CME JOURNAL OF MAGNETIC RESONANCE IMAGING 41:1581–1590 (2015)
Technical Note
In Vivo Imaging of the Time-Dependent Apparent Diffusional Kurtosis in the Human Calf Muscle Anja Maria Marschar, MSc,1 Tristan Anselm Kuder, Dipl Phys,1 Bram Stieltjes, PhD, MD,2 Armin Michael Nagel, Dr rer nat,1 Peter Bachert, Dr rer nat,1 and Frederik Bernd Laun, Dr rer nat1,2* Purpose: To evaluate the time dependency of apparent diffusion coefficient Dapp and apparent diffusional kurtosis Kapp in vivo in the human calf. Materials and Methods: Diffusion-weighted images of five healthy male volunteers were acquired using a 1.5T MR scanner. A stimulated echo sequence with echo planar imaging readout was used with diffusion gradients oriented along the three main axes. Mixing times (TM) of 100, 300, 500, and 700 ms and b-values ranging from 0 to 5600 s/mm2 were used. Dapp and Kapp were determined. Results: Dapp and Kapp decreased with increasing TM. As an example for absolute values, Dapp of the tibialis anterior drops from 1.18 6 0.04 mm2/ms (TM ¼ 100 ms) to 0.86 6 0.02 mm2/ms (TM ¼ 700 ms) (P ¼ 0.001) and Kapp from 0.38 6 0.06 to 0.32 6 0.03 (P ¼ 0.046) for a diffusion weighting along the left–right direction. Kapp was smaller than 0.43 in all muscles and at all TMs. Conclusion: The clearly observed time-dependence of Dapp and Kapp is an indicator of restricted diffusion in muscle tissue and may thus be a promising marker to investigate alterations of the microstructure. Compared to typical kurtosis values in white matter tissue of the brain, the kurtosis in muscle tissue is much smaller, which we attribute to the absence of the almost impermeable myelin sheath. Key Words: calf muscle; diffusion; kurtosis; dependence J. Magn. Reson. Imaging 2015;41:1581–1590. C 2014 Wiley Periodicals, Inc. V
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1 Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany. 2 Quantitative Imaging Based Disease Characterization, German Cancer Research Center (DKFZ), Heidelberg, Germany.. *Address reprint requests to: F.B.L., Medical Physics in Radiology & Quantitative Imaging Based Disease Characterization, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany. E-mail: [email protected] Received November 20, 2013; Accepted July 24, 2014. DOI 10.1002/jmri.24743 View this article online at wileyonlinelibrary.com. C 2014 Wiley Periodicals, Inc. V
DIFFUSION-WEIGHTED magnetic resonance imaging (DWI) is an established noninvasive imaging method that is routinely applied in radiology (1). While historically, DWI studies were focused on the brain, several more recent reports on applications of DWI to abdominal organs (eg, (2–4)) and muscles (eg, (5–12)) have been published. One main application in DWI of muscle tissue has been the detection of the orientation and course of the muscle fibers using diffusion tensor imaging (DTI) in humans (13,14) and in animal models (15). Moreover, the eigenvalues of the diffusion tensor have been linked to structural properties of the underlying muscle tissue (5,10) and have been shown to be indicative of muscle injuries and diseases (16–18). Two approaches beyond classical DTI measurements have been proposed to gain further information about the tissue microstructure. The first approach is to measure diffusion-time-dependent diffusion parameters, which are known to yield additional information about the tissue structure (19,20). For example, the time-dependence of the diffusion coefficient is linked directly to the surface-to-volume ratio in the shorttime limit (21–23). One interesting example of an application to muscle tissue is the work of Fieremans et al (24), where structural parameters, eg, permeability and fiber size, were extracted from the timedependent diffusion coefficient using a model introduced by Novikov et al (25). Moreover, the time-dependent diffusion coefficient in ex vivo muscle tissue of tongue and heart was measured by Kim et al (26), who estimated fiber diameter, volume fractions and intra-/extracellular diffusivities using a twocompartment model. Second, probing the dependence of diffusion parameters on the diffusion weighting (b-value) is a further approach aiming at inferring microstructure information. This technique aims to quantify deviations from Gaussian diffusion (27–29). Diffusion kurtosis imaging is a model-free and generally usable technique to quantify these deviations (30,31). The obtained kurtosis values have been shown to be good diagnostic markers, in eg, stroke (32) and prostate carcinoma (33). To the best of our knowledge, the diffusional kurtosis and its diffusion time-dependence have not been
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measured in human muscle tissue so far. They may yield important information on the tissue structure and may be a valuable marker for disease characterization. Thus, the aim of this work was to investigate the direction- and time-dependent diffusion coefficient and the diffusional kurtosis in the healthy human calf muscle to establish an initial basis of comparison for future measurements investigating the effects of tissue alterations. THEORY Details about the theory of diffusion kurtosis imaging can be found in the articles by Jensen et al and Lu et al (30,31). Assume that a bipolar pair of diffusion weighting gradients is applied generating a diffusion weighting with a certain b-value b. The resulting signal decay can be described by ln
SðbÞ 1 2 ¼ bDapp ðtÞ þ b2 Dapp ðtÞKapp ðtÞ; Sð0Þ 6
[1]
where Dapp(t) is the apparent diffusion coefficient and Kapp(t) is the apparent diffusional kurtosis. In general, Dapp(t) and Kapp(t) are direction-dependent. The cumulant expansion used in Eq. (1) is usually cut after the quadratic term and the b-values are chosen sufficiently high for detection of the quadratic term and small enough to neglect the cubic term (see Discussion). In the rest of the article we neglect the arguments of Dapp(t) and Kapp(t) and write only Dapp and Kapp. MATERIALS AND METHODS Subjects The study was performed measuring five healthy male volunteers (20–28 years, mean: 24.8 6 3.3 years), who all gave informed consent according to the institutional guidelines.
Figure 1. Depiction of the calf of a 28-year-old volunteer. a: Transversal T1-weighted image of the calf at location of the largest circumference. b: In the EPI-image (b ¼ 0 s/mm2), the different muscle groups are marked with ROIs (tibialis anterior (1), soleus (2), medial gastrocnemius (3), and lateral gastrocnemius (4)). Regions of vessels and bones, visible in (a) in the center of the calf (white arrows), were not taken into account in the ROI analysis.
image acquisition parameters were the following: TE ¼ 61/45/39/36 ms, which were the minimal possible echo times for the mixing times TM ¼ 100/300/500/ 700 ms, respectively, TR ¼ 2.6 s, field of view (FOV) ¼ 250 250 mm2, image matrix 36 36, acquisition bandwidth ¼ 1804 Hz/pixel, voxel size ¼ 6.9 6.9 10 mm3, slice thickness ¼ 10 mm, 6/8 partial Fourier encoding, 10 repetitions, three diffusion gradient directions (read, slice, and phase, which were parallel to the scanner system), total acquisition time 50 minutes (75 s 10 repetitions 4 mixing times). As the acquisition time was already rather long, the full kurtosis tensor was not sampled, which would require an increase of measurement time by at least a factor of five (corresponding to 15 gradient directions). Before acquiring the DWI data, the volume of interest was shimmed. A water selective binominal excitation pulse and spectral fat suppression were used. Additionally, high-resolution T1-weighted spin echo images were acquired at the same calf position to confirm the location of the muscle groups (Fig. 1a). The following parameters were used: TR/TE ¼ 512/11 ms, FOV ¼ 159 159 mm2, image matrix 384 384, slice thickness ¼ 8 mm.
Image Acquisition Images were acquired from the mid-calf region of the left leg on a 1.5T scanner (Magnetom Avanto, Siemens, Healthcare Sector, Erlangen, Germany) with 45 mT/m maximal gradient strength and 200 T/m/s slew rate using a one-channel knee coil. The volunteers were in a supine position with a relaxed leg. Transversal images were acquired at the position of the largest circumference of the calf. The phase encoding direction was anterior–posterior. A stimulated echo acquisition mode sequence (STEAM) (34) with echo planar imaging readout was used to measure diffusion-weighted images (DWIs) with the diffusion gradients oriented along read, phase, and slice direction. One advantage of the STEAM sequence is that long diffusion times can be used, because the magnetization is stored in the longitudinal direction between the application of the diffusion gradient pulses. The diffusion time was varied using mixing times (TM) of 100, 300, 500, and 700 ms. The following b-values were used: 0, 700, 1400, 2100, 2800, 3500, 4200, 4900, 5600 s/mm2. The
Data Analysis The free parameters Dapp and Kapp and S0 in Eq. (2) were obtained by fitting to the measured signal with the help of the Levenberg-Marquardt algorithm (30). 1 2 [2] Kapp : S ¼ S0 exp -bDapp þ b2 Dapp 6 In Eq. (2), Dapp and Kapp represent values measured for the chosen gradient direction. They are the projections of the diffusion and kurtosis tensor as described previously (31). Because the signal is potentially dropping to the noise level at high b-values and high diffusion coefficients in the muscle fiber direction (slice direction), some high b-values were excluded from the fit. To this end, a noise level value h was estimated for each TM by setting h equal to the mean signal in the respective region of interest (ROI) averaged over all repetitions using the highest b-value in slice direction (before the outlier rejection was performed, as described below).
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Table 1 Number of b-Values Used for Fitting of the Different Configurations TM ¼ 100 ms
Read P1 P2 P3 P4 P5 Phase P1 P2 P3 P4 P5 Slice P1 P2 P3 P4 P5
TM ¼ 300 ms
TM ¼ 500 ms
TM ¼ 700 ms
TA
SL
GM
GL
TA
SL
GM
GL
TA
SL
GM
GL
TA
SL
GM
GL
5 5 5 4 5
4 5 5 4 5
5 5 5 5 5
5 5 5 6 5
7 7 7 6 7
5 5 6 5 5
5 6 6 5 6
6 7 6 7 6
8 7 8 8 8
6 6 6 6 5
6 7 6 6 6
7 7 6 8 7
8 8 9 8 8
6 6 7 6 6
6 7 6 6 6
7 7 7 8 7
5 5 5 5 5
4 5 5 4 5
5 6 5 5 6
6 6 6 6 7
7 7 7 7 7
5 6 6 6 6
6 7 5 6 7
6 7 7 7 7
8 8 8 9 7
6 7 7 7 6
7 8 6 7 7
7 7 7 8 8
8 8 9 9 8
5 7 7 7 6
7 8 6 7 7
7 7 7 8 8
4 4 3 3 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 5 4 5 5
4 5 5 4 5
4 5 5 5 4
4 4 4 4 4
5 5 5 5 4
5 5 5 4 5
4 4 5 5 4
4 4 4 4 4
5 5 5 5 5
4 5 5 4 5
4 4 4 4 4
The stated numbers correspond to the following maximal b-values: 1–0 s/mm2, 2–700 s/mm2, 3–1400 s/mm2, 4– 2100 s/mm2, 5–2800 s/mm2, 6–3500 s/mm2, 7–4200 s/mm2, 8– 4900 s/mm2, 9–5600 s/mm2. P1-P5 are the five volunteers of the acquired datasets with read, phase, and slice gradient direction; TA (tibialis anterior), SL (soleus), GM (medial gastrocnemius), GL (lateral gastrocnemius) represent the regions of interest; TM the mixing time.
For voxel-by-voxel evaluations, the signal in the voxel was chosen instead of the mean signal in an ROI, but again, h was set equal to the signal averaged over the 10 repetitions in slice direction. Then the threshold bvalue for which the mean signal—averaged over ROI and repetitions—was smaller than 5h was determined. The signal values acquired up to this b-value were used for the fit. All other data were discarded. The resulting used b-values are listed in Table 1. The ROI was intentionally placed in the respective muscle to include the effect of residual fat signal at high bvalues, which was present in the TM ¼ 100 ms data and may cause artificial kurtosis values. It was observed that frequently more than 50% of the measured data points showed a presumably pulsation driven signal drop (see Results). To compensate for this issue, an outlier rejection similar to the “informed RESTORE” algorithm by Chang et al (35,36) was implemented. The maximum negative residual was identified as outlier and excluded from the fit. This was repeated iteratively until a reduced chi-square value of 1 was reached or until half the number of measured data points was excluded. The latter occurred in 16 of 240 fits (5 volunteers 4 ROIs 4 TM 3 directions). The standard deviation sM of the noise was determined in a region of the image background in one representative high b-value image of the respective volunteer. Since a single channel coil was used, the artifact-free standard deviation s of the signal can be determined using pffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ sM = 2-p=2. The reduced chi-square is defined P 2 x2red ¼ 1y residuals , where v ¼ n – p is the number of s2 degrees of freedom, where n is the number of data points and p is the number of unknown parameters. The outlier rejection was performed after the exclusion of b-values with insufficient signal.
For the quantitative evaluation, ROIs were manually placed in the muscle tissue omitting regions near skin, bones, and vessels. Four different muscle groups of the lower leg were investigated: tibialis anterior (TA), soleus (SL), medial gastrocnemius (GM), and lateral gastrocnemius (GL). ROIs were drawn on the diffusion-weighted images in correspondence with the anatomical T1-weighted images (Fig. 1). The signal was averaged in each ROI before fitting. Due to spoiler gradients and slice selection gradients, the b-values of the vendor-provided sequence, which calculated the b-values resulting from the diffusion gradients only, were not exactly equal to the actual b-values and, thus, they were corrected before fitting by calculating them numerically using the sequence timing table. The angular shift resulting from not computing the whole b-matrix could not be corrected using the three acquired diffusion directions, but the largest angular derivation was below 1.6 and thus quite negligible. For the calculation of Dapp- and Kapp-maps, the raw data were smoothed with a Gaussian kernel (full width at half maximum: 6.9 mm). Then the h-value was determined voxel-by-voxel and high b-values were discarded as described above. Then the outlier rejection algorithm was applied. A correction for eddy currents was not applied and was not necessary due to the coarse resolution.
Statistical Analysis Data were analyzed using the Kruskal–Wallis test (37) for testing for significant differences in the four groups of mixing times TM containing the values of five volunteers. Statistical testing was performed in MATLAB (MathWorks, Natick, MA).
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Figure 2e shows representative high b-value images that prove the signal-to-noise ratio (SNR) sufficiency. The longest mixing time and diffusion gradient orientation in slice direction was chosen exemplarily because this configuration has the highest diffusion coefficient and possibly smallest SNR. The highest bvalues allowed by the SNR threshold in Table 1 are 2100 s/mm2 (for tibialis anterior and lateral gastrocnemius) or 2800 s/mm2 (for soleus and medial gastrocnemius). The SNR values averaged over the 10 repetitions for the four ROIs are 5.4, 3.4, 3.0, and 5.4 (TA, SL, GM, GL). In other tested configurations the SNR was on the same level or higher. Figure 3 depicts the signal distributions for all nine diffusion-weightings and the three diffusion gradient directions in two different ROIs at TM ¼ 100 ms. Due to the aforementioned pulsation effects, the signal shows a larger variance in the soleus than in the tibialis anterior. Thus, using the mean signal of the 10 repetitions (square marker) in the soleus would result in an underestimated signal. Also the median value (middle line of the boxplots) is often not appropriate, because more than 50% of the measured values are affected sometimes. To overcome this issue, the mentioned outlier rejection algorithm was used (see Materials and Methods). Diffusion and Kurtosis Values
Figure 2. Diffusion-weighted images of a volunteer for 10 repetitions with b ¼ 0 s/mm2 (a) and b ¼ 700 s/mm2 for three diffusion gradient orientations in read (b), phase (c), and slice (d) direction for TM ¼ 100 ms. The phase direction runs along anterior–posterior. Pulsation-driven signal extinctions arise with exception for the images acquired with b ¼ 0 s/mm2. The extinctions are mostly located in the center of the calf. It is clearly visible that the signal of the soleus muscle is strongly affected (eg, six of ten images in (c)) such that the median of the signal is also influenced. We thus chose an outlier rejection algorithm for the quantitative estimation of diffusion coefficient and diffusional kurtosis. e: SNR worst-case images; diffusion weighting along slice direction and highest mixing time TM ¼ 700 ms. The highest allowed b-value for this configuration was 2100 s/mm2 (for tibialis anterior and lateral gastrocnemius) or 2800 s/mm2 (for soleus and medial gastrocnemius).
RESULTS Image Quality First, the diffusion-weighted images were analyzed. It was noticed that signal drops occurred, which are likely to result from pulsation (Fig. 2). The signal drops are observable in the diffusion-weighted images, but not in the images with b ¼ 0. They were most prominent in the neighborhood of vessels in the center of the calf and the soleus is more affected than the other muscles. They are visible for all diffusion directions.
In Table 2, the diffusion coefficients and kurtosis values are stated for the four muscle groups (TA, SL, GM, GL) for TM ¼ 100 ms and TM ¼ 700 ms. Additionally, the P-values calculated using the Kruskal–Wallis test are given in Table 2 to investigate the significance of the observed parameter changes. Almost all values show a significant decrease with increasing mixing time. Figure 4 shows the values of Dapp and Kapp. The plotted values were averaged over the five volunteers and the indicated error represents the respective standard deviation. The drop of the apparent diffusion coefficient Dapp at increasing TM is clearly visible for all diffusionweighting directions and all muscle groups, except for the slice direction for the soleus muscle. Here, the Pvalue is P ¼ 0.22 and due to large error bars, a significant reduction of Dapp could not be detected. In all other configurations, P is smaller than 0.05. The drop of Dapp is largest stepping from TM ¼ 100 ms to TM ¼ 300 ms. The Dapp-values in slice direction (head-feet) are always higher than in phase and read direction, and in the latter two directions the values of Dapp are almost equal. The observed diffusion anisotropy is smallest in the soleus and largest in the tibialis for all TM. The standard deviation of Dapp is highest for the soleus (slice direction) and the medial gastrocnemius (phase direction) presumably owing to the remaining influence of pulsation artifacts. Kapp shows a significant diffusion time-dependence and generally decreases at longer TM, except for read direction in the lateral gastrocnemius, where the Pvalue is 0.5. In all other configurations, P is smaller than 0.05. As for Dapp, the drop of Kapp is largest when stepping from TM ¼ 100 ms to TM ¼ 300 ms, while
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Figure 3. Signal intensities for three diffusion gradient directions measured in tibialis anterior and soleus with the same dataset and the same ROIs as in Fig. 1 (one volunteer, TM is 100 ms). For each b-value, signal distributions of 10 repeated measurements are plotted left of the boxplots, in which the small square marker stands for the mean, the line inside the box for the median, and the edges of the box for the upper and lower quartile. While the signal of the tibialis anterior shows a stable behavior, the soleus is more prone to signal dropouts.
going to even longer TM does not result in a major further decrease of Kapp. Kapp in slice direction is generally smaller than for the other two directions. This meets the expectations since the muscle fibers are mainly orientated in slice direction; thus, the diffusion restriction is smallest in this direction yielding smaller kurtosis values. The absolute Kapp-values of the different muscles are approximately of the same magnitude. In Fig. 5, maps of Dapp and Kapp are shown and the general behavior of the ROI-averaged results of Fig. 4 can be appreciated. In particular, Dapp and Kapp decrease with increasing TM, Dapp is largest along slice direction while Kapp is smallest. As in Fig. 4, the tibialis, for example, again has the largest diffusion coefficient along the slice direction and, moreover, the
other displayed values match those plotted in Fig. 4. Some artifacts are clearly visible. Voxels near the skin show a very high kurtosis compared to the muscle tissue. We attribute this to the residual fat signal which is located in the skin. DISCUSSION In this work, the apparent diffusion coefficient and the apparent diffusional kurtosis of the human calf muscle as well as their time-dependence were measured. Measured apparent diffusion coefficients in muscle tissue have been reported by several investigators (7,12,16,38,39). In most reports, the first eigenvalue
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Table 2 Fit results for Five Volunteers in Four Muscle Types and Three Diffusion Gradient Directions at TM ¼ 100 ms and 700 ms (Exemplarily)
TA Read Phase Slice SL Read Phase Slice GM Read Phase Slice GL Read Phase Slice
Dapp [mm2/ms] TM ¼ 100 ms
Dapp [mm2/ms] TM ¼ 700 ms
P value
Kapp TM ¼ 100 ms
Kapp TM ¼ 700 ms
P value
1.18 6 0.04 1.19 6 0.09 1.97 6 0.08
0.86 6 0.02 0.87 6 0.05 1.77 6 0.04
0.001* 0.005* 0.004*
0.38 6 0.06 0.43 6 0.06 0.33 6 0.05
0.32 6 0.03 0.33 6 0.03 0.13 6 0.02
0.046* 0.033* 0.002*
1.39 6 0.02 1.34 6 0.07 1.69 6 0.14
1.16 6 0.09 1.10 6 0.09 1.51 6 0.13
0.005* 0.006* 0.220
0.40 6 0.08 0.40 6 0.04 0.35 6 0.04
0.26 6 0.02 0.25 6 0.03 0.18 6 0.01
0.011* 0.005* 0.008*
1.37 6 0.06 1.32 6 0.12 1.80 6 0.07
1.12 6 0.06 1.02 6 0.14 1.61 6 0.06
0.003* 0.020* 0.006*
0.34 6 0.04 0.40 6 0.03 0.27 6 0.07
0.17 6 0.03 0.23 6 0.02 0.12 6 0.03
0.005* 0.010* 0.012*
1.26 6 0.10 1.24 6 0.07 1.86 6 0.03
0.98 6 0.10 0.99 6 0.09 1.70 6 0.02
0.015* 0.007* 0.003*
0.20 6 0.10 0.39 6 0.02 0.24 6 0.03
0.24 6 0.06 0.25 6 0.02 0.10 6 0.04
0.503 0.011* 0.005*
Data are presented as the mean and standard deviation of the values of the five volunteers. The P values were obtained with the Kruskal-Wallis test comparing the four groups of mixing times TM ¼ 100, 300, 500, and 700 ms. Significant differences at P < 0.05 are marked with * and confirm a decrease of Dapp and Kapp with time. TA (tibialis anterior), SL (soleus), GM (medial gastrocnemius), GL (lateral gastrocnemius) represent the regions of interest.
of the diffusion tensor in the in vivo human calf was found to be larger (2.0–2.4 mm2/ms) than in our study, which is explicable because the slice direction may deviate from the actual fiber direction. We did not perform a full tensor measurement to keep the acquisition time adequately short, considering that a kurtosis tensor measurement would require the acquisition of images with at least 15 different diffusion directions. Most investigators have reported secondary and tertiary eigenvalues l2 and l3 and it is probably best to compare lradial ¼ (l2 þ l3)/2 to our values Dapp,radial ¼ (Dapp,phase þ Dapp,read)/2. For the tibialis anterior, for example, Sinha et al (7) reported lradial ¼ 1.32 6 0.09 mm2/ms, Galban et al (10) reported lradial 1.1 mm2/ms (note: we write “” because the values were reported in graphs, where it is difficult to read off the standard deviation) and our value for TM ¼ 100 ms is Dapp,radial ¼ 1.19 6 0.06 mm2/ms, which is in good agreement considering that different acquisition protocols were used. Kim et al (26) measured the time-dependent diffusion coefficient ex vivo in tongue and muscle tissue. In accordance with their results, we find a decrease of Dapp with increasing TM. Sigmund et al (17) reported that lradial averaged over all muscle groups in the human calf decreased from 1.339 6 0.088 mm2/ms to 0.773 6 0.056 mm2/ms using mixing times of about 30 ms and 1 second, respectively. This range of mixing times is larger than in our study, but the absolute values roughly compare to the values we obtained. To our knowledge, apparent kurtosis values have not been reported so far. At longer mixing times, Kapp decreases, which may be interpreted as an indicator that the diffusion propagator approaches a Gaussian function. The drop is most prominent when stepping from TM ¼ 100 ms to TM ¼ 300 ms and flattens at longer mixing times. It is
tempting to associate this finding with a diffusion process approaching the motional narrowing limit in this time regime. This is somewhat astonishing if one assumes that the main restrictions are caused by the cell boundary of a muscle cell with 50 mm diameter (40), which is a length scale that would entail that the motional narrowing regime is not yet reached with these mixing times. Following this line of reasoning, the main restriction would have to be characterized by smaller distances than the cell diameter, a result which is in keeping with non-proton experiments by de Graaf et al (41). Besides this, we found Kapp to be smaller along the slice direction, which may be interpreted as reduced restrictions at this length scale along this direction. Compared to Kapp-values of about 1 in white matter tissue of the brain (31), Kapp in muscle tissue is much smaller. We attribute this difference to the absence of the almost impermeable hydrophobic myelin sheath in muscle tissue (30,31). One problem in interpreting the data is that the change of mixing time not only changes the diffusion time but also the effect of relaxation. An experiment to separate these effects would be highly valuable, but is not straightforward to perform, since one would have to obtain relaxation times for different tissue components separately. Relaxation times T1 and T2 of the calf muscle at 1.5T were reported in several articles. Fisher et al (42) specified T2 with T2 ¼ 29.9 6 0.2 ms in the anterior tibialis and with T2 ¼ 28.2 6 0.8 ms in the gastrocnemius. Houmard et al (43) reported T2 and T1 of the gastrocnemius to be T2 ¼ 35.8 6 2.1 ms and T1 ¼ 1158.6 ms. Thus, T1 is approximately equally long as the mixing times used in our study, which might entail that relaxation weighting effects of compartments are present. This weighting may be one of the major sources of the observed kurtosis effect if the kurtosis is supposed to
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Figure 4. Time dependence of the apparent diffusion coefficient Dapp (a) and the kurtosis value Kapp (b) in the human calf muscle averaged over the five volunteers (with error bars indicating the standard deviation). A reduction of the obtained Dapp- and Kapp-values with increasing TM is clearly visible in most of the shown configurations.
be caused mainly by tissue and diffusion heterogeneity rather than by restrictions. The decrease at longer TM could then be interpreted such that mainly the signal of a single compartment remains, and the thus reduced heterogeneity causes a reduction of the kurtosis. Our findings show that, in order to obtain a good estimate for the Kapp-values, the pseudo-random signal drops should be taken into account. This can be done by using an outlier identification algorithm like the RESTORE algorithm (35,36). Karampinos et al (44) also used the RESTORE algorithm in DWI measurements of the calf and observed outliers more frequently close to the main feeding arteries, which is in keeping with our observation that the soleus muscle, which is closest to these blood vessels, is most prone to signal drops. One reason why these signal drops
might be more pronounced than reported in previous studies can be the large voxel size (6.9 6.9 10.0 mm3) that was used in our study to ensure a sufficient SNR for the kurtosis fit. For example, the voxel sizes of some recent studies investigating the calf muscle with DWI are 1.6 1.6 5 mm3 (7), 3 3 3 mm3 (11), 1.8 1.8 6 mm3 (38), and 0.7 0.7 6 mm3 (10). One would expect that smaller voxels result in a decreased vulnerability to signal drops, which occur if an inhomogeneous phase distribution is present within a voxel, which is more likely the case in larger voxels. In a preliminary experiment, we observed this effect, but finally decided to use large voxels in light of the required SNR. Considering the need for the outlier rejection, smaller voxels cannot be obtained easily by increasing the number of averages.
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Figure 5. Dapp and Kapp maps in the calf muscle of a volunteer for the three diffusion gradient directions and the four mixing times TM. Outliers of Kapp in skin regions occur due to the influence of fat signal.
Another approach to overcome the pulsation effects is to use peripheral gating which was shown to yield an improved data quality (8) at the price of a prolonged acquisition time. Investigators have also used stimulated echo sequences, where the mixing time was adjusted such that first and second diffusion gradient are applied during the diastole of two subsequent heart beats (eg, (45)) to minimize pulsation artifacts. Using stimulated echoes and adjusting the mixing time could be a more viable option for mixing times in the range of our longest mixing time TM ¼ 700 ms, but might not be adequate for TM ¼ 300 ms or TM ¼ 500 ms. In preparatory experiments it was difficult to find appropriate delay times when using peripheral gating. We finally decided against applying gating, thus also circumventing the problem of varying signal amplitudes resulting from varying repetition times. Moreover, flow compensated diffusion gradients can be used (46–49); this approach, however, does not permit the investigation of long diffusion times because spin echoes must be used. It is important to take care when comparing kurtosis values of different studies, as the accurate deter-
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mination of kurtosis values is in general more difficult than that of the diffusion coefficient. The obtained Kapp-values depend heavily on the exact fitting procedure and it is not evident a priori, which range of bvalues should be used. If the b-values are too large, higher cumulants would have to be included in the fit. If the b-values are too small, the fit becomes imprecise. A proposed criterion to find an expression for bmax is that the signal curve should be decreasing monotonically, which results in the demand that bmax 3/Dapp/Kapp (50). At TM ¼ 100 ms, where Dapp and Kapp are largest, one finds, eg, for the soleus in read, phase and slice direction bmax 5400, 5600, and 5070 s/mm2, respectively. Thus, the chosen range of b-values in Table 1 does comply with this criterion at all TM. Moreover, we have observed that the fit of Kapp is in general less precise than that of Dapp. When evaluating the data, care must be taken when using large voxels as in our study because of the resulting partial volume effect of residual fat signal in skin regions. This can be observed in the maps of Dapp and Kapp, where the skin is clearly visible as a red border around the muscle. Concerning the signal of fat, one must distinguish between the signal arising from aliphatic and from olefinic fat protons (51). While the frequency difference of aliphatic fat protons and of water protons is rather large (up to 254 Hz at 1.5T), such that the fat suppression usually is quite successful, the Larmor frequency of olefinic fat protons and water protons differs only by 44 Hz at 1.5T (51). The associated chemical shift of the olefinic fat signal in our setting is approximately one voxel, and thus the voxels that are corrupted by subcutaneous fat signal are mainly located at the rim of the muscle. Considering partial volumes, it should be noted that kurtosis is also a measure for diffusion heterogeneity. The measured Kapp may depend on the voxel size if the dominant length scale of the heterogeneity is of the same size as the voxel dimension. Thus, when comparing Kapp values, the potential presence of this effect should be considered. Muscle DWI has been used to characterize muscle lesions in humans (16–18) and, remarkably, in animal models, it was found that—unlike in brain tissue—the apparent diffusion coefficient increases in severely ischemic muscle tissue (9). Diffusion kurtosis measurements are a promising tool to further investigate these findings. Future studies need to explore which parameters are altered in the case of pathological tissue changes; time-dependent kurtosis measurements may yield additional insight into such processes compared to conventional DTI.
CONCLUSION In conclusion, we measured the time- and directiondependent diffusion parameters Kapp and Dapp in muscle tissue, which both are potentially valuable markers for the tissue structure. While Dapp can be regarded as marker for cell restrictions, the measurement of Kapp promises to gain insights into deviations from Gaussian diffusion and tissue heterogeneity in
Diffusional Kurtosis in Human Calf Muscle
pathological cases. Kapp and Dapp decrease with increasing mixing time and Kapp is much smaller than in brain tissue. ACKNOWLEDGMENTS We are grateful to Thorsten Feiweier and Kecheng Liu for developing the used pulse sequence with stimulated echo diffusion weighting capability. REFERENCES 1. Jones DK. Diffusion MRI: theory, methods, and applications. New York: Oxford University Press; 2011. 2. Yoshikawa T, Kawamitsu H, Mitchell DG, et al. ADC measurement of abdominal organs and lesions using parallel imaging technique. AJR Am J Roentgenol 2006;187:1521–1530. 3. Luciani A, Vignaud A, Cavet M, et al. Liver cirrhosis: intravoxel incoherent motion MR imaging—pilot study. Radiology 2008;249: 891–899. 4. Lemke A, Laun FB, Simon D, Stieltjes B, Schad LR. An in vivo verification of the intravoxel incoherent motion effect in diffusionweighted imaging of the abdomen. Magn Reson Med 2010;64: 1580–1585. 5. Cleveland GG, Chang DC, Hazlewood CF, Rorschach HE. Nuclear magnetic resonance measurement of skeletal muscle: anisotropy of the diffusion coefficient of the intracellular water. Biophys J 1976;16:1043–1053. 6. Sinha S, Sinha U. Reproducibility analysis of diffusion tensor indices and fiber architecture of human calf muscles in vivo at 1.5 Tesla in neutral and plantarflexed ankle positions at rest. J Magn Reson Imaging 2011;34:107–119. 7. Sinha S, Sinha U, Edgerton VR. In vivo diffusion tensor imaging of the human calf muscle. J Magn Reson Imaging 2006;24:182– 190. 8. Sinha U, Yao L. In vivo diffusion tensor imaging of human calf muscle. J Magn Reson Imaging 2002;15:87–95. 9. Heemskerk AM, Drost MR, van Bochove GS, van Oosterhout MF, Nicolay K, Strijkers GJ. DTI-based assessment of ischemiareperfusion in mouse skeletal muscle. Magn Reson Med 2006;56: 272–281. 10. Galban CJ, Maderwald S, Uffmann K, de Greiff A, Ladd ME. Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf. Eur J Appl Physiol 2004;93:253–262. 11. Saupe N, White LM, Sussman MS, Kassner A, Tomlinson G, Noseworthy MD. Diffusion tensor magnetic resonance imaging of the human calf: comparison between 1.5 T and 3.0 T-preliminary results. Invest Radiol 2008;43:612–618. 12. Steidle G, Schick F. Echoplanar diffusion tensor imaging of the lower leg musculature using eddy current nulled stimulated echo preparation. Magn Reson Med 2006;55:541–548. 13. Heemskerk AM, Sinha TK, Wilson KJ, Ding Z, Damon BM. Quantitative assessment of DTI-based muscle fiber tracking and optimal tracking parameters. Magn Reson Med 2009;61:467–472. 14. Gilbert RJ, Napadow VJ. Three-dimensional muscular architecture of the human tongue determined in vivo with diffusion tensor magnetic resonance imaging. Dysphagia 2005;20:1–7. 15. Heemskerk AM, Strijkers GJ, Vilanova A, Drost MR, Nicolay K. Determination of mouse skeletal muscle architecture using threedimensional diffusion tensor imaging. Magn Reson Med 2005;53: 1333–1340. 16. Zaraiskaya T, Kumbhare D, Noseworthy MD. Diffusion tensor imaging in evaluation of human skeletal muscle injury. J Magn Reson Imaging 2006;24:402–408. 17. Sigmund EE, Sui D, Ukpebor O, et al. Stimulated echo diffusion tensor imaging and SPAIR T(2)-weighted imaging in chronic exertional compartment syndrome of the lower leg muscles. J Magn Reson Imaging 2013;38:1073–1082. 18. Qi J, Olsen NJ, Price RR, Winston JA, Park JH. Diffusionweighted imaging of inflammatory myopathies: polymyositis and dermatomyositis. J Magn Reson Imaging 2008;27:212–217. 19. Sen PN. Time-dependent diffusion coefficient as a probe of geometry. Concepts Magn Reson A 2003;23:1–21.
1589 20. Grebenkov DS. NMR survey of reflected Brownian motion. Rev Mod Phys 2007;79:1077–1137. 21. Mitra PP, Sen PN, Schwartz LM. Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phys Rev B Condens Matter 1993;47:8565–8574. 22. Latour LL, Svoboda K, Mitra PP, Sotak CH. Time-dependent diffusion of water in a biological model system. Proc Natl Acad Sci U S A 1994;91:1229–1233. 23. Novikov DS, Fieremans E, Jensen JH, Helpern JA. Time-dependent diffusion and kurtosis as a probe of tissue structure. In: Proc 19th Annual Meeting ISMRM, Montreal; 2011. p 1988. 24. Fieremans E, Novikov DS, Sigmund EE, Liu C, Jensen JH, Helpern JA. In vivo measurement of membrane permeability and fiber size in calf muscle using time-dependent DWI. In: Proc 19th Annual Meeting ISMRM, Montreal; 2011 (abstract 1153). 25. Novikov DS, Fieremans E, Jensen JH, Helpern JA. Random walk with barriers. Nat Phys 2011;7:508–514. 26. Kim S, Chi-Fishman G, Barnett AS, Pierpaoli C. Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart. Magn Reson Med 2005;54:1387–1396. 27. Stejskal EO. Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. J Chem Phys 1965;43:3597–3603. 28. Mitra PP, Sen PN. Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments — simple pore geometries. Phys Rev B 1992;45:143–156. 29. Niendorf T, Dijkhuizen RM, Norris DG, van Lookeren Campagne M, Nicolay K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn Reson Med 1996;36:847–857. 30. Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 2005;53:1432–1440. 31. Lu H, Jensen JH, Ramani A, Helpern JA. Three-dimensional characterization of non-gaussian water diffusion in humans using diffusion kurtosis imaging. NMR Biomed 2006;19:236–247. 32. Hui ES, Fieremans E, Jensen JH, et al. Stroke assessment with diffusional kurtosis imaging. Stroke 2012;43:2968–2973. 33. Rosenkrantz AB, Sigmund EE, Johnson G, et al. Prostate cancer: feasibility and preliminary experience of a diffusional kurtosis model for detection and assessment of aggressiveness of peripheral zone cancer. Radiology 2012;264:126–135. 34. Hahn EL. Spin echoes. Phys Rev 1950;77:746–746. 35. Chang LC, Walker L, Pierpaoli C. Informed RESTORE: a method for robust estimation of diffusion tensor from low redundancy datasets in the presence of physiological noise artifacts. Magn Reson Med 2012;68:1654–1663. 36. Chang LC, Jones DK, Pierpaoli C. RESTORE: robust estimation of tensors by outlier rejection. Magn Reson Med 2005;53:1088–1095. 37. Kruskal WH, Wallis WA. Use of ranks in one-criterion variance analysis. J Am Stat Assoc 1952;47:583–621. 38. Deux JF, Malzy P, Paragios N, et al. Assessment of calf muscle contraction by diffusion tensor imaging. Eur Radiol 2008;18: 2303–2310. 39. Schwenzer NF, Steidle G, Martirosian P, et al. Diffusion tensor imaging of the human calf muscle: distinct changes in fractional anisotropy and mean diffusion due to passive muscle shortening and stretching. NMR Biomed 2009;22:1047–1053. 40. Alberts B. Molecular biology of the cell. New York: Garland Science; 2008. 41. de Graaf RA, van Kranenburg A, Nicolay K. In vivo (31)P-NMR diffusion spectroscopy of ATP and phosphocreatine in rat skeletal muscle. Biophys J 2000;78:1657–1664. 42. Fisher MJ, Meyer RA, Adams GR, Foley JM, Potchen EJ. Direct relationship between proton T2 and exercise intensity in skeletalmuscle MR images. Invest Radiol 1990;25:480–485. 43. Houmard JA, Smith R, Jendrasiak GL. Relationship between MRI relaxation-time and muscle-fiber composition. J Appl Physiol 1995;78:807–809. 44. Karampinos DC, Banerjee S, King KF, Link TM, Majumdar S. Considerations in high-resolution skeletal muscle diffusion tensor imaging using single-shot echo planar imaging with stimulated-echo preparation and sensitivity encoding. NMR Biomed 2011;25:766–778.
1590 45. Nielles-VallespinS,MekkaouiC,GatehouseP,etal.Invivodiffusiontensor MRI of the human heart: reproducibility of breath-hold and navigator-basedapproaches.MagnResonMed2013;70:454–465. 46. Gamper U, Boesiger P, Kozerke S. Diffusion imaging of the in vivo heart using spin echoes—considerations on bulk motion sensitivity. Magn Reson Med 2007;57:331–337. 47. Wirestam R, Greitz D, Thomsen C, Brockstedt S, Olsson MB, Stahlberg F. Theoretical and experimental evaluation of phasedispersion effects caused by brain motion in diffusion and perfusion MR imaging. J Magn Reson Imaging 1996;6:348–355. 48. Brockstedt S, Thomsen C, Wirestam R, et al. Use of an enhanced gradient system for diffusion MR-imaging with motion-artifact reduction. Acta Radiol 1995;36:662–670.
Marschar et al. 49. Christiansen P, Gideon P, Thomsen C, Stubgaard M, Henriksen O, Larsson HBW. Increased water self-diffusion in chronic plaques and in apparently normal white matter in patients with multiple-sclerosis. Acta Neurol Scand 1993;87:195–199. 50. Jensen JH, Helpern JA. MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed 2010;23:698– 710. 51. Hernando D, Karampinos DC, King KF, et al. Removal of olefinic fat chemical shift artifact in diffusion MRI. Magn Reson Med 2011;65:692–701. 52. Andreasen NC, Ehrhardt JC, Swayze VW 2nd, et al. T1 and T2 relaxation times in schizophrenia as measured with magnetic resonance imaging. Schizophr Res 1991;5:223–232.
Technical Note
In Vivo Imaging of the Time-Dependent Apparent Diffusional Kurtosis in the Human Calf Muscle Anja Maria Marschar, MSc,1 Tristan Anselm Kuder, Dipl Phys,1 Bram Stieltjes, PhD, MD,2 Armin Michael Nagel, Dr rer nat,1 Peter Bachert, Dr rer nat,1 and Frederik Bernd Laun, Dr rer nat1,2* Purpose: To evaluate the time dependency of apparent diffusion coefficient Dapp and apparent diffusional kurtosis Kapp in vivo in the human calf. Materials and Methods: Diffusion-weighted images of five healthy male volunteers were acquired using a 1.5T MR scanner. A stimulated echo sequence with echo planar imaging readout was used with diffusion gradients oriented along the three main axes. Mixing times (TM) of 100, 300, 500, and 700 ms and b-values ranging from 0 to 5600 s/mm2 were used. Dapp and Kapp were determined. Results: Dapp and Kapp decreased with increasing TM. As an example for absolute values, Dapp of the tibialis anterior drops from 1.18 6 0.04 mm2/ms (TM ¼ 100 ms) to 0.86 6 0.02 mm2/ms (TM ¼ 700 ms) (P ¼ 0.001) and Kapp from 0.38 6 0.06 to 0.32 6 0.03 (P ¼ 0.046) for a diffusion weighting along the left–right direction. Kapp was smaller than 0.43 in all muscles and at all TMs. Conclusion: The clearly observed time-dependence of Dapp and Kapp is an indicator of restricted diffusion in muscle tissue and may thus be a promising marker to investigate alterations of the microstructure. Compared to typical kurtosis values in white matter tissue of the brain, the kurtosis in muscle tissue is much smaller, which we attribute to the absence of the almost impermeable myelin sheath. Key Words: calf muscle; diffusion; kurtosis; dependence J. Magn. Reson. Imaging 2015;41:1581–1590. C 2014 Wiley Periodicals, Inc. V
time-
1 Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany. 2 Quantitative Imaging Based Disease Characterization, German Cancer Research Center (DKFZ), Heidelberg, Germany.. *Address reprint requests to: F.B.L., Medical Physics in Radiology & Quantitative Imaging Based Disease Characterization, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany. E-mail: [email protected] Received November 20, 2013; Accepted July 24, 2014. DOI 10.1002/jmri.24743 View this article online at wileyonlinelibrary.com. C 2014 Wiley Periodicals, Inc. V
DIFFUSION-WEIGHTED magnetic resonance imaging (DWI) is an established noninvasive imaging method that is routinely applied in radiology (1). While historically, DWI studies were focused on the brain, several more recent reports on applications of DWI to abdominal organs (eg, (2–4)) and muscles (eg, (5–12)) have been published. One main application in DWI of muscle tissue has been the detection of the orientation and course of the muscle fibers using diffusion tensor imaging (DTI) in humans (13,14) and in animal models (15). Moreover, the eigenvalues of the diffusion tensor have been linked to structural properties of the underlying muscle tissue (5,10) and have been shown to be indicative of muscle injuries and diseases (16–18). Two approaches beyond classical DTI measurements have been proposed to gain further information about the tissue microstructure. The first approach is to measure diffusion-time-dependent diffusion parameters, which are known to yield additional information about the tissue structure (19,20). For example, the time-dependence of the diffusion coefficient is linked directly to the surface-to-volume ratio in the shorttime limit (21–23). One interesting example of an application to muscle tissue is the work of Fieremans et al (24), where structural parameters, eg, permeability and fiber size, were extracted from the timedependent diffusion coefficient using a model introduced by Novikov et al (25). Moreover, the time-dependent diffusion coefficient in ex vivo muscle tissue of tongue and heart was measured by Kim et al (26), who estimated fiber diameter, volume fractions and intra-/extracellular diffusivities using a twocompartment model. Second, probing the dependence of diffusion parameters on the diffusion weighting (b-value) is a further approach aiming at inferring microstructure information. This technique aims to quantify deviations from Gaussian diffusion (27–29). Diffusion kurtosis imaging is a model-free and generally usable technique to quantify these deviations (30,31). The obtained kurtosis values have been shown to be good diagnostic markers, in eg, stroke (32) and prostate carcinoma (33). To the best of our knowledge, the diffusional kurtosis and its diffusion time-dependence have not been
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measured in human muscle tissue so far. They may yield important information on the tissue structure and may be a valuable marker for disease characterization. Thus, the aim of this work was to investigate the direction- and time-dependent diffusion coefficient and the diffusional kurtosis in the healthy human calf muscle to establish an initial basis of comparison for future measurements investigating the effects of tissue alterations. THEORY Details about the theory of diffusion kurtosis imaging can be found in the articles by Jensen et al and Lu et al (30,31). Assume that a bipolar pair of diffusion weighting gradients is applied generating a diffusion weighting with a certain b-value b. The resulting signal decay can be described by ln
SðbÞ 1 2 ¼ bDapp ðtÞ þ b2 Dapp ðtÞKapp ðtÞ; Sð0Þ 6
[1]
where Dapp(t) is the apparent diffusion coefficient and Kapp(t) is the apparent diffusional kurtosis. In general, Dapp(t) and Kapp(t) are direction-dependent. The cumulant expansion used in Eq. (1) is usually cut after the quadratic term and the b-values are chosen sufficiently high for detection of the quadratic term and small enough to neglect the cubic term (see Discussion). In the rest of the article we neglect the arguments of Dapp(t) and Kapp(t) and write only Dapp and Kapp. MATERIALS AND METHODS Subjects The study was performed measuring five healthy male volunteers (20–28 years, mean: 24.8 6 3.3 years), who all gave informed consent according to the institutional guidelines.
Figure 1. Depiction of the calf of a 28-year-old volunteer. a: Transversal T1-weighted image of the calf at location of the largest circumference. b: In the EPI-image (b ¼ 0 s/mm2), the different muscle groups are marked with ROIs (tibialis anterior (1), soleus (2), medial gastrocnemius (3), and lateral gastrocnemius (4)). Regions of vessels and bones, visible in (a) in the center of the calf (white arrows), were not taken into account in the ROI analysis.
image acquisition parameters were the following: TE ¼ 61/45/39/36 ms, which were the minimal possible echo times for the mixing times TM ¼ 100/300/500/ 700 ms, respectively, TR ¼ 2.6 s, field of view (FOV) ¼ 250 250 mm2, image matrix 36 36, acquisition bandwidth ¼ 1804 Hz/pixel, voxel size ¼ 6.9 6.9 10 mm3, slice thickness ¼ 10 mm, 6/8 partial Fourier encoding, 10 repetitions, three diffusion gradient directions (read, slice, and phase, which were parallel to the scanner system), total acquisition time 50 minutes (75 s 10 repetitions 4 mixing times). As the acquisition time was already rather long, the full kurtosis tensor was not sampled, which would require an increase of measurement time by at least a factor of five (corresponding to 15 gradient directions). Before acquiring the DWI data, the volume of interest was shimmed. A water selective binominal excitation pulse and spectral fat suppression were used. Additionally, high-resolution T1-weighted spin echo images were acquired at the same calf position to confirm the location of the muscle groups (Fig. 1a). The following parameters were used: TR/TE ¼ 512/11 ms, FOV ¼ 159 159 mm2, image matrix 384 384, slice thickness ¼ 8 mm.
Image Acquisition Images were acquired from the mid-calf region of the left leg on a 1.5T scanner (Magnetom Avanto, Siemens, Healthcare Sector, Erlangen, Germany) with 45 mT/m maximal gradient strength and 200 T/m/s slew rate using a one-channel knee coil. The volunteers were in a supine position with a relaxed leg. Transversal images were acquired at the position of the largest circumference of the calf. The phase encoding direction was anterior–posterior. A stimulated echo acquisition mode sequence (STEAM) (34) with echo planar imaging readout was used to measure diffusion-weighted images (DWIs) with the diffusion gradients oriented along read, phase, and slice direction. One advantage of the STEAM sequence is that long diffusion times can be used, because the magnetization is stored in the longitudinal direction between the application of the diffusion gradient pulses. The diffusion time was varied using mixing times (TM) of 100, 300, 500, and 700 ms. The following b-values were used: 0, 700, 1400, 2100, 2800, 3500, 4200, 4900, 5600 s/mm2. The
Data Analysis The free parameters Dapp and Kapp and S0 in Eq. (2) were obtained by fitting to the measured signal with the help of the Levenberg-Marquardt algorithm (30). 1 2 [2] Kapp : S ¼ S0 exp -bDapp þ b2 Dapp 6 In Eq. (2), Dapp and Kapp represent values measured for the chosen gradient direction. They are the projections of the diffusion and kurtosis tensor as described previously (31). Because the signal is potentially dropping to the noise level at high b-values and high diffusion coefficients in the muscle fiber direction (slice direction), some high b-values were excluded from the fit. To this end, a noise level value h was estimated for each TM by setting h equal to the mean signal in the respective region of interest (ROI) averaged over all repetitions using the highest b-value in slice direction (before the outlier rejection was performed, as described below).
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Table 1 Number of b-Values Used for Fitting of the Different Configurations TM ¼ 100 ms
Read P1 P2 P3 P4 P5 Phase P1 P2 P3 P4 P5 Slice P1 P2 P3 P4 P5
TM ¼ 300 ms
TM ¼ 500 ms
TM ¼ 700 ms
TA
SL
GM
GL
TA
SL
GM
GL
TA
SL
GM
GL
TA
SL
GM
GL
5 5 5 4 5
4 5 5 4 5
5 5 5 5 5
5 5 5 6 5
7 7 7 6 7
5 5 6 5 5
5 6 6 5 6
6 7 6 7 6
8 7 8 8 8
6 6 6 6 5
6 7 6 6 6
7 7 6 8 7
8 8 9 8 8
6 6 7 6 6
6 7 6 6 6
7 7 7 8 7
5 5 5 5 5
4 5 5 4 5
5 6 5 5 6
6 6 6 6 7
7 7 7 7 7
5 6 6 6 6
6 7 5 6 7
6 7 7 7 7
8 8 8 9 7
6 7 7 7 6
7 8 6 7 7
7 7 7 8 8
8 8 9 9 8
5 7 7 7 6
7 8 6 7 7
7 7 7 8 8
4 4 3 3 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 5 4 5 5
4 5 5 4 5
4 5 5 5 4
4 4 4 4 4
5 5 5 5 4
5 5 5 4 5
4 4 5 5 4
4 4 4 4 4
5 5 5 5 5
4 5 5 4 5
4 4 4 4 4
The stated numbers correspond to the following maximal b-values: 1–0 s/mm2, 2–700 s/mm2, 3–1400 s/mm2, 4– 2100 s/mm2, 5–2800 s/mm2, 6–3500 s/mm2, 7–4200 s/mm2, 8– 4900 s/mm2, 9–5600 s/mm2. P1-P5 are the five volunteers of the acquired datasets with read, phase, and slice gradient direction; TA (tibialis anterior), SL (soleus), GM (medial gastrocnemius), GL (lateral gastrocnemius) represent the regions of interest; TM the mixing time.
For voxel-by-voxel evaluations, the signal in the voxel was chosen instead of the mean signal in an ROI, but again, h was set equal to the signal averaged over the 10 repetitions in slice direction. Then the threshold bvalue for which the mean signal—averaged over ROI and repetitions—was smaller than 5h was determined. The signal values acquired up to this b-value were used for the fit. All other data were discarded. The resulting used b-values are listed in Table 1. The ROI was intentionally placed in the respective muscle to include the effect of residual fat signal at high bvalues, which was present in the TM ¼ 100 ms data and may cause artificial kurtosis values. It was observed that frequently more than 50% of the measured data points showed a presumably pulsation driven signal drop (see Results). To compensate for this issue, an outlier rejection similar to the “informed RESTORE” algorithm by Chang et al (35,36) was implemented. The maximum negative residual was identified as outlier and excluded from the fit. This was repeated iteratively until a reduced chi-square value of 1 was reached or until half the number of measured data points was excluded. The latter occurred in 16 of 240 fits (5 volunteers 4 ROIs 4 TM 3 directions). The standard deviation sM of the noise was determined in a region of the image background in one representative high b-value image of the respective volunteer. Since a single channel coil was used, the artifact-free standard deviation s of the signal can be determined using pffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ sM = 2-p=2. The reduced chi-square is defined P 2 x2red ¼ 1y residuals , where v ¼ n – p is the number of s2 degrees of freedom, where n is the number of data points and p is the number of unknown parameters. The outlier rejection was performed after the exclusion of b-values with insufficient signal.
For the quantitative evaluation, ROIs were manually placed in the muscle tissue omitting regions near skin, bones, and vessels. Four different muscle groups of the lower leg were investigated: tibialis anterior (TA), soleus (SL), medial gastrocnemius (GM), and lateral gastrocnemius (GL). ROIs were drawn on the diffusion-weighted images in correspondence with the anatomical T1-weighted images (Fig. 1). The signal was averaged in each ROI before fitting. Due to spoiler gradients and slice selection gradients, the b-values of the vendor-provided sequence, which calculated the b-values resulting from the diffusion gradients only, were not exactly equal to the actual b-values and, thus, they were corrected before fitting by calculating them numerically using the sequence timing table. The angular shift resulting from not computing the whole b-matrix could not be corrected using the three acquired diffusion directions, but the largest angular derivation was below 1.6 and thus quite negligible. For the calculation of Dapp- and Kapp-maps, the raw data were smoothed with a Gaussian kernel (full width at half maximum: 6.9 mm). Then the h-value was determined voxel-by-voxel and high b-values were discarded as described above. Then the outlier rejection algorithm was applied. A correction for eddy currents was not applied and was not necessary due to the coarse resolution.
Statistical Analysis Data were analyzed using the Kruskal–Wallis test (37) for testing for significant differences in the four groups of mixing times TM containing the values of five volunteers. Statistical testing was performed in MATLAB (MathWorks, Natick, MA).
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Figure 2e shows representative high b-value images that prove the signal-to-noise ratio (SNR) sufficiency. The longest mixing time and diffusion gradient orientation in slice direction was chosen exemplarily because this configuration has the highest diffusion coefficient and possibly smallest SNR. The highest bvalues allowed by the SNR threshold in Table 1 are 2100 s/mm2 (for tibialis anterior and lateral gastrocnemius) or 2800 s/mm2 (for soleus and medial gastrocnemius). The SNR values averaged over the 10 repetitions for the four ROIs are 5.4, 3.4, 3.0, and 5.4 (TA, SL, GM, GL). In other tested configurations the SNR was on the same level or higher. Figure 3 depicts the signal distributions for all nine diffusion-weightings and the three diffusion gradient directions in two different ROIs at TM ¼ 100 ms. Due to the aforementioned pulsation effects, the signal shows a larger variance in the soleus than in the tibialis anterior. Thus, using the mean signal of the 10 repetitions (square marker) in the soleus would result in an underestimated signal. Also the median value (middle line of the boxplots) is often not appropriate, because more than 50% of the measured values are affected sometimes. To overcome this issue, the mentioned outlier rejection algorithm was used (see Materials and Methods). Diffusion and Kurtosis Values
Figure 2. Diffusion-weighted images of a volunteer for 10 repetitions with b ¼ 0 s/mm2 (a) and b ¼ 700 s/mm2 for three diffusion gradient orientations in read (b), phase (c), and slice (d) direction for TM ¼ 100 ms. The phase direction runs along anterior–posterior. Pulsation-driven signal extinctions arise with exception for the images acquired with b ¼ 0 s/mm2. The extinctions are mostly located in the center of the calf. It is clearly visible that the signal of the soleus muscle is strongly affected (eg, six of ten images in (c)) such that the median of the signal is also influenced. We thus chose an outlier rejection algorithm for the quantitative estimation of diffusion coefficient and diffusional kurtosis. e: SNR worst-case images; diffusion weighting along slice direction and highest mixing time TM ¼ 700 ms. The highest allowed b-value for this configuration was 2100 s/mm2 (for tibialis anterior and lateral gastrocnemius) or 2800 s/mm2 (for soleus and medial gastrocnemius).
RESULTS Image Quality First, the diffusion-weighted images were analyzed. It was noticed that signal drops occurred, which are likely to result from pulsation (Fig. 2). The signal drops are observable in the diffusion-weighted images, but not in the images with b ¼ 0. They were most prominent in the neighborhood of vessels in the center of the calf and the soleus is more affected than the other muscles. They are visible for all diffusion directions.
In Table 2, the diffusion coefficients and kurtosis values are stated for the four muscle groups (TA, SL, GM, GL) for TM ¼ 100 ms and TM ¼ 700 ms. Additionally, the P-values calculated using the Kruskal–Wallis test are given in Table 2 to investigate the significance of the observed parameter changes. Almost all values show a significant decrease with increasing mixing time. Figure 4 shows the values of Dapp and Kapp. The plotted values were averaged over the five volunteers and the indicated error represents the respective standard deviation. The drop of the apparent diffusion coefficient Dapp at increasing TM is clearly visible for all diffusionweighting directions and all muscle groups, except for the slice direction for the soleus muscle. Here, the Pvalue is P ¼ 0.22 and due to large error bars, a significant reduction of Dapp could not be detected. In all other configurations, P is smaller than 0.05. The drop of Dapp is largest stepping from TM ¼ 100 ms to TM ¼ 300 ms. The Dapp-values in slice direction (head-feet) are always higher than in phase and read direction, and in the latter two directions the values of Dapp are almost equal. The observed diffusion anisotropy is smallest in the soleus and largest in the tibialis for all TM. The standard deviation of Dapp is highest for the soleus (slice direction) and the medial gastrocnemius (phase direction) presumably owing to the remaining influence of pulsation artifacts. Kapp shows a significant diffusion time-dependence and generally decreases at longer TM, except for read direction in the lateral gastrocnemius, where the Pvalue is 0.5. In all other configurations, P is smaller than 0.05. As for Dapp, the drop of Kapp is largest when stepping from TM ¼ 100 ms to TM ¼ 300 ms, while
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Figure 3. Signal intensities for three diffusion gradient directions measured in tibialis anterior and soleus with the same dataset and the same ROIs as in Fig. 1 (one volunteer, TM is 100 ms). For each b-value, signal distributions of 10 repeated measurements are plotted left of the boxplots, in which the small square marker stands for the mean, the line inside the box for the median, and the edges of the box for the upper and lower quartile. While the signal of the tibialis anterior shows a stable behavior, the soleus is more prone to signal dropouts.
going to even longer TM does not result in a major further decrease of Kapp. Kapp in slice direction is generally smaller than for the other two directions. This meets the expectations since the muscle fibers are mainly orientated in slice direction; thus, the diffusion restriction is smallest in this direction yielding smaller kurtosis values. The absolute Kapp-values of the different muscles are approximately of the same magnitude. In Fig. 5, maps of Dapp and Kapp are shown and the general behavior of the ROI-averaged results of Fig. 4 can be appreciated. In particular, Dapp and Kapp decrease with increasing TM, Dapp is largest along slice direction while Kapp is smallest. As in Fig. 4, the tibialis, for example, again has the largest diffusion coefficient along the slice direction and, moreover, the
other displayed values match those plotted in Fig. 4. Some artifacts are clearly visible. Voxels near the skin show a very high kurtosis compared to the muscle tissue. We attribute this to the residual fat signal which is located in the skin. DISCUSSION In this work, the apparent diffusion coefficient and the apparent diffusional kurtosis of the human calf muscle as well as their time-dependence were measured. Measured apparent diffusion coefficients in muscle tissue have been reported by several investigators (7,12,16,38,39). In most reports, the first eigenvalue
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Table 2 Fit results for Five Volunteers in Four Muscle Types and Three Diffusion Gradient Directions at TM ¼ 100 ms and 700 ms (Exemplarily)
TA Read Phase Slice SL Read Phase Slice GM Read Phase Slice GL Read Phase Slice
Dapp [mm2/ms] TM ¼ 100 ms
Dapp [mm2/ms] TM ¼ 700 ms
P value
Kapp TM ¼ 100 ms
Kapp TM ¼ 700 ms
P value
1.18 6 0.04 1.19 6 0.09 1.97 6 0.08
0.86 6 0.02 0.87 6 0.05 1.77 6 0.04
0.001* 0.005* 0.004*
0.38 6 0.06 0.43 6 0.06 0.33 6 0.05
0.32 6 0.03 0.33 6 0.03 0.13 6 0.02
0.046* 0.033* 0.002*
1.39 6 0.02 1.34 6 0.07 1.69 6 0.14
1.16 6 0.09 1.10 6 0.09 1.51 6 0.13
0.005* 0.006* 0.220
0.40 6 0.08 0.40 6 0.04 0.35 6 0.04
0.26 6 0.02 0.25 6 0.03 0.18 6 0.01
0.011* 0.005* 0.008*
1.37 6 0.06 1.32 6 0.12 1.80 6 0.07
1.12 6 0.06 1.02 6 0.14 1.61 6 0.06
0.003* 0.020* 0.006*
0.34 6 0.04 0.40 6 0.03 0.27 6 0.07
0.17 6 0.03 0.23 6 0.02 0.12 6 0.03
0.005* 0.010* 0.012*
1.26 6 0.10 1.24 6 0.07 1.86 6 0.03
0.98 6 0.10 0.99 6 0.09 1.70 6 0.02
0.015* 0.007* 0.003*
0.20 6 0.10 0.39 6 0.02 0.24 6 0.03
0.24 6 0.06 0.25 6 0.02 0.10 6 0.04
0.503 0.011* 0.005*
Data are presented as the mean and standard deviation of the values of the five volunteers. The P values were obtained with the Kruskal-Wallis test comparing the four groups of mixing times TM ¼ 100, 300, 500, and 700 ms. Significant differences at P < 0.05 are marked with * and confirm a decrease of Dapp and Kapp with time. TA (tibialis anterior), SL (soleus), GM (medial gastrocnemius), GL (lateral gastrocnemius) represent the regions of interest.
of the diffusion tensor in the in vivo human calf was found to be larger (2.0–2.4 mm2/ms) than in our study, which is explicable because the slice direction may deviate from the actual fiber direction. We did not perform a full tensor measurement to keep the acquisition time adequately short, considering that a kurtosis tensor measurement would require the acquisition of images with at least 15 different diffusion directions. Most investigators have reported secondary and tertiary eigenvalues l2 and l3 and it is probably best to compare lradial ¼ (l2 þ l3)/2 to our values Dapp,radial ¼ (Dapp,phase þ Dapp,read)/2. For the tibialis anterior, for example, Sinha et al (7) reported lradial ¼ 1.32 6 0.09 mm2/ms, Galban et al (10) reported lradial 1.1 mm2/ms (note: we write “” because the values were reported in graphs, where it is difficult to read off the standard deviation) and our value for TM ¼ 100 ms is Dapp,radial ¼ 1.19 6 0.06 mm2/ms, which is in good agreement considering that different acquisition protocols were used. Kim et al (26) measured the time-dependent diffusion coefficient ex vivo in tongue and muscle tissue. In accordance with their results, we find a decrease of Dapp with increasing TM. Sigmund et al (17) reported that lradial averaged over all muscle groups in the human calf decreased from 1.339 6 0.088 mm2/ms to 0.773 6 0.056 mm2/ms using mixing times of about 30 ms and 1 second, respectively. This range of mixing times is larger than in our study, but the absolute values roughly compare to the values we obtained. To our knowledge, apparent kurtosis values have not been reported so far. At longer mixing times, Kapp decreases, which may be interpreted as an indicator that the diffusion propagator approaches a Gaussian function. The drop is most prominent when stepping from TM ¼ 100 ms to TM ¼ 300 ms and flattens at longer mixing times. It is
tempting to associate this finding with a diffusion process approaching the motional narrowing limit in this time regime. This is somewhat astonishing if one assumes that the main restrictions are caused by the cell boundary of a muscle cell with 50 mm diameter (40), which is a length scale that would entail that the motional narrowing regime is not yet reached with these mixing times. Following this line of reasoning, the main restriction would have to be characterized by smaller distances than the cell diameter, a result which is in keeping with non-proton experiments by de Graaf et al (41). Besides this, we found Kapp to be smaller along the slice direction, which may be interpreted as reduced restrictions at this length scale along this direction. Compared to Kapp-values of about 1 in white matter tissue of the brain (31), Kapp in muscle tissue is much smaller. We attribute this difference to the absence of the almost impermeable hydrophobic myelin sheath in muscle tissue (30,31). One problem in interpreting the data is that the change of mixing time not only changes the diffusion time but also the effect of relaxation. An experiment to separate these effects would be highly valuable, but is not straightforward to perform, since one would have to obtain relaxation times for different tissue components separately. Relaxation times T1 and T2 of the calf muscle at 1.5T were reported in several articles. Fisher et al (42) specified T2 with T2 ¼ 29.9 6 0.2 ms in the anterior tibialis and with T2 ¼ 28.2 6 0.8 ms in the gastrocnemius. Houmard et al (43) reported T2 and T1 of the gastrocnemius to be T2 ¼ 35.8 6 2.1 ms and T1 ¼ 1158.6 ms. Thus, T1 is approximately equally long as the mixing times used in our study, which might entail that relaxation weighting effects of compartments are present. This weighting may be one of the major sources of the observed kurtosis effect if the kurtosis is supposed to
Diffusional Kurtosis in Human Calf Muscle
1587
Figure 4. Time dependence of the apparent diffusion coefficient Dapp (a) and the kurtosis value Kapp (b) in the human calf muscle averaged over the five volunteers (with error bars indicating the standard deviation). A reduction of the obtained Dapp- and Kapp-values with increasing TM is clearly visible in most of the shown configurations.
be caused mainly by tissue and diffusion heterogeneity rather than by restrictions. The decrease at longer TM could then be interpreted such that mainly the signal of a single compartment remains, and the thus reduced heterogeneity causes a reduction of the kurtosis. Our findings show that, in order to obtain a good estimate for the Kapp-values, the pseudo-random signal drops should be taken into account. This can be done by using an outlier identification algorithm like the RESTORE algorithm (35,36). Karampinos et al (44) also used the RESTORE algorithm in DWI measurements of the calf and observed outliers more frequently close to the main feeding arteries, which is in keeping with our observation that the soleus muscle, which is closest to these blood vessels, is most prone to signal drops. One reason why these signal drops
might be more pronounced than reported in previous studies can be the large voxel size (6.9 6.9 10.0 mm3) that was used in our study to ensure a sufficient SNR for the kurtosis fit. For example, the voxel sizes of some recent studies investigating the calf muscle with DWI are 1.6 1.6 5 mm3 (7), 3 3 3 mm3 (11), 1.8 1.8 6 mm3 (38), and 0.7 0.7 6 mm3 (10). One would expect that smaller voxels result in a decreased vulnerability to signal drops, which occur if an inhomogeneous phase distribution is present within a voxel, which is more likely the case in larger voxels. In a preliminary experiment, we observed this effect, but finally decided to use large voxels in light of the required SNR. Considering the need for the outlier rejection, smaller voxels cannot be obtained easily by increasing the number of averages.
1588
Figure 5. Dapp and Kapp maps in the calf muscle of a volunteer for the three diffusion gradient directions and the four mixing times TM. Outliers of Kapp in skin regions occur due to the influence of fat signal.
Another approach to overcome the pulsation effects is to use peripheral gating which was shown to yield an improved data quality (8) at the price of a prolonged acquisition time. Investigators have also used stimulated echo sequences, where the mixing time was adjusted such that first and second diffusion gradient are applied during the diastole of two subsequent heart beats (eg, (45)) to minimize pulsation artifacts. Using stimulated echoes and adjusting the mixing time could be a more viable option for mixing times in the range of our longest mixing time TM ¼ 700 ms, but might not be adequate for TM ¼ 300 ms or TM ¼ 500 ms. In preparatory experiments it was difficult to find appropriate delay times when using peripheral gating. We finally decided against applying gating, thus also circumventing the problem of varying signal amplitudes resulting from varying repetition times. Moreover, flow compensated diffusion gradients can be used (46–49); this approach, however, does not permit the investigation of long diffusion times because spin echoes must be used. It is important to take care when comparing kurtosis values of different studies, as the accurate deter-
Marschar et al.
mination of kurtosis values is in general more difficult than that of the diffusion coefficient. The obtained Kapp-values depend heavily on the exact fitting procedure and it is not evident a priori, which range of bvalues should be used. If the b-values are too large, higher cumulants would have to be included in the fit. If the b-values are too small, the fit becomes imprecise. A proposed criterion to find an expression for bmax is that the signal curve should be decreasing monotonically, which results in the demand that bmax 3/Dapp/Kapp (50). At TM ¼ 100 ms, where Dapp and Kapp are largest, one finds, eg, for the soleus in read, phase and slice direction bmax 5400, 5600, and 5070 s/mm2, respectively. Thus, the chosen range of b-values in Table 1 does comply with this criterion at all TM. Moreover, we have observed that the fit of Kapp is in general less precise than that of Dapp. When evaluating the data, care must be taken when using large voxels as in our study because of the resulting partial volume effect of residual fat signal in skin regions. This can be observed in the maps of Dapp and Kapp, where the skin is clearly visible as a red border around the muscle. Concerning the signal of fat, one must distinguish between the signal arising from aliphatic and from olefinic fat protons (51). While the frequency difference of aliphatic fat protons and of water protons is rather large (up to 254 Hz at 1.5T), such that the fat suppression usually is quite successful, the Larmor frequency of olefinic fat protons and water protons differs only by 44 Hz at 1.5T (51). The associated chemical shift of the olefinic fat signal in our setting is approximately one voxel, and thus the voxels that are corrupted by subcutaneous fat signal are mainly located at the rim of the muscle. Considering partial volumes, it should be noted that kurtosis is also a measure for diffusion heterogeneity. The measured Kapp may depend on the voxel size if the dominant length scale of the heterogeneity is of the same size as the voxel dimension. Thus, when comparing Kapp values, the potential presence of this effect should be considered. Muscle DWI has been used to characterize muscle lesions in humans (16–18) and, remarkably, in animal models, it was found that—unlike in brain tissue—the apparent diffusion coefficient increases in severely ischemic muscle tissue (9). Diffusion kurtosis measurements are a promising tool to further investigate these findings. Future studies need to explore which parameters are altered in the case of pathological tissue changes; time-dependent kurtosis measurements may yield additional insight into such processes compared to conventional DTI.
CONCLUSION In conclusion, we measured the time- and directiondependent diffusion parameters Kapp and Dapp in muscle tissue, which both are potentially valuable markers for the tissue structure. While Dapp can be regarded as marker for cell restrictions, the measurement of Kapp promises to gain insights into deviations from Gaussian diffusion and tissue heterogeneity in
Diffusional Kurtosis in Human Calf Muscle
pathological cases. Kapp and Dapp decrease with increasing mixing time and Kapp is much smaller than in brain tissue. ACKNOWLEDGMENTS We are grateful to Thorsten Feiweier and Kecheng Liu for developing the used pulse sequence with stimulated echo diffusion weighting capability. REFERENCES 1. Jones DK. Diffusion MRI: theory, methods, and applications. New York: Oxford University Press; 2011. 2. Yoshikawa T, Kawamitsu H, Mitchell DG, et al. ADC measurement of abdominal organs and lesions using parallel imaging technique. AJR Am J Roentgenol 2006;187:1521–1530. 3. Luciani A, Vignaud A, Cavet M, et al. Liver cirrhosis: intravoxel incoherent motion MR imaging—pilot study. Radiology 2008;249: 891–899. 4. Lemke A, Laun FB, Simon D, Stieltjes B, Schad LR. An in vivo verification of the intravoxel incoherent motion effect in diffusionweighted imaging of the abdomen. Magn Reson Med 2010;64: 1580–1585. 5. Cleveland GG, Chang DC, Hazlewood CF, Rorschach HE. Nuclear magnetic resonance measurement of skeletal muscle: anisotropy of the diffusion coefficient of the intracellular water. Biophys J 1976;16:1043–1053. 6. Sinha S, Sinha U. Reproducibility analysis of diffusion tensor indices and fiber architecture of human calf muscles in vivo at 1.5 Tesla in neutral and plantarflexed ankle positions at rest. J Magn Reson Imaging 2011;34:107–119. 7. Sinha S, Sinha U, Edgerton VR. In vivo diffusion tensor imaging of the human calf muscle. J Magn Reson Imaging 2006;24:182– 190. 8. Sinha U, Yao L. In vivo diffusion tensor imaging of human calf muscle. J Magn Reson Imaging 2002;15:87–95. 9. Heemskerk AM, Drost MR, van Bochove GS, van Oosterhout MF, Nicolay K, Strijkers GJ. DTI-based assessment of ischemiareperfusion in mouse skeletal muscle. Magn Reson Med 2006;56: 272–281. 10. Galban CJ, Maderwald S, Uffmann K, de Greiff A, Ladd ME. Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf. Eur J Appl Physiol 2004;93:253–262. 11. Saupe N, White LM, Sussman MS, Kassner A, Tomlinson G, Noseworthy MD. Diffusion tensor magnetic resonance imaging of the human calf: comparison between 1.5 T and 3.0 T-preliminary results. Invest Radiol 2008;43:612–618. 12. Steidle G, Schick F. Echoplanar diffusion tensor imaging of the lower leg musculature using eddy current nulled stimulated echo preparation. Magn Reson Med 2006;55:541–548. 13. Heemskerk AM, Sinha TK, Wilson KJ, Ding Z, Damon BM. Quantitative assessment of DTI-based muscle fiber tracking and optimal tracking parameters. Magn Reson Med 2009;61:467–472. 14. Gilbert RJ, Napadow VJ. Three-dimensional muscular architecture of the human tongue determined in vivo with diffusion tensor magnetic resonance imaging. Dysphagia 2005;20:1–7. 15. Heemskerk AM, Strijkers GJ, Vilanova A, Drost MR, Nicolay K. Determination of mouse skeletal muscle architecture using threedimensional diffusion tensor imaging. Magn Reson Med 2005;53: 1333–1340. 16. Zaraiskaya T, Kumbhare D, Noseworthy MD. Diffusion tensor imaging in evaluation of human skeletal muscle injury. J Magn Reson Imaging 2006;24:402–408. 17. Sigmund EE, Sui D, Ukpebor O, et al. Stimulated echo diffusion tensor imaging and SPAIR T(2)-weighted imaging in chronic exertional compartment syndrome of the lower leg muscles. J Magn Reson Imaging 2013;38:1073–1082. 18. Qi J, Olsen NJ, Price RR, Winston JA, Park JH. Diffusionweighted imaging of inflammatory myopathies: polymyositis and dermatomyositis. J Magn Reson Imaging 2008;27:212–217. 19. Sen PN. Time-dependent diffusion coefficient as a probe of geometry. Concepts Magn Reson A 2003;23:1–21.
1589 20. Grebenkov DS. NMR survey of reflected Brownian motion. Rev Mod Phys 2007;79:1077–1137. 21. Mitra PP, Sen PN, Schwartz LM. Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phys Rev B Condens Matter 1993;47:8565–8574. 22. Latour LL, Svoboda K, Mitra PP, Sotak CH. Time-dependent diffusion of water in a biological model system. Proc Natl Acad Sci U S A 1994;91:1229–1233. 23. Novikov DS, Fieremans E, Jensen JH, Helpern JA. Time-dependent diffusion and kurtosis as a probe of tissue structure. In: Proc 19th Annual Meeting ISMRM, Montreal; 2011. p 1988. 24. Fieremans E, Novikov DS, Sigmund EE, Liu C, Jensen JH, Helpern JA. In vivo measurement of membrane permeability and fiber size in calf muscle using time-dependent DWI. In: Proc 19th Annual Meeting ISMRM, Montreal; 2011 (abstract 1153). 25. Novikov DS, Fieremans E, Jensen JH, Helpern JA. Random walk with barriers. Nat Phys 2011;7:508–514. 26. Kim S, Chi-Fishman G, Barnett AS, Pierpaoli C. Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart. Magn Reson Med 2005;54:1387–1396. 27. Stejskal EO. Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. J Chem Phys 1965;43:3597–3603. 28. Mitra PP, Sen PN. Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments — simple pore geometries. Phys Rev B 1992;45:143–156. 29. Niendorf T, Dijkhuizen RM, Norris DG, van Lookeren Campagne M, Nicolay K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn Reson Med 1996;36:847–857. 30. Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 2005;53:1432–1440. 31. Lu H, Jensen JH, Ramani A, Helpern JA. Three-dimensional characterization of non-gaussian water diffusion in humans using diffusion kurtosis imaging. NMR Biomed 2006;19:236–247. 32. Hui ES, Fieremans E, Jensen JH, et al. Stroke assessment with diffusional kurtosis imaging. Stroke 2012;43:2968–2973. 33. Rosenkrantz AB, Sigmund EE, Johnson G, et al. Prostate cancer: feasibility and preliminary experience of a diffusional kurtosis model for detection and assessment of aggressiveness of peripheral zone cancer. Radiology 2012;264:126–135. 34. Hahn EL. Spin echoes. Phys Rev 1950;77:746–746. 35. Chang LC, Walker L, Pierpaoli C. Informed RESTORE: a method for robust estimation of diffusion tensor from low redundancy datasets in the presence of physiological noise artifacts. Magn Reson Med 2012;68:1654–1663. 36. Chang LC, Jones DK, Pierpaoli C. RESTORE: robust estimation of tensors by outlier rejection. Magn Reson Med 2005;53:1088–1095. 37. Kruskal WH, Wallis WA. Use of ranks in one-criterion variance analysis. J Am Stat Assoc 1952;47:583–621. 38. Deux JF, Malzy P, Paragios N, et al. Assessment of calf muscle contraction by diffusion tensor imaging. Eur Radiol 2008;18: 2303–2310. 39. Schwenzer NF, Steidle G, Martirosian P, et al. Diffusion tensor imaging of the human calf muscle: distinct changes in fractional anisotropy and mean diffusion due to passive muscle shortening and stretching. NMR Biomed 2009;22:1047–1053. 40. Alberts B. Molecular biology of the cell. New York: Garland Science; 2008. 41. de Graaf RA, van Kranenburg A, Nicolay K. In vivo (31)P-NMR diffusion spectroscopy of ATP and phosphocreatine in rat skeletal muscle. Biophys J 2000;78:1657–1664. 42. Fisher MJ, Meyer RA, Adams GR, Foley JM, Potchen EJ. Direct relationship between proton T2 and exercise intensity in skeletalmuscle MR images. Invest Radiol 1990;25:480–485. 43. Houmard JA, Smith R, Jendrasiak GL. Relationship between MRI relaxation-time and muscle-fiber composition. J Appl Physiol 1995;78:807–809. 44. Karampinos DC, Banerjee S, King KF, Link TM, Majumdar S. Considerations in high-resolution skeletal muscle diffusion tensor imaging using single-shot echo planar imaging with stimulated-echo preparation and sensitivity encoding. NMR Biomed 2011;25:766–778.
1590 45. Nielles-VallespinS,MekkaouiC,GatehouseP,etal.Invivodiffusiontensor MRI of the human heart: reproducibility of breath-hold and navigator-basedapproaches.MagnResonMed2013;70:454–465. 46. Gamper U, Boesiger P, Kozerke S. Diffusion imaging of the in vivo heart using spin echoes—considerations on bulk motion sensitivity. Magn Reson Med 2007;57:331–337. 47. Wirestam R, Greitz D, Thomsen C, Brockstedt S, Olsson MB, Stahlberg F. Theoretical and experimental evaluation of phasedispersion effects caused by brain motion in diffusion and perfusion MR imaging. J Magn Reson Imaging 1996;6:348–355. 48. Brockstedt S, Thomsen C, Wirestam R, et al. Use of an enhanced gradient system for diffusion MR-imaging with motion-artifact reduction. Acta Radiol 1995;36:662–670.
Marschar et al. 49. Christiansen P, Gideon P, Thomsen C, Stubgaard M, Henriksen O, Larsson HBW. Increased water self-diffusion in chronic plaques and in apparently normal white matter in patients with multiple-sclerosis. Acta Neurol Scand 1993;87:195–199. 50. Jensen JH, Helpern JA. MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed 2010;23:698– 710. 51. Hernando D, Karampinos DC, King KF, et al. Removal of olefinic fat chemical shift artifact in diffusion MRI. Magn Reson Med 2011;65:692–701. 52. Andreasen NC, Ehrhardt JC, Swayze VW 2nd, et al. T1 and T2 relaxation times in schizophrenia as measured with magnetic resonance imaging. Schizophr Res 1991;5:223–232.
