dependent nervous multisen of effects and laws symmetric dynamic bilateral, with a depression by featured visual s the central is mode from called syndrome equidistant functional he cortex, what the parieto-occipital to on the relation made in is (1910-1986), review Gonzalo a processing, cerebral ucinlgainstruhtecre,mliesr int multisensory cortex, the through gradients Functional ntecneto h nraignme fwrso multisens on works of number increasing the of context the In .INTRODUCTION I. nvria opues eMdi.Cua nvriai s Universitaria Ciudad . de Complutense Universidad utsnoy rs-oa ffcs aiiain neuroph facilitation, effects, cross-modal multisensory, eatmnode Departamento n cln asi ri dynamics brain in laws scaling and sblGonzalo-Fonrodona Isabel -al igonzalo@fis.ucm.es E-mail: pia autdd inisF´ısicas. Ciencias de Facultad Optica. ´ esn oes[3 4 0 1 2 3,aato historical of apart 33], 32, 35]. 31, [34, pro- 30, notes cerebral 24, of [23, development models cessing the 29]) towards The 28, [27, later process. (e.g., diverted research cerebral this integrative of level, repercussion the functional immediate a of at 26]. aspects understand 25, 24, to several 23, framework 22, a 21, offers 20, [16] 18, It in [17, part in in developed exposed further was and It physiological excitability. by nervous supported of laws systems, dynamic of laws ling npcfi o utseic erlms n scharac- is functional and a mass rather by neural of terized loss multispecific) center a (or involves the syndrome from unspecific involvement This and periphery. the (Fig. the bilateral of field to gradation a visual with is the A) of there 1, reduction disorders, with concentric other and symmetric example, to functions for addition its system visual in all the in In bilaterality. affected, symmetric equally sys- area auditory are and of tems tactile the posterior visual, 19, affection; multisensory most a symmetric area the presents and of It and terminology). middle Brodmann 18 in (the area 39, A of Fig.1, part (“central” in anterior areas shown projection as auditory zone) the and from tactile equidistant visual, lesion parieto-occipital unilateral a xiaiiywihdpn nteqatt fnua mass neural nervous of quantity central the the on of depend in which transformations than excitability pheno- to greater dynamic presents related are depression T mena This sma- of man. a thresholds normal (with are the a T M case and intense case lesion), less acute the ller this the of In of those 18]. thresholds than the [16, greater that 2 see Fig. we in figure curves threshold excitation the h eta ydoe[6 7 8 soiiae from originated is 18] 17, [16, syndrome central The atl n uioypoeto ra) The areas). projection auditory and tactile , . odn osaiglw.Acniut from continuity A laws. scaling to cording l stcieadadtv neso,under inversion, auditive and tactile as ell n h ydoervasapcso the of aspects reveals syndrome The on. otevsa system. visual the to s tl oe as htwudrflc basic reflect would that laws, power ately nrm cue yuiaea einin lesion unilateral by (caused yndrome yo h otx ucinlgradients functional A cortex. the of ty oyivleet n yafunctional a by and involvement, sory srbtdwt otnosvariation. continuous a with istributed rwhb nices ftestimulus the of increase an by growth fhmnbanpooe yJusto by proposed brain human of l u xiaiiyo h ytm the system, the of excitability ous o,bigams orce under corrected almost being ion, otadrltdt physiological to related and lost r n rs-oa ffcsin effects cross-modal and ory n 84-ard 28040-Madrid. /n. sooy netdperception, inverted ysiology, depression egration hw o xml in example for shown 2

Figura 1: Position of cortical lesions and respective visual fields (involved zones are dark). A: central, B: paracentral, Figura 3: Perceived tilt and diminution in size of a vertical test C: marginal or peripheral, syndromes. (Adapted from Fig. arrow in the center of the visual field of right eye in central 1(a) of [20] with permission of the MIT Press). syndrome, as the illumination of the arrow diminishes. Spiral branches described by the extremes of the arrow are indicated. (Adapted from Fig. 3(a) of [20] with permission of Springer Science and Business Media).

M). In the , there was a dissociation be- tween simple sonorousness (weak stimulus) and real tone (stronger stimulus) of a particular sound. Contralateral localization (spatial inversion) of a sound stimulus occu- rred only in the most acute case M when the stimulus was weak and the patient was in inactive state (free of facilitation). The inverted perception always lacked tonal quality. In language, diverse aphasic aspects occurred de- Figura 2: Excitation threshold curves for electrical stimulation pending on the stimulation, it will be exposed in a future of the retina (cathode on eyelid) in acute central syndrome work. case M, less intense case T, each one in inactive state and fa- (b) Capability to multisensory facilitation (the percep- cilitated state by strong muscular stress (see the text), and in a normal case. Electrical intensity (indirectly given by volts) tion of a stimulus is improved by adding simultaneously versus time (given by microfarads) necessary to obtain mini- one or more different stimuli). It modifies the cerebral mum luminous sensation. (From Fig. 2 of [25] with permission system essentially, becoming more rapid and excitable, of Viguera Editores, S.L.). i.e., it supplies in part the neural mass lost in the “cen- tral”lesion, thus reducing the mentioned dissociation. It was found that a strong muscular stress was very efficient at improving the perception (see the facilitated cases in lost. These phenomena are [16, 18]: Fig. 2. Other types of facilitation to we- (a) Functional disgregation or dissociation of sensory re binocular summation and tactile and acoustic stimuli, qualities (normally united in perception) according to for example. their excitability demands, i.e., sensory qualities are gra- (c) Capability to temporal summation, which is me- dually lost as the stimulus intensity diminishes. For ins- rely a particular means of stimulation. The slowness of tance, when the illumination of an upright white arrow the cerebral system in central syndrome makes the cere- was diminishing, the arrow perceived is at first upright bral excitation to a short stimulus to decay slowly. If a and well defined, next it is perceived to be more and second stimulus arrives before this excitation has comple- more rotated in the frontal plane (Fig. 3) becoming at tely fallen down, excitations are summed up, so that it is the same time smaller and losing its form and colors in possible to achieve an excitation threshold to produce a a well-defined physiological order, the perceived tilt (al- sensory perception, reducing so the mentioned patholo- most inverted vision in the acute syndrome case M) being gical dissociation. It was shown [23] that it is possible to dependent on the size, distance, illumination and exposu- model the temporal dynamics of simple sensory functions re time of the test object. In the tactile system, five stages as a first-order linear time-dispersive system having as a − were distinguished successively in the dissociated percep- first approach a time response χ0e a/t (t is time) to a tion of a mechanical pressure stimulus on one hand, as short impulse stimulus. The reaction velocity a and the the energy of the stimulus was increased: first, primiti- permeability to the excitation χ0 of the cerebral system ve tactile sensation without localization, then, contrala- decrease when the deficit (due to the lesion) of active teral localization (inverted perception), and finally, nor- “central”neural mass is greater, but the ratio a/χ0 in- mal localization which required intense stimulus. A mo- creases significantly and can be considered as a constant bile stimulus was perceived in the inversion phase with for each sensory function of a given cerebral system wit- a very shortened trajectory (approximately 1/10 in case hout facilitation. 3

Thus, the importance of the central syndrome (say, symmetric multisensory syndrome) lies in the fact that changes in the stimulation intensity (and then in ner- vous excitation) reveal aspects of the dynamics of the , , and organiza- tion of sensory structures combined with the direction function manifested in the tilted or almost inverted per- ception. Spatial inversion appears as an essential fact in the sensory organization. In a recent review [25], the in- verted or tilted perception disorder observed and inter- preted by Gonzalo, is put in relation with the increasing number of reported cases with this anomaly in the last years (for example [37, 38, 39, 40, 41, 42] among many others reviewed in [25]). In tilted vision, a rather similar degradation of the perception to that referred in (a) was reported in [42]. We expose in the following the principal features of the model proposed by Gonzalo highlighting the connection with recent research.

II. FUNCTIONAL CEREBRAL GRADIENTS

From the first hand cases and others reported in the Figura 4: Lower part: visual fields and tactile sensitivity of cases ordered according to the position and magnitude of the literature, the diverse syndromes were ordered according lesion. The degree of the defect is greater in darker regions. to the position and magnitude of the lesion [18]. The Upper part: scheme of visual and tactile functional densities central syndrome refers, as said above, to lesions in the f, and the unspecific functional gradation which represents “central”zone, equidistant from the visual, tactile and the multisensory and bilateral effect. Brodmann areas are in- auditive projection paths. Syndromes corresponding to dicated. (Adapted from Fig. 5 of [20] with permission of The lesions in the projection paths were called in this con- MIT Press). text “marginal” or “peripheral”syndromes, the defect - functional suppression- is restricted to the contralateral half of the corresponding sensory system and scarcely presents the multisensory effect in the anomalies and the present dynamic effects. Intermediated syndromes were bilaterality or interhemispheric effect by the action of the called “paracentral”syndromes, with different degree in corpus callosum. Each point of the cortex is then charac- the bilateral symmetry involvement (see Fig. 1). terized by a combination of specific contralateral action The complete gradation found between the central syn- with unspecific “central” and bilateral action. drome, and a marginal syndrome, through the variety In the visual system for example, for the visual func- of paracentral syndromes lead to the definition of two tion to be normal, the action of the region with grea- types of continuous functions through the cortex called test visual sensory function density is not enough, and “cerebral gradients”[18], shown schematically in Fig. 4. the whole specific functional density, say f, in gradation One type comprises the specific sensory functional den- through the cortex, must be involved in the integrati- sities, of contralateral character, with maximum value in ve cerebral process, leading to the normal sensory visual the respective projection area and decreasing gradually function F . Analogously for the other senses and quali- towards more “central”zone and beyond so that the final ties. In a schematic way, f is related to the derivative decline of the specific visual function density, for exam- of this integration through the cortex, which justifies it ple, must reach all the tactile area, as shown in Fig. 4, was named gradient. This function f takes into account as well as other specific areas including their primary the density of specific neurons through the cortex and zones. This type of function takes into account and com- their connections, representing the dynamic aspect of its bines the factors of position and magnitude of the lesion, anatomic basis. A sensory signal in a projection area is since the more “central”is the lesion, the more extensi- only an inverted and constricted outline that must be ela- ve must be the lesion to originate the same intensity in borated (magnified, reinverted, ...), i.e., integrated over a specific anomaly. For a given position of the lesion, its the whole region of the cortex where the corresponding magnitude determines de degree of functional depression. specific sensory functional density f is extended. Magni- The other type of function, of unspecific (or multispeci- fication would be due to the increase in recruited cerebral fic) character, is maximum in the “central” region (whe- mass, and reinversion due to some effect of cerebral plas- re the decline of the above mentioned specific functions ticity, (following an spiral growth as the growth of the overlap) and vanishes towards the projection areas. It re- arrow in Fig. 3). In the visual system, reinversion and 4

Figura 6: Sensibility profiles of visual fields in different cen- tral syndrome cases (M and T included) and in a normal ca- se. (Adapted from Fig. 2 of [21] with permission of Springer Science and Business Media).

III. SCALE REDUCTION IN CENTRAL Figura 5: Schematic visual, tactile and auditory functional SYNDROME. ALLOMETRIC SCALING LAWS IN densities. THE DISPLAY OF SENSORY QUALITIES

The cerebral system after a “central”lesion, once the bilateralization would occur in the 18 and 19 Brodmann new dynamic equilibrium is reached, was considered a areas where the sensory representation is already reinver- scale reduction in the nervous excitability of the cerebral ted. A remarkable result is, for example, the significant system since the originated functional depression main- participation of the traditionally “extravisual” cortex in tains, nevertheless, the same cerebral organization as in the maintenance of the visual field. normal case. This can be appreciated, for example, in the The projection zones where the respective specific hypoexcitability of the nervous centers shown in the ex- functional gradients are maximum, are highly organized citability (Fig. 2) and luminosity threshold curves, and and differentiated (in biological terms), i.e., highly spe- also in the concentric reduction of the visual field, its cialized. They are phylogenetically the oldest zones of sensibility profile (see Fig. 6) and visual acuity. All these the isocortex and the nervous activity has an anatomic functions experienced a down shifting in their values, but representation. In contrast, the “central”zone which is keeping the same form as in a normal case [18]. more recent, is rather unspecific with capacity for adap- Then, the concept of dynamic similitude, according to tation or learning. It is very small in animals, even in which different parts of a dynamic system change dif- other mammals, but it has great extension in man. A ferently under a change in the size of the system, was schematic representation of the visual, tactile and audi- applied. In particular, in biological growth, the sizes of tory gradients is shown in Fig. 5. two parts (say x and y) of a biological system are appro- ximately related by a scaling power law of the type Certain sensory functional densities would arise from the superposition of functional gradients of different sys- y = Axn, (1) tems, as in the case of primary alexia where the corres- ponding functional specific (lexical) gradient would result n being different for different parts (y1,y2, ...) of the sys- from the superposition of auditory and visual ones, lea- tem. These parts change then differently, i.e., allometri- ding to a lexical bell gradient between the two systems. cally [43]. This power relation means that the rates of In some cases, a gradient with hemispherical dominance growth of the two parts compared are proportional, i.e., has to be added. (1/y)(dy/dt)= n(1/x)(dx/dt) (obtained from Eq. (1) by As opposed to the rigid separation of zones, the func- taking the logarithm and differentiating). These ideas we- tional gradients account for a functional continuity and re applied by Gonzalo [21] to the growth (or reduction) physiological heterogeneity of the cortex, this one being of the sensory qualities, linked each one to a nervous ex- subjected to a common principle of organization. This citation demand (i.e., to a quantity of neural mass). An scheme, mere abstraction of the observed facts, offers a allometric variation of the sensory qualities was then pro- dynamic conception of quantitative localizations which posed. permits an ordering and an interpretation of multiple For the pure central syndrome cases studied [18], nor- phenomena and syndromes. Also, this scheme is in re- malized values of the visual direction function y1 and of lation to recent works suggesting that traditional specific the acuity function y2, versus normalized untouched vi- cortical domains are separated from one another by tran- sual field surface x, are plotted in Fig. 7 (a). The acute sitional multisensory zones [15], and that multisensory case M (with considerable neural mass lost), the less in- interactions occur even in the primary sensory cortices tense case T (with less neural mass lost than M) and a [1, 3, 13]. normal case N are indicated. Errors are greater in cases 5

(a) in the pathological disgregation of the sensorium in cen- 1,0 tral syndrome, the loss of direction function (1 − y1) and

0,8 direction − y the loss of visual acuity (1 y2) are plotted in Fig. 7(b)

1

acuity −

y versus the loss of visual field (1 x), together with a qua-

2 0,6 litative representation of the loss of other functions: an

0,4 elementary one as luminosity and a higher one as gnosia, according to the observed facts. The origin of the graphs

0,2

y (sensory function) (sensory y corresponds to a normal man (N). We can see that for a

0,0 particular loss of visual field (due to the scale reduction M T N originated by a particular central lesion), a split of the

0,0 0,2 0,4 0,6 0,8 1,0

x (visual field) different qualities occurs so that the higher ones (e.g., gnosia) are loss in a higher degree than the lower (ele-

(b) mentary) ones (e.g., luminosity). The order of the split corresponds to the order of complexity (or excitability 0,6 demand) of the sensory functions and to the order they are lost due to the shifts in their threshold excitabilities.

0,4 This is the formal description of the mentioned func- gnosia

acuity tional depression where the most complex qualities, with

1 1-y greatest nervous excitability (and integration) demand, 0,2 become lost or delayed in greater degree than the most

direction

1-y 2

luminosity simple ones (with lower excitability demand). Sensations 1-y (sensory function loss) function (sensory 1-y

0 (N) usually considered as elementary are then seen to be de- 0,2 0,4 0,6

1-x (visual field loss) composed into several functions, one of them being the direction function, thus revelling up to a certain extent, the organization of the sensorium. Very small differences Figura 7: (a)Normalized direction function (squares), fitting in the excitation of different qualities occur already in 0,5 to y1 = x , and normalized acuity function (circles), fitting the normal individual (in colors for example), and they 0,1 to y2 = x , for central vision, versus normalized untouched grow considerably in central syndrome. In this context, it visual field surface x of the observing eye. Cases M, T and could be said that the cerebral system of the normal man normal (N) are indicated. (b) Curves for the loss of visual works like an almost saturated system, in the sense that acuity, 1 − y1, and loss of direction, 1 − y2, versus loss of the visual field, 1 − x, for the same conditions and normalizations a very low stimulus induces cerebral excitation enough to as in (a). Qualitative indications for the loss of the higher perceive not only the simplest sensory functions but also sensory function gnosia and lower sensory function luminosity the most complex ones in a synchronized way. are shown as examples. In relation to the scheme of cerebral gradients, and for a sensory system, the functional gradient in normal man must be understood as an ensemble of several functional with intense central syndrome because of their high sen- densities fi for different qualities in gradation through sory degradation and the high capability to facilitation by the cortex, each one with different slope according to its temporal and multisensory summation. The values plot- excitability and integration demand. In the new equili- ted are normalized with respect to the normal value. The brium achieved in central syndrome the deficit of neu- o direction function is considered 0 for the total inverted ral excitation affects these functions fi differently. Their perception of the upright test arrow, and 180o for the incomplete cerebral integration gives place to the res- upright perception (normal), i.e., the maximum value is pective reduced sensory qualities Fi, each one reduced achieved in a normal integrative process from the inver- differently (allometrically). The mentioned disgregation ted signal in the projection path. For a normal case, N, phenomenon of the perception in the functional depres- the normalized values x, y1 and y2 are the unity, the ma- sion corresponds then to different stages of incomplete ximum value. For case M, the corresponding values are integration in different degree for the different qualities. very small since the non-normalized values are, 6 degrees for the visual field width, 0.04 for the acuity and 160 degrees for the perceived direction. IV. SENSORY GROWTH, MULTISENSORY We can see in Fig. 7(a) that the data fit approximately EFFECTS AND MORE SCALING POWER LAWS to power laws. Since y1 and y2 are 1 for x = 1, the value A of Eq. (1) is 1 and the approximate allometric power In a reduced cerebral system as was described above, 0 5 laws found are y1 = x , for the direction function and the sensory level may grow by intensifying the stimulus 0,1 y2 = x for the acuity function. If the widths of the (it includes iterative temporal summation) and by sen- visual fields are considered instead of the surface values sory facilitation by adding other different stimuli, as was x, there is no evidence of power laws. said in the first section. These mechanisms involve an In order to appreciate the loss of the sensory functions increase of central nervous excitation being able to com- 6

90 pensate in part for the neural mass lost. This capability (a)

75 to improve the perception is greater as the magnitude of 1/8

60

T the central lesion is greater, and is null or very low in a 1/4 normal man. The best example is the extreme case M, 45 who could approach the physiological and sensory level 30 1/4 of the less intense case T, by the use of strong muscular M facilitated stress (M facilitated) as shown in Fig. 2. The inactive

15

state, free of facilitation is difficult to achieve in acute Visualfield (degess) M inactive cases as M since mere postural changes or weak stimuli modify the perception. 0,1 1 10 100 Concerning the effect of the intensity of the stimulus, Light intensity

Fig. 8 shows some examples of visual functions or quali- 0,1

(b) ties versus intensity of stimulation in a stationary regime Normal

(acuity x 1/10)

T

[16, 18]. The well-known Stevens law relating perception 1/8

P and stimulus S by a power law of the type (acuity x 1/5)

m 1/4 P = pS (2) Acuity

1/4

M facilitated

(considered an improvement of the Fechner law) was used 0,01

1/4 to fit the data, the slope of the straight line in a log-log M inactive representation being the exponent m. Fig. 8 (a) shows 0,005

0,1 1 10

the visual field amplitude of right eye in cases M, M Light intensity (foot-candle) facilitated by strong muscular stress (40 kg held in his hands), and case T, versus the illumination of a test ob- ject. As seen, the data fit rather well to Stevens straight lines, not very close of the highest values. The slope m of the fitting straight lines is remarkably close to 1/4 for M and M facilitated, and 1/8 for T. In Fig. 8(b), similar representation is shown for the visual acuity in central vision, including a normal case. Straight lines with slope 1/4 fit rather well to the data of case M inactive, the cen- tral range of the data for M facilitated and T; and with slope 1/8 for a normal case. In Fig. 8(c), it is shown in linear scale representation, how the perceived direction of an upright test white arrow tends to the normal va- lue (upright direction) as the illumination of the arrow Figura 8: (a) Visual field of right eye versus relative illumina- increases, for M inactive and facilitated. These data do tion (test object: 1 cm diameter, white disk). M (m ≈ 1/4), not show an admissible agreement with a simple power M facilitated (m ≈ 1/4), T (m ≈ 1/8). (b) Acuity of right eye law and the curves merely join the experimental points. versus illumination. M (m ≈ 1/4), M facilitated (m ≈ 1/4), T Concerning facilitation, its effect is shown in Fig. 9, in (m ≈ 1/4) and normal man (m ≈ 1/8). (Adapted from Fig. log-log representation. Now the intensity of light on the 1(a)(b) of [26] with permission of Springer Science and Busi- test object was kept constant and low, say s. The data ness Media). (c) Visual direction function versus illumination correspond also to a stationary regime [16, 18]. Fig. 9(a) of an upright test arrow. (Adapted from Fog. 3(c) of [20] with shows the visual field amplitude of right eye in case M, permission of The MIT Press). versus facilitation by muscular stress holding in his hands increasing weights. The data fit to straight lines with slo- pes (Stevens’ powers) 1/2 and 1/3 for the two different than those of simple stimulation. diameters of the white circular test object. A greater test The sensory growth by facilitation through other sti- object implies a greater stimulus, and we can see that it muli is a multisensory or cross-modal effect in the cere- leads to a lower slope, i.e., to a lower effect of the faci- bral integrative process. Along all the cases reported in litation. Fig. 9 (b) shows data under similar conditions the literature on reversal of vision [25], there are some as in Fig. 9 (a) but the sensory function measured is of them in which the image was reinverted by multisen- the recovery of the upright direction (180o) of an upright sory facilitation (e.g., [36, 38]). Facilitation by multisen- test white arrow that the patient perceived tilted or al- sory or cross-modal effects have been also observed in most inverted (0o) under low illumination. The data fit patients with visual deficits, e.g. [7, 9], and also in nor- to power 1/4. The novelty in Fig. 9(c) is that facilita- mals, e.g.[1, 2, 6, 44, 45, 46, 47]. tion is supplied by illuminating the left eye which is not The capability to improve the perception in central observing the object, the power of the fitting being 1/8 syndrome by multisensory facilitation was found to be [26]. Note that the fittings of facilitation are much better greater as the deficit of excitability in the reduced ce- 7

90

75 (a) biological observable quantities are statistically seen to 60 scale with the mass M of the organism, according to 45 power laws Y = kM r, where most of the exponents r are 30 test 1.0 cm multiples of 1/4. These scaling laws are supposed to arise

1/3

M 1515 from universal mechanisms in all biological systems (in test 0.5 cm our case, neural networks) as the optimization to regu-

1/2 late the activity of its subunits, as cells [51, 52]. Under

Visual field (degrees) field Visual the assumption that a stimulus S activates a neural mass

3 β Mneur = αS [26, 53], the above power law of percep- 1 10 100 β/m r Facilitation (weight in Kg) tion (2) becomes P = k(Mneur) = k(Mneur) , i.e., we recover a biological scaling power law of growth whi- 180 ch would be the basis of the perception laws shown above. 150 (b) ≈ 120 In cases where β would be close to unity [53], then r m,

90 and Stevens laws would exhibit quarter powers as seen 1/4

M in some of the cases here analyzed.

60

30 V. CONCLUSIONS Visaul direction (degrees) direction Visaul

1 10 100 The functional model described highlights a functional Facilitation (weight in Kg) unity and continuity of the cerebral cortex. This is re- flected in the functional gradients according to which the 180

(c)

170 specificity of the cortex is distributed with a continuous

160 variation, giving place to regions where several specifici-

150 1/8 ties overlap significantly. A functional unity is suggested

M 140 in the sense that for a sensory function to be normal, 130 the integrative process must involve the whole specific

120 gradient extended over the cortex and not only over the

110 region with higher functional density. Multisensory inte-

Visual direction (degrees) direction Visual gration would be involved in a greater degree in regions 100

10 100 where the overlapping of the specific functional gradients Facilitation (light on left eye) is greater. This scheme affords an interpretation of the great variety of syndromes and responds to requirements formulated recently, as said in the introduction. Figura 9: Case M, right eye. (a) Log-log representation of visual field amplitude versus facilitation by muscular stress A neural mass lost in the rather unspecific region where holding weight in his hands. Squares: 0.5 cm diameter test size the decline of several gradients overlap, as in the so-called (m ≈ 1/2). Circles: 1.0 cm diameter test size (m ≈ 1/3). (b) central zone, is interpreted as a scale reduction in the ner- Visual direction (reinversion) versus facilitation by muscular vous excitability of the cerebral system. The functional stress (m ≈ 1/4). (c) Visual direction versus facilitation by gradients associated to the different sensory qualities of a illumination on left eye (m ≈ 1/8). (From the respective Figs. given sensory system become then affected allometricaly, 2(a), 2(b) and 3 of [26], with permission of Springer Science leading to stages in perception of incomplete integration and Business Media). in a different degree for each quality. Inverted or tilted perception appears as an stage of incomplete integration. The higher or complex functions, which require greater rebral system is greater, and as the primary stimulus nervous excitation (and then integration), are more affec- (e.g., the constant value of light s and the size of the test ted and lost first. A functional continuity is manifested object) is weaker [16] (see Fig. 9(a)). The first of the- from elementary sensory functions to higher ones, accor- se conditions is in relation to what is observed recently ding to their excitability thresholds, following a physio- [7, 48, 49], and the last condition is also in agreement logical order, as is shown in the dynamic disgregation with recent observations [2, 47].It was suggested [24] that of qualities as excitation diminishes. Allometric scaling the multisensory interaction in central syndrome leads to laws account for the continuous variation of each qua- a nonlinear contribution to the cerebral excitation with lity (e.g., visual direction, acuity) in relation to another stimuli, this being also in relation to recent suggestions quality (e.g., visual field). [50]. A growth in the sensory level, and then a more com- For the Stevens power laws, note that their validity plete integration, is achieved by means of an increase is assumed to be restricted to limited ranges of stimu- in the primary stimulus or by multisensory facilitation, li, and they are not exempt from criticism. However, in mechanisms which supply in part the neural mass lost. connection with these laws, it is remarkable that many This capability is greater as the deficit is greater and the 8 primary stimulus is weaker. The growth of the sensory le- bral processing and its adaptive and long-distance inte- vel follows approximately scaling power laws that would grative aspects (e.g, [54, 55]). emerge from the dynamics of biological neural networks. Note that the approach exposed could be connected Acknowledgement. I am very grateful to M.A. Porras with those based on a distributed character of the cere- for his valuable assistance in preparing this manuscript.

[1] R. Martuzzi, M.M.Murray, C.M. Michel et al., Multisen- Consejo Superior de Investigaciones Cient´ıficas, Inst. S. sory interactions within human primary cortices revealed Ram´on y Cajal, Madrid, Vol. I 1945, Vol. II 1950). (Ava- by BOLD dynamics, Cerb. Cortex 17 (2007) 1672-1679. lable in: Instituto Cajal, CSIC, Madrid). [2] H. Gillmeister and M. Eimer, Tactile enhancement of au- [17] J. Gonzalo, La cerebraci´on sensorial y el desarrollo en es- ditory detection and perceived loudness, Brain Res. 1160 piral. Cruzamientos, magnificaci´on, morfog´enesis, Trab. (2007) 58-68. Inst. Cajal Invest. Biol. 43 (1951) 209-260. [3] C. Kayser and N.K. Logothetis, Do early sensory cortices [18] J. Gonzalo, Las funciones cerebrales humanas seg´un nue- integrate cross-modal information?, Brain Struct. Funct. vos datos y bases fisiol´ogicas: Una introducci´on a los es- 212 (2007) 121-132. tudios de Din´amica Cerebral, Trab. Inst. Cajal Invest. [4] C. Kayser, C.I. Petkov, M. Augath and N.K. Logothetis, Biol. 44 (1952) 195-157. Functional Imaging reveals visual modulation of specific [19] K. Goldstein and A. Gelb, Psychologische Analysen hirn- fields in auditory cortex, J. Neurosci. 27 (2007) 1824- pathologischer F¨alle auf Grund Untersuchungen Hirnver- 1835. letzer, Zeitschrift f¨ur die gesamte Neurologie und Psy- [5] J.C. Alvarado, J.W. Vaughan, T.R. Stanford and B.E. chiatrie 41 (1918) 1-142. Stein, Multisensory versus Unisensory Integration: Con- [20] I. Gonzalo and A. Gonzalo, Functional gradients in cere- trasting Modes in the Superior Colliculus, J. Neurophy- bral dynamics: The J. Gonzalo theories of the sensorial siol. 27 (2007) 1824-1835. cortex, in: R. Moreno-D´ıaz and J.Mira, eds., Brain Pro- [6] A. Diederich and H. Colonius, Why two “Distractors.are cesses, Theories and Models. An Int. Conf. in honor of better than one: modeling the effect of non-target audi- W.S. McCulloch 25 years after his death (The MIT Press, tory and tactile stimuli on visual saccadic reaction time, Massachusetts 1996) 78-87. Ex. Brain Res. 179(2007) 43-54. [21] I. Gonzalo, Allometry in the J. Gonzalo’s model of the [7] D.A. Poggel, E. Kasten, E.M. Muller-Oehring et al., Im- sensorial cortex, Lect. Not. Comp. Sci. 1240 (1997) 169- proving residual vision by attentional cueing in patients 177. with brain lesions, Brain Res. 1097 (2006) 142-148. [22] I. Gonzalo, Spatial Inversion and Facilitation in the J. [8] J.K. Bizley, F.R. Nodal, V.M. Bajo et al., Physiological Gonzalo’s Research of the Sensorial Cortex. Integrative and Anatomical Evidence for Multisensory Interactions Aspects, Lect. Not. Comp. Sci. 1606 (1999) 94-103. in Auditory Cortex, Cereb. Cortex 17 (2007)2172-2189. [23] I. Gonzalo and M.A. Porras, Time-dispersive effects in [9] F. Frassinetti, N. Bolognini, D. Bottari et al., Audiovi- the J. Gonzalo’s research on cerebral dynamics, Lect. sual integration in patients with visual deficit, J. Cogn. Not. Comp. Sci. 2084 (2001) 150-157. Neurosci. 17 (2005) 1442-1452. [24] I. Gonzalo and M.A. Porras, Intersensorial summation [10] E. Macaluso, C.D. Frith, J. Driver, Multisensory stimu- as a nonlinear contribution to cerebral excitation, Lect. lation with or without saccades: fMRI evidence for cross- Not. Comp. Sci. 2686 (2003) 94-101. modal effects on sensory-specific cortices that reflect mul- [25] I. Gonzalo-Fonrodona, Inverted or tilted inversion disor- tisensory location-congruence rather than task-relevance, der, Rev. Neurol. 44 (2007) 157-165. Meuroimage 26 (2005) 414-425. [26] I. Gonzalo-Fonrodona and M.A. Porras, Physiological [11] H. Th´eoret, L. Merabet, A. Pascual-Leone, Behavioral Laws of Sensory Visual System in Relation to Scaling and neuroplastic changes in the blind: evidence for func- Power Laws in Biological Neural Networks, Lect. Not. tionally relevant cross-modal interactions, J. Physiol. Pa- Comp. Sci. 4527 (2007) 96-102. ris. 98 (2004) 221-33. [27] M Critchley, The Parietal Lobes (Arnold, London 1953) [12] G.A. Calvert and T. Thesen, Multisensory integration: Chap 9. methodological approaches and emerging principles in [28] M.B. Bender and H.L. Teuber, Neuro-ophthalmology, the human brain, J. Physiol. Paris 98 (2004) 191-205. Prog. Neurol. Psychiatry III (1948) 163-182. [13] K. Sathian and A.Zangaladze, Feeling with the mind´s [29] J.de Ajuriaguerra J and H. H´ecaen, Le Cortex C´er´ebral eye: contribution of visual cortex to tactile perception, Etude´ Neuro-psycho-pathologique (Masson, Paris 1949). Behav. Brain Res. 135 (2002) 127-132. [30] A.E. Delgado, Modelos Neurocibern´eticos de Din´amica [14] L.G. Cohen, P. Celnik, A. Pascual-Leone et al., Functio- Cerebral. Ph.D.Thesis, E.T.S. de Ingenieros de Teleco- nal relevance of cross-modal plasticity in blind humans, municaci´on, Universidad Polit´ecnica de Madrid, 1978. Nature 389 (1997) 180-3. [31] J. Mira, A.E. Delgado and R. Moreno-D´ıaz, The fuzzy [15] M.T. Wallace, R. Ramachandran and B.E. Stein, A revise paradigm for knowledge representation in cerebral dyna- view of sensory cortical parcellation, Proc. Natl. Acad. mics, Fuzzy Sets and Systems 23 (1987) 315-330. Sci. USA 101 (2004) 2167-2172. [32] J. Mira, A. Manjarr´es, S. Ros et al., Cooperative Organi- [16] J. Gonzalo, Investigaciones sobre la nueva din´amica cere- zation of Connectivity Patterns and Receptive Fields in bral. La actividad cerebral en funci´on de las condiciones the Visual Pathway: Application to Adaptive Threshol- din´amicas de la excitabilidad nerviosa (Publicaciones del dig, Lect. Not. Comp. Sci. 930 (1995) 15-23. 9

[33] A. Manjarr´es, Modelado Computacional de la Deci- J. Neurosc. 27 (2007) 5879-5884. si´on Cooperativa: Perspectivas Simb´olica y Conexionista. [46] B. Baier, A. Kleinschmidt and N.G. M¨uller, Cross-modal Ph.D. Thesis, Ciencias F´ısicas, Facultad de Ciencias de processing in early visual and auditory cortices depends la UNED, Madrid, 2001. on expected statistical relationship of multisensory infor- [34] M. Arias and I. Gonzalo, La obra neurocient´ıfica de Justo mation, J. Neurosci. 26 (2006) 12260-12265. Gonzalo (1910-1986): El s´ındrome central y la metamor- [47] J.W. Schnupp, K.L. Dawe and G.L. Pollack, The detec- fopsia invertida, Neurolog´ıa 19 (2004) 429-433. tion of multisensory stimuli in an orthogonal sensory spa- [35] L. Barraquer, La din´amica cerebral de Justo Gonzalo en ce, Exp. Brain Res. 162 (2005) 181-190. la historia, Neurolog´ıa 20 (2005) 169-173. [48] P.J. Laurienti, J.H. Burdette, J.A. Maldjian and M.T. [36] Y. River, T. Ben Hur and I. Steiner, Reversal of vision Wallace, Enhanced multisensory integration in older metamorphopsia, Arch. Neurol. 53 (1998) 1362-1368. adults, Neurobiol Aging 27 (2006) 1155-1163. [37] M. Arias, C. Lema, I. Requena et al., Metamorfopsia in- [49] A.M. Peiffer, J.L. Mozolic, C.E. Higenschmidt and P.J. vertida: una alteraci´on en la percepci´on de la situaci´on Laurienti, Age-related multisensory enhancement in a espacial de los objetos, Neurolog´ıa 16 (2001) 149-153. simple audiovisual detection task, Neuroreport 18 (2007) [38] A. Arjona and E. Fern´andez-Romero, Ilusi´on de inclina- 1077-1081. ci´on de la imagen visual. Descripci´on de dos casos y re- [50] T.R. Standford and B.E. Stein, Superadditivity in multi- visi´on de la terminolog´ıa, Neurolog´ıa 17 (2002) 338-341. sensory integration: putting the computation in context, [39] D.D. Malis and J.P. Guyot, Room tilt illusion as a ma- Neuroreport 18 (2007) 787-792. nifestation of peripheral vestibular disorders, Ann. Otol. [51] G.B. West and J.H. Brown, The origin of allometric sca- Rhinol. Laryngol. 112 (2003) 600-605. ling laws in from genomes to ecosystems: towards [40] A. H. Hern´andez, F. Pujadas, F. Purroy et al., Upside a quantitative unifying theory of biological structure and down reversal of vision due to an isolated acute cerebellar organization, J. Exper. Biol. 208 (2005) 1575-1592. ischemic infarction, J. Neurol. 253 (2006) 953-954. [52] R.B. Anderson, The power law as an emergent property, [41] A. Unal, A. Cila and S. Saygi, Reversal of vision me- Mem. Cogn. 29 (2001) 1061-1068. tamorphopsia: A manifestation of focal seizure due to [53] O.J. Arthurs, C.M.E. Stephenson, K. Rice et al., Do- cortical dysplasia, Epilepsy Behav. 8 (2006) 308-311. paminergic effects on electrophysiological and functional [42] E. Kasten, and D.A. Poggel, A Mirror in the Mind: A MRI measures of human cortical stimulus-response power Case of Visual Allaesthesia in Homonymous Hemianopia, laws, NeuroImage 21 (2004) 540-546. Neurocase 12 (2006) 98-106. [54] S. Yuval-Greenberg, L. Deouell, What You See Is Not [43] J. Perkki¨oand R. Keskinen, The relationship between (Always) What You Hear: Induced Gamma Band Res- growth and allometry, J. theor. Biol. 113 (1985) 81-87. ponses Reflect Cross-Modal Interactions in Familiar Ob- [44] N.P. Holmes, G.A. Calvert and C. Spence, Tool use chan- ject Recognition, J. Neurosci. 27 (2007) 1090-1096. ges multisensory interactions in seconds: evidence from [55] E. Rodr´ıguez, N. George, J.P. Lachaux et al., Percep- crossmodal congruency task. Exp. Brain Res. 183 (2007) tion´s shadow: long-distance synchronization of human 465-476. brain activity, Nature 397 (1999) 430-433. [45] B.A. Rowland, S. Quessy, T.R. Standford and B.E. Stein, Multisensory integration shortens physiological latencies,