Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5T

Abstract

Diffusion tensor imaging (DTI) is used to study tissue composition and architecture in vivo. To increase the signal to noise ratio (SNR) of DTI contrasts, studies typically use more than the minimum of 6 diffusion weighting (DW) directions or acquire repeated observations of the same set of DW directions. Simulation-based studies have sought to optimize DTI acquisitions and suggest that increasing the directional resolution of a DTI dataset (i.e., the number of distinct directions) is preferable to repeating observations, in an equal scan time comparison. However, it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability. Furthermore, the effect of different DW schemes on in vivo DTI findings is not fully understood. This study characterizes how the makeup of a DW scheme, in terms of the number of directions, impacts the precision and accuracy of in vivo fractional anisotropy (FA), mean diffusivity (MD), and principal eigenvector (PEV) findings. Orientation dependence of DTI reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results. As long as sampling orientations are well balanced, differences in DTI contrasts due to different DW schemes are shown to be small relative to intra-session variability. These differences are accentuated at low SNR, while minimized at high SNR. This result suggests that typical clinical studies, which use similar protocols but different well-balanced DW schemes, are readily comparable within the experimental precision.

Introduction

Diffusion tensor imaging (DTI) is a magnetic resonance (MR) imaging technique that is sensitive to the random thermal motions of water and can provide contrasts which give insight about tissue architecture. A diffusion tensor is a simple, yet powerful, mathematical description of the underlying, three-dimensional diffusion process that can be estimated from a series of diffusion-weighted (DW) MR images (Basser et al., 1994). Typically, a DW image is created by applying a pair of magnetic field gradients (so-called dephasing and rephasing gradients) along a distinct direction in 3D space. The resulting image, therefore, shows signal attenuation in the direction of the applied gradient, and the degree of signal attenuation is proportional to the water diffusivity. A diffusion tensor may be estimated from as few as 6 DW images acquired along non-collinear directions and 1 minimally weighted (b₀) image. However, to increase the signal-to-noise ratio (SNR), more than 6 DW images are commonly acquired along 6 or more non-collinear directions. In the latter case there are two options: either to add additional DW directions or repeat existing DW directions. For example, if time permits the acquisition of 12 DW images in total, one can increase the directional resolution (DW images in 12 distinct directions) or increase the number of scan repetitions (2 repetitions of DW images in 6 distinct directions); both of which take the same amount of time.

A source of confusion may be how to properly interpret the literature when selecting a DW scheme. Substantial theoretical and experimental work has gone into developing optimized DW schemes (Alexander and Barker, 2005, Conturo et al., 1996, Hasan et al., 2001, Jones, 2004, Jones et al., 1999, Skare et al., 2000) that permit accurate and precise calculation of a diffusion tensor and diffusion tensor-derived contrasts (such as fractional anisotropy, mean diffusivity, etc.) which result from the tensor formalism (Batchelor et al., 2003, Hasan et al., 2004, Jones, 2003, Jones and Basser, 2004). Several commonly used DW schemes have emerged through research addressing different constraints and imaging objectives. For example, 6 DW direction schemes can be constructed with tetrahedral distributions (Conturo et al., 1996) that provide simple geometric sampling or dual gradient methods (Pierpaoli et al., 1996) that maximize gradient power, thereby achieving a shorter echo time (TE). When additional DW directions are desired, potential energy (PE) minimization methods (Jones et al., 1999) have been shown to ensure regular sampling and minimize the rotational dependence of noise propagation (Batchelor et al., 2003, Jones, 2004). It is important to note that when the number of directions in a DW scheme corresponds to a member of an icosahedral group (e.g., 6, 10, 15, 31), the minimized PE solution can be expressed analytically as the vertices of the corresponding polyhedron (Batchelor et al., 2003, Hasan et al., 2004). The diversity of available DW schemes is also increased by schemes with more than 6 directions that maximize gradient power at the expense of less evenly spaced sampling (Jones, 2004, Muthupallai et al., 1999).

Moreover, practical constraints, such as available scan time, propensity for data corruption due to patient motion, gradient hardware performance, and manufacturer software limitations, often dominate the decision regarding which set of DW directions is optimal for use in a DTI experiment. However, the use of different DW schemes may lead to different computed tensors, and ultimately inconsistencies in the derived contrasts. The effects of relevant DW schemes on the accuracy and precision of tensor estimations and the derived contrasts have been investigated by simulation (Jones, 2004, Skare et al., 2000) and with in vivo data (Jones, 2003, Ni et al., 2006, Skare et al., 2000). There is strong simulation evidence that increasing the directional resolution is preferable to increased scan repetitions in an equal scan time comparison with a decreasing effect size as the number of DW directions increases (Hasan et al., 2001, Jones, 2003, Jones, 2004, Jones et al., 1999, Papadakis et al., 1999, Skare et al., 2000).

In this study, we investigate how the number of directions, in a well-balanced DW scheme, affects DTI-derived contrasts through direct in vivo analyses of experimental data. This methodology exposes the potential impacts of real world factors including subject motion and imaging artifacts/distortion. In addition to the in vivo experiments, simulations were performed to understand the characteristics of the experimental data (e.g., experimental data used as a basis for simulation with modeled noise). With this approach, we investigate the explanatory power of the single tensor model and interpret the experimental results in the context of the simulation literature.

Ultimately, this study addresses the differential hypothesis that either (1) the theoretical estimation benefits of using 30 DW directions as opposed to five repeats of 6 DW directions are realized in practice, or (2) other intra-session and inter-session factors, such as physiological noise, registration accuracy, distortion artifacts, or gradient performance, dominate the accuracy of DW experiments so that the choice of the direction scheme is non-significant in practice. Stated simply, this study addresses a fundamental question: given a certain amount of time for a DTI study, which DW scheme should be used for optimally precise and accurate DTI-derived contrasts, and why? This is an important question to consider when designing experiments and comparing data from different institutions but remains largely unanswered. Furthermore, a principled theoretical framework is provided to support and interpret experimental findings relative to simulation results.

The specific objective of the present study was to characterize how the choice of DW scheme impacts the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the principal eigenvector (PEV) based on in vivo experimental data, with simulations to clarify and interpret these results. We present methods to partition a general, high directional resolution DTI dataset into subsets with a lower directional resolution. Without these partition techniques, a substantially larger dataset would be required to investigate the differences due to different DW schemes. This study is a part of the Biomedical Informatics Research Network (BIRN) studies. Acquired and processed DTI data as well as the acquisition protocol for this study are freely available through the BIRN website (http://www.nbirn.net/Resources/Downloads/) and can be used as a data resource and reference for 1.5T scanners.