Human soleus muscle architecture at different ankle joint angles from magnetic resonance diffusion tensor imaging

Abstract

The orientation of muscle fibers influences the physiological cross-sectional area, the relationship between fiber shortening and aponeurosis shear, and the total force produced by the muscle. Such architectural parameters are challenging to determine particularly in vivo in multicompartment structures such as the human soleus with a complex arrangement of muscle fibers. The objective of this study was to map the fiber architecture of the human soleus in vivo at rest in both neutral and plantarflexed ankle positions using an MRI-based method of diffusion tensor imaging (DTI). Six subjects were imaged at 3 Tesla with the foot at rest in the two ankle positions. Eigenvalues, fractional anisotropy (FA), and eigenvector orientations of fibers in the different soleus subcompartments were evaluated after denoising of the diffusion tensor. The fiber architecture from DTI was similar to earlier studies based on a 3D fiber model from cadavers. The three eigenvalues of the diffusion tensor increased by ∼14% on increasing the joint plantarflexion angle in all of the soleus subcompartments, whereas FA showed a trend to decrease in the posterior and marginal soleus and to increase in the anterior soleus. The angle change in the lead eigenvector between the two foot positions was significant: ∼41° for the posterior soleus and ∼48° for the anterior soleus. Fibers tracked from the subcompartments support these changes seen in the eigenvector orientations. DTI-derived, subject-specific, muscle morphological data could potentially be used to model a more complete description of muscle performance and changes from disease.

imaging techniques, using both ultrasound and MRI, have provided a wealth of information related to the morphology and functioning of skeletal muscle (13, 14, 18, 29, 36, 41). One potential goal for imaging is to develop subject-specific data where muscle morphological and mechanical data may be combined to develop more complete descriptions of muscle performance, intersubject variability, and changes arising from onset of disease. One important issue in skeletal muscle is the orientation of muscle fibers within a muscle and the potential curvature of those fibers (33). The orientation of the fibers influences the physiological cross-sectional area and the relationship between fiber shortening and aponeurosis shear (4, 9, 41). Determination of such data is particularly challenging in the relatively complex structure of the human soleus muscle, which is composed of several subcompartments with a complex arrangement of muscle fiber orientations (1, 22). It should be noted that the subcompartments identified here are not strictly anatomic compartments, and the nomenclature refers to regions within the soleus with distinct fiber orientations (specified by the lead eigenvector direction). In this article, we describe the application of diffusion tensor imaging (DTI) to define voxel-by-voxel orientations of muscle fibers within the human soleus muscle (and thus the potential orientation of stress vectors).

Diffusion tensor magnetic resonance imaging is a relatively recent advancement that allows the in vivo study of microstructural organization (2, 3, 31). This method sensitizes the MR signal to water diffusion through large motion-probing magnetic field gradients. Anisotropy in diffusion arises from underlying tissue microstructure that presents regularly oriented barriers to water diffusion that limit molecular excursions arising from Brownian motion in specific directions. DTI involves application of motion-sensitizing gradients along different directions to resolve the anisotropic diffusion patterns. Diffusion anisotropy has been identified in several tissues: white matter and cardiac, skeletal, and lingual muscle (7, 17, 31, 43). Muscle fiber direction determined from DTI has been validated by direct anatomic examination and by optical imaging (10, 34). In vivo human DTI studies of the calf muscle have also reported the dependency on sex and age as well as the effect of injury (15, 16, 47). Furthermore, feasibility of tracking muscle fibers from in vivo diffusion tensor images of the calf has been demonstrated (42) and extended to more quantitative assessment of fiber tracks such as muscle fiber length and pennation angle (20, 21, 26). Recent studies have also identified changes in the eigenvalues and fractional anisotropy (FA) since muscle lengths change under passive and active conditions of plantar and dorsi flexion (12, 18, 35, 39). However, a number of technical challenges still remain in muscle fiber tracking. Particularly, as mentioned above, a detailed and comprehensive overview of the microstructure of the soleus muscle with the foot at neutral and plantar-flexion positions has not been explored, possibly because it has several subcompartments and presents complex, multipennate fiber architecture (1, 22).

In this article, we report 1) a qualitative overview of the fiber architecture in the soleus along the length of the calf muscle with the foot in two positions: at angles of 90 (neutral) and 120° (plantarflexion); 2) an evaluation of changes in diffusion indices (λ₁, λ₂, λ₃, FA) and leading eigenvector orientation (in polar coordinates) between the two foot positions in the different subcompartments of the soleus; and 3) an evaluation of fibers tracked from regions of interest (ROIs) in the different subcompartments of the soleus at the two foot positions.

MATERIALS AND METHODS

Image Acquisition

Studies were performed on six healthy subjects (5 males, 1 female, with an average age of 40 yr) after appropriate consent forms approved by the University of California San Diego Institutional Review Board were signed. One subject was scanned under neutral and plantarflexed conditions on 3 separate days to determine the coefficient of variation of the diffusion tensor-derived indices. Images in the axial view were acquired from the midcalf region on a 3T system (GE; GE Medical Systems), with the subject's leg in a relaxed state, using a custom-built transmit/receive 8 channel phased array extremity coil (Millennium). The advantage of this coil is that it affords a large field of view, enabling ≤25 cm of coverage without the need for coil repositioning. The foot was taped with a surgical band to a plastic cradle through an extension at the end of the coil; this ensured that the foot was immobile and comfortable during the acquisition for both ankle positions, even for the longer scan times of the current protocol. The subjects were in a supine state, and care was taken to position the subjects with the long axis of the leg placed parallel to the magnetic field, with the center of the coil ∼10 cm below the knee joint. The coil was fixed to the magnet table, always at the same position, to ensure similar parallel positioning for all of the subjects. Imaging was performed with the ankle in the neutral position (ankle angle 90°) and repeated with the ankle held in plantarflexion (ankle angle 120°) both under passive conditions. The ankle position was confirmed (in both neutral and plantarflexed) by imaging the foot/ankle with the body coil without any change in the subject foot position from the diffusion weighted scan.

The spin echo planar imaging-based high-speed DTI acquisition consisted of one baseline and 13 diffusion-weighted images (b factor: 500 s/mm²) along 13 noncollinear gradient directions. Image acquisition parameters were as follows: echo time/repetition time/field-of-view/matrix: 48 ms/6,400 ms/24 cm/128 × 128 with parallel imaging. Images were reconstructed to a matrix size of 256 × 256. The sensitivity encoding method was employed in the parallel image reconstruction, and a reference scan for coil sensitivity calculation was acquired prior to each DTI acquisition (27); a parallel imaging reduction factor of two was used in the current study. The volume of interest was also shimmed prior to the DTI acquisition. A total of 29–30 slices were acquired contiguously, and six repeats of the acquisition were magnitude averaged for a total scan time of 9 min. All sequences were acquired with the same geometric parameters: 0.94 × 0.94 mm in-plane resolution (after reconstruction to a 256 × 256 matrix) with a slice thickness of 5 mm. A spatial spectral fat-saturation pulse was used to suppress the fat signal. High-resolution images that matched the anatomic location of the DTI images were also acquired using T2-weighted fast-spin echo (FSE) sequence.

Image Analysis

There are several challenges to extracting the diffusion tensor from the imaging data. Some of these issues as well as the implementation of postprocessing methods to overcome these difficulties and derive accurate indices are discussed below.

Motion and eddy current correction.

The images acquired as part of a DTI scan include one set of baseline (b0) images with no diffusion sensitization. This is followed by a set of images acquired at the same locations as the b0 images but with diffusion sensitization applied in different directions. Diffusion tensor, which is a positive definite symmetric 3 × 3 tensor, is derived on a voxel-by-voxel basis from the combination of the baseline and diffusion-weighted images. This implicitly assumes that voxels in the different image sets are in complete alignment. Voxel mismatch can arise from two sources: 1) motion that may occur in the time duration between image acquisitions at b0 and different gradient directions and 2) image distortions from residual currents (eddy currents) of the large diffusion gradients. It is important to correct for these voxel mismatches and confirm the alignment prior to tensor calculations.

Motion-induced mismatch can be corrected by a rigid transformation, whereas the correction for eddy current-induced distortions requires an affine transformation. In the current study, we combined the motion and eddy current corrections into a single affine registration using the baseline diffusion-weighted image as the reference image. The 12-parameter (translation, rotation, scale, and shear) affine transform in Automated Image Registration (AIR) was used to correct for both motion and eddy current effects (44, 45). The standard deviation of ratio images was the cost function minimized by the registration algorithm, and trilinear interpolation was used to reslice the diffusion-weighted images to match to the baseline images. The AIR algorithm has been validated extensively for inter- and intrasubject registration and is part of the DTIStudio software used in the current study for fiber tracking (44, 45, 24). There is no need to rotate diffusion gradients (represented by the b-matrix) when correcting for distortions related to eddy currents, since the distortions are the only mismapping of intensity. However, it is important to reorient the diffusion gradient directions when motion artifact is corrected (32). Because both eddy current and motion corrections were combined into one registration, we used the transform to reorient the diffusion gradients as well. Thus, diffusion gradient directions were rotated using the rotational component of the affine transform matrix obtained from the alignment.

The tensor model of diffusion assumes that the underlying diffusion transport can be represented by a single symmetric Gaussian displacement distribution (6). The tensor components are calculated by fitting to a linear regression model. Difference images are obtained by a voxel-based subtraction of the calculated (from the fitting) and acquired diffusion-weighted images. Images/voxels that are corrupted by motion and/or other artifacts will deviate from the tensor model and will not be close to the fitted line and will show up in the difference images with non-zero pixel intensities, thus enabling identification of the distortions. Difference images of each subject were verified after affine registration to confirm that artifacts from motion and eddy current were minimized. It should be noted that the difference images were not used to drive the registration program; the latter algorithm uses its own cost function (standard deviation of ratio images) to drive the registration. The difference images were used to visualize that the registration had corrected motion and eddy current artifacts.

Denoising.

An important limitation of DTI of muscle is the low signal-to-noise ratio (SNR) of the images. This has serious consequences on the ability to extract accurate diffusion tensor indices; FA and fiber orientations are especially sensitive to noise. Furthermore, SNR requirements for fiber tracking are even more stringent (11). Although SNR can be increased by a higher number of averages, it increases scan time and can cause motion artifacts. Thus, image processing-based methods to decrease noise (known as denoising or smoothing) are a viable solution. The smoothing is typically performed on scalar data (image voxel intensity), but here it is performed directly on a tensor (6 values at each voxel).

Tensor data derived from the DTI data were smoothed using the log-Euclidean anisotropic filter available from the software package MedINRIA (38). The tensor-smoothing algorithm is based on first transforming to the matrix logarithm L of a tensor D, L = log(D), and running computations on L. Smoothing is then performed on L to obtain ∼L, from which the regularized tensor is obtained by taking the matrix exponential: ∼D = exp(∼L). The 3D iterative smoothing algorithm is based on a tensor version of the anisotropic diffusion proposed by Perona and Malik (37). The extent of smoothing is controlled in the implementation by two factors, κ (which controls the gradient threshold for smoothing; higher κ-values result in greater smoothing) and the number of iterations. In this study, κ was set at 0.2 and the number of iterations to 250. These values were selected based on the balance between smoothing and blurring. Tensor blurring was estimated from profiles of the leading eigenvector color map. The reduction in variance of FA and eigenvector data was tested for significance, comparing values in the same ROIs in the original and denoised images using Pitman's statistics (R 2.11.1; free statistical package downloaded from http://cran.stat.ucla.edu) (23). Pitman's statistic is a method that tests for the significance in the difference in variances between matched groups.

DTI analysis.

The denoised tensor was diagonalized to calculate the eigenvalues (λ₁, λ₂, λ₃), FA, and the primary eigenvector direction (ν₁, corresponding to the largest eigenvalue). The eigenvector orientation was expressed in polar coordinates (θ and φ) calculated from the normalized eigenvector orientation, ν₁ = (sinφ sinθ, cosφ sinθ, cosθ). θ is the primary eigenvector angle with the z-axis of the scanner coordinate system, and φ is the angle of the projection of the primary eigenvector on the x-y plane of the scanner coordinate system (with the y-axis defining 0°). Because the fiber orientations have 180° degeneracy, the value of θ was calculated between 0 and 90° to enable comparisons between the measurements. The acute angle between the primary eigenvectors in the two foot positions was calculated from the scalar product of the vectors; cos⁻¹ (ν_1N ν_1PF), where the N and PF refer to the neutral and plantarflexed foot positions. The angle of elevation is routinely defined as the vector “elevation” from the x-y plane. In the rest of the discussion, the fiber orientation with respect to the z-axis (θ) is thus referred to as the complementary of the angle of elevation (c-elevation), and φ is referred to as the azimuthal angle. Analysis was performed on 3 × 3 pixels ≡ 8.44 mm² or 4 × 4 pixels ≡ 15.0 mm² ROIs placed in soleus subcompartments. The axial slices were examined for the anterior subcompartment using the FSE and diffusion baseline images. The middle slice of this set of slices with maximal cross-section of the anterior compartment was selected for analysis.

Tracking.

Fibers were tracked from the smoothed tensor using the free software package DTIStudio (24). The FA threshold was set in the range of 0.08 to 0.1 to avoid missing fibers in regions of low FA. To prevent fibers from tracking into isotropic or noise regions (given the low FA threshold), the angular threshold was set low at 12° (i.e., the fiber tracking stopped if the fiber orientation changed by >12° in adjacent voxel locations in the track). This latter condition is in conformance with the knowledge that muscle fibers do not exhibit a high curvature.

In all the images shown here, the lead eigenvector of the tensors is displayed as arrows with the following color-mapping scheme; blue color indicates superior to inferior or craniocaudal direction of the eigenvector, red color indicates medial to lateral direction, and green color indicates anterior to posterior direction. Intermediate orientations are displayed with varying color contributions from those attributed to the three orthogonal directions. The color map of the eigenvector also follows the same conventions as for the arrows, and both are in conformance with the literature (28).

RESULTS

Tensor Smoothing

The SNR was low given the limitations of echo planar-based image acquisition and the low T2 of the muscle tissue. Images of the leading eigenvector (represented as arrows in Fig. 1A) indicate a fairly large amount of noise. This noise level was sufficient to confound fiber tracking. Figure 1B shows the corresponding image of the leading eigenvector after the tensors were smoothed using the log-Euclidean filter described in materials and methods.

Fig. 1.

The leading eigenvector is shown in resliced coronal images as arrows with the color indicating vector direction, as explained in the text. A: original unsmoothed image. B: corresponding smoothed image. Outside the muscle regions, residual peripheral fat that is not completely suppressed is seen as random and erroneous eigenvectors (e.g., near the medial gastrocnemius). Coronal image shown is resliced from the axially acquired 0.94 × 0.94 × 5 mm (slice thickness) sections so that the coronal resliced images are 0.94 (in-plane, x-axis) × 5 (in-plane, y-axis) × 0.94 mm (slice/slab thickness).

Table 1 lists the standard deviation of the FA and the lead eigenvector orientations in six ROIs in the soleus averaged over five subjects. Care was taken to place the ROIs in the soleus muscle in homogenous regions of the different subcompartments (corresponding to those listed in Table 2). The P values from the Pitman statistic were all significant and ranged from 0.001 to 0.04. The mean value of the actual FA values in the ROIs was higher in the original than in the denoised images, but this difference was not significant. The standard deviation of the lead eigenvector orientation was also reduced with the smoothing (average standard deviation of orientation in the original images: 3.1 ± 2.5°; and in the denoised tensor images: 1.01 ± 0.6°). An average difference of 3° was found in the mean value of the principal eigenvector orientation (measured along the scanner x-, y-, and z-axes), comparing the original and denoised images, but this difference was not significant. The significance in the reduction in eigenvector orientation variance was assessed for each ROI and for each axis separately with the Pitman statistic; changes were significant (P < 0.05).

Table 1.

Effect of denoising

	SD, FA		SD, Eigenvector Orientation
ROI	Raw images	Denoised images	Original	Denoised
1	0.0200	0.0011	(2.01, 1.84, 1.37)	(0.35, 0.55, 0.40)
2	0.0100	0.0014	(4.86, 3.06, 3.30)	(1.60, 0.41, 0.89)
3	0.0200	0.0016	(2.49, 4.53, 1.37)	(0.51, 2.41, 0.71)
4	0.0083	0.0033	(1.45, 3.21, 0.63)	(0.53, 1.49, 1.04)
5	0.0200	0.0050	(11.26, 3.88, 1.20)	(1.93, 1.03, 1.08)
6	0.0097	0.0020	(3.34, 4.67, 1.98)	(1.27, 1.20, 0.80)

FA, fractional anisotropy; ROI, region of interest. SD of the FA and of the lead eigenvector direction in 6 ROIs in the soleus in the original and denoised images acquired with the foot in the neutral position averaged over all subjects. The 3 × 3 or 4 × 4 ROIs were at the same locations in the original and denoised images and were placed in homogenous regions of the lateral and medial marginal and anterior soleus as well as at 2 locations in the posterior soleus. The SDs of the eigenvector orientation (in the same ROIs) with respect to the magnet x-, y-, and z-axes are listed in parantheses (in degrees).

Table 2.

Changes in eigenvalues and FA between the ankle in N and at PF positions

	λ1		λ2		λ3		FA
Muscle Regions	N	PF	N	PF	N	PF	N	PF
MS-med	1.91 ± 0.08*	2.09 ± 0.10	1.38 ± 0.06*	1.53 ± 0.03	1.2 ± 0.05*	1.33 ± 0.03	0.24 ± 0.02	0.22 ± 0.02
MS-lat	1.87 ± 0.04**	2.09 ± 0.07	1.53 ± 0.14	1.77 ± 0.13	1.24 ± 0.08*	1.57 ± 0.15	0.20 ± 0.03	0.18 ± 0.04
POS-SOL1	1.78 ± 0.05*	2.07 ± 0.17	1.42 ± 0.07*	1.72 ± 0.20	1.22 ± 0.16*	1.49 ± 0.21	0.20 ± 0.07	0.17 ± 0.04
POS-SOL2	1.82 ± 0.04	2.04 ± 0.21	1.51 ± 0.06	1.66 ± 0.25	1.26 ± 0.08	1.44 ± 0.20	0.19 ± 0.03	0.20 ± 0.02
AS-med	1.92 ± 0.08*	2.25 ± 0.09	1.51 ± 0.09*	1.73 ± 0.09	1.36 ± 0.06	1.45 ± 0.05	0.18 ± 0.04	0.23 ± 0.02
AS-lat	2.01 ± 0.14*	2.25 ± 0.08	1.59 ± 0.14*	1.79 ± 0.02	1.38 ± 0.04*	1.52 ± 0.12	0.21 ± 0.04	0.24 ± 0.04

Values are means ± SD of FA from 3 × 3 or 4 × 4 ROIs in the different soleus subcompartments averaged over 5 subjects are given for the 2 angles. N, neutral; PF, plantarflexion; MS-med, marginal soleus-medial; MS-lat, marginal soleus-lateral; AS-med, anterior soleus-medial; AS-lat, anterior soleus-lateral; POS-SOL1, posterior soleus, ROI1; POS-SOL2, posterior soleus, ROI2. Values for the eigenvalues are ×10⁻³ mm²/s; significant differences in eigenvalues and FA between neutral and plantarflexed foot positions are shown.

^*P < 0.05,

^**P < 0.005.

Blurring was assessed by examining the profile of the lead eigenvector color image. Figure 2 shows the red, green, and blue values of each pixel along a horizontal profile of the noisy and denoised color map of the lead eigenvector images. The differences in fiber orientation are preserved (note the sharp transitions between subcompartments with different orientations) in the smoothed image, whereas the homogeneous regions are clearly smoothed. Figure 2 also shows the FSE and corresponding b0 images, with the contour of the soleus from the FSE image overlaid on the b0 image. The close match confirms that distortions in the diffusion-weighted images are small.

Fig. 2.

Effect of smoothing on delineation of different soleus muscle subcompartments by lead eigenvector orientation. Top: the structural fast-spin echo (FSE) image (left) and the corresponding diffusion weighted b0 image (right) with the soleus contoured in the FSE image (dotted line) and overlaid on the b0 image. The contour match shows that distortions in the diffusion-weighted images are small. Middle: the color map of the lead eigenvector from the original data (slice corresponding to top) and the plot of pixel red, green, and blue values along the horizontal dotted line. Transitions to regions (subcompartments) with different lead eignvector orientations are sharp; however, the noise is clearly affecting image quality. Bottom: same as the middle row but using the smothed images. The fluctuations within each region are greatly reduced, whereas the sharp transitions between muscle subcompartments are clearly preserved.

Qualitative Assessment of Soleus Muscle Architecture

The figures presented here are images of one subject (Figs. 3–5); however the other four subjects showed similar orientations in the different soleus subcompartments. The sixth subject in the cohort showed a deviant soleus architecture, which is presented at the end of this subsection.

Fig. 3.

The most distal slice in the acquired volume. The axial b0 morphological image in the neutral ankle position (A), an image at an approximately corresponding location from the Visible Human dataset (B), and lead eigenvector images corresponding to the axial image at rest (C) and in plantarflexion (D). In the Visible Human image (B), the soleus is outlined in green, the white arrows indicate the inferred fiber direction, and the blue dotted line (dividing the soleus into 2 compartments) corresponds to the median septum. The median septum is also identified on the eigenvector image (arrow 2) which separates the posterior soleus at this level into medial (arrow 1) and lateral (arrow 3) subcompartments. The color map for the eigenvectors is similar to that shown in Fig. 2. In this and the next figure, eigenvectors are displayed in every other voxel for visual clarity.

Fig. 4.

Axial image located approximately in the middle of the imaged volume. The axial FSE morphological image at plantarflexion (A), same image as in A with contours of muscle regions (B), and b0 morphological image at the same level as in A with the contours from B overlaid on it (C). An image at an approximately corresponding location from the Visible Human dataset (D) and lead eigenvector images corresponding to the morphological image at rest (E) and in plantarflexion (F). In B, the posterior soleus (arrow 5), anterior soleus (medial; arrow 1), lateral (arrow 3) and median septum (arrow 2), and tibialis anterior are contoured in thin black lines. Overlay on C confirms that spatial distortions are small in both the soleus as well as in the tibialis anterior. In the Visible Human image (D), the soleus is outlined in green, the white arrows indicate the inferred fiber direction, and the blue dotted lines correspond to the anterior soleus and the median septum. The median septum is also identified on the eigenvector image (E, arrow 2) and separates the anterior soleus into medial (E, arrow 1) and lateral (E, arrow 3) subcompartments. Other subcompartments seen at this level are the posterior soleus (E, arrow 5) and 2 subcompartments located laterally (E, arrow 4) and medially (E, arrow 6) with strong medial-lateral fiber orientation as well. On plantar flexion, large orientation changes are seen in the anterior soleus (E, arrows 1 and 3) as well as in the posterior soleus (E, arrow 5) subcompartments. Labels on the FSE images correspond to that of the eigenvector images; however, the marginal subcompartments could not be identified on the FSE images.

Fig. 5.

Coronal view of the soleus. The coronal morphological image in the neutral position (A), an image at an approximately corresponding location from the Visible Human data set (B), and lead eigenvector images corresponding to the coronal morphological image at rest (C) and in plantarflexion (D). In the Visible Human image (B), the soleus is outlined in solid green, the white arrows are the inferred fiber directions, and the blue dotted lines correspond to the anterior soleus. The subcompartments identified in the Visible Human image are posterior soleus (B, arrow 1), the medial anterior soleus (B, arrow 2), the median septum (B, arrow 3), and the lateral anterior soleus (B, arrow 4). These subcompartments are also identified on the eigenvector image at rest (C) with the same arrow labels as in B. On plantar flexion, there are large fiber orientation changes in both subcompartments of the anterior soleus and in the posterior soleus.

Neutral ankle position.

The leading eigenvector is displayed in the axial plane at two levels along the length of the calf muscle (Figs. 3 and 4). For comparison, the fiber direction inferred from the Visible Human dataset histological images at approximately corresponding locations is also shown in each of these images (Figs. 3B and 4D). There is an overall agreement of the inferred fiber directions from the Visible Human data (white arrows in these images) and that derived from the present DTI. At the most distal axial level imaged, an aponeurosis is seen (Fig. 3C, arrow 2), which divides the posterior soleus muscle into medial and lateral regions (also noted in Ref. 22). Visual examination of the two subcompartments shows fiber directions predominantly in the inferolateral-superomedial direction in the medial subcompartment and fiber directions predominantly in the medial-lateral direction, with a smaller superior-inferior component in the lateral subcompartment. Figure 4 shows a more proximal axial slice from the middle of the imaged volume and a complex arrangement of fibers in the different muscle subcompartments. The medial and lateral subcompartments identified in the distal slices can still be seen; however, both of these subcompartments have fibers with larger components of medial-lateral orientation than in the distal slices. These two subcompartments at this level are not identified in the Visible Human data set or on the morphological FSE image (Fig. 4, A and B) but possibly correspond to the marginal soleus that was identified in the 3D cadaveric analysis by Agur et al. (1). They are tentatively labeled as the marginal soleus (medial and lateral) in the rest of this article. In addition to the marginal soleus, the posterior subcompartment with a strong anterior-posterior fiber direction is also visible at this level (Fig. 4, B and E, arrow 5). A careful examination of the direction shows that fibers in the posterior soleus run in the anterosuperior-posteroinferior direction. The anterior soleus (Fig. 4, arrows 1 and 3) and the median septum (Fig. 4, arrow 2) are also visible at this level. The medial anterior soleus subcompartment has fibers with a strong superior-inferior orientation, whereas the lateral anterior soleus subcompartment has fibers with some lateral-medial component in addition to the superior-inferior orientation. As one proceeds more proximally, the posterior soleus is the largest subcompartment with a strong anterior-posterior and superior-inferior orientation. The marginal soleus is seen medially as well. Figure 5 shows a coronal image with an approximately corresponding slice from the Visible Human data set. The overall agreement with the fiber orientation inferred from the Visible Human images is striking. The bipennate structure of the anterior soleus and the anterior-posterior orientation of the posterior soleus are clearly seen in the eigenvector images.

Plantarflexed ankle position.

The eigenvector images of the calf muscle in the plantarflexed position are shown in Figs. 3D, 4F, and 5D. At the most distal slice, the medial subcompartment shows fiber orientation changes that result in a stronger lateral-medial component to the fiber direction (Fig. 3). The lateral subcompartment remains relatively unchanged. Proceeding superiorly, dramatic changes in the fiber direction are seen in the anterior and posterior subcompartments (Figs. 4F and 5D). Here, the fibers of both the anterior medial and anterior lateral subcompartment have pronounced lateral-medial directions in the plantarflexed position. The posterior soleus also has a stronger anterior-posterior direction in the plantarflexed images.

In summary, the qualitative evaluation shows that fibers in the various soleus subcompartments rotate so that they have a larger in-plane (either anterior-posterior or medial-lateral) directional component. This translates to increases in pennation angles, which in turn supports shorter fiber lengths while a constant muscle volume is maintained. Figure 5D shows the coronal view of the plantarflexed state, and this confirms the key observations of fiber direction changes inferred from the axial images; the posterior soleus is compressed proximally by the anterior soleus, causing the former subcompartment to extend more distally. The fibers in the posterior soleus have a stronger anterior-posterior orientation on plantarflexion, and the medial and lateral anterior soleus subcompartments show large changes in fiber orientation rotating from a strong superior-inferior to a lateral-medial direction.

Deviant Soleus Architecture

One of the six subjects presented with a deviation from the fiber arrangement described above (Fig. 6). In the structural FSE images, it is difficult to visualize the fascicle orientations to check for differences in fiber orientations between deviant and normal soleus anatomy; however, there was no aponeurosis of origin in the lateral subcompartment (Fig. 6, A and B). The DTI data show that the deviant soleus anatomy has differences in fiber orientations compared with the more common soleus anatomy (Fig. 6C). These differences are more pronounced in the plantarflexed foot position (Fig. 6F). In the neutral position, both subcompartments in this subject revealed fibers in the distal-proximal orientation. In the plantarflexed position, the lateral soleus fibers have a strong anterior posterior component, similar to the orientation of the posterior soleus in the other subjects. Furthermore, one of the regions of the medial subcompartment showed a strong medial lateral component on plantarflexion that is similar to the changes seen in the anterior soleus subcompartments of the other subjects. The marginal soleus was hard to visualize in this deviant soleus architecture (Fig. 6, C and F). This type of soleus architecture without an aponeurosis of origin in the lateral subcompartment was seen in 10% of subjects in an earlier study using structural MRI (22). In the latter study, no noticeable differences were observed in motor performance of the deviant soleus architecture subjects relative to the rest with the anterior/posterior subcompartments.

Fig. 6.

Deviant soleus anatomy of one of the subjects showing no aponeurosis of origin in the lateral compartment. Top: FSE (A), b0 (B), and color map of the lead eigenvector (C) images with the foot in the neutral position. Bottom: slices corresponding to above but with the ankle in the plantarflexed position. The change in orientation of the lateral subcompartment coincides with changes seen in the posterior subcompartment in the other subjects. The soleus (region labeled 1) and tibialis anterior (region labeled 2) are contoured on the FSE images (A and D) and overlaid on the corresponding b0 images (B and E), confirming that distortions are minimal in the DTI images in both the soleus as well as the tibialis anterior compartments. In this subject, the soleus was divided into the lateral (arrow 3) and medial (arrow 4) subcompartments, in contrast to the routine anterior and posterior subcompartments (e.g., in Fig. 5). The aponeurosis of origin in the medial compartment is also contoured.

Quantitative Assessment of Soleus Muscle Architecture

The coefficient of variation (CV), defined as the ratio of the standard deviation to the mean value expressed as a percentage, was computed from the three repeated measurements on one subject. For the three eigenvalues and averaging over the different subcompartments, CV (%) for λ₁ averaged 1.87 (N) and 2.85 (P), for λ₂ averaged 2.81 (N) and 3.87 (P), and for λ₃ averaged 3.92 (N) and 3.34 (P), where N is the neutral and P is the plantarflexed ankle positions. For FA, the CV ranged from 3.2 to 6.1% in the neutral position and from 4.1 to 6.9% for the plantarflexed position. Table 2 lists the λ₁, λ₂, λ₃, and FA in the soleus subcompartments at neutral and plantar flexion positions as the average over five subjects (the 6th subject with the deviant architecture was not included for lack of corresponding subcompartments). The diffusion indices were measured in small 3 × 3 or 4 × 4 ROIs placed in the different muscle subcompartments; a typical anatomic level for the analysis is shown in Fig. 4A. The color map of the leading eigenvector image was used to guide the placement of the ROIs, since the different subcompartments were best visualized in this image. The three eigenvalues increased as the foot position changed from the neutral to plantarflexed position for all of the soleus subcompartments, with some of the changes being significant (paired 2-tailed, t-test; Table 2). The FA did not show any significant changes, although the trend was a decrease in FA for the marginal and posterior soleus subcompartments and an increase in FA for the anterior soleus subcompartments.

Table 3 lists the fiber orientation in terms of the polar coordinates of the leading eigenvector in the neutral and plantarflexed states. The last column in the table lists the angle between the lead eigenvectors, with the foot in the neutral and plantarflexed ankle position. The posterior and anterior soleus subcompartments clearly showed large changes in the c-elevation angle ≈30°, with angles increasing for plantarflexion. The azimuthal angle changes for the posterior soleus subcompartment clearly show that, on plantarflexion, the eigenvector is aligned primarily in the anterior-posterior direction (y-axis of scanner coordinate). The azimuthal angle changes for the two anterior soleus subcompartments show that, on plantarflexion, the eigenvector is aligned primarily in the medial-lateral direction (x-axis of scanner coordinate). Fiber orientation changes in the marginal soleus subcompartments are much smaller, and in addition, the lateral marginal soleus has a high variability. Significant differences in θ and φ between neutral and plantarflexed ankle positions were assessed by paired two-tailed t-test; changes were significant in the azimuthal angles of the posterior soleus and in the c-elevation angle of the lateral anterior subcompartments. However, changes in the c-elevation angles of the posterior soleus and medial anterior soleus also approached significance.

Table 3.

Changes in lead eigenvector angles (θ and φ) between the ankle in N and at PF positions for the different soleus subcompartments

	θ		Φ
Muscle Regions	N	PF	N	PF	Angle (N-PF)
MS-med	53.9 ± 3.6	61.5 ± 9.8	95.9 ± 12.6	94.7 ± 16.9	12.1 ± 8.3**
MS-lat	38.0 ± 40.3	65.5 ± 10.3	86.8 ± 29.3	116.6 ± 16.1	23.8 ± 67.8
POS-SOL1	31.3 ± 13.6	69.2 ± 16.7	155.2 ± 13.4**	4.6 ± 2.4	43.7 ± 30.1**
POS-SOL2	36.7 ± 4.5	68.2 ± 13.3	169.2 ± 6.6*	12.8 ± 3.7	39.1 ± 28.0**
AS-med	21.3 ± 13.1	67.2 ± 37.0	122.5 ± 49.7	98.4 ± 30.9	50.9 ± 31.2**
AS-lat	25.2 ± 7.6*	66.3 ± 9.5	93.6 ± 36.0	109.8 ± 18.3	45.7 ± 21.9**

The lead eigenvector angles (in degrees) in polar coordinates (θ and φ) in the soleus subcompartments in N and PF states. The last column [Angle (N-PF)] is the acute angle between the lead eigenvectors in the N and PF ankle positions. Significant differences in orientation angles between neutral and plantarflexed ankle positions are shown;

^*P < 0.05,

^**P < 0.01.

The angle change between the fiber orientations (represented by the lead eigenvectors) at neutral and plantarflexion foot position was ∼41° for the posterior soleus subcompartments and ∼48° for the anterior soleus subcompartments. For all regions, the one-tailed probability that the angular change between the fiber orientations at neutral and plantarflexion was different from zero was significant at P < 0.01, except for the lateral marginal soleus (Table 3).

Fiber Tracking

Fibers were tracked from the smoothed tensors with single voxel seed points placed in the different subcompartments. Figure 7 shows a subject with the fibers tracked in the medial and lateral subcompartments of the anterior soleus in the neutral and plantarflexed positions. The bipennate structure of the anterior soleus is clearly confirmed in these images; the directions in the two subcompartments are superomedial and superolateral. In the plantar flexed state, fibers are aligned in the lateral-medial direction. Figure 8 shows fibers tracked from the posterior soleus and displayed with the 3D color image volume rotated to the sagittal plane. A preliminary estimate of fiber lengths (averaged over 3 subjects) in the neutral and plantarflexed positions yielded for the following: posterior soleus 21.8 ± 2.7 (neutral) and 17.7 ± 3.1 mm (plantarflexed); anterior medial soleus 19.31 ± 3.4 (neutral) and 20.04 ± 2.9 mm (plantarflexed); anterior lateral soleus 10.69 ± 2.6 (neutral) and 14.47 ± 2.8 mm (plantarflexed). As anticipated, the posterior soleus fibers decrease in length on contraction. However, the changes in the anterior soleus are contradictory since the fiber length increases on contraction. This can be explained by the fact the anterior soleus cross-section increases (at the location where the fibers were tracked) in the plantarflexed ankle position (Figs. 5 and 7).

Fig. 7.

Coronal color map of the lead eigenvector at neutral (A) and at plantar flexion (C), with arrows showing the anterior soleus medial and lateral subcompartments (arrows 1 and 2, respectively) separated by the median septum. A vertical dotted line is placed at the location of the median septum. Fibers (in red for neutral and in blue for plantarflexed ankle positions) tracked from seed points located in the lateral and medial subcompartments of the anterior soleus in the neutral (C) and in the plantarflexed positions (D). Fiber colors are assigned by the user so as to maximize the contrast with the underlying eigenvector images.

Fig. 8.

Sagittal color map at neutral (A) and at plantar flexion (C), with arrow 1 showing the posterior soleus. The color maps show that the posterior soleus has a strong anterior-posterior orientation at plantarflexion. Fibers (in blue) tracked from seed points located along the length of the posterior soleus run anterosuperior to posteroinferior in neutral (B) and plantarflexed positions (D); in the latter position, the fibers are shorter with larger pennation angles (D).

DISCUSSION

Denoising

Muscle DTI is rendered difficult by a low SNR arising from much shorter T2 values compared with brain white matter (∼33 vs. ∼80 ms). Furthermore, muscle FA is low compared with white matter, and earlier studies have shown that regions with low FA values are more sensitive to image noise (5). In addition, within the calf muscle, the soleus muscle has lower FA values (42). Furthermore, to visualize the different soleus subcompartments, the current study uses a higher resolution than prior muscle DTI studies (20, 39, 42). A larger number of averages can increase SNR; however, the resultant increase in scan time will make it difficult to maintain the ankle positions for long periods. Image smoothing provides a retrospective method of reducing noise, and the use of a nonlinear smoothing filter allows noise reduction without significant blurring of edges. It should be noted that the smoothing was critical for both visualization of muscle architecture (Fig. 1) and robust fiber tracking. Table 1 shows that the variance in FA and eigenvector direction in homogeneous regions is reduced by the denoising, whereas Fig. 2 confirms that the boundaries between the muscle subcompartments are preserved. It should be noted that tensor denoising is more effective in preserving the boundaries than scalar denoising of the diffusion-weighted images, because the eigenvector orientation differs significantly between the soleus subcompartments.

Qualitative Assessment of Soleus Muscle Architecture

Neutral ankle position.

The current report of the complex architecture within the soleus highlights the potential for DTI studies. Overall, the fiber directions and subcompartments agreed with the fiber directions inferred using the Visible Human dataset by Hodgson et al. (22). In the latter study, fibers were identified indirectly from the direction of the fascicles and can thus be considered only as rough indicators of fiber direction. The 3D cadaveric analysis by Agur et al. (1) identifies three muscle subcompartments: posterior, anterior, and marginal soleus. The latter study identifies the posterior soleus fiber bundles as attaching to the posterior surface of the anterior aponeurosis and to the anterior surface of the posterior aponeurosis. The fiber bundles are directed from anterosuperior to posteroinferior. This direction is confirmed in the eigenvector images and in the tracked fibers (Figs. 5 and 8). Agur et al. (1) identify the anterior soleus as bipennate, where the fiber bundles join the median septum and the anterior aponeurosis. The median septum is a tapering vertical sheet of aponeurosis with fiber bundles attaching to the medial and lateral surfaces and directed superomedially and superolaterally. The bipennate structure and the median septum as well as the superomedial and superolateral directions of the anterior soleus are confirmed by the eigenvector and fiber visualization (Figs. 5 and 7). The marginal soleus fiber bundles have been identified by Agur et al. (1) as spanning the medial, lateral, and superior margins of the posterior aponeurosis to the anterior aponeurosis medially and laterally and tibia and fibula superiorly. It is likely that, in the current study, the medial and lateral subcompartments (Fig. 4E, arrows 4 and 6) with strong mediolateral orientation for the fibers may correspond to the marginal soleus identified by Agur et al. (1). As mentioned earlier in the results, the marginal soleus was not identified in the Visible Human study, but this may be due to the indirect nature by which the fiber orientations were inferred.

Plantarflexed ankle position.

Agur et al. (1) also addressed the functional considerations based on structural arrangement of the fiber bundles. They postulated that since the posterior soleus has a high pennation angle, it will be capable of generating high forces with little excursion. However, in the current study, fairly large changes in orientation angles in the posterior soleus close to ∼41° were observed. Thus, contrary to the postulate described by Agur et al. (1), there are large orientation excursions of the posterior soleus on plantarflexion. These orientation changes are comparable with that shown by the anterior soleus fibers (∼48°). Electromyography studies by Campbell et al. (8) indicate that the medial and lateral aspects of the anterior soleus differ functionally, with the lateral aspect being a stabilizer of the leg and the medial aspect being an ankle plantar flexor. Agur et al. (1) also suggest that the anterior soleus, because of its attachment to the median septum and bipennate structure, can potentially play a role in ankle plantarflexion. The largest angular changes are seen in the anterior soleus subcompartments, confirming its postulated role in ankle plantarflexion (Table 3). Furthermore, on the basis of fiber lengths, they postulate the medial part as the leg stabilizer, whereas the lateral part may be more effective for ankle plantarflexion. However, in the current study, the changes in fiber orientation angles are larger in the medial anterior soleus subcompartments (average change of 46° in the lateral and 51° in the medial compartments), possibly in conformance with the postulate described by Campbell et al. (8). In both the anterior and posterior soleus, fiber orientation changes are such that fibers oriented primarily along the proximal-distal (superior-inferior) directions in the neutral position change to either a medial-lateral (anterior soleus) or an antero-posterior (posterior soleus) direction (Table 3). Because the aponeurosis run approximately parallel to the proximal-distal direction, the directional change seen in both the posterior and anterior soleus translates to larger pennation angles.

Evaluation of Changes in the DTI Indices in the Soleus Muscle Subcompartments

There have been differing reports on the changes under passive and active muscle plantarflexion (12, 18, 35, 39). Hatakenaka et al. (18) reported that in the medial gastrocnemius (mGM), passive plantarflexion resulted in a decrease in λ₁, no change in λ₂, and an increase in λ₃, which leads to a lower FA value. The opposite effect was seen in the tibialis anterior (TA). Deux et al. (12) reported that in the mGM, the three eigenvalues and apparent diffusion coefficient increased, whereas FA decreased during an active plantarflexion (neutral to plantarflexion). The reverse trend was observed in the anterior tibialis (TA). Deux et al. (12) attributed the observed changes to the fact the TA elongated, whereas the mGM contracted for dorsiflexion (or rest/neutral) to plantarflexion of the foot. There is agreement with the observations of Deux et al. (12) on the mGM with the findings of the current study on the soleus muscle with the ankle in two positions. Okamoto et al. (35) also performed DTI under active contraction and found higher values for λ₁ and λ₂ as well as FA in the mGM, with an opposite effect for the TA, and attributed some of the changes to changes in focal temperature and perfusion. Of the previous studies on the DTI of muscle contraction, only Schwenzer et al. (39) measured orientation changes in the soleus under neutral and plantarflexed ankle positions. For the soleus, they report increase in λ₂ and λ₃, no change in λ₁, a decrease in FA, and a small change of 4° in the fiber orientation with respect to the z-axis. The discrepancies between the Schwenzer et al. (39) study and the current study could arise from methodological differences in acquisition and processing: 1) the lower resolution of the DTI data and 2) analysis of the soleus as one homogeneous subcompartment in the previous study.

Tseng et al. (43) and Wu et al. (46) proposed that λ₁, λ₂, and λ₃ of the of myocardial muscle corresponded to diffusion in the direction along the long axis of the fibers parallel to the myocardial sheets and normal to the sheets. This myocardial muscle model has been confirmed by histological examination as well (40). In contrast, there are currently no validated skeletal muscle models that correlate the observed diffusion tensor data to underlying architecture. Tentative skeletal models have been proposed; Galbán and colleagues (15, 16) were the first to suggest a model to explain the observed diffusion tensor eigenvalues in muscle. In their model of skeletal muscle diffusion, Galbán and colleagues (15, 16) proposed that λ₁, λ₂, and λ₃ represent diffusion along the long axis of the fiber within the endomysium and the cross-section of the muscle fiber. Karampinos et al. (25) proposed an interesting alternate model of skeletal muscle diffusion that took into account the cross-sectional asymmetry of muscle fiber geometry. In the former model λ₃ is predicted to be proportional to muscle fiber diameter, and in the latter model λ₃ and λ₂ are hypothesized to be the principal diameters of the muscle cross-section. Thus, a contracting muscle for a constant muscle volume will increase in diameter with a concomitant increase in λ₃ and possibly λ₂ as well, leading to a decrease in FA. A reverse trend is expected for an elongating muscle. Changes in λ₁ have been reported to be small, and this may arise from the fact that the skeletal muscle lengths are much longer than the diffusion length for typical diffusion times used in the DTI measurements, and thus λ₁ will not be affected by changes in skeletal muscle length.

Hatakenaka et al. (18) have built on diffusive models in skeletal muscle in the literature to propose a model for contraction. Sarcomeres (2 μm in length) are shortened on contraction, whereas cross-sectional diameter of muscle fiber (40–120 μm), as well as that of myofibrils (3 μm), increases. Since myofibril dimensions are of the order of the observed diffusion lengths (10 μm), the diffusion in the radial direction increases due to an increase in myofibril diameter; this is confirmed by observations on λ₃. Hatakenaka et al. (18) also suggested that sarcomere shortening may contribute to a decrease in λ₁. Other models propose that λ₁ should not change with contraction since whole muscle fiber lengths are far greater than diffusion lengths, resulting in λ₁ being insensitive to muscle fiber length changes (39). Neither model explains the observation in the current study that λ₁ increased with plantarflexion in the subcompartments; however, it should be noted that the most significant changes were seen in λ₃ (Table 2). However, an increase in λ₁ has been observed in the mGM and TA by Deux et al. (12) and by Okamoto et al. (35) on calf contraction. The increase in λ₃ can be attributed to an increase in muscle fiber diameter since the muscle contracts on plantarflexion. The small (but not significant) decrease in FA in the posterior and marginal soleus follows as a consequence of the slightly larger percent increase in λ₃ compared with λ₁. In contrast to the posterior and marginal soleus, there is a trend toward an increase in the FA in both subcompartments of the anterior soleus. It should be noted that in the anterior soleus, the fiber length did not decrease in the plantarflexed position, although the fiber clearly rotated in plane. The reason was that, at the location of the tracked fibers, the anterior soleus had a larger cross-section on plantarflexion (Figs. 5 and 7), and the length decrease from in-plane rotation was more than compensated for by the cross-sectional increase. This difference in fiber length changes with flexion between the posterior and anterior soleus may account for the observed differences in FA changes.

The limitation of these ROI-based measurements is that there are displacements between the rest and plantarflexed state so that an ROI placed in the same image space may not correspond to the same anatomic location. Care was taken in placing the ROIs in anatomically corresponding locations, and the leading eigenvector image was used for the ROI placement since the different muscle subcompartments could be most readily identified on it. A more accurate method would be to track corresponding points in the rest and plantarflexed images and calculate voxel-based changes.

Evaluation of fiber tracking.

Muscle diffusion tensor imaging has been validated on a rat model where fiber pennation angles from DTI were compared with those determined by direct anatomic inspection (10); the values were highly correlated. Fiber lengths determined from DTI on mice also showed good correlation with values obtained from dissection (19). Heemskerk et al. (21) also showed that reproducibility of fiber track lengths from in vivo human DTI studies was comparable with reproducibility from ultrasound measurements.

The fibers tracked in the medial and lateral subcompartments of the anterior soleus are in good agreement with fiber directions identified by Agur et al. (1). The latter study showed that fibers in the two subcompartments run superomedially and superolaterally, and this is confirmed in the current study as well (Fig. 7). The posterior soleus was shown by Agur et al. (1) to be arranged as short fibers in rows and columns. This is in part seen in Fig. 8, where one can see the parallel arrangement of the fibers. The soleus fiber lengths in the neutral and plantarflexed positions from this study are lower than that reported by Martin et al. (30) using ultrasound measurements. One reason for lower fiber lengths in the current study is that a very low threshold was set for angular deviations of successive fiber orientations to prevent fibers from being tracked across the different muscle subcompartments. This low threshold may have prevented fibers from tracking across voxels with even moderate changes in curvature, leading to shorter fiber lengths. An important observation is that fiber tracking is not robust in that many seed points give rise to either very small tracks or none.

It is important to recognize that there are several factors that limit fiber tracking of muscle in vivo. Although fibers tracked from DT-MRI reflect underlying muscle anatomy, they are also strongly influenced by image acquisition parameters, noise, the diffusion gradient strength and duration, and the fat admixture as well as the fiber-tracking algorithm (11, 21, 26). The choice of the angular threshold (12° in the current study) also influences the length of the fiber tracks; higher values generate clearly erroneous fibers, whereas lower values cause early termination (before the fiber reached the aponeurosis). Furthermore, slice anisotropy will also influence the accuracy of fiber track lengths, although the effect will be minimal for fibers that are oriented perpendicular to the slices. For fibers that are oriented oblique to the slice, volume averaging of orientations will decrease the accuracy of fiber orientations and impact the quality of tracking. It should be noted that for a muscle such as the soleus, which has a complex multipennate fiber pattern, it is difficult to select a slice orientation where all of the fibers run normal to the imaging plane. It should be noted though that muscle fiber curvature changes are very gradual so that, even with a 5-mm slice thickness, there may only be small errors due to interpolation between slices. However, even a one-voxel error in the slice direction translates to fiber length miscalculation by as much as 2× (slice thickness) (21).

In conclusion, the present study shows that the soleus subcompartments and the muscle fiber orientations in each can be noninvasively measured with DTI in humans at different ankle positions. Fiber orientations in the different subcompartments are in general agreement with earlier 3D cadaveric analysis of the soleus. Changes in the DTI indices at different ankle positions can be monitored accurately in the soleus subcompartments. The SNR requirements for robust fiber tracking in muscle are rather high and can be achieved by combining image averaging during acquisition with postprocessing to regularize the diffusion tensors.

GRANTS

This study was supported by National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant RO1-AR-53343.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.