Kernel regression estimation of fiber orientation mixtures in diffusion MRI - PubMed (original) (raw)
Kernel regression estimation of fiber orientation mixtures in diffusion MRI
Ryan P Cabeen et al. Neuroimage. 2016.
Abstract
We present and evaluate a method for kernel regression estimation of fiber orientations and associated volume fractions for diffusion MR tractography and population-based atlas construction in clinical imaging studies of brain white matter. This is a model-based image processing technique in which representative fiber models are estimated from collections of component fiber models in model-valued image data. This extends prior work in nonparametric image processing and multi-compartment processing to provide computational tools for image interpolation, smoothing, and fusion with fiber orientation mixtures. In contrast to related work on multi-compartment processing, this approach is based on directional measures of divergence and includes data-adaptive extensions for model selection and bilateral filtering. This is useful for reconstructing complex anatomical features in clinical datasets analyzed with the ball-and-sticks model, and our framework's data-adaptive extensions are potentially useful for general multi-compartment image processing. We experimentally evaluate our approach with both synthetic data from computational phantoms and in vivo clinical data from human subjects. With synthetic data experiments, we evaluate performance based on errors in fiber orientation, volume fraction, compartment count, and tractography-based connectivity. With in vivo data experiments, we first show improved scan-rescan reproducibility and reliability of quantitative fiber bundle metrics, including mean length, volume, streamline count, and mean volume fraction. We then demonstrate the creation of a multi-fiber tractography atlas from a population of 80 human subjects. In comparison to single tensor atlasing, our multi-fiber atlas shows more complete features of known fiber bundles and includes reconstructions of the lateral projections of the corpus callosum and complex fronto-parietal connections of the superior longitudinal fasciculus I, II, and III.
Keywords: Atlasing; Diffusion MRI; Image processing; Interpolation; Multi-fiber; Tractography.
Copyright © 2015 Elsevier Inc. All rights reserved.
Figures
Figure 1
A flowchart illustrating the steps in the proposed method, detailed in Algo. 2. The input is a position for estimation and model-valued volumetric data. Then, kernel weights are computed from the product of spatial and data-adaptive factors and normalized to sum to one. Then, weights are distributed among the fiber compartments and multiplied by volume fraction. Finally, the estimated model is found by a clustering-based optimization procedure, detailed in Algo. 1.
Figure 2
Example uses of the proposed estimator for interpolation, smoothing, and fusion tasks. Slices were taken from average human brain data at the junction of the corpus callosum (pink), corona radiata (blue), and cingulum (green). Fibers are colored according to their orientation, and thickness encodes volume fraction. The top panel shows interpolation at twice the original resolution, demonstrating continuity of both fiber orientations and volume fractions. The middle panel shows smoothing to reduce noise-induced angular error. The bottom panel shows fusion of 80 aligned subjects to produce an atlas representing the population.
Figure 3
The phantom used in the first experiment in Sec. 5.2. This represents a complex boundary between fiber bundles and includes “off-boundary” and “on-boundary” regions-of-interest.
Figure 4
Qualitative results from the first experiment described in Sec. 5.2. The first panel shows the ground truth phantom at the boundary voxels. The second panel shows fibers fit after adding Rician noise at S NR = 21.5. The third and fourth panels show smoothing results using linear (Eq. 4) and bilateral (Eq. 9) kernel weights. The results show that both estimation techniques reduce noise-induced angular error; however, adaptive estimation can avoid the orientation blurring at the boundary voxels, due to the inclusion of the Km kernel weights.
Figure 5
Results from the first experiment in Sec. 5.2. The labels on the left indicate the region where results were aggregated, and each plot shows either orientation or volume fraction error rates. The plot titles also show the volume fraction of the compartments (_f_1 and _f_2). The top two rows show results with SNR from 15 to 25, comparing the noisy, rank-based, linear, and adaptive estimation conditions (with hp = 1.5 and hm = 0.5). We see that all methods perform well at reducing volume fraction, with rank-based estimation performing slightly better with on-boundary fiber fractions. We see that rank-based estimation rates poorly in orientation error, particularly in regions where bundle volume fractions are within 0.05 apart. We also see that linear estimation introduces high orientation error in on-boundary voxels, while adaptive estimation avoids this issue. By sweeping across the data-adaptive parameter hm, we see a local minima in orientation error occurs between 0.3 and 0.5, depending on the SNR.
Figure 6
Results from the second experiment in Sec. 5.3 The first panel shows the phantom and region-of-interest, and the following three panels show tractography using nearest-neighbor, rank-based, and adaptive estimation (SNR = 14). We see that nearest neighbor includes early terminations due to high orientation error and compartment count error. We also compare to the rank-based approach, which creates many spurious connections due to poor matching of compartments in the crossing region. Adaptive estimation can improve both of these issues through smoothing and clustering-based compartment matching.
Figure 7
Results from the second experiment in Sec. 5.3. The first panel shows the phantom and region-of-interest, and the following three panels show tractography results using nearest neighbor interpolation, local-max model selection, and adaptive model selection (Eq. 8). This shows how local-max selection can sometimes introduce “fiber splitting” due to noise (SNR 16.5 shown). Adaptive selection can reduce this effect, resulting in smoother streamline curves and lower orientation and volume fraction errors (see Fig. 8).
Figure 8
Results from the second experiment in Sec. 5.3 using the phantom shown in Fig. 6. Evaluation was first performed by measuring voxel-wise orientation error, volume fraction error, missing fiber error, extra fiber error (lower is better). Tractography-based evaluation was performed to evaluate performance in connectivity mapping using the Dice coefficient and fraction of valid connections (higher is better). Several methods for model selection were compared including: fixed count, local-max selection, mean selection, and our proposed adaptive selection. We also included rank-based estimation and nearest neighbor interpolation to serve as a baseline. The top two rows show performance across noise levels from SNR 15 to 25. We see that adaptive estimation provided significantly lower orientation error than other methods. Across all noise levels, fixed and local-max selection introduced a high volume fraction error and extra fiber error, due to “fiber-splitting”. Adaptive performance significantly reduced these errors with a slight increase in missing fiber error. We also varied the regularization parameter and plotted with semilog axes, x = _log_10(1 − λ). We found performance to be acceptable between λ = 0.99 and 0.9999, with a tradeoff between extra and missing fiber error.
Figure 9
Quantitative results from the third experiment described in Sec. 5.4. Scan-rescan reproducibility and reliability were measured for fiber bundle metrics of eight fiber bundles. Reproducibility was measured with the coefficient of variation (CV), which gives a normalized measure of error across scans. Reliability was measured with the intra-class correlation (ICC), which indicates the proportion of total variation that exists between subjects. A lower CV and a high ICC are preferable, with an ICC above 0.75 being highly reliable. The top row shows reference visualizations of the bundles. The middle row shows results by bundle type, with aggregation across bundle measures and hemisphere. The bottom row shows results by bundle measure, with aggregation across bundle type. We found linear and adaptive estimation to show an improvement in nearyly all cases by the ICC metric and improvement in most cases by the CV metric.
Figure 10
Results from the fourth experiment described in Sec. 5.5, which included the construction of a multi-fiber atlas of 80 normal human subjects. Our proposed method was used for interpolation and fusion with deformation fields computed by DTI-TK. The top panel (A) shows a comparison of major bundles in the standard single-tensor atlas and our proposed the multi-fiber atlas. Bundles include the corona radiata (green), inferior longitudinal fasciculus (blue), inferior fronto-occipital fasciculus (orange), uncinate fasciculus (pink), corpus callosum (red), and the arcuate fasciculus (yellow). We found the multi-fiber atlas included nearly all features found in the single tensor atlas and more complete reconstructions of the frontal projections of the arcuate and lateral projections of the corpus callosum. The bottom panels show tractography results for complex fiber bundles including the lateral projections of the corpus callosum (B) and fronto-parietal connections of the superior longitudinal fasciculus I, II, III (C). The detail view in panel B also shows a triple crossing inferred at the intersection of the corona radiata, superior longitudinal fasciuculus, and corpus callosum. The three portions of the superior longitudinal fasciculus are also shown in panels A and C and include crossings with the corona radiata and corpus callosum. These reconstructions compare favorably to related work that examined these bundles in single human diffusion MRI reconstructions, dissection, and tracing studies in non-human primates.
Figure 11
Results from the fourth experiment described in Sec. 5.5, which included the construction of a multi-fiber atlas of 80 normal human subjects. The top row shows principal tensor orientations overlaid on fractional anisotropy, and the bottom row shows fibers from the multi-fiber atlas overlaid on total fiber volume fraction. Fiber tube thickness reflects fractional anisotropy and per-fiber volume fraction in the top and bottom rows, respectively. The left column (A) shows an axial slice of the brainstem, demonstrating crossing fibers of cerebellar and pyramidal tracts. The right column (B) shows a sagittal slice demonstrating crossing fibers of the corona radiata and superior longitudinal fasciculus I.
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