In-Vivo Estimation of Anisotropic Mechanical Properties of the Gastrocnemius during Functional Loading with MR Elastography

Abstract

Objective:

In-vivo imaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.

Approach:

In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness (μ₁, substrate shear stiffness (μ₂), shear anisotropy (ϕ), and tensile anisotropy (ζ) of the gastrocnemius muscle in response to both passive and active tension.

Main Results:

In passive tension, we found a significant increase in μ₁, ϕ, and ζ with increasing muscle length. While in active tension, we observed increasing μ₂ and decreasing ϕ and ζ during active dorsiflexion and plantarflexion – indicating less anisotropy – with greater effects when the muscles act as agonist.

Significance:

The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction.

1. Introduction

Non-invasive evaluation of skeletal muscle health in-vivo allows for longitudinal assessments of tissue structure and function. Primary assessment tools include measurement of muscle activation through surface electromyography (sEMG) [1–3], and imaging of tissue structure with ultrasound imaging [4–6] and magnetic resonance imaging (MRI) [7,8]. These techniques each have their advantages, with sEMG and ultrasound imaging providing high temporal resolution during muscle activation, while MRI provides a large field-of-view (FOV) to better investigate multiple muscles and their interactions simultaneously. An additional benefit of MRI is the ability to more comprehensively examine the complex structure of skeletal muscle by combining standard MRI contrasts, such as T1-weighted [9–11] and T2-weighted [12–14] imaging, with quantitative contrasts sensitive to tissue biophysics, such as diffusion tensor imaging (DTI) [15–17] and MR spectroscopy [18,19].

One such MRI modality is magnetic resonance elastography (MRE), which is a phase-contrast technique that measures propagating time-harmonic shear waves to probe the mechanical properties of tissues and has been successfully used to analyze the health of other human organs [20–23]. In skeletal muscle, MRE has shown to capture changes in tissue mechanical properties reflecting muscle microstructure due to aging [24,25], exercise [26,27], and pathology, including Duchenne muscle dystrophy [28–30]. MRE has also shown to reflect muscle activation through changes in the apparent mechanical stiffness of the tissue. In particular, Zonnino, et al. [31] quantified the effects of variable isometric contraction on MRE estimates in the human forearm, as well as how changing muscle length affected the responses of those muscles. Additionally, Schrank, et al. [32] used a real-time MRE method to quantify parameter changes in calf muscles during isometric contraction loading conditions. In these examples, muscles appeared stiffer during contraction, indicating an avenue to better understand muscle force output.

While previous studies have demonstrated the potential of MRE for characterizing skeletal muscle, they have largely employed isotropic material models when estimating tissue mechanical properties, which are then susceptible to inaccuracies given the fibrous composition of muscle that leads to anisotropic mechanical behavior [33,34]. Several recent MRE studies of skeletal muscle have attempted to incorporate mechanical anisotropy, including works by Green, et al. [35], Guo, et al. [36], and Babaei, et al. [37]. These studies each modeled muscle as an incompressible, transversely isotropic tissue with two anisotropic shear parameters defining the tissue response to shear deformations parallel and perpendicular to the muscle fibers. Fiber stretching, a critical component of the mechanical response of muscle during contraction, cannot be represented by two shear parameters alone, and instead requires an additional parameter to capture the tensile mechanical response. Recently, a nearly incompressible, transversely isotropic (NITI) material model, which incorporates three parameters to describe the tissue – substrate shear stiffness, shear anisotropy, and tensile anisotropy – has shown promise in modeling both the shear and tensile components of anisotropy in fibrous human tissue when combined with MRE displacement data [38–42]. Through estimation of the three independent mechanical property parameters, the NITI material model provides an effective framework from which to quantify the mechanical response of skeletal muscle as it is functionally activated.

Most studies analyzing the link between measurements of anisotropic mechanical properties of skeletal muscle and tissue structure and function have utilized ex-vivo techniques and have shown significant variations in tissue mechanical response during both passive stretching and active contraction [43,44]. These prior works have characterized muscle force production and transmission in both the axial and lateral directions [45–47], with greater axial loading in the direction of the muscle fibers occurring during passive stretching, while active contraction produces higher forces in the lateral direction [48,49]. Capturing these variations in muscle mechanics in-vivo would allow for more accurate assessments of skeletal muscle functional responses that incorporate the entire muscle volume, and other muscles and bone that make up the lower leg. Additionally, it would establish MRE as sensitive to tissue structure and function to allow for the assessment of longitudinal effects of injury and pathology in individual subjects.

Therefore, the purpose of this study is use MRE to capture anisotropic mechanical behavior in skeletal muscle in-vivo consistent to previous ex-vivo studies. To test this, we estimated the anisotropic mechanical properties of skeletal muscle using the recently developed transversely isotropic, nonlinear inversion algorithm (TI-NLI) that incorporates wave motion fields from MRE with fiber orientation data acquired with diffusion tensor imaging (DTI) [50,51]. We performed two experiments to probe the mechanical reaction of skeletal muscle: the first to investigate passive contraction through muscle stretching, and the second to explore the mechanical variations caused by active isometric contraction.

2. Methods

2.1. Experimental Setup

Eight healthy young adult subjects (4/4 M/F; ages 23-26) completed the study approved by our Institutional Review Board. All participants were imaged in a Siemens 3T Prisma MRI scanner. Each subject was positioned supine, feet first in the bore with legs draped over an adjustable support as shown in Figure 1. Two RF receiver coils were wrapped around the calf with two custom-made passive drivers to generate the necessary shear waves for MRE in conjunction with the Resoundant pneumatic actuation system. For Experiment 1, the right ankle of each subject was placed in a custom brace to limit range of motion while the height of the knee was adjusted to achieve three different angles: 105°, 135°, and 165°. For Experiment 2, the right foot of each subject was positioned on a pedal device. Individuals were instructed to press and hold down one side of the footplate to compress fully one of the plastic springs, as illustrated in Figure 1B, for the duration of each MRE scan. This positioning induced isometric dorsi- or plantar-flexion depending on which spring the subject compressed. Subjects practiced these movements prior to scanning to acclimate themselves to the force required to minimize variability between participants and acquisitions.

Figure 1:

(A) Experiment 1 entailed placing the subject’s foot in a custom ankle brace to maintain a constant ankle angle while the angle of subject’s knee was altered through raising or lowering the leg support. (B) Experiment 2 replaces the ankle brace with a pedal-like device which induced isometric contraction when the subject pushed against one of the two springs during dorsi- or plantar-flexion, while the leg was supported at a constant knee angle.

2.2. Imaging Protocol

MRE data was collected using an echo-planar imaging (EPI) sequence with the following parameters: 2 x 2 x 3 mm³ voxel size; FOV = 160 x 160 mm; 80 x 80 matrix; 20 slices with 3 mm thickness; repetition time (TR)/ echo time (TE) = 2400/59 ms; vibration frequency = 50 Hz; 4 phase offsets; dual gradient polarity; total acquisition time = 65 sec. Thicker slices were used to increase signal-to-noise ratio, and were positioned axially where anatomical features and mechanical properties are assumed to vary more slowly along the leg. We also acquired a diffusion tensor imaging (DTI) scan with resolution and FOV matched to the MRE data with TR/TE = 2200/69 ms, b = 400 s/mm² and 30 directions, as well as a T1-weighted scan with the following parameters: 1.25 x 1.25 x 3 mm³ voxel size; FOV = 160 x 160 mm; 128 x 128 matrix; 20 slices; TR/TE = 2200/11 ms;

Each subject completed both Experiment 1 and Experiment 2 within the same scanning session. Experiment 1 consisted of a set of image acquisitions at each of three knee angles (105°, 135°, and 165°). At each position, we collected three repeated MRE scans, one DTI scan, and one T1-weighted anatomical scan. Experiment 2 consisted of three repeated MRE acquisitions during each contraction condition – dorsi-flexion, plantar-flexion, and rest – for a total of nine MRE scans. Additionally, we acquired one DTI scan and one T1-weighted anatomical scan as in Experiment 1. All imaging volumes were manually aligned to be axial to the leg for different leg positions in both experiments.

2.3. Data Processing

Diffusion data was processed with the FMRIB’s Diffusion Toolbox (FDT) from FMRIB’s Software Library (FSL) [52]. We then used FMRIB’s Linear Image Registration Tool (FLIRT) to register the diffusion-weighted images with MRE image space using the diffusion gradient directions for each image rotated according to the registration. From there, fractional anisotropy and the first eigenvector (V₁) were calculated using FDT.

Wave motion fields were calculated from MRE data after subtraction to remove background phase, phase unwrapping with FSL PRELUDE [53], and temporal Fourier filtering to isolate the harmonic motion of interest. We then used a transversely isotropic, non-linear inversion algorithm (TI-NLI) to estimate anisotropic material parameters based on the acquired wave motion fields and the primary eigenvector from DTI, the assumed fiber direction [50,51], as shown in Figure 2. TI-NLI is an iterative, finite element-based inversion that estimates spatial maps of the three material property parameters used to describe a NITI model: substrate shear modulus, G₂, shear anisotropy, $\varphi =\left|G_1\right|/\left|G_2\right|-1$, and tensile anisotropy, $\zeta =\left|E_1\right|/\left|E_2\right|-1$, where G and E are defined as a material shear and tensile moduli respectively. Subscript 1 denotes a property parallel to the direction of the fiber, or normal to the plane of isotropy, while a subscript 2 denotes a property perpendicular to the fiber direction, or in the plane of isotropy. The substrate shear modulus is defined by the equation: $G_2=G_2^{\prime }+i{G}_2^{\prime \prime }$, where $G_2^{\prime }$ is the substrate storage modulus, and $G_2^{\prime \prime }$, is the substrate loss modulus. Here we calculate the substrate shear stiffness as ${\mu }_2=\frac{2{\left|G_2\right|}^2}{G_2^{\prime }+\left|G_2\right|}$, which describes the square of the wave speed perpendicular to the fibers. We also considered the shear stiffness parallel to the fibers as μ₁ = μ₂(1 + ϕ). We note that the parameters estimated in this study are “effective” mechanical properties due to the nonlinear acoustoelastic effects of the pre-strain fields on the skeletal muscle [54].

Figure 2:

(A) Two primary muscles, medial and lateral heads of the gastrocnemius, were investigated to determine anisotropic material parameters. Three material property parameters were estimated by combining (B) MRE displacement fields with (C) DTI fiber directions. The anisotropic parameters included (D) substrate shear stiffness (μ), shear anisotropy (Φ), and tensile anisotropy (ζ).

We estimated the average anisotropic properties in individual calf muscles, specifically the medial and lateral heads of the gastrocnemius, which were manually traced from anatomical images. Within TI-NLI, we applied soft prior regularization using these generated volumes as a priori spatial information to stabilize the estimation of properties [55]. To analyze differences in muscle parameters between contraction states, we applied a linear mixed model with variables of muscle, subject, and position as fit parameters for Experiment 1, and a one-way ANOVA with repeated measures within subject and muscle with relationships between a post-hoc Tukey test for Experiment 2.

3. Results

3.1. Experiment 1 – Passive Muscle Lengthening

Figure 3 displays results from Experiment 1 and shows changes in the anisotropic material parameters in the gastrocnemii when placed in the three knee positions: 105°, 135°, and 165°. Associated descriptive statistics are summarized in Table 1. We found increases in μ₁, ϕ, and ζ as knee angle increases (each p < 0.05), while μ₂ stayed relatively stable. Using data from both muscles individually, μ₁ increased by approximately 7.6% overall, from 1.66 kPa to 1.79 kPa, between the initial and final position (p = 0.061). ϕ, however, increased 7.6% between a knee angle of 105° and 135° and 1.8% between a knee angle of 135° and 165°, for a total increase of 9.5% from 0.30 to 0.33 (p < 0.05). ζ exhibited similar increases the three knee positions – 38% between a knee angle of 105° and 135° and 33% between a knee angle of 135° and 165° for an overall increase of 84% (p < 0.05).

Figure 3:

Results from Experiment 1 comparing the effects of increasing muscle length with knee angle on fiber shear stiffness, substrate shear stiffness, shear anisotropy, and tensile anisotropy (left to right) in both heads of the gastrocnemius muscle. Statistically significant differences are denoted by *.

Table 1:

Average and standard deviations of four mechanical property parameters at the three knee angles measured during Experiment 1.

	μ1(kPa)	μ2(kPa)	Φ	ζ
105°	1.49 ± 0.41	1.28 ± 0.27	0.20 ± 0.17	0.40 ± 0.24
135°	1.62 ± 0.40	1.23 ± 0.27	0.35 ± 0.12	0.62 ± 0.16
165°	1.67 ± 0.57	1.21 ± 0.26	0.38 ± 0.24	0.74 ± 0.25

Figure 4 highlights the anisotropic parameter estimates of gastrocnemius during isometric contraction in dorsi-flexion and plantar-flexion relative to rest from Experiment 2. Here, the parameters – μ₂, ϕ, and ζ – exhibited significant changes between the contraction states (p < 0.05), while μ₁ was relatively stable. From the rest condition, μ₂increased from 1.39 kPa to 1.56 kPa during dorsiflexion (p < 0.05) and to 1.73 kPa during plantarflexion (p < 0.05), increases of 20% and 13%, respectively. ϕ and ζ had opposite responses, instead showing non-significant decreases from 0.13 to 0.03 (34.6%; p = 0.106) and 0.39 to 0.36 (6.9%; p = 0.72) during dorsiflexion, respectively, and significant decreases from 0.13 to −0.02 (66.7%; p < 0.05) and 0.39 to 0.12 (67.5%; p < 0.05) during plantarflexion.

Figure 4:

Results from Experiment 2 comparing the effects of isometric contraction on fiber shear stiffness, substrate shear stiffness, shear anisotropy, and tensile anisotropy (left to right) in both heads of the gastrocnemius muscle. Statistically significant differences are denoted by *.

4. Discussion

In this study, we used MRE to capture the mechanical response occurring in skeletal muscle during isometric contraction and passive lengthening, specifically captured variations in anisotropic mechanical properties of the medial and lateral heads of the gastrocnemius muscle. Most in-vivo evaluations of anisotropic mechanical properties of skeletal muscle quantify the resting state shear stiffness and shear anisotropy. In this study, measurements of shear stiffness and shear anisotropy were relatively similar to results from previous reports in the MRE literature with similar vibration frequencies (μ₁ = 1.26 - 1.32 kPa , μ₂ = 1.53 – 2.00 kPa, and ϕ = 0.18 – 0.59) [35–37]. The repeatability of the estimated shear moduli were within the range of previous MRE studies, with the coefficient of variation, defined as $\frac{ Mean}{ St.Dev!}$ , for the repeated measurements of a single subject averaging 5.0% in experiment 1 and 10.9% in experiment 2 [42,56]. None of the prior published studies reported ζ as a material parameter; hence, comparisons were not possible with the data presented here. In previous studies, MRE-measurements of calf muscles have utilized large knee angles with a nearly-straight leg and a non-flexed ankle, most similarly to our Position 3 at 165° knee angle during Experiment 1. The TI-NLI employed in this study has been demonstrated to accurately recover μ, ϕ and ζ images using realistic simulated data which supports the accuracy of our measurements. [50,57].

In Experiment 1, we showed the degree of anisotropic parameter change during alterations in passive tension on a muscle through changes in muscle length. The gastrocnemius is the only dual-joint muscle in the calf, meaning it crosses both knee and ankle joints. Therefore, by limiting the motion of the ankle, we can alter the length and pennation angle of the gastrocnemius by changing knee angle and increase the length of the sarcomeres within the muscle fibers [58,59]. Previous literature has shown that this increases in muscle length also increases the applied load on the muscle fibers [60–62]. This outcome is reflected in results from Experiment 1, where μ₁, the shear stiffness in planes parallel to the fiber direction, increased with increasing knee angle. One of the primary drivers of this increased stiffness and anisotropy is likely the stretching of collagen-based structures within the muscle, including epimysium, perimysium, and endomysium as well as the muscle fiber extracellular matrix, resulting in higher levels of pre-stress and pre-strain within the tissue [63]. As these collagen structures are stretched, the collagen becomes more highly aligned [64,65], which has also been reflected in diffusion imaging studies [15,17]. The pathway for the increase in tension is likely also related to titin, the third structural protein within sarcomeres which studies suggest causes passive force enhancement [66,67]. Titin primarily acts as a molecular spring with the ability to alter stiffness during muscle activation to maintain stability in muscles that are stretched to long lengths. Previous ex-vivo studies have also shown that muscle fibers and their sarcomeres produce low levels of lateral forces during muscle lengthening [45,48], though in this work we observed no significant change in μ₂ during passive muscle lengthening, suggesting that the mechanism of lateral force creation may not be significant enough to be detected via changes in substrate stiffness.

In a previous MRE study of skeletal muscle, Babaei et al. [37] found a similar relationship between μ₁ and muscle length, though results differed for μ₂ and ϕ, as μ₂ significantly increased while ϕ stayed relatively stable as the muscle stretched. One possible reason for differences in these results is the different material models used in the two studies. Babei, et al. assumed tissue incompressibility with only the presence of slow propagating shear waves, and accordingly, no fast propagating shear wave effects (i.e. only shear anisotropy and no tensile anisotropy). Ignoring the fast shear wave component in skeletal muscle may bias estimates of shear moduli, since fast waves are likely to be present in an NITI material unless care is taken to avoid their excitation [39]. Under the assumption of full incompressibility, tissue stretching must be represented in other measurements, possibly resulting in the mismatch in outcomes between the two studies. Another possible explanation could be the lack of knee restraint in the Babei study. As previously noted, the gastrocnemius muscle can be stretched or shortened by changing the angle of either the ankle or knee; hence, while the ankle angle was controlled, any readjustment of the subject’s knee angle will cause changes in length and pennation angle of the muscle, and potentially change the resulting material property parameter estimates.

In Experiment 2, we demonstrated the effects of isometric contraction on the anisotropic material properties of the gastrocnemius. Results from this experiment indicate that as this activation occurs, the muscle increases its shear stiffness in the direction perpendicular to the fiber direction. Previous studies utilizing MRE for estimation of skeletal muscle during activation, such as works by Zonnino, et al. [31] and Schrank, et al. [32], also reported increases in stiffness estimates during isometric contractions. These studies also found greater increases during agonist actions than antagonist actions, with the gastrocnemius functioning as an agonist during plantar-flexion, displaying larger parameter changes than in dorsi-flexion, or antagonist action for the gastrocnemius. Our TI-NLI anisotropic property estimates suggest the increase in stiffness estimated in these previous studies was a result of stiffening of the tissue in the perpendicular direction with little to no increase in stiffness in the fiber direction during activation. We expect these increases during isometric contraction are a consequence of the cross-bridge model attributed to Huxley, et al. [68], which indicates that cross-bridges are created by myosin and actin bonding, which exert forces along the bridge during bonding that occurs in conjunction with conversion of ATP into ADP. This cross-bridge loading creates lateral stresses between sarcomeres, specifically the z-disc, the region of the muscle fiber linking sarcomeres together, and upon the surrounding collagen supportive structures [46,47]. However, the forces are not a constant, as the cross-bridge only spends a portion of time strongly attached to actin. The amount of time these cross-bridges spend attached to actin fibrils increases in response to load. Thus, the cross-bridge “duty cycle” is high frequency, meaning that MRE likely captures an averaged state of the cross-bridge loading and unloading [67,69].

The two experiments reported here highlight how anisotropic MRE utilizing TI-NLI can be an effective tool for in-vivo mechanical evaluation of skeletal muscle structural and functional health and agree with mechanical responses of muscle shown in previous ex-vivo experiments. First, we observed how shear stiffness parallel and perpendicular to muscle fibers, μ₁ and μ₂, influenced the complex relationship between ϕ and muscle loading. μ₁ correlates with increasing tension caused by muscle lengthening through passive loading, while μ₂ captures the lateral loading across cross-bridges and between sarcomeres and the surrounding collagen-based structures that occurs during isometric contraction. On the other hand, while ζ appears to be a necessary component of the parameter estimation process and shows changes with both passive lengthening and active contraction, ζ is the most common anisotropic material parameter explored in previous ex-vivo experiments. While the responses of ζ are similar to those of ϕ in these experiments, differences between the two parameters in future experiments could help provide greater insight into tissue behavior.

Muscle under tension not only changes the shape and structure of cells, which are expected to affect tissue mechanics, but also generates significant pre-strain fields which further influence shear wave propagation. Muscle stress fields can be reasonably approximated as having symmetry around an axis along the length of the muscle, so these effects can be adequately modeled by effective parameters of a NITI model [49]. A simple model of passive stretching produces tensile pre-stress fields along the muscle, and radially symmetric compressive pre-stress perpendicular to the muscle axis due to the Poisson effect [70]. This will increase shear wave speed along the muscle axis and perpendicular to the muscle axis, though likely a lesser amount, resulting in an increased apparent anisotropy. Active muscle contraction also has tensile stress along the muscle axis; however, this is generated by shortening the muscle which increases cross-sectional area which gives a tensile pre-strain. This increases wave speed in both directions, giving an increased overall effective stiffness, and lower effective anisotropy. Accurate modeling of these acoustoelastic effects [54,71,72] requires a nonlinear computational model and knowledge of the both the pre-strain field, requiring the unstressed state to be known, and the nonlinear mechanical properties. As these requirements are difficult to achieve with in-vivo imaging, separation of the mechanical property changes from acoustoelastic changes is not currently feasible. Therefore, a small displacement assumption is used in the estimation of “effective” mechanical properties which consist of the true unstressed properties mixed with the nonlinear acoustoelastic effects from the pre-strain field. These effective properties are altered by both changes in cellular structure and changes in muscle function, so provided conditions are controlled carefully they can provide useful insight into muscle health.

While the methods utilized in this study were effective at capturing the viscoelastic responses of muscle function with MRE, the study had several limitations. While the MRE and DTI scans have standard imaging noise, other biological tissues and structures within the volume create additional noise and discontinuities that may affect outcomes [73]. These structures include the fibula, major blood vessels, fatty tissue, and muscle fascia, each of which create challenges for MRE, as they introduce model-data mismatch in multiple small ROIs that we sought to minimize by incorporating spatial information in the inversion process. Muscle fatigue also potentially affected outcomes from Experiment 2 that required consistent force generation over a period of time [74,75]. Experiment 2 was designed using springs that generate a load below 15% mean voluntary contraction for an average human adult, to avoid significant fatigue during the short imaging time, but this threshold is variable from subject to subject and levels of force application were imprecise as no in-situ measurements were recorded. One additional limitation is possible differences in assumed fiber direction for anisotropic estimation and the true fiber direction, especially during Experiment 2, as DTI data was not acquired during each isometric contraction condition but rather was acquired at rest and registered to MRE data from active contraction prior to TI-NLI. Recommendations for future studies include a tailored force output requirement based on an individual subject’s MVC and a visual feedback system adjusted to each subject’s necessary output level so that a participant can maintain the proper level of contraction. Additionally, subject knee and ankle positions in both experiments were relatively well controlled and consistent within an individual subject’s data set, however they were unmeasured and could not be accounted for during statistical analysis, and differences between individuals may account for some of the variability in observed outcomes.

5. Conclusions

In this work, we use anisotropic MRE to capture functional effects on muscle mechanics, including passive muscle lengthening and active contraction to the medial and lateral heads of the gastrocnemius. Using TI-NLI, we generated anisotropic material parameter maps and estimated each parameter within the muscle volumes of participants for each of three conditions during each experiment capturing both passive lengthening and active contraction. Anisotropic mechanical parameters exhibited different trends based on the loading condition, and MRE with TI-NLI may allow us to examine healthy functional response of muscle tissue as well as tissue affect by injuries or pathologies, such as cerebral palsy.

Table 2:

Average and standard deviations of four mechanical property parameters at the three different active contraction states measured during Experiment 2.

	μ1(kPa)	μ2(kPa)	Φ	ζ
Dorsiflexion	1.43 ± 0.29	1.56 ± 0.36	0.03 ± 0.20	0.36 ± 0.18
Rest	1.43 ± 0.38	1.39 ± 0.30	0.13 ± 0.19	0.39 ± 0.24
Plantarflexion	1.45 ± 0.19	1.73 ± 0.45	−0.02 ± 0.19	0.12 ± 0.23