A multiple fascicle muscle force model of the human triceps surae

Coronal As Well As Sagittal Fascicle Dynamics Can Bring About a Gearing Effect in Muscle Elongation by Passive Lengthening

PURPOSE

The amount of muscle belly elongation induced by passive lengthening is often assumed to be equal to that of fascicles. But these are different if fascicles shorter than the muscle belly rotate around their attachment sites. Such discrepancy between fascicles and muscle belly length changes can be considered as gearing. As the muscle fascicle arrangement is 3D, the fascicle rotation by passive lengthening may occur in the coronal as well as the sagittal planes. Here we examined the fascicle 3D dynamics and resultant gearing during passive elongation of human medial gastrocnemius in vivo .

METHODS

For 16 healthy adults, we reconstructed fascicles three-dimensionally using diffusion tensor imaging and evaluated the change in fascicle length and angles in the sagittal and coronal planes during passive ankle dorsiflexion (from 20° plantar flexion to 20° dorsiflexion).

RESULTS

Whole muscle belly elongation during passive ankle dorsiflexion was 38% greater than the fascicle elongation. Upon passive lengthening, the fascicle angle in the sagittal plane in all regions (-5.9°) and that in the coronal plane in the middle-medial (-2.7°) and distal-medial (-4.3°) regions decreased significantly. Combining the fascicle coronal and sagittal rotation significantly increased the gearing effects in the middle-medial (+10%) and distal-medial (+23%) regions. The gearing effect by fascicle sagittal and coronal rotations corresponded to 26% of fascicle elongation, accounting for 19% of whole muscle belly elongation.

CONCLUSIONS

Fascicle rotation in the coronal and sagittal planes is responsible for passive gearing, contributing to the whole muscle belly elongation. Passive gearing can be favorable for reducing fascicle elongation for a given muscle belly elongation.

Mechanism of elastic energy storage of honey bee abdominal muscles under stress relaxation

Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.

Three-dimensional architecture of human medial gastrocnemius fascicles in vivo: Regional variation and its dependence on muscle size

Fascicle architecture (length and pennation angle) can vary regionally within a muscle. The architectural variability in human muscles has been evaluated in vivo, but the interindividual variation and its determinants remain unclear. Considering that within‐muscle non‐uniform changes in pennation angle are associated with change in muscle size by chronic mechanical loading, we hypothesized that the regional variation in fascicle architecture is dependent on interindividual variation in muscle size. To test this hypothesis, we reconstructed fascicles three‐dimensionally along and across the whole medial gastrocnemius in the right lower leg of 15 healthy adults (10 males and 5 females, 23.7 ± 3.3 years, 165.8 ± 8.3 cm, 61.9 ± 11.4 kg, mean ± standard deviation) in neutral ankle joint position with the knee fully extended, using magnetic resonance diffusion tensor imaging and tractography. The 3D‐reconstructed fascicles arose from the deep aponeurosis with variable lengths and angles both in sagittal and coronal planes. The fascicle length was significantly longer in the middle (middle‐medial: 52.4 ± 6.1 mm, middle‐lateral: 52.0 ± 5.1 mm) compared to distal regions (distal‐medial: 41.0 ± 5.0 mm, distal‐lateral: 38.9 ± 3.6 mm, p < 0.001). The 2D pennation angle (angle relative to muscle surface) was significantly greater in distal than middle regions, and medial than lateral regions (middle‐medial: 26.6 ± 3.1°, middle‐lateral: 24.1 ± 2.3°, distal‐medial: 31.2 ± 3.6°, distal‐lateral: 29.2 ± 3.0°, p ≤ 0.017), while only a proximo‐distal difference was significant (p < 0.001) for 3D pennation angle (angle relative to line of action of muscle). These results clearly indicate fascicle's architectural variation in 3D. The magnitude of regional variation evaluated as standard deviation across regions differed considerably among individuals (4.0–10.7 mm for fascicle length, 0.9–5.0° for 2D pennation angle, and 3.0–8.8° for 3D pennation angle), which was positively correlated with the muscle volume normalized to body mass (r = 0.659–0.828, p ≤ 0.008). These findings indicate muscle‐size dependence of the variability of fascicle architecture.

Three-dimensional modelling of human quadriceps femoris forces

Quadriceps intramuscular anatomy is typically described in two dimensions. However, anatomical descriptions indicate fascicles in the quadriceps may have a three-dimensional orientation. The purpose of this investigation was to quantify the maximum force generating capacity of the individual quadriceps' muscles in three dimensions. Muscle architectural parameters were obtained from three cadaver specimens (two female) and input into a geometry-based multiple fascicle muscle force model. Vastus lateralis, vastus medialis, and rectus femoris had partitions which could be defined based on differences in the sense and direction of fascicles between partitions. Vastus lateralis and rectus femoris were bipennate due to partitions sharing an aponeurosis. Vastus lateralis deep and superficial partitions exerted posterior- (maximum: -29 ± 5 N) and anterior-directed (maximum: 58 ± 15 N) forces on their shared distal aponeurosis. Rectus femoris medial and lateral partitions exerted medial- (maximum: -38 ± 17 N) and lateral-directed (maximum: 19 ± 12 N) forces on their shared proximal aponeurosis. All vastus medialis fascicles ran along the proximal-distal axis. However, fascicles arising near the lesser trochanter also ran along the superficial-deep axis, while fascicles arising from the linea aspera ran along the medial-lateral axis. Thus, vastus medialis could be divided into longus and oblique partitions. Due to the large pennation angle, vastus medialis oblique could exert maximum medial-directed (-219 ± 93 N) and proximal-directed (279 ± 168 N) forces at approximately -40° and -70° knee flexion, respectively, indicating dual roles for vastus medialis oblique dependent on knee flexion angle.