Mathematical framework for simulating diffusion tensor MR neural fiber bundles

Abstract

White matter (WM) fiber tractography (i.e., the reconstruction of the 3D architecture of WM fiber pathways) is known to be an important application of diffusion tensor magnetic resonance imaging (DT-MRI). For the quantitative evaluation of several fiber-tracking properties, such as accuracy, noise sensitivity, and robustness, synthetic ground-truth DT-MRI data are required. Moreover, an accurate simulated phantom is also required for optimization of the user-defined tractography parameters, and objective comparisons between fiber-tracking algorithms. Therefore, in this study a mathematical framework for simulating DT-MRI data, based on the physical properties of WM fiber bundles, is presented. We obtained a model of a WM fiber bundle by parameterizing the various features that characterize this bundle. We then evaluated three different synthetic DT-MRI models using experimental data in order to test the proposed methodology, and to determine the optimum model and parameter settings for constructing a realistic simulated DT-MRI phantom. Diffusion tensor magnetic resonance imaging (DT-MRI) is currently the only method available to obtain quantitative information about the three-dimensional (3D) anisotropic diffusion of water molecules in biological tissue (1,2). This DT anisotropy reflects the presence of spatially oriented microstructures (e.g., neural fibers in the central nervous system), where the mobility of the diffusing particles is mainly determined by the fiber pathway (3). On the basis of this intrinsic property, which assumes that the orientation of the DT field matches the orientation of the corresponding underlying fiber system, DT-MRI has been applied in several studies to infer microstructural characteristics and obtain valuable diagnostic information regarding various neuropathological conditions. Excellent reviews on white matter (WM) and neuropsychiatric diseases can be found in Refs. 4 and 5.It is known that ambiguous results are obtained when DT-MRI is used to study regions in which WM fibers cross or multiple fibers merge (e.g., Ref. 6). In such regions, the second-rank DT model is incapable of describing multiple fiber orientations within an individual voxel. To overcome this problem, a number of new techniques have been proposed, such as high-angular-resolution diffusion-weighted imaging (HARDI) (7), Q-ball imaging (QBI) (8), diffusion spectrum imaging (DSI) (9), persistent angular structure (PAS) reconstruction (10), and generalized DT imaging (GDTI) (11). Although these recently developed techniques can provide more accurate and unambiguous results, for simplicity the focus in this paper is confined to classic DT-MRI.An important application of DT-MRI is the reconstruction of the 3D WM fiber network, which is referred to as DT tracking (DTT) or fiber tractography. This technique is based on the assumption that it can accurately retrieve the spatial information of the underlying fiber network, using the available diffusion information of the corresponding tensor field. DTT provides exciting...

Phantoms for diffusion-weighted imaging and diffusion tensor imaging quality control: a review and new perspectives

“…Some authors propose applying the ACR MRI head phantom to evaluate scanner parameters related to degradation of DWI and DTI images, such as SNR, low contrast detectability and uniformity (Wang et al, 2011). Computational phantoms can also contribute to QC of DWI and DTI image processing algorithms, being useful to evaluate tractography based on High-Resolution Angle Diffusion Imaging (HARDI), Q-Ball and Diffusion Spectral Imaging (DSI), applicable to analysis of crossing fibers in a voxel (Leemans et al, 2005).…”

On the Reliability of Diffusion Neuroimaging

“…Thereby, tracts are defined by circular helixes. A mathematical framework for simulating the partial volume between fiber and background tissue has been proposed in (Leemans et al, 2005). The authors obtain a model of a fiber bundle by parameterizing the various features which characterize the bundle.…”

“…Next, we resample the spline s at (small) equidistant t steps and obtain a final set of points which we denote by {r i } i=1,...,N . As suggested in (Leemans et al, 2005), we define a piecewise differential 3D space curve t(r), which is 1 if r is on the backbone of the fiber and 0 else. t(r) is given by…”

Diffantom: whole-brain diffusion MRI phantoms derived from real datasets of the Human Connectome Project

“…Digital simulations are increasingly popular because the complexity of whole-brain tractography can not be accounted for with current materials and proposed methodologies to build physical phantoms. Early digital phantoms started with simulation of simple geometries (Basser et al, 2000;Gössl et al, 2002;Tournier et al, 2002;Leemans et al, 2005) to evaluate the angular resolution as well. These tools generally implemented the multi-tensor model (Alexander et al, 2001;Tuch et al, 2002) to simulate fiber crossing, fanning, kissing, etc.…”