Diffusion Compartmentalization Using Response Function Groups with Cardinality Penalization
Spherical deconvolution (SD) of the white matter (WM) diffusion-attenuated signal with a fiber signal response function has been shown to yield high-quality estimates of fiber orientation distribution functions (FODFs). However, an inherent limitation of
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Department of Radiology and Biomedical Research Imaging Center, The University of North Carolina at Chapel Hill, U.S.A. 2 Department of Psychiatry and Behavioral Sciences, Stanford University, U.S.A. [email protected]
Abstract. Spherical deconvolution (SD) of the white matter (WM) diffusion-attenuated signal with a fiber signal response function has been shown to yield high-quality estimates of fiber orientation distribution functions (FODFs). However, an inherent limitation of this approach is that the response function (RF) is often fixed and assumed to be spatially invariant. This has been reported to result in spurious FODF peaks as the discrepancy of the RF with the data increases. In this paper, we propose to utilize response function groups (RFGs) for robust compartmentalization of diffusion signal and hence improving FODF estimation. Unlike the aforementioned single fixed RF, each RFG consists of a set of RFs that are intentionally varied to capture potential signal variations associated with a fiber bundle. Additional isotropic RFGs are included to account for signal contributions from gray matter (GM) and cerebrospinal fluid (CSF). To estimate the WM FODF and the volume fractions of GM and CSF compartments, the RFGs are fitted to the data in the least-squares sense, penalized by the cardinality of the support of the solution to encourage group sparsity. The volume fractions associated with each compartment are then computed by summing up the volume fractions of the RFs within each RFGs. Experimental results confirm that our method yields estimates of FODFs and volume fractions of diffusion compartments with improved robustness and accuracy.
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Introduction
Diffusion magnetic resonance imaging (DMRI) is a powerful imaging modality due to its unique ability to extract microstructural information by utilizing restricted diffusion to probe compartments that are much smaller than the voxel size. One important goal of DMRI is to estimate axonal orientations, tracing of which will allow one to gauge connectivity between brain regions. For estimation of axonal orientations, a widely used method, constrained spherical deconvolution (CSD) [1], estimates the fiber orientation distribution function (FODF) by
This work was supported in part by a UNC BRIC-Radiology start-up fund and NIH grants (EB006733, EB009634, AG041721, MH100217, and 1UL1TR001111).
c Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part I, LNCS 9349, pp. 183–190, 2015. DOI: 10.1007/978-3-319-24553-9_23
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P.-T. Yap, Y. Zhang, and D. Shen
deconvolving the measured diffusion-attenuated signal with a spatially-invariant kernel representing the signal response function (RF) of a single coherent fiber bundle. Unlike the multi-tensor approach, CSD does not require the specification of the number of tensors to fit to the data. However, it has been recently reported that a mismatch between the kernel used in CSD and the actual fiber RF can cause spurious peaks in the estimated FODF [2]. Although CSD has been recently extende
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