NeuroImage PDF: An Investigation of Functional and Anatomical Connectivity (2002)

NeuroImage 16, 241–250 (2002) doi:10.1006/nimg.2001.1052, available online at http://www.idealibrary.com on An Investigation of Functional and Anatomical Connectivity Using Magnetic Resonance Imaging Martin A. Koch, 1 David G. Norris, 2 and Margret Hund-Georgiadis Max Planck Institute of Cognitive Neuroscience, Stephanstraße 1a, D-04103 Leipzig, Germany Received May 1, 2001 Key Words: connectivity; functional MRI; diffusion This article examines functional and anatomical tensor imaging; fiber tracking. connectivity in healthy human subjects measured with magnetic resonance imaging methods. Anatomi- cal connectivity in white matter is obtained from mea- INTRODUCTION surements of the diffusion tensor. A Monte-Carlo sim- ulation determines the probability that a particle It is a fundamental aim in cognitive neuroscience to diffuses between two points, with the probability of a discover anatomical features that reflect the functional jump in a particular direction from a given voxel being organization of the brain. In this paper both functional based on the local value of the diffusion tensor com- and anatomical connectivity in the human brain are ponents. Functional connectivity between grey matter examined using Magnetic Resonance Imaging (MRI) pixels is assessed without recourse to a specific acti- techniques and the results of the investigations are vation paradigm, by calculating the correlation coef- compared. Specifically, anatomical connectivity is as- ficient between random fluctuations in the blood oxy- sessed using parameters obtained from the diffusion genation level-dependent signal time course in tensor of water in anisotropic white matter, and func- different pixels. The methods are used to examine the tional connectivity is examined by measuring the cor- anatomical and functional connectivities between relation in spontaneous fluctuations of the Blood Oxy- crowns of adjacent gyri. A high functional connectiv- genation Level-Dependent (BOLD) (Ogawa et al., ity was found between grey matter pixels, with white 1990a,b) signal between voxels (Biswal et al., 1995). matter displaying only very low correlation. A com- The rationale for this choice of methods is as follows: parison of the measurements of anatomical and func- diffusion tensor imaging (DTI) (Basser et al., 1994a,b) tional connectivity found that there is no simple cor- is unique in its ability to obtain information concerning relation between these measures, except that low the orientation of white matter fiber tracts with cross values of functional connectivity were not found to- sections of at least several imaging voxels in size. Us- gether with high values of anatomical connectivity. ing this method it has proven possible to track fiber Furthermore pairs of regions situated around the cen- pathways over extended regions of the brain, produc- tral sulcus indicated a dependence of the two connec- ing results that are in accordance with general ana- tivity measures on each other. These results are in tomical knowledge (Mori et al., 1999; Conturo et al., accordance with an interpretation that regions which 1999). The connectivity between voxels placed in grey are clearly directly linked by white matter fiber tracts matter is examined by means of a Monte-Carlo simu- should show high functional connectivity, but that the lation, which allows particles to diffuse between voxels, inverse need not be true as functional connectivity with the probability for a “jump” in a particular direc- may also be indirectly mediated via more distant grey tion being derived from the diffusion tensor in the voxel matter regions. © 2002 Elsevier Science (USA) and the adjacent voxels. The anatomical connectivity between two voxels in grey matter is then defined in terms of the probability that a particle starting at one 1 To whom correspondence and reprint requests should be ad- voxel will “diffuse” to the other. dressed at present address: Universitätsklinikum Hamburg-Eppen- For some functionally associated regions it has been dorf, Neurologische Klinik, Martinistraße 52, D-20246 Ham- shown that their spontaneous fluctuations in the burg, Germany. Fax: !49-40-42803-5086. E-mail: [email protected] BOLD signal are correlated (Biswal et al., 1995). This hamburg.de. 2 Present address: FC Donders Centre for Cognitive Neuroimag- phenomenon is an example of functional connectivity ing, Trigon 181, P.O. Box 9101, NL-6500 HB Nijmegen, The Neth- as defined by Friston et al. (1993). Previously such erlands. regions have been defined by means of a conventional 241 1053-8119/02 $35.00 © 2002 Elsevier Science (USA) All rights reserved. 242 KOCH, NORRIS, AND HUND-GEORGIADIS functional magnetic resonance (fMR) experiment and principle is achieved that opens new avenues for future the correlation between signal fluctuations subse- work in both the healthy and pathological brain. quently examined (Biswal et al., 1995; Lowe et al., 1998). There is, however, no explicit requirement to MATERIALS AND METHODS perform a standard fMR experiment to define these regions: anatomically defined regions of interest can We investigated the anatomical and functional con- equally well be employed. The practical advantage of nectivity of cortical areas on adjacent gyri in 7 healthy this approach is that no stimulation paradigm is re- volunteers who declared written informed consent. The quired, and hence all grey matter can in principle be experiments were generally approved by the ethics investigated using this method. The measurement du- committee of Leipzig University. We restricted the ration is also short: less than 10 min are usually suf- study to cortical regions in close proximity to each ficient. It has been assumed, though not conclusively other since long fibre tracts are more difficult to follow proven, that the origin of spontaneous fluctuations in and are usually not confined to a single plane. In ad- the BOLD signal is spontaneous bursts of electrical dition, it is known that in many cases the crowns of activity, which occur at low frequency in grey matter adjacent gyri are connected by U-shaped fibers. (Biswal et al., 1995). It has been shown that blood flow The experiments were performed with a whole-body changes are associated with these bursts (Golanov et MRI system (Medspec 30/100, Bruker Medizintechnik, al., 1994), and it is a plausible assumption (Biswal et Ettlingen, Germany) operating at 3 Tesla (29.2 mT m "1 al., 1995) that these translate to changes in the BOLD max. gradient strength, 65 Ts "1m "1 slew rate, quadra- signal intensity. It is known that the signal fluctua- ture birdcage head resonator transmit/receive). For tions arise from changes in BOLD contrast and are not data evaluation the programming language IDL (Inter- the result of inflow effects (Biswal et al., 1997). In more active Data Language, Research Systems Inc., CO) was conventional activation studies it has been shown that used. The subjects were protected from acoustic noise the degree of functional connectivity between regions by earplugs. can be modulated by such factors as the level of atten- tion. For example, it has been demonstrated that the BOLD Imaging degree of connectivity between the motion-sensitive For fluctuation imaging we used a stimulus-free cortical area V5 and the posterior parietal cortex can setup similar to that used by Biswal et al. (1995). In be modified by the level of attention to visual motion contrast to Biswal et al., however, we examined the (Büchel and Friston, 1998). By measuring spontaneous correlation between cortical gyri in the same hemi- fluctuations it is hoped to examine a functional connec- sphere rather than between symmetric areas in differ- tivity that is directly related to the underlying anat- ent hemispheres. Likewise, we did not perform a stim- omy and not one modulated by the transient activity in ulus-induced activation experiment to identify the the brain. In terms of the development of the brain this function of cortical regions. A time series of 1024 gra- hypothesis is in accordance with Hebb’s widely ac- dient-recalled blipped EPI images was acquired for a cepted theory (Hebb, 1949, p. 337) that cells which 5-mm axial slice (64 # 64 matrix, 3 mm in-plane res- have a synchronized electrical activity will strengthen olution, TR $ 250 ms, TE $ 30 ms, excitation with their synaptic connections (Frégnac, 1996). One exam- Ernst angle: 36°). The subjects were instructed to re- ple of this is spontaneous prenatal activity in the ret- frain from any voluntary movement during the approx. ina, which exerts a structuring influence on the devel- 4-min scan time. During the scan, acoustic and optical opment of the visual system (Meister et al., 1991). stimuli were absent apart from the noise produced by Further support is given by data suggesting that the scanner. The images were corrected for subject schizophrenia may well be caused by disconnection motion (Friston et al., 1996) and slightly smoothed. between cortical regions (Friston and Frith, 1995; Then the signal time courses of all image pixels above Fletcher et al., 1999), combined with the discovery that a noise threshold were digitally low-pass (%0.08 Hz) the integrity of white matter tracts is compromised in frequency filtered (finite impulse response filter of or- this disease (Lim et al., 1999). der 40, see Press et al. (1992)) to remove signal fluctu- This study is to the best of the authors’ knowledge ations due to the respiratory and cardiac cycle (Biswal the first to attempt to examine the relationship be- et al., 1995). The first 10 images were discarded to tween functional and anatomical connectivity in a exclude the transition to steady state. Linear Pearson quantitative way. Previous investigations have gener- correlation coefficients (Pearson, 1896) between time ally attempted to relate changes in the diffusion tensor courses were calculated for all possible pairs of pixels. with functional deficits (Werring et al., 1998; Wiesh- In order to emphasize ubiquitious fluctuations that mann et al., 1999; Klingberg et al., 2000). Although the arise from spontaneous neuronal activity as opposed to data presented here are limited by not being acquired those of limited duration due to other activity, each from a full 3-dimensional volume, a demonstration of time course was split into four equal parts of about FUNCTIONAL AND ANATOMICAL CONNECTIVITY 243 FIG. 1. Simplified flowchart of the algorithm for estimating anatomical connectivity from DTI data. The integer variables “dir” and “dir_k” specify one of the eight possible jump directions, “m” and “n” specify voxels. The sum over all possible directions is denoted by “sum_over_dir().” The expression “target (m, dir)” is the target voxel of a jump from voxel “m” in direction “dir,” and “d(dir, m)” is the diffusion coefficient defined in Eq. (3). The angle between the direction “dir” and the direction used for the preceding jump is denoted as “angle(dir, lastdir).” After normalization, “p(dir)” is the probability defined in Eq. (1). “Region of interest” is abbreviated as “ROI,” and “a target ROI” means any region other than the region containing the start voxel. The condition “fiber perpendicular to slice” was evaluated by means of two diagonal elements of the diffusion tensor, see text. The trace of the tensor is denoted by “Tr D.” 1-min duration. For each part the correlation coeffi- selected for further processing. We expect to sup- cient between pixels was determined separately, and press “real task activation” to some degree by this among the four coefficients the smallest one was procedure. 244 KOCH, NORRIS, AND HUND-GEORGIADIS FIG. 2. Example for the pattern of correlation between BOLD signal time courses, overlaid on the corresponding T 1-weighted anatomical image. The color scale represents the magnitude of the correlation (c f) with the reference pixel which is shown in yellow (pixels with c f & 0.4 only). Diffusion Tensor Imaging lution, we accepted the lower SNR of U-FLARE and its Subsequent to the EPI scans, DTI was performed for inability to map a large number of slices in a short the same slice in order to determine the anatomical time. In order to reduce power deposition and effective connections between cortical areas. To achieve high echo time, we did not use dummy echoes for signal spatial resolution we used a displaced U-FLARE (Nor- stabilization. Instead, we determined a phase encoding ris et al., 1992) imaging sequence with spin-echo diffu- order, which leads to a monotonous amplitude varia- sion preparation (Stejskal and Tanner, 1965). We re- tion along the phase encode direction in k-space. This frained from the use of EPI due to its lower spatial approach (TIPE, template interactive phase-encoding) resolution and higher susceptibility to eddy current was originally suggested for GRASE imaging (Jovicich effects (Koch and Norris, 2000). In favor of high reso- and Norris, 1998). It requires the acquisition of a ref- FUNCTIONAL AND ANATOMICAL CONNECTIVITY 245 FIG. 3. Fiber orientation map calculated from the DTI data, overlaid on an anatomical T 1-weighted image (transaxial slice, top is anterior). The straight lines represent the projection of the calculated fiber direction onto the image plane. In voxels with low anisotropy (FA % 0.2) these lines are suppressed. The raw images were also masked to remove the background ghost signal in the phase encode direction (see text). Only a 6.75 # 6.75-cm part of the field-of-view is shown. The sulcus at the bottom is the postcentral sulcus. erence scan without phase encoding gradients. The in-plane resolution (11.25-mm 3 voxel volume). To re- phase encoding gradients in the imaging sequence are duce the number of RF pulses further, only 54 of 96 ordered according to the echo amplitudes in the refer- k-space lines were actually acquired. Zero-filling to the ence data. Since no even echo is present before the full 128 # 96 matrix before image reconstruction led to second refocusing pulse, one dummy cycle is still nec- a slight decrease in spatial resolution. After recon- essary. The phase encode direction was chosen along struction, the images were transformed to the 19.2 # the volunteer’s left–right direction to allow a minimum 19.2-cm format (128 # 128 pixels) by symmetric addi- field-of-view (FOV). At 19.2 # 14.4-cm FOV, the 128 # tion of zero lines. To ensure a sufficiently narrow point 96 data matrix corresponds to 1.5 # 1.5-mm nominal spread function (PSF), linear instead of center-out 246 KOCH, NORRIS, AND HUND-GEORGIADIS phase encoding was employed, starting six lines off the and 0...1 represents an ensemble average. This equa- k-space centre. The reduction in the number of RF tion can be generalized to an expression for the r.m.s. pulses results in an overall SNR improvement because displacement along an arbitrary unit vector ř, the refocusing angle can be increased without violation of power deposition limits, and because the U-FLARE 0+s+t, ! ř, 21 ! 2 t ř ! Dř, (2) echo train length is usually much larger than the op- timum in terms of SNR. PSF broadening due to relax- for diffusion in a not necessarily isotropic medium ation during the echo train did not exceed the width of which is characterized by the diffusion tensor D. a pixel. For the DTI experiment we used ' ( 120° Hence, the “diffusion coefficient d(r, m) in voxel m refocusing angle, interecho spacing 7.5 ms, effective along r” can be defined by echo time TE eff ( 140 ms, and TR $ 3 s. We used diffusion gradients with 4 different amplitudes (b $ 20, d +r, m, ! ř ! D+m,ř, (3) 280, 540, 800 s mm "2 with approx. 15, 20, 30, 50 aver- ages, respectively) and 7 directions ((1, 1, 0), (1, 0, 1), (0, 1, 1), (1, "1, 0), ("1, 0, 1), (0, "1, 1), (1, 1, 1) in where D(m) is the diffusion tensor in voxel m, and ř $ read-phase-slice coordinates). Separation and duration r/!r!. This definition was used in Eq. (1). The probabil- of the diffusion gradient pulses were ) $ 40 ms and * $ ity defined in Eq. (1) satisfies 2 n8$1 p(m 3 n) $ 1. The 22 ms, respectively. The acquisition of the tensor map exponent a was introduced to make the probability took approximately 35 min. Due to the high power distribution sufficiently narrow. Let us consider a ho- deposition in U-FLARE, multislice imaging would mogeneous sample for simplicity, where d(r mn, m) $ have required a considerably longer scan time, or a d(r mn, n) $: d(r mn). Then Eq. (1) implies reduction in the number of averages. A high quality tensor map of a single slice was preferred to multislice imaging with lower effect-to-noise ratio. p a$1+ m 3 n , p a$1+ m 3 n /, ! d +r mn, d +r mn/, # " d +r mn, d +r mn/, # 7 ! p a$7+ m 3 n , p a$7+ m 3 n /, (4) Estimating Anatomical Connectivity from DTI Data For the assessment of anatomical connectivity be- for the jump probabilities to the voxels n and n/, given tween brain regions we implemented a Monte-Carlo that d(r mn/) % d(r mn). The chosen value of a was such type algorithm. It is based on the idea of a particle that that most particle paths followed the fibers on the DTI performs a macroscopic random walk through the set fiber orientation map. To ensure a minimum smooth- of voxels. However, the probability for a jump in a ness of the particle path, the particle was only allowed given direction was chosen to depend monotonously on to jump in a direction that deviated by %90° from the the diffusion coefficient along the jump direction in the preceding jump direction, i.e., only the 3 “forward” start and target voxel of the jump. The particle then jump directions were possible. We excluded (i) voxels moves with a higher probability along the fiber direc- where the fractional anisotropy index FA (Basser and tion than perpendicular to it. In a number of such Pierpaoli, 1996) was less than FA $ 0.2 and (ii) voxels random walks starting in a region “A,” it is counted where trace(D)/3 & 10 "9 m 2 s "1. These threshold values how often some other region “B” was reached. This varied slightly between subjects and were adjusted to yields a relative measure of the anatomical connectiv- suppress grey matter (low FA) and CSF (high trace(D) ity between the regions “A” and “B.” For each elemen- but possibly high FA due to flow) as accurately as tary jump, the probability for a jump from the start possible. Before tensor calculation, a brain mask was voxel, m, to the neighboring voxel n in the imaging slice applied to the U-FLARE images. For each jump, a was set to pseudo-random integer, n, between 0 and 7 was gener- ated and used to select the jump direction. The trans- formation method (Press et al., 1992) was used to - d +r mn, m , " d +r mn, n ,. a achieve that these numbers were distributed according p+m 3 n, ! , (1) ¥ n8 /$1 - d +r mn/, m , " d +r mn/, n /,. a to Eq. (1). The particle path was terminated when an excluded voxel was reached or when 60 jumps had been performed. This maximum number of jumps was well with a $ 7, where d(r mn, m) is the “diffusion coefficient” above the minimum number of jumps required for the in voxel m along the line connecting the centers of m particle to travel from a gyrus crown to a neighboring and n. The definition of this coefficient is based on crown. The path was also terminated if the sum of the Einstein’s equation (Einstein, 1905) for the r.m.s. dis- in-plane diagonal tensor elements was less than 10 "9 placement of a freely diffusing particle after a time t, m 2 s "1. This rule terminates the path where the fibre which states 0s x2(t)1 $ 2tD for the x component of the direction is perpendicular to the slice, allowing for displacement s(t), where D is the diffusion coefficient paths to leave the image plane. The frequency with FUNCTIONAL AND ANATOMICAL CONNECTIVITY 247 which each voxel was encountered (as a result of any the results of Biswal et al. (1995). An example of a particle jump during a path or at its terminating point) correlation map is shown in Fig. 2. The typical signal during 4000 paths was recorded and divided by the variation during the time course of 4 min is of the order maximum over all pixels in the slice. Increasing the of 3%. This is compatible with the variation of 0.5 to 1% number of experiments beyond 4000 did not alter the observed by Biswal et al. at 1.5 T main field strength results significantly. Figure 1 shows a flowchart of the when the difference in B 0 is taken into account. Trans- program which was written in the programming lan- lation due to subject motion during the BOLD scan was guage C. below 0.2 voxels. An example of a fiber orientation map Comparing the simulation results with functional calculated from the acquired DTI data is shown in Fig. connectivity is not straightforward since DTI provides 3. As an example of the result of the simulation, Fig. 4 reliable information on fiber orientation only for white demonstrates that the most frequently encountered matter (WM), whereas BOLD fluctuations occur pre- voxels correspond to those that constitute a fiber tract dominantly in grey matter (GM). It is difficult to decide in the fiber orientation map according to subjective which of the voxels in superficial WM contains the perception. For each pair of regions on adjacent gyri in extracortical connections of a given GM voxel. The the four subjects evaluated, Fig. 5 shows the correla- situation may be further complicated because EPI im- tion coefficients and the simulation results based on ages are prone to distortions (Johnson and Hutchison, the DTI experiment. The anatomical connectivity is 1985), in contrast to U-FLARE images. We therefore given for both possible choices of the start region. For manually defined regions of interest in the 64 # 64 some region pairs the difference between the simula- matrix on the crowns of selected gyri on the convex tion results with start and target region interchanged surface of the brain, containing subcortical WM voxels is very large. There is also a considerable variation in that could serve as starting pixels in the simulation. A anatomical and functional connectivity between adja- region consisted of typically ten pixels of the 64 # 64 cent gyri, which is not due to interindividual differ- matrix. Three of the seven volunteers in the study did ences alone as there is also a substantial variation for not clearly exhibit U-shaped fibers between adjacent each subject (not shown). gyri in the DTI maps and were excluded from the In Fig. 5, high c d values seem not to occur in combi- simulation. This criterion excludes volunteers where nation with low c f values. Moreover, a positive correla- we might have failed to map such fiber tracts due to tion between c f and c d was evident when considering inadequate slice position. The Monte-Carlo simulation region pairs around the central sulcus only. was performed on the 128 # 128 DTI map and started from the voxels that belonged to one of the regions of DISCUSSION interest. As some regions of interest were directly ad- jacent to another region, direct jumps between adja- The absolute number of axons connecting two corti- cent regions were explicitly excluded. It was further cal regions can hardly be calculated from DTI because verified that the correlation coefficient was below 0.2 the diffusion tensor depends on density and diameter for any two neighboring voxels which belonged to dif- of axons, degree of axon myelination, and variance in ferent regions. The particle paths were terminated if a axon direction. However, the particle jump simulation region of interest other than the starting region was provides a relative estimate of the number of connect- reached. Finally, a value of anatomical (c d) and func- ing axons, as the following argument shows. The sim- tional (c f) connectivity was assigned to every ordered ulation result for paths from a region “A” to a region pair of regions by taking the maximum of c d and c f in “B,” c d (A 3 B), is high if a fiber tract exists between all pixels in both regions. The matrix of the c d values is “A” and “B.” It is reduced if a large number of possibil- not necessarily symmetric, in contrast to the c f matrix. ities is encountered on the way between “A” and “B” to As it is not obvious how these matrices should be divert from the track leading to “B.” A diverging fiber compared, the c d values for both possible choices of the path means that the population of axons in the first starting region were computed and displayed. voxel(s) of the tract can be divided into two groups with different targets. Let us assume that n i axons leave or RESULTS enter a region “A i,” n j axons leave or enter some other region “A j,” and k ij axons connect these regions. We can All seven subjects in the study (including those then interpret c d( A i 3 A j) as an estimate of k ij/n i, and which were excluded from the DTI evaluation) showed c d(A j 3 A i) as an estimate of k ij/n j. Hence, c d(A i 3 A j) high correlations between various cortical areas. In estimates the fraction of axons originating in “A i” that contrast, most of the white matter voxels exhibited represent a link with “A j.” This justifies the term “an- very low correlation with other voxels. Many grey mat- atomical connectivity” for c d. The case c d(A 3 B) 3 ter voxels showed high correlation with voxels approx- c d(B 3 A) reflects that two brain regions may maintain imately at the corresponding location in the contralat- connections to a different number of areas (Felleman eral hemisphere. This observation is in agreement with and Van Essen, 1991). 248 KOCH, NORRIS, AND HUND-GEORGIADIS FIG. 4. Example for the result of the particle-jump algorithm. The start pixel is shown in blue and marked with an arrow. The c d values for individual pixels are indicated by colors: red (yellow) voxels were crossed by a low (high) number of particle paths. The colors for five selected c d values are shown in the color scale. Uncolored pixels were never reached by the particle. Fiber directions as described in the legend of Fig. 3 are shown in blue. FUNCTIONAL AND ANATOMICAL CONNECTIVITY 249 fiber tract. As one proceeds along a fiber bundle, the axons may gradually be replaced by other axons joining the bundle, which is invisible in the DTI map. This could explain the group of points in Fig. 5 with c f % 0.4 and 0.075 % c d % 0.16. The observation in Fig. 5 that only the region pairs around the central sulcus show a clear correlation between c d and c f might be explained by anatomical arguments. Cytoarchitecture, gross function, and probably connection pattern of the corti- cal areas on both sides of the central sulcus are more or less the same over the length of the sulcus, in contrast to the pre- or postcentral sulcus (Brodmann, 1909, p. 153). This implies a reduced variance contribution from a varying slice position. Conventional fiber tracking algorithms (Conturo et al., 1999; Mori et al., 1999; Jones et al., 1999) usually generate a trajectory by following the direction corre- sponding to the largest eigenvalue of the diffusion ten- FIG. 5. Correlation coefficient c f between regions on adjacent gyri versus the corresponding anatomical connectivity measure c d. sor. However, this approach does not provide a quan- Each region pair is represented by two symbols: since in the simu- titative measure of anatomical connectivity. In lation the start pixel can be set in either of the two regions, two c d addition, it does not discriminate between voxels with values per region pair are shown, connected by a horizontal line. the same principal directions but different degrees of Symbols with vertical lines pointing downwards represent paths where the starting region is more anterior, symbols with lines point- anisotropy, and isotropic regions cannot be traversed. ing upward represent paths where the starting region is more pos- The algorithm presented here is substantially differ- terior. Identified location of evaluated gyrus pairs: inferior frontal ent. It provides a quantitative measure of anatomical and precentral gyrus (diamond), precentral and postcentral gyrus connection strength, and it reflects the statistical na- (filled circle), and postcentral and supramarginal gyrus (triangle). ture of the information obtained with DTI. It can deal All other gyrus pairs are shown with squares. The plot comprises the data from left and right hemispheres of the four evaluated subjects with fiber bifurcations and with isotropic voxels. Be- (the number of regions differs between subjects). cause the full tensor information is used, the degree of anisotropy is taken into account. The algorithm can easily be adapted to 3-dimensional DTI data (Koch et If DTI-visible fiber connections are the basis for the al., 2001). In order to incorporate data from 3-dimen- observed correlations then the c f distribution should sional q-space imaging (Tuch et al., 1999; Wedeen et depend on the c d value. This holds even if we are not al., 2000), the calculation of jump probabilities could be able to register all existing connections. The data pre- based on the measured probability distribution of mo- sented in Fig. 5 provide some support for such a de- lecular displacements rather than on the diffusion ten- pendence. There are a number of reasons why a sor. In the relatively isotropic region at a fiber crossing, straightforward correlation between anatomical and the particle paths would then follow the directions of functional connectivity may not be expected. Observed the crossing fibers with a higher probability. signal correlations between two cortical regions could In this article we presented a new approach for ex- be mediated by indirect anatomical connections. In this tracting a quantitative measure of anatomical connec- case the BOLD signal times courses may be highly tivity from DTI data. A comparison of anatomical and correlated, although no connecting fiber is present in functional connectivity between regions of interest on the DTI fiber map. Such cases are likely to exist since adjacent cortical gyri revealed that low functional con- an interhemispheric correlation of BOLD signal fluc- nectivity rarely occurs in combination with high ana- tuations has been observed in cortical regions that tomical connectivity. In contrast, high functional and have only few direct commissural connections, such as low anatomical connectivity do occur in combination. the left and right hand representation in the primary This is interpreted as an indication of BOLD signal motor cortex (Biswal et al., 1995) and the left and right correlation mediated by undetected or indirect connec- primary visual cortex (Lowe et al., 1998). The occur- tions. Using a 3-dimensional DTI data set, the pre- rence of high c f values at low c d values in Fig. 5 is sented approach is expected to shed further light on consistent with these observations. Furthermore, we the anatomical foundations of functional connectivity. cannot detect intracortical connections or genuine U fibers (Miodoński, 1974) in superficial WM. Our proto- ACKNOWLEDGMENTS col also misses out fibers that are not contained in the image slice. On the other hand, fiber bundles in DTI M.A.K. enjoyed partial financial support from the BIOMED II fiber maps do not necessarily represent a continuous scheme of the European Union project BMH4-96-0861. Echo order- 250 KOCH, NORRIS, AND HUND-GEORGIADIS ing for TIPE phase encoding was supplied by J. Jovicich and adapted poro-parietal white matter as a basis for reading ability: Evidence to linear encoding by V. Nebe. from diffusion tensor magnetic resonance imaging. Neuron 25: 493–500. REFERENCES Koch, M., Glauche, V., Finsterbusch, J., Nolte, U., Frahm, J., and Büchel, C. 2001. Estimation of anatomical connectivity from dif- Basser, P. J., Mattiello, J., and Le Bihan, D. 1994a. MR diffusion fusion tensor data. Neuroimage 13: S176. tensor spectroscopy and imaging. Biophys. J. 66: 259 –267. Koch, M. and Norris, D. G. 2000. An assessment of eddy current Basser, P. J., Mattiello, J., and LeBihan, D. 1994b. Estimation of the sensitivity and correction in single-shot diffusion-weighted imag- effective self-diffusion tensor from the NMR spin echo. J. Magn. ing. Phys. Med. Biol. 45: 3821–3832. Reson. B 103: 247–254. Lim, K. O., Hedehus, M., Moseley, M., de Crespigny, A., Sullivan, Basser, P. J., and Pierpaoli, C. 1996. Microstructural and physiolog- E. V., and Pfefferbaum, A. 1999. Compromised white matter tract ical features of tissues elucidated by quantitative-diffusion-tensor integrity in schizophrenia inferred from diffusion tensor imaging. MRI. J. Magn. Reson. B 111: 209 –219. Arch. Gen. Psychiatry 56: 367–374. Biswal, B. B., Van Kylen, J., and Hyde, J. S. 1997. Simultaneous Lowe, M. J., Mock, B. J., and Sorenson, J. A. 1998. Functional assessment of flow and BOLD signals in resting-state functional connectivity in single and multislice echoplanar imaging using connectivity maps. NMR Biomed. 10: 165–170. resting-state fluctuations. Neuroimage 7: 119 –132. Biswal, B. B., Yetkin, F. Z., Haughton, V. M., and Hyde, J. S. 1995. Meister, M., Wong, R. O. L., Baylor, D. A., and Shatz, C. J. 1991. Functional connectivity in the motor cortex of resting human brain Synchronous bursts of action potentials in ganglion cells of the using echo-planar MRI. Magn. Reson. Med. 34: 537–541. developing mammalian retina. Science 252: 939 –943. Brodmann, K. 1909. Vergleichende Lokalisationslehre der Großhirn- Miodoński, A. 1974. The angioarchitectonics and cytoarchitectonics rinde, in ihren Prinzipien dargestellt auf Grund des Zellenbaues, (impregnation modo Golgi–Cox) structure of the fissural frontal 1st ed., reprint 1985. J. A. Barth, Leipzig. neocortex in dog. Folia Biol. (Kraków) 22: 237–279. Büchel, C. and Friston, K. J. 1998. Dynamic changes in effective Mori, S., Crain, B. J., Chacko, V. P., and van Zijl, P. C. M. 1999. connectivity characterized by variable parameter regression and Three-dimensional tracking of axonal projections in the brain by Kalman filtering. Hum. Brain Mapp. 6: 403– 408. magnetic resonance imaging. Ann. Neurol. 45: 265–269. Conturo, T. E., Lori, N. F., Cull, T. S., Akbudak, E., Snyder, A. Z., Norris, D. G., Börnert, P., Reese, T., and Leibfritz, D. 1992. On the Shimony, J. S., McKinstry, R. C., Burton, H., and Raichle, M. E. application of ultra-fast RARE experiments. Magn. Reson. Med. 1999. Tracking neuronal fiber pathways in the living human brain. 27: 142–164. Proc. Natl. Acad. Sci. USA 96: 10422–10427. Ogawa, S., Lee, T. M., Kay, A. R., and Tank, D. W. 1990a. Brain Einstein, A. 1905. Über die von der molekularkinetischen Theorie magnetic resonance imaging with contrast dependent on blood der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten oxygenation. Proc. Natl. Acad. Sci. USA 87: 9868 –9872. suspendierten Teilchen. Annalen Physik Chemie (4. Folge) 17: 549 –560. Ogawa, S., Lee, T. M., Nayak, A. S., and Glynn, P. 1990b. Oxygen- ation-sensitive contrast in magnetic resonance image of rodent Felleman, D. J. and Van Essen, D. C. 1991. Distributed hierarchical brain at high magnetic fields. Magn. Reson. Med. 14: 68 –78. processing in the primate cerebral cortex. Cerebral Cortex 1: 1– 47. Pearson, K. 1896. Mathematical contributions to the theory of evo- Fletcher, P., McKenna, P. J., Friston, K. J., Frith, C. D., and Dolan, R. J. 1999. Abnormal cingulate modulation of fronto-temporal lution, III. Regression, heredity, and panmixia. Phil. Trans. R. connectivity in schizophrenia. Neuroimage 9: 337–342. Soc. Lond. A 187: 253–318. Frégnac, Y. 1996. Dynamics of functional connectivity in visual cor- Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. tical networks: An overview. J. Physiology (Paris) 90: 113–139. 1992. Numerical Recipes in C. The Art of Scientific Computing. Cambridge Univ. Press, Cambridge, 2nd ed. Friston, K. J. and Frith, C. D. 1995. Schizophrenia: A disconnection syndrome? Clin. Neurosci. 3: 89 –97. Stejskal, E. O., and Tanner, J. E. 1965. Spin diffusion measure- ments: Spin echoes in the presence of a time-dependent field gra- Friston, K. J., Frith, C. D., Liddle, P. F., and Frackowiak, R. S. J. dient. J. Chem. Phys. 42: 288 –292. 1993. Functional connectivity: The principal-component analysis of large (PET) data sets. J. Cereb. Blood Flow Metab. 13: 5–14. Tuch, D. S., Weisskoff, R. M., Belliveau, J. W., and Wedeen, V. J. 1999. High angular resolution diffusion imaging of the human Friston, K. J., Williams, S., Howard, R., Frackowiak, R. S. J., and brain. In Proceedings, ISMRM, 7th Annual Meeting, p. 321. Phil- Turner, R. 1996. Movement-related effects in fMRI time-series. adelphia, PA. Magn. Reson. Med. 35: 346 –355. Wedeen, V. J., Reese, T. G., Tuch, D. S., Weigel, M. R., Dou, J.-G., Golanov, E. V., Yamamoto, S., and Reis, D. J. 1994. Spontaneous Weiskoff, R. M., and Chessler, D. 2000. Mapping fiber orientation waves of cerebral blood flow associated with a pattern of electro- spectra in cerebral white matter with Fourier-transform diffusion cortical activity. Am. J. Physiol. 266: R204 –R214. MRI. In Proceedings, ISMRM, 8th Annual Meeting, p. 82. Denver, Hebb, D. O. 1949. The Organization of Behavior. Wiley, New York. CO. Johnson, G., and Hutchison, J. M. S. 1985. The limitations of NMR Werring, D. J., Clark, C. A., Barker, G. J., Miller, D. H., Parker, recalled-echo imaging techniques. J. Magn. Reson. 63: 14 –30. G. J. M., Brammer, M. J., Bullmore, E. T., Giampietro, V. P., and Jones, D. K., Simmons, A., Williams, S. C. R., and Horsfield, M. A. Thompson, A. J. 1998. The structural and functional mechanisms 1999. Non-invasive assessment of axonal fiber connectivity in the of motor recovery: Complementary use of diffusion tensor and human brain via diffusion tensor MRI. Magn. Reson. Med. 42: functional magnetic resonance imaging in a traumatic injury of 37– 41. the internal capsule. J. Neurol. Neurosurg. Psychiatry 65: 863– Jovicich, J., and Norris, D. G. 1998. GRASE Imaging at 3 Tesla with 869. template interactive phase-encoding. Magn. Reson. Med. 39: 970 – Wieshmann, U. C., Clark, C. A., Symms, M. R., Franconi, F., and 979. Barker, G. J. Shorvon, S. D. 1999. Anisotropy of water diffusion in Klingberg, T., Hedehus, M., Temple, E., Salz, T., Gabrieli, J. D. E., corona radiata and cerebral peduncle in patients with hemipare- Moseley, M. E., and Poldrack, R. A. 2000. Microstructure of tem- sis. Neuroimage 10: 225–230.

NeuroImage PDF: An Investigation of Functional and Anatomical Connectivity (2002)

Document Details

Tags

Related

Summary

Full Transcript

Upgrade to continue