LNCS 8674 - Group-Wise Optimization Of Common Brain .

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Group-Wise Optimization of Common Brain Landmarkswith Joint Structural and Functional RegulationsDajiang Zhu1, Jinglei Lv1,2, Hanbo Chen1, and Tianming Liu11Cortical Architecture Imaging and Discovery Laboratory, Department of Computer Scienceand Bioimaging Research Center, The University of Georgia, Athens, GA, USA{djzhu,lv,cojoc,tliu}@uga.edu2School of Automation, Northwestern Polytechnical University, Xi’an, ChinaAbstract. An unrelenting human quest regarding the brain science is: what isthe intrinsic relationship between the brain’s structural and functional architectures, which partly defines what we are and who we are. Recent studies suggestthat each brain’s cytoarchitectonic region has a unique set of extrinsic inputsand outputs, named as “connectional fingerprint”, which largely determines thefunctions that each brain area performs. However, their explicit connections arelargely unknown. For example, in what extent they are inclined to be coherentwith each other and otherwise they will intend to show more heterogeneity? Inthis work, based on a widely used brain structural atlas which represents themost consistent structural connectome across different populations, we proposed a novel group-wise optimization framework to computationally modelthe functional homogeneity behind them. The optimization procedure is conducted under the joint structural and functional regulations and therefore theachieved common brain landmarks reflect the consistency of brain structure andfunction simultaneously. The Human Connectome Project (HCP) Q1 dataset,which includes 68 subjects with high quality imaging data, was used as test bedand the results imply that there exists extraordinary accordance between brainstructural and functional architectures.Keywords: optimization, sparse coding, fMRI, brain structure and function.1IntroductionAn unrelenting human quest regarding the brain science is: what is the intrinsic relationship between the brain’s structural and functional architectures, which partly defines what we are and who we are. Recent neuroscience studies suggest that eachbrain’s cytoarchitectonic region has a unique set of extrinsic inputs and outputs,named as “connectional fingerprint” [1], which largely determines the functions thateach brain area performs. This close relationship between structural connectivity patterns and brain function has also been confirmed and replicated in recent studies [1,2], e.g., structural connectivity is accompanied by relatively strong functional connectivity [2]. Based on this phenomenon, a few methodologies were proposed to jointlymodel the structural and functional information of the human brain. For example, theP. Golland et al. (Eds.): MICCAI 2014, Part II, LNCS 8674, pp. 716–723, 2014. Springer International Publishing Switzerland 2014

Group-Wise Optimization of Common Brain Landmarks717work in [3] redefined the measurement of functional connectivity by introducing thestructural interference that the new measurement will emphasize the areas whichshow both high functional and structural connectivity. Another interesting example ofstructure/function joint modeling is the landmark distance (LD) model [4], whichutilized the stable relations (spatial distance) among white matter fiber, anatomicalatlases and functional activations to describe the fiber tracts. However, it is far fromfull understanding of the intrinsicconnections behind the structuralfoundation and functional responsesthat we observed, and their explicitconnections are still largely unknown.For instance, in what extent they areFig. 1. Illustration of the frameworkinclined to be coherent with each otherand otherwise they will intend to showmore heterogeneity [5]? We need a comprehensive understanding of the principlesthat regulate the information processing (function) in a particular structural pattern,and between the interacting structural units in the brain as a whole.Recently, a novel structure-based atlas, named as DICCCOL [6], was proposed andit is a successful attempt in the field to construct group-wise Regions of Interest(ROIs) by identifying the most consistent white matter connectivity patterns acrossdifferent individuals. Many studies already demonstrated that it is an effective androbust ROI modeling framework and has significant improvement compared to theprevious image registration method [6]. Despite that DICCCOL system is an important advancement in human brain mapping, however, it did not consider the functionalhomogeneity and heterogeneity behind those brain structural consistencies. To tacklethis problem and further reveal the intrinsic relationship between the brain structureand function, in this paper, we proposed a novel group-wise optimization framework(Fig.1) to computationally model the functional homogeneity under the structuralconsistency regulations. First, through an innovative sparse representation of thewhole-brain fMRI signals and similar strategies in detecting functional networks in[7], the most consistent functional networks are recovered and identified as functionaltemplates. At the same time, the structural landmarks on the HCP dataset are initialized by applying the DICCCOL prediction procedure [6]. Then, we use the achievedfunctional templates and trace-map model [6] as functional and structural regulations,respectively, to optimize the initial landmarks. Particularly, the optimization procedure is conducted under the join structural and functional regulations. Therefore, theachieved common brain landmarks reflect the consistency of brain structure andfunction simultaneously.2Methods2.1Data AcquisitionOur data source is the HCP Q1 release [8]. The HCP Q1 dataset has seven task-fMRIdatasets of 68 participants including working memory, gambling, motor, language,

718D. Zhu et al.social cognition, relational processing and emotion processing. For task-fMRI, theacquisition parameters are as follows: 72 slices, TR 0.72s, TE 33.1ms and 2.0 mmisotropic voxels. For the rsfMRI data, the L-R phase encoding rs-fMRI data of run 1in HCP Q1 data was used in this paper. The acquisition parameters were as follows:2 2 2 mm spatial resolution, 0.72 s temporal resolution and 1200 time points. FordMRI, spatial resolution 1.25mm 1.25mm 1.25mm. More detailed data acquisitionand preprocessing are referred to literature report [7, 9].2.2Sparse Representations of fMRI Signals and Identification of FunctionalTemplatesRecently, we have developed a novel computational framework for sparselyrepresenting whole brain’s fMRI signals [7] and successfully applied it on the HumanConnectome Project (HCP) [8] high-quality imaging data. Similar to [13], the basicidea of this framework is to assemble all the fMRI signals (either task or resting) intoone matrix, which is further decomposed into an over-complete dictionary basis matrix and a reference weight matrix via the efficient online dictionary learning method[10]. The cost function is defined as:ℓ min sDα λ α (1)denotes the whole brain signals which have n voxels withwhere S s , s , st time length. D represents the dictionary (k t and k n). According to Eq.1, aspecific signal, s , can be represented as the product of basis dictionary D and α ,where α is the corresponding coefficient vector in the coefficient weight matrix. λ isa regularization parameter which is used as a trade-off item between the sparsity levelof coefficient (α ) and the regression residual. A particularly important characteristicof this framework is that the reference weight matrix ( ) naturally reveals the spatialoverlap patterns among those reconstructed brain networks, which are represented bythe time series of the over-complete basis dictionaries.The rational of using sparse coding instead of traditional fMRI analysis has twoaspects: 1) It has been widely reported that a variety of brain regions and networksexhibit strong functional diversity and heterogeneity [11]. That is, the same brainregion could participate in multiple functional processes/domains simultaneously anda single functional network might recruit various neuroanatomic areas at differentstages as well. Our novel sparse coding strategy naturally accounts for the above mentioned neuroscience fact that one single brain region intend to be involved in multiplefunctional processes and thus its fMRI signal is composed of various components(functional networks). 2) Our sparse coding method can recognize multiple functionalnetworks simultaneously, including task-evoked networks, resting state networks andthose latent networks which are not necessarily following the task paradigm [7].This advancement is critical for constructing a comprehensive functional regulationprofiles in section 2.4.

Group-Wise Optimization of Common Brain Landmarks2.3719Initialization of Structural LandmarksWe adopted a widely used data-driven strategy, named DICCCOL [6], to initialize thelandmarks which are needed to be optimized. Each of the 358 DICCCOL landmarkswas optimized to possess maximal group-wise consistency of DTI-derived fiber shapepatterns [6]. In this work, we applied DICCCOL prediction procedure which is similar to its optimizations process [6]: we only need to optimize the new individual toensure the maximal consistency of structural connectivity patterns is satisfied betweenthe subject that is needed to be predicted and the provided models. Briefly, the initialization process can be summarized as:E(,) (2)represents the DICCCOL models,is the new brain that needs to be prewheredicted,is defined as the trace-map distance [6]. In general, the DICCCOLlandmarks provide a reliable and neuroscience grounded foundation for further jointoptimization with both structural and functional regulations.2.4Group-wise Optimization under Joint Structural and Functional RegulationsAfter we have all 358 DICCCOL landmarks in the new brain, we can functionallylabel them using the functional network templates derived in section 2.2. We construct a functional regulation profile for each predicted DICCCOL landmark. Thisfunctional regulation profile is a binary vector with L-dimension and L is the numberof network templates. For example, if one DICCCOL landmark is located in the region of a specific template, the correspondingitem in the regulation vector will be 1, otherwisewill be 0. Through this way, the functional regulation profile can effectively encode the functional expression of every DICCCOL landmarkin individual space.Because the DICCCOL landmarks alreadypossess the most consistent structural connectivity across different populations, our primary ob- Fig. 2. Illustration of functionaljective is to maximize the functional homogenei- regulated optimization process usingty and minimize the potential affection to the two functional network templatesestablished structural consistency simultaneously. This process includes two steps: 1) Construction of the functional regulation model. Since for each subject and each DICCCOL landmark, we already achieved itsfunctional regulation profile through functional labeling. For each DICCCOL, weassemble all the functional profiles within the group (68 subjects) and do a simple butefficient voting for each template. Thus we arrive with a 358*L matrix. Here L is thenumber of functional network templates. Each element represents the subject numberthat in those subjects the current DICCCOL is consistently located in a specific functional template. The larger number means more individuals have agreement that thecurrent DICCCOL should belong to this functional network. In this work, we adopt a

720D. Zhu et al.relatively strict criterion that if more than half of the group individuals commit thistemplate, the corresponding matrix element will be considered as value 1 in the functional regulation model. 2) Optimization. In brief, using the predicted location as theinitial searching point, we move the DICCCOL landmark within a small neighborhood and examine if there exist an appropriate location at which the functional profiles become more consistent to the functional regulation model, and at the same timethe structural connectivity has not significant change. The neighborhood is defined asa circle with radius with 3mm because the average registration error is considered as6mm [6]. The basic idea is illustrated in Fig.2. The green bubble represents the initiallocation. According to its current functional regulation profile, the green one willmove to the neighboring locations that makes it more consistent to the functionalregulation model. For example, if its current functional profile is 0, 0 and the regulation model is 1, 0 , it will intend to move along the red arrow. Otherwise, it willmove to the other two directions or stay at the initial location given the regulationmode as 0, 0 . It should be noted that this optimization process is performed withthe structural constraints, which can effectively preserve the already established structural consistency through DICCCOL prediction.The overall optimize function is summarized as:E ɸ(,)· (3)Here and represent the initial location and the candidate location need to be examined, respectively. FR is the functional regulation vector., is the trace-mapdistance between the candidate location and the initial location. ɸ (, ) is definedas:ɸ( 1, if ,) ơ, if ơ ơ(4)Here ơ is the standard deviation of the group-wise trace-map distance of the predictedDICCCOL landmarks.Intuitively, if the structural connectivity does not change much, the functional regulation item will be the driving force for the optimization process. If not, the functional regulation item will be penalized that the DICCCOL landmark will be inclinedto stay at the initial location to maintain its already established structural consistency.This process will be applied to each DICCCOL landmark separately and eventuallywe can achieve the optimized landmarks, which reflect both the structural and functional cons