A Geometry-Based Particle Filtering Approach to White Matter Tractography

Abstract

Abstract. We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a 'streamline flow' using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows for a robust inference of local tract geometry, which, in the context of the causal filter estimation, guides tractography through regions with partial volume effects. We validate the method on synthetic data and present results on two types in vivo data: diffusion tensors and a spherical harmonic reconstruction of the fibre orientation distribution function (fODF).

Tracking and validation techniques for topographically organized tractography

“…Acknowledging the limitations of the noisy, low resolution dMRI data, there has been a shift towards addressing the uncertainty. This lead to several propagation or walker based solutions including techniques based on (i) front evolution and marching methods (Parker et al, 2002; Tournier et al, 2003; Kang et al, 2005; Pichon et al, 2005; Jackowski et al, 2005; Prados et al, 2006; Li et al, 2014), (ii) probabilistic and combinatorial techniques based on random walks and various sampling schemes (Bjrnemo et al, 2002; Behrens et al, 2003; Hagmann et al, 2003; Parker et al, 2003; Lu et al, 2006; Friman et al, 2006; Behrens et al, 2007; Lifshits et al, 2009; Descoteaux et al, 2009; Tournier et al, 2012; Jeurissen et al, 2014), (iii) Kalman filtering (Gössl et al, 2002; Malcolm et al, 2009, 2010), (iv) bootstrap methods (Lazar and Alexander, 2005; Jones, 2008; Jeurissen et al, 2011; Vorburger et al, 2013; Campbell et al, 2014; Jeurissen et al, 2011), (v) graph theoretical techniques (Iturria-Medina et al, 2007; Sotiropoulos et al, 2010) and (vi) particle filtering (Zhang et al, 2009; Savadjiev et al, 2010; Pontabry et al, 2013; Stamm et al, 2013; Rowe et al, 2013). Simultaneous to these efforts, there have been several creative approaches proposed for a global solution using (i) fast marching methods and geodesics (Parker et al, 2002; O’Donnell et al, 2002; Campbell et al, 2005; Jbabdi et al, 2007a; Zalesky, 2008; Péchaud et al, 2009; Hageman et al, 2009; Lenglet et al, 2009) (ii) spin glass models (Mangin et al, 2002; Fillard et al, 2009) (iii) Bayesian model (Jbabdi et al, 2007b) (iv) Gibbs sampling (Kreher et al, 2008; Reisert et al, 2011) (v) Hough transform (Aganj et al, 2011) and (vi) ant colony optimization (Feng and Wang, 2011).…”

An Improved Fiber Tracking Method for Crossing Fibers

“…The third synthetic data set was designed by Peter [15]. It contains 15 Â 30 Â 5 voxels and 162 gradient directions with b = 1500 s/mm 2 .…”

Probabilistic tractography using Q-ball imaging and particle filtering: Application to adult and in-utero fetal brain studies

“…The interpolated spherical functions on the boundaries may not be correct. In this work, a mask has been used to prevent the particles going out the white matter, which is a common strategy Savadjiev et al, 2010).…”

“…These local deterministic approaches can be affected by the accumulation of errors and influenced by local irregularities in the diffusion data. A way to avoid such issues is to consider a filtering approach Savadjiev et al, 2010). Another way to avoid such issues is to use a global framework for optimal trajectory estimation (Fillard et al, 2009;Jbabdi et al, 2007;Lifshits et al, 2009;Parker et al, 2002;Staempfli et al, 2006;Wu et al, 2009).…”