A simple geometrical model accounting for 3D muscle architectural changes across muscle lengths

Influence of muscle packing on the three-dimensional architecture of rabbit M. plantaris

In their physiological condition, muscles are surrounded by connective tissue, other muscles and bone. These tissues exert transverse forces that change the three-dimensional shape of the muscle compared to its isolated condition, in which all surrounding tissues are removed. A change in shape affects the architecture of a muscle and therefore its mechanical properties. The rabbit M. plantaris is a multi-pennate calf muscle consisting of two compartments. A smaller, bi-pennate inner muscle compartment is embedded in a larger, uni-pennate outer compartment (Böl et al., 2015). As part of the calf, the plantaris is tightly packed between other muscles. It is unclear how packing affects the shape and architecture of the plantaris. Therefore, we examined the isolated and packed plantaris of the contralateral legs of three rabbits to determine the influence of the surrounding muscles on its shape and architectural properties using photogrammetric reconstruction and manual digitization, respectively. In the packed condition, the plantaris showed a 27% increase in fascicle pennation and a 54% increase in fascicle curvature compared to the isolated condition. Fascicle length was not affected by muscle packing. The change in muscle architecture occurred mainly in the outer compartment of the plantaris. Furthermore, the isolated plantaris showed a more circular shape and a reduced width of its muscle belly. It can be concluded that the packed plantaris is flattened by the forces exerted by the surrounding muscles, causing a complex architectural change. The data provided improve our understanding of muscle packages in general and can be used to develop and validate realistic three-dimensional muscle models.

Impact of contraction intensity and ankle joint angle on calf muscle fascicle length and pennation angle during isometric and dynamic contractions

During muscle contraction, not only are the fascicles shortening but also the pennation angle changes, which leads to a faster contraction of the muscle than of its fascicles. This phenomenon is called muscle gearing, and it has a direct influence on the force output of the muscle. There are few studies showing pennation angle changes during isometric and concentric contractions for different contraction intensities and muscle lengths. Therefore, the aim was to determine these influences over a wide range of contraction intensities and ankle joint angles for human triceps surae. Additionally, the influence of contraction intensity and ankle joint angle on muscle gearing was evaluated. Ten sport students performed concentric and isometric contractions with intensities between 0 and 90% of the maximum voluntary contraction and ankle joint angles from 50° to 120°. During these contractions, the m. gastrocnemius medialis and lateralis and the m. soleus were recorded via ultrasound imaging. A nonlinear relationship between fascicle length and pennation angle was discovered, which can be described with a quadratic fit for each of the muscles during isometric contraction. A nearly identical relationship was detected during dynamic contraction. The muscle gearing increased almost linearly with contraction intensity and ankle joint angle.

Influence of muscle length on the three-dimensional architecture and aponeurosis dimensions of rabbit calf muscles

The function of a muscle is highly dependent on its architecture, which is characterized by the length, pennation, and curvature of the fascicles, and the geometry of the aponeuroses. During in vivo function, muscles regularly undergo changes in length, thereby altering their architecture. During passive muscle lengthening, fascicle length (FL) generally increases and the angle of fascicle pennation (FP) and the fascicle curvature (FC) decrease, while the aponeuroses increase in length but decrease in width. Muscles are differently structured, making their change during muscle lengthening complex and multifaceted. To obtain comprehensive data on architectural changes in muscles during passive length, the present study determined the three-dimensional fascicle geometry of rabbit M. gastrocnemius medialis (GM), M. gastrocnemius lateralis (GL), and M. plantaris (PLA). For this purpose, the left and right legs of three rabbits were histologically fixed at targeted ankle joint angles of 95° (short muscle length [SML]) and 60° (long muscle length [LML]), respectively, and the fascicles were tracked by manual three-dimensional digitization. In a second set of experiments, the GM aponeurosis dimensions of ten legs from five rabbits were determined at varying muscle lengths via optical marker tracking. The GM consisted of a uni-pennated compartment, whereas the GL and PLA contained multiple compartments of differently pennated fascicles. In the LML compared to the SML, the GM, GL, and PLA had on average a 41%, 29%, and 41% increased fascicle length, and a 30%, 25%, and 33% decrease in fascicle pennation and a 32%, 11%, and 35% decrease in fascicle curvature, respectively. Architectural properties were also differentiated among the different compartments of the PLA and GL, allowing for a more detailed description of their fascicle structure and changes. It was shown that the compartments change differently with muscle length. It was also shown that for each degree of ankle joint angle reduction, the proximal GM aponeurosis length increased by 0.11%, the aponeurosis width decreased by 0.22%, and the area was decreased by 0.20%. The data provided improve our understanding of muscles and can be used to develop and validate muscle models.

Histomorphological and functional contralateral symmetry in the gastrocnemius muscles of the laboratory rat

It is usual in anatomical and physiological research to assess the effects of some intervention on extremities (e.g., training programmes or injury recovery protocols) using one muscle for the intervention and its contralateral as control. However, the existence of laterality (left‐handedness or right‐handedness) in athletes of different specialities is widely recognized. In rats, gastrocnemius is one of the muscles most widely used because of its importance in locomotion and high relative limb mass. Since we have not found studies reporting laterality assessment on the morphology and function in rat gastrocnemius, our study aimed to evaluate the fibre histochemical, morphometrical and muscle force contractile properties between right and left gastrocnemius of the laboratory rat. Fibre‐type proportion, fibre morphometrical measurements, muscle capillarization and muscle force properties were analysed in the right and left gastrocnemius of six male rats. No statistically significant differences (p = 0.265) were found in gastrocnemius to body weight ratio (‰) between right (6.55 ± 0.40) and left (6.49 ± 0.40) muscles. The muscles analysed showed a great degree of heterogeneity in fibre type distribution, having three clearly distinguished regions named red, mixed and white. In the three regions, there were no statistical differences in fibre type proportions between right and left gastrocnemius, as is indicated by the p‐values (from 0.203 to 0.941) obtained after running t‐Student paired tests for each fibre type. When analysing fibre cross‐sectional area, individual fibre capillarization and fibre circularity, no significant differences between right and left gastrocnemius in any of these morphometrical parameters were found in any muscle region or fibre type. Most of the p‐values (70%) resulting from running t‐Student paired tests were higher than 0.400, and the lowest p‐value was 0.115. Seemingly, global capillary and fibre densities were not statistically different between right and left sides in all muscle regions with p‐values ranging from 0.337 to 0.812. Force parameters normalized to gastrocnemius mass (mN g⁻¹) did not show any significant difference between right (PF = 74.0 ± 13.4, TF = 219.4 ± 13.0) and left (PF = 70.9 ± 10.7, TF = 213.0 ± 18.0) muscles with p = 0.623 (PF) and p = 0.514 (TF). Twitch time parameters (ms) also lacked significant differences between the two sides (CT: 43.4 ± 8.6 vs. 45.0 ± 14.3, p = 0.639; HRT: 77.6 ± 15.0 vs. 82.3 ± 25.3, p = 0.475). Finally, both muscles also showed similar (p = 0.718) fatigue properties. We did find an absence of laterality at the morphological and functional levels, which raises the possibility of using right and left gastrocnemius muscles interchangeably for experimental designs where one muscle is used to analyse data after a physiological intervention and its contralateral muscle plays the control role, thus allowing unbiased paired comparisons to derive accurate conclusions.

Architectural model for muscle growth during maturation

Muscle architecture, which includes parameters like fascicle length, pennation angle, and physiological cross-sectional area, strongly influences skeletal muscles' mechanical properties. During maturation, the muscle architecture has to adapt to a growing organism. This study aimed to develop an architectural model capable of predicting the complete 3D fascicle architecture for primarily unipennate muscles of an arbitrary age, based on fascicle data for an initial age. For model development, we collected novel data on 3D muscle architecture of the rabbit (Oryctolagus cuniculus) M. plantaris of eight animals ranging in age from 29 to 106 days. Experimental results show that plantaris muscle belly length increases by 73%, whereas mean fascicle length and mean pennation angle increases by 39 and 14%, respectively. Those changes were incorporated into the model. In addition to the data collected for M. plantaris the predictions of the model were compared to existing literature data of rabbit M. soleus and M. gastrocnemius medialis. With an error of −1.0 ± 8.6% for relative differences in aponeurosis length, aponeurosis width, muscle height, and muscle mass, the model delivered good results matching interindividual differences. For future studies, the model could be utilized to generate realistic architectural data sets for simulation studies.

Modeling of muscular activation of the muscle-tendon complex using discrete element method

The tearing of a muscle-tendon complex (MTC) is caused by an eccentric contraction; however, the structures involved and the mechanisms of rupture are not clearly identified. The passive mechanical behavior the MTC has already been modeled and validated with the discrete element method. The muscular activation is the next needed step. The aim of this study is to model the muscle fiber activation and the muscular activation of the MTC to validate their active mechanical behaviors. Each point of the force/length relationship of the MTC (using a parabolic law for the force/length relationship of muscle fibers) is obtained with two steps: 1) a passive tensile (or contractile) test until the desired elongation is reached and 2) fiber activation during a position holding that can be managed thanks to the Discrete Element model. The muscular activation is controlled by the activation of muscle fiber. The global force/length relationship of a single fiber and of the complete MTC during muscular activation is in agreement with literature. The influence of the external shape of the structure and the pennation angle are also investigated. Results show that the different constituents of the MTC (extracellular matrix, tendon), and the geometry, play an important role during the muscular activation and enable to decrease the maximal isometric force of the MTC. Moreover, the maximal isometric force decreases when the pennation angle increases. Further studies will combine muscular activation with a stretching of the MTC, until rupture, in order to numerically reproduce the tearing of the MTC.