Despite great deal of effort in comparing various denoising algorithms for DKI in previous studies (45, 46, 52) and inter-subject variability of DKI metrics in brain of healthy subjects (54, 55), the direct impact of Rician noise correction on DKI data has not been sufficiently studied, especially related to improvement on SNR and error measures in various anatomical regions. In this study, we evaluate the influence of the Rician NLM filter in combination with CLLS algorithm on the brain DKI and the spinal cord DTI data. Rician NLM filter in combination with CLLS algorithm has the potential to be useful in clinical research because it is easy and efficient to implement. To the best of our knowledge, this is the first study to assess the influence of combining the NLM filter with CLLS in DTI of the spinal cord and DKI in the brain and to report ROI-based changes in SNR and the associated error estimates. To compare diffusional measures using different processing methods (CLLS and CLLS-R), we obtained whole brain DKI data from 9 healthy volunteers and compared mean DT- and KT-derived indices using CLLS and CLLS-R. Rician NLM filter was also applied to the previously acquired spinal cord data retrospectively (64).
Measurement of SNR
SNR assessment is important for reliable quantification of diffusional metrics (71). When SNR is low, Rician noise does not only cause random fluctuations but also a signal dependent bias to the data, which may lead to difficulty in postprocessing such as tensor calculation. However, SNR levels are not routinely reported although previous reports suggest that low SNR causes a bias in FA which may vary with numerous other technical factors such as the region of brain being studied, field strength, hardware and software (68, 72, 73). As a first step to evaluate the influence of Rician denoising, we have measured SNR in various anatomical areas of the brain and the spinal cord with and without Rician denoising. Our results show that Rician NLM filtering yields the significant increase of SNR in the brain DKI and the spinal cord DTI data (Tables 1 and 2). The ROI-based SNR values with noise correction in our study are consistent with the previous study by Seo et al. (74) which has reported SNR thresholds 20 in the CC and 70 in the PUT for bias-free estimation of tensor metrics. It should be noted that those SNR values from the literatures were obtained from different acquisition protocols. Thus, when comparing those values with literature values, care should be taken to ensure the similarity of protocol chosen for comparison. For instance, the eddy current and off-resonance effects in a DWI sequence may substantially vary with b-value and diffusion gradient direction. Additionally, the spatial noise distribution can be varied by coil geometry, phase-encoding direction and acceleration factor of parallel imaging (38, 75, 76) which also need to be taken into account for. In our study, it is also observed that the degree of SNR improvement relates to the underlying structures. For instance, the CC has the smallest SNR increase among other regions, which might be attributed to the previous findings that the noise within accelerated images is nonhomogeneous with higher signal peripherally and noise centrally when parallel imaging is used (77–79). As the levels and spatial distributions of noise are not an equal across the DW image, it is expected that various anatomical areas with different SNR requirements have diverse range of SNR increase rate.
While denoising DTI with low SNR addressing the strong influence of Rician bias in the brain has been well presented by different studies (48, 80, 81), Rician NLM denoising has not been established in the spinal cord DTI where most of previous studies have focused on data acquisition or motion correction methods to improve SNR (25, 27, 58, 82). The mean SNR values without Rician denoising in C1-C3 in our study are within a range of values from a multi-centre study reported by Samson et al. (6.74–10.9) (27). However, our mean SNR values significantly increased in both lateral and dorsal areas of the spinal cord levels C1-C6 after a Rician denoising (Table 2). Our results indicate that a simple noise correction method in the spinal cord such as Rician denoising being used in our study increases SNR (Table 2) and thereby can reduce error estimates (Fig. 4B). This is not surprising given the improved quantification of dMRI in the brain, however worth reporting for the growing need of the spinal cord DTI in the clinical research despite more intrinsic challenges in the spinal cord as compared to the brain.
Estimation errors
Significantly reduced number of erroneous pixels (black holes) was observed in AK, RK and MK using CLLS-R as compared to CLLS in the brain (Fig. 5). In particular, clear difference is observed in cortical GM, where the voxel values with the erroneously estimated tensor are lower using CLLS as compared to CLLS-R (Fig. 3A). Note that voxels with extreme (negative or zero tensor) values were excluded from the computation. Even after all of extremely erroneous voxels were removed, the ROI-based mean χ2 values significantly decreased over all ROIs when estimated using CLLS-R compared to CLLS in all examined anatomical regions (Fig. 3B), suggesting the impact of Rician denoising step towards KT estimation in the brain. Additionally, the mean χ2 values in the spinal cord show that Rician NLM filtering significantly reduced error estimates in both lateral and dorsal columns (Fig. 4B). Reduced χ2 values both in the brain and the spinal cord, imply that accuracy of tensor estimation is significantly improved with Rician NLM filtering (Fig. 3B and 4B).
Regional values of DT- and KT-derived Metrics
Currently, a few reports in the literature are available for comparison with our results (54–56, 83, 84). Table 5 provides an overview of those works in the literature that include values of parameter estimates. Our ROI-based measurements of DT- and KT-derived metrics (Table 3) are consistent with some of the previously reported values. However, it is observed that the discrepancy in diffusional metrics values exists amongst various studies in the literature. There are a few factors that may explain discrepancy between studies, from data acquisition to postprocessing perspective. In DTI, it has been well known that low SNR causes a bias in DT-derived metrics, leading to overestimation of FA (68, 72, 73). When SNR is low, Rician noise does not only cause random fluctuations but also a signal dependent bias to the data, which may lead to difficulty in postprocessing such as tensor calculation. Therefore bias-free measurements require adequate SNR (85) and DTI studies often report SNR values to assure the reliability of the estimated metrics. However, SNR levels are not routinely reported in DKI, resulting in the challenges of comparing results between studies. Therefore it is desirable to ensure the DT- and KT-derived indices are estimated with adequate SNR levels before the comparison between studies. Our results show that the mean MK varied from 0.70 (PUT) to 1.27 (IC) while AK and RK varied from 0.58 (CC) to 0.92 (Cg) and from 0.70 (PUT) to 1.98 (CC), respectively, with a range of SNR levels (from 25.25 in CC to 60.75 in PUT) in various anatomical structures of the brain. Additionally, inter-subject differences substantially contribute the within-group variability (86), and may partially explain discrepancy between studies. In particular, various choice of ROIs among studies (i.e. selection of structure from only contiguous voxels with the highest values to the entire structure) hampers comparisons between studies. For instance, the difference of FA in the genu of the CC between 0.44 in (55) and 0.80 in (54), may be largely due to the ROI used for measurement. Therefore it is important to ensure the DT- and KT-derived indices are reliable across raters within-group, as ROI-based measurement often required rater decisions which may have impacted ROI placement between observers. Our results show that ICC values are near 1 for various ROIs over all metrics, indicating high reliability of ROI-based measurement performed in the brain. It should be also noted that regional variability of DTI values between publications may relate to age differences within-group aside from selection of ROIs, acquisition parameters and SNR. Considerable inter-subject variability of DTI parameters has been shown in previous studies that mostly reported the age dependence of DTI metrics (87–89). Our subjects were young adults (mean age 24 ± 2) and this may contribute on variability of diffusion metrics as compared to those in the literature.
Table 5
Regional values in the healthy brain from the literature. Abbreviations: PUT = putamen; GP = globus pallidus; CC = corpus callosum; IC = internal capsule; ALIC = anterior limb of IC; PLIC = posterior limb of IC; EC = external capsule; Cg = cingulum.
Region | Reference | Number of directions (DIR), b-values (ms/µm2) | Voxel size (mm3) | MK | RK | MD (mm2/s) | FA | RD (mm2/s) |
PUT | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 0.67 ± 0.08 | 0.61 ± 0.08 | 0.79 ± 0.03 | 0.15 ± 0.02 | 0.73 ± 0.03 |
PUT | (55) | 50 DIR, 3 b-values (0, 1000, 2000) | 1.9 × 1.9 × 5 | 0.77 ± 0.01 | 0.85 ± 0.01 | 1.72 ± 0.01 | 0.16 ± 0.01 | 1.57 ± 0.03 |
GP | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.06 ± 0.08 | 1.05 ± 0.10 | 0.86 ± 0.08 | 0.27 ± 0.04 | 0.74 ± 0.06 |
GP (Left) GP (Right) | (56) | 60 DIR, 3 b-values (0, 1000, 2800) | 2.2 × 2.2 × 2.2 | 1.76 ± 0.15 1.85 ± 0.17 | - | - | - | - |
CC (genu) | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.06 ± 0.11 | 2.07 ± 0.45 | 0.93 ± 0.06 | 0.80 ± 0.04 | 0.36 ± 0.07 |
CC (genu) | (55) | 50 DIR, 3 b-values (0, 1000, 2000) | 1.9 × 1.9 × 5 | 0.90 ± 0.05 | 0.90 ± 0.07 | 1.82 ± 0.08 | 0.70 ± 0.05 | 1.04 ± 0.07 |
CC (genu) | (83) | 64 DIR, 3 b-values (0, 1000, 2000) | 2.5 × 2.5 × 2.5 | 0.94 ± 0.07 | - | 1.38 ± 0.12 | 0.44 ± 0.04 | - |
CC (splenium) | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.32 ± 0.09 | 2.72 ± 0.41 | 0.89 ± 0.09 | 0.83 ± 0.03 | 0.31 ± 0.07 |
CC (splenium) | (55) | 50 DIR, 3 b-values (0, 1000, 2000) | 1.9 × 1.9 × 5 | 1.07 ± 0.08 | 1.05 ± 0.07 | 1.70 ± 0.06 | 0.76 ± 0.04 | 0.87 ± 0.03 |
CC (splenium) | (83) | 64 DIR, 3 b-values (0, 1000, 2000) | 2.5 × 2.5 × 2.5 | 1.14 ± 0.09 | - | 1.17 ± 0.10 | 0.54 ± 0.05 | - |
IC | (84) | 15 DIR, 6 b-values (0, 500, 1000, 1500, 2000, 2500) | 2 × 2 × 2 | 1.05 ± 0.08 | 0.84 ± 0.03 | - | - | - |
IC (Left) IC (Right) | (56) | 60 DIR, 3 b-values (0, 1000, 2800) | 2.2 × 2.2 × 2.2 | 1.45 ± 0.06 1.49 ± 0.07 | - | - | - | - |
ALIC | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.04 ± 0.10 | 1.60 ± 0.28 | 0.87 ± 0.05 | 0.60 ± 0.04 | 0.53 ± 0.05 |
PLIC | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.23 ± 0.09 | 2.04 ± 0.23 | 0.89 ± 0.09 | 0.71 ± 0.04 | 0.45 ± 0.07 |
EC | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 0.81 ± 0.05 | 1.02 ± 0.09 | 0.90 ± 0.05 | 0.41 ± 0.03 | 0.70 ± 0.04 |
EC | (55) | 50 DIR, 3 b-values (0, 1000, 2000) | 1.9 × 1.9 × 5 | 0.85 ± 0.01 | 0.93 ± 0.05 | 1.73 ± 0.19 | 0.38 ± 0.03 | 1.28 ± 0.03 |
Cg | (54) | 15 DIR, 5 b-values (0, 500, 1000, 2500, 2750) | 2 × 2 × 2 | 1.07 ± 0.07 | 1.85 ± 0.26 | 0.86 ± 0.07 | 0.66 ± 0.06 | 0.48 ± 0.08 |
Cg | (55) | 50 DIR, 3 b-values (0, 1000, 2000) | 1.9 × 1.9 × 5 | 0.94 ± 0.03 | 0.96 ± 0.07 | 1.64 ± 0.05 | 0.55 ± 0.05 | 1.08 ± 0.05 |
In the spinal cord, there are numerous reports in the literature available for comparison with our results. In order to ensure the similarity of the acquisition sequences and parameters, here we focus on comparing our DT-derived values with those by Qian et al. (64) (a study that our raw data were originally obtained) and Samson et al. (27) (a multi-centre study with the compatible acquisition protocols as ours). Our FA values with Rician denoising are found to be significantly lower than those previous reported by Qian et al. (0.81–0.84; p < 0.05) while our MD, AD and RD values with Rician denoising are not significantly different from those from the same study (64). This suggests that Rician NLM filtering might reduce overestimation of FA in the spinal cord, which is common observed in DTI of the brain (68, 85, 90), by decreasing estimation error. Our column specific measurements of MD are at the lower end of the previously reported range of 0.93–1.29 mm2/ms by Samson et al. (27) while FA measurements are higher than the range measured by the same study (0.59–0.63). Our RD values are lower than the range measured by Samson et al. (0.68–0.84 mm2/ms) (27) while AD values are at the higher end of the previously reported range of 1.43–2.22 mm2/ms by the same study. Overall, DTI metrics are likely to be within similar ranges, however difference among protocols and the associated SNR in each study must be taken into account when comparing between those DTI metrics.
Consideration for clinical applications
It is worth noting that the DKI data acquisition took around 20 min per person, because we obtained whole brain DKI data with 2 averages in order to evaluate quality of different processing methods through a whole brain with reasonable SNR. Our results showed significant decrease of χ2 values, indicating quality of DKI-derived maps improved through a whole brain within reasonable scan time when CLLS-R estimation was performed. Thus, by reducing the number of slices carefully selected for areas of interest, neurology- or neuroscience-related application studies should be feasible, which would last a clinically acceptable time frame (less than 10 min). Additionally, Rician NLM denoising in combination with CLLS can be readily implemented as it is based on a LSE algorithm available through existing commercial programs. Therefore, practical use of the combined Rician denoising method is widely expected in characterizing microarchitectural integrity of normal and pathological states.