Investigating the Correlation between Force Output, Strains, and Pressure for Active Skeletal Muscle Contractions.

Experimental observations suggest that the force output of the skeletal muscle tissue can be correlated to the intra-muscular pressure generated by the muscle belly. However, pressure often proves difficult to measure through in-vivo tests. Simulations on the other hand, offer a tool to model muscle contractions and analyze the relationship between muscle force generation and deformations as well as pressure outputs, enabling us to gain insight into correlations among experimentally measurable quantities such as principal and volumetric strains, and the force output. In this work, a correlation study is performed using Pearson's and Spearman's correlation coefficients on the force output of the skeletal muscle, the principal and volumetric strains experienced by the muscle and the pressure developed within the muscle belly as the muscle tissue undergoes isometric contractions due to varying activation profiles. The study reveals strong correlations between force output and the strains at all locations of the belly, irrespective of the type of activation profile used. This observation enables estimation on the contribution of various muscle groups to the total force by the experimentally measurable principal and volumetric strains in the muscle belly. It is also observed that pressure does not correlate well with force output due to stress relaxation near the boundary of muscle belly.

Effect of different ankle joint positions on medial gastrocnemius muscle fiber strains during isometric plantarflexion.

Muscle force production is influenced by muscle fiber and aponeurosis architecture. This prospective cohort study utilizes special MR imaging sequences to examine the structure-function in-vivo in the Medial Gastrocnemius (MG) at three-ankle angles (dorsiflexion, plantar flexion-low and high) and two sub-maximal levels of maximum voluntary contraction (25% and 50%MVC). The study was performed on 6 young male participants. Muscle fiber and aponeurosis strain, fiber strain normalized to force, fiber length and pennation angle (at rest and peak contraction) were analyzed for statistical differences between ankle positions and %MVC. A two-way repeated measures ANOVA and post hoc Bonferroni-adjusted tests were conducted for normal data. A related samples test with Friedman's 2-way ANOVA by ranks with corrections for multiple comparisons was conducted for non-normal data. The dorsiflexed ankle position generated significantly higher force with lower fiber strain than the plantarflexed positions. Sarcomere length extracted from muscle fiber length at each ankle angle was used to track the location on the Force-Length curve and showed the MG operates on the curve's ascending limb. Muscle force changes predicted from the F-L curve going from dorsi- to plantarflexion was less than that experimentally observed suggesting other determinants of force changes with ankle position.

Time-dependent diffusion tensor imaging and diffusion modeling of age-related differences in the medial gastrocnemius and feasibility study of correlations to histopathology.

PURPOSE: Implement STEAM-DTI to model time-dependent diffusion eigenvalues using the random permeable barrier model (RPBM) to study age-related differences in the medial gastrocnemius (MG) muscle. Validate diffusion model-extracted fiber diameter for histological assessment. METHODS: Diffusion imaging at different diffusion times (Δ) was performed on seven young and six senior participants. Time-dependent diffusion eigenvalues (λ2 (t), λ3 (t), and D⊥ (t); average of λ2 (t) and λ3 (t)) were fit to the RPBM to extract tissue microstructure parameters. Biopsy of the MG tissue for histological assessment was performed on a subset of participants (four young, six senior). RESULTS: λ3 (t) was significantly higher in the senior cohort for the range of diffusion times. RPBM fits to λ2 (t) yielded fiber diameters in agreement to those from histology for both cohorts. The senior cohort had lower values of volume fraction of membranes, ζ, in fits to λ2 (t), λ3 (t), and D⊥ (t) (significant for fit to λ3 (t)). Fits of fiber diameter from RPBM to that from histology had the highest correlation for the fit to λ2 (t). CONCLUSION: The age-related patterns in λ2 (t) and λ3 (t) could tentatively be explained from RPBM fits; these patterns may potentially arise from a decrease in fiber asymmetry and an increase in permeability with age.

Strain and Strain Rate Tensor Mapping of Medial Gastrocnemius at Submaximal Isometric Contraction and Three Ankle Angles.

INTRODUCTION: The aim of this study is to analyze the muscle kinematics of the medial gastrocnemius (MG) during submaximal isometric contractions and to explore the relationship between deformation and force generated at plantarflexed (PF), neutral (N) and dorsiflexed (DF) ankle angles. METHOD: Strain and Strain Rate (SR) tensors were calculated from velocity-encoded magnetic resonance phase-contrast images in six young men acquired during 25% and 50% Maximum Voluntary Contraction (MVC). Strain and SR indices as well as force normalized values were statistically analyzed using two-way repeated measures ANOVA for differences with force level and ankle angle. An exploratory analysis of differences between absolute values of longitudinal compressive strain (Eλ1) and radial expansion strains (Eλ2) and maximum shear strain (Emax) based on paired t-test was also performed for each ankle angle. RESULTS: Compressive strains/SRs were significantly lower at 25%MVC. Normalized strains/SR were significantly different between %MVC and ankle angles with lowest values for DF. Absolute values of Eλ2 and Emax were significantly higher than Eλ1 for DF suggesting higher deformation asymmetry and higher shear strain, respectively. CONCLUSIONS: In addition to the known optimum muscle fiber length, the study identified two potential new causes of increased force generation at dorsiflexion ankle angle, higher fiber cross-section deformation asymmetry and higher shear strains.

MRI Based Fiber Strain Mapping of the Medial Gastrocnemius Muscle at Submaximal Isometric Contractions at Different Ankle Angles.

Muscle force production is influenced by muscle fiber and aponeurosis architecture. This prospective cohort study utilizes special MR imaging sequences to examine the structure-function in-vivo in the Medial Gastrocnemius (MG) at three-ankle angles (dorsiflexion, neutral, and plantar flexion) and two sub-maximal levels of maximum voluntary contraction (25% and 50% MVC). The study was performed on 6 young male subjects. Muscle fiber and aponeurosis strain, fiber strain normalized to force, fiber length and pennation angle (at rest and peak contraction) were analyzed for statistical differences between ankle positions and %MVC. A two-way repeated measures ANOVA and post hoc Bonferroni-adjusted tests were conducted for normal data. A related samples test with Friedman's 2-way ANOVA by ranks with corrections for multiple comparisons was conducted for non-normal data. The dorsiflexed ankle position generated significantly higher force with lower fiber strain than neutral and plantarflexed positions. Sarcomere length extracted from muscle fiber length at each ankle angle was used to track the location on the Force-Length curve and showed the MG operates on the curve's ascending limb. Muscle force changes predicted from the F-L curve going from dorsi- to plantarflexion was less than that experimentally observed suggesting other determinants of force changes with ankle position.

Spin Lattice (T1) and Magnetization Transfer Saturation (MTsat) Imaging to Monitor Age-Related Differences in Skeletal Muscle Tissue.

BACKGROUND: The aim was to compare spin-lattice relaxation (T1) mapping from sequences with no fat suppression and three fat suppression methods and Magnetization Transfer Saturation (MTsat) mapping, to identify regional and age-related differences in calf muscle. These differences may be of clinical significance in age-related loss of muscle force. METHODS: Ten young and seven senior subjects were imaged on a 3T MRI scanner using a 3D Fast Low Angle Shot sequence without and with different fat suppression and with MT saturation pulse. Bland-Altman plots were used to assess T1 maps using the fat unsuppressed sequence as the reference image. Age and regional differences in T1 and in MTsat were assessed using two-way factorial analyses of variance (ANOVAs) with Bonferroni-adjusted independent sample t-tests for post hoc analyses. RESULTS: A significant age-related increase in T1 and decrease in MTsat was seen in the calf muscles. The largest size effect was observed in the T1 sequence with fat saturation. CONCLUSIONS: T1 increase with age may reflect increase in inflammatory processes while the decrease in MTsat may indicate that magnetization transfer may also be associated with muscle fiber macromolecules. T1 and MTsat maps of calf muscle have the potential to detect regional and age-related compositional differences in calf muscle.

Multiscale modeling of passive material influences on deformation and force output of skeletal muscles.

Passive materials in human skeletal muscle tissues play an important role in force output of skeletal muscles. This paper introduces a multiscale modeling framework to investigate how age-associated variations on microscale passive muscle components, including microstructural geometry (e.g., connective tissue thickness) and material properties (e.g., anisotropy), influence the force output and deformations of the continuum skeletal muscle. We first define a representative volume element (RVE) for the microstructure of muscle and determine the homogenized macroscale mechanical properties of the RVE from the separate mechanical properties of the individual components of the RVE, including muscle fibers and connective tissue with its associated collagen fibers. The homogenized properties of the RVE are then used to define the elements of the continuum muscle model to evaluate the force output and deformations of the whole muscle. Conversely, the regional deformations of the continuum model are fed back to the RVE model to determine the responses of the individual microscale components. Simulations of muscle isometric contractions at a range of muscle lengths are performed to investigate the effects of muscle architectural changes (e.g., pennation angles) due to aging on force output and muscle deformation. The correlations between the pennation angle, the shear deformation in the microscale connective tissue (an indicator for the lateral force transmission), the angle difference between the fiber direction and principal strain direction and the resulting shear deformation at the continuum scale, as well as the force output of the skeletal muscle are also discussed.

Dynamics of Quadriceps Muscles during Isometric Contractions: Velocity-Encoded Phase Contrast MRI Study.

OBJECTIVE: To quantify the spatial heterogeneity of displacement during voluntary isometric contraction within and between the different compartments of the quadriceps. METHODS: The thigh muscles of seven subjects were imaged on an MRI scanner while performing isometric knee extensions at 40% maximal voluntary contraction. A gated velocity-encoded phase contrast MRI sequence in axial orientations yielded tissue velocity-encoded dynamic images of the four different compartments of the thigh muscles (vastus lateralis (VL), vastus medialis (VM), vastus intermedius (VI), and rectus femoris (RF)) at three longitudinal locations of the proximal-distal length: 17.5% (proximal), 50% (middle), and 77.5% (distal). The displacement, which is the time integration of the measured velocity, was calculated along the three orthogonal axes using a tracking algorithm. RESULTS: The displacement of the muscle tissues was clearly nonuniform within each axial section as well as between the three axial locations. The ensemble average of the magnitude of the total displacement as a synthetic vector of the X, Y, and Z displacements was significantly larger in the VM at the middle location (p < 0.01), and in the VI at the distal location than in the other three muscles. The ensemble average of Z-axis displacement, which was almost aligned with the line of action, was significantly larger in VI than in the other three muscles in all three locations. Displacements of more than 20 mm were observed around the central aponeuroses, such as those between VI and the other surrounding muscles. CONCLUSIONS: These results imply that the quadriceps muscles act as one functional unit in normal force generation through the central aponeuroses despite complex behavior in each of the muscles, each of which possesses different physiological characteristics and architectures.

Biomechanical Gain in Joint Excursion from the Curvature of the Achilles Tendon: Role of the Geometrical Arrangement of Inflection Point, Center of Rotation, and Calcaneus.

The dorsal movement of the Achilles tendon during ankle rotation is restricted by anatomical obstructions. Previously, we demonstrated that the anatomical obstruction provides a gain (gainAT) in the proximal displacement of the calcaneus compared to the change in the Achilles tendon length. Here, we empirically validate and extend our previous modeling study by investigating the effects of a broad range of obstruction locations on gainAT. The largest gainAT could be achieved when the obstruction was located on the most ventral and distal sides within the physiological range of the Achilles tendon, irrespective of the ankle position.

Developing a Technique for the Imaging-Based Measurement of ACL Elongation: A Proof of Principle.

Towards the goal of obtaining non-invasive biomarkers reflecting the anterior cruciate ligament's (ACL) loading capacity, this project aimed to develop a magnetic resonance imaging (MRI)-based method facilitating the measurement of ACL elongations during the execution of knee stress tests. An MRI-compatible, computer-controlled, and pneumatically driven knee loading device was designed to perform Lachman-like tests and induce ACL strain. A human cadaveric leg was used for test purposes. During the execution of the stress tests, a triggered real-time cine MRI sequence with a temporal resolution of 10 Hz was acquired in a parasagittal plane to capture the resultant ACL elongations. To test the accuracy of these measurements, the results were compared to in situ data of ACL elongation that were acquired by measuring the length changes of a surgical wire directly sutured to the ACL's anteromedial bundle. The MRI-based ACL elongations ranged between 0.7 and 1.7 mm and agreed very well with in situ data (root mean square errors, RMSEs ≤ 0.25 mm), although peak elongation rates were underestimated by the MRI (RMSEs 0.19-0.36 mm/s). The high accuracy of elongation measurements underlines the potential of the technique to yield an imaging-based biomarker of the ACL's loading capacity.

3D Muscle Deformation Mapping at Submaximal Isometric Contractions: Applications to Aging Muscle.

3D strain or strain rate tensor mapping comprehensively captures regional muscle deformation. While compressive strain along the muscle fiber is a potential measure of the force generated, radial strains in the fiber cross-section may provide information on the material properties of the extracellular matrix. Additionally, shear strain may potentially inform on the shearing of the extracellular matrix; the latter has been hypothesized as the mechanism of lateral transmission of force. Here, we implement a novel fast MR method for velocity mapping to acquire multi-slice images at different % maximum voluntary contraction (MVC) for 3D strain mapping to explore deformation in the plantar-flexors under isometric contraction in a cohort of young and senior subjects. 3D strain rate and strain tensors were computed and eigenvalues and two invariants (maximum shear and volumetric strain) were extracted. Strain and strain rate indices (contractile and in-plane strain/strain rate, shear strain/strain rate) changed significantly with %MVC (30 and 60% MVC) and contractile and shear strain with age in the medial gastrocnemius. In the soleus, significant differences with age in contractile and shear strain were seen. Univariate regression revealed weak but significant correlation of in-plane and shear strain and shear strain rate indices to %MVC and correlation of contractile and shear strain indices to force. The ability to map strain tensor components provides unique insights into muscle physiology: with contractile strain providing an index of the force generated by the muscle fibers while the shear strain could potentially be a marker of lateral transmission of force.

Role of the Extracellular Matrix in Loss of Muscle Force With Age and Unloading Using Magnetic Resonance Imaging, Biochemical Analysis, and Computational Models.

The focus of this review is the application of advanced MRI to study the effect of aging and disuse related remodeling of the extracellular matrix (ECM) on force transmission in the human musculoskeletal system. Structural MRI includes (i) ultra-low echo times (UTE) maps to visualize and quantify the connective tissue, (ii) diffusion tensor imaging (DTI) modeling to estimate changes in muscle and ECM microstructure, and (iii) magnetization transfer contrast imaging to quantify the macromolecular fraction in muscle. Functional MRI includes dynamic acquisitions during contraction cycles enabling computation of the strain tensor to monitor muscle deformation. Further, shear strain extracted from the strain tensor may be a potential surrogate marker of lateral transmission of force. Biochemical and histological analysis of muscle biopsy samples can provide "gold-standard" validation of some of the MR findings. The review summarizes biochemical studies of ECM adaptations with age and with disuse. A brief summary of animal models is included as they provide experimental confirmation of longitudinal and lateral force transmission pathways. Computational muscle models enable exploration of force generation and force pathways and elucidate the link between structural adaptations and functional consequences. MR image findings integrated in a computational model can explain and predict subject specific functional changes to structural adaptations. Future work includes development and validation of MRI biomarkers using biochemical analysis of muscle tissue as a reference standard and potential translation of the imaging markers to the clinic to noninvasively monitor musculoskeletal disease conditions and changes consequent to rehabilitative interventions.

Magnetic resonance imaging based muscle strain rate mapping during eccentric contraction to study effects of unloading induced by unilateral limb suspension.

Age- and disuse- related loss of muscle force is disproportionately larger than the loss of muscle mass. Earlier studies reported that comparing concentric and eccentric contractions, there is a significant age-related decrease in force only in concentric contractions. Magnetic Resonance Imaging enables mapping of muscle deformation and has been used to study isometric but not eccentric contractions. We report MRI based strain rate mapping of the medial gastrocnemius in subjects pre- and post-unloading induced by Unilateral Limb Suspension. In contrast to isometric contraction, no difference in strain rate indices were observed post-unloading, in conformance with preserved force during eccentric contractions.

Compressed sensing velocity encoded phase contrast imaging: Monitoring skeletal muscle kinematics.

PURPOSE: This study implements a compressed sensing (CS) 3-directional velocity encoded phase contrast (VE-PC) imaging for studying skeletal muscle kinematics within 40 s. METHODS: Independent variable density random sampling in the phase encoding direction for each temporal frame was implemented for various combinations of CS-factors and views per segment. CS reconstruction was performed for the combined multicoil, temporal datasets using temporal Fourier transform followed by temporal principal component analysis sparsifying transformations. The method was tested on a flow phantom and in vivo, on velocity and strain rate of the medial gastrocnemius muscle of 11 subjects performing isometric contractions. RESULTS: For the flow phantom, velocity from 8 undersampled sequences matched very well with the flowmeter values over a range of velocities spanning in vivo muscle velocities. Bland-Altman plots of the peak strain rate eigenvalues comparing 7 undersampled sequences was in good agreement with the reference (full k-space) scan. CS-factor of 4 combined with views per segment of 4 (scan times reduced by 4) yielded images with no visual artifacts allowing and yielded velocities and strain rate maps in the lower leg muscle in 40 s. CONCLUSION: This study shows that a reduction in scan time of velocity encoded phase contrast imaging up to a factor of 4 is possible using the proposed CS reconstruction.

Microstructural analysis of skeletal muscle force generation during aging.

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions.

Contemporary image-based methods for measuring passive mechanical properties of skeletal muscles in vivo.

Skeletal muscles' primary function in the body is mechanical: to move and stabilize the skeleton. As such, their mechanical behavior is a key aspect of their physiology. Recent developments in medical imaging technology have enabled quantitative studies of passive muscle mechanics, ranging from measurements of intrinsic muscle mechanical properties, such as elasticity and viscosity, to three-dimensional muscle architecture and dynamic muscle deformation and kinematics. In this review we summarize the principles and applications of contemporary imaging methods that have been used to study the passive mechanical behavior of skeletal muscles. Elastography measurements can provide in vivo maps of passive muscle mechanical parameters, and both MRI and ultrasound methods are available (magnetic resonance elastography and ultrasound shear wave elastography, respectively). Both have been shown to differentiate between healthy muscle and muscles affected by a broad range of clinical conditions. Detailed muscle architecture can now be depicted using diffusion tensor imaging, which not only is particularly useful for computational modeling of muscle but also has potential in assessing architectural changes in muscle disorders. More dynamic information about muscle mechanics can be obtained using a range of dynamic MRI methods, which characterize the detailed internal muscle deformations during motion. There are several MRI techniques available (e.g., phase-contrast MRI, displacement-encoded MRI, and "tagged" MRI), each of which can be collected in synchrony with muscle motion and postprocessed to quantify muscle deformation. Together, these modern imaging techniques can characterize muscle motion, deformation, mechanical properties, and architecture, providing complementary insights into skeletal muscle function.

Diffusion tensor imaging and diffusion modeling: Application to monitoring changes in the medial gastrocnemius in disuse atrophy induced by unilateral limb suspension.

BACKGROUND: Diffusion tensor imaging (DTI) 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: Seven moderately active subjects (29.1 ± 5.7 years). 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; coefficient of planarity) 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: Changes in the DTI indices of the MG between pre- and postsuspension were assessed using repeated-measures two-way analysis of variance (ANOVA). RESULTS: All the eigenvalues (λ1 : P = 0.025, λ2 : P = 0.035, λ3 : P = 0.049) as well as anisotropic diffusion coefficient (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 82-60 µm) postsuspension. 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. LEVEL OF EVIDENCE: 2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2018.

Connectivity of the Superficial Muscles of the Human Perineum: A Diffusion Tensor Imaging-Based Global Tractography Study.

Despite the importance of pelvic floor muscles, significant controversy still exists about the true structural details of these muscles. We provide an objective analysis of the architecture and orientation of the superficial muscles of the perineum using a novel approach. Magnetic Resonance Diffusion Tensor Images (MR-DTI) were acquired in 10 healthy asymptomatic nulliparous women, and 4 healthy males. Global tractography was then used to generate the architecture of the muscles. Micro-CT imaging of a male cadaver was performed for validation of the fiber tracking results. Results show that muscles fibers of the external anal sphincter, from the right and left side, cross midline in the region of the perineal body to continue as transverse perinea and bulbospongiosus muscles of the opposite side. The morphology of the external anal sphincter resembles that of the number '8' or a "purse string". The crossing of muscle fascicles in the perineal body was supported by micro-CT imaging in the male subject. The superficial muscles of the perineum, and external anal sphincter are frequently damaged during child birth related injuries to the pelvic floor; we propose the use of MR-DTI based global tractography as a non-invasive imaging technique to assess damage to these muscles.