Synopsis

Diffusion magnetic resonance imaging is still the unique tool capable of probe the structure of the brain connectivity in vivo. Although some great advances have been made in the past decade, reconstructed tractograms often lack of anatomically accuracy. The introduction of anatomical priors has become a promise land to tackle this issue, so in this work, we propose a general spin-glass-based global tractography framework constrained by anatomical priors to better represent the sharp turns of fibers entering a gyrus and connecting to the pial surface.

Purpose

Diffusion magnetic resonance imaging remains the unique technique available to probe in-vivo the human brain structural connectivity. The introduction of probabilistic [1,2] or global methods tackle the underlying ill-posed problem of creating more realistic numerical fibers. Those global approaches allow to keep a low curvature between connections [3,4,5,6] but tractograms still remain poorly anatomically reliable and some proposals have been made to increase the anatomical priors level [7,8,9]. In this work, we propose a global spin-glass-based tractography algorithm constraining anatomically the spins direction to embrace sharp turns when entering gyri and connecting to the cortex.

Methods

MRI dataset – One subject of the CONNECT/Archi database [12] was used. This protocol includes a millimeter T1-weighted MPRAGE scan (TE=2.98ms/TR=2.3s), a HARDI dataset acquired at b=1500s/mm² using 60 diffusion directions (TE=117ms/TR=14s ) with a 1.7mm isotropic resolution and a fieldmap to correct susceptibility artifacts. The T1-weighted dataset was processed using Freesurfer [13] to infer the pial surface (81924 vertices). The DWI dataset was preprocessed using Connectomist [12] for artifacts correction, registration between DWI and T1, and computation of local CSD model (spherical harmonics order = 6, regularization factor = 0.006) [14].

Global tractography method – A novel tractography method was developed using a spin-glass model [3,4,5,6] with a non generative approach to seed spins. We initialize a set of spins (8 per voxel) uniformly distributed in a propagation domain defined robustly using a mask computed from T1-weighted data [15]. Initial spin directions are computed using a Gibb's sampler randomly choosing one of the most likely directions provided by the underlying diffusion model. The method was developed with a generic design allowing to use any diffusion model (DTI, Q-ball, CSD, SHORE...). As in [6], the optimization algorithm is composed of a connection energy imposing a low curvature between two connected spins and of a data attachment energy corresponding to -log(P(ps, ds)) where P is the probability stemming from the diffusion model at the spin position (p_s) and direction (d_s). The optimization process consists of randomly choosing between: connection, move, creation_and_connection or destruction (especially for isolated spins within the white matter). The modification type is randomly chosen using a predefined set of probabilities p_connect(0.45)/p_move(0.3)/p_{create_and_connect}(0.15)/p_destroy(0.10).

Embedded anatomical prior – Due to the poor resolution of DWI data, the spins direction within gyri cannot be accurately modeled by the underlying map of diffusion models. Following the approach of [11], we constrain the spins direction during the optimization process by the knowledge of the cortical surface distance (d) and the normal direction at the closest vertex of the cortex (d_n): d_s' = α * d_s + ( 1 – α ) * d_n. α is the regularization factor and d_s corresponds to the direction driven by a Gibb's sampler built from the probabilities of the underlying angular profile given by the chosen local model limited to the directions contained in a cone aligned with the former d_s and of aperture angle (20°). To get a direction equal to d_s when far from the cortex and equal to d_n when close to it, we used a sigmoid function: $$ψ(d) = 2 * exp( - λ d ) / ( 1 + exp( -λ d )$$

Results and Discussion

Figure 1 and 2 depict the initial spins configuration with and without the anatomical constraint in a gyrus region, showing the modification of the spins directions when adding the constraint. Figure 3 and 4 displays the results of the tracking using the global approach with and without the anatomical constraint. Whereas the global approach creates some rectilinear fibers mainly connecting the end of the gyrus but missing the sharp turns described in [16], the anatomically constrained one partially succeeds in reconstructing both fibers with low curvature far from the cortex and taking sharp turns when entering the gyrus or getting closer to the pial surface but still needs future improvements. Unlike [11] where the constraint is only performed during the initial seeding procedure, our anatomical constraint is active during the whole optimization process and at low computational cost. In addition, it was embedded in a global tractography approach, thus avoiding the pitfalls of “blind” deterministic and probabilistic streamlining methods.

Conclusion

Acknowledgements

This work was partially funded by the SAMENTA program of the French National Research Agency (ANR) - project HYPSY ANR-13-SAMA-0013

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