A flocking based method for brain tractography Ramon Aranda a,⇑ , Mariano Rivera a , Alonso Ramirez-Manzanares b a Department of Computer Science, Centro de Investigacion en Matematicas (CIMAT), A.C., Guanajuato, Gto 36240, Mexico b Department of Mathematics, University of Guanajuato, Guanajuato, Gto 36000, Mexico article info Article history: Received 25 November 2012 Received in revised form 5 November 2013 Accepted 25 January 2014 Available online 10 February 2014 Keywords: Tractography Diffusion tensor Stochastic walks Anatomical brain connectivity Flocking abstract We propose a new method to estimate axonal fiber pathways from Multiple Intra-Voxel Diffusion Orien- tations. Our method uses the multiple local orientation information for leading stochastic walks of par- ticles. These stochastic particles are modeled with mass and thus they are subject to gravitational and inertial forces. As result, we obtain smooth, filtered and compact trajectory bundles. This gravitational interaction can be seen as a flocking behavior among particles that promotes better and robust axon fiber estimations because they use collective information to move. However, the stochastic walks may gener- ate paths with low support (outliers), generally associated to incorrect brain connections. In order to eliminate the outlier pathways, we propose a filtering procedure based on principal component analysis and spectral clustering. The performance of the proposal is evaluated on Multiple Intra-Voxel Diffusion Orientations from two realistic numeric diffusion phantoms and a physical diffusion phantom. Addition- ally, we qualitatively demonstrate the performance on in vivo human brain data. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction White matter tractography is a technique that estimates neuro- nal tract pathways to determine both the structure and the con- nectivity of the brain. The existence of the neural tracts had only been demonstrated by histochemical and biological techniques in post-mortem specimens. Many white matter structures have been well documented in anatomic studies, for instance see Williams et al. (1997). However, the brain tracts are not well identified by direct examination of computed tomography scans or regular Mag- netic Resonance Imaging (MRI). This explains the poorly under- stood white matter functions and the inaccurate description of the neuro-anatomical atlas based on those technologies. The neural-tract structure estimation in vivo is one of the most important goals in neuroimaging, as it provides information on normal human brain development and about some neurological diseases; e.g., strokes, multiple sclerosis, epilepsy, neurodegenera- tive diseases and spinal cord disorders (Clark et al., 2000; Mukher- jee et al., 2000; Sotak, 2002; Ciccarelli et al., 2008). It can also be used to investigate the spectrum of neuropsychiatric disorders; e.g., language problems and reading disability (Klingberg et al., 2000; Catani et al., 2005). Recently, brain planning surgery procedures take into account the white matter tracts that are at risk in an intervention (Romano et al., 2009; Castellano et al., 2012). Neural tracts for in vivo human brain can indirectly be esti- mated by using the Diffusion-Weighted (DW) modality of MRI. These images provide information about the local brain structure by measuring the molecular water diffusion at local points of the brain. The most popular parametric model for representing and analyzing DW-MR signals is the Diffusion-Tensor MRI [DT-MRI, Basser et al. (1994)]. However, the DT-MRI provides only one Prin- cipal Diffusion Direction (PDD) per voxel and this estimation is insufficient to explain the brain structure at fiber crossings or bifurcations. For this reason, more sophisticated models for esti- mating Multiple Intra-Voxel Diffusion Orientations (MIVDO) have been proposed; see for instance the works of: Tuch et al. (2002) (Diffusion Multi-Tensor), Behrens et al. (2003) (Ball-and-Stick), Tuch (2004) (Q-Ball), Wedeen et al. (2005) (Diffusion Spectrum Imaging), Ramirez-Manzanares et al. (2007) (Diffusion Basis Functions), Tournier et al. (2007) (Spherical Deconvolution), Kaden et al. (2007) (Parametric Spherical Deconvolution), Scherrer and Warfield (2012) (CUSP-MFM), Zhang et al. (2012) (NODDI), Sotiropoulos et al. (2012) (Ball and Rackets), among others. Once the intra-voxel structure is estimated at each voxel of a DW- MRI volume, one can try to estimate the neural tract pathways and to determine connectivity information. The accurate computation of the brain connectivity relies completely on the accurate estimation of the cerebral tract pathways. For this reason, in this paper we propose a http://dx.doi.org/10.1016/j.media.2014.01.009 1361-8415/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Address: Department of Computer Science, Centro de Investigacion en Matematicas (CIMAT), A.C., Jalisco S/N, Col. Valenciana, Guanaju- ato, Gto 36240, Mexico. Tel.: +52 473 732 7155/735 0800x730; fax: +52 473 732 5749. E-mail address: arac@cimat.mx (R. Aranda). Medical Image Analysis 18 (2014) 515–530 Contents lists available at ScienceDirect Medical Image Analysis journal homepage: www.elsevier.com/locate/media