{"title": "Individualized ROI Optimization via Maximization of Group-wise Consistency of Structural and Functional Profiles", "book": "Advances in Neural Information Processing Systems", "page_first": 1369, "page_last": 1377, "abstract": "Functional segregation and integration are fundamental characteristics of the human brain. Studying the connectivity among segregated regions and the dynamics of integrated brain networks has drawn increasing interest. A very controversial, yet fundamental issue in these studies is how to determine the best functional brain regions or ROIs (regions of interests) for individuals. Essentially, the computed connectivity patterns and dynamics of brain networks are very sensitive to the locations, sizes, and shapes of the ROIs. This paper presents a novel methodology to optimize the locations of an individual's ROIs in the working memory system. Our strategy is to formulate the individual ROI optimization as a group variance minimization problem, in which group-wise functional and structural connectivity patterns, and anatomic profiles are defined as optimization constraints. The optimization problem is solved via the simulated annealing approach. Our experimental results show that the optimized ROIs have significantly improved consistency in structural and functional profiles across subjects, and have more reasonable localizations and more consistent morphological and anatomic profiles.", "full_text": "Individualized ROI Optimization via \n\nMaximization of Group -wise Consistency  of \n\nStructural and Functional Profiles  \n\n1, 2*Kaiming Li, 1Lei Guo, 3Carlos Faraco, 2Dajiang Zhu, 2Fan Deng, 1Tuo Zhang, 1Xi \n\nJiang, 1Degang Zhang, 1Hanbo Chen, 1Xintao Hu, 3Steve Miller, 2Tianming Liu \n1School of Automation, Northwestern Polytechnical University,China;2Department of \nComputer Science, the University of Georgia, USA;3Department of Psychology, the \n\nUniversity of Georgia, USA; *Email:likaiming@gmail.com \n\nAbstract \n\nFunctional segregation and integration are fundamental characteristics of the \nhuman  brain.  Studying  the  connectivity  among  segregated  regions  and  the \ndynamics of integrated brain networks has drawn increasing interest . A very \ncontroversial, yet fundamental issue in these studies is how to determine the \nbest  functional  brain  regions  or  ROIs  (regions  of  interests)  for  individuals. \nEssentially,  the  computed  connectivity  patterns  and  dynamics  of  brain \nnetworks  are  very sensitive to the locations, sizes,  and shapes of  the  ROIs. \nThis  paper  presents  a  novel  methodology  to  optimize  the  locations  of  an \nindividual's ROIs in the working memory system. Our strategy is to formulate \nthe individual ROI optimization as a group variance minimization problem, \nin  which  group-wise  functional  and  structural  connectivity  patterns,  and \nanatomic profiles  are defined as optimization constraints. The optimization \nproblem  is  solved  via  the  simulated  annealing  approach.  Our  experimental \nresults  show \nimproved \nconsistency  in  structural  and  functional  profiles  across  subjects,  and  have \nmore  reasonable  localizations  and  more  consistent  morphological  and \nanatomic profiles. \n\nthe  optimized  ROIs  have  significantly \n\nthat \n\n1  \n\nI n t ro d u c t i o n  \n\nThe human brain\u2019s function is segregated into distinct regions and integrated via axonal fibers \n[1].  Studying  the  connectivity  among  these  regions  and  modeling  their  dynamics  and \ninteractions has drawn increasing interest and effort from the brain imaging and neuroscience \ncommunities [2-6]. For example, recently, the Human Connectome Project [7] and the 1000 \nFunctional  Connectomes  Project  [8]  have  embarked  to  elucidate  large-scale  connectivity \npatterns  in  the  human  brain.  For  traditional  connectivity  analysis,  a  variety  of  models \nincluding  DCM  (dynamics  causal  modeling),  GCM  (Granger  causality  modeling)  and  MVA \n(multivariate autoregressive modeling) are proposed [6, 9-10] to model the interactions of the \nROIs. A fundamental issue in these studies is how to accurately identify the ROIs, which are \nthe structural substrates for measuring connectivity. Currently, this is still an open, urgent, yet \nchallenging  problem  in  many  brain  imaging  applications.  From  our  perspective,  the  major \nchallenges  come  from  uncertainties  in  ROI  boundary  definition,  the  tremendous  variability \nacross individuals, and high nonlinearities within and around ROIs.   \n\nCurrent approaches for identifying brain ROIs can be broadly classified into four categories. \nThe  first  is  manual  labeling  by  experts  using  their  domain  knowledge.  The  second  is  a \ndata-driven clustering of ROIs from the brain image itself. For instance, the ReHo  (regional \nhomogeneity) algorithm [11] has been used to identify regional homogeneous regions as ROIs. \nThe third is to predefine ROIs in a template brain, and warp them back to  the individual space \nusing image registration [12]. Lastly, ROIs can be defined from the activated regions observed \nduring  a  task-based  fMRI  paradigm.  While  fruitful  results  have  been  achieved  using  these \napproaches,  there  are  various  limitations.  For  instance,  manual  labeling  is  difficult  to \nimplement for large datasets and may be vulnerable to inter-subject and intra-subject variation; \n\n\fit  is  difficult  to  build  correspondence  across  subjects  using  data -driven  clustering  methods; \nwarping  template  ROIs  back  to  individual  space  is  subject  to  the  accuracy  of  warping \ntechniques and the anatomical variability across subjects. \n\nEven identifying ROIs using task-based  fMRI paradigms, which is  regarded as the standard \napproach  for  ROI identification,  is  still  an open question.  It  was  reported  in  [13] that  many \nimaging-related  variables  including  scanner  vender,  RF  coil  characteristics  (phase  array  vs. \nvolume coil), k-space acquisition trajectory, reconstruction algorithms, susceptibility -induced \nsignal  dropout,  as  well  as  field  strength  differences,  contribute  to  variations  in  ROI \nidentification.  Other  researchers  reported  that  spatial  smoothing,  a  common  preprocessing \ntechnique in fMRI analysis to enhance SNR, may introduce artificial localization shift s (up to \n12.1mm  for  Gaussian  kernel  volumetric  smoothing)  [14]  or  generate  overly  smoothed \nactivation maps that may obscure important details [15]. For example, as shown in Fig.1a, the \nlocal  maximum  of  the  ROI  was  shifted  by  4mm  due  to  the  spatial  smoothing  process. \nAdditionally, \nits  structural  profile  (Fig.1b)  was  significantly  altered.  Furthermore, \ngroup-based activation maps may show different patterns from an individual's activation map; \nFig.1c  depicts  such  differences.  The  top  panel  is  the  group  activation  map  from  a  working \nmemory study, while the bottom panel is the activation map of one subject in the study. As we \ncan  see  from  the  highlighted  boxes,  the  subject  has  less  activated  regions  than  the  group \nanalysis  result.  In  conclusion,  standard  analysis  of  task-based  fMRI  paradigm  data  is \ninadequate to accurately localize ROIs for each individual.    \n\n \n\nFig.1. (a): Local activation map maxima (marked by the cross) shift of one ROI due to  spatial \nvolumetric smoothing. The top one was detected using unsmoothed data while the bottom one \nused smoothed data (FWHM: 6.875mm). (b): The corresponding fibers for the ROIs in (a). The \nROIs are presented using a sphere (radius: 5mm). (c): Activation map differences between the \ngroup (top) and one subject (bottom). The highlighted boxes show two of the missing activated \nROIs found from the group analysis.  \n\nWithout accurate and reliable individualized ROIs, the validity of brain connectivity analysis, \nand  computational  modeling  of  dynamics  and  interactions  among  brain  networks ,  would  be \nquestionable. In response to this fundamental issue, this paper presents a novel computational \nmethodology  to  optimize  the  locations  of  an  individual's  ROIs  initialized  from  task-based \nfMRI. We use the ROIs identified in a block-based working memory paradigm as a test bed \napplication to develop and evaluate our methodology. The optimization of ROI locations was \nformulated  as  an  energy  minimization  problem,  with  the  goal  of  jointly  maximizing  the \ngroup-wise  consistency  of  functional  and  structural  connectivity  patterns  and  anatomic \nprofiles.  The  optimization  problem  is  solved  via  the  well-established  simulated  annealing \napproach. Our experimental results show that the optimized ROIs achieved our optimization \nobjectives and demonstrated promising results.               \n\n2  \n\nM a t e r i a l s   a n d   M e t h o d s  \n\n2 . 1  \n\nD a t a   a c q u i s i t i o n   a n d   p r e p r o c e s s i n g  \n\n\fTwenty-five university students were recruited to participate in \nthis study. Each participant performed an fMRI modified version \nof  the  OSPAN  task  (3  block  types:  OSPAN,  Arithmetic,  and \nBaseline)  while  fMRI  data  was  acquired.  DTI  scans  were  also \nacquired  for  each  participant.  FMRI  and  DTI  scans  were \nacquired on a 3T GE Signa scanner. Acquisition parameters were \nas follows : fMRI: 64x64 matrix, 4mm slice  thickness, 220mm \nFOV,  30  slices,  TR=1.5s,  TE=25ms,  ASSET=2;  DTI:  128x128 \nmatrix,  2mm  slice \nthickness,  256mm  FOV,  60  slices, \nTR=15100ms,  TE=  variable,  ASSET=2,  3  B0  images,  30 \noptimized gradient directions, b-value=1000). Each participant\u2019s \nfMRI  data  was  analyzed  using  FSL.  Individual  activation  map \nreflecting the OSPAN (OSPAN > Baseline) contrast was used. In \ntotal, we identified the 16 highest activated ROIs, including left \nand right insula, left and right medial frontal gyrus, left and right \nprecentral gyrus, left and right paracingulate gyrus, left and right \ndorsolateral prefrontal cortex, left and right inferior parietal lobule, left occipital pole, right \nfrontal pole, right lateral occipital gyrus, and left and right precuneus. Fig.2 shows the 16 ROIs \nmapped  onto  a  WM(white  matter)/GM(gray  matter)  cortical  surface.  For  some  individuals, \nthere  may  be  missing  ROIs  on  their  activation  maps.  Under  such  condition,  we  adapted  the \ngroup activation map as a guide to find these ROIs using linear registration.  \n\n \nFig.2. working memory \nROIs mapped on a \nWM/GM surface  \n \n\nDTI pre-processing consisted of skull removal, motion correction, and eddy current correction. \nAfter the pre-processing, fiber tracking was performed using MEDINRIA (FA threshold: 0.2; \nminimum fiber length: 20).  Fibers were extended along their tangent directions to reach into \nthe gray matter when necessary. Brain tissue segmentation was conducted on DTI data by the \nmethod  in  [16]  and  the  cortical  surface  was  reconstructed  from  the  tissue  maps  using  the \nmarching cubes algorithm. The cortical surface was parcellated into anatomical regions using \nthe HAMMER tool [17]. DTI space was used as the standard space from which to generate the \nGM  (gray  matter)  segmentation  and  from  which  to  report  the  ROI  locations  on  the  cortical \nsurface.  Since  the  fMRI  and  DTI  sequences  are  both  EPI  (echo  planar  imaging)  sequences, \ntheir  distortions  tend  to  be  similar  and  the  misalignment  between  DTI  and  fMRI  images  is \nmuch less than that between T1 and fMRI images [18]. Co-registration between DTI and fMRI \ndata was performed using FSL FLIRT [12]. The activated ROIs and tracked fibers  were then \nmapped onto the cortical surface for joint modeling. \n\n2 . 2  \n\nJ o i n t   m o d e l i n g   o f   a n a t o m i c a l ,   s t r u c t u r a l   a n d   f u n c t i o n a l   p r o f i l e s  \n\nDespite the high degree of variability across subjects, there are several aspects of regularity on \nwhich we base the proposed solution. Firstly, across subjects, the functional ROIs should have \nsimilar anatomical locations, e.g., similar locations in the atlas space. Secondly, these  ROIs \nshould  have  similar  structural  connectivity  profiles  across  subjects.  In  other  words,  fibers \npenetrating the same functional ROIs should have at least similar target regions across subjects. \nLastly,  individual  networks  identified  by  task-based  paradigms,  like  the  working  memory \nnetwork  we  adapted  as  a  test  bed  in  this  paper,  should  have  similar  functional  connectivity \npattern across subjects.  The neuroscience bases of  the  above premises include: 1) structural \nand  functional  brain  connectivity  are  closely  related  [19],  and  cortical  gyrification  and \naxongenesis processes are closely coupled [20]; Hence, it is reasonable to put these three types \nof information in a joint modeling framework. 2) \nExtensive studies have already demonstrated the \nexistence of a common structural and functional \narchitecture of the human brain [21, 22], and it \nmakes sense to assume that the working memory \nnetwork  has  similar  structural  and  functional \nconnectivity patterns across individuals.   \n\nBased  on  these  premises,  we  proposed  to \noptimize  the  locations  of  individual  functional \nROIs  by  jointly  modeling  anatomic  profiles, \nstructural  connectivity  patterns,  and  functional \nconnectivity patterns, as illustrated in Fig 3. The \n\nFig.3. ROIs optimization scheme.  \n \n\n \n\n\fgoal was to minimize the group-wise variance (or maximize group-wise consistency) of these \njointly modeled profiles. Mathematically, we modeled the group-wise variance as energy \n as \nfollows.  A  ROI  from  fMRI  analysis  was  mapped  onto  the  surface,  and  is  represented  by  a \ncenter vertex and its neighborhood. Suppose \ud835\udc45\ud835\udc56\ud835\udc57 is the ROI region \n on the cortical surface of \n identified in Section 2.1; we find a corresponding surface ROI region \ud835\udc46\ud835\udc56\ud835\udc57 so that the \nsubject \nenergy\n(contains energy from \n\n ROIs) is minimized:  \n\n subjects, each with \n\n\ud835\udc38 = \ud835\udc38\ud835\udc4e (\ud835\udf06\n\n\ud835\udc38\ud835\udc50\u2212\ud835\udc40\ud835\udc38\ud835\udc50\n\n\ud835\udf0e\ud835\udc38\ud835\udc50\n\n+ (1 \u2212 \ud835\udf06)\n\n\ud835\udc38\ud835\udc53\u2212\ud835\udc40\ud835\udc38\ud835\udc53\n\n\ud835\udf0e\ud835\udc38\ud835\udc53\n\n)                                           (1) \n\nwhere \n\nis  the  anatomical  constraint; \n\n is  the  structural  connectivity  constraint, \n\nand \n\nare  the  mean  and  standard  deviation  of \n\nin  the  searching  space;   \n\nis  the  functional \n\nconnectivity constraint, \n\nand \n\nare the mean and standard deviation of \n\nrespectively; \n\nis the number of ROIs in this paper. The details of these \n\nand is a weighting parameter between 0 and 1. If not specified, \nand \nenergy terms are provided in the following sections.   \n \n2 . 2 . 1   A n a t o m i c a l   c o n s t r a i n t   e n e r g y  \n\nis the number of subjects, \n\nAnatomical  constraint  energy\nis  defined  to  ensure  that  the \noptimized ROIs have similar anatomical locations in  the atlas \nspace  (Fig.4  shows  an  example  of  ROIs  of  15  randomly \nselected subjects in the atlas space). We model the locations for \nall  ROIs  in  the  atlas  space  using  a  Gaussian  model  (mean:  \n\ud835\udc40\ud835\udc4b\ud835\udc57 ,and  standard  deviation: \n).  The  model \nparameters were estimated using the initial locations obtained \nfrom Section 2.1. Let \n \n\nbe the center coordinate of region \n\nfor  ROI \n\nin the atlas space, then\n\nis expressed as  \n\n       \ud835\udc38\ud835\udc4e = {\n\n1\n\n\ud835\udc52\ud835\udc51\ud835\udc5a\ud835\udc4e\ud835\udc65\u22121     (\ud835\udc51\ud835\udc5a\ud835\udc4e\ud835\udc65\u22641)\n\n \n\nFig.4. ROI distributions \nin Atlas space.  \n \n\n(\ud835\udc51\ud835\udc5a\ud835\udc4e\ud835\udc65>1)                                               (2) \n\nwhere \n\n\ud835\udc51\ud835\udc5a\ud835\udc4e\ud835\udc65 = \ud835\udc40\ud835\udc4e\ud835\udc65 {  \u2016\n\n\ud835\udc4b\ud835\udc56\ud835\udc57\u2212\ud835\udc40\ud835\udc4b\ud835\udc57\n\n3\ud835\udf0e\ud835\udc4b\ud835\udc57\n\n\u2016 , 1 \u2264 \ud835\udc56 \u2264 \ud835\udc5b;  1 \u2264 \ud835\udc57 \u2264 \ud835\udc5a. }                   (3) \n\nUnder the above definition, if any\n\nis within the range of \n\nfrom the distribution model \n\ncenter\n\n,  the  anatomical  constraint  energy  will  always  be  one;  if  not,  there  will  be  an \n\nexponential  increase  of  the  energy  which  punishes  the  possible  involvement  of  outliers.    In \nother words, this energy factor will ensure the optimized ROIs  will not significantly deviate \naway from the original ROIs.  \n \n2 . 2 . 2   S t r u c t u r a l   c o n n e c t i v i t y   c o n s t r a i n t   e n e r g y  \nStructural  connectivity  constraint  energy\n\n is  defined  to  ensure  the  group  has  similar \n\nstructural  connectivity  profiles  for  each  functional  ROI,  since  similar  functional  regions \nshould have the similar structural connectivity patterns [ 19],  \n\n                         (4) \n\nwhere \n\n is the  connectivity pattern  vector  for ROI  of subject \n\n, \n\nis the  group  mean \n\nfor ROI \n\n, and \n\nis the inverse of the covariance matrix.  \n\nThe connectivity pattern vector \n\n is a fiber target  region distribution histogram. To  obtain \n\nthis histogram, we first parcellate all the cortical surfaces into nine regions ( as shown in Fig.5a, \nfour  lobes  for  each  hemisphere,  and  the  subcortical  region)  using  the  HAMMER  algorithm \n\nEjiEnmaEcEcEMcE\uf073cEfEfEMfE\uf073fE\uf06cnmaEjX\uf073jijXijSaEijX3jXsjXMcE111()()jjnmTcijCijCijECMCovcCM\uf02d\uf03d\uf03d\uf03d\uf02d\uf02d\uf0e5\uf0e5ijCjijCMj1Covc\uf02dijC\f[17].  A  finer  parcellation  is  available  but  not  used  due  to  the  relatively  lower  parcellation \naccuracy, which might render the histogram too sensitive to the parcellation result. Then, we \nextract fibers penetrating region \n, and calculate the distribution of the fibers\u2019 target cortical \n\nregions. Fig.5 illustrates the ideas.  \n \n\n \n\nFig.5.  Structural  connectivity  pattern  descriptor.  (a):  Cortical  surface  parcellation  using \nHAMMER  [17];  (b):  Joint  visualization  of  the  cortical  surface,  two  ROIs  (blue  and  green \nspheres), and fibers penetrating the ROIs (in red and yellow, respectively); (c): Corresponding \ntarget region distribution histogram of ROIs in Fig.5b. There are nine bins corresponding to the \nnine cortical regions.  Each bin contains the  number of fibers that penetrate the ROI and are \nconnected to the corresponding cortical region. Fiber numbers are normalized across subjects. \n\n2 . 2 . 3   F u n c t i o n a l   c o n n e c t i v i t y   c o n s t r a i n t   e n e r g y  \n\nFunctional connectivity constraint energy \n\nis defined to ensure each individual has similar \n\nfunctional connectivity patterns  for the working  memory system, assuming the human brain \nhas similar functional architecture across individuals [21].    \n\n\ud835\udc38\ud835\udc53 = \u2211 \u2016\ud835\udc39\ud835\udc56 \u2212 \ud835\udc40\ud835\udc39\u2016\n is the functional connectivity matrix for subject\n\n\ud835\udc5b\n\ud835\udc56=1\n\n                                                  (5) \nis the group mean of the \n, and \n\nHere, \n\ndataset. The connectivity between each pair of ROIs is defined using the Pearson correlation. \nThe matrix distance used here is the Frobenius norm.  \n\n2 . 3  \n\nE n e r g y   m i n i m i z a t i o n   s o l u t i o n  \n\nThe  minimization  of  the  energy  defined  in  Section  2.2  is  known  as  a  combinatorial \noptimization problem. Traditional optimization methods may not fit this problem, since there \nare two  noticeable  characteristics  in  this  application. First, we  do  not   know how  the energy \nchanges  with  the  varying  locations  of  ROIs.  Therefore,  techniques  like  Newton\u2019s  method \ncannot  be  used.    Second,  the  structure  of  search  space  is  not  smooth,  which  may  lead  to \nmultiple local minima during optimization. To address this p roblem, we adopt the simulated \nannealing (SA) algorithm [23] for the energy minimization. The idea of the SA algorithm is \nbased  on  random  walk  through  the  space  for  lower  energies.  In  these  random  walks,  the \nprobability of taking a step is determined by the Boltzmann distribution, \n\n                                                    (6) \n\nif\n\n, and \n\n when \n\n. Here, \ud835\udc38\ud835\udc56 and \ud835\udc38\ud835\udc56+1 are the system energies at solution \nconfiguration  \ud835\udc56  and  \ud835\udc56 + 1  respectively;  \ud835\udc3e is  the  Boltzmann  constant;  and  \ud835\udc47  is  the  system \ntemperature. In other words, a step will be taken when a lower energy is found. A step will also \nbe taken with probability \nif a higher energy is found. This helps avoid the local minima in \n\nthe search space.  \n\n 3  \n\nR e s u l t s  \n\nCompared  to  structural  and  functional  connectivity  patterns,  anatomical  profiles  are  more \n\nijSfEiFiFM1()/()iiEEKTpe+--=1iiEE\uf02b\uf03e1p\uf03d1iiEE\uf02b\uf0a3p\feasily affected by variability across individuals. Therefore, the anatomical constraint energy is \ndesigned to provide constraint only to ROIs that are obviously far away from  reasonableness.  \nThe reasonable range was statistically modeled by the localizations of ROIs warped into the \natlas space in Section 2.2.1. Our focus in this paper is the structural and functional profiles.  \n\n3 . 1  \n\nO p t i m i z a t i o n  u s i n g  a n a t o m i c a l  a n d   s t r u c t u r a l  c o n n e c t i v i t y  p r o f i l e s  \n\nIn this section, we use only anatomical and structural  connectivity profiles to optimize the \n\nlocations of ROIs. The goal is to check whether the structural constraint energy \n works as \nexpected. Fig.6 shows the fibers penetrating the right precuneus for eight subjects before (top \npanel) and after optimization (bottom panel). The ROI is highlighted in a red sphere for each \nsubject. As we can see from the figure (please refer to the highlighted yellow arrows), after \noptimization, the third and sixth subjects have significantly improved consistency with the rest \nof the group than before optimization, which proves the validity of the energy function Eq.(4).  \n\n \n\nFig.6. Comparison of structural profiles before and after optimization. Each column shows the \ncorresponding before-optimization (top) and after-optimization (bottom) fibers of one subject. \nThe ROI (right precuneus) is presented by the red sphere.  \n\n3 . 2  \n\nO p t i m i z a t i o n  u s i n g  a n a t o m i c a l  a n d  f u n c t i o n a l  c o n n e c t i v i t y  p r o f i l e s  \n\nIn this section, we  optimize the locations of ROIs using anatomical  and  functional profiles, \naiming to validate the definition of functional connectivity constraint energy\n. If this energy \n\nconstraint worked well, the functional connectivity variance of the working memory system \nacross  subjects  would  decrease.  Fig.7  shows  the  comparison  of  the  standard  derivation  for \nfunctional connectivity before (left) and after (right) optimization. As we can see, the variance \nis significantly reduced after optimization. This demonstrated the effectiveness of the defined \nfunctional connectivity constraint energy.  \n\nFig.7. Comparison of the standard derivation for functional connectivity before and after the \noptimization.   Lower values mean more consistent connectivity pattern cross subjects.   \n\n \n\ncEfE\f3 . 3  \ns t r u c t u r a l   p r o f i l e s  \n\nC o n s i s t e n c y   b e t w e e n   o p t i m i z a t i o n   o f   f u n c t i o n a l   p r o f i l e s   a n d  \n\n \n\n \n\nFig.8.  Optimization  consistency  between  functional  and  structural  profiles.  Top:  Functional \nprofile  energy  drop  along  with  structural  profile  optimization;  Bottom:  Structural  profile \nenergy  drop  along  with  functional  profile  optimization.  Each  experiment  was  repeated  15 \ntimes with random initial ROI locations that met the anatomical constraint.  \n\nThe  relationship  between  structure  and  function  has  been  extensively  studied  [24],  and  it  is \nwidely believed that they are closely related. In this section, we study the relationship between \nfunctional profiles and structural profiles by looking at how the energy for one of them changes \nwhile the energy of the other decreases. The optimization processes in Section 3.1 and 3.2 were \nrepeated  15  times  respectively  with  random  initial  ROI  locations  that  met  the  anatomical \nconstraint. As shown in Fig.8, in general, the functional profile energies and structural profile \nenergies are closely related in such a way that the functional profile energies tend to decrease \nalong with the structural profile optimization process, while the structural profile energies also \ntend to decrease as the functional profile is optimized. This positively correlated decrease of \nfunctional profile energy and structural profile energy not only proves the close relationship \nbetween  functional  and  structural  profiles,  but  also  demonstrates  the  consistency  between \nfunctional and structural optimization, laying down the foundation of the joint optimiza tion, \nwhose results are detailed in the following section.  \n\n3 . 4  \nc o n n e c t i v i t y   p r o f i l e s  \n\nO p t i m i z a t i o n   u s i n g  \n\na n a t o m i c a l ,  \n\ns t r u c t u r a l  \n\na n d  \n\nf u n c t i o n a l  \n\nIn this section, we used all the constraints in Eq. (1) to optimize the individual locations of all \nROIs  in  the  working  memory  system.  Ten  runs  of  the  optimization  were  performed  using \nrandom  initial  ROI  locations  that  met  the  anatomical  constraint.  Weighting  parameter \n \nequaled  0.5  for all these runs. Starting and ending temperatures  for the simulated annealing \nalgorithm  are  8  and  0.05;  Boltzmann  constant\n.  As  we  can  see  from  Fig.9,  most  runs \nstarted  to  converge  at  step  24,  and  the  convergence  energy  is  quite  close  for  all  runs.  This \nindicates that the simulated annealing algorithm provides a valid solution  to our problem.  \n\nBy visual inspection, most of the ROIs move to more reasonable and consistent locations after \nthe joint optimization.  As an example, Fig.10 depicts the location movements of the ROI in \nFig. 6 for eight subjects.  As we can see, the ROIs for these subjects share a similar anatomical \n\n\uf06c1K\uf03d\flandmark, which appears to be the tip of the upper bank of the  parieto-occipital sulcus. If the \ninitial ROI was not at this landmark, it  moved to the landmark after the optimization, which \nwas the case for subjects 1, 4 and 7. The structural profiles of these ROIs are very similar to \nFig.6. The results in Fig. 10 indicate the significant improvement of ROI locations achieved by \nthe joint optimization procedure.   \n\nFig.9.    Convergence  performance  of  the  simulated  annealing  .  Each  run  has  28  temperature \nconditions.  \n\n \n\n \n\nC o n c l u s i o n  \n\nFig.10.  The  movement  of  right  precuneus  before  (in  red  sphere)  and  after  (in  green  sphere) \noptimization  for  eight  subjects.  The  \"C\"-shaped  red  dash  curve  for  each  subject  depicts  a \nsimilar anatomical landmark across these subjects.  The yellow arrows in subject 1, 4 and 7 \nvisualized the movement direction after optimization.  \n \n4  \nThis  paper  presented  a  novel  computational  approach  to  optimize  the  locations  of  ROIs \nidentified  from  task-based  fMRI.  The  group-wise  consistency  of  functional  and  structural \nconnectivity  patterns,  and  anatomical  locations  are  jointly  modeled  and  formulated  in  an \nenergy  function,  which  is  minimized  by  the  simulated  annealing  optimization  algorithm. \nExperimental results demonstrate the optimized ROIs have more reasonable localizations, and \nhave significantly improved the consistency of structural and functional connectivity profiles \nand morphological and anatomic profiles across subjects. 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PNAS, 106(6):2035-40. 2009.   \n \n \n \n \n \n \n \n \n\n\f", "award": [], "sourceid": 549, "authors": [{"given_name": "Kaiming", "family_name": "Li", "institution": null}, {"given_name": "Lei", "family_name": "Guo", "institution": null}, {"given_name": "Carlos", "family_name": "Faraco", "institution": null}, {"given_name": "Dajiang", "family_name": "Zhu", "institution": null}, {"given_name": "Fan", "family_name": "Deng", "institution": null}, {"given_name": "Tuo", "family_name": "Zhang", "institution": null}, {"given_name": "Xi", "family_name": "Jiang", "institution": null}, {"given_name": "Degang", "family_name": "Zhang", "institution": null}, {"given_name": "Hanbo", "family_name": "Chen", "institution": null}, {"given_name": "Xintao", "family_name": "Hu", "institution": null}, {"given_name": "Steve", "family_name": "Miller", "institution": null}, {"given_name": "Tianming", "family_name": "Liu", "institution": null}]}