Diffusion tensor imaging at low SNR: nonmonotonic behaviors of tensor contrasts

Abstract

Diffusion tensor imaging (DTI) provides measurements of directional diffusivities and has been widely used to characterize changes in the tissue microarchitecture of the brain. DTI is gaining prominence in applications outside of the brain, where resolution, motion and short T₂ values often limit the achievable signal-to-noise ratio (SNR). Consequently, it is important to revisit the topic of tensor estimation in low-SNR regimes. A theoretical framework is developed to model noise in DTI, and by using simulations based on this theory, the degree to which the noise, tensor estimation method and acquisition protocol affect tensor-derived quantities, such as fractional anisotropy and apparent diffusion coefficient, is clarified. These results are then validated against clinical data. It is shown that reliability of tensor contrasts depends on the noise level, estimation method, diffusion-weighting scheme and underlying anatomy. The propensity for bias and errors does not monotonically increase with noise. Comparative results are shown in both graphical and tabular forms, so that decisions about suitable acquisition protocols and processing methods can be made on a case-by-case basis without exhaustive experimentation.

Introduction

Diffusion tensor imaging (DTI) is a magnetic resonance (MR) imaging technique that is sensitive to the random thermal motions of water [1]. DTI has proven especially useful in providing insight into the intravoxel microarchitecture of the white matter tracts of the brain [2]. Previous studies have shown that the diffusivity in the direction of the fiber bundle is larger than that across the bundle because there are comparatively few barriers to water diffusion [2]. DTI provides measurements of these directional diffusivities, enabling inferences about white matter structural integrity and connectivity [3]. DTI has been widely used to characterize changes in microarchitecture associated with stroke [4], [5], white matter damage [6] and edema [7], [8].

The estimation process used in DTI has been shown to be sensitive to noise [9], [10], [11]. At low signal-to-noise ratios (SNRs), the derived diffusivities (i.e., eigenvalues of the estimated diffusion tensor) tend to systematically diverge from their true values, subsequently altering the estimated diffusion anisotropy while leaving measures of the mean diffusivity (MD) relatively less affected [9], [10], [11], [12]. The SNR [9], [10], [11], diffusion-weighting scheme [7], [8] and tensor estimation method [13], [14] have all been shown to affect derived tensor contrasts such as fractional anisotropy (FA) and MD. Fortunately, DTI can be readily accomplished in vivo in the human brain at sufficient SNR to avoid severe problems related to noise contamination [15], [16].

DTI is gaining prominence in applications outside of the brain such as the spinal cord [17], optic nerve [18] and musculature [19] (including the tongue [20]). These regions are small, prone to motion or have substantially shorter T₂ values than a typical brain tissue. To achieve sufficient resolution in small structures while simultaneously maintaining high SNR, long acquisition times may be necessary. However, tissue motion may cause undesirable image artifacts or blurring in such cases. Additionally, when T₂ is short or when the field strength is low (e.g., 0.4–1.0 T), the available signal is reduced, driving the SNR further down. Despite these significant limitations, a substantial amount of DTI research is being conducted, with data at much lower SNR than is typical for brain research at 1.5 or 3 T, and DTI images are being generated with relevant and interesting structures under these conditions. However, a detailed study of the effects of noise on this low-SNR regime has yet to be undertaken.

This study develops a theoretical framework to explain how noise propagates from acquired diffusion-weighted (DW) images to tensor-derived quantities. Using this model, we present simulations that utilize data from an in vivo DTI study and provide insight into the qualitative and quantitative properties of noise propagation. These simulations demonstrate how seemingly innocuous differences in estimation method at low SNR can lead to very different behaviors. Overall, this study clarifies the relative degree to which the noise, tensor estimation method and acquisition protocol influence the derived tensor contrasts.

Careful reading of the existing literature permits one to arrive at many conclusions that are presented herein; in this sense, our study reiterates important points presented previously. However, rather than simply duplicating previous work, we feel that our article contributes in two significant ways. Firstly, it presents relevant results in a comprehensive single body of work, which can serve as an effective resource. The need for this is clear, given the multitude of articles that tackle individual pieces of the DTI–SNR relationship. Effectively comparing results across studies is always challenging, even more so given the intricacies of the DTI–SNR relationship. Secondly, our study provides a comprehensive framework based on a theoretical model that enables characterization of FA and MD measurements over a wide range of SNRs. This treatment enables the effects of different parameters to be compared side by side, which has important consequences on experiment design and optimization. Through multiple simulations at closely spaced SNRs, the bias and variability of FA and MD are mapped, and nonmonotonic trends in low-SNR behavior are well exposed. Finally, a suggested error metric provides a simple method for evaluating the tradeoffs of using various DTI approaches in specific anatomical contexts.