High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity

“Several recent techniques (Tuch et al., 2002; Tuch et al., 2003; Jansons and Alexander, 2003; Tournier et al., 2004; Liu et al., 2004; Alexander, 2005; Hosey et al., 2005; Van Wedeen et al., 2005) have been proposed that aim to describe local diffusion within an imaging voxel without imposing the Gaussian constraint c…”

“For example, if one assumes that within a voxel there are two or more relatively coherent fiber populations with different orientations, onemay extend the simple tensormodel by summing up the contributions of multiple tensors (Liu et al., 2004; Tuch et al., 2002).”

“Use of higher-resolution imaging and of analysis approaches that explicitly model complex fiber structures within a voxe”

“Unfortunately, the diffusion tensor model is not always adequate, particularly in voxels containing contributions from differently oriented fibre bundles (Alexander et al., 2002; Frank, 2002; Tuch et al., 2002; Behrens et al., 2007).”

“Among such strategies, the direct processing (bypassing the tensor calculation) of diffusion-weighted images acquired with a high angular resolution (through diffusion measurements along many directions) has proved successfu”

“Areas of tissue partial volume (where white/gray matter or white matter/CSF reside in the same pixel) or of white matter partial volume (where two fiber systems cross the same pixel often in different orientations) are examples of where the DTI model will fail (Papadakis et al. 2002; Tuch et al. 2002; Jansons and Alex…”

“First, voxels are selected for which the fractional anisotropy (FA) derived with DTI exceeds a threshold value (FA N 0.7), as these voxels are deemed to contain a single, clearly defined fibre orientation.”

“Due to their practical mathematical properties, there have been several proposals using spherical harmonics to describe the apparent diffusion coefficient (ADC) computed from HARDI, starting from the work of Frank (2001, 2002) and Alexander et al. (2002) and Tuch et al. (2002).”

“This acquisition sequence now forms the basis of most higher-order fiber orientation estimation algorithms (Tuch et al., 2002; Jansons and Alexander, 2003; Tournier et al., 2004, 2011; Tuch, 2004; Alexander and Barker, 2005; Alexander, 2005; Anderson, 2005; Özarslan et al., 2006; Dell’Acqua et al., 2007; Tournier, 201…”

“alx l [25]”

“The diffusion sampling schemes included the HARDI-253 (shell scheme) and DSI-203 (grid scheme) schemes that were previously documented in an optimization study [35].”

“With recent advances in high-angular resolution diffusion imaging (HARDI) [Tuch et al., 2002], it is now possible to reliably extract fiber orientations in regions of increased complexity [Alexander, 2006; Tournier et al.”

“…spectrum imaging (DSI), an essentially model-free imaging approach that has the ability to map complex fibre architecture at the scale of single MRI voxels (Tuch et al., 2002; Wedeen et al., 2005; Wedeen VJ, Wang RP, Schmahmann JD, Benner T, Tseng WYI, D’Arcuiel H et al. submitted for publication).”

“These model-based methods include the multiple Gaussian model [9]–[11], generalized diffusion tensor [12], [13], spherical harmonic decomposition [14], continuous axially symmetric tensors [15],”

“…to alternative strategies of diffusion encoding, many methods of high angular resolution diffusion encoding have now been reported in the literature including the present method DSI (Wedeen et al., 2005), as well as Q-ball imaging (Tuch et al., 2002) and HARDI imaging (Parker and Alexander, 2005).”

“Its anisotropy is also typically fixed (90,97,127), although some implementations allow the anisotropy to vary (127,130).”

“The WU-Minn consortium, however, decided instead to use the high-angular resolution diffusion imaging (HARDI) approach (Tuch et al., 2002) but modified to incorporate multiple shells of b values (Caruyer et al., 2011; Sotiropoulos et al., 2013a).”

“…1977; Stehling et al., 1991; Turner et al., 1991; Nana et al., 2008) the typical strategy employed to reduce this sensitivity (Stehling et al., 1991; Turner et al., 1991; Nana et al., 2008); however, alternative sequences, such as Fast Spin Echo (FSE) (Seifert et al., 2000; Pipe et al., 2002),…”

“Despite the success of the ball & stick model in resolving fibre crossings in HARDI datasets (Behrens et al., 2007), the employed kernel R can capture only monoexponential decay of the signal in q-space.”

“9 shows the same but for the two-fiber data modeled by a dual tensor (Inglis et al., 2001; Tuch et al., 2002) and CHARMED framework with one hindered and two restricted compartments.”

“Moreover, higher angular data can be used to solve the problem of fiber crossings, and to guide fiber tracking in areas where the anisotropy is low, and where uncertainty exists with respect to the major direction of diffusion (Tuch et al., 2002; Frank, 2002).”

“However, Dyrby et al. (55) found that someHARDImethods, such as Q-ball showed optimal tractography results with higher bvalues.”

“Unlike previous multishell HARDI acquisitions, all three variables of the PGSE sequence (gradient strength |G|, pulse width δ, and separation Δ) vary between different shells, which provides the sensitivity to axon diameter.”

“…2009; Behrens et al., 2003b; Johansen-Berg et al., 2004; Tomassini et al., 2007) and (b) (Johansen-Berg et al., 2008). diffusion, and estimate these directions (as well as the number of such directions) from the diffusion data (Assaf et al., 2004; Parker and Alexander, 2003; Tuch et al., 2002).”

“Acquisition techniques such as high angular resolution diffusion imaging (HARDI)(Tuch et al., 2002) and diffusion spectrum imaging (DSI)(Wedeen et al.”

“The method is based on the assumption that the measured HARDI signal can be expressed as the convolution over spherical coordinates of a single canonical fibre response function with the fibre orientation distribution (FOD).”

“A simple evolution of DTI was proposed by Behrens et al. (2003) to distinguish between water molecules that diffuse inside and around the axons, which are modeled as ideal cylinders with zero radius, and those moving freely with isotropic diffusion.”

“To address this issue, a number of approaches have recently been proposed to estimate fibre orientations robustly in the presence of partial volume effects (Tuch, 2004; Wedeen et al., 2005; Jansons and Alexander, 2003; Özarslan et al., 2006; Tuch et al., 2002; Hosey et al., 2005; Behrens et al., 2007; Anderson, 2005;…”

“, 2002), based on non-tensor models (Frank, 2001; Tuch et al., 2002), would be necessary.”

“However, the diffusion tensor is not able to fully describe crossing of the fiber tracts.(12,13) The popularity of DTI has been enormous.”

“To satisfy these purposes, studies have been conducted using affine transform (Jones et al., 2002; Mori et al., 2008; Muller et al., 2007) or nonlinear transformation (Ardekani and Sinha, 2006;Goodlett et al., 2006; Park et al., 2003; Penget al., 2009; VanHecke et al., 2008; Xu et al., 2003; Zhang et al., 2006, 2011).”

“In voxels containing n different fiber directions, a multi-Gaussian model is more appropriate (Alexander et al., 2001, 2002; Frank, 2002; Tuch et al., 2002): S ˆ k k; b À Á ¼ S 0 ð Þ X n i ¼ 1 a i exp À b ˆ k k T D i ˆ k k à :  ð3Þ We use a spherical harmonic (SH) model of d(k) to identify voxels…”

“High angular resolution diffusion imaging and diffusion spectrum imaging both attempt to deal with the misidentification of pathways due to crossing fibres (Tuch et al., 2002; Tuch, 2004; Wedeen et al., 2005, 2008; Schmahmann et al., 2007; Lazar, 2010).”

“Techniques that can resolve multiple axon directions within a single voxel (43), such as q-ball imaging, may solve the problem of white matter fiber crossings, as well as white matter insertions into the cortex (44).”

“…from its earliest origins (Basser et al., 1994, 2000; Jones et al., 1999; Le Bihan et al., 1986) with many advances in acquisition, e.g. HARDI (Tuch et al., 2002) and analysis (Behrens et al., 2007; Canales-Rodríguez et al., 2010a, 2010b; Jbabdi et al., 2007; Lazar et al., 2003; Mori et al.,…”

“…• the " BallStick " model (Behrens et al., 2003), • the " Bizeppelin " model (Alexander and Barker, 2005; Parker and Alexander, 2003; Peled et al., 2006; Tuch et al., 2002), which is a three-dimensional analogue of the biexponential model (Clark and Le Bihan, 2000; Niendorf et al., 1996) •…”

“…of diffusion (diffusivity), the directionality of the motion (anisotropy) and the principal orientation(s) of diffusion for each voxel (Jansons and Alexander, 2003; Pierpaoli et al., 1996; Pierpaoli and Basser, 1996; Tournier et al., 2004; Tuch et al., 2002, 2003; Tuch, 2004) may be calculated.”

“Many of these higher order models rely on data acquired using so-called high-angular-resolution diffusion-weighted imaging (HARDI) (12), whereby a relatively large number of diffusion-weighted (DW) images are acquired with the same b value, each sensitised to diffusion along a distinct direction so as to sample orient…”

“Therefore, the TDI method benefits from the use of so-called high angular resolution diffusion imaging (HARDI) data (Tuch et al., 2002).”

“It has been shown that the diffusivity profile has a complicated structure in voxels with orientational heterogeneity (von dem Hagen and Henkelman, 2002; Tuch et al., 2002).”

“Thus, an alternative approach based on sampling only on one or multiple spherical shells in q-space has been proposed, referred to as high angular resolution diffusion imaging (HARDI) (2).”

“However, in voxels containing multiple fiber orientations, this model has been shown to be inadequate [Alexander et al., 2002; Frank, 2001, 2002; Tuch et al., 2002].”

“Even in WM, the DTI model can fail if the tissue contains substantial crossing or diverging fibers (7).”

“DT imaging is based on a very limited sampling of q-space, and the resulting ellipsoids rely on several assumptions regarding the properties of diffusion in a voxel (49,55).”

“…methods can identify more than one fibre population within a voxel, but again require the use of an explicit model of the multi-fibre population, and to date have not shown the capability to distinguish more than two fibre populations per voxel (Tuch et al. 2002; Parker & Alexander 2003a,b).”

“Fibre orientation distribution Registration Spatial normalisation HARDI Diffusion MRI Registration of diffusion-weighted images is an important step in comparing white matter fibre bundles across subjects, or in the same subject at different time points.”

“…methods were applied to the human brain in vivo (Basser et al., 1994; Pierpaoli and Basser, 1996; Beaulieu, 2002; Conturo et al., 1999; Hagmann et al., 2003; Schmahmann et al., 2007; Naidich et al., 2008; Mori and Zhang, 2006; Johansen-Berg and Rushworth, 2009; Tuch et al., 2002, 2003; Tuch, 2004).”

“Methods to enhance spatial [40,42,43] and angular [84,85] resolution will be necessary to fully exclude concerns about eddy current and susceptibility artifact distortions.”

“[10] and solve for d , recalling that dK1 I:dA and Eq.”

“As the number of angular samples increases (for example, in Q-Ball imagin”

“Another advanced technique that could be used to circumvent the problem may be the high-angular-resolution diffusion imaging technique, which has the potential to resolve multiple fiber orientations within a single voxel.(27) It would be ideal if a simple coefficient could be defined that could correct for the differe…”

“The orientational neuroarchitecture can be inferred from DTI, but it is inadequate to resolve the heterogeneity within a voxel (Tuch et al., 2002).”

“q-ball imaging (Descoteaux et al., 2007; Tuch, 2004; Tuch et al., 2002; Tuch et al., 2003), spherical deconvolution (Anderson, 2005; Dell'Acqua et al.”

“First, in contrast to gray-matter, white-matter tracts can cross each other, thereby mixing the signal from different functional systems in the same locations (Alexander et al., 2001, 2002; Tuch et al., 2002; Tournier et al., 2004).”

“Tuch (2002) formalises the tractography problem also as a global optimum search, in terms of maximising the likelihood of the data [as given by diffusion spectrum imaging (Tuch et al., 2002)].”

“Acquisition protocols, such as high angular resolution diffusion-weighted imaging (HARDI) (Tuch et al., 2002) and diffusion spectrum imaging (DSI) (Wedeen et al., 2005, 2008), extract more information from the diffusion-weighted signal and can resolve crossing fibers within voxels.”

“HARDI measures diffusion along n uniformly distributed directions on the sphere and can characterize more complex fiber geometries, where the acquired number of diffusion gradient directions is greater than that for DTI.”

“Recent techniques involving high angular resolution DT-MRI [Tuch, 2004; Tuch et al., 2002] could be used to solve the fiber crossing problem and might show more accurate mapping of CC topography in the lateral regions.”

“, 2000), but studies have also shown that FA is susceptible to the partial volume of crossing fibers (Alexander et al., 2001, Alexander et al., 2002; Oouchi et al., 2007; Tuch et al., 2002; Yendiki et al., 2013).”

“For example, [4] found the general multitensor model to be unstable for three or more components using data”

“, 2005a), HARDI (Tuch et al., 2002), q-space imaging (King et al.”

“Due to the relatively large voxel size, voxels may contain several different fiber tracts, and models that handle multiple fiber orientations within a voxel have been proposed [11], [12], [19].”

“We used methods that estimate the orientation of crossing fibres to avoid the limitations of single tensor tractography (Alexander et al., 2002; Tuch et al., 2002; Parker and Alexander, 2003; Tournier et al., 2004; Parker and Alexander, 2005).”

“In order to better describe the complexity of water motion, a clinically feasible approach, high angular resolution diffusion imaging (HARDI), has been proposed by Tuch et al [43, 40].”

“…(DTI) (Basser et al., 1994) and related methods such as q-ball imaging (Tuch, 2004), tensor-mixture models (Alexander, 2005; Assaf et al., 2004; Tuch et al., 2002), PASMRI (Jansons and Alexander, 2003) and spherical deconvolution (Frank, 2002; Tournier et al., 2004) quantify water-diffusion…”

“Solutions to these problems become more applicable in the form of multiple tensor field regularization (Tuch et al., 2002; Pasternak et al., 2005) and mutual information image registration procedures (Horsfield, 1999; Rohde et al.”