Free-water diffusion tensor imaging improves the accuracy and sensitivity of white matter analysis in Alzheimer’s disease

Magnetic resonance imaging (MRI) based diffusion tensor imaging (DTI) can assess white matter (WM) integrity through several metrics, such as fractional anisotropy (FA), axial/radial diffusivities (AxD/RD), and mode of anisotropy (MA). Standard DTI is susceptible to the effects of extracellular free water (FW), which can be removed using an advanced free-water DTI (FW-DTI) model. The purpose of this study was to compare standard and FW-DTI metrics in the context of Alzheimer’s disease (AD). Data were obtained from the Open Access Series of Imaging Studies (OASIS-3) database and included both healthy controls (HC) and mild-to-moderate AD. With both standard and FW-DTI, decreased FA was found in AD, mainly in the corpus callosum and fornix, consistent with neurodegenerative mechanisms. Widespread higher AxD and RD were observed with standard DTI; however, the FW index, indicative of AD-associated neurodegeneration, was significantly elevated in these regions in AD, highlighting the potential impact of free water contributions on standard DTI in neurodegenerative pathologies. Using FW-DTI, improved consistency was observed in FA, AxD, and RD, and the complementary FW index was higher in the AD group as expected. With both standard and FW-DTI, higher values of MA coupled with higher values of FA in AD were found in the anterior thalamic radiation and cortico-spinal tract, most likely arising from a loss of crossing fibers. In conclusion, FW-DTI better reflects the underlying pathology of AD and improves the accuracy of DTI metrics related to WM integrity in Alzheimer’s disease.


Materials and methods
Subjects. All data were downloaded from the OASIS-3 brain project (http:// oasis-brains. org/), which is a neuroimaging dataset for normal aging and Alzheimer's disease and is freely available to the scientific community. Inclusion criteria were participants between the ages of 60 and 90 years who had 3 T dMRI data available with more than 30 directions. Exclusion criteria were cognitively impaired participants with dementia not attributed to AD, healthy control participants with significant comorbidities, and participants for whom the MMSE was not available. Only one time-point was used per subject. Subsequently, this study included 30 HCs (17 females; age (standard deviation, S.D.) = 73 (6) years) and 28 AD subjects (primarily mild AD; 15 females; age = 75 (7) years). Four AD subjects had remote mood disorders and one had a remote hypothyroidism as secondary medical diagnoses. The Clinical Dementia Rating (CDR) 33 , which is a 5-point scale used to characterize multiple domains of cognitive and functional abilities, was zero for all HCs and between 0.5 and 3.0 for the AD group. The MMSE is a 30-point assessment commonly used to measure cognitive impairment. The mean value of MMSE was 29.10 (S.D. 1.24) for HC and 24.18 (S.D. 5.02) for AD. All subject characteristics are summarized in Table 1. MRI protocol for DTI. All dMRI data collected from the OASIS-3 database were acquired using a 3 T scanner (Siemens). For all subjects, the acquisition was performed using 64 diffusion-encoding directions (b value: Data preprocessing. DMRI data were downloaded in NIFTI format and processed as previously described 26,27 . Briefly, the data were preprocessed using the functional magnetic resonance imaging of the brain (FMRIB) software library tool (FSL, version 5.0.4) 34 . Following translation and rotation estimation, the raw dMRI images were corrected for eddy currents and motion 35 . After motion correction, the gradient orientations were compensated (prior to calculating B-matrices) to account for the rotational component of registration. A brain mask was defined for each subject using the Brain Extraction Toolbox (BET) 36 for the single B0 images. DTI standard (uncorrected for FW) and FW-corrected maps were calculated using an in-house MATLAB script 26 , which is available upon request. The FW maps were computed by fitting the following model at each voxel 18 : where A g is the modeled attenuated signal (normalized by B0) for the applied diffusion gradient g, and b is the b-value (1000 s/mm 2 ). The first term reflects the tissue compartment, where D is the diffusion tensor of this compartment, f is the fractional volume of the compartment, and g T is the transpose of the vector g. The second term reflects an isotropic free-water compartment with a fractional volume of (1 − f), where the diffusion coefficient D water is set to the diffusivity of water at body temperature (3 × 10 −3 mm 2 /s). AxD, RD, and FA were obtained from D. Standard DTI metrics are reported as AxD, RD, and FA, while FW-corrected DTI metrics are reported as AxD t , RD t , and FA t , where the t is indicative of greater tissue specificity from FW-DTI. While FA indicates deviation from a spherical-shaped tensor (FA = 0; isotropic diffusion), the mode of anisotropy (MA) is a complementary measure that discriminates between linear and planar anisotropy. MA is mathematically orthogonal to FA and relates to the skewness of the DTI eigenvalues ( 1 , 2 , 3 ) 37 : After quantifying all DTI-derived metrics, the B0 images from each subject were used to create a B0 groupwise template image using buildtemplateparallel.sh included in ANTs; this procedure has been demonstrated to improve the final normalization procedure 38 . The B0 group-wise template image was subsequently normalized to the IIT_mean_b0 image by ANTs symmetric image normalization (SyN) algorithm 39 . The warp fields obtained from this normalization and from the B0 group-wise template creation were used to transfer all DTI maps (standard and FW-corrected) to the Illinois Institute of Technology (IIT) Human Brain Atlas (v.4.1), which contains both anatomical and DTI brain templates in International Consortium for Brain Mapping (ICBM)-152 space 40 . All DTI maps in standard space were smoothed using FSL with an isotropic Gaussian kernel (sigma, 3 mm).
Statistical analysis. Age, MMSE, and CDR scores are presented as mean and standard deviation (SD) for each group. Differences in age, sex, and cognitive test scores between groups were assessed using the Student's t-test. Comparisons of all DTI-, FW-DTI-metrics, and FW maps between groups were performed using the FSL Randomise tool 41 with threshold-free cluster enhancement (TFCE) 42 and a correction for multiple comparisons via Family-Wise Error (FWE) rate 38 at a 0.01 level. A WM mask was defined using a threshold of 0.2 on the average values of FA (from standard DTI) and was applied to the other DTI maps. For each voxel, the DTI-derived metrics were fitted by an Analysis of Covariance model (ANCOVA), which included age and sex as covariates. The number of randomized permutations was set at 5,000. The clusters identified to be statistically different between groups were labeled according to the JHU DTI-based white-matter atlases 43,44 . All results are reported with a significance threshold of p value < 0.01, corrected for FWE, except where otherwise noted.
For the cognitively impaired group (AD only), the voxel-based relationship between MMSE scores and DTI metrics was assessed through Randomise with significance at p-value < 0.01 (FWE-corrected).
Standard DTI. Figure 1 shows the clusters of significant differences between the two groups obtained with standard DTI metrics with the corresponding violin plots quantifying the DTI differences for each group (across all combined clusters). For FA (panel (a)), lower FA was observed in AD compared with HC mainly in the fornix (cluster covering 93.3% of the fornix) and CC (covering 35.5% of CC). Small clusters where AD had higher FA values than HC were found in the right anterior thalamic radiation (ATR), cortical spinal tract (CST), posterior limb of internal capsule (PLIC), and superior corona radiata (SCR). More widespread differences between HC and AD were observed using AxD and RD (panel (b) and (c), respectively). Additionally, all significant clusters corresponded to higher values of AxD and RD metrics in the AD group, with no clusters corresponding to lower AxD or RD.
For each brain region, the significant cluster sizes (as percent volume) are reported in Table 2. Several clusters were observed where multiple DTI metrics were simultaneously altered between HC and AD groups, as shown in Supplementary Table 1. Regions where lower FA values overlapped with higher AxD and RD included the fornix, CC, forceps minor, and left cingulum. Higher FA values were found to overlap with higher AxD in www.nature.com/scientificreports/ the right PLIC, CST, and SCR. Substantial overlap was observed for clusters with higher AxD and higher RD, including 85% of the cingulum (hippocampus), 76% of the fornix, and 49% of the sagittal stratum. Finally, Supplementary Table 2 shows the corresponding mean DTI values inside each significant cluster for regions with higher and lower values for each group. Figure 2 shows the clusters of significant differences between groups for FW-DTI metrics with the corresponding violin plots quantifying the DTI differences for each group (across all combined clusters), where FA t , AxD t , and RD t are displayed in panels (a), (b), and (c) (at p < 0.01 FWE corrected, unless otherwise indicated). The clusters where AD had lower FA t values than HC correspond to the same WM locations as those observed using standard FA (specifically, fornix and CC); however, these clusters (covering 71% and 19.2% of fornix and CC, respectively) are smaller than standard FA (93.3% and 35.5%, respectively). Higher FA t values in AD compared with HC were found bilaterally for ATR, CST, limb of internal capsule (LIC), SCR, and superior fronto-occipital fasciculus (SFOF). With regard to AxD t and RD t , both higher and lower values were observed in multiple regions in the AD group (recall that only higher AxD and RD were observed using standard DTI). More specifically, AxD t was lower in the AD group in CC and fornix and predominantly higher in the ATR, CST, and retrolenticular part of internal capsule. Lower RD t was observed with AD mainly in the ATR, CST, PLIC, and SFOF, corresponding to similar areas with higher FA t . A small cluster inside the body of the CC showed higher RD t in the AD group, albeit at p < 0.05 FWE corrected. For each brain region, the significant cluster sizes (as percent volume) are reported in Table 2. As for standard DTI, several clusters were observed where multiple DTI metrics were simultaneously altered between HC and AD groups, as shown in Supplementary Table 1. No regions were observed where lower FA t values overlapped with higher AxD t and RD t ; however, lower FA t values overlapped with lower AxD t and RD t values in the fornix (4.8%), while lower FA t corresponded with lower AxD t in several regions including the CC and forceps minor. Higher FA t values were found to overlap with higher AxD t and lower RD t in the SFOF, right PLIC, SCR, and anterior LIC. Several clusters were observed with higher AxD t and lower RD t , including the left CST, right PLIC, and right SCR. Unlike standard DTI, no clusters demonstrated simultaneously higher AxD t and higher RD t . Finally, Supplementary Table 3 shows the corresponding mean FW-DTI values inside each significant cluster for regions with higher and lower values for each group. Figure 3 shows the significant differences between groups using the FW index (obtained from the fit in Eq. 1) at p < 0.01 FWE corrected. The corresponding violin plots are also shown for FW values for each group (across all combined clusters). Only clusters with higher FW values in AD compared with HC were found, The color bars indicate values that are lower in AD than HC (red-to-yellow) and higher in AD than HC (blue-to-cyan). For axial and radial diffusivities, only clusters with higher values in AD than HC were found. The corresponding violin plots represent the DTI metrics inside the significant clusters for each group. www.nature.com/scientificreports/   www.nature.com/scientificreports/ with clusters covering 34% of the total WM mask. These differences were observed in several WM regions, including most prominently the fornix, cingulum (both hippocampal and cingulate gyrus parts), and CC. The complete list of group-wise significant clusters for the FW index between HC and AD is reported in Table 3.

MA-index.
The results for MA are reported in Fig. 4. Significantly higher values of MA (from both standard DTI and FW-DTI) in AD compared with HC were observed in the right CST, right PLIC, right SCR, and right SFOF, corresponding to more linear anisotropy. On the other hand, lower MA values (from standard DTI and FW-DTI) in AD compared with HC were found mainly in the genu of CC and in the external capsule (EC), corresponding to more planar anisotropy. It should be noted that similar results for MA were obtained with both standard DTI and FW-DTI analysis. The complete list of group-wise significant clusters is reported in Table 4.  www.nature.com/scientificreports/  www.nature.com/scientificreports/

Voxel-based correlations between DTI/FW-DTI metrics and MMSE. No significant voxel-based
correlation was found between MMSE and either standard or FW-DTI metrics at p < 0.05 FWE corrected level. Supplementary Fig. 1 shows the population scatter-plots for standard and FW-DTI metrics, while the group-wise correlations for HC and AD are provided in each plot. Panels (a) and (b) show the correlations between FA and AxD, while panels (c) and (d) show the correlations between FA and RD. It should be noted that the correlations increased after FW correction (e.g., for the AD group: the correlations between FA and AxD increased from 0.160 (standard) to 0.856 (FW-corrected) and from − 0.464 (standard) to − 0.803 (FW-corrected) between FA and RD). Similar increases were observed for both HC and AD groups, suggesting that older HC participants also have substantial FW contributions to their dMRI-derived metrics. Panels (e)-(g) show the correlations between FA and FW-FA t , AxD and FW-AxD t , RD and FW-RD t , respectively. By removing the isotropic diffusion contribution, the impact of FW-correction is to increase FA t , decrease AxD t , and decrease RD t , relative to the corresponding standard DTI metrics. These panels also show that FA is less affected by the FW component than AxD and RD (i.e., the correlation for standard vs. FW FA is higher than that for AxD and RD). As AxD and RD metrics are more influenced by free-water components (i.e., have lower correlations between standard and FW metrics), this is consistent with the widespread AxD and RD changes without FW-correction. Here again, there is not a strong group difference in the correlations. Additionally, the striking differences for AxD and RD metrics between standard and FW-correction can be attributed to their biophysical origin; that is, raw diffusivity parameters AxD and RD are likely to be more impacted by intravoxel free-water diffusion than the composite metric FA.

Discussion
In this study, WM integrity was assessed in patients with Alzheimer's disease using both standard and FWcorrected DTI metrics. Although DTI is a commonly used method for assessing WM, PVEs can reduce the accuracy of DTI metrics, ultimately limiting their interpretation. To mitigate PVE, free water-contaminated voxels were removed by incorporating a FW component in the conventional diffusion modeling pipeline 18 , producing more accurate FW-corrected DTI metrics and the complementary FW index. Using both standard and FW-DTI, significant WM differences were observed between HC and AD subjects in several regions, including both higher and lower FA. Both AxD and RD were highly impacted by the effects of FW, and FW-corrected AxDt and RDt were more consistent with pathology-based expected spatial patterns of neurodegeneration. The FW index was higher in AD than HC across many regions, as expected. The FW correction method has shown promise in many neurological diseases of the WM 21,24-27 , particularly those with neurodegenerative aspects; similarly, we now demonstrate that the application of FW correction in AD improves the accuracy and sensitivity of the resulting DTI metrics. www.nature.com/scientificreports/ Lower FA values, indicative of more isotropic motion, are consistent with neurodegenerative changes and were observed in AD in multiple regions, including most prominently the fornix and CC. Of particular interest, the fornix is the major output tract of the hippocampus and plays a major role in episodic memory 2,45 . In the context of AD, pathological changes in the fornix may occur at an early disease stage before clinical manifestations. Lower FA and higher MD in the fornix has been a robust and consistent finding in AD 46,47 and may correlate with cognitive decline 46,48 . Similarly, FA reductions in the fornix have been identified using skeletonized tractbased spatial statistics (TBSS) in early-symptomatic individuals and those at high risk for developing AD [49][50][51][52] . However, the fornix is particularly prone to PVEs due to its proximity to the lateral ventricles 2 , which may be further exacerbated by atrophy-related ventricular expansion in AD. While decreases in standard FA may reflect a complex combination of atrophy and microstructural changes, these decreases remained after correction for FW, indicating that they reflect true pathological changes in the fornix.
Other significant changes were observed in AD in the CC, which is a major fiber bundle responsible for interhemispheric connection. Using both standard and FW-DTI, large clusters of lower FA were observed in the genu and body with minimal splenial changes, particularly using FW-DTI. Several other studies have similarly reported decreased FA in the CC; however, these studies have shown inconsistent regional changes with AD, with some studies finding changes throughout the CC 53 and others reporting predominant changes in the genu 9 or splenium 54 . Early involvement of the genu would support the anterior-to-posterior progression of the retrogenesis hypothesis, wherein degeneration occurs in reverse of myelination. In contrast, early changes in the splenium would be consistent the posterior-to-anterior progression of Wallerian degeneration following neuronal loss, wherein WM damage is subsequent to grey matter damage. To date, conclusive evidence of a gradient pattern has remained elusive 55,56 . Given the substantial FW component observed in the CC, the inclusion of FW correction algorithms could improve accuracy in the resulting DTI metrics in the presence of neurodegenerative changes, and future studies should consider whether the implementation of FW correction could increase confidence in the spatiotemporal patterns observed across DTI studies.
Higher FA t in AD compared with HC was observed seemingly paradoxically using FW-DTI in bilateral ATR and CST, as well as internal capsule and corona radiata; with standard DTI, much smaller clusters of higher FA were observed in the right hemisphere (versus bilateral for FW-DTI) in the ATR, CST, PLIC and SCR (see Table 2 and Supplementary Tables 2 and 3). In the presence of a unidirectional fiber tract, higher FA would suggest lower RD and/or higher AxD, which are in contrast to the expected changes in the presence of neurodegeneration. However, one of the major drawbacks of standard DTI methods is an inability to resolve different fiber orientations within a voxel 57 , which arises from the assumption of Gaussian diffusion implicit in the tensor model 58 .
In the presence of crossing fibers, FA is artificially diminished due to multi-directional fiber tracts; thus, ADrelated neurodegeneration in these regions may yield increased FA due to the loss of crossing fibers. In these cases, MA-a metric of diffusion anisotropy-may provide insight in areas of crossing fibers; moreover, higher MA has been related to a loss of crossing fibers in early AD pathology in regions with known complicated tract topologies 59 . Further corroborating the presence of fiber crossing, MA was higher in AD subjects in the right CST, PLIC, and SCR. Conversely, lower MA in AD was found in clusters in the left ATR, forceps major and minor, IFOF, UF, genu of CC, anterior CR, and EC. Similar to these results, other studies have found parallel increases of both FA and MA in AD patients in a large cluster extending along the CST and involving the ATR 54,60 . The higher MA in AD subjects, together with higher FA, suggests a more linear shape of the diffusion tensor, indicative of the loss of crossing fiber populations in these areas. As the CST is relatively preserved in AD pathology, these changes suggest degeneration of fiber tracts in the ATR, CC, and fasciculus.
Using standard DTI, non-specific higher AxD and RD were observed across WM, while FW-AxD t and FW-RD t had better agreement with regional FA t changes. This may be reflective of a larger impact of isotropic FW diffusion on AxD and RD metrics compared to FA. For example, lower FA in the CC and fornix is indicative of altered WM integrity (e.g., demyelination) in the AD group; these changes were driven by both higher AxD and RD with standard DTI, while FW correction showed that these changes in FA t may be driven by underlying lower AxD t . Using FW-DTI, lower FW-AxD t (AD < HC) were found in WM locations corresponding to lower FA t , while the fornix showed simultaneous lower FW-RD t (HC > AD) in a small cluster. With standard DTI, AxD was higher across multiple regions, consistent with prior literature 14,49,54,61,62 . However, the mechanism of higher AxD is unknown and contrary to prevailing theories of known AD pathology 61 . Using FW-DTI, regions of lower AxD t corresponded to lower FA t values, suggesting that prior reports of higher AxD may have been sensitive to the effects of FW. A similar trend of AxD decreasing with FW correction was previously reported using TBSS in the context of AD and cerebrovascular disease 21 . After FW correction, higher AxD t in AD, compared with HCs, was observed in regions with known crossing fibers, consistent with degeneration of select fiber tracts in these regions. Additionally, clusters with higher FW-FA t values in AD (e.g., ATR, CST, anterior/posterior LIC, and SFOF) were associated with higher FW-AxD t and lower FW-RD t . Using standard DTI analysis, no lower AxD or RD values were detected in AD subjects.
The FW volume fraction was quantified using the FW-correction algorithm and, consistent with AD-related neurodegeneration, was higher in AD in many WM areas and tracts. More specifically, large clusters of higher FW were located in the cingulum (hippocampal and cingulate gyrus parts, 85.16% and 56.34%, respectively), ILF and IFOF (52% and 40%, respectively), forceps major and minor (approximately 40% each), and ATR (31.39%). Similar clusters were also found in the fornix (95.6%) and CC (genu, body, and splenium; approximately 56% of the total CC). Additionally, approximately 42% of the FW clusters were located in WM outside the regions specified by the atlases; in particular, FW increases were found in several regions bordering various sulcal fundi. Consistent with DTI-based metrics, the FW index further demonstrates an important connection between the fornix, CC, and AD. The high volume of FW in these regions may be related to loss of WM integrity; moreover, the contaminating effects of FW further validates the significant differences observed between standard and FW-DTI metrics. This metric may itself be a valuable biomarker, consistent with our hypothesis, as previous studies www.nature.com/scientificreports/ have shown that higher FW values were associated with poorer executive functioning, visual construction, and visuomotor performance 21 . Overall, FW-DTI provides not only more accurate and consistent DTI-based biomarkers, but also provides quantitative FW volume fractions, which may be a potential biomarker of sub-voxel neurodegenerative processes. Correlations between DTI metrics and various neuropsychology assessments could lend insight into the role of WM changes on cognitive function in AD pathology. In this study, we did not observe any significant voxel-wise correlations between MMSE and DTI metrics before or after FW correction in the AD cohort. This may be attributable to the similar group characteristics (predominantly very mild to mild AD) and the relatively narrow range of MMSE scores, while future studies could consider including more sensitive measures of cognitive functioning, including various sub-domains such as memory and executive function. Despite the lack of correlation in this study, the overall finding that FW-DTI metrics are more consistent with the pathology may lend insight into the inconsistent correlative findings across the literature. While the relationship between WM integrity as assessed by DTI and cognitive functions remains unsettled, the implementation of FW correction to yield more accurate DTI metrics should be considered as a methodological improvement for future correlation studies, particularly for the diffusivity metrics AxD and RD.
There are several limitations to this study. First, we used a voxel-based approach for WM analysis rather than a skeletonized approach, such as TBSS. As TBSS minimizes tract variance across subjects using a common skeletonized tract, it uses fewer voxels and is inherently less sensitive to partial volume effects. However, the higher number of voxels available with voxel-based approaches may increase sensitivity to subtle differences in microstructure 63 . Even so, all of these approaches necessitate the use of atlases, which may be limited in the WM regions that are represented (in this case, the atlases covered 84% of the WM mask); this is particularly relevant for the FW index that showed widespread changes across WM, even outside of the atlas regions. In the present study, atrophy likely minimal due to the selected patient population, further enabling the use of a voxel-based approach. Second, no significant voxel-based correlations (p < 0.01 FWE corrected) were observed between standard DTI and FW-DTI metrics and the MMSE score, which is consistent with several previous studies [13][14][15][16] . This suggests that while WM is altered in AD, the relationship between global cognitive scores and WM pathology may not be linear. Future work could consider more sensitive measures of cognitive subdomains, and the inclusion of a longitudinal aspect may further pinpoint the temporal ordering of WM alterations relative to GM pathology and cognitive decline. Finally, as early biomarkers are of increasing interest, future studies should also include cohorts of MCI or subjects at high risk of developing AD.

Conclusion
In conclusion, this study demonstrates that the implementation of a FW correction algorithm for DTI improves both the sensitivity and specificity of derived DTI metrics by removing PVEs, and better captures underlying AD-related pathologic changes than standard DTI approaches. We found significantly altered DTI metrics in AD compared to HC for both standard and FW-DTI, but importantly FW-DTI identified changes were more consistent with known AD pathology as hypothesized (both in terms of magnitude and direction of DTI changes). In addition, MA may improve specificity related to crossing fibers, while the FW index may improve sensitivity to sub-voxel neurodegeneration. Overall, FW-DTI improves the reliability and inter-parameter consistency of DTI metrics in the presence of atrophy, and the resulting metrics provide more sensitive and specific insight into AD-related pathological changes in white matter.