Section: New Results
Joint modelling of anatomical and functional features from neuroimaging data
Participants : Bertrand Thirion, Alan Tucholka, Pierre Fillard.
In this research axis, Parietal as performed or participated to several contributions that aim at better characterizing the anatomical structure of the brain, but also at unveiling the relationships that might exist between anatomical and functional information.
Modelling the anatomical connectivity of the brain: Global Tractography using an Adaptive Spin Glass Model
Tractography consists in recovering the main fibre tracts in the brain white matter, starting from the local information conveyed by diffusion MRI.
We have introduced a novel framework for global diffusion MRI tractography inspired from a previously proposed spin glass model [32] . The entire white matter fascicle map is parametrized by pieces of fibers called spins. Spins are encouraged to move and rotate to align with the main fiber directions, and to assemble into longer chains of low curvature. Furthermore, they have the ability to adapt their quantity in regions where the spin concentration is not sufficient to correctly model the data. The optimal spin glass configuration is retrieved by an iterative minimization procedure, where chains are finally assimilated to fibers. As a result, all brain fibers appear as growing simultaneously until they merge with other fibers or reach the domain boundaries. In case of an ambiguity within a region like a crossing, the contribution of all neighboring fibers is used to determine the correct axon pathway.
This framework was tested on a Magnetic Resonance phantom representing a 45° crossing and a real brain dataset. Notably, the framework was able to retrieve the triple crossing between the callosal fibers, the corticospinal tract and the arcuate fasciculus (Fig. 2 ).
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Identification of brain sulci
Sulci recognition is an essential topic for the accurate localization of brain structure and the comparison of anatomical information across subjects.
We have collaborated with researchers from LNAO (CEA, Neurospin) to the setting of automatic recognition algorithms. We have contributed to the study presented in [22] on the recognition of about 60 sulcal structures over a new T1 MRI database of 62 subjects. This was an extension of previous work that improved the localization model of sulci (SPAM). Given that this model is sensitive to the common space chosen during the group study, the focus of the current work consisted in refining this space using registration techniques. Reciprocally, knowing the sulcus-wise localization variability also benefits to normalization accuracy. This results in a consistent Bayesian framework to jointly identify and register sulci, with two complementary normalization techniques and their detailed integration in the model: a global rigid transformation followed by a piecewise rigid-one, sulcus after sulcus. This resulted in an improved sulci labeling quality, reaching a global recognition rate of 86%, together with a basic but robust registration technique.
Comparison of surface-based and volume-based analysis
Being able to detect reliably functional activity in a population of subjects is crucial in human brain mapping, both for the understanding of cognitive functions in normal subjects and for the analysis of patient data. The usual approach proceeds by normalizing brain volumes to a common 3D template. However, a large part of the data acquired in fMRI aims at localizing cortical activity, and methods working on the cortical surface may provide better inter-subject registration than the standard procedures that process the data in 3D. Nevertheless, few assessments of the performance of surface-based (2D) versus volume-based (3D) procedures have been shown so far, mostly because inter-subject cortical surface maps are not easily obtained.
We have presented in [27] a systematic comparison of 2D versus 3D group-level inference procedures, by using cluster-level and voxel-level statistics assessed by permutation, in random effects (RFX) and mixed-effects analyses (MFX). We found that, using a voxel-level thresholding, and to some extent, cluster-level thresholding, the surface-based approach generally detects more, but smaller active regions than the corresponding volume-based approach for both RFX and MFX procedures (see Fig. 3 ). Finally we showed that surface-based supra-threshold regions are more reproducible by bootstrap.
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Joint analysis of anatomical and functional features
We have taken part to a medical study where the joint analysis of functional and anatomical connectivity data was crucial to draw meaningful results [14] . We take this is as an incentive to provide more tools for the joint study of anatomical and functional features in neuroimaging studies.
The objective of the study was to examine the functional neuro-anatomy that could account for pure Gerstmann syndrome, which is the selective association of acalculia, finger agnosia, left-right disorientation, and agraphia. We used structural and functional neuroimaging at high spatial resolution in healthy subjects to seek a shared cortical substrate of the Grundstörung posited by Gerstmann, i.e., a common functional denominator accounting for this clinical tetrad. We construed a functional activation paradigm that mirrors each of the four clinical deficits in Gerstmann syndrome and determined cortical activation patterns. We then applied fiber tracking to diffusion tensor images and used cortical activation foci in the four functional domains as seed regions.
None of the subjects showed parietal overlap of cortical activation patterns from the four cognitive domains. In every subject, however, the parietal activation patterns across all four domains consistently connected to a small region of sub-cortical parietal white matter at a location that is congruent with the lesion in a well-documented case of pure Gerstmann syndrome. Our functional neuroimaging findings are not in agreement with Gerstmann's postulate of damage to a common cognitive function underpinning clinical semiology. Our evidence from intact functional neuro-anatomy suggests that pure forms of Gerstmann's tetrad do not arise from lesion to a shared cortical substrate but from intraparietal disconnection after damage to a focal region of sub-cortical white matter.
