AGE RELATED DIFFERENCES IN STRAIN RATE TENSOR OF THE MEDIAL GASTROCNEMIUS MUSCLE DURING PASSIVE PLANTARFLEXION AND ACTIVE ISOMETRIC CONTRACTION USING VELOCITY ENCODED MR IMAGING

Abstract

Purpose

The strain rate (SR) tensor measures the principal directions and magnitude of the instantaneous deformation; this study aims to track age related changes in the 2D SR tensor in the medial gastrocnemius during passive joint rotation and active isometric contraction.

Methods

SR tensors were derived from velocity encoded magnetic resonance phase-contrast images in nine young (28 yrs) and eight senior (78 yrs) women. Strain rates along and in the cross-section of the fiber were calculated from the SR tensor and used to derive the out-plane SR. Age related and regional differences in the SR eigenvalues, orientation, and the angle between the SR and muscle fiber (SR-fiber angle) were statistically analyzed.

Results

SR along the fiber was significantly different between the cohorts during isometric contraction with higher values in the young (P<0.05). The SR-fiber angle was larger in the young for both motion types but this difference was not statistically significant. Significant regional differences in the SR indices was seen in passive joint rotation (P<0.05) for both cohorts.

Conclusion

SR mapping reflects age related and regional differences during active and passive motion respectively; this may arise from differences in contractility (active motion) and elastic properties (active and passive motion).

INTRODUCTION

The objective quantification of regional muscle deformation is a valuable clinical tool to evaluate normal and diseased muscle. Strain and strain rate (SR) are kinematic properties that can be derived from velocity encoded magnetic resonance (MR) images and have been used to characterize myocardial and lingual deformation (1, 2, 3, 4). Strain describes how the tissue is deformed with respect to a reference state and requires three-dimensional (3D^al) tissue tracking. SR describes the rate of regional deformation and does not require 3D^al tracking or a reference state since it is an instantaneous measure. A positive SR indicates a local expansion while a negative SR indicates a local contraction. Strain/SR are not scalar quantities, rather for 3D^al objects, three principal directions (and magnitudes) of deformation/deformation rate are required to completely characterize the deformation in tissue.

Shin et al evaluated the strain as a scalar quantity from 2D phase contrast velocity encoded MR images of the calf muscle and reported heterogeneity of strain along the proximal distal muscle directions as well as along the muscle fiber (5). Zhong et al. used displacement encoding with stimulated echoes MRI to quantify two dimensional strain fields in the biceps brachii (6). The latter study revealed that the first and second principal strains were non-uniform along the center-line region of the biceps brachii. Englund et al. mapped the 3D strain tensor and diffusion tensor in regions of interest in the superficial and deep compartments of the anterior tibialis (7). The strain was estimated by measuring the displacement of tag lines between the maximum contracted and relaxed states. Their study revealed a planar strain pattern where the principal shortening direction deviated from the muscle fiber direction (7).

SR tensor mapping provides important information on both the magnitude and orientation of the SR along its principal axes. The orientation of the principal axes of shortening will provide information on the alignment with respect to the muscle fiber orientation. SR in the fiber cross section provides information about the deformation in the plane perpendicular to the muscle long axis allowing one to explore possible deformation asymmetry. The SR orientation as well as the deformation asymmetry potentially enables inferences on the geometry of the muscle fiber arrangement as well as on the material properties of the non-contractile tissue (muscle’s extracellular matrix). There are known structural and material changes with age in muscle (8, 9); indices derived from the SR tensor could potentially be used as imaging biomarkers of these changes. During submaximal isometric muscle contraction, the medial gastrocnemius (MG) has been identified to display the highest activity (in terms of % electromyography) as well as highest glucose uptake (using positron emission tomography) (10). These results indicate that the MG is heavily involved in submaximal isometric muscle contraction. The current paper thus focuses on analyzing the 2D^al SR tensor and the muscle fiber orientation of the MG during passive joint rotation and isometric contraction in a cohort of senior and young subjects. Deformation during passive rotation is determined by the elastic properties of the fibers as well as the extracellular matrix while in isometric contraction, deformation depends on the muscle contractility in addition to elastic properties. Thus, age related differences in muscle mechanical properties and contractility can be explored with these two types of motion. The proposed MR imaging-based technique will yield valuable information not ascertainable by physical examination. Ultrasound imaging can map the strain tensor but the method is challenging and extremely susceptible to noise (11). Recent work from our group exploring age related changes in architecture and microstructure of the gastrocnemius muscle using Diffusion Tensor Imaging revealed aging related decreases in fiber length and pennation angles and increases in the diffusion indices that reflect fiber atrophy and increased fibrosis (12). Age related structural changes are related to and result in the functional changes reported in the current paper.

METHODS

SR Tensor

The 2D spatial gradient of the velocity vector, L was calculated from:

$$L=\left[\begin{array}{cc}\hfill \frac{\partial u}{\partial x}\hfill & \hfill \frac{\partial u}{\partial y}\hfill \\ \hfill \frac{\partial v}{\partial x}\hfill & \hfill \frac{\partial v}{\partial y}\hfill \end{array}\right]$$ [1]

where u and v are the x and y components of the velocity vector. The symmetric part of the SR tensor was calculated from:

$$D=0.5(L+L^T)$$ [2]

The 2×2 SR tensor, D, was diagonalized to obtain the eigenvalues and eigenvectors. The values were not sorted based on magnitude, rather the positive and negative values at each voxel (in s⁻¹) and their corresponding eigenvectors were stored as separate images. Table 1 lists the deformation direction corresponding to the positive and negative eigenvalues for the different movements during passive and isometric modes of motion. SR_fiber refers to the eigenvalue that has the same sign of the deformation as the muscle fiber whereas SR_in-plane refers to the eigenvalue that has a sign opposite to the deformation of the muscle fiber. The angle made by the eigenvector corresponding to the SR_fiber was measured with respect to the y-axis and is referred in the rest of the paper as the SR-angle. This convention is not followed for the SR-angle temporal plots where the SR-angle refers to the angle of the positive eigenvector with the y-axis; this maintains continuity through the change from contraction (plantarflexion) to relaxation (dorsiflexion).

Table 1.

Direction and sign of the Strain Rate for passive joint rotation and isometric contraction.

Motion	Phase	Positive eigenvalues	Negative eigenvalues
Passive Joint Rotation	Dorsiflexion	SRfiber	SRin-plane
	Plantar flexion	SRin-plane	SRfiber
Isometric Contraction	Contraction	SRin-plane	SRfiber
	Relaxation	SRfiber	SRin-plane

SR_out-plane, which is the SR in the fiber cross section perpendicular to the imaging plane (i.e., the plane of the fibers) was derived from the SR measured in the other two directions (Figure 1). This can be best understood based on the assumption of volume incompressibility of muscle tissue: a local expansion along the muscle will be accompanied by a local contraction in the plane perpendicular to the fiber. For a 3D volume like muscle that is incompressible (13, 14), the sum of the three strain rates should be zero. Here, only the 2D tensor is calculated, so the sum of the measured two eigenvalues should yield the magnitude of the third eigenvalue with an opposite sign.

$$\mathbf{S}{\mathbf{R}}_{\mathbf{\text{out}}\mathbf{-}\mathbf{\text{plane}}}=-(\mathbf{S}{\mathbf{R}}_{\mathbf{\text{fiber}}}+\mathbf{S}{\mathbf{R}}_{\mathbf{\text{in}}\mathbf{-}\mathbf{\text{plane}}})$$ [3]

Figure 1.

Schematic of the muscle fiber and the SR in the three orthogonal directions illustrated for muscle fiber contraction (a negative SR). The eigenvalue of the SR tensor which is negative is labeled the ‘fiber-SR’ since its deformation has the same sign as the contracting fiber. The second eigenvalue is labeled the ‘in-plane SR’ and will have a positive value associated with extension in the fiber cross-section. The eigenvalue in the third orthogonal direction, ‘out-plane SR’, is derived from the other two assuming volume incompressibility. Three potential deformations in the fiber cross section are illustrated: moderate asymmetry (b), severe asymmetry (c), and deformation of opposite signs along the principal axes of the fiber cross-section (d). The schematic is not drawn to scale; rather it illustrates the relative magnitude and sign of local deformations in the fiber cross-section.

Figure 1a is a schematic of the muscle and the principal directions of the SR as well as their labels; the situation corresponding to muscle shortening is shown as well as the magnitude and directions of deformation in the fiber cross section. Three types of deformation in the fiber cross section are illustrated: moderately (Fig. 1b) and severely (Fig. 1c) asymmetric with same direction of deformation along both axes and asymmetric with different directions of deformation along the two axes (Fig. 1d).

In Vivo Experiments

Subjects

Nine young (27.5 ± 4.8 yrs, height: 159.6 ± 6.5 cm, mass: 54.6 ± 7.3 kg) and eight senior (77.6 ± 7.3 yrs, height: 154.3 ± 2.9 cm, mass: 57.9 ± 3.7 kg) female subjects were included in this study after informed consent; all these subjects were included in the passive study. Further scans during isometric contraction of the plantarflexor muscles were obtained in a subset consisting of six young (26.1 ± 2.3 yrs, height: 158.6 ± 5.6 cm, mass: 50.8 ± 3.7 kg) and six senior (76.7 ± 8.3 yrs, height: 153.0 ± 2.0 cm, mass: 57.4 ± 4.3 kg) female subjects. Only female subjects were recruited to eliminate the confounding effects of gender differences since the total subjects was limited by the number of senior subjects who could perform the MR study. The criterion for inclusion was that subjects should be moderately active. Subjects participating in competitive sports or those with any surgical procedures on the lower leg were excluded. The study was approved by the Medical Research Ethics Board of University of California San Diego and conformed to all standards for the use of human subjects in research as outlined in the Declaration of Helsinki on the use of human subjects in research.

MR imaging

MR imaging was performed on a 1.5 Tesla Signa HDx MR scanner (GE Medical Systems, Milwaukee, WI), using a custom-made (Millennial MRI Co., NY), 8-channel 123 phased-array lower-leg coil system. Imaging was performed with the subject lying supine, feet first, with the dominant leg strapped to a specially designed foot-pedal device (5, 15), which was placed on top of the RF coil. The dominant leg was defined as the leg preferentially used to regain balance when unexpectedly jostled. Briefly, the foot-pedal device is a MR-compatible, computer-controlled, servo motor driven device, which is capable of rotating the foot through a pre-programmed angular range of motion. The ball of the foot rested on a carbon-fiber plate, onto which an optical pressure transducer (Luna Innovations, Roanoke, VA, USA) was glued, and which could rotate along with the foot. Pressure against the plate was detected by the transducer which was subsequently converted to a voltage and used to trigger the MR image acquisition. The voltages were converted into measures of torque (Nm) based on a calibration of the system using disc weights. Images were acquired under two experimental conditions: (i) during submaximal, isometric contraction of the plantarflexor muscles (35% of the individual maximum voluntary contraction (MVC)) and (ii) during passive rotation of the ankle joint over a 30° range of movement (from ~10° of dorsiflexion to ~20° of plantarflexion). MR image acquisition was completed in ~70 cycles; thus it is important to ensure consistency of motion. Therefore, for isometric contractions, the subject was provided with the feedback of the actual force generated by the subject superposed on the desired force curve to facilitate consistent contractions. During passive rotation of the ankle joint, the trigger pulse was directly derived from the servomotor driving the foot pedal device, so that the image acquisition always started when the foot was at its most plantarflexed position.

The MR images used in this report include high resolution water saturated oblique sagittal fast spin echo (FSE) images of the MG (TE: 12.9 ms, TR: 925 ms, NEX: 4, FA: 20°, slice thickness: 3 mm, interslice gap: 0 mm, FOV: 30 × 22.5 cm, 512 × 384 matrix). This sequence provides a high tissue contrast for the high signal fascicles in the background of suppressed muscle signal and was used to locate fascicle end points. The slice that best depicted the fascicles was selected for the Velocity-Encoded Phase Contrast (VE-PC) scan that followed. The VE-PC, single oblique sagittal slices (TE: 7.7 ms, TR: 16.4 ms, NEX: 2, FA: 20°, slice thickness: 5 mm, FOV: 30 cm × 22.5 cm (partial phaseFOV0.75), 256 × 192 matrix, 4 views/segment, 1 slice, 22 phases, 10 cm·s−1 3D velocity encoding). This resulted in 70 repetitions [(192×2×0.75)/4 =70] for the image acquisition. Twenty-two phases were collected within each contraction-relaxation cycle of ~2.5 s (isometric contraction) and plantarflexion-dorsiflexion movement cycle of 3.4 s (passive joint rotation) (Supplementary videos, RV-vel.mov and SI-vel.mov, show the phase contrast cine images).

Force measurements

During isometric contractions, VE-PC images were acquired at 35% of the individual MVC. The choice of 35%MVC was based on the ability of the senior cohort to sustain this force level for 70 repetitions. MVC was determined for each subject as the best of three trials recorded prior to MR imaging. During the subsequent execution of the ~70 contraction-relaxation cycles, torques were recorded at a sampling frequency of 200 Hz and averaged to produce curves of mean torque. To estimate muscular forces, the measured torque was divided by the Achilles tendon moment arm length, which was measured on an oblique sagittal-plane FSE MR images of the ankle (one slice passing through the center of the ankle joint) and defined as the perpendicular distance between the axis of the tendon and the joint’s center of rotation, assumed to coincide with the midpoint of a circle fitted around the talus.

Image Analysis

The flowchart of the image processing including calculation of strain tensors and muscle fiber orientation is shown in Figure 2.

Figure 2.

Flowchart of the image processing and analysis to determine the SR indices and muscle fiber orientation.

Preprocessing

Phase images were corrected for phase shading artifacts which arise from sources (B0 field inhomogeneities, chemical shift) other than the velocity encoding gradient (15). Velocity images were extracted from the phase corrected data. The velocity images are inherently noisy and the calculation of the SR involves estimation of the spatial gradients of the velocity images. As gradient images are sensitive to noise, an anisotropic diffusion filter was first applied to the velocity images. The anisotropic diffusion filter reduces noise in homogeneous regions while preserving edges; thus preserving the effective resolution of the velocity images. The filter was defined by the equation:

$$c(\Vert \nabla I\Vert )=\text{exp}(-{(\Vert \nabla I\Vert /K)}^2)$$ [4]

was applied iteratively to reduce noise in homogeneous regions. In the above equation, ‘c’ is the diffusion coefficient, ‘I’ is the image to be denoised, and ‘∇I’ is the image gradient. Low values of K (=2) and number of iterations (=10) were used as the phase contrast images do not have strong edge content.

ROI measurements

The entire length of the MG, for each subject was divided into three regions based on the distance from the most distal point of the muscle: bottom 25% (distal), mid-50% (middle), top 25% (proximal). Regional analysis of scalar indices derived from the SR tensor (SR eigenvalues, SR-angle) was performed on ROIs selected on the magnitude images at the proximal (ROI1), middle (ROI2) and distal (ROI3) regions (Figure 3). The size of the ROI was set at 7×7 voxels for the proximal and middle regions and at 5×10 for the distal region to accommodate the muscle taper. The ROI size was determined from empirical examinations of the biggest size ROI that could be placed within the region boundaries while avoiding the low intensity fat layers that ran along the fascicles. In order to ensure that the same anatomic region was reported, each pixel in the ROI was tracked (with respect to the first frame) to locate the new pixel position in successive frames, creating a frame based ROI. Figure 3 a–d shows the images with the ROIs that change both location and shape; ROIs changed between 5 to 20% in successive frames but the number of points was kept constant to ensure the average was based on the same number of points/frame). For the passive mode, the SR indices were identified at the peak values of the SR during dorsiflexion and plantar flexion. For the isometric mode, average ROI values of the SR indices were extracted at the same force level (159.7 N, chosen as the smallest peak force achieved by a subject (senior) in the two cohorts). The force recording was at much higher frequency than the MRI temporal resolution; to ensure accuracy of the SR indices at the required force, the temporal curves of the MR data were interpolated to the sampling frequency of the force curve. An additional analysis was also performed using values of the SR indices extracted at the location of the peak in the SR_fiber in the compression cycle. It should be noted that at the peak force, the SR values are close to the zero crossing as the deformation of the fiber transitions from compression to relaxation. The relevant parameters reflecting the 35% MVC are acquired at the location of the peak in the SR_fiber that just precedes this zero crossing.

Figure 3.

Four frames of the magnitude image from the dynamic phase contrast images acquired on one of the subjects during passive joint motion (dorsiflexion cycle). The foot angles in these frames correspond to 20° of plantarflexion (a); 10° of plantarflexion (b), 0° neutral (c), and 100 of dorsiflexion (d). The location of three ROIs (proximal: ROI1, middle: ROI2, distal: ROI3) placed along the gastrocnemius and used in the analysis is also shown (yellow boxes). The pixels in each ROI and the fascicle end points were tracked in each frame to obtain pixels corresponding to the same anatomical tissue through the dynamic cycle (a-d). ROI changes in both size and location can be appreciated by comparing the four frames. Fascicle end point tracking was used to calculate the orientation of the fiber through the cycle.

Muscle fiber tracking

Muscle fiber orientation was tracked by locating the endpoints of the fatty layers (at six locations) in the FSE images (the intramuscular fat runs parallel to the fascicles) and tracking these points on the dynamic data with the first frame as reference. The VE-PC cines were used to track the coordinates of these points across the contraction-relaxation (isometric contractions) or plantarflexion-dorsiflexion (passive joint rotations) cycle (Fig. 3b–3d). Muscle fiber orientation with respect to the positive y-axis was calculated at each phase using the tracked end points. The six locations were grouped into three groups (2 distal, 2 middle, 2 proximal) and averaged to represent the typical MG behavior in these regions. The angle subtended by the SR (SR_fiber) and the muscle fiber direction was determined and is referred to, in the rest of the paper, as the SR-fiber angle. Pennation angles and fiber lengths derived by this method agreed well the ultrasound data on similar cohorts (16, 17, 18).

Statistical analyses

The outcome variables of the analysis are the eigenvalues of the strain tensor (SR_fiber, SR_in-plane, SR_out-plane) and the strain tensor and fiber angles (SR-angle, fiber-angle, SR-fiber angle). All the SR eigenvalues are quoted as ×1000 s⁻¹ in the paper. Normality of data was tested using both the Shapiro-Wilk test and by visual inspection of Q-Q plots. For the SR indices obtained during isometric contraction, differences between age groups and intramuscular regions as well as potential interaction effects were assessed using two-way factorial ANOVAs (age × region). Here, Levene’s test was used to test the assumption of homogeneity of variance and, in case of significant ANOVA results for the factor ‘region’, Bonferroni-adjusted independent sample t-tests were used for posthoc analyses. The indices derived at the peak SR_fiber as well as the SR indices obtained during passive rotation of the ankle joint were not distributed normally (Shapiro-Wilk test, P < 0.05). In the absence of a non-parametric alternative to a factorial ANOVA, differences between age groups and muscle regions for these parameters were independently tested with Mann-Whitney U- and Kruskal-Wallis tests, respectively. For the latter, Bonferroni-adjusted U-tests were also used for posthoc analyses. Data are reported as mean ± SD for the variables that are normally distributed, and median ± Interquartile range (IQR) for those outcome variables that are not normally distributed. IQR is a descriptive statistic for the spread of the data and is equal to the difference between the upper and lower quartiles and the median is the corresponding measure of central tendency. For all tests, the level of significance was set at α = 0.05. The statistical analyses were carried out using SPSS for Mac OSX (SPSS 21.0, SPSS Inc., Chicago, IL, USA).

RESULTS

Figure 4 shows the SR eigenvalues for one young and one senior subject at plantarflexion during isometric contraction. Figure 5 shows the negative and positive eigenvalue/eigenvector maps respectively for passive joint rotation (top row) and for isometric contraction (bottom row) for a zoomed region in the MG. Supplemental videos of the streamline tracking (Positive_SR.mov and Neg_SR.mov) of the SR eigenvectors during passive joint rotation are included.

Figure 4.

The strain rate images along the three principal axes are shown for one young (first row) and one senior (second row) subject during isometric contraction. All the images have the same color map to facilitate comparisons. The SR_fiber and SR_in-plane have smaller magnitudes in the senior subject (pale shades). The SR_out-plane image has a magnitude that is much smaller than the magnitude of the SR_fiber and SR_in-plane images for both young and senior.

Figure 5.

Eigenvectors (lines) corresponding to the eigenvalues listed below are shown superposed on the eigenvalue images for a young subject. A zoomed area of the GM is shown during passive joint rotation (first row): SR_in-plane, negative eigen-value, dorsiflexion (a), SR_fiber, positive eigenvalue, dorsiflexion (b), SR_fiber, negative eigenvalue, plantar flexion (c), and SR_in-plane, positive eigenvalue, plantar flexion (d). A similar region of interest shown during isometric contraction (second row): SR_in-plane, negative eigenvalue, contraction (a), SR_fiber, positive eigenvalue, contraction (b), SR_fiber, negative eigenvalue, relaxation (c) and SR_in-plane, positive eigenvalue, relaxation. The outline of the medial gastrocnemius (in black) was manually contoured for ease of visualization. Area to the right of the GM is fat tissue. The pixel color is assigned according to the magnitude of the eigenvalue and ranges from 0 s⁻¹ (green) to −800 s⁻¹ (blue) for the negative eigenvalue images and from 0 s⁻¹ (red) to 800 s⁻¹ (yellow) for the positive eigenvalue images (note: values were scaled by 1000). In dorsiflexion, the negative strain rate direction is approximately perpendicular (a), while the positive strain rate is approximately parallel to the fiber direction (b), while the reverse is true for the plantarflexion phase (c,d). In the contraction phase the negative strain rate direction is approximately parallel (e) while the positive strain rate is approximately perpendicular to the fiber direction (f), while the reverse is true for the relaxation phase (g,h). Unlike the passive motion, the SR maps show regional variability in the SR eigenvector orientations.

Isometric Contraction

The temporal variation of the SR eigenvalues and SR-fiber angles with isometric contraction is shown in Figure 6 for the young and senior cohorts. The large jumps in the temporal plots of the SR-angle occur when the positive SR eigenvector direction changes abruptly as the cycle alternates between muscle relaxation and contraction. The value of the SR indices at the force value corresponding to 159.7 N and at the peak of the SR_fiber eigenvalue is shown in Table 2. For the same force value analysis, magnitude of SR_fiber was significantly smaller in senior women (F(1,35) = 11.367, P = 0.002). Differences between muscle regions and interaction effects were not significant. For the SR_out-plane, there was a trend towards larger values in the young cohort (F(1,35) = 3.360, P = 0.077). Differences between muscle regions similarly just failed to reach significance (F(2,35) = 3.002, P = 0.065). Here, absolute values of SR_out-plane tended to be smaller in distal as compared to proximal muscle regions (P = 0.099). The SR_in-plane, also tended to be larger in the young cohort (F(1,35) = 3.134, P = 0.087). ANOVA results further revealed that the factor ‘region’ affected SR_in-plane by trend (F(2,35) = 3.137, P = 0.058). Posthoc pairwise comparisons to follow up this finding showed that values tended to be larger in distal as compared to proximal muscle regions (P = 0.070). No significant age × region interaction effects were observed for the SR_in-plane. SR-angle were significantly smaller in the senior cohort (F(1,35) = 5.827, P = 0.022), with neither significant differences between muscle regions nor statistical interaction effects. Similarly, the SR-fiber angle was smaller in senior women in all muscular regions, although these differences failed to reach significance. No differences between muscle regions or interaction effects were observed.

Figure 6.

Temporal plots of the negative (a,e), positive (b,f), thru-plane (c,g) SR values and SR angle (d,h) measured with respect to the y-axis for young (left) and senior (right) subjects during isometric contraction. Plots represent the average over the three ROIs and subjects in each cohort.

Table 1.

Strain rate indices and muscle fiber orientation in the young and senior cohorts for isometric contraction. (same level of force and peak SR_fiber eigenvalues)

Isometric (same force level)		PROXIMAL	Young MEDIAL	DISTAL	PROXIMAL	Senior MEDIAL	DISTAL
SRfiber * [×1000 s−1]	mean ± SD1	−350.8 ± 92.8	−382.7 ± 94.4	−326.3 ± 161.7	−197.9 ± 114.8	−192.8 ± 131.2	−214.6 ± 187.1
SRin-plane [×1000 s−1]	mean ± SD	237.7 ± 133.8	240.8 ± 90.2	357.5 ± 110.9	154.9 ± 131.5	201.8 ± 116.9	267.5 ± 128.7
SRout-plane [×1000 s−1]	mean ± SD	113.1 ± 107.4	141.9 ± 68.1	−31.2 ± 139.2	43 ± 191.2	−9 ± 68.8	−52.9 ± 168.5
SR angle* [degrees]	mean ± SD	49.1 ± 5.9	51.5 ± 8	50.8 ± 2.4	38.3 ± 17.9	42.2 ± 15	44.6 ± 7.8
fiber angle [degrees]	mean ± SD	16.2 ± 5.2	19.8 ± 5.7	22.2 ± 4.9	18.5 ± 7.3	18.4 ± 4.6	16.9 ± 4.5
SR–fiber angle [degrees]	mean ± SD	32.9 ± 8.7	31.7 ± 12	28.6 ± 4.9	19.8 ± 21.1	23.8 ± 16.5	27.7 ± 10.7

Isometric (peak SRfiber eigenvalue)		PROXIMAL	Young MEDIAL	DISTAL	PROXIMAL	Senior MEDIAL	DISTAL
SRfiber * [×1000 s−1]	mean ± SD	−454.6 ± 79.4	−436.2 ± 125.5	−385 ± 204.4	−269.7 ± 122	−274.7 ± 194.6	−299.7 ± 285.4
SRin-plane* [×1000 s−1]	mean ± SD	279.5 ± 121.5	238.1 ± 85.1	384.5 ± 134.6	191.1 ± 132.4	160.4 ± 75	189.7 ± 107.2
SRout-plane [×1000 s−1]	mean ± SD	175.1 ± 122.6	198.1 ± 107.3	0.4 ± 183.6	78.6 ± 178.8	114.2 ± 244.9	109.9 ± 299.9
SR angle [degrees]	mean ± SD	49.6 ± 13.3	51.4 ± 4.7	49 ± 1.7	43.5 ± 16.6	46.4 ± 13.3	41.4 ± 7
fiber angle [degrees]	mean ± SD	16.1 ± 5.2	19.6 ± 5.7	21.7 ± 4.5	16.5 ± 4.5	17.7 ± 5.2	17.6 ± 7.6
SR–fiber angle [degrees]	mean ± SD	33.5 ± 14.4	31.8 ± 9.3	27.3 ± 5	27 ± 20.5	28.7 ± 15.2	23.8 ± 7.7

^*– significant differences between Young and Senior cohort

¹Standard Deviation

The SR indices extracted at the peak of the SR_fiber eigenvalue yielded a similar analysis to that at the same force level (Table 2). SR_fiber values (magnitude) were significantly smaller in the senior cohort (U = 64.0, P = 0.001); no significant differences between muscle regions were found. Similarly, a two-way ANOVA performed to examine differences in the peak SR_in-plane revealed a significant effect for the factor ‘age’ (values smaller in senior women; F(1,35) = 10.450, P = 0.003) but there were neither differences between different proximo-distal locations nor age × region interaction effects. Peak SR_out-plane values did not differ statistically between age groups or muscle regions.

Passive Joint Rotation

The temporal variation of the SR eigenvalues and SR-fiber angles with passive joint rotation is shown in Figure 7 for the two cohorts. The value of each of these indices at the peak value of plantarflexion and dorsiflexion cycles respectively is shown in Table 3. For the peak plantarflexion, Mann-Whitney U-tests showed that the differences in the medians of all three SR indices (median of all regions), were not significantly different between age groups. Comparisons between muscle regions showed no statistical differences for SR_fiber, in spite of increasing absolute median values (median of both age groups) from the proximal, to the middle, and the distal muscle region. Kruskal-Wallis tests were however significant for SR _in-plane (χ² = 11.816, P = 0.003). Here, the median indices measured in the distal section were significantly larger than those observed in the proximal (P < 0.001) and middle (P = 0.044) muscle region. Very similar results were obtained for the parameter SR_out-plane. Posthoc Mann-Whitney U-tests to follow up the significant Kruskal-Wallis test (χ² = 11.884, P = 0.003) revealed that the absolute median values measured distally were significantly smaller than those observed in the proximal (P = 0.002) or middle (P = 0.014) muscle region (the SR_out-plane in the distal region had a sign opposite to the SR_in-plane).

Figure 7.

Temporal plots of the negative (a,e), positive (b,f), thru-plane (c,g) SR values and SR angle (d,h) measured with respect to the y-axis for young (left) and senior (right) subjects during passive joint rotation. Plots represent the average over the three ROIs and subjects in each cohort.

Table 3.

Strain rate indices and muscle fiber orientation in the young and senior cohorts for passive joint rotation at the peak SR_fiber eigenvalue for plantar flexion and dorsiflexion

Passive (plantar flexion)		PROXIMAL	Young MEDIAL	DISTAL	PROXIMAL	Senior MEDIAL	DISTAL
SRfiber [×1000 s−1]	median ± IQR1	−272.3 ± 128.9	−300.7 ± 122.3	−307.6 ± 142.2	−300.8 ± 311	−281.4 ± 120.2	−225.4 ± 363.5
SRin-plane†,‡ [×1000 s−1]	median ± IQR	197.9 ± 126.8	235.6 ± 154.5	288.9 ± 81	217.9 ± 103.9	189.3 ± 194.1	322.9 ± 299.9
SRout-plane†,‡ [×1000 s−1]	median ± IQR	85.1 ± 149.7	57 ± 114.8	32.9 ± 85.9	87.6 ± 303.7	81.8 ± 70.9	−30.7 ± 159.9
SR angle†,‡ [degrees]	mean ± SD2	57.5 ± 8.3	52.8 ± 5.6	45.1 ± 2.4	53.5 ± 4.6	51.5 ± 5.9	44.7 ± 8.8
fiber angle [degrees]	mean ± SD	12.1 ± 5.2	15.9 ± 5.8	20.2 ± 3.9	15.5 ± 7.2	19.1 ± 7.6	20.4 ± 7.9
SR–fiber angle†,‡ [degrees]	mean ± SD	45.4 ± 9	37 ± 9.5	24.9 ± 6.2	37.9 ± 8.4	32.4 ± 11.2	24.3 ± 14.1

Passive (dorsiflexion)		PROXIMAL	Young MEDIAL	DISTAL	PROXIMAL	Senior MEDIAL	DISTAL
SRfiber† [×1000 s−1]	median ± IQR	−191.4 ± 173	−257.9 ± 164	−365.2 ± 152.9	−281.6 ± 319.5	−310.3 ± 428.8	−322.3 ± 478.8
SRin-plane [×1000 s−1]	median ± IQR	329.6 ± 194.8	318.9 ± 116.2	358.7 ± 284.1	359.6 ± 465.2	334.1 ± 400.6	287.4 ± 620.2
SRout-plane† [×1000 s−1]	median ± IQR	−111.6 ± 51.1	−32.1 ± 134.7	−11.4 ± 180	−89.8 ± 221	−87.3 ± 152	37.2 ± 107.4
SR angle†,‡ [degrees]	mean ± SD	58.2 ± 4.3	54.4 ± 4.3	47.2 ± 2	56.2 ± 8.4	53.5 ± 6.1	52.2 ± 12
fiber angle [degrees]	mean ± SD	13.7 ± 5.1	19.7 ± 6.3	21.5 ± 5	19.5 ± 7.3	24.4 ± 7.7	25.1 ± 7.9
SR–fiber angle†,‡ [degrees]	mean ± SD	44.5 ± 6.5	34.7 ± 7.8	25.7 ± 5.5	36.7 ± 11.2	29.1 ± 11.8	27.1 ± 11.7

^†– significant differences between PROXIMAL and DISTAL

^‡– significant differences between MEDIAL and DISTAL (all P < 0.05)

¹Interquartile Range: difference between the upper and lower quartiles

²Standard Deviation

SR-angle did not differ between age groups. However, a two-way factorial ANOVA showed significant effects for the factor ‘region’ (F(2,50) = 12.592, P < 0.001). Here, posthoc pairwise comparisons revealed that the values in the distal muscle region were significantly smaller than those in the middle (P = 0.005) and proximal (P = 0.000) ROIs. Similarly, SR-fiber angles did not differ between age groups but statistical differences were found between muscle regions (F(2,45) = 10.364, P < 0.001). The SR-fiber angles were smaller in the distal as compared to the middle (P = 0.030) and proximal (P < 0.001) muscle region. The values of the SR indices extracted at peak dorsiflexion and the results of the statistical analysis are also listed in Table 3. No age related differences were seen while the regional differences for values extracted at peak dorsiflexion followed a pattern similar to that obtained at peak plantarflexion.

DISCUSSION AND CONCLUSION

A significant increase in strain rate magnitude was seen in the young cohort at isometric contraction determined at either the same force level and at the peak of SR_fiber values. A recent publication from our group (19) analyzing the 1D scalar strains along the fascicle on the same subjects as reported here found no significant differences in fascicle strains between the young and senior cohorts at the same force level (in spite of the significantly greater tendon compliance in seniors) and a significantly higher fascicle strain in the younger cohort when the two groups were compared at 35% MVC. In the latter paper, Csapo et al. speculated about mechanisms decreases fascicle strains in the senior cohort (despite a more compliant tendon). These are (i) fascicle slack which increases with fiber length and may result in a higher slack in the young cohort that translates to larger strain in muscle fibers and (ii) an increase in muscle stiffness with age which may be related to remodeling of the extracellular matrix. Computational models have predicted that a stiffer extracellular matrix will result in reduced fascicle strain as well as force output (20). In contrast to the 1D strain measurements, the current study shows a significant increase in the SR magnitude in the young cohort even when the comparison is performed at the same force level. The reason for the discrepancy may be related to smaller SR-fiber angles in the senior group. The fascicle strain is a measure of the projection of the strain along the principal axes of shortening along the fascicle. Since SR-fiber angles are larger for the young cohort, the larger strain is offset by the smaller projection along the fascicle. This finding also emphasizes the need to measure strains along the principal axis of shortening rather than along the fascicle orientation.

The asymmetry of the deformation in the muscle cross-section is evident from the much lower strain rates in the SR_out-plane for both isometric and passive joint rotation and in both cohorts. Previous studies have reported asymmetric deformation in animal models (21) and in human subjects (7, 22). Two potential mechanisms have been hypothesized to explain asymmetric deformations: one related to the orientation of the curvature of fibers in the 3D^al muscle structure and the other to the incorporation of tensile materials (such as costameres) oriented along the through-plane axis of the fiber to limit relaxation in that direction (22). For the SR_out-plane, there was a trend towards larger values in the young cohort during isometric contraction. If the integrity of the costameres is compromised in the senior cohort, the relaxation in the through plane would be expected to be less limited, leading to decreased asymmetry; this is contrary to the current findings. Alternately, the asymmetry may be related to the curvature of muscle fibers which are also known to increase with isometric contraction (23); however age related changes in curvature have not been investigated. Another plausible explanation for the increase in deformation asymmetry with age may be related to the presence of more eccentric fiber cross-sections in the aging muscle (24). This implies that aging muscles fibers are already flattened and tightly packed in one direction and deformation along this direction may be limited.

Regional differences in eigenvalues were significant during passive joint motion in contrast to isometric contraction where there were no significant regional differences in any of the SR indices. It is possible that during the isometric contraction, fibers along the entire length are recruited at the same level as opposed to the passive joint rotation, which can be supported with significantly less SR at the proximal end. SR_in-plane and SR_out-plane heterogeneity (significant for passive motion) is related to the asymmetry of deformation in the fiber cross section and its regional variation. The trend in both cohorts is illustrated in Figure 1 from the proximal (Fig. 1b) to the distal (Fig. 1d). The increasing deformation asymmetry at the distal end may be related to the fiber packing density along the muscle length that increases from proximal to distal regions. Earlier studies have also reported regional heterogeneity in strain in the calf muscles (5) and in the brachis plexus (6).

The SR angles in both cohorts and modes of motion are larger than the pennation angle of the fiber. The direction of the SR may potentially define an effective pennation angle that is higher which translates to larger physiological cross-sectional area and, consequently, greater total force. The smaller SR-angles (smaller effective pennation angles) in the senior cohort (significant difference between cohorts in isometric contraction, same force level only) may contribute to the force loss with aging, which is known to be disproportionate to the loss of mass (16, 17).

The SR-fiber angle is in approximate agreement with the findings by Englund et al. where the difference between the lead eigenvector of the diffusion tensor (fiber direction) and the negative strain tensor directions was ~24° for the deep compartment and ~40° for the superficial compartment of the anterior tibialis muscle (7). The latter paper postulated that the average strain vector direction will be biased away from the fiber direction toward the longest fibers if different fiber lengths undergo the same relative shortening and this was potentially mediated by the inter-fiber connections formed by the intramuscular connective tissue network. A similar hypothesis can be advanced to account for the SR-fiber angles found in the current paper as the distal fibers in the MG are known to be longer and thus, the SR eigenvector is rotated toward it. The SR-fiber angle was lower for the senior subjects as compared to the young cohort (trend toward significance during isometric contractions). The smaller SR-fiber angle in the senior cohort may be due to reduced heterogeneity in fiber length and pennation angle and reduced lateral transmission of force from loss of integrity in the connective tissue; both of these have been shown in the aging rat model (25).

The limitations of this study are as follows. The total of 70 repetitions required for the image acquisition could potentially cause muscle fatigue especially at higher MVCs; this limited the study to 35%MVC. The number of subjects in the two cohorts is small; however this was still sufficient to find significant age related and regional differences during active and passive motion respectively. Further, muscle fiber and its direction were indirectly determined and the accuracy of the fiber orientation depends on the accuracy of locating fascicles end-points. However, it should be noted that the method used in the current paper is the only way to track muscle fibers over a large region of interest through the dynamic cycle.

The main findings of this paper are (i) SR_fiber, SR_in-plane, and SR-angle were significantly different between the cohorts during isometric contraction, (ii) asymmetry of fiber cross section deformation was observed in both cohorts and for both modes of motion with asymmetry decreasing from distal to proximal; (iii) SR-fiber angle was reduced in the senior cohort during active and passive motion, this difference tended to significance ; and (iv) significant regional differences were seen in the fiber cross section strain rates during passive motion. The accumulation of excess extracellular matrix is a signature of many pathologic conditions including muscular dystrophies, diabetes, and aging (26). The clinical application of SR tensor imaging, which provides an indirect probe of the extracellular matrix, may allow accurate diagnosis and tracking of these disease states.