Passive and dynamic muscle architecture during transverse loading for gastrocnemius medialis in man

Determination of muscle shape deformations of the tibialis anterior during dynamic contractions using 3D ultrasound

Purpose

In this paper, we introduce a novel method for determining 3D deformations of the human tibialis anterior (TA) muscle during dynamic movements using 3D ultrasound.

Materials and Methods

An existing automated 3D ultrasound system is used for data acquisition, which consists of three moveable axes, along which the probe can move. While the subjects perform continuous plantar- and dorsiflexion movements in two different controlled velocities, the ultrasound probe sweeps cyclically from the ankle to the knee along the anterior shin. The ankle joint angle can be determined using reflective motion capture markers. Since we considered the movement direction of the foot, i.e., active or passive TA, four conditions occur: slow active, slow passive, fast active, fast passive. By employing an algorithm which defines ankle joint angle intervals, i.e., intervals of range of motion (ROM), 3D images of the volumes during movement can be reconstructed.

Results

We found constant muscle volumes between different muscle lengths, i.e., ROM intervals. The results show an increase in mean cross-sectional area (CSA) for TA muscle shortening. Furthermore, a shift in maximum CSA towards the proximal side of the muscle could be observed for muscle shortening. We found significantly different maximum CSA values between the fast active and all other conditions, which might be caused by higher muscle activation due to the faster velocity.

Conclusion

In summary, we present a method for determining muscle volume deformation during dynamic contraction using ultrasound, which will enable future empirical studies and 3D computational models of skeletal muscles.

3D ultrasound-based determination of skeletal muscle fascicle orientations

Architectural parameters of skeletal muscle such as pennation angle provide valuable information on muscle function, since they can be related to the muscle force generating capacity, fiber packing, and contraction velocity. In this paper, we introduce a 3D ultrasound-based workflow for determining 3D fascicle orientations of skeletal muscles. We used a custom-designed automated motor driven 3D ultrasound scanning system for obtaining 3D ultrasound images. From these, we applied a custom-developed multiscale-vessel enhancement filter-based fascicle detection algorithm and determined muscle volume and pennation angle. We conducted trials on a phantom and on the human tibialis anterior (TA) muscle of 10 healthy subjects in plantarflexion (157 ± 7∘ ), neutral position (109 ± 7∘ , corresponding to neutral standing), and one resting position in between (145 ± 6∘ ). The results of the phantom trials showed a high accuracy with a mean absolute error of 0.92 ± 0.59∘ . TA pennation angles were significantly different between all positions for the deep muscle compartment; for the superficial compartment, angles are significantly increased for neutral position compared to plantarflexion and resting position. Pennation angles were also significantly different between superficial and deep compartment. The results of constant muscle volumes across the 3 ankle joint angles indicate the suitability of the method for capturing 3D muscle geometry. Absolute pennation angles in our study were slightly lower than recent literature. Decreased pennation angles during plantarflexion are consistent with previous studies. The presented method demonstrates the possibility of determining 3D fascicle orientations of the TA muscle in vivo.

A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years

Both the Hill and the Huxley muscle models had already been described by the time the International Society of Biomechanics was founded 50 years ago, but had seen little use before the 1970s due to the lack of computing. As computers and computational methods became available in the 1970s, the field of musculoskeletal modeling developed and Hill type muscle models were adopted by biomechanists due to their relative computational simplicity as compared to Huxley type muscle models. Muscle forces computed by Hill type muscle models provide good agreement in conditions similar to the initial studies, i.e. for small muscles contracting under steady and controlled conditions. However, more recent validation studies have identified that Hill type muscle models are least accurate for natural in vivo locomotor behaviours at submaximal activations, fast speeds and for larger muscles, and thus need to be improved for their use in understanding human movements. Developments in muscle modelling have tackled these shortcomings. However, over the last 50 years musculoskeletal simulations have been largely based on traditional Hill type muscle models or even simplifications of this model that neglected the interaction of the muscle with a compliant tendon. The introduction of direct collocation in musculoskeletal simulations about 15 years ago along with further improvements in computational power and numerical methods enabled the use of more complex muscle models in simulations of whole-body movement. Whereas Hill type models are still the norm, we may finally be ready to adopt more complex muscle models into musculoskeletal simulations of human movement.

TimTrack: A drift-free algorithm for estimating geometric muscle features from ultrasound images

Ultrasound imaging is valuable for non-invasively estimating fascicle lengths and other features of pennate muscle, especially when performed computationally. Effective analysis techniques to date typically use optic flow to track displacements from image sequences, but are sensitive to integration drift for longer sequences. We here present an alternative algorithm that objectively estimates geometric features of pennate muscle from ultrasound images, without drift sensitivity. The algorithm identifies aponeuroses and estimates fascicle angles to derive fascicle lengths. Length estimates of human vastus lateralis and gastrocnemius fascicles in healthy subjects (N = 9 and N = 17 respectively) compared well (overall root-mean-square difference, RMSD = 0.52 cm) to manual estimates by independent observers (n = 3), with overall coefficient of multiple correlation (CMC) of 0.98. Our tests yielded accuracy (CMC, RMSD) and processing speed similar to or exceeding that of state-of-the-art algorithms. The algorithm requires minimal manual intervention and can optionally extrapolate fascicle lengths that extend beyond the image frame. It thus facilitates automated analysis of ultrasound images without drift.

The high energetic cost of rapid force development in muscle

Muscles consume metabolic energy for active movement, particularly when performing mechanical work or producing force. Less appreciated is the cost for activating muscle quickly, which adds considerably to the overall cost of cyclic force production. However, the cost magnitude relative to the cost of mechanical work, which features in many movements, is unknown. We therefore tested whether fast activation is costly compared with performing work or producing isometric force. We hypothesized that metabolic cost would increase with a proposed measure termed force rate (rate of increase in muscle force) in cyclic tasks, separate from mechanical work or average force level. We tested humans (N=9) producing cyclic knee extension torque against an isometric dynamometer (torque 22 N m, cyclic waveform frequencies 0.5-2.5 Hz), while also quantifying quadriceps muscle force and work against series elasticity (with ultrasonography), along with metabolic rate through respirometry. Net metabolic rate increased by more than four-fold (10.5 to 46.8 W) with waveform frequency. At high frequencies, the hypothesized force-rate cost accounted for nearly half (40%) of energy expenditure. This exceeded the cost for average force (17%) and was comparable to the cost for shortening work (43%). The force-rate cost is explained by additional active calcium transport necessary for producing forces at increasing waveform frequencies, owing to rate-limiting dynamics of force production. The force-rate cost could contribute substantially to the overall cost of movements that require cyclic muscle activation, such as locomotion.

The Energy of Muscle Contraction. III. Kinetic Energy During Cyclic Contractions

During muscle contraction, chemical energy is converted to mechanical energy when ATP is hydrolysed during cross-bridge cycling. This mechanical energy is then distributed and stored in the tissue as the muscle deforms or is used to perform external work. We previously showed how energy is distributed through contracting muscle during fixed-end contractions; however, it is not clear how the distribution of tissue energy is altered by the kinetic energy of muscle mass during dynamic contractions. In this study we conducted simulations of a 3D continuum muscle model that accounts for tissue mass, as well as force-velocity effects, in which the muscle underwent sinusoidal work-loop contractions coupled with bursts of excitation. We found that increasing muscle size, and therefore mass, increased the kinetic energy per unit volume of the muscle. In addition to greater relative kinetic energy per cycle, relatively more energy was also stored in the aponeurosis, and less was stored in the base material, which represented the intra and extracellular tissue components apart from the myofibrils. These energy changes in larger muscles due to greater mass were associated lower mass-specific mechanical work output per cycle, and this reduction in mass-specific work was greatest for smaller initial pennation angles. When we compared the effects of mass on the model tissue behaviour to that of in situ muscle with added mass during comparable work-loop trials, we found that greater mass led to lower maximum and higher minimum acceleration in the longitudinal (x) direction near the middle of the muscle compared to at the non-fixed end, which indicates that greater mass contributes to tissue non-uniformity in whole muscle. These comparable results for the simulated and in situ muscle also show that this modelling framework behaves in ways that are consistent with experimental muscle. Overall, the results of this study highlight that muscle mass is an important determinant of whole muscle behaviour.

Passive skeletal muscle can function as an osmotic engine

Muscles are composite structures. The protein filaments responsible for force production are bundled within fluid-filled cells, and these cells are wrapped in ordered sleeves of fibrous collagen. Recent models suggest that the mechanical interaction between the intracellular fluid and extracellular collagen is essential to force production in passive skeletal muscle, allowing the material stiffness of extracellular collagen to contribute to passive muscle force at physiologically relevant muscle lengths. Such models lead to the prediction, tested here, that expansion of the fluid compartment within muscles should drive forceful muscle shortening, resulting in the production of mechanical work unassociated with contractile activity. We tested this prediction by experimentally increasing the fluid volumes of isolated bullfrog semimembranosus muscles via osmotically hypotonic bathing solutions. Over time, passive muscles bathed in hypotonic solution widened by 16.44 ± 3.66% (mean ± s.d.) as they took on fluid. Concurrently, muscles shortened by 2.13 ± 0.75% along their line of action, displacing a force-regulated servomotor and doing measurable mechanical work. This behaviour contradicts the expectation for an isotropic biological tissue that would lengthen when internally pressurized, suggesting a functional mechanism analogous to that of engineered pneumatic actuators and highlighting the significance of three-dimensional force transmission in skeletal muscle.

The Effect of Multidirectional Loading on Contractions of the M. Medial Gastrocnemius

Research has shown that compression of muscle can lead to a change in muscle force. Most studies show compression to lead to a reduction in muscle force, although recent research has shown that increases are also possible. Based on methodological differences in the loading design between studies, it seems that muscle length and the direction of transverse loading influence the effect of muscle compression on force production. Thus, in our current study we implement these two factors to influence the effects of muscle loading. In contrast to long resting length of the medial gastrocnemius (MG) in most studies, we use a shorter MG resting length by having participant seated with their knees at a 90° angle. Where previous studies have used unidirectional loads to compress the MG, in this study we applied a multidirectional load using a sling setup. Multidirectional loading using a sling setup has been shown to cause muscle force reductions in previous research. As a result of our choices in experimental design we observed changes in the effects of muscle loading compared to previous research. In the present study we observed no changes in muscle force due to muscle loading. Muscle thickness and pennation angle showed minor but significant increases during contraction. However, no significant changes occurred between unloaded and loaded trials. Fascicle thickness and length showed different patterns of change compared to previous research. We show that muscle loading does not result in force reduction in all situations and is possibly linked to differences in muscle architecture and muscle length.

The Energy of Muscle Contraction. II. Transverse Compression and Work

In this study we examined how the strain energies within a muscle are related to changes in longitudinal force when the muscle is exposed to an external transverse load. We implemented a three-dimensional (3D) finite element model of contracting muscle using the principle of minimum total energy and allowing the redistribution of energy through different strain energy-densities. This allowed us to determine the importance of the strain energy-densities to the transverse forces developed by the muscle. We ran a series of in silica experiments on muscle blocks varying in initial pennation angle, muscle length, and external transverse load. As muscle contracts it maintains a near constant volume. As such, any changes in muscle length are balanced by deformations in the transverse directions such as muscle thickness or muscle width. Muscle develops transverse forces as it expands. In many situations external forces act to counteract these transverse forces and the muscle responds to external transverse loads while both passive and active. The muscle blocks used in our simulations decreased in thickness and pennation angle when passively compressed and pushed back on the load when they were activated. Activation of the compressed muscle blocks led either to an increase or decrease in muscle thickness depending on whether the initial pennation angle was less than or greater than 15°, respectively. Furthermore, the strain energy increased and redistributed across the different strain-energy potentials during contraction. The volumetric strain energy-density varied with muscle length and pennation angle and was reduced with greater transverse load for most initial muscle lengths and pennation angles. External transverse load reduced the longitudinal muscle force for initial pennation angles of β₀ = 0°. Whereas for pennate muscle (β₀ > 0°) longitudinal force changed (increase or decrease) depending on the muscle length, pennation angle and the direction of the external load relative to the muscle fibres. For muscle blocks with initial pennation angles β₀ ≤ 20° the reduction in longitudinal muscle force coincided with a reduction in volumetric strain energy-density.

In vivo oscillations of the soleus muscle can be quantified using b-mode ultrasound imaging during walking and running in humans

Impact forces, due to the foot contacting the ground during locomotion, can be considered input signals to the body that must be dissipated to prevent impact-related injuries. One proposed mechanism employed by the body to damp the impact is through vibrations of the skeletal muscles. However, there is yet to be direct in vivo measures of muscle oscillations during locomotion. This study investigated the use of 2D ultrasound imaging to quantify transverse muscle oscillations (deep-superficial displacement of the muscle boundary relative to the skin) in response to impact forces elicited by walking and running at a range of speeds. Increases in vertical impact forces with faster walking and running was consistent with changes in both magnitude and frequency in the measured oscillations of the soleus muscle; one of the main human ankle plantar flexors. Muscle oscillations contained more higher frequency components at fast running (50% signal power in frequencies below ~ 14 Hz) compared with slow walking (50% signal power contained in frequencies below ~ 5 Hz). This study provides a platform for ultrasound imaging to examine muscle oscillation responses to impact forces induced by changes in external interfaces such as shoe material, locomotion type and ground surface properties.

The Energy of Muscle Contraction. I. Tissue Force and Deformation During Fixed-End Contractions

During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

The Multi-Scale, Three-Dimensional Nature of Skeletal Muscle Contraction

Muscle contraction is a three-dimensional process, as anyone who has observed a bulging muscle knows. Recent studies suggest that the three-dimensional nature of muscle contraction influences its mechanical output. Shape changes and radial forces appear to be important across scales of organization. Muscle architectural gearing is an emerging example of this process.

Ultrasound imaging to assess skeletal muscle architecture during movements: a systematic review of methods, reliability, and challenges

B-mode ultrasound is often used to quantify muscle architecture during movements. Our objectives were to 1) systematically review the reliability of fascicle length (FL) and pennation angles (PA) measured using ultrasound during movements involving voluntary contractions; 2) systematically review the methods used in studies reporting reliability, discuss associated challenges, and provide recommendations to improve the reliability and validity of dynamic ultrasound measurements; and 3) provide an overview of computational approaches for quantifying fascicle architecture, their validity, agreement with manual quantification of fascicle architecture, and advantages and drawbacks. Three databases were searched until June 2019. Studies among healthy human individuals aged 17-85 yr that investigated the reliability of FL or PA in lower-extremity muscles during isoinertial movements and that were written in English were included. Thirty studies (n = 340 participants) were included for reliability analyses. Between-session reliability as measured by coefficient of multiple correlations (CMC), and coefficient of variation (CV) was FL CMC: 0.89-0.96; CV: 8.3% and PA CMC: 0.87-0.90; CV: 4.5-9.6%. Within-session reliability was FL CMC: 0.82-0.99; CV: 0.0-6.7% and PA CMC: 0.91; CV: 0.0-15.0%. Manual analysis reliability was FL CMC: 0.89-0.96; CV: 0.0-15.9%; PA CMC: 0.84-0.90; and CV: 2.0-9.8%. Computational analysis FL CMC was 0.82-0.99, and PA CV was 14.0-15.0%. Eighteen computational approaches were identified, and these generally showed high agreement with manual analysis and high validity compared with phantoms or synthetic images. B-mode ultrasound is a reliable method to quantify fascicle architecture during movement. Additionally, computational approaches can provide a reliable and valid estimation of fascicle architecture.

Internal fluid pressure influences muscle contractile force

Fluid fills intracellular, extracellular, and capillary spaces within muscle. During normal physiological activity, intramuscular fluid pressures develop as muscle exerts a portion of its developed force internally. These pressures, typically ranging between 10 and 250 mmHg, are rarely considered in mechanical models of muscle but have the potential to affect performance by influencing force and work produced during contraction. Here, we test a model of muscle structure in which intramuscular pressure directly influences contractile force. Using a pneumatic cuff, we pressurize muscle midcontraction at 260 mmHg and report the effect on isometric force. Pressurization reduced isometric force at short muscle lengths (e.g., -11.87% of P₀ at 0.9 L₀), increased force at long lengths (e.g., +3.08% of P₀ at 1.25 L₀), but had no effect at intermediate muscle lengths ∼1.1-1.15 L₀ This variable response to pressurization was qualitatively mimicked by simple physical models of muscle morphology that displayed negative, positive, or neutral responses to pressurization depending on the orientation of reinforcing fibers representing extracellular matrix collagen. These findings show that pressurization can have immediate, significant effects on muscle contractile force and suggest that forces transmitted to the extracellular matrix via pressurized fluid may be important, but largely unacknowledged, determinants of muscle performance in vivo.

Ultrasound-derived changes in thickness of human ankle plantar flexor muscles during walking and running are not homogeneous along the muscle mid-belly region

Skeletal muscle thickness is a valuable indicator of several aspects of a muscle’s functional capabilities. We used computational analysis of ultrasound images, recorded from 10 humans walking and running at a range of speeds (0.7–5.0 m s⁻¹), to quantify interactions in thickness change between three ankle plantar flexor muscles (soleus, medial and lateral gastrocnemius) and quantify thickness changes at multiple muscle sites within each image. Statistical analysis of thickness change as a function of stride cycle (1d statistical parametric mapping) revealed significant differences between soleus and both gastrocnemii across the whole stride cycle as they bulged within the shared anatomical space. Within each muscle, changes in thickness differed between measurement sites but not locomotor condition. For some of the stride, thickness measures taken from the distal-mid image region represented the mean muscle thickness, which may therefore be a reliable region for these measures. Assumptions that muscle thickness is constant during a task, often made in musculoskeletal models, do not hold for the muscles and locomotor conditions studied here and researchers should not assume that a single thickness measure, from one point of the stride cycle or a static image, represents muscle thickness during dynamic movements.