- Email: [email protected]
Projecting the sulcal pattern of human brains onto a 2D plane — a new approach using potential theory and MRI
Psychiatry Research: Neuroimaging Section 83 Ž1998. 75]84
Projecting the sulcal pattern of human brains onto a 2D plane } a new approach using potential theory and MRI Mark A. Haidekker a,U , Carl J.G. Evertsz a , Clemens Fitzek b , Stephan Boor b , Reimer Andresen c , Peter Falkai d , Peter Stoeter b , Heinz-Otto Peitgen a a
MeVis (Center for Medical Diagnostic Systems and Visualization), Uni¨ ersity of Bremen, Uni¨ ersitatsallee 29, ¨ 28359 Bremen, Germany b Department of Neuroradiology, Uni¨ ersity Hospital of Mainz, Langenbeckstr. 1, 55131 Mainz, Germany c Department of Radiology, Behring Municipal Hospital, Gimpelstieg 3]5, 14160 Berlin, Germany d Clinic for Psychiatry, Friedrich-Wilhelm-Uni¨ ersity, Sigmund-Freud-Str. 25, 53105 Bonn, Germany Received 7 January 1998; accepted 22 May 1998
Abstract A new method is introduced to project the sulcal pattern of the brain surface onto a 2D plane. Twin brains are compared against each other using the planar representation. We obtained T1-weighted Flash-3D MRI volumes from 14 male twins Žseven monozygotic, seven dizygotic. with 3mm-thick coronal slices. The projection is based on potential theory: A virtual electrostatic field is calculated between the area of the segmented brain and a surrounding spherical electrode. Field lines starting from each border point of the segmented brain follow the gradient towards the sphere, leading to field line concentrations due to the underlying sulci. The unwrapped sphere surface with the number of field lines per area unit is used as the 2D representation of the sulcal pattern. The resulting brain projections show a distinctive pattern, and a visual assignment of the twin pairs from the unsorted set is possible because of a high similarity of the patterns between twin pairs. Global correlation coefficients for each pair of maps yield significantly higher values for matching monozygotic twin pairs Žmean s 20.2, range 12.3]25.6. than for unmatched pairs Žmean s 13.0, range 1.1]28.5.. As a conclusion, our method allows us to map the location and depth of the sulci on a 2D plane. The resulting maps allow quantitative inter-individual comparisons on the entire brain or parts of the brain surface. Q 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Magnetic Resonance Imaging; Brain mapping; Twins; 3-Dimensional Image Processing
U
Corresponding author. Tel.: q49 421 218 2439; fax: q49 421 218 4236; e-mail: [email protected]
0925-4927r98r$19.00 Q 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0925-4927Ž98. 00029-8
76
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
1. Introduction
2. Methods
For the investigation of macro-anatomical changes of the cerebrum in psychiatric disorders, postmortem and Magnetic resonance imaging ŽMRI. techniques have been applied extensively, but mainly in a volumetric way ŽDeakin, 1996.. Although experienced pathomorphologists claim to be able to diagnose schizophrenia from the abnormal pattern of gyrification, mainly in the frontal lobes, this morphological aspect has not received much attention in the recent literature about MRI methods. In order to detect deviations from the normal pattern of convolutions, quantitative analysis and interindividual comparison have to be carried out. Apart from examinations of the gross asymmetry of the temporal lobes ŽDeLisi et al., 1994; Hasboun et al., 1996., the comparison of the gyral pattern is usually limited to circumscribed areas such as the Sylvian fissure, the plana temporalia or the gyri of Heschl ŽFalkai et al., 1992; Bartley et al., 1993; Kleinschmidt et al., 1994; Rossi et al., 1994; Falkai et al., 1995; Kulynych et al., 1995; Petty et al., 1995; Mazanek et al., 1997.. A more ´ general assessment of the convolutional pattern is obtained from semi-automatic brainprint analysis ŽJouandet et al., 1989., or by the active contour model ŽVaillant and Davatzikos, 1997. by unfolding the cerebral surface into a 2D map. These techniques allow evaluations and measurements of limited areas, but are not aimed at the quantitative comparison of the entire sulcal pattern. However, the global complexity of gyrification may be described by fractal analysis of the boundary between white matter and the cerebral cortex ŽBullmore et al., 1994., but without comparing the individual gyral anatomy. The new method described in this report tries to combine both aspects: preserving the morphological information by projecting the individual sulcal pattern onto the surface of a surrounding virtual sphere and by allowing a quantitative correlation of the sulcal indentations between individuals at the same time. The applicability of the new technique is demonstrated by comparing the sulcal anatomy of twins to test the hypothesis of a higher degree of similarity in twins as compared to unmatched pairs.
We examined 14 healthy male twin pairs Ž28 individuals., out of which seven were monozygotic, 19]34, and seven dizygotic, aged 24]35 years. All individuals were informed about the study and gave their consent. MR images were obtained on a Philips S15-ACS Ž1.5 T. with a flash-3D-sequence ŽTR s 17 ms, T E s 5 ms, flip angle s 358.. To achieve a balance between a short acquisition time Ž5 min. and a good signalto-noise ratio, 3-mm-thick coronal slices were acquired. The MRI data were then transferred to an external workstation ŽSilicon Graphics Onyx-2. for all further image processing steps which included the segmentation of the brain, the calculation of the result of the Laplace equation D Es 0, the calculation of the field lines, and the generation of a 2D projection of the sulcal pattern based on the above calculation. To demonstrate the properties of the projection, we used the phantom displayed in Fig. 1: a filled sphere with a series of clefts of different shape and depth. The cross-sectional cut through the phantom reveals the geometry of the clefts: Ž1. a wedge-shaped cleft running from the anterior to the posterior pole; Ž2. a bent cleft; Ž3. a rectangular, diagonal cleft; and Ž4. a small and shallow rectangular cleft, wider than high. 2.1. Segmentation of the brain and pre-processing The segmentation is based on a 2D flood fill algorithm. In each slice, an initial point within the brain area is marked manually. The flood filling process is aborted when any of the following conditions are met: v
v
v
The pixel value lies above or below selected threshold values; the average value of the current pixel and its eight neighbors lies above or below selected threshold values; and the variance of the values of the current pixel and its eight neighbors lies above or below selected threshold values. In some slices, additional manual corrections
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
77
Fig. 1. The phantom used to demonstrate the properties of the projection. Top row: 3D rendering of the phantom with its clefts to simulate sulci Žleft., cut open to reveal the structure of the clefts Žmiddle., and one slice with a schematical representation of the field lines starting from the surface of the phantom and arriving at the border of the outer electrode Žright.. Below: 2D projection of the phantom. The white areas are positions on the unwrapped sphere, where many field lines arrive due to the underlying clefts.
are necessary, mainly to remove parts of the sinus sagittalis superior. After the segmentation process, we scaled the slices to 256 = 256 pixels and inserted three additional slices between any two slices of the original volume by interpolation. This was done in order to achieve an isotropic voxel size without exceeding memory limits.
tial of zero. The fundamental differential equation of potential theory, the Laplace equation D E s 0, is solved iteratively using the Gauss]Seidel Method with accelerated iteration by successive over-relaxation ŽGerald and Wheatley, 1984.: the potential value of each voxel is determined iteratively in 3D out of the value of its six neighbors according to Eq. Ž1.:
2.2. Iterati¨ e solution of the Laplacian equation
Ukq 1Ž x, y, z .
A virtual sphere-shaped electrode is placed around the brain so that the center of the sphere is identical with the center of gravity of the segmented brain. The surface of the spherical electrode is set to a constant potential of Us 1, while the brain area itself is set to the constant poten-
s
b w Ukq 1Ž xy 1, y, z . q Uk Ž xq 1, y, z . 6
qUkq 1Ž x, y y 1, z . q Uk Ž x, y q 1, z . qUkq 1Ž x, y, zy 1 . q Uk Ž x, y, z q 1 .x q Ž 1 y b . Uk Ž x, y, z .
Ž1.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
78
where Uk Ž x,y,z . is the potential value at the voxel coordinates x,y,z after the kth iteration, and b is the successive over-relaxation parameter which allows a faster approximation of the iterated values and is empirically set to 1.2. The iteration is stopped as soon as the relative error e according to Eq. Ž2.
e Ž x, y, z . s
Uk Ž x, y, z . y Uky1Ž x, y, z . Uk Ž x, y, z .
Ž2.
is found to be below 0.0001 for all voxels between the brain area and the spherical electrode, i.e. the maximum relative change between two iterations is less than 0.01 percent. This generally requires approx. 600]800 iterations.
ª
Any field line s Ž t . is the solution of the ª differential Eq. Ž3. and its initial condition s 0 : ª d s Žt. sy \ U dt ª
ª
ª
2.5. Correlation of the projections
CA B s nS a x y bx y y S a x y Sbx y
ª
s Ž t iq1 . s s Ž t i . q h \ U
ª
ž s Žt ./ i
Ž4.
Therefore the gradient must be calculated for non-integer coordinates. For this purpose, the partial derivation UŽ x,y,z .r x is based on a quadratic polynomial interpolation of the potential values at the coordinates w x x ,y,z, w x x y h,y,z, and w x x q h,y,z, where w x x is the integer part of x. Ur y and Ur z are calculated accordingly. Any field line ends at the border of the sphere, i.e. when the potential value of 1 is reached. The
2 xy
. y Ž S a x y .2
2 = nS Ž bx2 y . y Ž Sbx y .
Ž5.
Ž3.
0
In practical terms, a field line starts from each border point of the brain surface and follows the rising gradient towards the spherical electrode. The field lines are calculated numerically by executing discrete steps of length h Žwhich is in this case set to pixel distance. in the direction of the rising gradient according to the Euler method as outlined in Eq. Ž4.. ª
The number of field lines arriving at each surface unit of the spherical electrode is recorded, then the sphere is unwrapped. This results in a planar image, where each pixel value equals the number of field lines arriving at this specific point. The projection of the phantom is shown in the lower part of Fig. 1, where the white lines represent areas with many arriving field lines per area unit.
' nS Ž a
ž s Žt./
ª
s Ž t s 0. s s
2.4. Generation of the 2D projection
The global correlation coefficient CA B is calculated for each pair of planes according to Eq. Ž5.
2.3. Calculation of the field lines
ª
course of the field lines can be seen in Fig. 1 for one slice of the phantom.
between the individuals A and B with a x , y and bx , y as the maximum gray value Žnumber of arriving field lines. in a 3 = 3 neighborhood of the point Ž x,y . in the plane. The use of the neighborhood allows for small geometric tolerances in the calculation of the correlation. The comparison of 28 individuals leads to 378 correlation coefficients out of which seven result from dizygotic twin pairs, seven from monozygotic ones, and 364 from non-matched pairs. A test for statistical significance is performed using the Mann]Whitney Rank Sum test. 3. Results The calculation of the projection for the phantom reveals the fundamental behavior of the method. In Fig. 1, the areas of the unwrapped sphere surface, where many field lines arrive, are rendered as white lines. The number of arriving field lines depends on the depth and width of the
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
underlying cleft: a deep cleft leads to a high number of field lines per area unit. In other words, the projection contains information about the location and the depth of the sulci. To identify the properties of the projection of the brain, which is much more complex than the phantom, we marked several important sulci with different colors. One slice of the sample brain, and the projection of the entire brain can be seen in Fig. 2. In Fig. 3, there are the planar projections from three sample twin pairs. Five such pairs, including
79
these three, were given to eight untrained observers with the task to identify the pairs out of the unsorted set. All of them correctly identified the matching pairs. Any pairs of projections were correlated, and the correlation coefficients divided into four groups: monozygotic twins Ž n s 7., dizygotic twins Ž n s 7., all twins Ž n s 14., and non-matched pairs Ž n s 364. out of a total of 378 possible combinations on the set of 28 projections. The statistical analysis of the correlation coefficients can be seen in Table 1. Since the data are not distributed
Fig. 2. Generation of a 2D projection of the brain, where the major sulci have been marked with different colours. Above, a simplified representation of one single coronal slice with the colour-marked areas; below, the planar projection of the entire brain on a 3D basis. For didactical purposes, and to facilitate visual identification, the field lines in the upper part were calculated in 2D, and the coloured dots in the lower part were expanded.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
80
Fig. 3. Planar projections from three monozygotic sample twin pairs. Each row displays one twin pair, where the similarities of the sulcal pattern are clearly recognizable. The pairs show a correlation of 24.7, 24.2, and 25.6 Žfrom top to bottom..
Table 1 Statistical values over the correlation coefficients for the different groups of pair combinations of brainprint images Group
Twins n s 14
Unmatched n s 364
Monozygotic Dizygotic ns7 ns7
Average Standard deviation Median Max Min
17.4 7.5
13.0 5.6
20.2 5.7
14.5 8.4
16.3 29.0 3.9
12.5 28.5 1.1
23.3 25.6 12.3
13.8 29.0 3.9
normally, the Mann]Whitney Rank Sum Test was chosen to determine whether the differences between the groups are statistically significant. The test shows the difference between the twin group and the unmatched pairs to be significant Ž P- 0.05., as well as the difference between the monozygotic twins and unmatched pairs Ž P0.0005.. The difference between the dizygotic group and the unmatched pairs and between the monozygotic and the dizygotic group does not show statistical significance.
4. Discussion The development of tomography techniques and fast computing hardware allowed a rapid progress in the non-invasive acquisition and processing of images of the brain. There is a widespread interest in brain topography. A multitude of different algorithms for the segmentation and analysis of different aspects of brain images have been presented in recent years. A special focus lies on the generation of brain maps, because many processes are easier to visualize and to understand on planar projections. The methods applied for this purpose cover a wide range. Early attempts to create 2D projections of the sulcal or gyral pattern were mostly based on manual methods. Geometric projections ŽHollander, 1995; Hollander et al., 1997. and non-lin¨ ¨ ear approaches ŽDavatzikos et al., 1996; Schormann et al., 1996; Vaillant and Davatzikos, 1997. allow an automated processing of the images. Fractal methods have been applied to images of the brain as well, although the fractal nature of
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
tomographical brain images is still being discussed ŽMajumdar and Prasad, 1988; Besthorn et al., 1997.. For this study, we developed a new method. This is basically derived from a 2D model to determine harmonic measures in fractal objects like the Koch Tree and Diffusion Limited Aggregation ŽDLA. dendrites ŽEvertsz et al., 1991a,b; Evertsz and Mandelbrot, 1992.. The principle is, that in the fjords an electric potential is shielded, so that both gradient and potential are lowest in the inner parts of the fjord. We adapted the method for 3D. As the most important extension to the above method, the actual projection is performed by analyzing the field lines. As a result, our algorithm allows the mapping of the location and depth of the sulci onto a plane, primarily because the number of field lines starting from a sulcus is proportional to the inner surface area of that sulcus. The resulting planar projection shows a distinctive pattern. It is possible to identify the projections of the major sulci, as shown in Fig. 2. Moreover, similarities between the patterns belonging to twin pairs can be found both by visual examination and calculation of the correlation between pairs of 2D projections. The fundamental behavior was explained by generating the projection of a phantom and of a color-coded brain. The projection contains information about the location and the shape Ždepth and surface . of the sulci. While the algorithm is able to follow bends and convolutions, only the inner surface area is recognized Žas shown with cleft no. 2 in Fig. 1.. Moreover, the field lines have a tendency to follow tunnel-like extensions and wider channels, consequentially clustering together when the algorithm is applied in 3D. In a basic morphological aspect however, the projection described above contains less information than an original 3D-image of the brain reconstructed with surface or volume rendering techniques ŽCline et al., 1990; Cohen et al., 1992; Bullmore et al., 1994.. But 3D images, like surface reconstructions, can be compared interindividually only in a descriptive way like fingerprints according to qualitative features, e.g. the number and main direction of gyri of a certain area, the
81
number of ramifications, bends or interruptions of a gyrus, or by measurement of its extension, a surface area, or the volume of a defined structure ŽSteinmetz et al., 1989; DeLisi et al., 1994.. A more general comparison of the gyral pattern is usually achieved by transforming a 3D data set into a 2D map. The brainprint method ŽJouandet et al., 1989. uses a semi-automatic placement of reference points to the gyral summits and valleys and results in a 2D map of connecting reference lines. This allows a quantitative comparison of brain growth during pre- and post-natal development ŽMarc et al., 1993.. But due to the characteristics of this transformation, individual information concerning the smaller convolutions is lost and interindividual comparison has been limited so far to the course of the major sulci. Moreover, the method requires manual interaction and is thus subject to influences from the observer. Even more information about the individual gyral pattern is lost if purely quantitative methods like volume measurements ŽHarris et al., 1994; Hasboun et al., 1996; Heun et al., 1997; Laakso et al., 1997., or fractal analysis of the boundary between white matter and the cerebral cortex ŽBullmore et al., 1994., or of the brain surface ŽBesthorn et al., 1997. are used. Although the fractal dimension, as calculated in these studies, is proposed as a measure of cerebral complexity and can be used to characterize different groups of psychiatric patients, it does not allow the assessment of the interindividual similarity of the gyral pattern. The recently presented Active Contour Model ŽVaillant and Davatzikos, 1997. uses parametric representations of the cortical sulci and thus preserves information about the individual sulcal course and depth in a similar way as our method, but by now has been applied only to limited areas like the central sulcus. With the application of our projection technique, the entire brain surface including first to third order convolutions is considered for testing individual similarity. Although there are some limitations such as a certain sensitivity to rotation artifacts during MRI data acquisition, we could prove that our 2D projections are capable of
82
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
showing similarities in the sulcal pattern of twin pairs both when inspected by untrained observers and when compared mathematically. Although the average correlation was higher in the monozygotic group, showing statistical significance, we found that the degree of similarity varies strongly within the groups. As indicated in Fig. 4, this observation can be supported by visual inspection. Some parameters of the Laplacian Brainprint algorithm were selected by experience. This is mainly valid for the successive over-relaxation factor b in Eq. Ž1., which only influences the calculation of the Laplace equation and has no influence on the projection itself. The segmentation process of the brain requires some manual
interaction, but experiments showed that relevant changes of the threshold values only resulted in minor changes of the gray values in the 2D plane while the location of the sulcal traces remained unchanged. This indicates a robustness of the method against variations of the global gray intensity of the MRI images. This finding of a high degree of similarity of the sulcal pattern between twins was suspected in analogy to the similarity of other surface markers, such as the shape of the face and stature but has not been described so far. Other examinations based on qualitative ŽSteinmetz et al., 1994; Mazanek et al., 1997. or semi-quantitative ´ ŽJouandet et al., 1989. analyses of the convolutio-
Fig. 4. Examples for a well-matching twin pair from the monozygotic set Žabove. with a correlation value of 25.6, and a different pair from the dizygotic group Žbelow. with a lower correlation value of 13.8. In both cases, two maps were overlaid, with one twin drawn in red, the other one in green. Identical pixels of the pattern appear in yellow.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
nal pattern as well as measurements of the plana temporalia or length of the Sylvian fissure ŽBartley et al., 1993; Steinmetz et al., 1995; Mazanek et ´ al., 1997. could not find a higher correlation in twin pairs as compared to unmatched pairs. This discrepancy may be due to the difficulties of the techniques mentioned above to assess the total gyral pattern without losing too much information about the individual course of the convolutions. A further improvement of our method can be expected from replacing the correlation method for the comparison of different patterns by a more sophisticated pattern-matching technique, which is currently being investigated. If the capability of our Laplacian Brainprint technique for the evaluation of similarities between twins can be confirmed by further studies, this method could be used for twin and other family studies of schizophrenia to evaluate possible differences in gyrification between healthy and affected members of a group. Moreover, some statement about the complexity of gyrification should be possible by generating a histogram of the field line densities. This could be applied to assess brain morphology of psychiatric diseases similar to the fractal analysis, but without losing too much of the individual information about the convolutional pattern. References Bartley, A.J., Jones, D.W., Torrey, E.F., Zigun, J.R., Weinberger, D.R., 1993. Sylvian fissure asymmetries in monozygotic twins: a test of laterality in schizophrenia. Biological Psychiatry 34, 853]863. Besthorn, C., Zerfaß, R., Hentschel, F., 1997. Die fraktale Dimension als Bildverarbeitungsparameter im CT bei Alzheimer-Demenz. Klinische Neuroradiologie 7, 12]16. Bullmore, E., Brammer, M., Harvey, I., Persaud, R., Murray, R., Ron, M., 1994. Fractal analysis of the boundary between white matter and cerebral cortex in magnetic resonance images: a controlled study of schizophrenic and manic depressive patients. Psychological Medicine 24, 771]781. Cline, H.E., Iorensen, W.E., Kikinis, R., Jolesz, F., 1990. Three-dimensional segmentation of MR images of the head using probability and connectivity. Journal of Computer Assisted Tomography 14, 1037]1045. Cohen, G., Andreasen, N.C., Alliger, R., Arndt, S., Kuan, J., Yuh, W.T., 1992. Segmentation techniques for the classifi-
83
cation of brain tissue using magnetic resonance imaging. Psychiatry Research: Neuroimaging 45, 33]51. Davatzikos, C., Vaillant, M., Resnick, S., Prince, J.L., Letovsky, S., Bryan, R.N., 1996. Morphological analysis of brain structures using spatial normalization. In: Hohne, K.H., Kikinis, ¨ R. ŽEds.., Visualization in Biomedical Computing, Springer, Berlin, pp. 355]360. Deakin, J.F.W., 1996. Neurobiology of schizophrenia. Current Opinion in Psychiatry 9, 50]56. De Lisi, L.E., Hoff, A.L., Chance, N., Kushner, M., 1994. Asymmetries in the superior temporal lobe in male and female first-episode schizophrenic patients: measures of the planum temporale and superior temporal gyrus by MRI. Schizophrenia Research 12, 9]18. Evertsz, C.J.G., Jones, P.W., Mandelbrot, B.B., 1991a. Behaviour of the harmonic measure at the bottom of fjords. Journal of Physics A 24, 1889]1901. Evertsz, C.J.G., Mandelbrot, B.B., Normant, F., 1991b. Fractal aggregates and the current lines of their electrostatic potential. Physica A 177, 589]592. Evertsz, C.J.G., Mandelbrot, B.B., 1992. Harmonic measure around a linearly self-similar tree. Journal of Physics A 25, 1781]1797. Falkai, P., Bogerts, B., Greve, B., Pfeiffer, U., Machus, B., Folsch-Reetz, B., Majtenyi, C., Ovary, I., 1992. Loss of ¨ Sylvian fissure asymmetry in schizophrenia. A quantitative post-mortem study. Schizophrenia Research 7, 23]32. Falkai, P., Bogerts, B., Schneider, T., Greve, B., Pfeiffer, U., Pitz, K., Gonsiorzcyk, C., Majtenyi, C., Ovary, I., 1995. Disturbed planum temporale asymmetry in schizophrenia. A quantitative postmortem study. Schizophrenia Research 14, 161]176. Gerald, C.F., Wheatley, P.O., 1984. The Laplacian operator in three dimensions. In: Applied Numerical Analysis, 3rd ed. Addison-Wesley, Reading, Massachussetts, pp. 431]437. Harris, G.J., Barta, P.E.W., Peng, L.W., Lee, S., Brettschneider, P.D., Shah, A., Henderer, J.D., Schlaepfer, T.E., Pearlson, G.D., 1994. MR volume segmentation of gray matter and white matter using manual thresholding: dependence on image brightness. American Journal of Neuroradiology 15, 225]230. Hasboun, D., Chantome, M., Zouaoui, A., Sahel, M., Delaˆ doeuille, M., Sourour, M., Duyme, M., Baulac, M., Marsault, C., Dormont, D., 1996. MR determination of hippocampal volume: comparison of three methods. American Journal of Neuroradiology 17, 1091]1098. Heun, R., Mazanek, M., Atzor, K.R., Tintera, J., Gawehn, J., ´ Burkart, M., Gansicke, M., Falkai, P., Stoeter, P., 1997. ¨ Amygdala-hippocampal atrophy and memory performance in dementia of Alzheimer type. Dementia and Geriatric Cognitive Disorders 8, 329]336. Hollander, I., 1995. Cerebral cartography } a method for ¨ visualizing cortical structures. Computerized Medical Imaging and Graphics 19, 397]415. Hollander, I., Petsche, H., Dimitrov, L.I., Filz, O., Wenger, E., ¨ 1997. The reflection of cognitive tasks in EEG and MRI
84
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
and a method of its visualization. Brain Topography 4, 177]189. Jouandet, M.L., Tramo, M., Herron, D., 1989. Brainprints: computer generated two-dimensional maps of the human cerebral cortex in vivo. Journal of Cognitive Neurosciences 1, 92]120. Kleinschmidt, A., Falkai, P., Huang, Y., Schneider, T., Furst, ¨ G., Steinmetz, H., 1994. In-vivo morphometry of planum temporale asymmetry in first-episode schizophrenia. Schizophrenia Research 12, 9]18. Kulynych, J.J., Vladar, K., Fantie, B.D., Jones, D.W., Weinberger, D.R., 1995. Normal asymmetry of the planum temporale in patients with schizophrenia. Three-dimensional cortical morphometry with MRI. British Journal of Psychiatry 166, 742]749. Laakso, M.P., Juottonen, K., Partanen, K., Vainio, P., Soininen, H., 1997. MRI volumetry of the hippocampus: the effect of slice thickness on volume formation. Magnetic Resonance Imaging 15, 263]265. Majumdar, S., Prasad, R.R., 1988. The fractal dimension of cerebral surfaces using magnetic resonance images. Computers in Physics, 69]73. Marc, L., Jouandet, M.D., Deck, M.D.F., 1993. Prenatal growth of the human cerebral cortex: brainprint analysis. Radiology 188, 765]774. Mazanek, M., Angert, T., Atzor, K.R., Falkai, P., Gansicke, ´ ¨ M., Boor, S., Mehrtens, C., Maier, W., Stoeter, P., 1997. Asymmetrie des Planum temporale bei Zwillingen und Schizophrenen. Klinische Neuroradiologie 7, 83]92.
Petty, R.G., Barta, P.E., Pearlson, G.D., McGilchrist, I.K., Lewis, R.W., Tien, A.Y., Pulver, A., Vaughn, D.D., Casanova, M.F., Powers, R.E., 1995. Reversal asymmetry of the planum temporale in schizophrenia. American Journal of Psychiatry 152, 715]721. Rossi, A., Serio, A., Stratta, P., Petruzzi, C., Schiazza, G., Mancini, F., Casacchia, M., 1994. Planum temporale asymmetry and thought disorders in schizophrenia. Schizophrenia Research 12, 1]7. Schormann, T., Henn, S., Zilles, K., 1996. A new approach to fast elastic alignment with applications to human brains. In: Hohne, K.H., Kikinis, R. ŽEds.., Visualization in ¨ Biomedical Computing, Springer, Berlin, pp. 337]342. Steinmetz, H., Herzog, A., Huang, Y., Hacklander, T., 1994. ¨ Discordant brain-surface anatomy in monozygotic twins. New England Journal of Medicine 6, 952]953. Steinmetz, H., Herzog, A., Schlaug, G., Huang, Y., Jancke, L., ¨ 1995. Brain Ža.symmetry in monozygotic twins. Cerebral Cortex 5, 20]24. Steinmetz, H., Rademacher, J., Huang, Y., Hefter, H., Zilles, K., Thron, A., Freund, H.J., 1989. Cerebral asymmetry: MR planimetry of the human planum temporale. Journal of Computer Assisted Tomography 13, 986]1005. Vaillant, M., Davatzikos, C., 1997. Finding parametric representations of the cortical sulci using an active contour model. Medical Image Analysis 1, 295]315.
Projecting the sulcal pattern of human brains onto a 2D plane } a new approach using potential theory and MRI Mark A. Haidekker a,U , Carl J.G. Evertsz a , Clemens Fitzek b , Stephan Boor b , Reimer Andresen c , Peter Falkai d , Peter Stoeter b , Heinz-Otto Peitgen a a
MeVis (Center for Medical Diagnostic Systems and Visualization), Uni¨ ersity of Bremen, Uni¨ ersitatsallee 29, ¨ 28359 Bremen, Germany b Department of Neuroradiology, Uni¨ ersity Hospital of Mainz, Langenbeckstr. 1, 55131 Mainz, Germany c Department of Radiology, Behring Municipal Hospital, Gimpelstieg 3]5, 14160 Berlin, Germany d Clinic for Psychiatry, Friedrich-Wilhelm-Uni¨ ersity, Sigmund-Freud-Str. 25, 53105 Bonn, Germany Received 7 January 1998; accepted 22 May 1998
Abstract A new method is introduced to project the sulcal pattern of the brain surface onto a 2D plane. Twin brains are compared against each other using the planar representation. We obtained T1-weighted Flash-3D MRI volumes from 14 male twins Žseven monozygotic, seven dizygotic. with 3mm-thick coronal slices. The projection is based on potential theory: A virtual electrostatic field is calculated between the area of the segmented brain and a surrounding spherical electrode. Field lines starting from each border point of the segmented brain follow the gradient towards the sphere, leading to field line concentrations due to the underlying sulci. The unwrapped sphere surface with the number of field lines per area unit is used as the 2D representation of the sulcal pattern. The resulting brain projections show a distinctive pattern, and a visual assignment of the twin pairs from the unsorted set is possible because of a high similarity of the patterns between twin pairs. Global correlation coefficients for each pair of maps yield significantly higher values for matching monozygotic twin pairs Žmean s 20.2, range 12.3]25.6. than for unmatched pairs Žmean s 13.0, range 1.1]28.5.. As a conclusion, our method allows us to map the location and depth of the sulci on a 2D plane. The resulting maps allow quantitative inter-individual comparisons on the entire brain or parts of the brain surface. Q 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Magnetic Resonance Imaging; Brain mapping; Twins; 3-Dimensional Image Processing
U
Corresponding author. Tel.: q49 421 218 2439; fax: q49 421 218 4236; e-mail: [email protected]
0925-4927r98r$19.00 Q 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0925-4927Ž98. 00029-8
76
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
1. Introduction
2. Methods
For the investigation of macro-anatomical changes of the cerebrum in psychiatric disorders, postmortem and Magnetic resonance imaging ŽMRI. techniques have been applied extensively, but mainly in a volumetric way ŽDeakin, 1996.. Although experienced pathomorphologists claim to be able to diagnose schizophrenia from the abnormal pattern of gyrification, mainly in the frontal lobes, this morphological aspect has not received much attention in the recent literature about MRI methods. In order to detect deviations from the normal pattern of convolutions, quantitative analysis and interindividual comparison have to be carried out. Apart from examinations of the gross asymmetry of the temporal lobes ŽDeLisi et al., 1994; Hasboun et al., 1996., the comparison of the gyral pattern is usually limited to circumscribed areas such as the Sylvian fissure, the plana temporalia or the gyri of Heschl ŽFalkai et al., 1992; Bartley et al., 1993; Kleinschmidt et al., 1994; Rossi et al., 1994; Falkai et al., 1995; Kulynych et al., 1995; Petty et al., 1995; Mazanek et al., 1997.. A more ´ general assessment of the convolutional pattern is obtained from semi-automatic brainprint analysis ŽJouandet et al., 1989., or by the active contour model ŽVaillant and Davatzikos, 1997. by unfolding the cerebral surface into a 2D map. These techniques allow evaluations and measurements of limited areas, but are not aimed at the quantitative comparison of the entire sulcal pattern. However, the global complexity of gyrification may be described by fractal analysis of the boundary between white matter and the cerebral cortex ŽBullmore et al., 1994., but without comparing the individual gyral anatomy. The new method described in this report tries to combine both aspects: preserving the morphological information by projecting the individual sulcal pattern onto the surface of a surrounding virtual sphere and by allowing a quantitative correlation of the sulcal indentations between individuals at the same time. The applicability of the new technique is demonstrated by comparing the sulcal anatomy of twins to test the hypothesis of a higher degree of similarity in twins as compared to unmatched pairs.
We examined 14 healthy male twin pairs Ž28 individuals., out of which seven were monozygotic, 19]34, and seven dizygotic, aged 24]35 years. All individuals were informed about the study and gave their consent. MR images were obtained on a Philips S15-ACS Ž1.5 T. with a flash-3D-sequence ŽTR s 17 ms, T E s 5 ms, flip angle s 358.. To achieve a balance between a short acquisition time Ž5 min. and a good signalto-noise ratio, 3-mm-thick coronal slices were acquired. The MRI data were then transferred to an external workstation ŽSilicon Graphics Onyx-2. for all further image processing steps which included the segmentation of the brain, the calculation of the result of the Laplace equation D Es 0, the calculation of the field lines, and the generation of a 2D projection of the sulcal pattern based on the above calculation. To demonstrate the properties of the projection, we used the phantom displayed in Fig. 1: a filled sphere with a series of clefts of different shape and depth. The cross-sectional cut through the phantom reveals the geometry of the clefts: Ž1. a wedge-shaped cleft running from the anterior to the posterior pole; Ž2. a bent cleft; Ž3. a rectangular, diagonal cleft; and Ž4. a small and shallow rectangular cleft, wider than high. 2.1. Segmentation of the brain and pre-processing The segmentation is based on a 2D flood fill algorithm. In each slice, an initial point within the brain area is marked manually. The flood filling process is aborted when any of the following conditions are met: v
v
v
The pixel value lies above or below selected threshold values; the average value of the current pixel and its eight neighbors lies above or below selected threshold values; and the variance of the values of the current pixel and its eight neighbors lies above or below selected threshold values. In some slices, additional manual corrections
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
77
Fig. 1. The phantom used to demonstrate the properties of the projection. Top row: 3D rendering of the phantom with its clefts to simulate sulci Žleft., cut open to reveal the structure of the clefts Žmiddle., and one slice with a schematical representation of the field lines starting from the surface of the phantom and arriving at the border of the outer electrode Žright.. Below: 2D projection of the phantom. The white areas are positions on the unwrapped sphere, where many field lines arrive due to the underlying clefts.
are necessary, mainly to remove parts of the sinus sagittalis superior. After the segmentation process, we scaled the slices to 256 = 256 pixels and inserted three additional slices between any two slices of the original volume by interpolation. This was done in order to achieve an isotropic voxel size without exceeding memory limits.
tial of zero. The fundamental differential equation of potential theory, the Laplace equation D E s 0, is solved iteratively using the Gauss]Seidel Method with accelerated iteration by successive over-relaxation ŽGerald and Wheatley, 1984.: the potential value of each voxel is determined iteratively in 3D out of the value of its six neighbors according to Eq. Ž1.:
2.2. Iterati¨ e solution of the Laplacian equation
Ukq 1Ž x, y, z .
A virtual sphere-shaped electrode is placed around the brain so that the center of the sphere is identical with the center of gravity of the segmented brain. The surface of the spherical electrode is set to a constant potential of Us 1, while the brain area itself is set to the constant poten-
s
b w Ukq 1Ž xy 1, y, z . q Uk Ž xq 1, y, z . 6
qUkq 1Ž x, y y 1, z . q Uk Ž x, y q 1, z . qUkq 1Ž x, y, zy 1 . q Uk Ž x, y, z q 1 .x q Ž 1 y b . Uk Ž x, y, z .
Ž1.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
78
where Uk Ž x,y,z . is the potential value at the voxel coordinates x,y,z after the kth iteration, and b is the successive over-relaxation parameter which allows a faster approximation of the iterated values and is empirically set to 1.2. The iteration is stopped as soon as the relative error e according to Eq. Ž2.
e Ž x, y, z . s
Uk Ž x, y, z . y Uky1Ž x, y, z . Uk Ž x, y, z .
Ž2.
is found to be below 0.0001 for all voxels between the brain area and the spherical electrode, i.e. the maximum relative change between two iterations is less than 0.01 percent. This generally requires approx. 600]800 iterations.
ª
Any field line s Ž t . is the solution of the ª differential Eq. Ž3. and its initial condition s 0 : ª d s Žt. sy \ U dt ª
ª
ª
2.5. Correlation of the projections
CA B s nS a x y bx y y S a x y Sbx y
ª
s Ž t iq1 . s s Ž t i . q h \ U
ª
ž s Žt ./ i
Ž4.
Therefore the gradient must be calculated for non-integer coordinates. For this purpose, the partial derivation UŽ x,y,z .r x is based on a quadratic polynomial interpolation of the potential values at the coordinates w x x ,y,z, w x x y h,y,z, and w x x q h,y,z, where w x x is the integer part of x. Ur y and Ur z are calculated accordingly. Any field line ends at the border of the sphere, i.e. when the potential value of 1 is reached. The
2 xy
. y Ž S a x y .2
2 = nS Ž bx2 y . y Ž Sbx y .
Ž5.
Ž3.
0
In practical terms, a field line starts from each border point of the brain surface and follows the rising gradient towards the spherical electrode. The field lines are calculated numerically by executing discrete steps of length h Žwhich is in this case set to pixel distance. in the direction of the rising gradient according to the Euler method as outlined in Eq. Ž4.. ª
The number of field lines arriving at each surface unit of the spherical electrode is recorded, then the sphere is unwrapped. This results in a planar image, where each pixel value equals the number of field lines arriving at this specific point. The projection of the phantom is shown in the lower part of Fig. 1, where the white lines represent areas with many arriving field lines per area unit.
' nS Ž a
ž s Žt./
ª
s Ž t s 0. s s
2.4. Generation of the 2D projection
The global correlation coefficient CA B is calculated for each pair of planes according to Eq. Ž5.
2.3. Calculation of the field lines
ª
course of the field lines can be seen in Fig. 1 for one slice of the phantom.
between the individuals A and B with a x , y and bx , y as the maximum gray value Žnumber of arriving field lines. in a 3 = 3 neighborhood of the point Ž x,y . in the plane. The use of the neighborhood allows for small geometric tolerances in the calculation of the correlation. The comparison of 28 individuals leads to 378 correlation coefficients out of which seven result from dizygotic twin pairs, seven from monozygotic ones, and 364 from non-matched pairs. A test for statistical significance is performed using the Mann]Whitney Rank Sum test. 3. Results The calculation of the projection for the phantom reveals the fundamental behavior of the method. In Fig. 1, the areas of the unwrapped sphere surface, where many field lines arrive, are rendered as white lines. The number of arriving field lines depends on the depth and width of the
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
underlying cleft: a deep cleft leads to a high number of field lines per area unit. In other words, the projection contains information about the location and the depth of the sulci. To identify the properties of the projection of the brain, which is much more complex than the phantom, we marked several important sulci with different colors. One slice of the sample brain, and the projection of the entire brain can be seen in Fig. 2. In Fig. 3, there are the planar projections from three sample twin pairs. Five such pairs, including
79
these three, were given to eight untrained observers with the task to identify the pairs out of the unsorted set. All of them correctly identified the matching pairs. Any pairs of projections were correlated, and the correlation coefficients divided into four groups: monozygotic twins Ž n s 7., dizygotic twins Ž n s 7., all twins Ž n s 14., and non-matched pairs Ž n s 364. out of a total of 378 possible combinations on the set of 28 projections. The statistical analysis of the correlation coefficients can be seen in Table 1. Since the data are not distributed
Fig. 2. Generation of a 2D projection of the brain, where the major sulci have been marked with different colours. Above, a simplified representation of one single coronal slice with the colour-marked areas; below, the planar projection of the entire brain on a 3D basis. For didactical purposes, and to facilitate visual identification, the field lines in the upper part were calculated in 2D, and the coloured dots in the lower part were expanded.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
80
Fig. 3. Planar projections from three monozygotic sample twin pairs. Each row displays one twin pair, where the similarities of the sulcal pattern are clearly recognizable. The pairs show a correlation of 24.7, 24.2, and 25.6 Žfrom top to bottom..
Table 1 Statistical values over the correlation coefficients for the different groups of pair combinations of brainprint images Group
Twins n s 14
Unmatched n s 364
Monozygotic Dizygotic ns7 ns7
Average Standard deviation Median Max Min
17.4 7.5
13.0 5.6
20.2 5.7
14.5 8.4
16.3 29.0 3.9
12.5 28.5 1.1
23.3 25.6 12.3
13.8 29.0 3.9
normally, the Mann]Whitney Rank Sum Test was chosen to determine whether the differences between the groups are statistically significant. The test shows the difference between the twin group and the unmatched pairs to be significant Ž P- 0.05., as well as the difference between the monozygotic twins and unmatched pairs Ž P0.0005.. The difference between the dizygotic group and the unmatched pairs and between the monozygotic and the dizygotic group does not show statistical significance.
4. Discussion The development of tomography techniques and fast computing hardware allowed a rapid progress in the non-invasive acquisition and processing of images of the brain. There is a widespread interest in brain topography. A multitude of different algorithms for the segmentation and analysis of different aspects of brain images have been presented in recent years. A special focus lies on the generation of brain maps, because many processes are easier to visualize and to understand on planar projections. The methods applied for this purpose cover a wide range. Early attempts to create 2D projections of the sulcal or gyral pattern were mostly based on manual methods. Geometric projections ŽHollander, 1995; Hollander et al., 1997. and non-lin¨ ¨ ear approaches ŽDavatzikos et al., 1996; Schormann et al., 1996; Vaillant and Davatzikos, 1997. allow an automated processing of the images. Fractal methods have been applied to images of the brain as well, although the fractal nature of
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
tomographical brain images is still being discussed ŽMajumdar and Prasad, 1988; Besthorn et al., 1997.. For this study, we developed a new method. This is basically derived from a 2D model to determine harmonic measures in fractal objects like the Koch Tree and Diffusion Limited Aggregation ŽDLA. dendrites ŽEvertsz et al., 1991a,b; Evertsz and Mandelbrot, 1992.. The principle is, that in the fjords an electric potential is shielded, so that both gradient and potential are lowest in the inner parts of the fjord. We adapted the method for 3D. As the most important extension to the above method, the actual projection is performed by analyzing the field lines. As a result, our algorithm allows the mapping of the location and depth of the sulci onto a plane, primarily because the number of field lines starting from a sulcus is proportional to the inner surface area of that sulcus. The resulting planar projection shows a distinctive pattern. It is possible to identify the projections of the major sulci, as shown in Fig. 2. Moreover, similarities between the patterns belonging to twin pairs can be found both by visual examination and calculation of the correlation between pairs of 2D projections. The fundamental behavior was explained by generating the projection of a phantom and of a color-coded brain. The projection contains information about the location and the shape Ždepth and surface . of the sulci. While the algorithm is able to follow bends and convolutions, only the inner surface area is recognized Žas shown with cleft no. 2 in Fig. 1.. Moreover, the field lines have a tendency to follow tunnel-like extensions and wider channels, consequentially clustering together when the algorithm is applied in 3D. In a basic morphological aspect however, the projection described above contains less information than an original 3D-image of the brain reconstructed with surface or volume rendering techniques ŽCline et al., 1990; Cohen et al., 1992; Bullmore et al., 1994.. But 3D images, like surface reconstructions, can be compared interindividually only in a descriptive way like fingerprints according to qualitative features, e.g. the number and main direction of gyri of a certain area, the
81
number of ramifications, bends or interruptions of a gyrus, or by measurement of its extension, a surface area, or the volume of a defined structure ŽSteinmetz et al., 1989; DeLisi et al., 1994.. A more general comparison of the gyral pattern is usually achieved by transforming a 3D data set into a 2D map. The brainprint method ŽJouandet et al., 1989. uses a semi-automatic placement of reference points to the gyral summits and valleys and results in a 2D map of connecting reference lines. This allows a quantitative comparison of brain growth during pre- and post-natal development ŽMarc et al., 1993.. But due to the characteristics of this transformation, individual information concerning the smaller convolutions is lost and interindividual comparison has been limited so far to the course of the major sulci. Moreover, the method requires manual interaction and is thus subject to influences from the observer. Even more information about the individual gyral pattern is lost if purely quantitative methods like volume measurements ŽHarris et al., 1994; Hasboun et al., 1996; Heun et al., 1997; Laakso et al., 1997., or fractal analysis of the boundary between white matter and the cerebral cortex ŽBullmore et al., 1994., or of the brain surface ŽBesthorn et al., 1997. are used. Although the fractal dimension, as calculated in these studies, is proposed as a measure of cerebral complexity and can be used to characterize different groups of psychiatric patients, it does not allow the assessment of the interindividual similarity of the gyral pattern. The recently presented Active Contour Model ŽVaillant and Davatzikos, 1997. uses parametric representations of the cortical sulci and thus preserves information about the individual sulcal course and depth in a similar way as our method, but by now has been applied only to limited areas like the central sulcus. With the application of our projection technique, the entire brain surface including first to third order convolutions is considered for testing individual similarity. Although there are some limitations such as a certain sensitivity to rotation artifacts during MRI data acquisition, we could prove that our 2D projections are capable of
82
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
showing similarities in the sulcal pattern of twin pairs both when inspected by untrained observers and when compared mathematically. Although the average correlation was higher in the monozygotic group, showing statistical significance, we found that the degree of similarity varies strongly within the groups. As indicated in Fig. 4, this observation can be supported by visual inspection. Some parameters of the Laplacian Brainprint algorithm were selected by experience. This is mainly valid for the successive over-relaxation factor b in Eq. Ž1., which only influences the calculation of the Laplace equation and has no influence on the projection itself. The segmentation process of the brain requires some manual
interaction, but experiments showed that relevant changes of the threshold values only resulted in minor changes of the gray values in the 2D plane while the location of the sulcal traces remained unchanged. This indicates a robustness of the method against variations of the global gray intensity of the MRI images. This finding of a high degree of similarity of the sulcal pattern between twins was suspected in analogy to the similarity of other surface markers, such as the shape of the face and stature but has not been described so far. Other examinations based on qualitative ŽSteinmetz et al., 1994; Mazanek et al., 1997. or semi-quantitative ´ ŽJouandet et al., 1989. analyses of the convolutio-
Fig. 4. Examples for a well-matching twin pair from the monozygotic set Žabove. with a correlation value of 25.6, and a different pair from the dizygotic group Žbelow. with a lower correlation value of 13.8. In both cases, two maps were overlaid, with one twin drawn in red, the other one in green. Identical pixels of the pattern appear in yellow.
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
nal pattern as well as measurements of the plana temporalia or length of the Sylvian fissure ŽBartley et al., 1993; Steinmetz et al., 1995; Mazanek et ´ al., 1997. could not find a higher correlation in twin pairs as compared to unmatched pairs. This discrepancy may be due to the difficulties of the techniques mentioned above to assess the total gyral pattern without losing too much information about the individual course of the convolutions. A further improvement of our method can be expected from replacing the correlation method for the comparison of different patterns by a more sophisticated pattern-matching technique, which is currently being investigated. If the capability of our Laplacian Brainprint technique for the evaluation of similarities between twins can be confirmed by further studies, this method could be used for twin and other family studies of schizophrenia to evaluate possible differences in gyrification between healthy and affected members of a group. Moreover, some statement about the complexity of gyrification should be possible by generating a histogram of the field line densities. This could be applied to assess brain morphology of psychiatric diseases similar to the fractal analysis, but without losing too much of the individual information about the convolutional pattern. References Bartley, A.J., Jones, D.W., Torrey, E.F., Zigun, J.R., Weinberger, D.R., 1993. Sylvian fissure asymmetries in monozygotic twins: a test of laterality in schizophrenia. Biological Psychiatry 34, 853]863. Besthorn, C., Zerfaß, R., Hentschel, F., 1997. Die fraktale Dimension als Bildverarbeitungsparameter im CT bei Alzheimer-Demenz. Klinische Neuroradiologie 7, 12]16. Bullmore, E., Brammer, M., Harvey, I., Persaud, R., Murray, R., Ron, M., 1994. Fractal analysis of the boundary between white matter and cerebral cortex in magnetic resonance images: a controlled study of schizophrenic and manic depressive patients. Psychological Medicine 24, 771]781. Cline, H.E., Iorensen, W.E., Kikinis, R., Jolesz, F., 1990. Three-dimensional segmentation of MR images of the head using probability and connectivity. Journal of Computer Assisted Tomography 14, 1037]1045. Cohen, G., Andreasen, N.C., Alliger, R., Arndt, S., Kuan, J., Yuh, W.T., 1992. Segmentation techniques for the classifi-
83
cation of brain tissue using magnetic resonance imaging. Psychiatry Research: Neuroimaging 45, 33]51. Davatzikos, C., Vaillant, M., Resnick, S., Prince, J.L., Letovsky, S., Bryan, R.N., 1996. Morphological analysis of brain structures using spatial normalization. In: Hohne, K.H., Kikinis, ¨ R. ŽEds.., Visualization in Biomedical Computing, Springer, Berlin, pp. 355]360. Deakin, J.F.W., 1996. Neurobiology of schizophrenia. Current Opinion in Psychiatry 9, 50]56. De Lisi, L.E., Hoff, A.L., Chance, N., Kushner, M., 1994. Asymmetries in the superior temporal lobe in male and female first-episode schizophrenic patients: measures of the planum temporale and superior temporal gyrus by MRI. Schizophrenia Research 12, 9]18. Evertsz, C.J.G., Jones, P.W., Mandelbrot, B.B., 1991a. Behaviour of the harmonic measure at the bottom of fjords. Journal of Physics A 24, 1889]1901. Evertsz, C.J.G., Mandelbrot, B.B., Normant, F., 1991b. Fractal aggregates and the current lines of their electrostatic potential. Physica A 177, 589]592. Evertsz, C.J.G., Mandelbrot, B.B., 1992. Harmonic measure around a linearly self-similar tree. Journal of Physics A 25, 1781]1797. Falkai, P., Bogerts, B., Greve, B., Pfeiffer, U., Machus, B., Folsch-Reetz, B., Majtenyi, C., Ovary, I., 1992. Loss of ¨ Sylvian fissure asymmetry in schizophrenia. A quantitative post-mortem study. Schizophrenia Research 7, 23]32. Falkai, P., Bogerts, B., Schneider, T., Greve, B., Pfeiffer, U., Pitz, K., Gonsiorzcyk, C., Majtenyi, C., Ovary, I., 1995. Disturbed planum temporale asymmetry in schizophrenia. A quantitative postmortem study. Schizophrenia Research 14, 161]176. Gerald, C.F., Wheatley, P.O., 1984. The Laplacian operator in three dimensions. In: Applied Numerical Analysis, 3rd ed. Addison-Wesley, Reading, Massachussetts, pp. 431]437. Harris, G.J., Barta, P.E.W., Peng, L.W., Lee, S., Brettschneider, P.D., Shah, A., Henderer, J.D., Schlaepfer, T.E., Pearlson, G.D., 1994. MR volume segmentation of gray matter and white matter using manual thresholding: dependence on image brightness. American Journal of Neuroradiology 15, 225]230. Hasboun, D., Chantome, M., Zouaoui, A., Sahel, M., Delaˆ doeuille, M., Sourour, M., Duyme, M., Baulac, M., Marsault, C., Dormont, D., 1996. MR determination of hippocampal volume: comparison of three methods. American Journal of Neuroradiology 17, 1091]1098. Heun, R., Mazanek, M., Atzor, K.R., Tintera, J., Gawehn, J., ´ Burkart, M., Gansicke, M., Falkai, P., Stoeter, P., 1997. ¨ Amygdala-hippocampal atrophy and memory performance in dementia of Alzheimer type. Dementia and Geriatric Cognitive Disorders 8, 329]336. Hollander, I., 1995. Cerebral cartography } a method for ¨ visualizing cortical structures. Computerized Medical Imaging and Graphics 19, 397]415. Hollander, I., Petsche, H., Dimitrov, L.I., Filz, O., Wenger, E., ¨ 1997. The reflection of cognitive tasks in EEG and MRI
84
M.A. Haidekker et al. r Psychiatry Research: Neuroimaging 83 (1998) 75]84
and a method of its visualization. Brain Topography 4, 177]189. Jouandet, M.L., Tramo, M., Herron, D., 1989. Brainprints: computer generated two-dimensional maps of the human cerebral cortex in vivo. Journal of Cognitive Neurosciences 1, 92]120. Kleinschmidt, A., Falkai, P., Huang, Y., Schneider, T., Furst, ¨ G., Steinmetz, H., 1994. In-vivo morphometry of planum temporale asymmetry in first-episode schizophrenia. Schizophrenia Research 12, 9]18. Kulynych, J.J., Vladar, K., Fantie, B.D., Jones, D.W., Weinberger, D.R., 1995. Normal asymmetry of the planum temporale in patients with schizophrenia. Three-dimensional cortical morphometry with MRI. British Journal of Psychiatry 166, 742]749. Laakso, M.P., Juottonen, K., Partanen, K., Vainio, P., Soininen, H., 1997. MRI volumetry of the hippocampus: the effect of slice thickness on volume formation. Magnetic Resonance Imaging 15, 263]265. Majumdar, S., Prasad, R.R., 1988. The fractal dimension of cerebral surfaces using magnetic resonance images. Computers in Physics, 69]73. Marc, L., Jouandet, M.D., Deck, M.D.F., 1993. Prenatal growth of the human cerebral cortex: brainprint analysis. Radiology 188, 765]774. Mazanek, M., Angert, T., Atzor, K.R., Falkai, P., Gansicke, ´ ¨ M., Boor, S., Mehrtens, C., Maier, W., Stoeter, P., 1997. Asymmetrie des Planum temporale bei Zwillingen und Schizophrenen. Klinische Neuroradiologie 7, 83]92.
Petty, R.G., Barta, P.E., Pearlson, G.D., McGilchrist, I.K., Lewis, R.W., Tien, A.Y., Pulver, A., Vaughn, D.D., Casanova, M.F., Powers, R.E., 1995. Reversal asymmetry of the planum temporale in schizophrenia. American Journal of Psychiatry 152, 715]721. Rossi, A., Serio, A., Stratta, P., Petruzzi, C., Schiazza, G., Mancini, F., Casacchia, M., 1994. Planum temporale asymmetry and thought disorders in schizophrenia. Schizophrenia Research 12, 1]7. Schormann, T., Henn, S., Zilles, K., 1996. A new approach to fast elastic alignment with applications to human brains. In: Hohne, K.H., Kikinis, R. ŽEds.., Visualization in ¨ Biomedical Computing, Springer, Berlin, pp. 337]342. Steinmetz, H., Herzog, A., Huang, Y., Hacklander, T., 1994. ¨ Discordant brain-surface anatomy in monozygotic twins. New England Journal of Medicine 6, 952]953. Steinmetz, H., Herzog, A., Schlaug, G., Huang, Y., Jancke, L., ¨ 1995. Brain Ža.symmetry in monozygotic twins. Cerebral Cortex 5, 20]24. Steinmetz, H., Rademacher, J., Huang, Y., Hefter, H., Zilles, K., Thron, A., Freund, H.J., 1989. Cerebral asymmetry: MR planimetry of the human planum temporale. Journal of Computer Assisted Tomography 13, 986]1005. Vaillant, M., Davatzikos, C., 1997. Finding parametric representations of the cortical sulci using an active contour model. Medical Image Analysis 1, 295]315.