Microscopic diffusion anisotropy in the human brain: reproducibility, normal values, and comparison with the fractional anisotropy.

YNIMG-11931; No. of pages: 15; 4C: 3, 5, 6, 7, 11 NeuroImage xxx (2015) xxx–xxx

Contents lists available at ScienceDirect

NeuroImage journal homepage: www.elsevier.com/locate/ynimg

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Technical Note

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Marco Lawrenz, Stefanie Brassen, Jürgen Finsterbusch ⁎

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Department of Systems Neuroscience, University Medical Center Hamburg—Eppendorf, Hamburg, Germany Neuroimage Nord, University Medical Centers Hamburg–Kiel–Lübeck, Germany

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Article history: Accepted 6 January 2015 Available online xxxx

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Keywords: Microscopic diffusion anisotropy MA IMA index FA White matter integrity Double-wave-vector diffusion weighting DWV d-PFG

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Human neuroimaging of tissue microstructure, such as axonal density and integrity, is key in clinical and neuroscience research. Most studies rely on diffusion tensor imaging (DTI) and the measures derived from it, most prominently fractional anisotropy (FA). However, FA also depends on fiber orientation distribution, a more macroscopic tissue property. Recently introduced measures of so-called microscopic diffusion anisotropy, diffusion anisotropy on a cellular or microscopic level, overcome this limitation because they are independent of the orientation distributions of axons and fibers. In this study, we evaluate the feasibility of two measures of microscopic diffusion anisotropy IMA and MA indices, for human neuroscience and clinical research. Both indices reflect the eccentricity of the cells but while IMA also depends on the cell size, MA is independent of the cell size and, like FA, scaled between 0 and 1. In whole-brain measurements of a group of 19 healthy volunteers, we measured average values and variability, evaluated their reproducibility, both within and between sessions, and compared MA to FA values in selected regions-of-interest (ROIs). The within- and between-session comparison did not show substantial differences but the reproducibility was much better for the MA than IMA (coefficient of variation between sessions 10.5% vs. 28.9%). The reproducibility was less for MA than FA overall, but comparable in the defined ROIs and the average group sizes required for between-group comparisons was similar (about 60 participants for a relative difference of 5%). Group-averaged values of MA index were generally larger and showed less variation across white-matter brain ROIs than FA (mean ± standard deviation of seven ROIs 0.83 ± 0.10 vs. 0.58 ± 0.13). Even in some gray-matter ROIs, MA values comparable to those of white matter ROIs were observed. Furthermore, the within-group variation of the values in white matter ROIs was lower for the MA compared to the FA (mean standard deviation over volunteers 0.038 vs. 0.049) which could be due to significant variability in the distribution of fiber orientation contributing to FA. These results indicate that MA (i) should be preferred to IMA, (ii) has a reproducibility and group-size requirements comparable to those of FA; (iii) is less sensitive to the fiber orientation distribution than FA; and (iv) could be more sensitive to differences or changes of the tissue microstructure than FA. R1.1 © 2015 Elsevier Inc. All rights reserved.

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dominating in a voxel, it can be used to track nerve fiber bundles in brain white matter (Mori et al., 1999) making DTI very valuable for neuroscience. From the underlying diffusion tensor, scalar measures of the diffusion anisotropy can be derived, the most prominent of which is fractional anisotropy (FA; Basser and Pierpaoli, 1996). FA reflects microstructural tissue properties like axons' size and density, but also depends on the orientation distribution of axons in a voxel. This makes it difficult to infer axon or fiber integrity from FA values, for example, from FA differences observed between groups or longitudinally. For instance, a lower FA value could reflect a reduced axon density (fewer fibers), or a broader axon-orientation distribution due to increased fanning of fibers. In extreme cases, such as several fibers crossing a voxel in different directions, the FA value may even vanish even though the diffusion for each individual fiber is highly anisotropic. On the other hand, larger FA values could indicate not only increased axon density, but also

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Microscopic diffusion anisotropy in the human brain: Reproducibility, normal values, and comparison with the fractional anisotropy

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Introduction

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Conventional anatomical imaging, e.g., T1- or T2-weighted measurements, is ideal to distinguish white matter, gray matter, and cerebrospinal fluid. However, to investigate white matter tissue properties that reflect axonal or fiber integrity, the fiber connections linking the different brain regions, and the fiber's role for particular brain functions diffusion-weighted imaging has become an important tool. Diffusiontensor imaging (DTI; Basser et al., 1994; Basser and Pierpaoli, 1996) can determine the principal direction of water diffusion in white matter. Because this direction often is collinear with the fiber orientation

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⁎ Corresponding author at: Institut für Systemische Neurowissenschaften, Geb. W34, Universitätsklinikum Hamburg—Eppendorf, 20246 Hamburg, Germany. Fax: + 49 40 7410 59955. E-mail address: j.fi[email protected] (J. Finsterbusch).

http://dx.doi.org/10.1016/j.neuroimage.2015.01.025 1053-8119/© 2015 Elsevier Inc. All rights reserved.

Please cite this article as: Lawrenz, M., et al., Microscopic diffusion anisotropy in the human brain: Reproducibility, normal values, and comparison with the fractional anisotropy, NeuroImage (2015), http://dx.doi.org/10.1016/j.neuroimage.2015.01.025

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Experiments were performed on a 3 T whole-body MR system (TIM Trio, Siemens Healthcare, Erlangen, Germany; 40 mT m−1 maximum gradient strength) with a 32-channel head coil. 19 healthy volunteers (21–32 y, mean age ± standard deviation 26.03 ± 2.47 y, 12 male/7 female) were investigated after their informed consent was obtained. Diffusion-weighted images were acquired using spin-echo echoplanar imaging with 7/8 partial Fourier encoding covering 35 slices with an in-plane resolution of 3.0 × 3.0 mm2 (field-of-view 216 × 216 mm2) and a slice thickness of 3.0 mm (0.5 mm gap). The DWV experiments involved two diffusion-weighting periods (Fig. 1), each with a b value of 500 s mm−2 (pulse duration δ = 22 ms, diffusion time Δ = 25 ms, mixing time τm = 45 ms) with a wave vector q = γ × G × qδ (γ: gyromagnetic ratio, G: gradient amplitude) of 0.168 μm− 1, yielding an echo time (TE) of 150 ms and a repetition time (TR) of 6.5 s. These parameters were identical to previous studies that detected microscopic diffusion anisotropy in the living human brain (e.g., Lawrenz and Finsterbusch, 2013). 96 direction combinations as reported recently (Lawrenz and Finsterbusch, 2014a), were applied to be able to determine MA (and IMA) values. Including preparation scans to achieve steady-state conditions as well as non-diffusionweighted images acquired every 16 direction combinations for motion correction, the total acquisition time (TA) was 11 min 10 s per DWV measurement. Conventional DTI measurements were performed with a single diffusion-weighting period with a b value of 1000 s mm− 2 (TE 100 ms, TR 4.8 s) and were based on a double-spin-echo preparation to minimize eddy-current-induced geometric distortions (Reese et al., 2003). The gradient pulse durations were 10.7 + 14.6 ms for the dephasing and 20.7 + 4.6 ms for the rephasing gradients with a gap of 0.4 ms between the de- and rephasing and gaps of 14.1 ms between the two gradients of the de- or rephasing for the refocusing RF pulses. 60 directions that were derived from a bucky ball schema were applied. With two averages and one non-diffusion-weighted image per 15 directions, a TA of 10 min. 19 s was obtained. The signal-to-noise ratio (SNR) of both diffusion-weighted measurements was estimated by taking the ratio of the mean signal intensity in a frontal white matter region and in a noise-only background region outside of the head in the same slice. For the DTI measurement SNR was 45.2 while for the DWV measurement SNR was 31.4. Thus, the DTI measurement had about 40% higher SNR due to its considerably shorter echo time (100 ms vs. 150 ms). Two sessions were performed for each volunteer on different days (mean/maximum interval 11/21 days). Within each session, a localizer and two DWV measurements were followed by a DTI measurement (measurement time about 30 min). The first session was completed by another two DWV measurements to allow for a within-session comparison of two DWV averages and a final T1-weighted anatomical measurement (MPRAGE, voxel size 1.0 × 1.0 × 1.0 mm3, TA 7 min. 23 s) yielding a total measurement time of about 1 h for session 1. One male participant was excluded because of excessive head motion (more than 4 cm translation within a single acquisition). For the remaining 18 participants, maximum translations and rotations did not exceed 1.5 mm and 2°, respectively.

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Data analysis: motion correction, co-registration, and segmentation

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Data analysis was performed with SPM08 (http://www.fil.ion.ucl.ac. uk/spm). For each diffusion-weighted measurement, all images were motion corrected and re-sliced. The mean of the motion-corrected, non-diffusion-weighted images was calculated and co-registered to

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a more coherent orientation of the axons in a fiber or the degeneration of crossing fibers where the fiber density remains unaffected or even is reduced. Thus, findings showing FA changes or differences (e.g., Klingberg et al., 2000; Sommer et al., 2002) are often hard to interpret in terms of the underlying structural changes or mechanism. It would therefore be helpful to disentangle two types of diffusion properties: (i) the diffusion anisotropy on a cellular or microscopic scale as a measure of the axon density and fiber integrity and (ii) the effect of the axon orientation distribution that reflects the more macroscopic geometric arrangement of the fibers. Several approaches to assess the diffusion anisotropy on a microscopic level have been presented. Recently, a method based on measurements of the diffusion kurtosis and a single-shot trace-weighted acquisition has been presented (Lasič et al., 2014). Its feasibility to detect diffusion anisotropy in a macroscopically isotropic system has been demonstrated and a measure for the microscopic diffusion anisotropy, the so-called μFA, has been determined (Lasič et al., 2014; Szczepankiewicz et al., 2015). A more established method involves two diffusion-weighting periods applied successively in a single acquisition, so-called double-wave-vector (DWV) or double-pulsed-fieldgradient (d-PFG) experiments (Cory et al., 1990; Mitra, 1995; Cheng and Cory, 1999). Such experiments are sensitive to the microscopic diffusion anisotropy in the fourth order of the gradient amplitude (i.e., in the second order of the b value) for arbitrary axon- or fiberorientation distributions (e.g., Komlosh et al., 2007, 2008; Özarslan, 2009; Shemesh et al., 2010, 2012; Lawrenz et al., 2010; Lawrenz and Finsterbusch, 2011, 2013, 2014a; Shemesh and Cohen, 2011), which is in contrast to conventional DTI. For instance, in a region-ofinterest (ROI) in human–brain white matter containing multiple fiber orientations such that the FA is 0, a DWV experiment was still sensitive to anisotropic diffusion exhibiting a difference in signal between acquisitions with parallel and orthogonal diffusion weightings (Lawrenz and Finsterbusch, 2013; Mitra, 1995). From DWV experiments performed with appropriate direction combination schemes for the two diffusion weightings, rotationally invariant measures of the microscopic diffusion anisotropy can be determined that are independent of the axon or fiber orientation distribution, e.g., the IMA and MA indices (Lawrenz et al., 2010; Lawrenz and Finsterbusch, 2013) and the fractional eccentricity (FE; Jespersen et al., 2013). These measures reflect the cellular eccentricity; for example, for an ellipsoidal cell with semi-axes a, b, and c IMA and MA contain (a2 − b2)2 + (b2 − c2)2 + (a2 − c2)2 and are 0 for spherical cells (a = b = c). However, while the IMA increases with cell size (and its dimension is a length to the fourth power), MA is normalized by the cell size and, like FE and FA, dimensionless and scaled to values between 0 and 1 (Lawrenz et al., 2010; Jespersen et al., 2013). Initial in vivo experiments have demonstrated that MA can be mapped in white matter throughout the human brain within a reasonable acquisition time (about 10 min; Lawrenz and Finsterbusch, 2014a). In these experiments, white-matter regions known to contain fiber crossings exhibited reduced FA but “normal” MA values (Lawrenz and Finsterbusch, 2014a). Thus, the microscopic anisotropy measures from DWV experiments could provide information that is complementary to the FA and more specific to axon or fiber integrity because they lack the additional influence of the fiber orientation distribution. This could allow one to distinguish differences and changes at the axonal level, reflected in the MA, from those occurring macroscopically for the fiber connections in the brain that are visible in the FA only. The difference between the two measures could be an indicator for the fiber orientation dispersion in the voxel. The goal of this study is to test the feasibility of IMA and MA for applications, e.g., in neuroscience or clinical research. Repeated whole-brain measurements were performed in a group of healthy volunteers to evaluate the reproducibility within and between sessions, document normal values and their variation in a group of healthy volunteers, compare them with FA values obtained in the same group in selected regionsof-interest, and estimate index differences and group sizes required to

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were temporarily excluded because they showed a large covariance difference from the group mean (difference N 0.1) but they were included retrospectively into the calculated template (Ashburner, 2007). The maps of the calculated indices (FA, MA, IMA) were normalized with the individual flow fields that were used to transform the anatomical T1-weighted data sets to the template. Because only the MA is dimensionless and scaled to values between 0 and 1, comparisons of microscopic anisotropy values with the FA were limited to the MA. The IMA was scaled with q4 to obtain a dimensionless value with a range similar

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the corresponding T1-weighted anatomical data set. This transformation was then applied to all motion-corrected diffusion-weighted images. From the DWV data, maps of the MA and IMA indices were obtained as described previously (Lawrenz et al., 2010; Lawrenz and Finsterbusch, 2013). Maps of FA were calculated from the DTI data. The anatomical data sets were segmented and the resulting gray and white matter tissue classes were used to create a normalized template using the diffeomorphic anatomical exponentiated Lie algebra (DARTEL) approach (Ashburner, 2007). At this stage, two participants

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Fig. 1. Basic spin-echo echo-planar pulse sequence for DWV measurements used in the present study. Two diffusion weighting periods are applied in a single acquisition with a mixing time (τm) between the two weightings. Note that the directions of both diffusion weightings were not always orthogonal as illustrated, but were varied independently.

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Fig. 2. Normalized, group-averaged FA maps with the 14 ROIs considered in the present study: middle cerebellar peduncle right (MCP), pyramidal tract left (Pyr), superior cerebellar vermis (SCV), cerebral peduncle (CP), genu of corpus callosum (GCC), globus pallidus (GP), putamen (Put), anterior thalamus (AT), posterior thalamus (PT), anterior/posterior limb of capsula interna (ACI/PCI), forceps minor (FM), splenium of corpus callosum (SCC), and corona radiate (CR). The locations have been chosen in accordance with Lee et al., 2009.


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To investigate the within- and between-session reproducibility of the IMA and MA values, two DWV measurements were averaged: the two initial measurements of both sessions and the last two measurements of session 1, respectively. To estimate within-session reproducibility, the first two measurements of session 1 were compared with the last two measurements of session 1. To assess the betweensession reproducibility, the first two measurements of session 1 were compared with the two measurements of session 2. To determine normal values and their variation across volunteers, all four measurements of session 1 were averaged. The analysis of the measurement reproducibility, the normal values and variation within the group was performed on the basis of Heiervang et al. (2006). To assess the reproducibility, the differences of the MA, IMA, and FA (ΔMA, ΔIMA, ΔFA) between the two time points (within or between sessions) were calculated for each voxel. For each index X, the mean ΔX and standard deviation (SD(ΔX)) of these differences

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over all (N) volunteers were calculated: ΔX ¼ and SD(ΔX) ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N 1 N−1 ∑i¼1 ΔX i −ΔX . Furthermore, the ratio of these values with the mean index value X ¼ N1 ∑I¼1 X were calculated yielding ΔX and SDðX Þ, the N

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Within- and between-session reproducibility: overview

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Figs. 3 and 4 show results of the within-session reproducibility of IMA (scaled by q4) and MA indices, respectively. On a single-subject level, the within-session differences of both indices appear noisy, with absolute differences exceeding values of 0.1 (Figs. 3b and 4b). On a group level, the differences are much less pronounced (Fig. 3c and 4c), indicating that they level out to some extent, reflecting a random-like variation rather than a systematic trend over volunteers. The voxel-wise group

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Table 1 presents detailed results of the reproducibility for the defined ROIs (cf. Fig. 2). The average of the voxels of all ROIs (“All”) does not show a significant difference for any of the three measures, neither within nor between sessions. This also holds for the individual ROIs with only two exceptions, the within-session MA difference in the globus pallidus (GP) and the between-session MA difference of the pyramidal tracts (Pyr). Because only two ROIs are affected and in both cases the respective other MA differences are much lower, and within one standard deviation, it is unlikely that these two MA differences indicate a systematic effect. The standard deviations of MA and IMA for the individual ROIs show a clear trend of increased values for the between-session comparison. This is expected, because between sessions, more variability can occur, due to factors such as different head and slice positions and related partial volume effects. Comparing the relative standard deviations for MA and IMA, there is an obvious advantage for MA. Its values are lower and the difference between the within- and between-session comparisons is much less pronounced. For the within-session comparison of all voxels in all ROIs (“All”), the CVs are 6.4% and 19.9%, respectively, for the between-session comparison the CVs are 5.9% for MA but 26.8% for the IMA. These results underline the global findings mentioned above (see ‘Within- and between-session reproducibility: overview’): (i) the reproducibility of MA is much better in all defined ROIs and (ii) the increase in variability for the between-session comparisons is much lower.

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coefficient of variation (CV). These parameters reflect the measurement-induced variance or precision of the measurements, e.g., the influence of systematic differences caused by short- or longterm drifts of the MR system as well as the variations present in the individual volunteers, e.g., due to different head positions and orientations that tend to cancel when averaging over the group. These values were then used to calculate the requirements for longitudinal studies with within- or between-session comparisons: (i) the MA, IMA, and between-session FA differences that reach statistical significance for group sizes of 18 (the actual sample size), 40, and 100, and (ii) the group sizes that are needed to consider longitudinal MA, IMA and between-session FA changes of 10%, 5%, and 2% as being statistically significant. These calculations were based on a significance level α of 0.05 and a power level 1-β of 0.8. Analogously, the normal MA and FA values of the group were analyzed on a voxel-by-voxel basis and for the defined ROIs to estimate requirements for between-group comparisons. The standard deviation and mean values over volunteers as well as their ratio (the CV) were calculated for one time point (session 1). The standard deviation and the CV reflect the absolute and relative inter-subject variability. The values were used to determine group sizes and MA and FA differences required to obtain statistically significant results for the same relative differences (10%, 5%, and 2%) and group sizes (18, 40, 100) as for the longitudinal setup and based on the same significance α = 0.05 and power level 1-β = 0.8.

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differences (Figs. 3e and 4e) are within ± 0.05 for both indices and show a bell-shaped distribution which is consistent with random variability, e.g., due to noise (Figs. 3e and 4e). The mean value ± standard deviation of all voxels is 0.001 ± 0.010 for the IMA (scaled with q4) and 0.004 ± 0.014 for the MA, respectively. Thus, no substantial difference is observed between the two measurements of session 1. The CV of the IMA and MA differences over volunteers calculated on a voxel-by-voxel basis are shown in Figs. 3d and 4d, with the corresponding histograms presented in Figs. 3f and 4f, respectively. For IMA, the values appear quite homogenous within white matter with some high-intensity regions in the frontal lobe and brain stem. The distribution of the CV (Fig. 3f) peaks around 10% and has a mean value of 18.9%. For MA, the CVs are much lower, with typical values around 5%, as can also be seen in the histogram of Fig. 4f. The mean value is only 8%, less than half the value for IMA. Noticeably lower values for the CV of the MA can be observed in white-matter regions known to cover major fiber bundles like the pyramidal tracts. Thus, the within-session reproducibility is much better for MA compared to IMA. Results for between-session reproducibility for IMA, MA, and FA are presented in Fig. 5. The overall pattern for the group-averaged IMA (Fig. 5a) and MA differences (Fig. 5c) is similar to the within-session comparison. The mean ± standard deviation are 0.002 ± 0.014 for IMA and 0.003 ± 0.023 for MA. In other words, there are no substantial changes of the mean values between sessions, but the standard deviations are increased compared to the within-session comparison as can also be seen in the slightly broader histograms (Fig. 5g). For the FA (Fig. 5e), the group-average difference has a mean ± standard deviation of 0.011 ± 0.016, indicating a slight shift of the mean while the standard deviation is smaller as compared to MA. Between-session CVs were comparable for MA and FA but were higher for IMA (Figs. 5b, d, and f), particularly in frontal and brainstem regions. This can also be seen in the corresponding histograms (Fig. 5h) with mean values of 8.2% for the FA and 10.5% for the MA, but 28.9% for the IMA. Compared to the within-session comparison, the mean coefficient of variation is much more increased for IMA (about 50%) than for MA (about 30%). Thus, the overall between-session reproducibility for MA is (i) much better than for IMA but (ii) slightly worse (+30%) than for FA.

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to that of the MA and FA in order to be able to use the same gray scaling and plot axes. For more detailed and quantitative results, 14 regions-ofinterest (ROIs), seven in white matter, four in gray matter, and three in the brain stem and cerebellum (Fig. 2), were defined as described previously (Lee et al., 2009).

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Fig. 3. Results of the within-session reproducibility of the IMA index. (a–d) Three cross-sections in transverse, coronal, and sagittal orientation of (a) the T1-weighted data set as an anatomical reference, (b, c) the within-session IMA difference (b) in a single subject and (c) averaged over all participants, and (d) the coefficient of variation (CV). (e, f) Histogram plots of white-matter voxels showing (e) the group-averaged IMA difference and (e) the CV. Note that IMA was scaled by q4 to obtain more convenient values.

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Compared to FA, MA has larger absolute standard deviations for almost all individual ROIs and for the average of the voxels in all ROIs. However, for the CV, the performance of MA is comparable to FA: the FA has lower coefficients of variation in only half of the ROIs, and for the average of the voxels of all ROIs (“All”), MA is even better (5.9% vs. 8.5% for the FA). This improvement compared to the overall results (variability of MA increased by 30% compared to FA) reflects the spatial variation of the MA's CV, with some regions, like several of the selected ROIs, showing lower values compared to the FA (see Figs. 5d and f).

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Next we translate the results of the reproducibility measurements to quantities that could guide the design of longitudinal studies: (i) the MA

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and IMA (scaled by q4) differences that would be considered to be statistically significant as a function of group size, and (ii) the group sizes required for relative MA and IMA (scaled by q4) differences to reach statistical significance (Table 2). As expected, the required differences and group sizes are usually larger for between-session comparisons. For a group size of N = 18, the maximum of the required within-session differences of the MA and IMA are 0.054 and 0.056, respectively, obtained for the anterior capsula interna (ACI); for the between-session differences, the values are 0.082 (ACI) and 0.118 (posterior thalamus, PT). For larger group sizes, these values are reduced accordingly, e.g., for N = 40 the values for between-session differences are 0.053 for MA and 0.077 for IMA. While these absolute differences are quite similar for MA and IMA, the required group sizes for given relative changes differ considerably. In


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most ROIs, a considerably larger group size is required to detect the same relative change for the IMA. For instance, for a MA difference of 10%, a maximum group size of 13 and 17 for within- and betweensession differences, respectively, is required when considering all ROIs. For the same relative change for IMA, group sizes of 317 and more than 1000, respectively, are needed. This is mainly due to the much larger CVs of the IMA (see ‘Within- and between-session reproducibility: overview’ and ‘Within- and between-session reproducibility: ROI analysis’ and Table 1). Thus, the MA provides a much higher sensitivity than the IMA and is a better target to detect changes of the microscopic

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Fig. 4. Results of the within-session reproducibility of the MA index. (a–d) Three cross-sections in transverse, coronal, and sagittal orientation of (a) the T1-weighted data set as an anatomical reference, (b, c) the within-session MA difference (b) in a single subject and (c) averaged over all participants, and (d) the CV. (e, f) Histogram plots of white matter voxels showing (e) the group-averaged MA difference and (e) the CV.

diffusion anisotropy. The IMA will therefore not be considered further in the subsequent sections. For a group size of 40, MA differences of 5% are detectable in 11 of the 14 ROIs for within- and between-session comparisons. Even differences of 2% are detectable in five of 14 ROIs for a group size of below 30.

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Fig. 5. Results of the between-session reproducibility of IMA, MA, and FA. (a–f) Three cross-sections in transverse, coronal, and sagittal orientation of (a, c, e) the between-session difference averaged over all participants and (b, d, f) the CV for (a, b) IMA, (c, d) MA, and (e, f) FA. (g, h) Histogram plots of white-matter voxels showing (g) the group-averaged differences and (h) the CV. The cross-sections shown are the same as in Figs. 3 and 4, i.e. the T1-weighted images of Figs. 3a and 4a can be used as anatomical reference. Note that the IMA was scaled by q4 to obtain more convenient values.



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5.0 2.5

0 (Δ x)

0.05

0

7.5

MA

MA

sag 0.4

0.1

x103

7.5 5.0

cor

sag

voxels

U

N C O

cor

0.1

0

FA MA

I 0.2 CV (Δ x)

MA

0.4


8

Table 1 Absolute and relative within- and between-session differences (mean ± standard deviationa across volunteers) for MA, IMA, and FA in 14 ROIs.

t1:6

PCI

24 −18 12

t1:7

SCC

−3 −33 19

t1:8

GCC

1 21 −1

t1:9

CP

−19 −19 −10

t1:10

CR

30 −18 25

t1:11

FM

18 33 10

t1:12

Put

−24 2 2

t1:13

GP

20 −1 −1

t1:14

PT

−15 −27 4

t1:15

AT

−9 −10 2

t1:16

SCV

1 −74 −30

t1:17

MCP

−22 −40 −39

t1:18

Pyr

5 −23 −38

t1:19

Alld

t1:20 t1:21 t1:22 t1:23

a b c

ΔFA

ΔMA

ΔIMA (scaled with q4)

−0.00 ± 0.06 −0.2% ± 6.5% 0.01 ± 0.05 0.5% ± 5.0% −0.03 ± 0.07 −4.1% ± 8.8% −0.02 ± 0.04 −3.3% ± 6.0% −0.02 ± 0.04 −2.1% ± 4.6% 0.00 ± 0.05 0.1% ± 5.6% −0.01 ± 0.02 −0.6% ± 1.9% 0.02 ± 0.01 4.3% ± 3.0% −0.04 ± 0.01 −7.8% ± 2.5% 0.01 ± 0.04 2.1% ± 9.5% −0.01 ± 0.06 −1.3% ± 9.2% 0.00 ± 0.04 1.2% ± 11.2% −0.01 ± 0.05 −1.0% ± 5.2% −0.01 ± 0.01 −0.8% ± 1.3% −0.008 ± 0.046 −1.1% ± 6.4%

0.02 ± 0.08 4.6% ± 19.4% −0.02 ± 0.05 −3.6% ± 12.0% −0.01 ± 0.03 −2.4% ± 8.3% 0.03 ± 0.03 9.7% ± 9.8% 0.00 ± 0.05 0.2% ± 10.4% −0.01 ± 0.04 −2.4% ± 10.8% −0.01 ± 0.05 −2.0% ± 15.7% −0.00 ± 0.04 −3.8% ± 34.6% 0.04 ± 0.03 27.6% ± 22.4% −0.01 ± 0.05 −3.6% ± 21.2% 0.01 ± 0.03 2.3% ± 14.0% −0.01 ± 0.05 −6.3% ± 63.3% 0.00 ± 0.08 0.7% ± 18.2% 0.01 ± 0.05 4.5% ± 15.2% 0.004 ± 0.058 1.2% ± 19.9%

0.00 ± 0.02 0.5% ± 3.6% 0.01 ± 0.02 0.8% ± 3.0% −0.01 ± 0.02 −1.4% ± 2.4% 0.00 ± 0.02 0.4% ± 3.5% 0.00 ± 0.03 0.3% ± 4.1% 0.01 ± 0.01 2.5% ± 2.7% 0.01 ± 0.02 1.7% ± 3.7% −0.00 ± 0.02 −1.0% ± 16.0% 0.00 ± 0.01 0.9% ± 4.4% 0.00 ± 0.03 0.7% ± 11.1% −0.01 ± 0.01 −1.6% ± 3.2% 0.01 ± 0.03 2.1% ± 13.9% −0.01 ± 0.04 −2.1% ± 6.7% 0.01 ± 0.01 3.2% ± 2.3% 0.002 ± 0.040 0.4% ± 8.5%

−0.00 ± 0.12 −0.1% ± 13.4% 0.03 ± 0.06 3.3% ± 6.0% 0.02 ± 0.08 2.7% ± 9.9% 0.04 ± 0.05 5.6% ± 6.9% 0.02 ± 0.03 2.4% ± 3.6% −0.00 ± 0.06 −0.1% ± 6.8%0.05 ± 0.03 6.1% ± 3.0% −0.04 ± 0.03 −8.3% ± 5.8% 0.02 ± 0.02 3.3% ± 3.3% −0.03 ± 0.04 −6.5% ± 9.0% −0.00 ± 0.02 −0.0% ± 3.2% −0.03 ± 0.04 −8.1% ± 11.7% 0.04 ± 0.11 3.8% ± 12.0% 0.07 ± 0.02 8.3% ± 2.6% 0.013 ± 0.043 1.9% ± 5.9%

0.03 ± 0.09 7.5% ± 22.3% 0.00 ± 0.06 0.7% ± 13.2% 0.04 ± 0.06 8.4% ± 14.6% 0.04 ± 0.06 12.9% ± 20.9% 0.06 ± 0.13 13.2% ± 27.1% 0.01 ± 0.07 1.9% ± 19.4% 0.02 ± 0.08 6.2% ± 27.2% 0.01 ± 0.09 13.3% ± 100.6% 0.01 ± 0.05 6.7% ± 42.0% −0.03 ± 0.17 −45.0% ± 211.3% −0.01 ± 0.04 −4.9% ± 26.7% −0.00 ± 0.14 −3.8% ± 181.1% 0.05 ± 0.10 11.6% ± 24.3% 0.04 ± 0.12 11.5% ± 38.4% 0.018 ± 0.077 6.4% ± 26.8%

the relative standard deviation is a measure of the coefficient of variation. See Fig. 2 for ROI positions and abbreviations. Not available for the FA. Average of all voxels of all ROIs.

386

E

C

d

20 2 13

ΔIMA (scaled with q4)

F

ACI

Between-session difference

ΔMA

O

t1:5

MNI coord (x y z)

R O

Abbr.

P

t1:4

Q1

Within-session differencec

D

ROIb

E

t1:3

T

t1:1 t1:2


t2:1 t2:2

Table 2 Required group sizesa N for several MA and IMA within-/between-session differences in 14 ROIs.

R

caused by noise or imaging artifacts, but reflect structural differences between the volunteers. Maps of the mean values of MA and FA in the group, and of their coefficient of variation, are shown in Fig. 7. Overall, the mean MA values (Fig. 7a) show less variation in the brain than the mean FA values (Fig. 7c). For instance, while the corpus callosum and the

O

C

389 390

R

391

similar across volunteers, but there are also differences in the absolute values and the contrast, for example, in the transverse section. These differences do not affect single voxels, but rather, larger structures. They also appear in “benign” regions like the centrum semiovale, which typically are not affected by artifacts (e.g. those caused by field inhomogeneities). Thus, it is very likely that these differences are not

387 388

ROIb

t2:4

Abbr.

MNI coord (x y z)

NMA

NIMA

NMA

NIMA

NMA

NIMA

t2:5 t2:6 t2:7 t2:8 t2:9 t2:10 t2:11 t2:12 t2:13 t2:14 t2:15 t2:16 t2:17 t2:18 t2:19

ACI PCI SCC GCC CP CR FM Put GP PT AT SCV MCP Pyr Maxc

20 2 13 24 −18 12 −3 −33 19 1 21 −1 −19 −19 −10 30 −18 25 18 33 10 −24 2 2 20 −1 −1 −15 −27 4 −9 −10 2 1 −74 −30 −22 −40 −39 5 −23 −38

9/17 5/6 9/10 6/6 4/4 5/6 3/3 4/5 3/4 13/9 9/4 12/13 5/14 3/3 13/17

32/41 14/16 8/19 10/37 11/60 12/32 22/61 96/796 42/141 38/N1000 18/59 317/N1000 28/49 22/118 317/N1000

26/58 10/14 29/33 14/17 10/7 12/17 4/6 7/13 4/6 43/28 29/6 42/46 11/48 3/5 43/58

121/158 47/57 24/69 33/140 37/234 39/121 79/235 378/N1000 160/557 143/N1000 64/227 N1000/N1000 106/187 82/465 N1000/N1000

152/352 52/72 168/195 74/95 46/27 64/94 10/20 28/69 9/23 258/160 168/22 250/273 55/287 6/15 258/352

744/975 284/345 138/421 191/864 215/N1000 230/744 483/N1000 N1000/N1000 986/N1000 881/N1000 384/N1000 N1000/N1000 652/N1000 500/N1000 N1000/N1000

t2:20 t2:21 t2:22

a b c

U

N

t2:3

10%

5%

2%

Group sizes based on a statistical significance (α) of 0.05 and a power (1 − β) of 0.8. See Fig. 2 for ROI positions and abbreviations. Maximum over all ROIs.


392 393 394 395 396 397


1

9

1

0

R O

O

0

F

vol 2

vol 1

E

vol 3

vol 4 0

R

E

C

T

0

1

D

P

1

N C O

R

1

1

vol 5 0

vol 6 0

U

Fig. 6. Maps of the MA for session 1 of the first six volunteers examined. The cross-sections shown are the same as in Figs. 3 and 4, i.e., the T1-weighted images of Figs. 3a and 4a can be used as anatomical reference.

398

403

pyramidal tracts have remarkably larger FA values compared to other white-matter regions, their MA values appear to be almost average (see also below). The CV differs between the MA (Fig. 7b) and FA (Fig. 7d), with lower MA values in deep white matter, indicating that there is less variability between volunteers for MA compared to FA.

404

Normal values: ROI analysis

405 406

Table 3 presents FA and MA values, their standard deviations over volunteers, and their CV in the defined ROIs (cf. Fig. 2), along with FA values from the literature for comparison. In general, the MA values

399 400 401 402

407

are larger than the FA values, and show less variation between the different white matter ROIs. FA and MA have comparable values in white-matter regions known to contain fiber bundles with minimum fiber orientation dispersion, such as the splenium of the corpus callosum (FA 0.778, MA 0.810). However, they differ significantly for white matter-regions with fanning and crossing fibers, such as the forceps minor (FA 0.462, MA 0.828), and for gray-matter regions, such as the thalamus (mean of anterior and posterior ROI: FA 0.29, MA 0.55) and the putamen (FA 0.10, MA 0.46; all values of session 1). In white-matter ROIs, MA varies by about ± 20% but FA by about ± 30% (all values of session 1), which may be due to greater variability of the fiber-orientation dispersion between volunteers.


408 409 410 411 412 413 414 415 416 417 418 419

10


a

b

1

0.4 MA CV

F

MA

d

R O

c

0

O

0

P

1

FA CV 0

T

0

E

D

FA

0.4

420 421

E

C

Fig. 7. Maps of normal values of MA and FA and their CV in a group of healthy volunteers. (a–d) Three cross-sections in transverse, coronal, and sagittal orientation showing maps of (a, c) the mean value and (b, d) the coefficient of variation of 18 volunteers for MA (a, b) and FA (c, d).

t3:1 t3:2

Table 3 Group mean ± standard deviation of 18 volunteers and coefficient of variation (CV) for FA and MA in 14 ROIs.

R

standard deviations of all white-matter ROIs, is lower for MA than for FA (0.041 vs. 0.056). Because the value for the MA is comparable in session 2 (0.035), where only two measurements were performed, this difference cannot be explained by the larger number of acquisitions

O

t3:3

ROIa

t3:4

Abbr.

MNI coord (x y z)


ACI PCI SCC GCC CP CR FM Put GP PT AT SCV MCP Pyr Meane

20 2 13 24 −18 12 −3 −33 19 1 21 −1 −19 −19 −10 30 −18 25 18 33 10 −24 2 2 20 −1 −1 −15 −27 4 −9 −10 2 1 −74 −30 −22 −40 −39 5 −23 −38

t3:20 t3:21 t3:22 t3:23 t3:24

a b c d e

FA

U

N

C

422

R

423

The variability across volunteers is not very pronounced for either the MA or FA index. For the CV, maximum values for the FA (all ROIs/ white-matter ROIs only) are 12.9% (globus pallidus, GP)/12.2% (anterior capsula interna, ACI) and for the MA are 13.8% (ACI). The average of the

MA

Mean ± std (session 1b)

CV

Mean ± std (Lee et al., 2009)

Mean ± std (session 1d)

CV

Mean ± std (session 2c)

0.622 ± 0.076 0.627 ± 0.048 0.778 ± 0.041 0.684 ± 0.050 0.736 ± 0.071 0.478 ± 0.060 0.462 ± 0.046 0.100 ± 0.008 0.225 ± 0.029 0.274 ± 0.033 0.313 ± 0.017 0.192 ± 0.017 0.643 ± 0.055 0.432 ± 0.022 –

12.2% 7.7% 5.3% 7.3% 9.6% 12.6% 10.0% 8.0% 12.9% 12.0% 5.4% 8.9% 8.6% 5.1% 9.0%

0.454 ± 0.030 0.714 ± 0.049 0.775 ± 0.052 0.806 ± 0.065 0.732 ± 0.075 0.530 ± 0.069 0.500 ± 0.047 0.121 ± 0.028 0.233 ± 0.046 0.257 ± 0.032 0.301 ± 0.025 0.188 ± 0.031 0.656 ± 0.078 0.553 ± 0.028 –

0.874 ± 0.052 0.947 ± 0.017 0.810 ± 0.051 0.645 ± 0.052 0.855 ± 0.054 0.938 ± 0.028 0.828 ± 0.037 0.464 ± 0.064 0.568 ± 0.026 0.472 ± 0.051 0.624 ± 0.079 0.326 ± 0.014 0.910 ± 0.055 0.774 ± 0.029 –

5.9% 1.8% 6.3% 8.1% 6.3% 3.0% 4.5% 13.8% 4.6% 10.8% 12.7% 4.3% 6.0% 3.7% 6.6%

0.877 ± 0.049 0.911 ± 0.024 0.820 ± 0.029 0.629 ± 0.046 0.715 ± 0.012 0.938 ± 0.032 0.782 ± 0.055 0.481 ± 0.077 0.592 ± 0.030 0.492 ± 0.062 0.632 ± 0.073 0.348 ± 0.020 0.884 ± 0.046 0.852 ± 0.044 –

See Fig. 2 for ROI positions and abbreviations. Based on one measurement. Based on two measurements. Based on four measurements. Mean CV of all ROIs.


424 425 426 427


442

Effect and group sizes for between-group and single-subject comparisons

443 444

462 463

The normal values and their variations within the group have been used to derive (i) MA and FA differences that would reach statistical significance for several group sizes and (ii) the required group sizes to detect given MA and FA differences (Table 4). The detailed values for the required differences and the group size are quite heterogeneous, with no clear advantage for one of the indices. Typical difference values are below 0.05, 0.03, and 0.02 for a group sizes of 18, 40, and 100, respectively, but can be as low as 0.01, even for a group size of 18, as for MA in the posterior capsula interna (PCI). For a comparison of a single-subject with the normal group values, FA and MA differences of 0.16, 0.10, and 0.05 would be considered to be statistically significant for all ROIs, for more than half of the ROIs, and for four of the 14 ROIs, respectively. Typical group sizes are below 15, below 40, and below 200 for differences of 10%, 5%, and 2%, respectively. Considering the maximum group size over all ROIs for the different relative changes yields only a minor difference between FA and MA (e.g., 55 vs. 62 for a difference of 5%). Thus, for group comparisons with a similar level of relative differences, MA may be as feasible as FA. For typical relative differences that have been reported for FA in group comparisons (N5–10%; e.g., Klingberg et al., 2000), group sizes of around 20–60 would be sufficient for MA.

464

Correlation of MA and FA

465 466 467 468

Fig. 8 presents scatter plots of the MA values vs. FA values for white matter in general (Fig. 8a) and individually for the 14 ROIs (Figs. 8b and c). Considering all white matter voxels (Fig. 8a), only a few scatter around the diagonal where MA equals FA; the vast majority show larger

t4:1 t4:2

Table 4 Required group sizesa N for different FA and MA between-group differences in 14 ROIs.

458 459 460 461

ROIb

t4:4

Abbr.

MNI coord (x y z)

NFA

NMA

NFA

NMA

NFA

NMA


ACI PCI SCC GCC CP CR FM Put GP PT AT SCV MCP Pyr Maxc

20 2 13 24 −18 12 −3 −33 19 1 21 −1 −19 −19 −10 30 −18 25 18 33 10 −24 2 2 20 −1 −1 −15 −27 4 −9 −10 2 1 −74 −30 −22 −40 −39 5 −23 −38

14 7 5 7 10 15 10 8 16 14 5 9 8 5 16

6 3 6 8 6 3 4 17 4 12 15 4 6 4 17

49 21 11 19 32 52 34 23 55 48 12 27 25 11 55

14 4 15 23 15 6 9 62 9 39 53 8 14 7 62

295 117 57 107 185 312 197 128 328 287 60 156 146 53 328

72 9 80 130 81 20 42 376 44 232 317 39 74 30 376

t4:20 t4:21 t4:22

a b c

U

5%

0.6

0.8

1

0.6

ACI PCI SCC GCC CP CR FM

0.4 0.2

c

0

0

0.2

0.4

0.6

0.8

1

FA 1 0.8 0.6

Put GP AT PT SCV MCP Pyr

0.4

t4:3

10%

0.4

MA

456 457

0.2

1 0.8

T

454 455

0

FA

C

452 453

E

450 451

R

448 449

R

447

0

b

N C O

445 446

0.2

F

441

50

O

439 440

0.4

R O

437 438

100

P

435 436

0.6

MA

434

150

0.8

MA

432 433

1

D

430 431

a

contributing to MA. The CV is lower for MA in 10 of 14 ROIs. Averaged over all ROIs, the CV is only 6.6% for MA but 9.0% for FA. Thus, the variation between volunteers in the selected ROIs seems to be much less pronounced for MA compared to FA. The agreement of the FA values determined in the present study with those reported by Lee et al. (2009), where similar ROIs were considered, is good for most ROIs. Exceptions include the anterior internal capsule (ACI) and the pyramidal tracts (Pyr). However, the FA depends on measurement parameters like diffusion time, the pulse duration of the diffusion-weighting gradients, and the SNR (Jones and Basser, 2004). This is reflected in the large variability of values reported in different studies. For example, for the internal capsule, the FA value ranges between 0.45 (Lee et al., 2009) and 0.66 (Snook et al., 2005), which also covers the value observed here.

E

428 429

11

2%

Group sizes based on a statistical significance (α) of 0.05 and a power (1 − β) of 0.8. See Fig. 2 for ROI positions and abbreviations. Maximum over all ROIs.

0.2 0 0

0.2

0.4

0.6

0.8

1

FA Fig. 8. Scatter plots of MA vs FA for (a) all voxels containing brain white matter with a probability larger than 0.8 and (b, c) the defined selected ROIs (cf. Fig. 2). The plot in (a) is based on the group MA map, those in (b) and (c) present all data for the individual volunteers. The labels in (a) are color-coded to represent their plot density due to the large number of labels, the color bar units are the numbers of voxels in an area of 0.02 × 0.02 (FA × MA).

MA than FA values. For FA values above around 0.3, typical MA values are between FA + 0.2 and 1.0 with the highest density being found between 0.8 and 0.9. In this range, FA seems to be a lower limit for MA, i.e. MA ≥ FA. But aside from that, there seems to be no obvious correlation between MA and FA (correlation coefficient = 0.121). These observations are in line with the expectations that (i) MA is a measure of the microscopic diffusion anisotropy and unlike FA is not affected by the fiber orientation distribution and (ii) MA provides information complementary to that of FA. For the few voxels with FA values lower than 0.3, MA values are only about 0.6 or below and substantially lower than for the other voxels.


469 470 471 472 473 474 475 476 477 478 479

533

Microscopic diffusion anisotropy

534

MA was defined mathematically as a measure of cell eccentricity; it is dimensionless and scaled to values between 0 and 1 (Lawrenz et al., 2010). Thus, it can be considered as a straight measure of the microscopic anisotropy that could be easily compared to the FA. In contrast, IMA also depends on cell size; the same cell shape yields higher IMA values if the cell is larger (Lawrenz et al., 2010). This makes IMA more difficult to interpret. Furthermore, the reproducibility for IMA is significantly lower than for MA, in both within- and between-session comparisons.

508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531

535 536 537 538 539 540 541

C

506 507

E

501 502

R

499 500

R

497 498

O

495 496

C

493 494

N

491 492

U

489 490

Comparison with FA

592

Overall, the between-session reproducibility of MA as expressed in the CV was worse compared to FA (+30%). To some extent, this lower performance of MA may be related to the lower SNR of the DWV measurements, which was reduced by about 40% compared to the DTI measurement, due to the longer echo time required. Furthermore, the signal variation targeted to estimate MA is of a higher order than that for FA (Lawrenz et al., 2010; Basser and Pierpaoli, 1996), making it more difficult to detect and susceptible to noise. However, the MA's CV varies over the brain. In our ROIs, the performance of MA was comparable to that of FA. Thus, it could be expected that for longitudinal studies, group sizes could be similar to those used in studies measuring FA. Generally, the MA values observed were larger than the FA values, even though both are scaled from 0 to 1 (Lawrenz et al., 2010; Basser

593 594

F

532

In this study, two indices of the microscopic diffusion anisotropy that can be derived from a DWV measurement, the IMA and MA index, were investigated in a group of healthy volunteers to test their feasibility for longitudinal and between-group comparisons in basic or clinical neuroscience studies. The protocol included two to four DWV and one DTI measurement in two sessions on different days. This allowed us to evaluate the measure's reproducibility within and between sessions, calculate normal values and their variation in healthy volunteers, compare them with FA values in selected regions-of-interest, and estimate index differences and group sizes needed to obtain statistically significant results in longitudinal and group-comparison studies. For both DWV indices, the within- and between session comparisons did not reveal a substantial difference between the two time points but increased variations between compared to within sessions. The reproducibility and CVs of IMA showed a much lower performance as compared to MA yielding required group sizes that are far from being feasible. Thus, MA is expected to provide a better sensitivity and specificity making it the primary target to investigate microscopic diffusion anisotropy. The performance of the MA was similar to that of FA with reasonable group sizes for longitudinal and between-group studies. Interestingly, the variation of MA between volunteers was less pronounced than for FA which could indicate that the fiber orientation distribution contributing to FA shows more inter-subject variability than the tissue microstructure reflected in MA. In regions with parallel fiber bundles, MA and FA values were very similar but MA values were substantially larger in gray matter and white-matter regions known to contain crossing fibers. Only a low correlation coefficient of MA and FA could be found.

487 488

O

505

486

R O

Discussion

484 485

542 543

P

504

482 483

For these reasons, MA is more informative, and may be the best measure for studies focussing on the microscopic diffusion anisotropy. However, it should be kept in mind that, having acquired the data to assess MA, IMA can always be computed from a subset of these data and may provide additional information on cell sizes when compared to MA. We observed no substantial differences of MA (and IMA) mean values within or between sessions, an important prerequisite for longitudinal studies. The averaged CV of MA was larger for the between-session comparison. A higher variability between sessions is expected because different head and slice positions and orientations may cause partial volume effects to vary between the acquisitions. Furthermore, SNR values and imaging artifacts like geometric distortions may differ between sessions due to different field inhomogeneities and shim settings. For the selected ROIs, the coefficients of variation were usually even smaller than the average because the reproducibility of MA varied across the brain, with the lowest values in deep white matter. Power sufficient to detect MA changes of 10% in any of the ROIs would require approximately 25 participants per group. For changes of about 2%, typical for FA in longitudinal studies (e.g., Teipel et al., 2010; Draganski et al., 2011), sufficient power would only be expected in low-noise regions such as posterior capsula interna (PCI), corona radiate (CR), and pyramidal tracts (Pyr). For the normal values and their variation within the group of healthy volunteers, the CVs were around 7% in the selected ROIs. The values were very similar for two and four averages of the DWV measurements. This could indicate that the MA variation between volunteers is not dominated by random effects, but by microstructural differences between volunteers. In other words, for the observed inter-individual differences the precision achieved with two averages (acquired in a total acquisition time of about 22 min) seems to be sufficient to obtain reliable MA values. For typical group differences as reported for the FA (≥5–10%; e.g. Klingberg et al., 2003), the coefficients of variation convert to group sizes of below 15–35 persons for typical ROIs. Thus, it seems that MA group comparisons are feasible in neuroscience and clinical studies. Although some ROIs were chosen in deep gray matter, cortical gray matter was not analyzed in the present study. Because a rather low spatial resolution had to be chosen to provide a sufficient SNR for the long echo times of the DWV experiment, partial volume effects with white matter are very likely for voxels considered to contain cortical gray matter. With the large MA values observed in white matter, MA in such voxels may be significantly contaminated, or even dominated, by white matter contributions. Consequently, MA values estimated for cortical gray matter voxels may be unreliable. A more reliable way to estimate microscopic diffusion anisotropy in cortical gray matter could be to apply inversion recovery adjusted to null the signal intensity of white matter (Lawrenz and Finsterbusch, 2014b). Any remaining microscopic anisotropy would then reflect tissue microstructure properties of cortical gray matter without contamination from white matter within the voxel.

T

503

This could indicate that such low FA values reflect a reduced density of axons and not only an above-average broadness of the fiber orientation distribution. Considering the individual ROIs in white matter (Fig. 8b), some ROIs, like the anterior capsula interna (ACI) and the genu of the corpus callosum (GCC), show a clear trend of reduced MA values for lower FA values. In contrast, in other ROIs, MA values seem to be quite independent of the corresponding FA values, e.g., in the corona radiata (CR; correlation coefficient −0.01). This reflects that FA is not a good measure of the diffusion anisotropy on a microscopic scale. For the gray-matter and brainstem ROIs, MA values are generally also larger than the corresponding FA values (Fig. 8c) and there is only slight overlap of the different ROIs in the scatter plot. In the middle cerebellar peduncle (MCP), MA values are usually close to 1, whereas the FA varies between 0.5 and about 0.8, similar to white matter regions. In contrast, the MA values of anterior and posterior thalamus (AT and PT), globus pallidus (GP), and putamen (Put) tend to decrease with decreasing FA. However, although the separation of these ROIs in the FA is quite pronounced, there is considerable overlap of their MA values. Because in some ROIs, like the superior cerebellar vermis (SCV), the distribution of MA values is compact, it seems unlikely that the large variation, for example, for the Putamen, reflects noise. This could, to some extent, reflect differences in the tissue microstructure such as the density of axons and dendrites, that are not as visible with FA.

D

480 481


E

12


544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 Q5 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591

595 596 597 598 599 600 601 602 603 604 605


627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659

665 666 667 668 669

C

625 626

E

623 624

R

F

621 622

R

619 620

N C O

617 618

U

615 616

O

The b value per diffusion weighting that was used in the present study could be considered to be quite low. However, first, it has been shown that the specific signal modulation reflecting microscopic diffusion anisotropy, can be successfully observed with the diffusionweighting parameters used here (cf. Lawrenz and Finsterbusch, 2013). Second, although an increased signal modulation can be expected for higher b values, the signal modulation is also known to decrease with

613 614

R O

663 664

612

P

Methodological and technical issues

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the required longer gradient pulse durations (Koch and Finsterbusch, 2009; Lawrenz and Finsterbusch, 2010), and the longer echo time required reduces the SNR accordingly. Thus, the current settings are a compromise between a sufficient b value and reasonable pulse durations and echo times. For stronger gradient systems, like the CONNECTOME system (Setsompop et al., 2013), that allow for much shorter pulse durations and echo times, a higher b value becomes feasible, and may improve the performance of the DWV experiments. For further optimization, in particular when one has a well-motivated hypothesis about the relevant tissue structure, simulations could be performed to determine the set of diffusion-weighting parameters (pulse duration, diffusion time, b value) that yield the highest sensitivity (e.g., Alexander, 2008). A rim of higher values around the white matter, in particular close to the ventricles, is observed for the MA. Most likely, these rims are caused by geometric distortions of the echo-planar images that are induced by eddy currents of the diffusion-weighting gradient pulses. These distortions vary with the direction(s) of the diffusion weighting(s) and, thus, can yield an over- or underestimation of anisotropy values at the border between regions with high and low anisotropies. Such effects can be expected to be more pronounced for the DWV experiments where two diffusion weightings were applied and varied in direction, in particular given that we did not use a pulse sequence that minimizes eddy current effects (cf. Reese et al., 2003). Field inhomogeneities also induce geometric distortions in EPI, and can cause cross-terms with the diffusion-weighting gradient pulses that amplify, weaken, and/or change the direction of the diffusion weightings. Both effects are not only sensitive to head displacements and rotations, but also vary (i) with the direction(s) of the diffusion weightings and (ii) temporally, in the presence of field drift (such as drift caused by gradient heating). The direction combination scheme and the data analysis were set up to compensate for linear cross-terms (Lawrenz and Finsterbusch, 2014a), but this approach does not address non-linear components of the cross-terms, and will also fail for linear components that vary in time. This is why increased sensitivity to head motion and scanner instabilities can be expected in such regions. Because the DWV measurements to determine IMA and MA values involve two diffusion weightings and considerably longer echo times, they can be expected to be more sensitive to such effects than DTI. A simple spin-echo sequence with one refocusing RF pulse applied between the two diffusion weightings was used in the present study to minimize the echo time and related T2 relaxation. This setup has been used successfully in previous studies investigating microscopic diffusion anisotropy with DWV experiments (e.g., Lawrenz and Finsterbusch, 2013). However, this approach may not always be optimal, for instance when much longer or shorter mixing times are required, for example, because of an optimization of the parameters as mentioned above. In such cases, other sequence variants may be more efficient. For instance, for long mixing times between the two diffusion weightings or long diffusion times, a stimulated echo acquisition mode (STEAM) could be used to store the magnetization longitudinally during the DWV mixing or the diffusion time and reduce T2-related signal decays accordingly. On the other hand, for very short mixing times, the time between the two diffusion-weightings may be too short to host a refocusing RF pulse. A solution could be to apply an RF pulse for each diffusion weighting as in a standard Stejskal–Tanner experiment. In the presence of significant field inhomogeneities, a double-spin echo preparation could be used for each of the diffusion weightings to minimize cross terms with the diffusion-weighting gradient pulses (e.g., Koch and Finsterbusch, 2011). However, recent tests of this sequence variant in the human brain (Lawrenz and Finsterbusch, 2014a) did not show a significant advantage compared to a cross-term compensation based on averaging data acquired with opposite gradient polarities (Neeman et al., 1991) that has been used in the present study. Water exchanging with other compartments does not “see” the restrictions present in tissue and behaves more like free water. In case of

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and Pierpaoli, 1996). The values were very similar in ROIs with major fiber bundles (with low fiber dispersion). In contrast, in deep gray matter and white matter regions known to contain fibers crossing on a voxel level, FA had significantly reduced values while the MA took on much larger values. Thus, MA appeared more homogenous, with only minor variations within white matter and between gray and white matter structures in the healthy human brain. These findings are in agreement with the expectation that the MA does not depend on the fiber orientation distribution and reflects solely tissue properties on a cellular or microscopic level. However, it should be kept in mind that despite scaling to the same range of values, a comparison of MA and FA values is of limited value because the measures are based on different models and assumptions (Lawrenz et al., 2010; Basser and Pierpaoli, 1996). This applies even to the very simple case of a single fiber population and orientation in a voxel and perfect timing parameters such as infinitely short gradient pulses. For diffusion in only a single direction (infinitely narrow and long fibers), both indices will have values of 1; for isotropic Gaussian diffusion, (an infinitely thick and long fiber), both indices will be 0. However, in the range between these two extremes (infinitely long fibers with a finite diameter), the scaling with fiber diameter may be different. Whereas MA was defined based on the fiber geometry parameters (Lawrenz et al., 2010), the dependency of the FA on the fiber diameter is more complex; so MA and FA cannot be expected to be proportional. Thus, the larger and more homogenous values observed for the MA in white matter do not imply a better “performance” of the MA per se. Assuming the same relative changes, the group sizes required for between-group comparisons are very similar for the MA and FA, with no clear advantage for either index. However, on average, the variability within the group seems to be smaller for MA than for FA; in other words, the MA values are more coherent over volunteers than the FA values. This could indicate that FA variability across healthy volunteers reflects mainly inter-individual differences in the fiber orientation distribution while the inter-individual variability on a microscopic scale as assessed by MA is much less pronounced. As a consequence, changes of fiber or axon integrity or density may be much more difficult to detect with FA with the background variability of the fiber orientation distribution than with MA, where this confound is absent or considerably reduced. In other words, the sensitivity of MA to changes of the tissue microstructure could be much better than FA. It should be noted that the FA can also be computed from the DWV measurements. However, only parallel or only antiparallel direction combinations should be considered to avoid DWV signal effects that vary between the directions and cannot be modeled with the conventional diffusion tensor. The FA maps calculated from the parallel direction combinations showed a contrast very similar to the maps obtained from the DTI measurements, but the values were generally larger, particularly in gray matter (data not shown). Most likely, this deviation is related to the different acquisition parameters. The DWV measurements were performed with a considerably longer echo time (and correspondingly reduced SNR), and parallel diffusion weightings were applied along only nine non-collinear directions. Such a sparse direction sampling is far from optimal for DTI (e,g., Jones and Basser, 2004). Thus, when targeting the diffusion tensor, a dedicated DTI measurement is recommended although a subset of the DWV data could be analyzed like conventional DTI.

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The MA and IMA indices of microscopic diffusion anisotropy that can be derived from DWV experiments involving two successively applied diffusion-weighting periods in a single acquisition, were evaluated for

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Recently, the FE index has been introduced as an alternative to the DWV indices considered here. It is also a rotationally invariant derived from the DWV experiment at long mixing times; however, it is based on the cumulant rather than the Taylor expansion of the signal equation, and considers finite pulse durations and diffusion times (Jespersen et al., 2013). In general, it can be expected to be more accurate than MA. However, whether it provides an advantage in the human brain in vivo at the rather low q values and for the short mixing times used here, is not yet clear. Another approach to estimate the microscopic anisotropy is based on a conventional diffusion-weighted measurement with a single diffusion-weighting period (Lasič et al., 2014; Szczepankiewicz et al., 2015). This approach considers the fourth-order signal behavior (kurtosis), to detect deviations from Gaussian diffusion as an indicator of restrictions. With a reference acquisition involving a single-shot trace weighting, the direction-dependency of the restrictions on a microscopic scale can be identified. Thus, the detection of diffusion anisotropy in the presence of macroscopic isotropic diffusion becomes possible. The derived anisotropy parameter, the so-called μFA, seems to be equivalent to the FE index mentioned above (Jespersen et al., 2014). Several other approaches are currently used to investigate tissue microstructure with conventional diffusion-weighted imaging like CHARMED (Assaf and Basser, 2005), AxCaliber (Assaf et al., 2008), NODDI (Zhang et al., 2012), and models presented by Alexander et al. (2010) and Jespersen et al. (2010). In these methods, the diffusionweighted signal for different b values and directions is fit by the signal expected for a model of the tissue, e.g., composed of an unrestricted, hindered, anisotropic compartment described by a diffusion tensor and a restricted compartment of cylindrical shape. This fit provides measures like the volume fractions of the compartments, their diffusion properties, and the sizes of the restricted compartment. The practical applicability of some of these approaches to arbitrary axon (or cylinder) orientation distributions is limited because a known predominant fiber orientation is assumed. Thus, applications involved brain regions with a major fiber bundle like the corpus callosum. In voxels with pronounced fiber orientation dispersion, these models could be expected to have difficulties in unraveling the degree of diffusion anisotropy present on a microscopic scale from (almost) isotropic signal characteristics. Still, all these models could benefit from including information from DWV measurements that detect the degree of microscopic diffusion anisotropy directly, without the need for a predominant fiber orientation.

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This work was supported by the Deutsche Forschungsgemeinschaft (FI 1544/3-1). The authors are grateful to Laura Sasse, M. Sc., for recruitment of the volunteers and to Jeremy B. Caplan and G. Elliott Wimmer for proofreading the manuscript.

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their applicability to research, and compared to FA obtained from a conventional DTI measurement. The reproducibility within and between sessions was much better for MA than IMA, making MA the preferred index for studying microscopic diffusion anisotropy. MA performed comparable to FA with respect to reproducibility and group sizes required to detect particular relative longitudinal and group differences. MA values had less variability between volunteers and were generally larger, in particular in gray matter and white matter regions known to contain crossing fibers. These observations indicate that the MA (i) can be applied to neuroscientific or clinical studies, (ii) reflects solely properties of the tissue microstructure, and (iii) may provide a better sensitivity to changes of the tissue microstructure than FA.

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eccentric cells this means that diffusion appears less anisotropic and cell eccentricities are expected to be underestimated. From the results of Nilsson et al. (2013), the volume fractions undergoing exchange between the two diffusion weightings, can be estimated to range between 1 and 3% in white matter and about 5% in gray matter. Thus, it is expected that the effect of exchange on MA values in brain tissue is marginal. Some dependency of MA (and IMA) values on the protocol parameters such as the gradient pulse duration can be expected (Koch and Finsterbusch, 2009; Lawrenz and Finsterbusch, 2010). Simulations performed (Koch and Finsterbusch, 2009; Lawrenz and Finsterbusch, 2010) indicate that the variation in the range accessible by standard wholebody gradient systems is not very pronounced. Nevertheless, to achieve the best accuracy and reliability, it is recommendable to compare only MA values that were measured with very similar or identical parameters of the diffusion weighting.

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Correlation between fractional anisotropy and motor outcomes in one-year-old infants with periventricular brain injury.

Conditional Tat protein brain expression in the GT-tg bigenic mouse induces cerebral fractional anisotropy abnormalities.

Quantification of microscopic diffusion anisotropy disentangles effects of orientation dispersion from microstructure: applications in healthy volunteers and in brain tumors.

Fractional anisotropy alterations in individuals born preterm: a diffusion tensor imaging meta-analysis.

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3-T diffusion tensor imaging (DTI) of normal uterus in young and middle-aged females during the menstrual cycle: evaluation of the cyclic changes of fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values.

Alterations in white matter fractional anisotropy in subsyndromal perimenopausal depression.

Transient increase of fractional anisotropy in reversible vasogenic edema.

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Relationship between diffusion tensor fractional anisotropy and long-term motor outcome in patients with hemiparesis after middle cerebral artery infarction.

Voxel-based analysis of fractional anisotropy in post-stroke apathy.