An accurate delineation of the optic radiation (OR) is useful in reducing the risk of a visual field deficit after temporal lobe resective surgery. However, tractography, especially of the probabilistic kind, is prone to generate spurious (false-positive) streamlines that are poorly aligned with the surrounding bundle. Fiber-to-bundle coherence measures are applied to identify and remove spurious fibers, which together with test-retest parameter estimation can provide a reconstruction of the OR that is robust to the stochastic realization of probabilistic tractography. Pre- and post-operative comparison of the OR is performed for epilepsy patients to quantify the accuracy of damage prediction.
To identify and remove spurious fibers, we consider fiber-to-bundle coherence (FBC) measures that provide a quantitative measure of the alignment of streamlines.4 In this procedure, a notion of alignment between neighboring streamline points is obtained by embedding the streamlines into the differentiable manifold of the rigid-body motion Lie group SE(3). Within this non-flat differential structure, a metric is defined that measures the distance between any two streamline points in both position and orientation of its tangent vectors.5,6,7 The metric is evaluated through kernel density estimation, applied using a hypo-elliptic Brownian motion kernel, as depicted in Figure 1.A.8 The FBC results from evaluating the kernel density estimator along each element of all lifted streamlines (see Figure 1.B) where the FBC is color-coded for each streamline. Lastly, a scalar measure for the entire streamline is introduced, called the relative FBC (RFBC), which computes the minimum of the average FBC in a sliding window along the streamline (see Figure 1.C). For a concise mathematical description see (goo.gl/9lZgcG).
Spurious streamlines can be identified by a low RFBC and removed from the tractography result. For this purpose, the threshold parameter ε is introduced, which is defined as the lower bound criterion on RFBC that retains a streamline. However, preservation of the Meyer’s loop requires a careful selection of thresholds such that spurious streamlines are removed while maintaining a high sensitivity. Standardized selection of ε is achieved through test-retest evaluation of the variability in ML-TP distance. To this end, the RFBC is computed of repeated tractograms. Subsequently, for increasing values of ε, the mean and standard deviation of the ML-TP distance are calculated, as illustrated in Figure 2. In this procedure we define the optimal choice of ε to be at the point when the variability first drops below 2 mm, which is a value reflecting surgical accuracy. The pipeline for optic radiation reconstruction and reliable ML-TP distance measures is available as open source software (goo.gl/WuqlkH) and the FBC measures are additionally available in DIPY.9
1. Winston GP, Daga P, White MJ, et al. Preventing visual field deficits from neurosurgery. Neurology 2014;83(7):604-611.
2. Winston GP, Daga P, Stretton J, et al. Optic radiation tractography and vision in anterior temporal lobe resection. Ann Neurol. 2012;71(3):334-341.
3. Lilya Y, Ljungberg M, Starck G, et al. Tractography of Meyer's loop for temporal lobe resection—validation by prediction of postoperative visual field outcome. Acta Neurochir. 2015;157(6):947-956.
4. Portegies JM, Fick RH, Sanguinetti GR, et al. Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution. PLoS ONE 2015;10(10):e0138122, doi: 10.1371/journal.pone.0138122
5. Mumford D. Algebraic Geometry and Its Applications. Springer-Verlag 1994;491–506.
6. Citti G, Sarti A. A Cortical Based Model of Perceptual Completion in the Roto-Translation Space. J Math Imaging Vis. 2006;24(3):307–326.
7. Duits R, Felsberg M, Granlund G, et al. Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group. Int J Comput Vision 2007;72(1):79–102.
8. Duits R, Franken E. Left-Invariant Diffusions on the Space of Positions and Orientations and their Application to Crossing-Preserving Smoothing of HARDI images. Int J Comput Vision 2011;92(3):231–264.
9. Garyfallidis E, Brett M, Amirbekian B, et al. Dipy, a library for the analysis of diffusion MRI data. Front Neuroinform. 2014:8(8), doi:10.3389/fninf.2014.00008