DHD vs CS case:

14 Will-be-set-by-IN-TECH

Healty subjects or SC

 B. Pattern detected for each brain using the mean of the graphics obtained in A.

1 4 7 10 13 16

CS1

Closing size

0 0,02 0,04

0 0,02 0,04

Mean volume Mean volume

0 0,02 0,04

Mean volume

1 4 7 10 13 16

Pattern obtained from a SS

Strabic subjects or SS

Closing size

Fig. 9. Procedure to obtain granulometric patterns. In step A the graphics obtained for one slice of each of the two CS and for one SS case are illustrated. In step B, a common mean pattern is obtained for both CS and one SS. Finally, in step C, a mean pattern is obtained for

1 4 7 10 13 16

Closing size

CS2

Closing size

1 5 9 13 17

Mean pattern obtained from two CS

 C. Mean pattern detected as the mean of the graphics in B.

Mean volume

.

0 0,02 0,04

Closing size

1 4 7 10 13 16

SS

Closing size

1 5 9 13 17

SS

Closing size

1 4 7 10 13 16

CS2

1 4 7 10 13 16

CS2

Closing size

1 4 7 10 13 16

Closing size

CS1

1 5 9 13 17

Closing size

CS1

A. Analysis of dark regions ( ζDark ) per slice.

> 0 0,02 0,04 0,06

0 0,02 0,04

0 0,02 0,04

0 0,02 0,04

ζDark

the two CS.

ζDark

ζDark

ζDark

ζDark

ζDark

0 0,01 0,02 0,03

 

0 0,05

Fig. 10. Mean volume of clear and dark structures corresponding to SS and SC.


DHD vs CS case:

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Mean volume Mean volume Mean volume Mean volume

SSAV vs CS case:


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Fig. 12. WM and GM granulometric patterns for the CS and SS groups.

structures, an index is proposed. Such index is expressed as follows:

*<sup>ι</sup>* <sup>=</sup> *vol*(*small structures*)

1 3 5 7 9 11 13 15 17

GM granulometric pattern

WM granulometric pattern

<sup>187</sup> Comparison of Granulometric Studies of Brain Slices

from Normal and Dissociated Strabismus Subjects Through Morphological Transformations

Opening size

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

WM granulometric pattern

Closing size

1 3 5 7 9 11 13 15 17

GM granulometric pattern

Opening size

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

In trying to obtain a parameter indicating the absence, thinning, or thickening of WM or GM

*vol*(*medium structures*) + *vol*(*large structures*) (5)

Closing size

CS Mean DHD2 DHD1

> CS mean DHD1 DHD2

> > CS Mean SSAV2 SSAV1

> > > CS Mean SSAV1 SSAV2

Fig. 11. Images illustrating the segmentation of WM and GM.

In order to explain this situation we divide the analysis of WM and GM as follows :

*a) WM analysis.-* In Fig. 13, the terms small, medium and large components are exemplified with some structures. Notice that small components in WM have the appearance of "fingers", and medium components have a characteristic neck that joins them to large structures.

The lack of small components in the SS with respect to CS group, indicates the absence of such components in the WM. Also, the graphs indicate that the existing small components are thin; therefore they are eliminated easily by small structuring elements. On the other hand, the prevalence of medium and large structures is due to absence the circumvolutions, this originates a non-smooth transition mainly between small and medium components; since medium and large components are not to much different.

In Fig. 14 small components are eliminated from slices that belong to DHD, SSAV and a CS. Notice that for DHD cases, WM has thin "fingers" which almost disappear after applying an opening of size 1; whereas for the SSAV case, "fingers" are not so thin and many of them remain after the same transformation is applied.

Note that, for the CS case, WM shows abundant appendages and coral forms. Also, observe that transitions between medium and large sizes are smooth; however for the DHD and SSAV cases, the appendages and coral forms decrease significantly.

*b) GM analysis.-* In the GM there is a prevalence of medium and large components. This is confirmed in the graphs of GM for DHD and SSAV cases ( Fig. 12). Small, medium and large size components in GM are illustrated in Fig. 13.

16 Will-be-set-by-IN-TECH

Fig. 11. Images illustrating the segmentation of WM and GM.

medium and large components are not to much different.

cases, the appendages and coral forms decrease significantly.

remain after the same transformation is applied.

size components in GM are illustrated in Fig. 13.

In order to explain this situation we divide the analysis of WM and GM as follows :

*a) WM analysis.-* In Fig. 13, the terms small, medium and large components are exemplified with some structures. Notice that small components in WM have the appearance of "fingers", and medium components have a characteristic neck that joins them to large structures.

The lack of small components in the SS with respect to CS group, indicates the absence of such components in the WM. Also, the graphs indicate that the existing small components are thin; therefore they are eliminated easily by small structuring elements. On the other hand, the prevalence of medium and large structures is due to absence the circumvolutions, this originates a non-smooth transition mainly between small and medium components; since

In Fig. 14 small components are eliminated from slices that belong to DHD, SSAV and a CS. Notice that for DHD cases, WM has thin "fingers" which almost disappear after applying an opening of size 1; whereas for the SSAV case, "fingers" are not so thin and many of them

Note that, for the CS case, WM shows abundant appendages and coral forms. Also, observe that transitions between medium and large sizes are smooth; however for the DHD and SSAV

*b) GM analysis.-* In the GM there is a prevalence of medium and large components. This is confirmed in the graphs of GM for DHD and SSAV cases ( Fig. 12). Small, medium and large

Fig. 12. WM and GM granulometric patterns for the CS and SS groups.

In trying to obtain a parameter indicating the absence, thinning, or thickening of WM or GM structures, an index is proposed. Such index is expressed as follows:

$$\mu = \frac{vol(small\,\,stnarrow)}{vol(medium\,\,structures) + vol(large\,\,structures)} \tag{5}$$

DHD

<sup>189</sup> Comparison of Granulometric Studies of Brain Slices

from Normal and Dissociated Strabismus Subjects Through Morphological Transformations

SSAV

CS

With respect to SS, index *ι* presents the following behavior: a large number of medium components in WM and GM, that yields an inferior value when compared against the index

In other words, index *ι* for WM and GM in SS suggests: a) a lack of small components in the analyzed WM, and whenever present they are characterized by their thinness. Medium structures predominate through the analyzed WM. Given the lack of small components, and the presence of thin small structures in WM, this originates the absence of small structures in

The absence of small components (´´fingers") in the WM may causes a lack of electrical connection among different cortical regions. As a consequence a right electrical

the GM, for which a predominance of medium and large structures is observed.

Fig. 14. Elimination of thin components.

for CS.

In Fig. 15, index *ι* was plotted for WM and GM based on the values obtained for graphs in Fig. 12. When index *ι* for the CS is compared with that for the SS group, significant differences are obtained, since the latter value is much smaller.

Index *ι*, indicates that in the WM of CS, the volume of small components is more than double that of medium and large structures together; while in GM of CS, index *ι* is almost equal to the unit, that is, vol(small structures) ≈ vol(medium structures) + vol(large structures).

18 Will-be-set-by-IN-TECH

Small size components

In Fig. 15, index *ι* was plotted for WM and GM based on the values obtained for graphs in Fig. 12. When index *ι* for the CS is compared with that for the SS group, significant differences are

Index *ι*, indicates that in the WM of CS, the volume of small components is more than double that of medium and large structures together; while in GM of CS, index *ι* is almost equal to the unit, that is, vol(small structures) ≈ vol(medium structures) + vol(large structures).

Fig. 13. Illustration of small, medium and large structures on WM and GM.

obtained, since the latter value is much smaller.

Small size components

Large size components

Large size components

> Medium size components

Medium size components

DHD

SSAV

CS

Fig. 14. Elimination of thin components.

With respect to SS, index *ι* presents the following behavior: a large number of medium components in WM and GM, that yields an inferior value when compared against the index for CS.

In other words, index *ι* for WM and GM in SS suggests: a) a lack of small components in the analyzed WM, and whenever present they are characterized by their thinness. Medium structures predominate through the analyzed WM. Given the lack of small components, and the presence of thin small structures in WM, this originates the absence of small structures in the GM, for which a predominance of medium and large structures is observed.

The absence of small components (´´fingers") in the WM may causes a lack of electrical connection among different cortical regions. As a consequence a right electrical

method to determine the functional relations among different brain areas. This coherence is altered when some association vias (short and large cortico-corticals, cortico-subcorticals, and short cortico-corticals), are affected structurally; this has been demonstrated in some diseases like Alzheimer's and dementia. Some aspects of the electrical behavior as in the coherence case, depend precisely on the neuro-structural substrate (28; 29). For some authors, a decrease in coherence represents a diagnostic marker. Therefore, further research is necessary on the interrelation between structure and neuronal function, to gain a better understanding into the origin of multiple diseases that have a seat in the cerebral cortex, or at least of those conditions in which the participation of the brain cortex plays a role in their physiopathology.

<sup>191</sup> Comparison of Granulometric Studies of Brain Slices

from Normal and Dissociated Strabismus Subjects Through Morphological Transformations

On the other hand, during the development of the cerebral cortex or corticogenesis, there is a cellular migration of neurons that travel from periventricular regions and at the same time start maturing, until they reach more superficial regions of the brain, where their maturation culminates. During this process, interconnection vias are liable to be damaged giving place to different neurological schemes, that can affect the neuronal maturity process as well as the performance of the association routes. In the case of strabismus it is still not known, which structural alterations are the cause of this condition. (30–32). Finally, the granulometric study presented in this work, helps us understand the morphology of WM and GM at macroestructural level; however further studies are necessary to analyze the structure of the

In this work we presented a method for segmenting MRI slices, as well as the computation of two granulometric studies. The first granulometric study, analyzes clear and dark structures in the whole deskulling brain; while the second one, consists in the analysis of WM and GM

Curves obtained for the whole deskulled brains were not appropriated for analyzing clear and

On the other hand, important differences were found in the granulometric plots of WM and GM of the SS when compared to the graphs of CS group. Main differences consist in the lack of small components ("fingers") and predominance of medium and large structures. From this analysis, index *ι* was introduced, which is useful to establish an immaturity degree. In the SS, index *ι* results to be much smaller than that of CS; given the presence of numerous

The information drawn from these results suggests that there is a faulty electrical communication among several cortical areas due to the lack of small components, and also to the thinness of these structures which are present both in WM and GM. Changes in nerve neuroconduction, similar to those observed by means of the DBM in strabismic patients (7; 8; 14; 15), could be related to the microstructural organization of the cerebral mass. Index *ι* values, obtained in this work from healthy and strabismic children, show significant differences in the proportion of granulometric elements in the GM and WM when healthy and SS are compared. Based on the calculated index, strabismic patients with SSAV present a

dark regions, since WM and GM are partly composed by pixels of similar intensities.

This knowledge enable the establishment of better treatments (28).

WM and GM at microestructural level.

medium and large structures.

**5. Conclusions**

separately.

Fig. 15. Table to analyze WM and GM in all subjects through the proposed index *ι*. Volume values(bottom of x-axis) to evaluate the index were obtained from graphs in Fig. 12.

communication between different cortical areas is hindered. Therefore, although there are great areas of GM and WM in the SS, the lack of small components identified as fingers or thin components in the WM and GM, may cause a faulty electrical conduction and communication between these areas.

On the other side, the presence of a large volume formed of medium components in WM can be associated with a certain immaturity process, which is identified by some authors with excessive glial proliferation or abnormalities in myelin maturation or composition (27). This produces a low quality WM characterized by axons presenting certain degree of damage, with the subsequent deficiency in impulse conduction. In our case, index *ι* is also called immaturity index, by means of which the absence and increment of certain structures in WM or GM are measured. In this way, morphometric changes in WM and GM seem to be intimately related to the electrical and neurofunctional behavior of the analyzed SS. The granulometric study carried out in this work suggests that changes in the nerve conduction, as we have observed by means of DBM in strabismic patients (7; 8; 14; 15), could be the consequence of changes in the microstructural organization of the cerebral mass. According to this study, these alterations may be manifested as presence of immaturity of certain brain regions and lack of electrical communication between the structures conforming the WM and GM. We consider that as a result of this immaturity, alternative vias are established affecting the processes of neuronal interconnections; with the subsequent affectation, in different degrees and ways of the grey and white substance; hence different clinical expressions of the dissociated strabismus are originated.

On the other hand, studies of electrical brain function carried out by means of computed neurometry, have revealed the close correlation between the structure and cerebral function. This has been determined from the study of electrical coherence, which is a non invasive

method to determine the functional relations among different brain areas. This coherence is altered when some association vias (short and large cortico-corticals, cortico-subcorticals, and short cortico-corticals), are affected structurally; this has been demonstrated in some diseases like Alzheimer's and dementia. Some aspects of the electrical behavior as in the coherence case, depend precisely on the neuro-structural substrate (28; 29). For some authors, a decrease in coherence represents a diagnostic marker. Therefore, further research is necessary on the interrelation between structure and neuronal function, to gain a better understanding into the origin of multiple diseases that have a seat in the cerebral cortex, or at least of those conditions in which the participation of the brain cortex plays a role in their physiopathology. This knowledge enable the establishment of better treatments (28).

On the other hand, during the development of the cerebral cortex or corticogenesis, there is a cellular migration of neurons that travel from periventricular regions and at the same time start maturing, until they reach more superficial regions of the brain, where their maturation culminates. During this process, interconnection vias are liable to be damaged giving place to different neurological schemes, that can affect the neuronal maturity process as well as the performance of the association routes. In the case of strabismus it is still not known, which structural alterations are the cause of this condition. (30–32). Finally, the granulometric study presented in this work, helps us understand the morphology of WM and GM at macroestructural level; however further studies are necessary to analyze the structure of the WM and GM at microestructural level.

#### **5. Conclusions**

20 Will-be-set-by-IN-TECH

0 0.5 1 1.5 2 2.5 ι

Fig. 15. Table to analyze WM and GM in all subjects through the proposed index *ι*. Volume values(bottom of x-axis) to evaluate the index were obtained from graphs in Fig. 12.

communication between different cortical areas is hindered. Therefore, although there are great areas of GM and WM in the SS, the lack of small components identified as fingers or thin components in the WM and GM, may cause a faulty electrical conduction and communication

On the other side, the presence of a large volume formed of medium components in WM can be associated with a certain immaturity process, which is identified by some authors with excessive glial proliferation or abnormalities in myelin maturation or composition (27). This produces a low quality WM characterized by axons presenting certain degree of damage, with the subsequent deficiency in impulse conduction. In our case, index *ι* is also called immaturity index, by means of which the absence and increment of certain structures in WM or GM are measured. In this way, morphometric changes in WM and GM seem to be intimately related to the electrical and neurofunctional behavior of the analyzed SS. The granulometric study carried out in this work suggests that changes in the nerve conduction, as we have observed by means of DBM in strabismic patients (7; 8; 14; 15), could be the consequence of changes in the microstructural organization of the cerebral mass. According to this study, these alterations may be manifested as presence of immaturity of certain brain regions and lack of electrical communication between the structures conforming the WM and GM. We consider that as a result of this immaturity, alternative vias are established affecting the processes of neuronal interconnections; with the subsequent affectation, in different degrees and ways of the grey and white substance; hence different clinical expressions of the dissociated strabismus are

On the other hand, studies of electrical brain function carried out by means of computed neurometry, have revealed the close correlation between the structure and cerebral function. This has been determined from the study of electrical coherence, which is a non invasive

0 0.5 1 1.5 2 2.5 ι

 **GM SSAV**

**GM DHD**

0.934150077 0.605504587 0.75 CS Mean DHD1 DHD2

0.934150077 0.686619718 0.633587786 CS Mean SSAV1 SSAV2

**WM SSAV**

1.937254902 0.997474747 0.913253012 CS Mean DHD1 DHD2

**WM DHD**

1.937254902 0.890818859 0.831797235 CS Mean SSAV1 SSAV2

0 0.5 1 1.5 2 2.5 ι

between these areas.

originated.

0 0.5 1 1.5 2 2.5 ι

> In this work we presented a method for segmenting MRI slices, as well as the computation of two granulometric studies. The first granulometric study, analyzes clear and dark structures in the whole deskulling brain; while the second one, consists in the analysis of WM and GM separately.

> Curves obtained for the whole deskulled brains were not appropriated for analyzing clear and dark regions, since WM and GM are partly composed by pixels of similar intensities.

> On the other hand, important differences were found in the granulometric plots of WM and GM of the SS when compared to the graphs of CS group. Main differences consist in the lack of small components ("fingers") and predominance of medium and large structures. From this analysis, index *ι* was introduced, which is useful to establish an immaturity degree. In the SS, index *ι* results to be much smaller than that of CS; given the presence of numerous medium and large structures.

> The information drawn from these results suggests that there is a faulty electrical communication among several cortical areas due to the lack of small components, and also to the thinness of these structures which are present both in WM and GM. Changes in nerve neuroconduction, similar to those observed by means of the DBM in strabismic patients (7; 8; 14; 15), could be related to the microstructural organization of the cerebral mass. Index *ι* values, obtained in this work from healthy and strabismic children, show significant differences in the proportion of granulometric elements in the GM and WM when healthy and SS are compared. Based on the calculated index, strabismic patients with SSAV present a

[6] Gallegos-Duarte M. "Exploratory maneuvers in congenital endotropy ". En: Temas Selectos de Estrabismo. Centro Mexicano de Estrabismo SC. México, Composición

<sup>193</sup> Comparison of Granulometric Studies of Brain Slices

from Normal and Dissociated Strabismus Subjects Through Morphological Transformations

[7] Gallegos-Duarte M; Moguel, S.; Rubín de Celis, B.; " Alterations in the cerebral mapping in the variable congenital endotropy ", Rev Mex Oftalmol; 2004; 78 (3): 122-126. [8] Gallegos-Duarte M. " Paradoxical cortical response during the intermittent fotoestimulation in the dissociated strabismus ", Cir y Cir 2005; 73 (3): 161-165. [9] Gallegos-Duarte M, Mendiola-Santibáñez JD, Ortiz-Retana JJ; Rubín de Celis B, Vidal-Pineda R, Sigala-Zamora. " Dissociated desviation. An strabismus of cortical

[10] Olivares, R; Godoy,G; Adaro,L; Aboitiz, F.: "Neuronal density of the visual cortex (area

[11] Horton, J.C., Hocking, D.R., "An adult-like pattern of ocular dominance columns in striate cortex of newborn monkeys prior to visual experience". J. Neuroscience 1996,

[12] Horton, J.C., Hocking, D.R., Timing of the critical period for plasticity of ocular dominance columns in macaque striate cortex. J. Neuroscience 1997; 17:3684-3709,. [13] Tychsen L; Wong AM; Burkhalter A.: Paucity of horizontal connections for binocular vision in V1 of naturally strabismic macaques: Cytochrome oxidase compartment

[14] Gallegos-Duarte, M, Moguel-Ancheita S: "Modifications neurologiques adaptatives après traitement médical et chirurgical du syndrome strabique avec variations des repères angulaires". En: Réunion de printemps, Association française de strabologie. 110 Congres de la société Française d´Ophtalmologie, Paris 2004.

[15] Moguel-Ancheita S, Orozco-Gómez L, Gallegos-Duarte M, Alvarado I, Montes C. " Metabolic changes in the cerebral cortex related to the strabismus treatment. Preliminary

[17] Serra, J. y P. Salembier. "Connected operators and pyramids" ., Proc. of SPIE. Image

[18] Salembier P., and Serra J.,: Flat zones filtering, connected operators and filters by reconstruction. IEEE Transactions on Image Processing, 3(8), (1995) 1153-1160. [19] Vincent L. and Dougherty E. R.:Morphological segmentation for textures and particles. In Digital IMage Processing Methods E.R. Dougherty, editor, . Marcel Dekker, New York,

[20] Mendiola-Santibañez, J.D ,Terol-Villalobos, I.R., Herrera-Ruiz G. , Fernández-Bouzas, A., "Morphological contrast measure and contrast enhancement: One application to the segmentation of brain MRI", *Signal Processing*, vol. 87 , no. 9, pp. 2125-2150, 2007. [21] Soille, P.,: Morphological image analysis: principle and applications, Springer-Verlag,

[23] L. Vincent, "Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms," *IEEE Transactions on Image Processing*, vol. 2, no. 2, pp. 176-201,

[16] Serra, J.: Mathematical Morphology vol. I, Academic Press., London, (1982 ).

[22] Heijmans H., "Morphological Image Operators", Academic Press, USA, 1994.

[24] Matheron G.: Eléments pour une théorie des milieux poreoux. Mason,Paris(1967).

Algebra and Mathematical Morphology'93, San Diego, July , 1993.

17) of two species of wild rodents". Int. J. Morphol 2004, 22 (4): 279-284.

Editorial Láser. México, D.F. 2005, 1-18.

origin". Cir y Cir 2007, 75 (4): (in printt).

specificity. J Com Neurol. 2004, 474 (2): 261-75

http://perso.orange.fr/hoc.lods/demo147.html.

results with SPECT". Cir y Cir 2004; 72:165-170

16:1789-1805.

(1994) 43–102.

2003.

Feb. 1993.

greater degree of immaturity than those patients with DHD; since *ι* index is smaller. This can be more clearly appreciated from the graphs and derived values in Fig. 15.

On the other hand, it is rather convenient that changes consistent with the alterations in the relation volume and granulometric density can be determined in alive subjects; besides this advantage can be complemented with neurofunctional studies such as the DBM. This technique offers a high temporary resolution, though its space resolution is significantly slower. Granulometric studies offer a finest structural analysis available in vivo, that allow the interpretation of neurofunctional studies. On the one hand, granulometry is outlined as an excellent diagnosis marker for several neurologic diseases. The study carried out in this work not only suggests the neuronal immaturity associated with strabismus, but also the lack of small components("fingers") and the predominance of medium size structures mainly in the SS group. These circumstances propitiate alterations in conduction of the neuroelectrical impulses, favoring the presence of strabismus, as well as the alterations encountered in the DBM. Therefore, granulometric studies may help to gain a better insight into the origin, diagnosis and prognosis of this prevalent disease, for which so little is known. Although the amount of brains analyzed here is only six, they provide important information to establish granulometric differences between SC and SS groups. Finally, for our future research, we are considering the following things: I) Improvement of the morphologic operators involved in the obtention of granulometric curves; these operators must be autodual with the purpose of treating clear and dark components of the image separately; and II) Inclusion of a larger sample of healthy children to obtain mean patterns, as well as a larger number of patients with strabismus.

#### **6. Acknowledgements**

The authors wish to thank the Mario Moreno Reyes foundation for the financial support. Jorge D. Mendiola-Santibañez thanks to CONACyT for the financial support.

#### **7. References**


22 Will-be-set-by-IN-TECH

greater degree of immaturity than those patients with DHD; since *ι* index is smaller. This can

On the other hand, it is rather convenient that changes consistent with the alterations in the relation volume and granulometric density can be determined in alive subjects; besides this advantage can be complemented with neurofunctional studies such as the DBM. This technique offers a high temporary resolution, though its space resolution is significantly slower. Granulometric studies offer a finest structural analysis available in vivo, that allow the interpretation of neurofunctional studies. On the one hand, granulometry is outlined as an excellent diagnosis marker for several neurologic diseases. The study carried out in this work not only suggests the neuronal immaturity associated with strabismus, but also the lack of small components("fingers") and the predominance of medium size structures mainly in the SS group. These circumstances propitiate alterations in conduction of the neuroelectrical impulses, favoring the presence of strabismus, as well as the alterations encountered in the DBM. Therefore, granulometric studies may help to gain a better insight into the origin, diagnosis and prognosis of this prevalent disease, for which so little is known. Although the amount of brains analyzed here is only six, they provide important information to establish granulometric differences between SC and SS groups. Finally, for our future research, we are considering the following things: I) Improvement of the morphologic operators involved in the obtention of granulometric curves; these operators must be autodual with the purpose of treating clear and dark components of the image separately; and II) Inclusion of a larger sample of healthy children to obtain mean patterns, as well as a larger number of patients

The authors wish to thank the Mario Moreno Reyes foundation for the financial support. Jorge

[1] Krachmer JH, Marti T.J, Corbett JJ.: Trastornos del quiasma y de las vías visuales retroquiasmáticas, En: Los requisitos en oftalmología: Neuroftalmología. Ed. Harcourt,

[2] Rakic, P; Lombroso, P.J. "Development of the cerebral cortex: I. Forming the cortical

[3] Zeki, SM., Watson, J.D.G, Lueck, C.J., Fristcn, K.J., Kennard, C. And Frackowiat, S.J. "A direct demostration of functional specialization in human visual cortex". J Neurosci 1991,

[4] Mendola JD, Conner IP, Anjali R, Chan ST, Schwartz TL, Odom JV, Kwong KK. "Voxel-based analysis of MRI detects abnormal visual cortex in children and adults with

[5] Suk-tak Ch; Kwok-win T; Kwok-cheung L; Lap-kong Ch; Mendola JD; Kwong KK. Neuroanatomy and adult strabismus: a voxel-based morphometric analisys of magnetic

structure". J. Am Acad Child Adolesc Psychiatry 1998, 37 (1): 116-117.

amblyopia". Human Brain Mapping 2005; 25(2) 222-236

resonance structural scans. Neuroimage 2004 (22) 986-994.

D. Mendiola-Santibañez thanks to CONACyT for the financial support.

be more clearly appreciated from the graphs and derived values in Fig. 15.

with strabismus.

**7. References**

**6. Acknowledgements**

11(3) 641-649.

Madrid, España. 2001; 101-108.


**1. Introduction**

terms of averaged waveforms.

between cortical areas.

Magnetoencephalography (MEG) can monitor the activation of a neuronal population with millisecond temporal resolution, and offer new noninvasive information about basic activities of the human brain. MEG is usable for the description of spontaneous brain activity and the detection of timely events such as stimulus evoked fields. The most recent advances in the field of MEG concerning cortical responses to stimulation are issued from development of multichannel recordings. We can study the temporal order of several cortical areas from averaged waveforms of MEG, e.g., auditory, visual, and somatosensory evoked responses. For three decades, dynamical information contained in MEG has been analyzed mainly in

**Intracerebral Communication Studied by** 

*Department of Information Science, Faculty of Engineering, Gifu University* 

**Magnetoencephalography** 

Kuniharu Kishida

*Yanagido, Gifu,* 

*Japan* 

**10**

However, lots of brain activities are included in original MEG data. For spontaneous fields there are huge activities in cortical areas. Generally, it is difficult to estimate source locations of current dipole data from MEG data correctly at the present stage, if the number of current dipoles becomes large. The estimation of their locations is an underdetermined problem. In the case of spontaneous fields it is hard to obtain intracerebral communication between active cortical areas. Hence, we consider an overdetermined problem in the case of evoked fields, since their locations of active cortical areas are limited. Furthermore, we should find a possibility to obtain dynamical information by signal processing of fluctuations around concatenate average waveforms, which have been discarded without signal processing in the conventional MEG analysis. The fluctuations may be induced magnetic fields to communicate

In this chapter, we will show this new direction of MEG analysis by way of example of somatosensory evoked field (SEF), and intracerebral communication between active somatosensory cortices can be expressed by system identification of fluctuations. That is, intracerebral communication between the primary somatosensory cortex in the contralateral hemisphere (cSI) and the contralateral secondary somatosensory cortex (cSII) in 2Hz median nerves stimuli will be discussed from correlation functions of SEF fluctuations by the identification method with feedback model (see Section 3.6). In this chapter, intracerebral communication between cSI and cSII will be studied not from averaged waveforms but from

fluctuations around concatenate averaged waveforms by following steps:

