Flow-based fiber tracking with diffusion tensor and q-ball data: Validation and comparison to principal diffusion direction techniques

Abstract

In this study, we evaluate the performance of a flow-based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity. We introduce a novel speed function for surface evolution that is derived from either diffusion tensor (DT) data, high angular resolution diffusion (HARD) data, or a combined DT-HARD hybrid approach. We use the model-free q-ball imaging (QBI) approach for HARD reconstruction. The anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts, noise, and subvoxel partial volume averaging of fiber directions. The surface evolution approach, using the full diffusion tensor as opposed to the principal diffusion direction (PDD) only, is compared to PDD-based line propagation fiber tracking. Additionally, DT reconstruction is compared to HARD reconstruction for fiber tracking, both using surface evolution. We show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions, which can be difficult to map with PDD-based methods. We then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly.

Introduction

Magnetic resonance diffusion imaging has a unique ability to provide information about the organization of fibrous tissue structures in vivo. It does so via the estimation of the 3D displacement distribution of diffusing water molecules, i.e., the diffusion probability density function (diffusion pdf). Water diffusion in fibrous tissue is anisotropic, with the preferred direction of diffusion lying along the dominant fiber orientation. This is of particular interest in the central nervous system (CNS), where diffusion imaging has the potential to assess neuronal connectivity, an application which has widespread implications for basic neuroanatomical research and for disease detection and assessment.

The first work on 3D fiber reconstruction in the CNS used diffusion tensor (DT) data, so named because it is obtained by modeling the diffusion pdf as an anisotropic 3D Gaussian function, which can be described by a second order tensor (Basser et al., 1994). The reconstruction of tracts was done by line propagation using the principal eigenvector of the diffusion tensor (Basser et al., 2000, Conturo et al., 1999, McGraw et al., 2004, Mori et al., 1999, Vemuri et al., 2002). Such principal diffusion direction (PDD) techniques can be confounded when there is more than one fiber direction within a single imaging voxel. With voxel sizes typical of diffusion acquisitions (10–30 mm²), there is significant partial volume averaging of fiber directions in anatomical regions of both research and clinical interest, such as the association fibers near the cortex. This partial volume averaging may be due to high curvature, crossing, branching, or splaying of tracts.

A number of solutions have been proposed to deal with the problem of subvoxel partial volume averaging of fiber directions. The diffusion tensor itself contains information about multiple fiber directions: for example, when the fibers are restricted to a plane, a level set of the tensor-described diffusion pdf is a planar ellipsoid. Although the principal eigenvector direction may not reflect the fiber directions in this case, the full tensor may be used for tracking, as has been proposed by several groups including ourselves (Batchelor et al., 2001, Campbell et al., 2002a, Lazar et al., 2003, O'Donnell et al., 2002, Tournier et al., 2003). Alternatively, given sufficient diffusion weighted images (DWIs), bootstrap methods may be used to estimate confidence intervals or a marginal posterior distribution for the direction of the principal eigenvector (Behrens et al., 2003, Jones, 2003). Although the full tensor does give us more information than its principal eigenvector alone, there has recently been increasing interest in forgoing the classic tensor description of the diffusion pdf in favor of high angular resolution diffusion (HARD) pdf reconstruction to infer multiple fiber directions within single voxels. HARD reconstruction techniques include multi-tensor modeling (Tuch et al., 2002), diffusion spectrum imaging to estimate the full 3D diffusion pdf using q-space methods (Wedeen et al., 2000), and model-free extraction of the radially persistent angular structure using either maximum entropy solutions (Alexander and Jansons, 2002) or modified q-space methods (Tuch et al., 2003). Additionally, regularization techniques can be used to infer multiple fiber directions from a single-tensor field (Cointepas et al., 2002, Ramírez-Manzanares and Rivera, 2003). In simple fiber systems involving partial volume averaging of fiber directions, it has been shown that the directions in which the high angular resolution diffusion pdf is maximal coincide with fiber directions (Lin et al., 2002). We note that there are also methods for measuring the apparent diffusion coefficient (ADC) profile at high angular resolution (Alexander et al., 2002, Frank, 2002, Zhan et al., 2003), however, the maxima of the ADC profile do not necessarily coincide with fiber directions (Tuch et al., 2002, von dem Hagen and Henkelman, 2001), hence further processing is necessary for fiber tracking applications.

In this paper, we extend our previously proposed flow-based fiber tracking approaches (Campbell et al., 2002a, Campbell et al., 2002b) in order to use the information in the full diffusion pdf estimated using either HARD or DT techniques. This algorithm is a modification and extension of the Fast Marching Tractography (FMT) technique (Parker et al., 2002a), which uses the principal diffusion direction only, and is similar to several surface evolution approaches that use the full diffusion tensor (Batchelor et al., 2001, O'Donnell et al., 2002, Tournier et al., 2003). Our extension of the FMT technique consists of using all of the information in the diffusion tensor or, if available, HARD measurements. The surface evolution approach has the advantage that it allows tracking to proceed in a continuum of directions, as may be desired in cases where there is uncertainty and/or multiple fiber directions. We show fiber tracking results using both HARD and DT data in the human brain, noting that the diffusion tensor can provide more information than that given by its principal eigenvector only and that HARD reconstruction can give us more information still. Additionally, we quantitatively compare the performance of the flow-based approach to that of line propagation using the PDD. To do so, we designed a physical phantom with known connectivity from excised rat spinal cord. Previous validation studies have been done using a single excised cord (Campbell et al., 2002b, Vemuri et al., 2002) and in the macaque (Parker et al., 2002b): in this study, complex known configurations of subvoxel curvature and fiber crossing are created and scanned at a standard human imaging resolution. While simulated data can provide a gold standard to which tracking results can be compared (Lazar and Alexander, 2003, Lori et al., 2002, Tournier et al., 2002), it is of additional value to evaluate the results of tracking on real MRI data in the presence of normal imaging artifacts, noise characteristics, and voxel size limitations. Doing so allows us to validate the fiber tracking process from acquisition of the MRI data, to estimation of the diffusion displacement distribution, and to the tracking algorithm itself.