Characterization of the passive mechanical properties of spine muscles across species

Linking myosin heavy chain isoform shift to mechanical properties and fracture modes in skeletal muscle tissue

Muscle fibers play a crucial role in the mechanical action of skeletal muscle tissue. However, it is unclear how the histological variations affect the mechanical properties of tissues. In this study, the shift of myosin heavy chain (MHC) isoforms is used for the first time to establish a linkage between tissue histological variation and passive mechanical properties. The shift of MHC isoform is found not only to induce significant differences in skeletal muscle passive mechanical properties, but also to lead to differences in strain rate responses. Non-negligible rate dependence is observed even in the conventionally defined quasi-static regime. Fidelity in the estimated constitutive parameters, which can be impacted due to variation in MHC isoforms and hence in rate sensitivity, is enhanced using a Bayesian inference framework. Subsequently, scanning electron microscopy and fluorescence microscopy are used to characterize the fracture morphology of muscle tissues and fibers. The fracture mode of both MHC I and II muscle fibers exhibited shearing of endomysium. Results show that the increase in strain rate only leads to stronger rebounding of the muscle fibers during tissue rupture without changing fracture modes.

Musculotendon Parameters in Lower Limb Models: Simplifications, Uncertainties, and Muscle Force Estimation Sensitivity

Musculotendon parameters are key factors in the Hill-type muscle contraction dynamics, determining the muscle force estimation accuracy of a musculoskeletal model. Their values are mostly derived from muscle architecture datasets, whose emergence has been a major impetus for model development. However, it is often not clear if such parameter update indeed improves simulation accuracy. Our goal is to explain to model users how these parameters are derived and how accurate they are, as well as to what extent errors in parameter values might influence force estimation. We examine in detail the derivation of musculotendon parameters in six muscle architecture datasets and four prominent OpenSim models of the lower limb, and then identify simplifications which could add uncertainties to the derived parameter values. Finally, we analyze the sensitivity of muscle force estimation to these parameters both numerically and analytically. Nine typical simplifications in parameter derivation are identified. Partial derivatives of the Hill-type contraction dynamics are derived. Tendon slack length is determined as the musculotendon parameter that muscle force estimation is most sensitive to, whereas pennation angle is the least impactful. Anatomical measurements alone are not enough to calibrate musculotendon parameters, and the improvement on muscle force estimation accuracy will be limited if the source muscle architecture datasets are the only main update. Model users may check if a dataset or model is free of concerning factors for their research or application requirements. The derived partial derivatives may be used as the gradient for musculotendon parameter calibration. For model development, we demonstrate that it is more promising to focus on other model parameters or components and seek alternative strategies to further increase simulation accuracy.

Towards improving the accuracy of musculoskeletal simulation of dynamic three-dimensional spine rotations with optimizing model and algorithm

BACKGROUND

The accuracy of musculoskeletal simulations greatly relies on model structures and optimization algorithms. This study investigated the unclarified influence of accounting for several commonly-simplified different model components and optimization criteria on spinal musculoskeletal simulations.

METHODS

The study constructed a full-body musculoskeletal model with passive components of functional spinal units and spinal muscles subject-specifically refined. A muscle redundancy solver was built with 15 optimization criteria. Three-dimensional spine rotations and spinal muscle activities were measured using optical motion capture and electromyogram techniques when eight healthy volunteers performed standing, flexion/extension, lateral bending, and axial rotation. The effect of the model with four different conditions of the passive components and the sensitivity of the 15 optimization criteria on simulations were investigated.

RESULTS

Accounting for the refined passive components significantly improved the simulation accuracy. Different optimization criteria behaved distinctly for different motions. Generally minimizing the sum of squared muscle activations outperformed the others, with the highest averaged correlation coefficient (0.82) between the estimated erector spinae muscle activations and measured electromyography and with the estimated joint compression forces comparable to in vivo reference data.

CONCLUSION

This study highlights the importance of passive model components and proposes a suitable optimization framework for realistic spinal musculoskeletal simulations.

Dysfunctional paraspinal muscles in adult spinal deformity patients lead to increased spinal loading

Purpose

Decreased spinal extensor muscle strength in adult spinal deformity (ASD) patients is well-known but poorly understood; thus, this study aimed to investigate the biomechanical and histopathological properties of paraspinal muscles from ASD patients and predict the effect of altered biomechanical properties on spine loading.

Methods

68 muscle biopsies were collected from nine ASD patients at L4–L5 (bilateral multifidus and longissimus sampled). The biopsies were tested for muscle fiber and fiber bundle biomechanical properties and histopathology. The small sample size (due to COVID-19) precluded formal statistical analysis, but the properties were compared to literature data. Changes in spinal loading due to the measured properties were predicted by a lumbar spine musculoskeletal model.

Results

Single fiber passive elastic moduli were similar to literature values, but in contrast, the fiber bundle moduli exhibited a wide range beyond literature values, with 22% of 171 fiber bundles exhibiting very high elastic moduli, up to 20 times greater. Active contractile specific force was consistently less than literature, with notably 24% of samples exhibiting no contractile ability. Histological analysis of 28 biopsies revealed frequent fibro-fatty replacement with a range of muscle fiber abnormalities. Biomechanical modelling predicted that high muscle stiffness could increase the compressive loads in the spine by over 500%, particularly in flexed postures.

Discussion

The histopathological observations suggest diverse mechanisms of potential functional impairment. The large variations observed in muscle biomechanical properties can have a dramatic influence on spinal forces. These early findings highlight the potential key role of the paraspinal muscle in ASD.

Investigating the active contractile function of the rat paraspinal muscles reveals unique cross-bridge kinetics in the multifidus

PURPOSE

Various aspects of paraspinal muscle anatomy, biology, and histology have been studied; however, information on paraspinal muscle contractile function is almost nonexistent, thus hindering functional interpretation of these muscles in healthy individuals and those with low back disorders. The aim of this study was to measure and compare the contractile function and force-sarcomere length properties of muscle fibers from the multifidus (MULT) and erector spinae (ES) as well as a commonly studied lower limb muscle (Extensor digitorum longus (EDL)) in the rat.

METHODS

Single muscle fibers (n = 77 total from 6 animals) were isolated from each of the muscles and tested to determine their active contractile function; all fibers used in the analyses were type IIB.

RESULTS

There were no significant differences between muscles for specific force (sF_o) (p = 0.11), active modulus (p = 0.63), average optimal sarcomere length (p = 0.27) or unloaded shortening velocity (V_o) (p = 0.69). However, there was a significant difference in the rate of force redevelopment (k_tr) between muscles (p =  < 0.0001), with MULT being significantly faster than both the EDL (p =  < 0.0001) and ES (p = 0.0001) and no difference between the EDL and ES (p = 0.41).

CONCLUSIONS

This finding suggests that multifidus has faster cross-bridge turnover kinetics when compared to other muscles (ES and EDL) when matched for fiber type. Whether the faster cross-bridge kinetics translate to a functionally significant difference in whole muscle performance needs to be studied further.

In vivo assessment of the passive stretching response of the bi-compartmental human semitendinosus muscle using shear wave elastography

The semitendinosus muscle contains distinct proximal and distal compartments arranged anatomically in-series but separated by a tendinous inscription, with each compartment innervated by separate nerve branches. Although extensively investigated in other mammals, compartment-specific mechanical properties within the human semitendinosus have scarcely been assessed in vivo. Experimental data obtained during muscle-tendon unit stretching (e.g., slack angle) can also be used to validate and/or improve musculoskeletal model estimates of semitendinosus muscle force. The purpose of this study was to investigate the passive stretching response of proximal and distal humans semitendinosus compartments to distal joint extension. Using two-dimensional shear wave elastography, we bilaterally obtained shear moduli of both semitendinosus compartments from 14 prone-positioned individuals at ten knee flexion angles (from 90° to 0° [full extension] at 10° intervals). Passive muscle mechanical characteristics (slack angle, slack shear modulus, and the slope of the increase in shear modulus) were determined for each semitendinosus compartment by fitting a piecewise exponential model to the shear modulus-joint angle curves. We found no differences between compartments or legs for slack angle, slack shear modulus, or the slope of the increase in shear modulus. We also found the experimentally determined slack angle occurred at ~15-80° higher knee flexion angles compared to estimates from two commonly used musculoskeletal models, depending on participant and model used. Overall, these findings demonstrate that passive shear modulus-joint angle curves do not differ between proximal and distal human semitendinosus compartments, and provide experimental data to improve semitendinosus force estimates derived from musculoskeletal models.

Systematic review of skeletal muscle passive mechanics experimental methodology

Understanding passive skeletal muscle mechanics is critical in defining structure-function relationships in skeletal muscle and ultimately understanding pathologically impaired muscle. In this systematic review, we performed an exhaustive literature search using PRISMA guidelines to quantify passive muscle mechanical properties, summarized the methods used to create these data, and make recommendations to standardize future studies. We screened over 7500 papers and found 80 papers that met the inclusion criteria. These papers reported passive muscle mechanics from single muscle fiber to whole muscle across 16 species and 54 distinct muscles. We found a wide range of methodological differences in sample selection, preparation, testing, and analysis. The systematic review revealed that passive muscle mechanics is species and scale dependent-specifically within mammals, the passive mechanics increases non-linearly with scale. However, a detailed understanding of passive mechanics is still unclear because the varied methodologies impede comparisons across studies, scales, species, and muscles. Therefore, we recommend the following: smaller scales may be maintained within storage solution prior to testing, when samples are tested statically use 2-3 min of relaxation time, stress normalization at the whole muscle level be to physiologic cross-sectional area, strain normalization be to sarcomere length when possible, and an exponential equation be used to fit the data. Additional studies using these recommendations will allow exploration of the multiscale relationship of passive force within and across species to provide the fundamental knowledge needed to improve our understanding of passive muscle mechanics.

Larger muscle fibers and fiber bundles manifest smaller elastic modulus in paraspinal muscles of rats and humans

The passive elastic modulus of muscle fiber appears to be size-dependent. The objectives of this study were to determine whether this size effect was evident in the mechanical testing of muscle fiber bundles and to examine whether the muscle fiber bundle cross-section is circular. Muscle fibers and fiber bundles were extracted from lumbar spine multifidus and longissimus of three cohorts: group one (G1) and two (G2) included 13 (330 ± 14 g) and 6 (452 ± 28 g) rats, while Group 3 (G3) comprised 9 degenerative spine patients. A minimum of six muscle fibers and six muscle fiber bundles from each muscle underwent cumulative stretches, each of 10% strain followed by 4 minutes relaxation. For all specimens, top and side diameters were measured. Elastic modulus was calculated as tangent at 30% strain from the stress–strain curve. Linear correlations between the sample cross sectional area (CSA) and elastic moduli in each group were performed. The correlations showed that increasing specimen CSA resulted in lower elastic modulus for both rats and humans, muscle fibers and fiber bundles. The median ratio of major to minor axis exceeded 1.0 for all groups, ranging between 1.15–1.29 for fibers and 1.27–1.44 for bundles. The lower elastic moduli with increasing size can be explained by relatively less collagenous extracellular matrix in the large fiber bundles. Future studies of passive property measurement should aim for consistent bundle sizes and measuring diameters of two orthogonal axes of the muscle specimens.

The effect of vertebral level on biomechanical properties of the lumbar paraspinal muscles in a rat model

INTRODUCTION

Passive mechanical properties of the paraspinal muscles are important to the biomechanical functioning of the spine. In most computational models, the same biomechanical properties are assumed for each paraspinal muscle group, while cross-sectional area or fatty infiltration in these muscles have been reported to differ between the vertebral levels. Two important properties for musculoskeletal modeling are the slack sarcomere length and the tangent modulus. This study aimed to investigate the effect of vertebral level on these biomechanical properties of paraspinal muscles in a rat model.

METHODS

The left paraspinal muscles of 13 Sprague-Dawley rats were exposed under anesthesia. Six muscle biopsies were collected from each rat: three from multifidus (one per each of the L1, L3, and L5 levels) and similarly three from longissimus. Each biopsy was cut into two halves. From one half, two to three single muscle fibers and two to six muscle fiber bundles (14 ± 7 fibers surrounded in their connective tissue) were extracted and mechanically tested in a passive state. From the resulting stress-strain data, tangent modulus was calculated as the slope of the tangent at 30% strain and slack sarcomere length (beyond which passive force starts to develop) was recorded. The other half of each biopsy, which represented the muscle at the fascicle level, was snap frozen, sectioned, stained for Collagen I and its area fraction was measured. To evaluate the effect of spinal level on these biomechanical properties of multifidus and longissimus, one-way repeated measures ANOVA (p < 0.05) was performed for tangent modulus and slack sarcomere length, while for collagen I content linear mixed-models analysis was adopted.

RESULTS

In total, 192 fibers and 262 fiber bundles were mechanically tested. For both muscle groups, no significant difference in tangent modulus of the single fibers was detected between the three spinal levels (p = 0.9 for multifidus and p = 0.08 for longissimus). Similarly, the tangent modulus values for the fiber bundles were not significantly different between the three spinal levels (p = 0.13 for multifidus and p = 0.49 for longissimus). In both muscle groups, the slack sarcomere lengths were not different among the spinal levels except for multifidus fibers (p = 0.02). Collagen I area fraction in muscle fascicles averaged 6.8% for multifidus and 5.3% for longissimus and was not different between the spinal levels.

DISCUSSION

The results of this study highlighted that the tangent modulus, slack sarcomere length, and collagen I content of the lumbar paraspinal muscles are independent of spinal level. This finding provides the basis for the assumption of similar mechanical properties along a paraspinal muscle group.

Training Induced Changes to Skeletal Muscle Passive Properties Are Evident in Both Single Fibers and Fiber Bundles in the Rat Hindlimb

Introduction: The passive mechanical behavior of skeletal muscle represents both important and generally underappreciated biomechanical properties with little attention paid to their trainability. These experiments were designed to gain insight into the trainability of muscle passive mechanical properties in both single fibers and fiber bundles.

Methods: Rats were trained in two groups: 4 weeks of either uphill (UH) or downhill (DH) treadmill running; with a third group as sedentary control. After sacrifice, the soleus (SOL), extensor digitorum longus (EDL), and vastus intermedius (VI) were harvested. One hundred seventy-nine bundles and 185 fibers were tested and analyzed using a cumulative stretch-relaxation protocol to determine the passive stress and elastic modulus. Titin isoform expression was analyzed using sodium dodecyl sulfate vertical agarose gel electrophoresis (SDS-VAGE).

Results: Single fibers: passive modulus and stress were greater for the EDL at sarcomere lengths (SLs) ≥ 3.7 μm (modulus) and 4.0 μm (stress) with DH training compared to UH training and lesser for the SOL (SLs ≥ 3.3 μm) with DH training compared with control; there was no effect of UH training. Vastus intermedius was not affected by either training protocol. Fiber bundles: passive modulus and stress were greater for the EDL at SLs ≥ 2.5 μm (modulus) and 3.3 μm (stress) in the DH training group as compared with control, while no affects were observed in either the SOL or VI for either training group. No effects on titin isoform size were detected with training.

Conclusion: This study demonstrated that a trainability of passive muscle properties at both the single fiber and fiber bundle levels was not accompanied by any detectable changes to titin isoform size.

Fiber Type and Size as Sources of Variation in Human Single Muscle Fiber Passive Elasticity

Studies on single muscle fiber passive material properties often report relatively large variation in elastic modulus (or normalized stiffness), and it is not clear where this variation arises. This study was designed to determine if the stiffness, normalized to both fiber cross-sectional area and length, is inherently different between types 1 and 2 muscle fibers. Vastus lateralis fibers (n = 93), from ten young men, were mechanically tested using a cumulative stretch-relaxation protocol. SDS-PAGE classified fibers as types 1 or 2. While there was a difference in normalized stiffness between fiber types (p = 0.0019), an unexpected inverse relationship was found between fiber diameter and normalized stiffness (r = -0.64; p < 0.001). As fiber type and diameter are not independent, a one-way analysis of covariance (ANCOVA) including fiber diameter as a covariate was run; this eliminated the effect of fiber type on normalized stiffness (p = 0.1935). To further explore the relationship between fiber size and elastic properties, we tested whether stiffness was linearly related to fiber cross-sectional area, as would be expected for a homogenous material. Passive stiffness was not linearly related to fiber area (p < 0.001), which can occur if single muscle fibers are better represented as composite materials. The rule of mixtures for composite materials was used to explore whether the presence of a stiff perimeter-based fiber component could explain the observed results. The model (R2 = 0.38) predicted a perimeter-based normalized stiffness of 8800 ± 2600 kPa/μm, which is within the range of basement membrane moduli reported in the literature.