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While diffusion-tensor-imaging tractography provides remarkable in vivo anatomical connectivity of the central nervous system, the majority of DTI studies to date are predominantly limited to tracking large white-matter fibers. This study investigated DTI tractography using long diffusion time (tdiff) to improve tracking of thinner fibers in fixed rhesus monkey brains. Stimulated Echo Acquisition Mode (STEAM) sequence on a 3T Siemens TRIO was modified to include a diffusion module. DTI was acquired using STEAM with tdiff of 48 and 192 ms with matched signal-to-noise ratios (SNR). Comparisons were also made with the conventional double-spin echo (DSE) at a short tdiff of 45 ms. Not only did the fractional anisotropy increase significantly with the use of long diffusion time, but directional entropy measures indicated that there was an increased coherence amongst neighboring tensors. Further, the magnitude of the major eigenvector was larger at the tdiff = 192 ms as compared to the short tdiff. Probabilistic connectivity maps at long tdiff showed larger areas of connectivity with the use of long diffusion time, which traversed deeper into areas of low anisotropy. With tractography, it was found that the length of the fibers, increased by almost 10% in the callosal fibers that branch into the paracentral gyrus, the precentral gyrus and the post central gyrus. A similar increase of about 20% was observed in the fibers of the internal capsule. These findings offer encouraging data that DTI at long diffusion time could improve tract tracing of small fibers in areas of low fractional anisotropy (FA), such as at the interfaces of white matter and grey matter.
Diffusion tensor imaging (DTI) (1,2) contrast in biological systems arises from water movement in the presence of barriers (such as cell membranes of axons and oligodendrocytes) that hinder water diffusion more in some orientations than others. DTI has been widely used to map whole-brain anatomical connectivity in a totally non-invasive fashion (3). This is in marked contrast to histological tracing techniques (invasive) where radioactive or fluorescent tracers are focally injected to track regional connections over a few synapses (limited coverage), precluding whole-brain, longitudinal and in vivo studies and human applications.
The majority of DTI tractography studies to date are limited to tracking large white-matter fibers. Novel approaches such as multiple high b-value DTI (4), high angular resolution DTI (HARD) (5) and Q-ball imaging (6) are being actively explored to improve diffusion-based tractography. A unique feature of many of these approaches is that, in contrast to conventional DTI tractography, they do not assume Gaussian diffusion (6). Yoshiura et al. measured DTI indices using very high values (500 to 5000 s/mm2) (36) and showed that, as the b-value increased, apparent diffusion coefficient (ADC) decreased in both the gray and white matter. They also found that non-monoexponential diffusion signal decay was more prominent in white matter than in gray matter. Surprisingly, there was no significant change in the relation of the b-value to the FA maps. High b-value appears to have a dissociating effect on gray and white matter in DWIs. Ronen et al. performed DTI tractography using multi-exponential decays. By decomposing into slow and fast diffusion tensors and compared with conventional DTI data (4), they reported that fibers generated on the basis of the slow diffusion component appear to follow the vertical fibers in gray matter. DTI of the slow component may provide a way for increasing the sensitivity to anisotropic structures in cortical gray matter. While these novel approaches are promising, they require very large b-values that are not readily achievable on clinical scanners due to gradient strength limitations. They are also generally more difficult to implement compared to conventional DTI techniques.
The root-mean-squared (7,8) displacement in diffusion measurement is dependent on diffusion time (tdiff). For a tdiff of 20 ms, the rms displacement is ≈10 μm in vivo (7,8), on the order of cell sizes in the brain, and diffusion is largely sensitive to restriction by cell membranes and subcellular organelles. At tdiff ≈ 200 ms, the rms displacement is ≈ 32 μm, substantially larger than the average cell sizes, and diffusion is also sensitive to restriction in the extracellular spaces along fiber tracts. Indeed, the ADC of water in vivo has been shown to be dependent on tdiff, with ADC decreasing rapidly for tdiff from 2 to 15 ms and gradually for tdiff greater than 20 ms (9–11). ADC in human brains is diffusion-time dependent (12). Fractional anisotropy (FA) at longer tdiff has been reported to be more sensitive to changes in myelin-deficient mice (13). These findings suggest that DTI at long diffusion time could improve tractography. DTI studies to date employed relatively short tdiff to minimize signal loss due to T2 decay and DTI tractography at long tdiff has not been reported.
The goal of this study was to determine whether DTI at long tdiff improves tracking of thinner fibers. To overcome T2 signal loss associated with long tdiff measurements, Stimulated-Echo-Acquisition-Mode (STEAM) sequence (14,15) was modified to include a diffusion module to sample 30 diffusion directions on a 3T Siemens TRIO. DTI tractography was performed with short (48 ms) and long (192 ms) diffusion time on post-mortem fixed monkey brains. Standard dual spin-echo (DSE) (16) DTI data were also acquired on the same monkey brains in the same setting for comparison in order to ascertain that the improvement was indeed due to the application of the longer diffusion time and not due to a different sequence. FA, tensor-field plots, connectivity maps based on entropy minimization (17) and deterministic fiber tractography using line propagation (3) were compared among the three methods with matched signal-to-noise ratio (SNR) and identical statistical thresholds.
Cross-term interactions among diffusion and imaging gradients in STEAM acquisition at long tdiff can be significant (18–20) and can adversely affect DTI measurements. While cross-term interactions could be calculated to derive the exact b values (19,21), geometric averaging approach was used to remove cross-term bias (19,22) without evaluating the exact b-values. This involved acquiring two DTI data sets in which two DWI were acquired in the same diffusion gradients but with opposite gradient polarities. The two images are multiplied on a pixel by pixel basis. The square root of the product results in an image with substantially reduced cross-term effects. Phantom studies were performed to evaluate and confirm the validity of this approach. A phantom, 45 mm in diameter, made of 0.5 M 1H-mannitol dissolved in dimethlysulfoxide (DMSO), was chosen because the ADC of mannitol in DMSO (as opposed to water phantom) is more similar to water ADC in fixed brain. This allows the use of identical b-values and imaging protocols for both phantom and brain studies.
Eight measurements were made on four rhesus monkey brains fixed with 4% formalin. Brains were perfused-fixed and stored in formalin for a maximum of 5 days before MRI. During imaging, the sample was submerged in water to minimize susceptibility on the surface of the brain. The strong bulk water signal along the sharp edges of the container, however, gave rise to Gibbs ringing artifacts. A small amount of MION (0.018 mg/mL) was added to eliminate Gibbs ringing. The large MION particles could not enter the interstitial space of the brain tissue, as confirmed by the absence of degradation of echo-planar images and SNRs acquired up to a week after the MION addition.
MRI studies were performed on a Siemens 3T Trio clinical scanner (Siemens AG, Erlangen, Germany). All samples were scanned at room temperature. T1-weighted images were acquired using conventional gradient- echo acquisition, with TR = 4000 ms, flip angle = 25°, TE = 7.7 ms, FOV = 70 × 70 mm, matrix size = 128 × 128, and slice thickness = 2 mm.
DTI data were acquired with a 16-shot STEAM (14,15) EPI sequence with TR = 1500 ms, TE = 80 ms, 30 diffusion directions with b = 1700 s/mm2 and a single b = 0 s/mm2 acquisition, FOV = 70 × 70 mm, matrix size = 128 × 128, 3 slices, slice thickness = 2 mm, and δ = 21 ms. Data were acquired at two mixing times (TM) of 25 and 169 ms, which corresponded to tdiff of 48 and 192 ms, respectively. The corresponding numbers of averages were 34 and 70, respectively, chosen so as to match SNR (determined as the ratio of an ROI intensity of the WM in the brain to the standard deviation of ROI intensity outside the brain). These two methods are hereby referred to as STEAM-48 ms and STEAM-192 ms. The b value of 1700 s/mm2 was used instead of the typical 1000 s/mm2 in vivo because fixation decreases ADC value. Note that the TE at long tdiff could be substantially shortened (to ~ 63 ms) to achieve the same b value which should reduce number of averaging needed. In this study, the same TE was employed for both long and short tdiff to avoid potential bias due to different T2 weighting in the WM and GM.
For comparison, DTI was also acquired using the standard double spin-echo (DSE) sequence (16) in the same imaging sessions with similar parameters except that the TE was 104 ms which was the minimum achievable value for the experimental parameters. The effective tdiff for DSE was 45 ms. The number of averages, chosen to match SNR of the STEAM acquisitions, was 48. Acquisitions of the three protocols were interleaved and randomized to minimize the effect of potential systematic drifts. The total imaging time for the STEAM-48 ms was 14.16 h. For the DSE sequence the time was 20 hours while for the STEAM-192 ms sequence, it was 29.16 h.
All analyses were performed using codes written in MATLAB® (Mathworks, Natick, MA) unless otherwise specified. FA maps were computed (1,23). White matter (WM) and gray matter (GM) pixels were separated using intensity-based segmentation on T1-weighted images and the mean WM and GM FA were calculated.
Spherical (CS), planar (CP) and linear (CL) anisotropy measures were calculated and plotted on the barycentric coordinate system (three-phase plot) (24)
where , and λ1, λ2, and λ3 are the eigen-values of the 3 × 3 diffusion tensor matrix, with . x and y are co-ordinates on the three-phase plot where isotropy is represented at the apex of the triangle and the left and right vertices correspond to linear and planar anisotropy respectively. The three-phase plot provides a convenient way to study the trend in anisotropy with increasing tdiff.
The tensor-field map was examined for tensor orientations. Long diffusion time could emphasize the dominant fiber in the voxels that comprise of multiple sparse fiber bundles. If these tensors indeed, represented an underlying fiber tract or a continuation of a fiber branch, then the tensors in the neighboring voxels would have similar orientations, i.e. the principal eigenvectors would be co-linear. Such co-linearity would then increase with increase in diffusion time. In order to measure this increase, directional entropy (DE) (26) was used.
For this purpose, a sphere was broken into many triangular faces. Each face was represented by a vector starting from the origin of the sphere and the centroid of the triangular face. Thus, discrete angular orientations, corresponding to each triangular face, were obtained. The principal eigenvectors obtained using DTI were then binned into these discrete vectors. The binning was determined on the basis of the dot product between the principal eigenvector and each discrete vector. The principal eigenvectors was binned into that angular orientation vector which produced the highest value for the dot product. This provided a distribution of the different orientations along a fiber tract. The probability of a tensor direction was evaluated from this distribution and then entropy for the given region of interest along a probable fiber tract was calculated for all three methods and compared. Since only three slices were acquired near the central sulcus, there were two prominent fiber tracts and their branches that could be delineated; the corpus callosum (CC) and the internal capsule (IC).
The value of DE depends on the number of triangular faces used to bin the tensor orientations. For this study, 60, 128, 160, 196 and 320 faces were obtained. It was found that the DE did not change significantly when the number of faces was greater than 160. This study triangulated the sphere into 192 faces to ensure as little variance in entropy as possible due to the binning process.
Front marching algorithm (17) was used to determine the probabilistic connectivity maps in the imaged brain volume. The rate at which the connectivity front propagates from one voxel at location r′ to another voxel at r depends on the co-linearity of the principal eigenvector ε1(r) amongst the neighbors and the direction in which the front continues to evolve. The rate function employed in this study (17) was
where n(r) is the unit vector normal to the front and determines the spread of the front. For comparison, identical cut-off thresholds (0.5 of the maximum value of probabilistic connectivity obtained with equation (2)) were used for all three methods to derive connectivity maps.
Fiber tracking was performed using DTI Studio v2.4 (27). A FA threshold < 0.1 and a turning angle > 65° were used as termination criteria for fiber prorogation for all three methods. DTI Studio v2.4 was also used to calculate the fiber lengths. Lowering the threshold increases the sensitivity to the random fibers and consequently affects the calculation of the fiber lengths. Nonetheless, the trend of increase in fiber length using STEAM192 was still observed at the lowered threshold.
All values in text and on graphs are reported as mean ± SD. Statistical testing utilized unpaired Student t-test with p < 0.05 taken as reaching statistical significance.
ADC of the 1H-mannitol phantom measured along the phase-encode direction was (0.39 ± 0.01) × 10−3 mm2/s (n = 8). ADC along the phase-encoding direction was used as reference for the other two principal directions. Before geometric averaging, ADC values among the three principal axes differed from each other up to 8.1 ± 1.2% for STEAM-48 ms and 16.7 ± 1.8% for STEAM-192 ms. After correction, ADC values among the three principal axes differed only up to 3.7 ± 1.7% for STEAM-48 ms and 6.6 ± 3.4% for STEAM-192 ms. As expected, ADC along the phase-encoding direction were not statistically different between before and after correction, consistent with the notion that cross-terms were minimal along the phase-encode direction. For DSE, ADC values among the three principal axes differed up to 5.4 ± 3.9% and no correction was applied. Smaller cross terms in the DSE is likely due to the use of two balancing 180° pulses.
For all comparisons, SNR among the three methods were matched. Figure 1 shows the FA comparisons among DSE, STEAM-48 ms and STEAM-192 ms of fixed monkey brains. Only WM FA of STEAM-192 ms were statistically different (p < 0.05) from those of STEAM-48 ms and DSE. Indeed, WM FA of STEAM-192 ms were larger than that of STEAM-48 ms by 11.5 ± 5.0% and of DSE by 11.2 ± 5.0%.
The ADC values by STEAM-48 ms, STEAM-192 ms, and DSE were, respectively, 0.18 ± 0.012 × 10−3 mm2/s, 0.16 ± 0.012 × 10−3 mm2/s and 0.16 ± 0.012 × 10−3 mm2/s in WM, and 0.26 ± 0.037 × 10−3 mm2/s, 0.26 ± 0.031 × 10−3 mm2/s and 0.25 ± 0.028 × 10−3 mm2/s in GM. The ADC obtained with the DSE sequence at a tdiff value of 45 ms is similar to that obtained by STEAM-192 ms while the STEAM-48 ms calculates a higher ADC value than STEAM-192 ms. Parallel and perpendicular diffusivities normalized by the trace ADC values were calculated and these values are shown in Table 1.
The directional entropy was evaluated along the callosal fiber tract and the internal capsule to determine if the neighboring tensors were more co-linear at long tdiff. The values of DE are depicted in Table 2. In comparison to STEAM-48 ms, the DE obtained by STEAM192 in the CC and IC was lower by 17.3 ± 6.3% and 10.5 ± 1.2% (p < 0.05) respectively. The decrease in DE with respect to DSE was 18.1 ± 7.2% in the CC and 8.4 ± 1.3% in the IC (p < 0.05). In addition Table 2 also shows the values of CL, CP, CS and FA in the same region.
Tensor-field maps were calculated for the three methods with matched SNR (DSE SNR: 36.5, STEAM-48 ms SNR: 33.9, STEAM-192 ms SNR: 34.6). STEAM-192 ms showed substantially larger magnitudes of the principal eigenvectors (Fig. 2) and improved coherence amongst adjacent tensors compared to those of STEAM-48 ms and DSE. Diffusion entropy indices were 2.03, 2.10 and 1.96 for DSE, STEAM-48 ms and STEAM-192 ms, respectively, for the region shown in the figure. The decreased entropy indicated that STEAM-192 ms had a higher degree of similarity in tensor orientation among neighboring voxels.
The three-phase plots of spherical, linear and planar anisotropy (Fig. 3) showed STEAM-192 ms had the highest linear anisotropy among the three methods with matched SNR. Planar diffusion was similar among the three methods.
Connectivity maps (Fig. 4) were constructed using the fast marching method. With the same cut-off statistical thresholds for all three methods for comparison, STEAM-192 ms revealed more extensive connectivity in the low FA regions compared to DSE and STEAM-48 ms. This was particularly evident in the regions of the post central gyrus (vertical arrows). DSE, on the other hand, showed less connectivity in this region. All three methods showed connectivity to large callosal fibers and the cortico-pontine/cortico-bulbar fibers as expected.
Fiber tracking was performed on multiple selected regions of interest, including the corpus callosum, internal capsule and external capsule (Fig. 5). The callosal fiber tracts extended further toward the cortical surface with STEAM-192 ms into the post central gyrus. Cortico-striatal and corticospinal fibers in the posterior internal capsule (white arrows) were significantly longer in STEAM-192 ms compared to DSE and STEAM-48 ms. Analysis of the group-averaged data indicated that the callosal fibers with STEAM-192 ms were 13.9 ± 0.7% longer than DSE and 14.6 ± 0.8% longer than STEAM-48 ms. The tracts in the internal capsule with STEAM-192 ms were 21.2 ± 1.1% longer than DSE and 24.8 ± 1.3% longer than STEAM-48 ms. The number of fibers traced were however not statistically different.
The major findings of this study are: DTI at longer tdiff increases linear anisotropy, yielding increased tensor magnitude and tensor coherence amongst adjacent voxels, and DTI at long tdiff improves connectivity and tractography outcome compared to DTI at short tdiff.
Geometric averaging is a simple and effective method to minimize diffusion cross-term interactions (19,22) and, thus, directional bias in DTI data. A drawback of geometric averaging is that the scan time is doubled but this is not an issue if signal averaging is needed. In principle, noise propagation of geometric averaging is worse than arithmetic averaging. The SNR of the geometric averaging in this study was slightly lower (by 5% in this study) than arithmetic averaging. Another method of cross-term correction is to experimentally determine a correction factor for each gradient direction for specific protocol parameters such that the same effective b-value can be achieved for different diffusion directions on a uniform phantom (13).
DTI using spin-echo acquisition at long tdiff requires long echo time and is thus not commonly used due to T2 signal loss. The modified STEAM sequence allows long tdiff measurements by placing the magnetization along the Z direction during the TM period where signal loss is governed by T1 as opposed to T2 processes. Given that T1 is substantially longer than T2, signal loss at longer tdiff is less for STEAM acquisition compared to DSE for the same tdiff. The drawback of the STEAM sequence is that only half of the magnetization is retained. Such SNR loss was compensated by a shorter echo time achievable by STEAM. Indeed, STEAM-48 ms and DSE yielded a similar SNR per unit time. STEAM-192 ms had a slightly poorer SNR than DSE and thus required more averaging. We anticipate that STEAM acquisition will be more favorable in vivo because of the longer in vivo T1 compared to fixed brain. Note that, TE of the long tdiff protocol herein was not minimized as described in the Methods section. Future studies can utilize minimal TE for long tdiff DTI to improve SNR.
Comparison between STEAM and DSE DTI data needs to be made with caution because they could have different T1 and T2 weighting. Each voxel of the DSE acquisition has larger contribution of the longer T2 water species, whereas each voxel of the STEAM acquisition at long tdiff has larger contribution from longer T1 water species. Indeed, FA, ADC, λ2 and λ3 were significantly different (p < 0.05) between short (60 ms) and long (80 ms) TE acquired using STEAM-192 ms. Nonetheless, these effects are unlikely to alter the fiber tracking outcome and the overall conclusions of this study.
Fixation prevents tissue degradation allowing studies to be performed over hours to days to improve high spatial resolution and to study multiple protocols in a single setting for robust comparison. Fractional anisotropy in fixed brains and in vivo studies are comparable (28–30). However, FA is affected by fixation and is dependent on the length of fixation duration until the tissue is completely fixed (31). Formalin fixation causes protein cross-linking and reduces ADC and T2 (32,33). Over the duration of the DTI measurements and the relatively short time after fixation that the samples were studied, 4% formalin adequately preserves tissue integrity. Importantly, acquisitions of the three methods were interleaved and, thus, minor tissue degradation over the course of measurements, if existed, should not affect our overall conclusions.
DTI at long tdiff generally increases WM FA while FA in the GM is unaltered. FA increase per se at long tdiff may not necessarily improve contrasts between WM and GM if both were to increase proportionally. Tensor field maps, probabilistic connectivity and fiber tracking were analyzed using the same cut-off thresholds and at similar SNR values. Increased tensor magnitude and increased coherence of the tensor directions amongst the neighboring voxels in regions of lower anisotropy at long tdiff further support the notion that DTI at long tdiff improved sensitivity towards thin fibers. Moreover, STEAM-192 ms showed considerable improvements in tracking smaller fibers and more extensive fiber connectivity with the fast marching technique. For example, the callosal fiber tracts in STEAM-192 ms extended further into the WM-GM interfaces toward the cortical surface than the other two methods. Fiber length measurements further corroborated that long tdiff indeed improved tracking of thinner fibers. Our findings are in good agreement with long tdiff DTI measurements in ex vivo calf tongue and heart (34) and in vivo mouse brain (13) although fiber tracking was not performed in those studies. A possible explanation that long tdiff improves DTI tractography is that water molecules improves sampling of the anisotropic media, and thus increases DTI sensitivity in regions of low diffusion anisotropy. The exact mechanism of improved DTI tractography at long tdiff remains to be investigated. A possible mechanism is that the rms displacement with tdiff of ~200 ms is substantially larger than the average cell sizes and, thus, DTI at long tdiff has an increased sensitivity to water movement in the extracellular spaces along the fiber tracts where it is less restricted by cell membranes, compared to DTI at short tdiff. Water exchange could become significant. However, the mean intracellular water resident time in the brain has been estimated to be on the order of 600 ms (38). Consequently, with tdiff of 200 ms, water exchange effect will be negligible.
Long tdiff acquisition can also be combined with other methods (such as multiple high b values) to further improve tractography. Long tdiff DTI can also be combined with fiber tracking methods, such as advanced fast marching methods (37), which makes use of the CL measure of anisotropy to detect the presence of branching fiber bundles in a given voxel, and the complete diffusion tensor information. If indeed the diffusion space is better probed at long tdiff, the resulting eigen analysis would better delineate branching fibers.
The total acquisition times of our fixed brain studies herein were long because of the short T1, T2 and ADC as well as the desire to compare the three protocols in the same subject. In vivo T1, T2 and ADC are substantially larger. This should shorten data acquisition time. The number EPI segmentations could also be reduced. Moreover, future DTI studies can utilize a single long tdiff DTI protocol and with minimal echo time once it is proven favorable. Our preliminary in vivo data indicate that DTI acquisition time of a single long tdiff is comparable to typical DTI measurements.
In conclusion, this study provides multiple corroborative evidences that DTI tractography at long diffusion time improves tracking of smaller fibers in regions of low fractional anisotropy. We predict that in vivo DTI at longer tdiff could improve tractography. If confirmed, this approach could have positive impact on DTI tractography studies.
Contract/grant sponsor: NIH; contract/grant number: R01NS45879.
Contract/grant sponsor: The Center for Behavioral Neuroscience; contract/grant number: NSF, IBN-9876754.
The authors would like to thank Dr Teijun Zhao for help with the STEAM sequence and Drs Xiaodong Zhang, Shawn Ma, Yoji Tanaka, and Chris Edmonds for helpful discussion and assistance. This work was supported by NIH (R01NS45879) and the Center for Behavioral Neuroscience (NSF, IBN-9876754).