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J Magn Reson Imaging. Author manuscript; available in PMC 2010 May 4.

Published in final edited form as:

PMCID: PMC2862967

NIHMSID: NIHMS182652

Jonathan A.D. Farrell, BS,^{1,}^{2,}^{3} Bennett A. Landman, MEng,^{4} Craig K. Jones, PhD,^{1,}^{2} Seth A. Smith, PhD,^{1,}^{2} Jerry L. Prince, PhD,^{2,}^{4,}^{5} Peter C.M. van Zijl, PhD,^{1,}^{2,}^{3} and Susumu Mori, PhD^{1,}^{2,}^{4}

The publisher's final edited version of this article is available at J Magn Reson Imaging

See other articles in PMC that cite the published article.

To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the principal eigenvector (PEV) as a function of the signal to noise ratio (SNR) *in vivo*.

A healthy male volunteer was scanned in three separate scanning sessions, yielding a total of 45 DTI scans. To provide FA, MD, and PEV as a function of SNR, sequential scans from a scan session were grouped into non-intersecting sets. Analysis of the accuracy and precision of the DTI-derived contrasts was done in both a voxel-wise and ROI-based manner.

An upward bias of FA and no significant bias in MD were present as SNR decreased, confirming results from simulation-based studies. Notably, while the precision of the PEV became worse at low SNR, no bias in the PEV orientation was observed. Overall, an accurate and precise quantification of FA values in GM requires substantially more SNR than the quantification of WM FA values

This study provides guidance for FA, MD, and PEV quantification and a means to investigate the minimal detectable differences within and across scan sessions as a function of SNR.

Diffusion tensor imaging (DTI) is an MRI technique that measures the spatial diffusion characteristics of water and provides novel contrasts to study the fiber architecture of the central nervous system *in vivo* (1-7). The diffusion characteristics of water are dependent on the composition and architecture of the biological environment and can be quantified by scalar and vector contrasts. Prominent scalar quantities include fractional anisotropy (FA), which describes the degree of diffusion anisotropy, and mean diffusivity (MD), which is a measure of the average amount of diffusion in a voxel, both of which have found useful applications in human imaging in the clinic. FA in white matter (WM) arises in part due to axonal and myelin barriers to water diffusion and has been used to assess and monitor WM damage (2,8). MD has been particularly useful in the study of the temporal evolution of stroke (9,10). Recent reviews (2,8,11-14) outline the methodology and clinical applications of DTI.

In addition to scalar quantities, DTI also provides vector contrasts such as the principal eigenvector (PEV) from which the predominant fiber orientation in a voxel can be inferred. The PEV has been used extensively to examine the architecture and connectivity of the brain with color-coded PEV orientation maps (5,15) and tractography methods (11,16-22). DTI continues to grow in prominence as a research tool and is increasingly included as part of routine clinical MRI protocols.

Quantitative comparison of findings from different DTI experiments is, in principle, feasible. However, it is quite possible that the accuracy and precision of DTI findings could differ substantially, both within and between imaging sites, due to differences in the quantity and quality of the acquired data. This negatively impacts the use of DTI technology in multi-site trials, particularly when compatibility is of primary importance, and reduces the confidence in the assessment and monitoring of disease progression in the clinic using DTI contrasts.

Previously, the effects of noise on diffusion anisotropy indices has been investigated *in vivo* in monkeys (23) and simulation based studies have investigated the effect of modeled noise (23-27) as well as the choice of b-value (28-30) on a number of DTI-derived contrasts such as eigenvalues, anisotropy indices and MD. These studies reveal that imaging parameters do indeed have an effect on DTI contrasts and on their relative uncertainty-- notably that measured FA values exhibit an upward bias at low SNR. The need for a sufficient number of diffusion weighting (DW) directions and the optimal arrangement of the DW scheme has been demonstrated by simulation (29,31,32) and *in-vivo* (32,33). Also, the reproducibility of *in vivo* DTI measures within subjects and across subjects has been studied (34,35). These previous studies point to the need to develop methods to assess the impact of SNR on individual experiments and to use this information to optimize and coordinate DTI studies across imaging sites.

The objectives of this study were to: 1) establish data acquisition and analysis protocols to investigate the relationship between SNR (scan repetition) and the DTI-derived contrasts of FA, MD, and PEV. 2) To compute the bias (inaccuracy) of these contrasts at low SNR relative to a high SNR gold standard and 3) to compute the reproducibility (precision) of these contrasts within scan sessions (intra-session) and between scan sessions (test-retest). Analysis was done in both a voxel-wise and in a ROI-based manner and results are reported using an extensive and comprehensive set of plots and metrics.

The observed SNR/DTI contrast relationships can be used to identify the minimum SNR requirements necessary to achieve unbiased (accurate) and reproducible measurements and can be used to guide the design of robust DTI protocols, especially for multi-center studies.

A healthy 24 year old male volunteer participated in this study. Local institutional review board approval and written informed consent were obtained prior to data acquisition. All data were acquired using a 1.5T MR unit (Intera, Philips Medical Systems, Best, The Netherlands) with body coil excitation and an adapted 8 channel phased array SENSE head-coil (6 effective channels) for reception. Three scanning sessions were performed over two days with the subject repositioned between each scan session. Fifteen DTI datasets were acquired in each of the three scanning sessions, yielding a total of 45 DTI scans.

Each DTI dataset was acquired with the following imaging protocol. A multi-slice, single-shot EPI (SENSE factor = 2.0), spin echo sequence (90° flip angle, TR/TE = 3632/100 ms) was used to acquire 25 transverse slices parallel to the line connecting the anterior and posterior commissures, with no slice gap and 2.5 mm nominal isotropic resolution (FOV = 240 × 240, data matrix = 96 × 96, reconstructed to 256 × 256). Diffusion weighting was applied along 30 directions using the Jones30 scheme (31,32) with a magnetic field gradient strength of G = 19.5 mT/m, yielding a b-factor of 1000 s/mm^{2} and a diffusion time t_{dif} of approximately 40 ms (t_{dif} = Δ-δ/3, where Δ is the leading edge spacing, and δ is the duration of the magnetic field gradients, respectively). Five minimally weighted images (5 b_{0}’s) (b ≈ 33s/mm^{2}) were acquired and averaged on the scanner as part of each DTI dataset. The total scan time to acquire one DTI dataset of 30 diffusion weighted images (DWIs) and 5 b_{0}’s was 2min 18s. The total time, including image reconstruction, to acquire 15 DTI datasets and an anatomical MRI in a scan session was approximately 45 min.

DTI datasets were processed offline using MATLAB (The Mathworks, Natick, MA) routines running on a Sun Fire V880 server (Sun Microsystems Inc., Santa Clara, CA). All data were co-registered with a previously described scheme (36) that utilized FLIRT (FMRIB’s Linear Image Registration Tool, Oxford, UK) (37) to remove rigid body motion. The gradient tables, which specify the direction of the magnetic field gradient corresponding to each particular DWI, were corrected to compensate for the rotational component of the co-registration procedure. These analysis methods were encapsulated as MATLAB code entitled DTI_gradient_table_creator (Johns Hopkins University School of Medicine, Baltimore, Maryland, USA) and are publicly available (http://www.nbirn.net/downloads/dti_gradient_table_creator/index.shtm). Diffusion tensors were calculated using a multivariate log-linear fitting method in which all DWIs and their corresponding vector from the gradient table entered the diffusion tensor calculation as unique entries – i.e., no averaging of DWIs was performed. The log-linear fit was performed with no restriction on the sign of the eigenvalues. To prevent taking the log of zero, all voxels with an intensity of zero in a DWI were set to half of the smallest non-zero voxel intensity recorded.

Diagonalization of the diffusion tensor $\overline{\stackrel{\u2012}{\mathrm{D}}}$ produced the three eigenvalues (λ_{1}, λ_{2}, λ_{3}), from which FA and MD were computed (38).

$$\mathrm{FA}=\frac{1}{\sqrt{2}}\sqrt{\frac{{({\lambda}_{1}-{\lambda}_{2})}^{2}+{({\lambda}_{1}-{\lambda}_{3})}^{2}+{({\lambda}_{2}-{\lambda}_{3})}^{2}}{{{\lambda}_{1}}^{2}+{{\lambda}_{2}}^{2}+{{\lambda}_{3}}^{2}}}$$

(1)

$$\mathrm{MD}=\frac{\text{trace}\left(\overline{\stackrel{\u2012}{\mathrm{D}}}\right)}{3}=\frac{{\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}}{3}$$

(2)

The eigenvector associated with the largest eigenvalue (λ_{1}), i.e. the principal eigenvector (PEV), is taken to represent the predominant fiber orientation in each voxel. In the color-coded PEV maps, the dominant fiber orientation in a voxel was represented by red, green, and blue colors which were assigned to right-left, anterior-posterior, and superior-inferior orientations, respectively.

To provide FA, MD, and PEV as a function of SNR, sequential scans from a scan session were grouped into non-intersecting sets. The grouping method provided N_{obs} = 15, 7, 5, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 observations of unique sets of 1 through 15 sequential DTI scans (N_{scans}) in each scan session. In all instances the ratio of the number of DWIs to the number of b_{0} images (N_{DWI}:N_{b0}) in each set was maintained at 6:1 (31) and subsequent diffusion tensor calculations utilized all DTI data in a given set. The accuracy (i.e. any bias due to low SNR) of the DTI-derived contrasts was assessed relative to the gold standard findings obtained when all 15 DTI acquisitions in a scan session were used in the tensor calculation which are denoted as *FA _{gs}*,

The measures computed for FA are discussed below, and an identical analysis was also performed for MD. Given that *N* FA images were observed for a given level of SNR, the mean value, $\stackrel{\u2012}{\mathit{FA}}$, standard deviation, σ(*FA*)and coefficient of variation $\mathit{CV}\left(\mathit{FA}\right)={100}^{\ast}\sigma \left(\mathit{FA}\right)\u2215\stackrel{\u2012}{\mathit{FA}}$ were computed for each voxel. Maps of σ(FA) and CV(FA) were computed at SNR levels of 1 through 5 DTI scans, for each scan session.

The precision of FA measurements were investigated as a function of the underlying PEV orientation. Analysis was confined to voxels with an FA_{gs} > 0.25 in the central 23 of 25 slices for the first scan session. The voxels were sorted into bins according to their PEV_{gs} orientation, using a 5° by 5° spherical coordinate (polar angle ϕ, azimuthal angle θ) grid. As a consequence of this binning procedure, the voxels assigned to a bin share a common fiber orientation. The σ(FA) value computed for each voxel was then sorted accordingly. The average σ(FA) over all the voxels in each bin was then computed. The bin average of σ(FA) is displayed as a function of ϕ and θ as well as on the surface of a sphere (after interpolation). This procedure was performed for SNR levels of 1 and 3 DTI scans, respectively.

The precision of FA and MD were computed using a coefficient of variation metric. The mean CV(FA), and standard deviation of CV(FA), over all voxels within an ROI were computed and are denoted as CV(FA) and σ(CV(FA)), respectively. These values were computed, for each scan session independently, at SNR levels of 1 to 5 DTI scans. The values and uncertainty reported in the corresponding section of results are the mean CV(FA) and the mean σ(CV(FA)) over all 3 scan sessions respectively, at each respective SNR level.

The reproducibility of FA and MD were computed using a test-retest variation metric. Each observation of an FA map in scan session *p* was paired with a corresponding observation (at the same SNR level) of an FA map in scan session *q*. The difference between each pairing of FA maps was computed and stored as a vector

$$\mathrm{diff}{\left(\mathrm{FA}\right)}_{\mathrm{p},\mathrm{q}}=[{\mathrm{FA}}_{1,\mathrm{p}}-{\mathrm{FA}}_{1,\mathrm{q}},{\mathrm{FA}}_{2,\mathrm{p}}-{\mathrm{FA}}_{2,\mathrm{q}},\dots ,{\mathrm{FA}}_{\mathrm{N},\mathrm{p}}-{\mathrm{FA}}_{\mathrm{N},\mathrm{q}}].$$

(3)

The test-retest variation of FA measurements in each voxel was computed as the standard deviation of the difference vector at that voxel, divided by the mean value of the FA measured in that voxel across all 2*N* observations in scan sessions *p* and *q*:

$$\mathrm{V}{\left(\mathrm{FA}\right)}_{\mathrm{p},\mathrm{q}}=\frac{\sigma \left(\mathrm{diff}{\left(\mathrm{FA}\right)}_{\mathrm{p},\mathrm{q}}\right)}{\text{mean}\left({\mathrm{FA}}_{\mathrm{p},\mathrm{q}}\right)}.$$

(4)

A test-retest variation map, V(FA)_{T}, was then calculated across the pairings of scan sessions

$$\mathrm{V}{\left(\mathrm{FA}\right)}_{\mathrm{T}}=\frac{1}{3}\left(\mathrm{V}{\left(\mathrm{FA}\right)}_{1,2}+\mathrm{V}{\left(\mathrm{FA}\right)}_{2,3}+\mathrm{V}{\left(\mathrm{FA}\right)}_{1,3}\right).$$

(5)

The values reported in the corresponding results section are the mean V(FA)_{T}, and standard deviation, σ(V(FA)_{T}), of V(FA)_{T} over all voxels within an ROI.

The mean FA over all voxels in an ROI is denoted as FA. The mean value, $\stackrel{\u2012}{\langle \mathit{FA}\rangle}$, the standard deviation, σ(*FA*) and the coefficient of variation,*CV _{p}*(

Each observation of FA in scan session *p* was paired with an observation (at the same SNR level) in scan session *q*. The difference between each pairing of FA was computed as

$$\mathrm{diff}\left({\langle \mathrm{FA}\rangle}_{\mathrm{p},\mathrm{q}}\right)=[{\langle \mathrm{FA}\rangle}_{1,\mathrm{p}}-{\langle \mathrm{FA}\rangle}_{1,\mathrm{q}},{\langle \mathrm{FA}\rangle}_{2,\mathrm{p}}-{\langle \mathrm{FA}\rangle}_{2,\mathrm{q}},\dots ,{\langle \mathrm{FA}\rangle}_{\mathrm{N},\mathrm{p}}-{\langle \mathrm{FA}\rangle}_{\mathrm{N},\mathrm{q}}].$$

(6)

The test-retest variation of ROI-based FA measurements was computed as the standard deviation of the difference vector, divided by the mean value of FA across all 2*N* observations in scan sessions *p* and *q*.

$$\mathrm{V}\left({\langle \mathrm{FA}\rangle}_{\mathrm{p},\mathrm{q}}\right)=\frac{\sigma \left(\mathrm{diff}\right({\langle \mathrm{FA}\rangle}_{\mathrm{p},\mathrm{q}}\left)\right)}{\text{mean}\left({\langle \mathrm{FA}\rangle}_{\mathrm{p},\mathrm{q}}\right)}$$

(7)

The test-retest variation values reported in the corresponding results section are

$${V}_{T}=\frac{1}{3}\left(V\left({\langle \mathit{FA}\rangle}_{1,2}\right)+V\left({\langle \mathit{FA}\rangle}_{2,3}\right)+V\left({\langle \mathit{FA}\rangle}_{1,3}\right)\right)$$

(8)

The uncertainty reported is the standard deviation of V_{p,q} over the three scan sessions.

The principal direction of diffusion can be equally well described by the orientation of a PEV with coordinates (x,y,z) and the corresponding anti-parallel vector with coordinates (−x,−y,−z). Consequently, the *N* unique observations of the PEV for each voxel must be oriented appropriately to ensure meaningful vector additions and comparisons. To do this, a PEV was selected as a reference vector. Each of the remaining *N*-1 PEVs was set to be the orientation (parallel or anti-parallel) that minimized the angle of separation with respect to the reference vector. The mean of *N* observations of a PEV is computed as the normalized vector sum of components,

$$\stackrel{\u2012}{\mathrm{PEV}}=\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{PEV}}_{\mathrm{i}}/\Vert \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{PEV}}_{\mathrm{i}}\Vert $$

(9)

where each PEV has unit length. The angular variation (AV) (i.e. precision) of PEV measurements, in each voxel, was computed as the variation, in degrees,

$$\mathrm{AV}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{cos}}^{-1}\left({\mathrm{PEV}}_{\mathrm{i}}\u2022\stackrel{\u2012}{\mathrm{PEV}}\right)$$

(10)

of the *N* observations about the observation mean. Where • denotes a vector dot product. The AV was calculated at SNR levels of 1 to 5 DTI acquisitions in order to allow at least three independent observations of the PEV orientation in each scan session. The accuracy of a PEV orientation, with respect to PEV_{gs} was computed in each voxel with an angular bias (AB) metric

$$\mathrm{AB}={\mathrm{cos}}^{-1}\left(\stackrel{\u2012}{\mathrm{PEV}}\u2022{\mathrm{PEV}}_{\mathrm{gs}}\right)$$

(11)

All computations of AV and AB were done on a voxel by voxel basis. The average value, AB_{p} and AV_{p} together with the standard deviation, σ(AB)_{p} and σ(AV)_{p} across all voxels in an ROI were computed for each scan session *p*. This provided metrics for the precision and accuracy of PEV measures, calculated on a voxel by voxel basis, averaged over a given anatomical region in each scan session. The angular variation and uncertainty values reported in the corresponding results section are *AV** _{T}* and σ(

The mean difference, in degrees, between the *i*^{th} observation of a PEV in scan session *p* and the mean PEV in scan session *q* was calculated as.

$${\mathrm{MAD}}_{\mathrm{i},\mathrm{p},\mathrm{q}}={\mathrm{cos}}^{-1}\left({\mathrm{PEV}}_{\mathrm{i},\mathrm{p}}\u2022{\stackrel{\u2012}{\mathrm{PEV}}}_{\mathrm{q}}\right)$$

(12)

The mean MAD across the pairings of *N* observations was computed as

$${\mathrm{MAD}}_{\mathrm{p},\mathrm{q}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{MAD}}_{\mathrm{i},\mathrm{p},\mathrm{q}}$$

(13)

and the mean MAD over the permutations of scan sessions was computed as

$${\mathrm{MAD}}_{\mathrm{T}}=\frac{1}{6}\left({\mathrm{MAD}}_{1,2}+{\mathrm{MAD}}_{2,1}+{\mathrm{MAD}}_{1,3}+{\mathrm{MAD}}_{3,1}+{\mathrm{MAD}}_{2,3}+{\mathrm{MAD}}_{3,2}\right)$$

(14)

The corresponding section of the results shows the anatomical profile of MAD_{T} while the values and uncertainty reported are the average value MAD_{T} and standard error σ(MAD_{T}) over all voxels in an ROI.

The SNR in this study is determined by, and is reported as, the number of DTI datasets (N_{scans}) used in the diffusion tensor calculation (where each dataset consists of 30 DWIs and 5 b_{0}’s). The computation of a numerical SNR value for DTI experiments is not straightforward because DWIs and b_{0} images have different signal intensity and noise profiles. As the SNR in a selected anatomical location in DWIs can depend on the DW direction, the SNR in the b_{0} image is typically reported. For comparison, a numerical value for SNR is this study was computed using two sequential observations of the minimally diffusion weighted images. First, the average image and the difference image of these two observations were computed. The SNR was then computed as the mean value in an ROI within the average image divided by the standard deviation over the voxels in the same ROI within the difference image. The minimally weighted images from the first 14 scans in the first scan session were paired sequentially, and the SNR in the splenium of the corpus callosum and internal capsule were calculated to be 22±2:1 (approximately 26 dB), and 24±2:1 (approximately 27 dB) respectively. These values reflect the SNR in the scanner average of 5 b_{0} images, which would indicate an approximate SNR of 10:1 (20 dB) in WM structures in a single b_{0} image.

Figure 1a shows representative FA maps calculated from 1, 3, and 15 DTI scans at the level of the lateral ventricles (left) and centrum semiovale (right). FA maps calculated from a single DTI scan demonstrate a grainier appearance indicating increased noise, particularly in gray matter (GM) regions, relative to the gold standard FA map (15 scans). The putamen and globus pallidus have a pronounced speckled appearance in the FA map calculated from 1 DTI acquisition, whereas the structures are more visually distinct in the FA map from 3 scans and even more so in the gold standard. Both the visual contrast between GM and WM, and the conspicuity of the boundary between these tissue types in FA maps, improves with increased SNR.

Images showing the relationship between the accuracy and precision of FA and the number of DTI scans used in the diffusion tensor calculation. Results are shown at two slice levels. (**a**) Representative FA maps computed from 1, 3 and 15 DTI scans, respectively. **...**

In practice, the quantity of DTI data acquired in a scan session is restricted by the available scan time. If one can acquire multiple repetitions of a DTI acquisition, a pertinent question is whether it is better to average the processed FA maps, or to use all acquired data, after motion correction, in one diffusion tensor calculation. In the context of 15 acquired DTI scans, the former approach implies calculating the average of N_{obs} FA maps, where each FA map is computed from N_{scans} respectively (results are shown for N_{obs} = 15, N_{scans} = 1 and N_{obs} = 5, N_{scans} = 3), while the latter approach implies using all 15 datasets (gold standard) in a single tensor calculation. Figure 1b shows the difference between these two DTI processing methods at two SNR levels. The results indicate that taking the average of FA maps reinforces the upward FA bias (which is already present in the individual FA maps themselves) in GM regions. The upward FA bias, relative to the gold standard FA map, is diminished when more data is used in the tensor calculation.

Figures 1c-d show the standard deviation, σ(FA), and the coefficient of variation CV(FA) of multiple observations of FA maps computed from single DTI scans (N_{obs} = 15, N_{scans} = 1, left) and 3 DTI scans (N_{obs} = 5, N_{scans} = 3, right). σ(FA), increases -- i.e., precision worsens -- with penetration depth from the receive coil elements. Using 3 scans, σ(FA) decreases globally. Figure 1d shows that the CV(FA) is larger in deep GM (putamen) than in adjacent WM (internal capsule), despite the fact that both tissue types are approximately equidistant from the receive coil elements. This occurs because the standard deviation of FA measurements in GM is a larger fraction of the underlying FA value than the standard deviation of FA measurements in WM. Regions of the brain that benefit most from the increased SNR include regions far from the receive coil elements (e.g. deep structures). The effects of SNR on MD were much smaller (for the range of SNR investigated) and were not easily visually appreciated in the MD images (images not shown).

To determine if the 30 orientation DW scheme used for this study provided a uniform precision profile *in vivo*, the standard deviation of FA measurements was computed and displayed as a function of the underlying PEV orientation. Figures 2a shows a relatively constant value of σ(FA) indicating that the precision of voxel-wise FA measurements are not substantially dependent on the underlying fiber orientation at an SNR level of 1 DTI scan. When 3 DTI scans are used to calculate the diffusion tensor, the precision of FA measurements improves (i.e. σ(FA) decreases) for all fiber orientations. These results agree with previous simulation results (Jones, 2004; Skare et al., 2000) which points out the benefit of using a DW scheme with high directional resolution. Figure 2b shows the data from Figure 2a represented on the surface of a sphere, with the location of the DW directions given by solid markers.

The effects of SNR on ROI-based measures of FA and MD were investigated with manually-defined ROIs in the putamen, globus pallidus, centrum semiovale, internal capsule and splenium of the corpus callosum. These ROI’s are shown in Figure 3 and included 143, 180, 158, 151, and 237 voxels, respectively. The mean FA in each ROI is shown in Figure 4a and demonstrates a reproducible upward bias of FA at low SNR, with respect to the gold standard, in deep GM structures (putamen and globus pallidus) which is consistent in all three scan sessions. Notably, dense WM regions such as the internal capsule, and splenium of the corpus callosum together with less anisotropic WM structures like the centrum semiovale exhibited no FA bias at low SNR. Analysis of FA and MD in the frontal WM ROI is not reported as this is a region of crossing fibers; however this region is used for subsequent voxel-wise PEV analysis.

Locations of regions of interest (ROIs) at four slice levels used for ROI-based analyses. These include internal capsule (ic), frontal white matter (fw), centrum semiovale (cs), globus pallidus (gp), putamen (put) and splenium of the corpus callosum (scc). **...**

ROI-based FA and MD as a function of the number of scans. (**a**) The mean FA in an ROI and (**c**) the mean MD in an ROI for each unique grouping of DTI data (solid circles). The 3 scan sessions are represented by red, green and blue solid circles. (**b** and **d** **...**

A more comprehensive analysis of the ROI-based FA results is given in Figure 4b. All data points from the three scan sessions in Figure 4a are consolidated to a representative single value in Figure 4b (solid circles). The spread of the FA values in Figure 4a was computed as the standard deviation of all points over all sessions and is shown as dotted lines in Figure 4b. Lastly, the standard deviation of FA measurements within each ROI was computed and averaged over all observations in all sessions (shown as error bars in Figure 4b). Figure 4b shows that the uncertainty associated with determining the ROI-based FA value is small, as indicated by the small range of the dotted lines. Secondly, the standard deviation of FA values within the ROI is large, even at high SNR.

In contrast to the results observed for FA, no bias trend at low SNR was observed for MD. Due to the small dynamic range of MD across different brain regions, the data series for ROIs in the putamen and centrum semiovale are shown as representative GM and WM structures, respectively. Figure 4c shows that although the variability associated with the determination of the mean value of MD in an ROI increases, (widening of the envelope of data points) no bias trend of MD was observed at low SNR. The data in Figure 4c is consolidated in Figure 4d in a similar fashion as was discussed for the ROI-based FA analysis.

The diffusivity of each eigenvalue was averaged separately over all voxels within an ROI in the putamen, a relatively isotropic diffusion medium. Figures 5a and 5b show a reproducible upward bias of the diffusivity for λ_{1}, while λ_{2} remains fairly stable and λ_{3} exhibits a downward bias. This eigenvalue repulsion trend, in the context of the equations for FA and MD, accounts for the observed increase in FA and corresponding stable MD as a function of SNR in low FA structures. In the case of the internal capsule, a more anisotropic medium, the diffusivity of the eigenvalues remained stable, and hence the FA and MD in WM structures exhibited no bias trends throughout the range of SNR investigated in this study (Figures 5c, d).

The reproducibility of voxel-wise measures of FA and MD within a scan session was investigated using a coefficient of variation (CV) metric. Figure 6a shows a large disparity, between GM and WM, of the intra-session reproducibility of voxel-wise measures of FA. Though both improve as a function of SNR, voxel-wise measures of FA were less reproducible in GM than in WM. Figure 6b shows that voxel-wise measures of MD are comparable in GM and WM and are more reproducibility than those of FA.

Reproducibility of voxel-wise FA and MD measurements. Intra-session reproducibility: (**a**) coefficient of variation of FA (**b**) coefficient of variation of MD. Inter-session reproducibility: (**c**) test retest variation of FA (**d**) test retest variation of MD. **...**

The reproducibility of voxel-wise measures of FA and MD across scan sessions was investigated using a test-retest variation (V) metric. Mirroring the trend observed for the intrasession results, Figure 6c shows a large disparity between the test-retest reproducibility of voxel-wise measures of FA in GM and WM. Figure 6d shows that the test-retest reproducibility of voxel measures of MD is comparable in GM and WM.

The effect of SNR on the reproducibility of ROI-based measurements of FA and MD within a scan session was investigated using a coefficient of variation (CV) metric. Figure 7a shows a disparity, between GM and WM, in the reproducibility of ROI-based measures of FA within scan sessions. Figure 7b shows that the reproducibility of ROI-based measures of MD within scan sessions was comparable for all regions investigated.

Reproducibility of ROI-based FA and MD measurements. Intra-session reproducibility: (**a**) coefficient of variation of FA (**b**) coefficient of variation of MD. Inter-session reproducibility: (**c**) test retest variation of FA (**d**) test retest variation of MD. **...**

The reproducibility of ROI-based measures of FA and MD across scan sessions was investigated using a test-retest variation (V) metric. Figure 7c shows that ROI-based measures of FA were less reproducible across scan sessions in GM than in WM. Figure 7d shows that, as in the intra-session results, the test-retest reproducibility of ROI-based measures of MD in GM and WM are comparable for all regions investigated.

Representative color coded PEV orientation maps calculated from 1, 3 and 15 DTI scans from a single scan session are shown in Figure 8a. The images show that increased SNR improves the visual definition of WM fiber bundles. Structures such as the anterior and posterior limbs of the internal capsule together with the centrum semiovale have a speckled appearance in the image computed from a single DTI scan whereas these structures appear more homogenous at higher SNR. Additionally, the U-fiber projections into cortical GM regions are more clearly defined on the higher SNR PEV colormaps. Though the benefits of increased SNR can be visually appreciated, the reproducibility and potential bias of the PEV as a function of SNR are difficult to discern in the PEV colormaps themselves. A quantitative assessment of PEV precision, accuracy and across session reproducibility was performed on a voxel by voxel basis in several WM fiber bundles.

Improvements in color-coded PEV orientation maps as a function of the number of scans. (**a**) Representative PEV orientation maps computed from 1, 3 and 15 DTI scans, at two slice levels. The precision and accuracy of the PEV orientation within a scan session **...**

An angular variation (AV) metric was used to compute the precision of PEV orientations within a scan session. The AV can be interpreted as the spread, in degrees, of individual observations from the observation mean. Figure 8b shows that the precision of the PEV orientation improved as a function of SNR, with an approximate two fold improvement in precision when three DTI scans were used to calculate the diffusion tensor, relative to PEV maps that used one DTI scan.

The accuracy of the PEV was computed using an angular bias (AB) metric. The AB is defined as the difference, in degrees, between the mean observation of a PEV at a given SNR level and the gold standard PEV in the same voxel. The accuracy of the PEV orientation is robust across the range of SNR investigated, with no discernable bias at low SNR for the WM structures investigated (Figure 8c).

Lastly, the test-retest reproducibility of the PEV orientation across scan sessions was investigated using a mean angular difference (MAD) metric. This metric can be interpreted as the combined error of the PEV orientation across scan sessions, with contributions from poor accuracy and poor precision. Increased SNR improves the reproducibility of the PEV orientation in WM (Figure 9a) with marked improvement in the test-retest reproducibility of the PEV orientation in frontal and posterior WM regions in particular. For the major WM tracts investigated, the improvement in across-session reproducibility of the PEV’s was less pronounced (Figure 9b).

In this paper, which is part of a series of *in vivo* human DTI calibration studies through BIRN, data acquisition and analysis protocols were established to investigate the relationship between DTI scan repetition (i.e., SNR) and the contrasts of FA, MD, and PEV. With several unique observations of the DTI contrasts at each SNR level, we compute the bias (inaccuracy) in these contrasts at low SNR relative to a high SNR gold standard and compute the reproducibility (precision) of FA, MD, and PEV measures within a scan session (intra-session) and between scan sessions (test-retest). The DTI acquisition protocol used in this study was adopted for three reasons. First, simulation-based studies suggest that a DW scheme with about 30 unique directions is required to ensure a uniform precision profile of FA measurements (29,31,32). Secondly, the optimal ratio of the number of DWIs to minimally weighted images has been shown to be approximately 9:1 (31). Thirdly, we believed that this scan protocol, with a moderate TE (100 ms), moderate gradient strength (19.5 mT/m), and 2.5 mm isotropic resolution should be well accepted as a clinically achievable DTI study at 1.5T. The imaging protocol for this study can be extended to whole brain coverage with an approximate total scan time of 5 min per DTI acquisition.

It is well known that cardiac pulsation often has a profound effect on DTI results (39-41), which could be a major contribution to intra and inter-session reproducibility. Unfortunately, cardiac gating has not been widely accepted in clinical studies because of lengthening of the scanning time and occasional instability of gating depending on subject conditions such as arrhythmia. In this study, we decided not to use cardiac gating to represent more common imaging protocols.

A concurrent goal of this work is that the acquired and processed DTI data, observed relationships between SNR and DTI contrasts, and the acquisition protocol for this study be made available as data resource and reference to establish robust DTI protocols, especially for multi-site studies. To facilitate the use of our *in vivo* human DTI calibration study for this purpose, the information is freely available through the BIRN website (http://www.nbirn.net/downloads/diffusion_calibration/index.shtm) and can be used as a data resource and reference for a 1.5T scanner.

The comparison of SNR values from simulation based studies with those of experimentally acquired MR data, or between different sets of MR data from different sites, is not straightforward and should be made with care. Whereas the noise in simulation based studies is a modeled parameter, data from MR scanners can be susceptible to artifacts due to non-uniform receive coil sensitivity, chemical shift artifacts, field inhomogeneity, eddy current distortions, EPI-based susceptibility artifacts, as well as subject motion. Additionally, parallel imaging techniques with phased-array coils produce an inhomogeneous SNR profile, with regions closer to the reception elements having a higher SNR. In DTI experiments, it is not clear how to compute SNR because diffusion weighted and non diffusion weighted (b_{0}) images have different signal intensity and noise profiles. As the SNR in a selected anatomical location in DWIs can depend on the DW direction, the SNR in the b_{0} image is typically reported. For comparison, the SNR in a single b_{0} image was reported for ROIs in the splenium of the corpus callosum and internal capsule. It is expected that SNR will scale, at best, with the square root of the number of DTI acquisitions used in the diffusion tensor calculation. However, differences in hardware performance means that it is unlikely that the same number of DTI acquisitions with a common protocol at two imaging sites will yield compatible results. Therefore, an important recommendation of this study is that each site that participates in a collective study should investigate the SNR/DTI contrast relationship on their MR system as a function of scan repetition, with a common protocol. This will enable each imaging site to calibrate their acquisition to meet the SNR requirements given by the study coordinators. This could be combined with the use of a traveling human volunteer, or a standardized non-human phantom.

Low SNR typically has detrimental effects on the precision of a given measurement, while the accuracy is generally unaffected. However, DTI-based contrasts can suffer from poor accuracy in addition to the expected loss of precision at low SNR. We confirmed that low SNR increases the noise and decreases the visual contrast between GM and WM in FA images. The regional variation of the precision of FA measurements agrees with recently reported results (34) that used multiple subjects and a statistical parametric mapping approach. One implication of the above result is that group analysis studies cannot achieve unbiased high SNR results by averaging data from multiple subjects if the DTI data acquired for each subject was of low SNR. Great care should therefore be taken to ensure sufficient SNR in the individual DTI datasets. Additionally, an equal number of DTI scans should be used for patients and controls to avoid a mismatch of SNR that could obscure group changes in FA values.

The precision of DTI-contrasts can be visualized as a function of the underlying PEV orientation. It can be seen in Figure 2 that the 30 direction DW scheme used in this study provides a largely uniform precision profile. A further extension of this method is that it may provide a means to validate hardware calibration with *in vivo* DTI results and may elucidate subtle effects that are otherwise difficult to isolate in individual FA maps or in tractography results. In particular, poor precision or inaccuracy due to decreased magnetic field gradient stability, static field inhomogeneity, receive coil sensitivity, or DW contributions from background gradients may be discovered in this way.

The behavior of the sorted eigenvalues (λ_{1}, λ_{2}, and λ_{3}) as a function of SNR readily accounts for the observed FA and MD results and has been reported in simulation-based studies (23,24,26). In GM, the increase of λ_{1} and concurrent decrease of λ_{3} at low SNR accounts for the upward FA bias. However, as the biases in λ_{1} and λ_{3} largely offset each other, a stable MD value was observed over the range of SNR investigated in this study. The bias in the computed eigenvalues is due to the Rician noise properties of magnitude MR data and has been investigated by previous studies (24,27,42,43).

The investigation of the effect of SNR on the precision (reproducibility, both within and between scan sessions) of FA and MD found that though ROI-based measures of FA and MD are more reproducible than voxel-wise measures, ROI-based analysis does not afford a solution to the problem of bias. This was illustrated for FA in Figure 4. In ROI-based analysis, with 3 DTI scans, FA and MD measurements have an intra-session CV of less than 2% in the WM regions investigated, but an intra-session CV ≈ 5% in GM (Figures 7 a, b). In voxel-wise analysis however (Figures 6 a, b), the precision of FA measurements in low FA regions is especially poor (intra-session CV ≈ 25%) with 3 DTI scans, though MD measurements are more robust (intra-session CV ≈ 5%).

Overall, an accurate and precise quantification of FA values in GM requires substantially more SNR (i.e. more DTI datasets) than the quantification of WM FA values. Our results indicate that an individual DTI scan of 30 DWIs + 5 b_{0}’s at 1.5T provides satisfactory accuracy for the quantitative assessment of FA in WM regions. However, because the precision of voxel-wise FA measures is particularly sensitive to SNR, studies that investigate the diffusion anisotropy of WM structures near the cortical boundary together with cortical GM would be especially vulnerable to FA bias caused by low SNR would likely require substantially more SNR than is typically acquired

Previous studies (29,32) have shown that a DW scheme with a low number of unique directions can cause bias and unequal variability of DTI contrasts as a function of PEV orientation, and variability in the determination of the PEV orientation itself. In this study, which utilized a 30 orientation DW scheme, the precision of FA measurements showed no dependence on the orientation of the PEV. Further investigation of the effect of the DW scheme on *in vivo* human DTI studies is deferred to future work.

The precision of the PEV orientation was found to improve as a function of SNR, with an AV of approximately 6° to 3° in the range of 1 to 3 DTI scans. An approximate twofold improvement in the precision of PEV measurements was observed when three DTI scans were used to calculate the diffusion tensor, relative to PEV maps that used only one DTI scan. The result that the PEV precision in the frontal WM is poor may be explained by the fact that this is a region of crossing fibers where each voxel contains two or more fiber populations. The observed PEV may therefore be especially sensitive to changes in the location of the imaged voxel relative to the underlying structure (inter-scan effects), together with partial volume and resolution effects, which could all contribute to poor PEV precision.

Notably, no significant angular bias was observed in the orientation of the PEV at low SNR relative to the gold standard PEV orientation. One consequence of upward FA bias and fidelity of the PEV orientation at low SNR is that the same FA termination criteria for tractography can produce very different results in the proximity of GM regions. It is conceivable that computed fibers from tractography may project into cortical or deep GM in a low SNR dataset, as the GM voxels exhibit elevated FA values and thus satisfy the FA tractography criteria, whereas the same GM voxel is excluded from tractography in a high SNR datasets because the voxel intensity has no upward FA bias.

In conclusion, the results from this study provide guidance for FA, MD, and PEV quantification and a means to investigate the minimal detectable differences within and across scan sessions as a function of SNR. In multi-center studies, where data compatibility is of primary importance, it is essential to confirm that a protocol is designed to achieve sufficient SNR to meet the aims of the study. Protocols designed in a low SNR regime could be highly sensitive to small differences in hardware performance, even if equivalent imaging parameters are adopted. To confront this, it is a recommendation of this study that imaging sites, particularly those in collaborative studies, should implement a protocol as a part of quality assurance testing to identify the appropriate SNR threshold necessary to achieve accurate (unbiased) DTI-derived contrasts, and should validate the compatibility of DTI data across different sites and scanners.

Preliminary results from this work were presented at Imaging Myelin: Formation, Destruction and Repair, Vancouver, BC, Canada, 2006; as well as at the 14^{th} annual scientific meeting of the International Society for Magnetic Resonance in Medicine, Seattle, Washington, USA, 2006 (Abstract # 1075). Dr. Peter C.M. van Zijl is a paid lecturer for Philips Medical Systems. This arrangement has been approved by Johns Hopkins University in accordance with its conflict of interest policies. Dr. Craig K. Jones is supported by a grant to the Kennedy Krieger Institute by Philips Medical Systems

**Grant Support**: P41 RR15241, RO1 AG20012, U24 RR021382-02

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