in functional neuroimaging ,   and particularly in pet and fmri ,   study design and analysis have been dominated by the concept of   functional segregation , which emphasizes the specialization of a brain structure for a 
 specific part of a cognitive function .
this has resulted in a large number of 
 studies in which differences in cognitive states are linked to the differential 
 activation of separate brain areas .
the concept of functional integration , on the other hand , has long been recognized as an equally important principle of brain organization .
functional integration 
 refers to the interaction between brain areas and has been studied with two 
 categories of analyses : functional connectivity analyses and effective 
 connectivity analyses . in functional connectivity analyses [ 24 ] , the covariance structure of a 
 measure of brain activity
is studied , from which differences in cognitive 
 states are linked to differences in correlations between regions .
these 
 analysis methods are thus limited in their capacity to make inferences about 
 the directionality of these correlations , which makes it difficult to address , for 
 instance , the functional hierarchy of the brain structures under investigation . 
 in effective connectivity analyses , on the other hand ,
models are defined a priori , comprising the brain 
 structures of interest and assumptions about the afferent / efferent connections 
 between them [ 5 , 6 ] .
these models are then fitted to the 
 activity of these brain areas to obtain the strength of these connections , 
 which enables inferences on changes in connection strengths in relationship to 
 cognitive states .
effective 
 connectivity has been defined as the influence one neural system or region 
 exerts over another .
there are two ways by which this 
 influence can be mediated : via a direct path between two regions , or via an 
 indirect path in which a third region is involved .
the analysis methods that 
 have been applied to functional neuroimaging data , structural equation modeling 
 ( sem ) and dynamic causal modeling ( dcm ) , differentiate between these two 
 possibilities , provided that the underlying model ( regions and their paths ) is 
 completely specified . if two regions are connected via a third region and 
 this third region has furthermore no other influence on the rest of the 
 network , one can choose to incorporate only an indirect path between the two 
 regions and to refrain from explicitly modeling the third region and its direct 
 paths .
we are 
 working here , however , on the premise that most of the specified paths should 
 reflect veridical direct paths , because we believe that too many  indirect  
 paths , involving these  third party  regions , which are not explicitly taken 
 into account in the model , will seriously decrease the biological validity of 
 the model .
sem has 
 also extensively been applied in the social sciences , where these paths 
 represent abstract causal connections between variables . when this method is 
 applied to functional neuroimaging however
, these paths should ultimately 
 correspond to the white matter connectivity of the brain regions under investigation . 

furthermore , mcintosh 
 and gonzalez - lima   have studied the effect of 
 erroneous model specification on the estimation of the path coefficients and 
 have found that it could seriously impinge on the estimation of these 
 coefficients
. therefore , it would be highly valuable to incorporate all 
 available knowledge regarding anatomical connections into effective 
 connectivity models .
it should be noted that we do not imply that each existing 
 anatomical connection should result in an effective connection in each and every 
 cognitive task .
however , it is the role of the model estimation to indicate 
 which anatomical connections have become effective for which task manipulation . 

therefore , leaving an anatomical connection , which is known to exist , out of a 
 model specification can only be justified when one has strong beliefs about the 
 functioning of this path in the present context , possibly combined with a 
 requirement for a decrease in model complexity . unfortunately
, 
 our knowledge about human anatomical connectivity is relatively sparse , because 
 a number of techniques that are used in other species ( active tracers ) are 
 highly invasive .
therefore , only two classical anatomical methods can be used : dissection 
 studies , which only provide information on a relatively coarse scale , and passive 
 tracer studies , which are not very well suited to investigate long - range 
 connectivity .
most effective connectivity studies thus can only validate their 
 connections with information from nonhuman primates , which in turn raises 
 problems with the homology of brain structures between different species . in the 
 last decade , a technique known as diffusion tensor imaging ( dti ) [ 9 , 10 ] has emerged as a good candidate to 
 resolve this situation . in dti ,
the sensitivity of the ( diffusion - weighted ) mr signal 
 to the self - diffusion of water on a microscopic scale is employed to 
 characterize the anisotropic structure of white matter in vivo .
it is assumed 
 that the direction in which diffusion is largest is collinear to the direction 
 of the axonal bundle in the voxel , because diffusion is assumed to be hindered 
 in directions perpendicular to this direction . with this information
, fiber 
 tracking [ 11 , 12 ] can be performed in which the main diffusion 
 directions of voxels are followed throughout white matter .
this method already 
 has provided useful insights in , for instance , the anatomy of the thalamus and 
 the striatum [ 13 , 14 ] .
first , 
 dti provides no information about the afferent or efferent character of the axons , 
 because the diffusion of water does not differentiate between these two 
 situations .
second , the tensor model can only provide one main direction per 
 voxel , which considerably increases the likelihood of erroneous tracking 
 results through a region of crossing fibers .
finally , in cerebral gray matter 
 there is generally no dominant fiber direction , making it difficult to track 
 fibers to their cortical origin .
the aim 
 of the current study is to investigate to what extent dti - based tractography 
 can provide support for the anatomical basis of the networks , proposed in 
 effective connectivity studies .
furthermore , we have investigated whether 
 dti - based tractography is able to reveal any connections that go beyond the 
 ones proposed in the original analysis . to address these questions
, we have 
 chosen eight effective connectivity studies all using structural equation modeling . 

sem was introduced at an early stage of the development of pet and fmri , with 
 the consequence that a body of sem studies is to be found in the literature .
dcm , 
 on the other hand , has only relatively recently been introduced , but is gaining 
 a rapid popularity . 

it should be noted that any conclusions we are able to draw in this study 
 within the context of sem models can be readily generalized to dcm studies as 
 there is no difference in the role of the underlying anatomical model in both 
 frameworks .
we have 
 chosen networks spanning a number of different cognitive domains , including 
 learning [ 15 , 16 ] , 
 cognitive control [ 17 , 18 ] , working memory , visual and auditory perception , major depression , and the thalamocortical network 
 involved in general - anaesthetic - induced unconsciousness .
we performed a standard dti 
 experiment on 6 subjects and used the coordinates of the network nodes as seed 
 regions for a fiber tracking analysis . in this analysis ,
we have established 
 whether dti - based fiber tractography provides evidence about the direct nature 
 of every possible connection , whether or not it was proposed in the original 
 studies .
we 
 studied 6 healthy subjects ( 2 females , age range 2532 years ) after 
 informed consent was given according to institutional guidelines of the local 
 ethics committee ( cmo protocol region arnhem - nijmegen , the netherlands ) .
dti was 
 performed using a twice refocused pulsed gradient spin echo epi sequence   at 1.5  t(sonata system , siemens , erlangen , germany)with a standard head coil .
axial slices were 
 obtained using the following imaging parameters : repetition time = 9900  milliseconds , 
 echo time = 88  milliseconds , flip angle = 90 , 128  128 matrix , 320  mm  320  mm field of view , and slice thickness = 2.5  mm with no gap ( 2.5  2.5  2.5  mm 
 isotropic voxels ) .
diffusion weighting was obtained along sixty noncollinear 
 directions   using a b - value of 
 700  s / mm . 

each 
 subject the five reference images with no diffusion weighting were averaged and 
 normalized to the mni t2 template in spm2 ( statistical parametric mapping , 
 http://www.fil.ion.ucl.ac.uk/spm ) .
the matrix of normalization parameters was 
 inverted to obtain the transformation matrix from standard space to world 
 space .
we have done this to avoid the extensive resampling and reorientation of 
 the data that is involved in the normalization of dti data [ 25 , 26 ] , because we hypothesize that this 
 would lead to a degradation of the finer details in the fiber tracts.only linear terms were used in the 
 normalization to ensure that the transformation matrices could be inverted .
diffusion tensors and fractional anisotropy ( fa ) 
 maps were calculated using the diffusion toolbox   in spm2 .
the fa maps were used for 
 displaying the anatomical location of the roi coordinates .
fiber tracking was 
 performed in the dti - studio package   using the fact algorithm .
tracking was terminated when the 
 angle of two consecutive eigenvectors was larger than 85 , or when a voxel was 
 reached with an fa value smaller than 0.20 . in most of the original studies [ 1519 , 22 ] ,
the rois that were used for 
 effective connectivity analysis were all spheres of 8  mm radius .
however , in 
 two studies [ 20 , 21 ] only the peak voxels of a partial 
 least - squares analysis   were used . because these voxels 
 represented larger clusters of voxels ,
we have used rois with roughly the same 
 size ( spheres of 8  mm radius ) as a starting point for all networks .
we have 
 chosen not to transform the whole original roi into subject space , as this 
 might lead to extensive seeding of the white matter adjacent to the seed 
 coordinate , and thus to many false positives . instead , we have drawn rois on 
 the individual subject s fa maps , taking care that the borders of the roi were 
 at the border of gray and white matters ( as visible on the fa map ) and that the 
 roi would approximately be of the same size as the original roi .
all 
 possible combinations of regions were tracked , including the connections that 
 were not proposed in the original effective connectivity studies .
the results for all networks under 
 investigation are visualized in figures 18 , in which the 
 thickness of the connecting lines indicates the number of subjects in which a 
 particular connection was found . in the appendix , we have also listed these 
 results in table 1 .
the most striking class of paths which are not supported by our findings contains 
 frontal interhemispheric paths .
this can however convincingly be explained by 
 methodological shortcomings in regions with crossing fibers in the frontal 
 parts of the brain .
we will discuss these issues further in section 4 . in half of the 
 studies
, we have also found connections indicating paths that were not included 
 in the original studies . in the following
this not only leads to the 
 situation that this nomenclature is inconsistent between studies , but may also 
 give the incorrect impression that similar connections are under investigation 
 in different networks .
it is therefore important to note that the regions of 
 interest normally are spheres of approximately 8  mm in diameter , 
 and thus two regions with 
 the label 
the network of this study can be separated 
 into a dorsal stream ( v1 , de , pp , and lp ) and a ventral stream ( v1 , itp , and 
 ita ) of visual areas .
the paths within these streams are supported in the 
 majority of subjects by our dti results .
however , the crucial path under 
 investigation is the path between the two streams ( pp - itp ) , which is 
 hypothesized to mediate the learning effect under investigation .
interestingly , 
 we have found no evidence for this path , but we have found support for a path ( de - ita ) , 
 which was not included in the proposed network and which could be a potential 
 candidate to mediate this effect . whereas we do not wish to suggest that the 
 original path ( pp - itp ) should be dismissed , it would be interesting to 
 investigate whether a part of the learning related effects , reported in the 
 original study , is mediated by the new path we have reported . in this network , a series of 
 regions ( occ , par , and pfc ) is proposed in both hemispheres with symmetrical 
 paths within the hemispheres and extensive interhemispheric connections .
the 
 paths between occipital and parietal cortices are supported by our findings as are the 
 interhemispheric connections between these regions .
furthermore , we have found 
 evidence for paths that were not included in the original model , namely , 
 interhemispheric connections between occipital and parietal cortices .
this is quite 
 remarkable , because interhemispheric connections between nonhomologous regions 
 are rarely found in this kind of analyses . also of interest
are the cases in 
 which the proposed paths are not supported by our results .
the interhemispheric 
 connections we did not find ( lpfc - rpfc , lpfc - rpar , and rpfc - lpar ) fall into the 
 aforementioned problematic class of frontal interhemispheric connections . the 
 most interesting negative result is the lack of connections between right 
 parietal and right prefrontal cortices , in contrast to the presence of these connections in 
 the left hemisphere . in this case , methodological shortcomings are not likely 
 to affect the results , as this would indicate that these shortcomings would 
 exist for the right hemisphere but not for the left hemisphere .
the same 
 argument makes the consideration of connections via an extra region , which has 
 not been included in the network , also unattractive .
therefore , we tentatively 
 interpret these findings as a support for an asymmetry in connectivity between 
 these areas in parietal and prefrontal cortices .
this network contains a set of 
 motor and prefrontal regions in both hemispheres which are symmetrically 
 connected within the hemispheres .
this last set of paths falls again in the class of frontal 
 interhemispheric connections and thus it is not surprising that we have found 
 no support for these paths .
have 
 proposed an alternative network in their study , which contained also paths 
 directly from premotor cortex to rostral prefrontal cortex .
this extra network 
 did not result in significant changes in the original paths , which is in 
 agreement with the lack of support for these paths in our results .
kondo et al . have proposed four 
 network nodes ( pfc , acc , spl , and ifc ) .
however , two of these nodes ( spl and 
 ifc ) can be further split up in four anatomically distinct regions ( spl1 , spl2 , 
 ifc1 , and ifc2 ) .
we have thus decided to treat each of these regions as a 
 separate node and have studied the connections between these nodes .
our results 
 show that the regions which constitute each original node ( e.g. , ifc1 and ifc2 ) 
 are connected with each other , but they show differential connectivity patterns 
 with the rest of the network , which suggest that they also have a different 
 role within this network .
the lack of support for paths from 
 and to the acc was surprising , especially given the fact that the acc is known to 
 connect extensively with the prefrontal cortex in the macaque . in this network , a set of regions 
 is proposed ranging from occipital , temporal , premotor , and prefrontal regions . 

given our 
 results in the other studies , it was not surprising that there was hardly any 
 support for the ( nonhomologous ) interhemispheric connections originating in 
 frontal and prefrontal cortices . 

support was found for paths between occipital cortex and frontal and superior 
 temporal cortices . 
 however , there are also two intrahemispheric paths for which no support was 
 given ( a6-a18r , a10-a6 ) .
furthermore , there was no evidence found for paths 
 which were not included in the original analysis .
therefore , within the context 
 of this network , dti did not deliver any extra information .
rowe et al . have proposed a network 
 with bilateral parietal , prefrontal , and prestriate areas and a motor area in 
 the left hemisphere only .
we have found only scarce support for the paths to 
 and from prestriate area , even after lowering the fa threshold . in the left 
 hemisphere , we have found consistent evidence for all other proposed paths . 
 however , as in the network of fletcher et al . , we have found support for 
 parietal - frontal connections in the left but not in the right hemisphere .
based 
 on the same arguments as in the network of rowe et al . , we again interpret this 
 as an evidence for an asymmetry in these connections .
this is even more 
 remarkable , because the locations of parietal and especially prefrontal areas 
 in both studies are quite widely separated .
the network of seminowicz et al . 
 consists predominantly of prefrontal subcortical areas in the right hemisphere , 
 with the lateral prefrontal cortex as the only region in the left hemisphere . 

this might directly explain why we have found only scarce evidence for paths 
 from this region to the rest of the network , because of the aforementioned 
 methodological problems with frontal interhemispheric connections .
in contrast to the study of kondo 
 et al . , we have found connections supporting the proposed paths from the anterior 
 cingulate cortex .
furthermore , we have found many connections from the 
 thalamus to the rest of the network which do not conform to proposed paths . 

this is however not surprising , as it is well known that the different nuclei 
 in the thalamus extensively connect to different parts of the cortex .
connections are 
 thus most probably the result of the fact that the seed region in this case was 
 too large to specifically select the nucleus of the thalamus involved in this 
 network .
further evidence for paths that were not proposed in the original 
 network was found for connections from medial prefrontal cortex to the 
 hippocampus and the subgenual cingulated cortex .
the hippocampus is a region of low 
 fa and thus in an initial analysis showed only very limited connectivity with 
 the rest of the network .
we have therefore repeated the analysis with a lowered 
 fa threshold ( 0.15 ) which yielded support for the proposed paths from the 
 hippocampus .
white et al . have proposed a model 
 with the left motor cortex and supplementary motor area , the thalamus , and two 
 areas from the right cerebellum .
we have found support for the intrahemispheric 
 paths but not for the interhemispheric ones .
this last finding contradicts 
 findings from the macaque literature in which there are connections found 
 between the primary motor cortex and the contralateral cerebellum deep nucleus .
moreover , there is evidence 
 that the pons , which is a region through which these fibers have to pass , 
 contains crossing fibers .
we , therefore , conclude that 
 it is valid to include these connections in an effective connectivity analysis .
in this study , we have for the 
 first time used dti - based fiber tractography to investigate the anatomical 
 basis of effective connectivity models .  
first , we wanted to establish that dti - based tractography is able to resolve the 
 connectivity between rois of the size typically used in effective connectivity 
 studies .
we hypothesized that the majority of the proposed paths were indeed 
 valid , and compared the results of our dti - based analysis with these paths .
however , we believe that the greatest 
 potential advantage of using dti - based tractography in the context of effective 
 connectivity models lies in establishing paths that are not suggested by the 
 available knowledge ( e.g. , macaque tracer literature ) .
our second aim was therefore 
 to investigate the evidence for connections which were not proposed in the 
 original studies .
we have found evidence for such connections in half of the models . 
 in the following
, 
 we will discuss these findings in the context of current methodological 
 limitations and we will evaluate their implications for the proposed models .
when there was no evidence found 
 for a proposed path , there are two explanations possible : 
 there is no 
 direct anatomical connection ; in this case , the proposed path can only be 
 supported by an indirect connection with a third region;there is a 
 direct connection , but it has not been found due to methodological limitations 
 ( false negative ) . 
 the second explanation is 
 especially relevant to a class of frontal interhemispheric connections .
as 
 mentioned in the introduction , dti - based tractography has profound difficulties 
 when tracking through voxels with multiple fiber populations .
the frontal 
 interhemispheric connections pass through the corona radiata , which is well 
 known to contain such voxels .
therefore , any negative 
 findings about this class of connections have to be interpreted as being 
 inconclusive .
there is no 
 direct anatomical connection ; in this case , the proposed path can only be 
 supported by an indirect connection with a third region ; there is a 
 direct connection , but it has not been found due to methodological limitations 
 ( false negative ) .
there is another set of negative 
 findings which merits further discussion : in both networks of fletcher et al . 
 and of rowe et al .
, we have found evidence for a connection between parietal 
 and prefrontal cortices 
 in the left hemisphere but not in the right hemisphere here , an explanation in terms of 
 methodological limitations seems unattractive , because this would suggest that 
 these limitations occur in the right hemisphere but not in the left hemisphere . 

therefore , we tentatively conclude that these connections are indeed absent in 
 the right hemisphere and that this is an evidence for an asymmetry in 
 parietal - frontal connectivity . we should point out , however , that this 
 asymmetry seems counterintuitive at first , since the right hemisphere is 
 hypothesized to be dominant for visuospatial processing and one would expect 
 that these connections would be especially strong for this hemisphere
. however , 
 as we are dealing with relatively small rois within the frontal and parietal 
 lobes , this does not rule out the possibility of there being any connections 
 between these lobes in the right hemisphere .
there are a number of paths for 
 which no evidence was found and which can not be interpreted directly in terms 
 of methodological limitations . as in many neuroimaging studies , these negative 
 findings are difficult to classify and it would certainly be imprudent to 
 conclude that these paths do not exist .
moreover , it is also possible that a 
 path is mediated by connections from and to a third region , which was not 
 included in the network .
this situation can be relatively harmless if the 
 function of the missing region is known to be restricted to  message passing  . however , 
 we hypothesize that , if there is a substantial number of such  indirect  connections 
 present in a network , the inclusion of these other regions , which mediate these 
 connections , becomes necessary to ensure the biological validity of the 
 network .
given the methodological issues 
 discussed above , it is clear that the potential contribution of dti to 
 connectivity studies lies not in disproving the existence of postulated 
 connections , but in the unique potential for detecting hitherto unconsidered 
 direct anatomical connections .
this is because dti may be prone to type ii 
 errors , but it is far less likely to consistently produce type i errors when 
 connections are averaged across subjects .
it is hence highly significant that we 
 have also found evidence for a number of paths which have not been taken into 
 account in the original studies .
incorporating these paths in a new analysis of 
 these models can potentially have a significant impact on the interpretation of 
 these models , since they point to improvements in the anatomical validity of 
 the models , which in turn leads to more veridical path coefficients . at the current state of technology in effective connectivity
, one has 
 considerable freedom to choose the connections in a model and to evaluate 
 different models with different connectivity profiles against each other .
this model selection procedure can 
 be augmented significantly with dti - based tractography , because models in which 
 the connections to a large extent overlap with the connections found in a dti analysis 
 should in turn be more likely .
one could potentially formalize this in a 
 bayesian framework by designing priors on the connections and by subsequently 
 making the priors on the  known  connections high and sharp and the priors on 
 the  unknown  connections relatively noninformative .
if this would be a veridical variability , it would 
 be a surprising and new finding , since the intersubject variability of 
 anatomical connections is generally considered to be low and is furthermore difficult 
 to assess with either dti or tracer methods . in dti , the normalization of 
 findings still makes it difficult to compare findings across subjects , whereas 
 tracer studies are normally performed in very few animals because of ethical 
 considerations , which makes any discussion about differences between animals 
 extremely difficult .
although we have not normalized the fiber tracks to a 
 template , we do believe that normalization problems still play an important 
 role in our studies because they might cause the erroneous placement of seed 
 regions in some subjects , which in turn would lead to misleading tractography 
 results and the above - mentioned intersubject variability .
the smoothing 
 strategy , employed in functional studies to reduce the effect of anatomical 
 differences between subjects , can not be applied in our framework because the 
 directional information , used in the tracking procedure , would be smeared out 
 over other voxels and potentially other tracks , with unpredictable implications 
 for the veridicality of the tracks found .
currently , there is no convincing way 
 of solving this problem , as the basic anatomical landmarks vary substantially 
 over subjects .
recently , advances have been made 
 towards the estimation of multiple fiber directions within one voxel and also 
 in probabilistic tractography .
we will now discuss each of these developments 
 and their potential use for our framework .
the estimation of multiple fiber 
 compartments per voxel , in general , brings this technique closer to producing 
 veridical anatomical connections , and a number of techniques have been proposed 
 to achieve this [ 33 , 3639 ] .
there is , however , one 
 problem which can not be solved by this technique alone , and that is the kissing / crossing 
 fiber problem : when a fiber has to track through a voxel with multiple 
 compartments , it is uncertain which compartment has to be used to determine the 
 direction in which the track is to be continued . in a number of studies ,
the 
 direction that is most collinear with the incoming fiber was chosen , but this 
 does not necessarily have to be the true direction . whereas the single tensor 
 model is probably too conservative in the connections it yields , multiple compartment 
 models might thus yield a number of false positives . in probabilistic fiber tracking , a 
 measure of uncertainty of the local fiber direction is estimated per voxel [ 4044 ] .
fiber tracking is now done 
 in a monte carlo type experiment : the tracking 
 is performed multiple times , each time with a different orientation drawn from 
 the local fiber direction distributions .
subsequently , the number of times a 
 target voxel was hit by this procedure is calculated , which then is converted 
 to an informal measure of  probability of connection  .
while this procedure by 
 itself seems valid , in practice this leads to widespread patterns of 
 connectivity and it is uncertain at which level of  probability  the map should 
 be thresholded .
moreover , the probability of connection tends to decrease with 
 increasing distance . in a sem network , both relatively local and long 
 connections can be included , which makes the comparison of these connections 
 difficult .
thus while both techniques ( multiple direction estimation and 
 probabilistic fiber tracking ) can potentially alleviate some of the problems , 
 we have encountered ( e.g. , interhemispheric connections ) , unresolved issues 
 remain . in conclusion , we have shown that dti - based tractography can be used to 
 explore the anatomical connections between regions , used in effective 
 connectivity studies , notwithstanding the current limitations of this method . 

we have observed evidence for the proposed paths in a large number of cases and , 
 more importantly , we have shown in several cases direct connections that were 
 not included in the original models .
we therefore conclude that dti - based 
 tractography is a valuable tool for exploring the anatomical basis of 
 functional networks .
 diffusion tensor imaging ( dti ) is considered to be a promising tool for revealing the anatomical basis of functional networks . in this study 
 , we investigate the potential of dti to provide the anatomical basis of paths that are used in studies of effective connectivity , using structural equation modeling . 
 we have taken regions of interest from eight previously published studies , and examined the connectivity as defined by dti - based fiber tractography between these regions . 
 the resulting fiber tracts were then compared with the paths proposed in the original studies . for a substantial number of connections , we found fiber tracts that corresponded to the proposed paths . 
 more importantly , we have also identified a number of cases in which tractography suggested direct connections which were not included in the original analyses . 
 we therefore conclude that dti - based fiber tractography can be a valuable tool to study the anatomical basis of functional networks . 