Purpose

Diffusion acquisitions are routinely used to study white matter architecture and brain connectivity $$$\textit{in vivo}$$$ [1,2]. A key step for successful tractography of neuronal tracts is the correct identification of the tract directions in each voxel. However, accurate fiber direction estimation is difficult due to the limited angular resolution of the acquisition and intrinsic ODF peak width [3,4] and most methods fail to detect fibers crossing at angles smaller than 30°-40° [3,5]. Simulations and initial qualitative $$$\textit{in vivo}$$$ studies suggest that ODF Fingerprinting (ODF-FP, Fig 1) can improve the detection of these fiber crossings [6,7] by assessing the similarity of the measured ODF and the elements in a pre-generated library of ODF-fingerprints [8,9].

Here, we quantitatively examine the performance of ODF-FP and several other fiber direction identification algorithms $$$\textit{in vivo}$$$ by analyzing a downsampled Human Connectome Protocol (HCP) DWI dataset and comparing the results to those obtained with the original high resolution dataset.

Methods

ODF-Fingerprinting: For ODF-Fingerprinting, a library $$$L_{ODF}$$$ was generated by simulating diffusion weighted signals as a sum of diffusion tensors (FA$$$\,=\,$$$[0.3,1], ADC$$$\,=\,0.9\,\mathrm{mm^2/s}$$$, 10% water component, assumption of cylindrical fibers $$$\lambda_2=\lambda_3$$$) on a Radial Diffusion Spectrum Imaging grid (RDSI, 177 q-space samples, three shells, bmax=$$$5000\,\mathrm{s/mm^2}$$$) and reconstructing ODFs [10]. Matching of a measured $$$ODF_m$$$ with the elements of library $$$L_{ODF}$$$ was assessed by maximizing the dot-product [8,9] with an added penalty term for the noise estimate $$$\sigma_n$$$ of the input diffusion data: $$$\mathrm{max}\left(\log(L_{ODF}\,.\,ODF_m) – n_{par}/{4n} \sigma_n\right)$$$ ($$$n_{par} = 1 + 5N_{fib}$$$ a measure of library element complexity and $$$n$$$ the number of elements in $$$ODF_m$$$) [7]. $$$\sigma_n$$$ is estimated using a linear mean square error estimator for the variance of the noise of diffusion weighted signals [11]. The size of the fingerprint-library is reduced by rotating the maximum value of ODF-traces to the Z-axis before matching. The ODF fingerprinting method is compared with local maximum search (DSIStudio), Newton search along a set of specified directions (MRtrix3, $$$\mathrm{sh2peaks}$$$) and probabilistic estimation (FSL, $$$\mathrm{bedpostx}$$$).

Data: A high resolution preprocessed $$$\textit{in vivo}$$$ DWI acquisition was provided by the HCP (3T Siemens Skyra System (MGH); 64ch head coil; b$$$\,=\,1000, 3000, 5000\,\mathrm{s/mm^2}$$$, 256 q-space volumes, TR/TE$$$\,=\,8800/57\,\mathrm{ms}$$$, 96 slices, $$$210\,\mathrm{mm}$$$ FoV, $$$1.5\,\mathrm{mm}$$$ isotropic resolution, PF5/8, GRAPPA 3; healthy volunteer). These preprocessed images were corrected for gradient non-linearity, motion (FreeSurfer) and eddy currents (FSL $$$\mathrm{eddy}$$$). RDSI reconstructions, incorporating variable sample density correction, were performed offline using custom-made software (Matlab, Mathworks). The $$$1.5\,\mathrm{mm}$$$ isotropic dataset was downsampled (MRtrix3, $$$\mathrm{mrresize}$$$) to a $$$3\,\mathrm{mm}$$$ isotropic resolution such that each voxel in the low resolution (LR) dataset corresponds to 8 high resolution (HR) voxels. Hence, for each $$$3\,\mathrm{mm}$$$ isotropic voxel we compared the identified fiber directions relative to the fibers found in the 8 corresponding HR voxels. From this comparison we calculated the number of correctly (true positive) and wrongly (false positive) identified fibers and the number of missed fibers (false negative). Display with Matlab and DSIStudio [Yeh2010].

Results and Discussion

Fig. 2 illustrates the setup of the experiment; the directions found in a LR voxel (yellow arrows) are compared to those found in the corresponding HR voxels (yellow square). In the indicated voxel, both ODF-FP and the probabilistic method successfully identify the second fiber bundle. However, the probabilistic method also identifies a large number of false positive fibers. Maps of the number of correctly and wrongly identified fibers (true positive, Fig. 3, second and third row) confirm these findings over the whole volume. With the improved detection of ODF-FP also a higher number of false positive fibers (Fig. 3, third row) are identified, though ODF-FP does not find as many as the probabilistic method. The main improvement of ODF-FP is, as expected, in voxels with two or more fibers where more pairs of fibers are correctly identified (Fig. 4, left).

Conclusion

ODF-Fingerprinting has been shown to improve detection of fiber pairs with small crossing angles in simulations and qualitative evaluations of $$$\textit{in vivo}$$$ data. Here we show the quantitative performance $$$\textit{in vivo}$$$ based on a higher resolution reference standard. The improved fiber identification by ODF-FP will aid fiber tracking algorithms in accurately calculating brain connectivity. Future work will focus on using more detailed diffusion models and on verifying the method in fiber phantoms.

Acknowledgements

This project is supported in part by PHS grants R01-CA111996, R01-NS082436 and R01-MH00380. DGP is supported by NIH/NINDS R01-NS102665, New York State DOH01-STEM5-2016-00221 and NIH/NIAID R21-AI130618. Data collection and sharing for this project was provided by the Human Connectome Project (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Weeden, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neurological Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of Southern California.

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