Fourier transform power spectrum is a potential measure of tissue alignment in standard MRI: A multiple sclerosis study

Abstract

Loss of tissue coherency in brain white matter is found in many neurological diseases such as multiple sclerosis (MS). While several approaches have been proposed to evaluate white matter coherency including fractional anisotropy and fiber tracking in diffusion-weighted imaging, few are available for standard magnetic resonance imaging (MRI). Here we present an image post-processing method for this purpose based on Fourier transform (FT) power spectrum. T2-weighted images were collected from 19 patients (10 relapsing-remitting and 9 secondary progressive MS) and 19 age- and gender-matched controls. Image processing steps included: computation, normalization, and thresholding of FT power spectrum; determination of tissue alignment profile and dominant alignment direction; and calculation of alignment complexity using a new measure named angular entropy. To test the validity of this method, we used a highly organized brain white matter structure, corpus callosum. Six regions of interest were examined from the left, central and right aspects of both genu and splenium. We found that the dominant orientation of each ROI derived from our method was significantly correlated with the predicted directions based on anatomy. There was greater angular entropy in patients than controls, and a trend to be greater in secondary progressive MS patients. These findings suggest that it is possible to detect tissue alignment and anisotropy using traditional MRI, which are routinely acquired in clinical practice. Analysis of FT power spectrum may become a new approach for advancing the evaluation and management of patients with MS and similar disorders. Further confirmation is warranted.

Fig 1. Method demonstration.

Shown are an example ROI in the right genu of corpus callosum (A, small box); Zoomed view of the ROI (B); and Fourier transform of the ROI (C). Then, Fourier transform power spectrum of the ROI is shown after normalization (D) and thresholding (E). Based on E, the orientation profile of the ROI is calculated (F), from which corresponding angular entropy can be computed.

Fig 2. Representative ROIs along with predicted major aligning orientations based on the anatomy of corpus callosum.

Panel A shows an example T₂-weighted MR image from a control subject, where 6 ROIs are highlighted, located respectively in the left (1), central (2), and right (3) aspects of the genu and splenium (4, 5, 6). The predicted major orientations of these ROIs are: ROI 1 = ROI 6 = 45°; ROI 2 = ROI 5 = 0°; and ROI 3 = ROI 4 = 135°, similar to the trajectory direction of specific fiber tracks. Note that the same angle between paired ROIs (1 versus 6; 2 versus 5; 3 versus 4) reflect a near parallel trajectory direction of fiber tracks going through correspondent ROIs.

Fig 3. Examples of calculated orientation profiles using our method from chosen corpus callosum ROIs.

Panel A shows the same T₂-weighted image and ROIs as seen in Fig 2. Panel B shows the major (the highest peak) and all aligning directions in each ROI in the frequency domain, which are perpendicular to the angles shown in Fig 2. Here, ROI 1 = ROI 6 = 135°; ROI 2 = ROI 5 = 90°; and ROI 3 = ROI 4 = 45°, 90° from the direction of fiber tracts.

Fig 4. Summarized dominant directions per ROI and subject group based on T₂-weighted MRI of corpus callosum.

Top row shows example images of corpus callosum from a control subject (A), and from patients with relapsing-remitting (B) and secondary progressive (C) MS, suggesting increasing degrees of brain atrophy. Bottom left plot shows the dominant aligning angles of each ROI from the 3 groups. Bottom right plot shows the correlation between predicted and calculated dominant orientations at each aligning angle. Data shown are mean and standard error in plots (L: left, C: centre and R: right).

Fig 5. Angular entropy in each ROI of the 3 subject groups.

Panel A shows the mean and standard error of angular entropy summarized by group and ROIs, and panel B demonstrates the distribution of angular entropy of all ROIs per group according to the severity of angular entropy. Note that large values close to 0 refer to high angular entropy, thus high tissue complexity. In panel B, the peak location of the distribution curves shifts toward lower values of angular entropy (less negative) from control to RRMS and then to SPMS, representing greater tissue complexity and injury in patients, particularly in those with SPMS (L: left, C: centre and R: right).