DIFFUSION TENSOR IMAGING AND DIFFUSION MODELING: APPLICATION TO MONITORING CHANGES IN THE MEDIAL GASTROCNEMIUS IN DISUSE ATROPHY INDUCED BY UNILATERAL LIMB SUSPENSION.

Abstract

BACKGROUND:

Diffusion tensor imaging assesses underlying tissue microstructure, and has been applied to studying skeletal muscle. Unloading of the lower leg causes decreases in muscle force, mass and muscle protein synthesis as well as changes in muscle architecture.

PURPOSE:

To monitor the change in DTI indices in the medial gastrocnemius (MG) after 4-week unilateral limb suspension (ULLS) and to explore the feasibility of extracting tissue microstructural parameters based on a two-compartment diffusion model.

STUDY TYPE:

Prospective cohort study.

SUBJECTS:

7 moderately active subjects (29.1 ± 5.7 yrs.).

FIELD STRENGTH/SEQUENCE:

3T, single shot fat suppressed echo planar spin echo sequence.

ASSESSMENT:

Suspension related changes in the DTI indices (eigenvalues: λ₁, λ₂, λ₃, fractional anisotropy: FA; coefficient of planarity: CP) were statistically analyzed. Changes in model derived tissue parameters (muscle fiber circularity and diameter, intracellular volume fraction and residence time) after suspension are qualitatively discussed.

STATISTICAL TESTS:

Change in the DTI indices of the medial gastrocnemius between pre- and post-suspension were assessed using repeated measures two-way analysis of variance (ANOVAs).

RESULTS:

All the eigenvalues (λ₁: p = 0.025, λ₂: p = 0.035, λ₃: p = 0.049) as well as anisotropic diffusion coefficient (ADC: p = 0.029) were significantly smaller post ULLS. Diffusion modeling revealed that fibers were more circular (circularity index increased from 0.55 to 0.95) with a smaller diameter (diameter decreased from 82 μm to 60 μm) post-suspension.

DATA CONCLUSION:

We have shown that DTI indices change with disuse and modeling can relate these voxel level changes to changes in the tissue microarchitecture.

Introduction:

The feasibility of diffusion tensor imaging (DTI) of skeletal muscle including muscle fiber tracking for extraction of fiber lengths and pennation angles has been established, and the technique has been applied to monitor muscle injury, aging, gender related differences, and compartmental syndrome (1–6). Additionally, some studies have explored changes in muscle DTI with atrophy; e.g. arising from age-related atrophy in human skeletal muscle (7), from denervation and from Achilles tenotomy-induced atrophy in rodent models (8, 9). Further, DTI combined with diffusion models is increasingly being used to explore tissue microstructural parameters such as fiber diameter, permeability or intracellular volume fraction (10). While most modeling studies have focused on the brain, a few recent studies have extended modeling efforts to the diffusion in skeletal muscle (11–13). Recent studies have combined magnetic resonance imaging deformation analyses and diffusion tensor imaging tractography in the medial gastrocnemius (14, 15). Karakuzu et al showed that submaximal plantar flexion activity at 15% MVC causes heterogeneous length changes along the fascicles of human medial gastrocnemius (MG) muscle (15). The heterogeneity of fascicle strains was explained on the basis of epimuscular myofascial force transmission.

It is well established that disuse (e.g., by chronic unloading) leads to skeletal muscle atrophy that is accompanied by a significant loss of muscle force (16). The Unilateral Limb Suspension (ULLS) is a validated model to study the effects of chronic unloading (17). Unilateral limb suspension results in both loss of muscle mass (muscle fiber atrophy) as well as a decrease in muscle force (17). Prior studies of induced immobilization indicate that muscle remodeling with inactivity is a fast process that occurs after about a week of unloading (17, 18) These studies documented the decrease in both fiber length and pennation angle, a decrease in Focal Adhesion Kinase content (−20%) and activity (−30%), associated with a 50% fall in muscle protein synthesis and a 5% decrease in quadriceps muscle anatomical cross-sectional area (ACSA) (17,18). DTI with its ability to probe at the microstructural level is ideally suited to investigate potential muscle remodeling that occurs with chronic unloading. The focus of this study is to monitor the change in DTI indices in the medial gastrocnemius (MG) after 4-week unilateral limb suspension (ULLS) and to explore the feasibility of extracting tissue microstructural parameters based on a two-compartment diffusion model.

METHODS

In-Vivo Experiments:

The study was carried out under the approval of the Medical Research Ethics Board of University of California at 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. IRB approval was obtained from of the Medical Research Ethics Board of University of California at San Diego and all subjects were recruited after obtaining written informed consent. A total of 7 normal healthy young subjects (2 females, 29.1 ± 5.7 years, body mass 75.4 ± 22.7 kg, height 168.1± 7.4 cm) were recruited for this study. The criterion for inclusion was that subjects should be moderately physically active. Subjects participating in competitive sports as well as those with any surgical procedures performed on the lower leg were excluded.

Study Design:

The effect of chronic unloading on the force production capability and diffusion tensor indices of the MG muscle were assessed by comparing the baseline (pre) to immediately after 4 weeks of limb suspension (post). During the 4-week suspension period, subject compliance to the protocol was monitored at 2 weeks to check for muscle atrophy (MRI morphological scan) and loss of force production. In addition, compliance was also monitored by a wireless activity tracker that was integrated into the crutches; the subject was not informed of the tracker to ensure that it was not removed or tampered with to simulate crutch usage. After the 4-week suspension, subjects were required to attend structured physical rehabilitation sessions. MRI morphological scans were performed at the end of the rehabilitation period (4 weeks) to confirm that the muscle had recovered to baseline status.

Unilateral Limb Suspension (ULLS):

The ULLS model is an established model of inducing controlled atrophy (19) and was used in the current study to induce muscle atrophy on the non-dominant leg with 4 weeks of chronic unloading. The dominant leg was self-identified by subjects as the one they preferentially used to regain balance from a jostle. The non-dominant leg was the left leg for all subjects in this study. The ULLS protocol allowed the subjects a reasonable amount of freedom to carry out their daily activities including driving since the dominant leg (right in this study) was not unloaded. A crutch was used to prevent the foot (of the left leg) from touching the ground. The right foot was raised with a 5-cm heel on the shoe to further minimize accidental loading of the foot.

MR Imaging:

Subjects were positioned supine in a 3.0-T whole-body scanner (GE Medical Systems, Milwaukee, WI, USA) and only the limb selected for suspension was scanned (pre- and post-suspension). A custom-built receive-only phased array coil with a large FOV was used to image approximately 30 cm of the lower leg without moving the subject or coil; the intent was to cover the medial gastrocnemius muscle from its origin to insertion in two acquisitions without having to reposition the subject in the coil. The coil moved relative to the magnet between acquisitions, the subject did not move with respect to the coil. One anatomical slice was common between the two sets of acquisitions and the two sets were reoriented by a transformation obtained from the rigid alignment of the slice common to both sets. The subject’s leg was fully extended while the foot was maintained in a fixed position at ~15° in plantarflexion; the foot rested on an adjustable wedge to maintain the angle constant for the scan duration. This foot position was used to ensure that there was no passive tension in the lower leg muscles.

The MRI pulse sequence used in the image acquisition was a fat suppressed single shot EPI spin-echo sequence with monopolar diffusion gradients (diffusion gradient duration, δ = 12 ms, and diffusion time, Δ = 20 ms). Spatial-spectral water selective excitation was used to suppress fat. The total number of slices (acquired in two multi-slice 2D sets) required to cover the calf muscles ranged from 32 to 40 slices. B₀ shimming in the selected region of interest was performed with vendor supplied automated second order shims. Thirty-two non-collinear gradient directions with a b-factor of 400 s/mm² were used to map the direction dependent diffusion. Imaging parameters were echo time (TE)/repetition time (TR): 57.2 ms/7000 ms with 4 signal averages. The FOV, slice thickness/gap, and acquisition matrix were 240 × 240 mm², 5 mm/0 mm, and 128 × 80 respectively; no parallel imaging was employed. The 128×80 matrix was homodyne filled to 128×128, then zero padded to 256×256 to reconstruct the final image, yielding a voxel resolution of 0.9375 mm × 0.9375 mm × 5.00 mm. The homodyne algorithm pre-weights the k-space data so that when the real part of the image is extracted, it corresponds to uniform weighting in k-space (20). In addition to the diffusion weighted images, a morphological volume was acquired with a fat saturated fast-gradient echo (fgre) sequence for two echo times with the following parameters: TE₁/TE₂/TR/FA: 3.2 ms/5.6 ms/350 ms/20˚; all geometric parameters were the same as in the DTI scans. The acquired morphological volume was used to generate phase maps to correct B₀ distortions in the echo planar images. The total scan time including the morphological images for each session was 17 minutes.

Force measurements:

Isometric MVC of the plantarflexor muscles was determined for each subject prior to MR imaging. For this purpose, the ankle was fixed in a neutral position (90° angle between the axis of the foot and the shank). To estimate the maximum force acting along the Triceps Surae tendon, the force recorded by the force transducer was divided by the Achilles tendon moment arm corresponding to an angle of 90° between the axis of the foot and the shank detailed in (21). In brief, a sagittal MR image of the lower leg and foot was used to identify the joint (ankle) center of rotation as well as Achilles tendon line of action (the latter marked as a straight line along the center of the tendon). The perpendicular distance of the joint center to the line of action was measured as the Achilles tendon moment arm (21). The measured muscle force is that generated by the gastrocnemius (lateral and medial) and the soleus muscles.

Muscle Volume measurements:

A muscle physiologist with ten years of experience (co-author, RC) manually contoured the soleus, lateral and medial gastrocnemius in pre- and post-suspension subjects using the morphological images. The manual contouring was performed using parametric Bezier curves every 5^th slice using Osirix (22). Automated interpolation was performed for the intervening slices; all automated contours were examined and edited if needed.

Image pre-processing and DTI indices computation:

Figure 1 is the flowchart of the sequence of image processing steps. All diffusion weighted image volumes were registered to the baseline (b₀) image to correct for eddy current and motion related artifacts using the eddy algorithm from fsl (23). The phase images of the dual echo (fgre) volumes were used to correct for B₀ field inhomogeneities using the fugue algorithm from fsl (23). Diffusion weighted images were then denoised using a Joint Rician Linear Minimum Mean Square Error (LMMSE) estimator (24). The noise in magnitude MR images is best modeled by a Rician distribution and the LMMSE estimator has been shown to out-perform other Rician denoising techniques (25). The tensor was calculated from the distortion corrected and denoised data using a Gaussian model of diffusion. The tensor was then diagonalized to yield the eigenvalues followed by the calculation of the fractional anisotropy (FA), Apparent diffusion coefficient (ADC) and coefficient of planarity (CP) maps. The latter is an index of the shape of the diffusion ellipsoid and is given by: (λ₂-λ₃)/(λ₁+λ₂+λ₃). If the secondary and tertiary eigenvalues are close to each other, CP will be low. The contour of the MG traced in the fgre volume slices was transferred to the DTI indices map. Average values of the DTI indices were obtained from a 5 × 5 region of interest (ROI) automatically placed at the centroid of the MG mask at each anatomical slice (in most subjects, 40 axial slices were required to cover the MG); this placement ensured that the ROI was not at the edges which would bias estimates due to partial volume effects. A manual check was also made to ensure that the ROI was not in the region of a blood vessel, fascia or contained artifacts; such ROIs were moved manually to avoid artifacts. Though the ROI was small at 25 pixels/slice, the total number of pixels across all slices was ~900 (25*36) ensuring the robustness of the DTI indices.

Figure 1:

The image processing flowchart showing the sequence of steps leading to the extraction of the diffusion tensor indices: eigenvalues, eigenvectors, Apparent diffusion coefficient (ADC), Fractional Anisotropy (FA) and Coefficient of planarity (CP).

Two Compartment Modeling:

The model used here closely follows that proposed originally by Karampinos et al. (12). In this model, the two compartments are the muscle fibers and the extra-cellular matrix with the muscle fibers (intra-myocellular space) embedded in an extracellular matrix (endomysium and perimysium). Briefly, the muscle fibers are modeled as infinite cylinders with an elliptical cross-section defined by the ratio of short axis (r_s) to long axis (r_l) length of the muscle fiber (r_s/r_l=α) with muscle fiber diameter d_m defined as the mean of the short axis and long axis lengths. The volume of the two compartments are denoted as v_in (intra-myocellular volume fraction) and v_ex (extracellular volume fraction) with v_in + v_ex = 1. The last parameter of the fit is the intracellular residence time, τ_in which is related to the permeability of the sarcolemma (i.e., the cell membrane of muscle fibers) through the relationship: τ_in= r_m/κ; where r_m (d_m/2) is the radius of the muscle and κ is the permeability. Further, the collagen fraction in the extracellular matrix is represented by v_coll. Appendix A summarizes the equations of the diffusion model that was fitted to the measured DTI eigenvalues. Simulations were carried out by varying the fit parameters (α, d_m, τ_in, v_in, v_coll) to compute DTI eigenvalues. The five parameter-space was searched to find the optimal combination of the parameters that minimized the normalized root mean square difference (NRMSE) between the eigenvalues computed from the simulation and those determined from experiments.

$$\text{NRMSE}\hspace{0.17em}=\hspace{0.17em}\sqrt{\frac{{\sum }_{i=1}^3{\left({\text{λ}}_{i,\text{exp}}-{\text{λ}}_{i,\text{sim}}\right)}^2}{{\sum }_{i=1}^3{\text{λ}}_{i,\exp }^2}}$$ [1]

where λ_i,exp is the experimentally determined eigenvalues while λ_i,sim is the eigenvalue from the model simulation. Since there are five variables that are fit to the model, the search space was limited to physiologically relevant ranges in order to prevent the search from minimizing at non-physiological values; these ranges were taken from Karampinos et. al. (12). The simulations were carried out with the values for D_in (intra-cellular diffusion coefficient), D_ex (extracellular matrix diffusion coefficient), T2_in (intra-cellular T2), and T2_ex (extra-cellular T2) taken from the literature (12, 26). It should be noted here that Karampinos et. al. fitted D_in and D_ex to the diffusion model, but these variables were kept fixed in the current paper at the values obtained for young normal subjects in the former paper (12). This was done to limit the number of model variables in order to increase the robustness of the fit. Further, as D_in is determined by the various intracellular membrane and protein structure; it is not anticipated to change with atrophy. D_ex, the diffusion in the extracellular compartment is determined by the collagen fraction in the endomysium and the diffusion coefficient of water. Based on the findings from imaging that % connective tissue fraction does not change with atrophy (unreported study on the same subjects), it is also anticipated that % collagen fraction in the endomysium may not change significantly with atrophy. The experimental values of the eigenvalues (λ_i,exp) used in obtaining the optimal solution from the simulation were the mean values of all the subjects for pre- and post-suspension. The optimization was performed in Wolfram Research, Inc., Mathematica, (Version 11.3, Champaign, IL). The conjugate gradient search algorithm was used to find the parameters that minimize NRMSE. As this method only guarantees a local minimum, the global minimum was obtained by a search performed over all combinations of the five-parameter space; the range and step size of the search space are provided in Table 2.

Table 2:

Tissue microstructural parameters from bi-compartmental model of diffusion.

	pre -ULLS	post- ULLS	range	step size
α	0.55	0.95	0.05–0.95	0.05
dm	82	65	50–110	5
τin	0.8	2.6	0.8–2.6	0.2
νin	0.95	0.89	0.89–0.95	0.0025
νcoll	0.5	0.6	0.5–0.6	0.0025

Range (last column) shows the search space for each parameter. α: ratio of short axis to long axis of the muscle fiber cross-section (unitless), d_m: diameter of muscle fiber cross-section (in microns), τ_in: intracellular residence time (in seconds), v_in: intra-myocellular volume fraction, v_coll: collagen fraction in the extracellular matrix.

Statistical Analysis:

The outcome variables of the analysis are the diffusion tensor indices (λ₁, λ₂, λ₃, FA and CP). The assumption of normality of data was tested using both the Shapiro-Wilk test and by visual inspection of quantile-quantile plots. Since deviations from normality were only minor and no non-parametric alternative to factorial ANOVA exists, differences between pre- and post-ULLS values were assessed using two-way repeated measures ANOVAs. Data are reported as mean ± standard deviation. For all tests, the level of significance was set at 0.05. The statistical analyses were carried out using SPSS for Mac OSX (SPSS 23.0, IBM Inc, Armonk, NY).

RESULTS:

Muscle force decreased significantly post-suspension (change of 32.6±24.7%; p=0.013); this is the average over the seven subjects. The average change (over all subjects) in the volume of the MG, LG, and SOL muscles after the 4-week suspension was −9.6±4.5% (p=0.001), −11.1±7.4% (p=.008), and −7.4±5.9% (p=0.006) respectively (significance of pre- and post-suspension volume changes indicated for each muscle). While the DTI measurements/modeling are focused on the MG, the measured isometric plantarflexion force is generated by the Triceps Surae muscles and thus the volume change of all three muscles are included here. Typical maps of the eigenvalues, ADC, FA, CP and color map of lead eigenvector at one anatomical location of the lower leg in one subject pre- and post-suspension are shown in Figure 2. Visual assessment of the parametric DTI maps confirms the image quality (SNR) and lack of image artifacts (good fat suppression as well as small image distortions). The DTI indices evaluated pre- and post-limb suspension in the medial gastrocnemius are summarized in Table 1; the values listed are the averages for all subjects. All three eigenvalues and apparent diffusion coefficient (ADC) decreased significantly post-suspension (λ₁: p = 0.025, λ₂: p = 0.035, λ₃: p = 0.049, ADC: p = 0.029) while FA increased and CP decreased with suspension, the latter indices two did not show significant changes (p=0.239 for FA and p=0.763 for CP). The maximum decrease was in the secondary eigenvalue that in turn resulted in a smaller difference between the secondary and tertiary eigenvalue post suspension (reflected also as a decrease in CP). In addition to the average values of all subjects listed in Table 1, the DTI indices (eigenvalues, ADC, FA and CP) pre- and post-suspension are also plotted for each subject individually in Figure 3. This was done to confirm the consistency of DTI changes with suspension across the seven subjects and hence the validity of the observations.

Figure 2:

The parametric maps extracted from the diffusion tensor. The two left columns are pre-suspension and the tow right columns are corresponding images from the same subjects post-suspension an antomical level close top row shows the maps pre-suspension and the bottom the maps at a corresponding anatomic location post-suspension. The maps are (top to bottom, column 1 and 3): λ₁, λ₂, λ₃, ADC. (top to bottom, column 2 and 4): FA, CP, eigenvector1, mask of MG muscle with ROI superposed on the eigenvalue weighted eigenvector color map. Eigenvalues are in units of x10⁻³mm²/sec, the FA and CP are unitless. EV1 is the colormap of the eigenvector corresponding to the lead eigenvalue, λ₁. The colormap is the projection of the primary eigenvector following the convention: L-->R (x-projection): Red, A-->P (y-projection): Green, S-->I (z-projection): Blue. The predominantly blue hue confirms the superio-inferior direction of the muscle fiber. The same anatomic location is shown pre- and post-suspension; the atrophy of the muscles is clearly seen comparing the pre- to the post-supension images. The effectiveness of the fat suppression can be seen by the absence of fat artifacts (shifted subcutaneous fat) in the image.

Table 1.

Diffusion tensor indices pre- and post- unilateral limb suspension (ULLS)^α

	pre- ULLS	post- ULLS
λ1*	2.06 ±0.11	1.91 ±0.15
λ2*	1.44 ±0.08	1.31 ±0.11
λ3*	1.30 ±0.11	1.17 ±0.10
ADC*	1.60 ±0.07	1.47 ±0.11
FA	0.25 ±0.04	0.27 ±0.04

^αAverage and standard deviation over all seven subjects.

^*significant difference between pre- and post-suspension.

λ₁: primary eigenvalue, λ₂: secondary eigenvalue, λ₃: tertiary eigenvalue; the eigenvalues are in units of x10⁻³mm²/sec.

FA: Fractional anisotropy, CP: coefficient of planarity.

Figure 3:

Individual plots of the DTI indices (clockwise from left top corner: eigenvalues, Coeffcient of planarity, Apparent diffusion coefficient, and Fractional Anisotropy) for each of the seven subjects. Pre- and post-values for each subject are connected for ease of visualization of the changes in the indices with suspension. For most of the DTI indices the majority of subjects show the same direction of changes: e.g., six out of seven subjects show a decrease in λ₁, λ₂, ADC and increase in FA while five out of seven subjects show a decrease in λ₃ and in CP.

Table 2 lists the model parameters obtained by the search of the parameter space for the values of (α, d_m, τ_in, v_in, v_coll) that yielded the lowest value of the error index (12). The increase in the circularity index (α) with disuse indicates that the fiber becomes more circular, while the decrease in muscle fiber diameter is as anticipated with atrophy.

DISCUSSION:

While it is known that the quadriceps muscles show greater atrophy than the medial gastrocnemius in aging and are a better correlate to physical function (27), the motivation for the focus on the MG in the current study is based on the ease of performing functional MRI studies on the MG for correlation to structural MRI studies (14, 15, 28, 29). Further, calf circumference (and by extension calf muscle mass as well) has been shown in a large-scale study to provide information on muscle related disability and physical function (30).

Muscle force loss was approximately greater by a factor of 3 compared to reduction in muscle mass. Prior work on gravitational unloading effects on fast and slow rat hind-limb muscles data indicate that predominantly slow muscles are more responsive to unloading than predominantly fast muscles (31). Since the soleus has a higher proportion of slow twitch muscles compared to the gastrocnemius muscles, it would be anticipated that the soleus would show the highest atrophy (volume decrease). However, comparing % volume changes in the three muscles in the current study, larger changes were seen in the gastrocnemius muscles. It should be noted though that the soleus muscle had the highest changes in terms of absolute volume changes comparing pre- and post-suspension muscles.

Comparing the values of DTI indices in the current study with that reported by Karampinos et al (12), there are considerable differences in FA and in CP between the two studies. The reasons for these differences may arise from differences in the measurement methodology. A simulated echo EPI diffusion weighted sequence was used by Karampinos et al (12) in contrast to the current study that uses a spin echo EPI diffusion weighted sequence. It has been shown earlier that the simulated echo is better for diffusion imaging of muscle than a spin echo (32). However, the sequence used by Karampinos et al has a TE of 52 ms (12) which is really long for a stimulated echo that has half the signal of a spin echo with a similar TE. This raises the issue that the SNR of the sequence used in (12) may not have been high and low SNR has been shown to bias the estimation of DTI indices (33). Further, values reported for the eigenvalues and FA for the MG are in good agreement between the current study with another recent rigorous study that evaluated DTI indices for voxels with SNR >20 (33).

Previous studies on denervation induced atrophy on rodent models showed a reduction in λ₂ and λ₃, an increase in fractional anisotropy (FA) while λ₁ was unchanged (8). It is well accepted that DTI measurements in muscle reflect water diffusion in the intracellular space, thus the authors of this paper attributed the decrease in the secondary and tertiary eigenvalues to a decrease in the diameter of myofibers (i.e., myofiber atrophy). In another study, the triceps surae was assessed with DTI after Achilles tenotomy in rats (9). Both muscle atrophy as well as a decrease in plantarflexion force was seen post-tenotomy. Significant decreases in λ₁, λ₂, and λ₃ and an increase in FA were seen between the control and treatment sides at 4 weeks post-tenotomy (9). This is in contrast to denervation induced atrophy where no changes were seen in λ₁. In the present study, decreases in all three eigenvalues were significant. The eigenvector corresponding to the lead eigenvalue is in the direction of the muscle fiber and thus λ₁ represents diffusion along the long axis of the muscle fiber. Since the muscle fiber is orders of magnitude greater than the diffusion distances, changes in muscle fiber length are not expected to cause changes in λ₁. Further, changes in fiber cross-section diameters should also not affect λ₁as the diffusion direction is along the long axis of the muscle fiber. Thus, the decrease in λ₁ is difficult to explain. Possibly, the reduced diffusivity along the fibers’ long axis is related to a loss in myosin content (34) and reduction in the packing density of actin filament proteins (35) that result in structurally weakened sarcomeres. While the underlying physiological mechanisms are unclear, our observation of a decrease in λ₁ is similar to that seen in the tenotomy induced atrophy (9). The decrease in λ₂ and λ₃ can potentially be related to a change in muscle fiber diameter and is similar to that seen in denervation induced atrophy (8). It should also be noted that the largest decrease was seen in λ₂. If the secondary and tertiary eigenvalues reflect the long axis and short axis diameters respectively of the muscle fiber cross-section, then the muscle fiber is more circular post-suspension. In this context, Karampinos et al. (12) advanced the hypothesis that the elliptic fiber cross-section arises from a response to the mechanical stimulus as the fiber is strained more along one direction in the muscle fiber cross-section than in the orthogonal direction. When the mechanical stimulus is reduced or removed as with ULLS induced disuse, the preferential deformation along one axis in the fiber cross-section is removed. This may well result in the fiber cross-section becoming more circular in the absence of a mechanical stimulus. As opposed to the progressive circularity accompanying disuse-atrophy, (36) reported increasing ellipticity coming along with muscle fiber growth. ADC decreased significantly with suspension and may potentially arise from a combination of a decrease in inherent intracellular diffusivity (decrease in all three eigenvalues) and a decrease in muscle fiber size (decrease in secondary and tertiary eigenvalues).

In the context of a reduction of a mechanical stimulus with suspension, the discussion of findings from related studies using strain/strain rate tensor imaging is worthwhile (14, 15, 28, 29). Strain and strain rate tensor imaging evaluate tissue deformation and the tensor provides information of the strain (or strain rate) in three orthogonal directions. The primary, secondary, and tertiary eigenvectors of the strain rate tensor correspond approximately to the muscle fiber direction and to two orthogonal directions in the muscle fiber cross-section, respectively. When the muscle fiber contracts, a negative strain will be seen along the muscle fiber direction and accompanying this, a positive strain from radial expansion will be seen in the fiber cross-section. However, this positive strain is not symmetric in the fiber cross-section, with much larger expansion along one direction than the orthogonal direction; this asymmetry has been reported in a number of studies (28,29,37). Further, a recent study on strain rate tensor imaging after unilateral limb suspension reported that the fiber cross-section strain rate asymmetry decreased post-suspension (28). This decrease in strain rate asymmetry may also be tied to the structural response to the lack of mechanical stimulus. This potentially may imply that the long axis of the elliptical cross-section (proportional to the secondary eigenvalue of the diffusion tensor) is a consequence of the external mechanical stimulus since the radial expansion is preferentially along this direction resulting in an elongation of the fiber cross-section in one direction. Once this stimulus is removed (as in limb suspension) the elongated axes is no longer preferentially stretched, and may potentially become less elliptical (more circular). This is reflected in a lower CP value post-suspension. Another potential explanation for the observed structural changes may be the altered muscle fiber-extracellular matrix interactions from limb suspension (14, 15).

The modeling part presented in the current paper is exploratory. The values of α reported in the literature for the vastus lateralis muscle are in the range of 0.4 to 0.68 (38, 39); the current value of 0.55 for MG circularity in the pre-suspension case appears to be reasonable. Karampinos et al report the value of alpha from the fit to the diffusion model with a range of 0.6–0.9; the lower end of this range is close to the current paper. The MG muscle fiber diameter extracted from the model in the current study (82 μm) is in agreement with values reported in the literature (38) and also with the range (70–110 μm) determined for the MG in the earlier diffusion modeling study by Karampinos et. al. (12). Further, the focus of the modeling was on determining if meaningful changes in microstructure with suspension can be extracted from the experimentally determined diffusion eigenvalues. With suspension, the ratio of the short axis to long axis muscle fiber length increases which implies that the fiber becomes more circular. In the light of the hypothesis that the elliptical muscle fiber shape arises from the mechanical stimulus, the modeling result of a more circular muscle fiber can be explained by the lack of mechanical stimulus during the 4-week suspension. The diameter of the muscle fiber decreases; this finding is consistent with muscle fiber atrophy. In fitting both pre- and post-suspension DTI data, the search algorithm converged on the upper or lower limits for τ_in, ν_in and ν_col. Thus, the best-fit values for these parameters may be in error. The NRMSE was quite flat with respect to these variables; this was noted for τ_in by Karampinos et al (12), and thus, fitting the available DTI data to this model does not allow one to draw conclusions regarding τ_in, ν_in or ν_col.

There are limitations to the current study: the study population is small but since it is a longitudinal study (pre- and post-ULLS), statistical significance was reached for the changes in the eigenvalues. A one-point diffusion measurement is not ideal for extracting tissue parameters through modeling; future work using multi-point DTI data (obtained for example, by varying diffusion time and/or b-values) will allow more robust modeling to extract accurate values for these microstructural features. Further, multi-point DTI data may allow greater flexibility to extend to single subject rather than limit to cohort modeling as in the current study. It should also be noted that if the fit was performed independently on each subject, it would have allowed testing of the significant changes in the microstructural parameters with limb suspension. Measurements on the contralateral leg would have provided information on the effects of a change in mechanical loading of the unsuspended leg. However, the current study was part of a larger protocol that besides DTI, included quantification of fat, connective tissue as well as functional measurements and acquiring data on the contralateral leg would have prolonged the scanning time excessively. Further, imaging both legs at the same time was restricted by the customized coil that accommodated only one leg. However, the customized coil provided higher SNR than vendor coils and allowed the acquisition of the entire lower leg without repositioning the subject.

In conclusion, the current study shows that the DTI eigenvalues decrease with suspension induced disuse atrophy. Experimentally, the secondary eigenvalue showed the largest decrease with suspension. This could potentially be related to a hypothesis that attributes the elliptical shape of the muscle fiber cross-section as arising from a response to an external load (12). While it is still a conjecture, the asymmetry of deformation in the fiber cross-section may result in one axis becoming longer than the orthogonal one and then unloading conditions can cause this shape asymmetry to be reduced. As the secondary and tertiary eigenvalues are related to the fiber cross-section diameters, this results in larger changes in the secondary eigenvalue as the fiber reduces the most in diameter along this direction with unloading. An exploratory modeling of the DTI data to extract microstructural parameters showed that it is feasible and the disuse atrophy related changes in muscle circularity, mean diameter, residence time, intracellular volume and collagen volume extracted from the model were physiologically reasonable.

Appendix A

The diffusion model is similar to that proposed by Karampinos paper but is included here for completeness (12). The bi-compartmental model extends the Karger model and is based on diffusion in two compartments, the intracellular space (inside the muscle fiber) and the extracellular space (collagenous intramuscular connective tissue consisting of endomysium and perimysium). Muscle fibers are modeled as infinite cylinders with an elliptical cross-section in which the ratio of the short axis length to long axis length (=α). The endomysium consists of a random network of collagen fibrils. The solution to the bi-compartmental model, S(q,t) is given below that includes the diffusion in the intracellular compartment, D’_in and in the extracellular compartment, D’_ex where these diffusion quantities are derived from the D^app_in and from D^app_ex; the latter two quantities are dependent on the tissue parameters (α, d_m, τ_in, v_in, v_coll). These relationships are defined in (12). The average eigenvalues (over all subjects separately for pre- and post-suspension) was fit to the diffusion model by searching the parameter space over the range defined in Table 2. This range was determined as reasonable physiological limits for the search from literature (12).

$$S\left(q,t\right)=\upsilon {\text{'}}_{\text{in}}\exp \left(-4{\pi }^2{q}^{2}tD{\text{'}}_{\text{in}}\right)+\upsilon {\text{'}}_{\text{ex}}\exp \left(-4{\pi }^2{q}^{2}tD{\text{'}}_{\text{ex}}\right)$$ [A. 1]

$${\lambda }_i=-\frac{1}{b}\ln \left(\frac{S_i\left(q,\Delta \right)}{S_i\left(q,0\right)}\right)$$ [A. 2]

$$D{\text{'}}_{\text{ex,in}}=\frac{1}{2}\left(D_{\text{in}}^{\text{app}}+D_{\text{ex}}^{\text{app}}+\frac{1}{4{\pi }^2{q}^2}\left(\frac{1}{{\tau }_{\text{in}}}+\frac{1}{{\tau }_{\text{ex}}}+\frac{1}{T_{2,\text{in}}}+\frac{1}{T_{2,\text{ex}}}\right)\right)\pm \frac{1}{2}\sqrt{\left(D_{\text{in}}^{\text{app}}+D_{\text{ex}}^{\text{app}}+\frac{1}{4{\pi }^2{q}^2}\left(\frac{1}{{\tau }_{\text{in}}}+\frac{1}{{\tau }_{\text{ex}}}+\frac{1}{T_{2,\text{in}}}+\frac{1}{T_{2,\text{ex}}}\right)\right)+\frac{1}{4{\pi }^4{q}^4{\tau }_{\text{in}}{\tau }_{\text{ex}}}}$$ [A. 3]

$$\begin{gathered} \upsilon {\text{'}}_{\text{ex}}=\frac{1}{D{\text{'}}_{\text{ex}}-D{\text{'}}_{\text{in}}}\left({\upsilon }_{\text{in}}\left(D_{\text{app}}^{\text{in}}+\frac{1}{4{\pi }^2{q}^2{T}_{2,\text{in}}}\right)+{\upsilon }_{\text{ex}}\left(D_{\text{app}}^{\text{ex}}+\frac{1}{4{\pi }^2{q}^2{T}_{2,\text{ex}}}\right)-D{\text{'}}_{\text{in}}\right) \\ \upsilon {\text{'}}_{\text{in}}=1-\upsilon {\text{'}}_{\text{ex}} \end{gathered}$$ [A. 4]

S – signal, i is an index 1–3 corresponding to the three eigenvalues.

$q=(\gamma /2\pi )\delta g$, where $\gamma$ is gyromagnetic ratio, $\delta$ length of the diffusion gradients, g diffusion gradient amplitude

t – time

T_{2, ex/in} – spin-spin relaxation time for intra- and extracellular compartments

${\tau }_{in/ex}$ – intra- and extracellular mean residence time

D^app_in/ex – apparent diffusion coefficient for intra- and extracellular compartments