Graph-partitioned spatial priors for functional magnetic resonance images.
Spatial models of functional magnetic resonance imaging (fMRI) data allow one to estimate the spatial smoothness of general linear model (GLM) parameters and eschew pre-process smoothing of data entailed by conventional mass-univariate analyses. Recently diffusion-based spatial priors [Harrison, L.M., Penny, W., Daunizeau, J., and Friston, K.J. (2008). Diffusion-based spatial priors for functional magnetic resonance images. NeuroImage.] were proposed, which provide a way to formulate an adaptive spatial basis, where the diffusion kernel of a weighted graph-Laplacian (WGL) is used as the prior covariance matrix over GLM parameters. An advantage of these is that they can be used to relax the assumption of isotropy and stationarity implicit in smoothing data with a fixed Gaussian kernel. The limitation of diffusion-based models is purely computational, due to the large number of voxels in a brain volume. One solution is to partition a brain volume into slices, using a spatial model for each slice. This reduces computational burden by approximating the full WGL with a block diagonal form, where each block can be analysed separately. While fMRI data are collected in slices, the functional structures exhibiting spatial coherence and continuity are generally three-dimensional, calling for a more informed partition. We address this using the graph-Laplacian to divide a brain volume into sub-graphs, whose shape can be arbitrary. Their shape depends crucially on edge weights of the graph, which can be based on the Euclidean distance between voxels (isotropic) or on GLM parameters (anisotropic) encoding functional responses. The result is an approximation the full WGL that retains its 3D form and also has potential for parallelism. We applied the method to high-resolution (1 mm(3)) fMRI data and compared models where a volume was divided into either slices or graph-partitions. Models were optimized using Expectation-Maximization and the approximate log-evidence computed to compare these different ways to partition a spatial prior. The high-resolution fMRI data presented here had greatest evidence for the graph partitioned anisotropic model, which was best able to preserve fine functional detail.
Harrison
L M
LM
Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London, WC1N 3BG UK. l.harrison@fil.ion.ucl.ac.uk
Penny
W
W
Flandin
G
G
Ruff
C C
CC
Weiskopf
N
N
Friston
K J
KJ
D000465:Algorithms; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D005074:Evoked Potentials, Visual / Q000502:physiology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D008959:Models, Neurological; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique; D014793:Visual Cortex / Q000502:physiology*
Med Image Comput Comput Assist Interv. 2006;9(Pt 2):831-8
17354850
Neuroimage. 2007 Feb 1;34(3):1160-70
17150376
Biometrics. 2001 Jun;57(2):554-62
11414583
Annu Rev Biomed Eng. 2000;2:315-37
11701515
J Neurophysiol. 2007 Feb;97(2):1495-502
17135475
Neuroimage. 2008 Jun;41(2):408-23
18387821
Neuroimage. 2005 Jun;26(2):635-41
15907321
Neuroimage. 2004 Nov;23(3):1203-16
15528120
Neuroimage. 2005 Jul 1;26(3):839-51
15955494
Neuroimage. 2004 Apr;21(4):1300-19
15050557
IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1768-83
17063682
IEEE Trans Pattern Anal Mach Intell. 2007 Nov;29(11):1873-90
17848771
IEEE Trans Med Imaging. 2004 Feb;23(2):213-31
14964566
Neuroimage. 2000 Jun;11(6 Pt 1):656-67
10860794
Science. 2000 Dec 22;290(5500):2319-23
11125149
IEEE Trans Med Imaging. 2001 Jan;20(1):45-57
11293691
Neuroimage. 2003 Jul;19(3):1240-9
12880849
Hum Brain Mapp. 2006 Aug;27(8):678-93
16281292
IEEE Trans Med Imaging. 2003 Apr;22(4):504-14
12774896
IEEE Trans Pattern Anal Mach Intell. 2006 Mar;28(3):469-75
16526432
Neuroimage. 2005 Jan 15;24(2):350-62
15627578
IEEE Trans Med Imaging. 1996;15(4):429-42
18215925
IEEE Trans Med Imaging. 2006 Oct;25(10):1380-91
17024841
IEEE Trans Med Imaging. 1997 Dec;16(6):878-86
9533587
Neuroimage. 2007 Feb 1;34(3):1108-25
17157034
Hum Brain Mapp. 1996;4(1):58-73
20408186
Science. 2007 Aug 24;317(5841):1079-83
17717184
Hum Brain Mapp. 2007 Apr;28(4):275-93
17133400
Neural Netw. 2002 Dec;15(10):1223-41
12425440