Transverse anisotropy in the deformation of the muscle during dynamic contractions

Muscles are made up of fibre bundles called fascicles that actively generate force through their actin–myosin interactions. In pennate muscle, fascicles are oriented at an oblique angle to the line of action of the muscle and run between sheets of connective tissue that form the aponeuroses. When pennate fascicles contract and shorten, a component of their force acts to draw the aponeuroses together and decrease the belly thickness; however, the fascicles will tend to increase in thickness to remain at a relatively constant volume, leading to an increase in their pennation and a contrasting tendency to increase the aponeurosis separation (Millard et al., 2013; Zajac, 1989; Baskin and Paolini, 1966). The actual change in the overall transverse deformation depends on the balance of these effects plus additional factors that include the contribution of the stiffness of the extracellular matrix and compression from forces external to the muscle. Changes to the internal geometry of contracting muscle are thus a complex and multifactorial phenomenon.

In order to simplify the geometrical representation of muscle, many models assume that the belly thickness remains constant during contraction (Zajac, 1989; Delp et al., 2007; van den Bogert et al., 2011; Millard et al., 2013; Rajagopal et al., 2016; Randhawa and Wakeling, 2015). This allows a straightforward prediction of fascicle pennation at a given fascicle length; however, such models do not allow us to understand the mechanisms by which shape changes influence muscle mechanics and the internal structure of muscles (Randhawa and Wakeling, 2015; Dick and Wakeling, 2018). Studying changes in the transverse belly deformation is functionally important as it can influence both fascicle strains (Azizi and Deslaurens, 2014) and tendon strains (Farris et al., 2013), and the resultant forces generated by the muscle. Understanding the interaction of the whole muscle shape with the fascicle deformations and geometry requires both 3D information of the deformations and a 3D mechanistic framework to describe the system.

Contracting muscles interact with adjacent muscles and surrounding tissues via both the myofascical connections between muscles (Huijing et al., 1998) and pressures exerted on surrounding tissues due to their tendency to bulge. For instance, connective tissues linking the aponeuroses of human soleus and gastrocnemius muscles (Kinugasa et al., 2013; Hodgson et al., 2006) may transmit force between these muscles (Bojsen-Moller et al., 2010), leading to a decrease in the relative displacement of the soleus and lateral gastrocnemius (LG) with increased activity during knee flexion (Finni et al., 2017). Additionally, transverse load acting on muscles, which may be caused by transverse expansion of adjacent muscle bellies or externally applied forces, can cause substantial decreases in the longitudinal forces developed by a muscle belly (Siebert et al., 2017, 2014). Thus, understanding how muscles expand and impinge on each other is important for understanding muscle force development and function.

The medial gastrocnemius (MG) and the LG show contrasting changes in transverse deformation of the muscle belly during contraction (Maganaris et al., 1998; Randhawa et al., 2013; Randhawa and Wakeling, 2013), despite their anatomical and functional similarities. While the LG increases in thickness during plantarflexion, the belly of the MG thins as it shortens (Randhawa et al., 2013). As a muscle belly shortens in length, it should expand transversely in order to conserve volume (Zajac, 1989; Millard et al., 2013; Abbott and Baskin, 1962; Baskin and Paolini, 1966). Therefore, if the MG muscle belly shortens and decreases in thickness, it must increase in the width-wise direction that is orthogonal to length and thickness. Recent modelling studies that predicted asymmetry in the transverse belly deformations suggested that such asymmetries at the muscle belly level may be reflected by asymmetries in the transverse deformations of its constituent fascicles (Rahemi et al., 2015; Randhawa and Wakeling, 2015). To date, there are no data to describe asymmetries in fascicle deformation during active contraction of skeletal muscle, and so we hypothesized that such asymmetries would be observed during active contractions.

3D imaging of muscle and estimation of fascicle trajectories has been achieved in a number of MRI studies (Blemker and Delp, 2005; Heemskerk et al., 2009; Wokke et al., 2014; Böl et al., 2011a; Mercuri et al., 2005), but these are largely limited to passive tissue because of the long scan times required for image acquisition. Diagnostic ultrasound provides a more rapid scanning duration (Maganaris and Paul, 2000; Rana et al., 2013), allowing active muscle contractions to be tracked, and has recently been used to quantify transverse deformations in the fascicles during contraction from 2D ultrasound images (Wakeling and Randhawa, 2014). Combining this approach with 3D tracking of the ultrasound probe (Prager et al., 1998; Rana and Wakeling, 2011) should allow the 3D deformations in contracting muscle fascicles to be tracked.

The purpose of this study was to identify whether asymmetries in the transverse deformations of muscle fascicles occur during active contractions of two pennate muscles, the LG and MG. We used a dual-probe ultrasound imaging technique to scan the contracting fascicles from orthogonal directions by tracking the position and orientation of the two probes. Using this technique, we quantified the 3D deformations of both the muscle belly and the fascicles during cyclic plantarflexion contractions.

Six male and six female physically active university students participated in this study (age 28.8±5.5 years; mass 78.3±6.2 kg; height 178±2.3 cm; means±s.d.). All subjects provided informed consent in accordance with requirements from the University Office of Research Ethics.

Subjects were seated on a dynamometer (System 3, Biodex, Shirley, NY, USA) with a fixed knee angle of 163.8±3.4 deg determined using a goniometer, with the horizontal shank and foot secured to a footplate using Velcro straps (Fig. 1A). The central axis of the dynamometer was aligned to the plantarflexion axis of the ankle, and the foot was held in a neutral position with respect to inversion/eversion and internal/external rotation. Subjects performed cyclic plantarflexion–dorsiflexion isokinetic contractions with the plantarflexion phase at maximal effort and the dorsiflexion phase at minimal effort. Subjects began each series of contractions with their ankle at 15 deg dorsiflexion; each trial consisted of 8 cycles of plantarflexion ending at a limit of 25 deg plantarflexion that was set on the dynamometer (Fig. 1B). Thus, the total ankle range of motion was 40 deg. Dorsiflexion movements were velocity limited to 60 deg s⁻¹. Five plantarflexion velocities were tested: 10, 45, 90, 150, 210 deg s⁻¹, in a randomized order with 1 min rest between trials. Ankle angle and ankle torque from the dynamometer were recorded at 1 kHz using a 16-bit data-acquisition system (USB-6229; National Instruments, Austin, TX, USA). The muscle bellies of the MG and LG were imaged using B-mode ultrasound during these plantarflexion movements.

Bi-planar ultrasound imaging was performed on each of the two gastrocnemius muscles. This imaging involved simultaneous ultrasound scans from two linear array probes that scanned in orthogonal directions, and where the intersection of the scanning planes occurred within the muscle of interest (Fig. 1B). Each ultrasound probe was aligned to scan nearly continuous fascicles, and the scanning planes approximated the frontal and medial planes of the lower leg.

Ultrasound scans were acquired using 128-element (60 mm field of view, 50 mm depth and 7 MHz frequency) linear array B-mode ultrasound probes (Echoblaster 128, Telemed, Vilnius, Lithuania) scanning at 40 Hz. Each probe was fixed within a rigid body frame that was attached to a triad of LED markers (total of 6 LED markers). An optical motion capture system (Certus Optotrak, NDI, Waterloo, ON, Canada) tracked the 3D positions of these LEDs at 100 Hz, and this was used to determine the relative orientations of the ultrasound scanning planes, and their line of intersection after prior calibration (Prager et al., 1998; Rana and Wakeling, 2011). Each probe and its marker triad was attached to a tripod. Tilting the tripod head allowed the probe to be aligned to the muscle of interest (Fig. 1B). The average angle between the two scanning planes was 88 deg for the MG and 90 deg for the LG, which was calculated from the angle between their normal vectors, and was averaged across all time points for all trials. Pressure on the skin applied by the ultrasound probe can affect muscle structure (Bolsterlee et al., 2015). This pressure artifact was minimized by using a water-filled latex balloon placed between each ultrasound probe and the skin (Fig. 1B). The balloon was secured on the probe using cable ties, and acoustic coupling ultrasound gel was placed between the balloon and both the skin and the probe surface. The balloon provided a continuous and deformable contact surface with the skin, allowing unrestricted skin motion and minimal contact pressure. The two ultrasound systems recorded simultaneously, and their trigger signals were used to synchronize all the data. The MG of the right leg was tested first followed by the LG of the left leg.

In each image, the muscle belly of interest was segmented by identifying the region of interest. Three coordinates were manually digitized on each of the superficial and deep boundaries of the muscle (ImageJ software, NIH, Bethesda, MD, USA): these boundaries correspond to the aponeuroses for the slices that intersected the aponeurosis regions of the muscle (Fig. 1C). The probe orientation that most closely approximated the typical orientation used in 2D ultrasound studies was considered to scan the XZ plane and was used to calculate the pennation; the images from this scanning view displayed the greatest changes in fascicle pennation. The second ultrasound probe scanned the muscle belly in an orthogonal YZ plane (Fig. 1B). The line of action of the muscle belly was considered the Z direction, and the longitudinal axis of the fascicles was considered the z direction.

Second-order polynomials were fitted to the digitized points on the superficial and deep muscle boundaries using least-square minimization. Two further points were digitized on a prominent fascicle in each image: fascicle length was approximated from the linear line passing through the fascicle coordinates that intersected the polynomials on the muscle boundary (Fig. 1C). Pennation angle was the mean of the angles made by the intersection of the fascicle and the aponeuroses in the XZ plane. The thickness of the muscle belly was the shortest distance from superficial to deep aponeurosis through the centre of the measured fascicle in the XZ plane.

Ultrasound images of the muscle bellies were further processed to calculate transverse fascicle deformations in the following manner. Multi-scale vessel enhancement filtering was used to enhance the vessel-like features in the muscle images that were depicted as alternating dark stripes (muscle fascicles) and light stripes (connective tissue), using scales of 1.5, 2, 2.5 and 3 pixels (Rana et al., 2009; Frangi et al., 1998). The region of interest of muscle tissue was segmented using the polynomials describing the muscle boundaries, and was eroded by 10 pixels to ensure features were of muscle fascicles and not the bright lines of the boundaries.

Spatial frequencies corresponding to the fascicular stripes were calculated for the regions of interest using 2D discrete Fourier transforms (Wakeling and Randhawa, 2014), with the frequency distributions being reduced to characteristic frequencies using their fifth moments of area (Wakeling and Randhawa, 2014). These characteristic frequencies were converted to wavelengths in the x–z and y–z directions from the different scanning planes, and subsequently normalized to the mean transverse wavelength across all cycles for that muscle and subject. Image analysis was performed using custom-written code (Mathematica v. 7.0, Wolfram Research), and data were analysed for the third to seventh plantarflexion cycles in each sequence of eight cycles.

Differences were considered significant at the P<0.05 level. Data are reported as means±s.e.m.

During these series of isokinetic plantarflexions, the right and left ankles moved through a similar range of motion and generated similar ankle torque for the MG and LG during muscle shortening (Table 1). The ankle torque showed phasic increases during each plantarflexion, with the peak plantarflexion torque decreasing with angular velocity of the ankle.

During each series of contractions, the bellies of the MG and LG muscles shortened during the plantarflexion phase in a similar manner (Table 1), and the MG and LG muscle fascicles shortened and rotated to greater pennation angles (Figs 2 and 3). The mean pennation for the MG (c₁) of 27 deg was greater than for the LG at 17 deg (Table 1) and this coincided with the MG showing a greater change in pennation (a₁) and fascicle length.

For the MG, the belly transverse deformation showed thinning in the X and Y directions during plantarflexion while the fascicle expanded transversely in the x and y directions (Figs 2 and 4B,C). In contrast, the LG belly expanded transversely in both the X and Y directions whilst the LG fascicle decreased transversely in the x direction and increased transversely in the y direction during plantarflexion (Figs 3 and 4E,F).

There was a significant difference in the normalized amplitude of the cyclic changes, a₁, between the transverse deformation of the belly in the X and Y directions and between the transverse deformation of the fascicles in the x and y directions for MG and LG (Fig. 5, Table 1). In addition, for the LG the phase angle o₁ was significantly different between the two directions for the fascicle transverse deformation (by about 180 deg), indicating that the transverse deformations were out of phase between the two x and y directions (Fig. 5B).

The purpose of this study was to identify whether transverse anisotropy in the muscle fascicles occurred during active contractions. Proving that asymmetries occur using data available from this imaging technique is an example of proof by contradiction. First, consider a fascicle with a circular cross-section that undergoes an asymmetrical deformation to become an ellipse with a strain of +10% along its major axis and −5% along its minor axis. If the x and y scanning directions were aligned at 45 and 135 deg to the major axis, respectively, then the measured strains would be ε_x=ε_y=+2.8%. Thus, it is possible that symmetrical strains could be calculated in the x and y directions even if the actual fascicle deformation was transversely anisotropic. However, if asymmetrical strains were calculated in orthogonal x and y directions at any alignment within a transverse section, then this cannot have occurred from a transversely isotropic deformation, and this would be a proof by contradiction that asymmetrical fascicle expansion does occur. Whilst the data from this study do not allow us to be certain about the nature of the deformations in MG, the results from this study do, indeed, show asymmetries in the fascicle deformations for the LG, as seen by the phase relationship of their strains ε_x and ε_y differing by 180 deg (Figs 4F and 5B, Table 1). Thus, the data support the proof that fascicle deformations can be transversely anisotropic during active muscle contractions.

During contraction, cross-bridge forces develop between the myosin and actin myofilaments, and these forces have a longitudinal component that acts to slide the filaments past each other and a transverse component that acts to squeeze the myofilament lattice together (Daniel et al., 2013; Williams et al., 2013). The muscle fibres are typically considered to be nearly isovolumetric (Abbott and Baskin, 1962), and so shortening caused by the longitudinal component of cross-bridge force is matched by a tendency of the muscle fibres to increase transversely in order to maintain their volume (Rahemi et al., 2014, 2015). This increase in girth is in a transverse or radial direction across the fibres, and is thus opposed by both the radial forces from the cross-bridges and cytoskeletal structures within the muscle fibres. The cytoskeletal elements within the muscle fibres are additionally distributed in a non-uniform manner (Neering et al., 1991) and the intracellular fluid moves into the myofilament space from the myofilament lattice during contraction (Cecchi et al., 1990). Thus, transverse anisotropy within the muscle fibres can even exceed transverse anisotropies that may occur in the myofilament lattice. The actual deformation of the fibres additionally depends on forces that are external to the fibres, and these external forces may derive from surrounding tissues or even be external to the body, and are transmitted through myofascial structures and the extracellular matrix. These external forces will often be directional, for instance the compressive force between aponeurosis sheets due to the muscle fibres drawing them together (Rahemi et al., 2014; Azizi et al., 2008), or external forces where the body contacts the environment (Holt et al., 2016; Wakeling et al., 2013; Siebert et al., 2017). Thus, there would be an asymmetry to the stress distribution through the muscle that would probably cause deformations in the fibres that are transversely anisotropic (Rahemi et al., 2014, 2015).

Muscle fascicles are bundles of fibres that create the striations seen in the ultrasound image. Fascicles additionally contain the extracellular matrix (ECM), blood vessels, nerves and intramuscular fat and are surrounded by the perimysium membrane. Thus, the material properties of the ECM and fluid movement within the fascicle can influence deformations in the fascicle that are additional to the deformations of their constituent fibres (Karakuzu et al., 2017; Yucesoy, 2010; Yucesoy and Huijing, 2007). A recent MRI study on muscle shape showed small decreases in volume as the muscle was passively stretched (Bolsterlee et al., 2017), although it was noted that these volume changes were within the realm of measurement error. However, this ratio of the changes in volume relative to longitudinal strain was of a similar magnitude to the changes in volume reported for the ECM, measured optically on the dissecting microscope, during passive stretch when larger magnitude displacements were used (Smith et al., 2011). When the muscle is active, increases in intramuscular pressure may additionally occlude blood flow in a process known as the skeletal muscle pump (Kagaya and Muraoka, 2005), and so it is not unreasonable to expect that changes to the fascicle volume may occur. Such changes in volume and fluid movement within the fascicle may again occur in a transversely anisotropic fashion as a result of similar stress asymmetries to those discussed for the muscle fibres above.

The muscle belly encloses the space available for the muscle fascicles. As the fascicles shorten, they act to draw the aponeuroses together, which tends to decrease the belly thickness. However, the fascicles increase in girth during shortening. The increase in girth may be in either the width or thickness direction, and indeed the relative deformations may vary between muscles (Randhawa and Wakeling, 2015). However, a general effect is for the muscles to increase in pennation angle to allow them to fit within the enclosed space (Zuurbier and Huijing, 1992; Fukunaga et al., 1997). This increase in pennation angle would tend to increase the distance of the muscle belly between the aponeuroses. Thus, the actual change in transverse deformation of the muscle belly depends on the balance between fascicle shortening and rotation, on compliance within the connective tissues such as the aponeurosis itself (Rahemi et al., 2014; Holt et al., 2016; Azizi et al., 2008; Azizi and Roberts, 2009) and on forces external to the muscle (Siebert et al., 2017). Previous studies have shown that the MG and LG show opposing changes in thickness, with the MG decreasing or maintaining a steady thickness (Maganaris et al., 1998; Randhawa et al., 2013; Randhawa and Wakeling, 2013) and the LG increasing in thickness (Maganaris et al., 1998; Wakeling et al., 2011; Azizi et al., 2008; Randhawa et al., 2013) during muscle belly or MTU shortening. This exemplifies the complexity that causes variations in the thickness of pennate muscle. Transverse deformations of the muscle belly in other directions (Böl et al., 2013, 2011b; Stark and Schilling, 2010) need to balance the changes in length, depth, width and maintenance of volume, and so deformations of the muscle belly may also be transversely anisotropic (Azizi et al., 2008; Randhawa et al., 2013; Rahemi et al., 2015).

This study showed transverse anisotropy for the contracting fascicles of the LG. The LG fascicles decreased in length by 36% on average and increased in pennation angle by 4.4±0.45 deg during these contractions. The LG fascicles thinned in their x direction and expanded in their y direction (Fig. 4F), with these transverse deformations being almost totally out of phase. By contrast, the MG fascicles decreased in length by 31% and increased in pennation angle by 8.0±0.44 deg but the fascicles decreased in both their transverse x and y directions (Fig. 4C). However, following the proof-by-contradiction arguments above, using these data we cannot be sure whether transverse deformations in the MG fascicles were asymmetrical or not; however, the presence of transverse anisotropy in the LG fascicles demonstrates that this is clearly a feature that can occur during active muscle contraction. Studies in the past have predicted (Randhawa and Wakeling, 2015) and measured (Wakeling and Randhawa, 2014) transverse expansion of muscle fascicles; however, the extent of these changes in comparison to longitudinal shortening of fascicles was smaller than predicted. Here, we found a similar result: a 33% decrease in fascicle length led to a change in transverse deformation of 3% and 1.2% in the x direction and 2.1% and 2.1% in the y direction for the MG and LG, respectively. Similar discrepancies in fascicle length and transverse deformation were observed in muscle models during maximal and submaximal muscle contractions (Rahemi et al., 2014, Randhawa et al., 2013).

The theory described above relates stress asymmetries within the muscle to asymmetries in the transverse deformations of the fascicles. Muscle stresses and intramuscular pressures will be greatest during maximal contractions and lowest when the muscle is relaxed. Indeed, during passive muscle length changes, the reduced or absent stress asymmetries may not be sufficient to cause transverse anisotropy in the muscle fascicles. Thus, these findings may not be evident in studies of passive muscle, and indeed pilot work from this study did not reveal transverse anisotropy at the fascicle level during passive muscle length changes.

In the current study, the LG belly showed transverse bulging between the aponeuroses (ε_X=+7%) whereas the MG belly decreased by ε_X=−3% during muscle shortening. These results are consistent with previous studies that have shown LG belly thickening transversely during isometric tasks, isotonic tasks and cycling (Maganaris et al., 1998; Wakeling et al., 2011; Azizi et al., 2008; Randhawa et al., 2013) and the MG belly thinning transversely during isokinetic and cycling tasks (Randhawa et al., 2013; Randhawa and Wakeling, 2013).

Deformations of the muscle belly in the Y direction were similar to those in the X direction, with LG ε_Y=+3% and MG ε_Y=−5%. The magnitude of the belly deformations in the X and Y directions was significantly different (Fig. 4, Table 1), although the phase was similar. These differences in magnitude support the hypothesis that transverse anisotropy occurs at the level of the muscle bellies of the LG and MG during in vivo active dynamic muscle contraction, although this effect is less pronounced than for their muscle fascicles.

The results for the MG are somewhat surprising, because the muscle belly within the scanning region of the ultrasound transducers appears to be shortening in all three directions. However, proximal movement of a muscle's volume during shortening can alter the shape of muscles by decreasing the cross-section in some regions of the muscle while simultaneously increasing the cross-section in adjacent regions as seen in both human and rabbit muscle (Raiteri et al., 2016; Böl et al., 2013). The ultrasound transducer used in this study had a linear field of 60 mm that may only be about one-third of the length of the whole muscle belly. Thus, proportional deformations in the three directions within the scanning region should not be extrapolated to predictions on changes in the whole muscle volume. Additionally, it should be noted that regional variations in factors such as the architecture (Rana et al., 2013; Rahemi et al., 2014; Azizi et al., 2008), intramuscular pressure (Sejersted et al., 1984) and externally applied forces may also affect regionalization of any transverse deformations in both the muscle fascicles and muscle belly.

Myofascial force transmission is a process by which forces can be transmitted laterally between muscles via connective tissues within and between the muscles (Siebert et al., 2014; Maas and Sandercock, 2010; Huijing, 1999; Bojsen-Moller et al., 2010). Within the triceps surae muscles, the LG and soleus can work in unison by decreasing the inter-aponeurosis shear, increasing the stiffness of connective tissue structures, and this unison may affect how muscles change shape during active dynamic tasks (Finni et al., 2017). However, asymmetries at the fascicle level can be additionally decoupled from belly level changes as a result of the additional contribution of dynamic factors such as change in fascicle length, pennation angle, reorientation of fascicles and 3D trajectories of fascicles during contraction.

A complete 3D analysis of the whole muscle belly during active dynamic tasks remains challenging, particularly when relying on non-invasive techniques such as in humans. Ultrasound allows for direct imaging from the region of muscle belly being scanned by the ultrasound transducer, and can be used to quantify changes in muscles and fascicles during active contractions (Rana et al., 2013; Randhawa and Wakeling, 2013; Maganaris and Paul, 2000). Ultrasound has a high temporal resolution and can be used to study both passive and active muscle structure (Cronin and Lichtwark, 2013; Narici et al., 1996; Fukashiro et al., 1995). The dual-probe imaging and processing approach described in this study provides a successful experimental framework for quantifying structural changes in a 3D perspective. Unlike the 3D ultrasound probe that scans in a single direction at any given time and acquires data sequentially in the 3D space, and requires longer scan times (Lindop et al., 2006; Lopata et al., 2010, 2007), the dual-probe technique used here employs two probes that scan a common region of the muscle from two orthogonal directions and acquire data simultaneously from the given directions.

The ultrasound scans in this study were aligned to maximize the line-like quality of the muscle fascicles in the images. For any straight section of fascicle, there are an infinite number of scanning orientations that can achieve this criterion, and here we selected two orthogonal directions that were roughly in the anterior–posterior and the medial–lateral directions across the muscle. It should be noted that (a) misalignment of the scanning directions relative to the fascicles can underestimate fascicle length and produce errors of up to 6% (Muramatsu et al., 2002), (b) the displacement of the fascicles relative to the probes during contraction can result in errors of up to 1 deg in pennation angle (Rana et al., 2013; Rana and Wakeling, 2011; van Leeuwen and Spoor, 1992), and (c) the fascicles typically curve during contraction so the quality of the probe alignment would vary along the length of each fascicle. Nonetheless, the main purpose of this study – to identify asymmetries in fascicle deformation – was achieved by observing totally opposite effects in the LG fascicle deformation during plantarflexion, and this finding would be robust relative to the smaller variabilities caused by probe misalignments.

Muscle aponeuroses are sheets of connective tissue to which muscle fascicles attach. The aponeurosis is an important feature that is digitized in an ultrasound image as it defines the muscle boundary and thus helps quantify fascicle length, fascicle pennation and muscle bulging. Because of the orthogonal probe alignment in this study, some ultrasound scans would probably miss the aponeuroses of the muscle belly (Fig. 1), making automatic detection of these boundaries more challenging. Thus, the muscle regions of interest were manually segmented; manual digitization of ultrasound images is a well-documented technique with strong inter-tester and intra-tester reliability (Kwah et al., 2013; Rana et al., 2009); therefore, this was our method of choice.

One potential limitation to the approach used here is that if the fascicles are asymmetric in cross-section (e.g. Sharafi and Blemker, 2010), then rotations of the muscle belly relative to the probes may result in asymmetric deformations being ascribed to the fascicles as they contract, and this would be of particular concern for the LG where we are reporting asymmetric deformations (Fig. 4). However, the fascicular features being analysed here were larger than actual muscle fascicles, in a manner typical of ultrasound studies, and there was no significant difference in their absolute transverse wavelengths (1.58±0.07 and 1.50±0.05 mm for the X and Y directions of the LG, respectively). If we were to speculate that the longitudinal rotations of the fascicles or muscle belly were as great as their changes in pennation angle, then they would need a pronounced asymmetry (a ratio of 1:0.32 for their lengths in the major:minor axes of their cross-section) in order for longitudinal rotations to explain the asymmetries shown in Fig. 4. However, the actual ratio of the transverse wavelengths of these fascicular features was 1:0.95 and so this rotational movement is unlikely to be the cause of the asymmetrical deformations reported here.

Active muscles change in length, pennation angle and belly thickness, and understanding the nature of these changes is important for understanding the length and velocity of the muscle fibres and thus the forces a muscle can produce. The results from this study reveal that during maximal plantarflexion contractions, the LG muscle shows transverse anisotropy at the level of the fascicles. This work provides the first 3D description of fascicle deformations during active muscle contraction. Many structures and forces both internal and external to the muscle may cause this anisotropy, and have been discussed, and regional variations in muscle structure, intramuscular pressure variations and myofascial force transmission may also influence the deformations and warrant further investigation. Future work should explore the structural properties of connective and elastic tissues that specifically connect the MG and LG muscle bellies, and the potential role these tissues may have on how muscles change shape and influence muscle mechanics. Experimental studies such as this study are necessary to quantify the 3D changes in muscle shape during active dynamic tasks and highlight the importance of studying muscle structure in all three dimensions.

The authors thank Dr Charlotte Waugh and Basant Chana for insightful discussions and assistance with data collection.