Musculoskeletal modelling of the dragonfly mandible system as an aid to understanding the role of single muscles in an evolutionary context

Insects originated approximately 480 million years ago (Misof et al., 2014) and developed an astonishing diversity of mouthpart and head capsule types during this time span (Grimaldi and Engel, 2005). From a biomechanical point of view, insect mouthparts are a construction optimized during an extremely long time frame with selection processes leading to an adaptation of mouthparts to changing ecological niches. However, the reasons for the absence or presence of certain mouthpart muscles are still unclear. Functional requirements related to food uptake are a potential cause, but the amount of ‘functional influence’ on the evolution of mouthpart musculature is difficult to determine (Spagna et al., 2008), although these muscles are used as characters for phylogenetic reconstruction (e.g. Staniczek, 2000). In this context, an analysis of insect mouthpart and muscle kinematics can provide a useful toolbox to assess the role of a given muscle equipment and compare it with other species in an evolutionary context.

Dragonflies (Odonata) are an interesting case in this regard. They possess a suite of six to seven mandibular muscles, thus showing a plesiomorphic muscle equipment with respect to all other winged insects except mayflies (Ephemeroptera), which possess eight (Staniczek, 2000). However, regarding their mandible joints and the configuration of the mandibular teeth (or incisivi), Odonata show the typical ball-and-socket joints and incisivi of many ‘higher’ insects (Neoptera; Blanke et al., 2012; Staniczek, 2000,, 2001; Wipfler et al., 2011). In particular, the mandibular system (joint types, muscles, mandible motion) of Odonata, Ephemeroptera and Neoptera has been intensely studied concerning its phylogenetic value to infer the relationships of these three groups to each other (Staniczek, 2000,, 2001). Two hypotheses, Metapterygota (Odonata+Neoptera) and Palaeoptera (Odonata+Ephemeroptera) are currently mainly discussed (Beutel and Gorb, 2006; Blanke et al., 2012,, 2013a; Brauckmann and Zessin, 1989; Misof et al., 2014; Ogden and Whiting, 2003; Pass, 2000,, 2006; Staniczek, 2000; Terry and Whiting, 2005; Wheeler et al., 2001; Willkommen and Hörnschemeyer, 2007).

There is fragmentary knowledge of the mouthpart kinematics for a few insect species, mostly within certain ant subfamilies (Gronenberg, 1995; Gronenberg et al., 1997; Spagna et al., 2008) or beetles (Evans, 1964; Forsythe, 1982,, 1983). Most of these studies provide external investigations on the movement of single mouthparts during food uptake without information on the role of related muscles and muscle actions (Evans, 1964; Forsythe, 1982,, 1983; Popham, 1959). A notable exception is the investigation of Schmitt et al. (2014), who used high-speed micro-computed tomography (µCT) to investigate the coordination of mandibles, maxillae and the labium during biting, but without primary data on mandible muscle geometry and activation during the biting cycle. However, there is to our knowledge no direct method to accurately study muscle activation patterns (MAPs) and muscle movement on a micrometre scale necessary for insects mouthparts (Julian, 1969).

Inverse dynamic models, including distinct muscles, would allow for indirect calculation to predict muscle forces and activation. To determine the resulting internal forces and moments of force, the models need as input parameters the individual geometry and kinematics of the considered segments (e.g. mandibles and head capsule) as well as the external forces (e.g. total bite force) and moments. Furthermore, by use of optimization procedures, muscle–specific force–length, force–velocity and force–activation relationships, muscle forces and muscle activations can be determined (Zatsiorsky, 2002). Such inverse dynamic models are becoming increasingly popular under the umbrella term ‘multibody dynamics analysis’ (MDA). MDA has been used to determine muscle activations and forces, joint reaction forces and mouthpart movement parameters in a range of extant (Curtis et al., 2010a; Gröning et al., 2013; Moazen et al., 2008) and extinct vertebrates (Bates and Falkingham, 2012), as well as in human movement analysis (e.g. Pandy, 2001). The prediction of muscle activation and bite force through MDA has been validated (Curtis et al., 2010b), but at the same time models are extremely sensitive to muscle geometry (Gröning et al., 2013).

Here, we developed and tested an MDA model based on µCT and bite force measurements. As an example, we analysed the muscle kinematics of a dragonfly by segmenting the CT data at the voxel level. We subsequently investigated the role of the mandibular muscles during biting in this dragonfly by using musculoskeletal modelling software that has been validated for vertebrate movement research (Curtis et al., 2010a,,b; Watson et al., 2014; Wehner et al., 2010). Bite force measurements provide the basis for the modelling of MAPs and the change of muscle geometries during biting. The proposed workflow has wider applications, as it generally allows for the prediction of MAPs in small animals with extremely small moving parts, principally only restricted by the resolution of the available µCT data, which influences the accuracy of the geometry of the resulting muscle model.

Five living Sympetrum vulgatum (Linnaeus 1758) males (Anisoptera: Libellulidae) were used for our measurements. The mouthparts of Odonata are directed ventrally (orthognathous) and the space between the outermost incisivi of the mandibles is species dependent in the range of 2–7 mm when fully abducted (Movie 1). In order to measure the bite force in the narrow space between the mandibular incisivi, a piezoelectric mini force sensor (SKB pin-force sensor Z18152X2A3sp, Kistler, Winterthur, Switzerland) of 0.60 mm thickness was used. The active surface zone of the sensor spans an area of 4×1.5 mm. The effective range of the sensor is 0–5 N with a sensitivity of 6 pC N⁻¹ (noise <0.01 Npp, where Npp is the peak to peak noise; linearity error <5%). The sensor signal was amplified using a charge amplifier (Charge Meter Type 5015, Kistler). Analog data were analog–digital converted (MX Ultranet HD, Vicon, Oxford, UK) and recorded with a frequency of 1000 Hz.

Dragonflies were fixed at the thorax with a custom-built fixation device consisting of a flexible cushioned plastic calliper on a metal base unit (Fig. 1A,B). The calliper strength was adjustable, allowing for optimal fixation of the dragonfly. The force sensor was similarly fixed with a calliper on a metal base unit. Both units were adjustable in the horizontal and vertical plane so that the sensor could be moved inside the oral opening of the specimen (Fig. 1B).

The natural reflex of captured dragonflies is to bite at objects between the mandibles, which meant that measurements could be taken immediately. The sensor was positioned between the mouthparts (Movie 1) and bites were recorded for 30–59 s, depending on the dragonflies' biting behaviour. In total, six bite series were captured. The longest bite series was chosen for further analysis. It was subsequently filtered (Butterworth, low pass, fourth order, 50 Hz cut-off, recursive) and the 10 strongest single bites were extracted and used for the inverse dynamic calculations. Single bites were selected, when the force–time curve showed a continuous increase of at least 0.02 N, an unambiguously identifiable absolute maximum, the absence of local minima between biting onset and peak force and the absence of movement artifacts due to movement of the insect (as visible, for example, between 0 and 2 s in Fig. 2A).

In order to build a geometrically precise kinematic muscle model of the dragonfly's head, we scanned one specimen using high-resolution synchrotron radiation µCT (SR-µCT) (Betz et al., 2007). The live specimen was put into Bouin solution (Romeis, 1989), stored for 3 days to allow full penetration of the fixative and subsequently washed in 70% ethanol. In order to avoid shrinking artifacts of the internal anatomy as much as possible, the sample was critical point dried (Model E4850, Bio-Rad) and afterwards mounted on beamline-specific specimen holders. SR-µCT was done at the Deutsches Elektronen Synchrotron (DESY, Hamburg, Germany), beamline DORIS III/BW2 at 8 keV in absorption contrast mode (Beckmann et al., 2008) with 2.7× magnification and a voxel size of 5 µm (isotropic). Additionally, specimens in 70% ethanol were manually dissected to observe the muscle attachments under natural conditions.

Subsequent segmentation of the reconstructed image stacks was accomplished with the open-source program ITK-SNAP (Yushkevich et al., 2006) (GPL licence; www.itksnap.org/pmwiki/pmwiki.php). We used the ‘region competition’ segmentation algorithm based on grey value differences for semi-automatic 3D segmentation. Because of the superior image data generated from the SR-µCT setup at DESY beamline BW2, grey values within the image data were tissue dependent, allowing for a clear discrimination of muscle, chitin and nervous tissue. ITK-SNAP allows for voxel-level segmentation of the image data; therefore, the precision of the resulting 3D objects is only limited by the voxel size of the underlying SR-µCT dataset (5 µm isotropic in our case). In order to analyse the muscle activation patterns, we segmented the head, mandibles and origin and insertion of the mandibular muscles (Fig. 3A).

Segmentations were exported in Standard Tessellation Language (STL) format and imported into Blender™ (GPL licence; www.blender.org). Origin and insertion fields of muscles were connected by joining the respective objects. Muscle representations were then exported as object files (OBJ) and imported into the AnyBody Modeling System™ (http://www.anybodytech.com/; Fig. 3B). Mandibles and the head were exported as STL files in ASCII syntax for import into the AnyBody Modeling System™. By choosing ‘Forward –Z’ and ‘Up Y’ in Blender, the export of both OBJ and STL files within the same coordinate reference system and with the same coordinate directions was ensured. The force sensor was modelled as a force plate between the mandibles in Blender and exported as an STL file for import into the AnyBody Modeling System™.

In the AnyBody Modeling System™, the segment coordinate systems of the imported head and mandible objects were attached to the respective centre of mass. The head capsule was furthermore linked to the environment coordinate system (global coordinate system). The segmentation data were used for surface definition, location of the segment's centre of mass and moments of inertia of each segment. The segment masses were measured with a Sartorius 1712 scale (Sartorius GMBH, Goettingen, Germany).

The model contains four spherical joints, an anterior and posterior one on each mandible (ama and pma; Fig. 3C,D). The rotation centre of each joint was assumed to be the middle of the spherical joint. The two joints of each mandible create a virtual revolute joint with an axis aligning the two spherical joints (Fig. 3C,D). This eliminates five of the originally six rotational degrees of freedom (three in each joint). In order to align the single rotation centres of the joints, we rotated the coordinate systems of each joint. A rotation matrix was generated, with the origin lying in the middle of the two joints, pointing with Y in the direction of joint pma (u). The second axis (v) was defined as perpendicular to u and pointing to the tip of the mandible; the third axis was defined as perpendicular to u and v (Fig. 3D).

The range of motion of the virtual revolute joints was extracted from the video footage of the biting sequences (Movie 1).

To attach the muscles to the segments, we defined segment nodes accounting for the origin or insertion of each muscle according to the segmentation data, thus linking the head segments with precise muscle origins and insertions (Fig. 3C). As most muscles cover a wide area of origin, we defined numerous single muscles in order to account for the pennation of a given muscle bundle.

The origin and insertion nodes were connected with ‘viapoint’ muscles in the AnyBody Modeling System™, which means that the muscle length is simulated as the shortest distance between the origin and insertion point of a given muscle in a non-static condition. This is in agreement with the geometric muscle relationships based on morphological data of dragonflies (Fig. 3A) (Blanke et al., 2013b,,c).

Muscles react to activation signals by changing their geometry, which produces force as an output (Hill, 1938; Thelen, 2003; Zajac, 1989). In inverse dynamics as used here, the measured external force is the input and the force generated by the muscle as well as the activation of the muscle are the outputs. Thus, the model is mathematically reversed (Zatsiorsky, 2002). The AnyBody Modeling System™ provides three different types of muscle models (‘AnySimpleMuscleModel’, ‘AnyMuscleModel2EL’ and ‘AnyMuscleModel3EL’). We modelled all muscles according to the simple muscle model, which contains one element and assumes a constant strength of the muscle. This muscle model requires only the definition of the initial muscle force; the rest of the parameters are modelled according to the assumptions of the Hill-type model (Hill, 1938; Zajac, 1989). Previous studies found good agreement between the simple muscle model and more parameter-intensive models when slower movements are simulated (Damsgaard et al., 2006; Duprey et al., 2015). The simple muscle model basically ignores the differing behaviour of non-contractile elements (e.g. tendons) and contractile elements (e.g. actin and myosin). Because factors like initial muscle force, contraction velocity and length of the non-contractile elements are unknown for dragonfly head muscles, the usage of the simple muscle model is currently the best working hypothesis (Zajac, 1989).

In the reverse direction approach, the initial muscle force was obtained by assuming that the testing situation simulates a life-threatening situation for the dragonfly (as the thorax is pressed by the fixation device). We thus hypothesized that the bite cycle is carried out with maximum neuronal stimulation.

This assumption affects the choice of the muscle recruitment criterion, which is the basis for determining which set of muscle forces will balance the external bite load (Damsgaard et al., 2006). The AnyBody Modeling System™ software allows the choice between several recruitment criteria. A linear criterion recruits a minimum number of muscles to balance the system. This is a non-physiological approach (Damsgaard et al., 2006) and therefore was not used here. The minimum/maximum criterion models the sum of all muscle activation levels as low as possible, i.e. with the lowest possible energy cost (Damsgaard et al., 2006; Rasmussen et al., 2001). This criterion is realistic when fatigue and maximal cost efficiency play a role in muscle activation (Damsgaard et al., 2006). Because it was shown that muscle activation-minimizing strategies (economic muscle activation) have not been found in animals yet (Hubel and Usherwood, 2015) and the dragonfly was able to continue biting over a period of 59 s with some of the highest bite forces measured during the end of the measurement cycle, the minimum/maximum criterion was not considered realistic.

The quadratic muscle criterion as used here optimizes fibre recruitment by evenly distributing activation across all involved fibres of the muscle, but also taking into account the geometric position of each fibre. Thus, fibres with an advantageous location are preferred for activation until other factors like force–length or force–velocity ratios are more advantageous for other fibres within the muscle. This criterion additionally agrees well with electromyographic (EMG) data, and measured muscle and joint reaction forces (Crowninshield and Brand, 1981; Siemienski, 1992). Because the dragonfly was able to continue biting over a longer period with some of the highest bite forces measured during the end of the measurement cycle, a maximum muscle activation of 80% was hypothesized. Starting from 0.4 N, which was obtained in previous studies on insect muscle (Blümel et al., 2012a), the inverse dynamics analysis recorded muscle activation well below 80% [probably since Blümel et al. (2012a) investigated a whole muscle instead of single fibres]. Therefore, the initial force of the muscle was lowered until a maximum muscle activation of 80% was reached during the strongest bite cycle. This approach leads to an initial force for each muscle fibre of 0.0029 N.

Although frequently termed ‘tendon’, these structures in insects are partly heavily sclerotized (Paul and Gronenberg, 1999). As we follow the terminology of Beutel et al. (2013) and Wipfler et al. (2011), and to allow for comparison with the literature record, we retained the term ‘tendon’ here. Because of this sclerotization, the material properties of this structure cannot be compared with tendon-like structures in, for example, vertebrates. Previous analyses in vertebrates revealed tendon to be very stiff in material behaviour (Kubo et al., 1999); thus, we modelled the large tendon of M. craniomandibularis internus as a rigid segment (Fig. 3). The tendon of the M. craniomandibularis internus is of flat, triangular form, inserting dorsal of the incisivi at the proximolateral ridge of the mandible.

For analysis of muscle activities during biting, we first studied the kinematics and inverse dynamics of the whole natural muscle set. In order to explore the role of single muscles or functional muscle groups, we ran separate analyses (artificial biting scenarios) with only the large mandibular adductor as the active muscle as well as analyses with only the smaller intramandibular muscles as active muscles (see below for an explanation of mandible muscle configuration).

Dragonflies possess an anterior and a posterior fixed ball-and-socket joint on each mandible (ama and pma; Fig. 3C,D). Thus, a virtual revolute joint is present between the two joints, which limits mandible motion to a rotation in the transversal plane around that virtual revolute joint (Fig. 3C). The mandible muscle system of S. vulgatum is composed of five muscles – one abductor (M. craniomandibularis externus posterior; 0md3) and four adductors (M. craniomandibularis internus, 0md1; M. tentoriomandibularis lateralis superior, 0md5; M. tentoriomandibularis lateralis inferior, 0md6; M. tentoriomandibularis medialis inferior, 0md8) – which are responsible for movement of the mandible (Fig. 3). While 0md1+3 originate at the head capsule (Fig. 3A), 0md5+6+8 (hereafter 0md5–8) all originate at the tentorium – an endoskeletal structure within the head of insects (Fig. 3C,D).

Time-normalized (0%: start of sensor contact; 100%: end of sensor contact) bite curves are bell shaped, with peak bite forces reached at 52.3±3.7% of the bite (Fig. 2B) and a steep increase of bite force during the first 30% of the contact phase. The earliest maximum was reached at 47.5%, the latest at 60.5%. Average bite duration was 197.5±51.3 ms (Fig. 2A). Maximum measured bite force was 0.31 N; mean peak bite force over the 10 strongest bites was 0.244±0.034 N. Bite force then rapidly decreased after 70% of the contact phase (Fig. 2B). During the strongest bites (Fig. 2B; Fig. S1), a short exponential increase of bite force was recorded from ca. 70% of the bite followed by a plateau-like progression towards maximum activation level.

In the following we will focus on the strongest measured bite cycle (SB=0.31 N), an intermediate bite cycle (IB=0.27 N) and the weakest bite cycle (WB=0.2 N) out of the 10 strongest measured bite cycles (0%: start of sensor contact, 100%: peak bite force). Percentage activation will be described in the following order: SB%/IB%/WB%. Percentage muscle activation for 0md1 is given as the mean of the maximum activation of each fibre group. Activation for 0md5–8 is given as the maximum activation of each fibre. For all muscles, activation was normalized against the respective maximum force modelled for each muscle fibre.

Generally, muscle activation of the mandible abductor 0md3 was characterized by a steep decrease of activation (Fig. S1). 0md3 activation remained at zero through the rest of the biting process. At the beginning of the contact with the force plate, the first activation was recorded for the main mandibular adductor 0md1, followed shortly after by 0md5–8 (Fig. 4A–C). 0md1 activities reached 40%/28%/28% of total potential muscle activation. After this first peak, all muscles showed a drop off in activation of ∼12% (SB) to over 20% (IB) and 17% (WB). Note that intermediate drop off in activation was higher in the IB scenario. Activation then gradually increased in the SB scenario while IB and WB showed a partly exponential increase followed by an asymptotic curve progression towards maximal muscle activation at 62%/52%/40%. Muscle fibre groups of 0md1 showed nearly 12%/15%/12% spread in activation (Fig. 4). The smaller muscles 0md5–8 showed percentage activation differences of 10%/8%/7% for 0md6+8 and 4%/4%/2% for 0md5.

Simulation of biting only with 0md1 activated resulted in an activation increase of 0md1 by 7%|7%|25% for the investigated bites (Fig. 4D–F). Without 0md1 but with muscles 0md5–8 active, the initial force of these muscles had to be increased fivefold to 0.014 N. Activation of these three muscles increased by ∼230%/230%/230% in order to execute the same bite force at the tips of the mandibles (Fig. 4D–F). Fibre activation spread was greater than in the natural muscle setup (Fig. 4A–C).

The single fibre groups of 0md1 showed a differing activation spread from each other and between the SB, IB and WB scenarios (Fig. 5). Within a fibre group, activation spread was widest in those groups that showed the highest activation (Fig. 5C–G). An exception is fibre group 9 which showed a 45% activation spread (Fig. 5I) comparable to that of the fibre groups with higher overall activation. During intermediate biting, the activation in all fibre groups was distinctly lower than the activation for the weakest bite cycle at 20–50% of the bite time. Muscle activation spread conformed with bite strength, where intermediate biting showed a greater spread than that for the weakest bite cycle.

The single fibre groups of 0md1 also showed a distinctive spatial activation pattern (Fig. 6). Highest activation was recorded for those fibres attached in the middle portion of the tendon, whereas the fibre groups inserting dorsally and ventrally at the tendon showed the lowest overall activation.

The bite cycle characteristic for S. vulgatum shows a stereotypical pattern with approximately 3 bite cycles s⁻¹ and overall similar bite curve geometries (Fig. 2A; Fig. S1). This suggests a highly stereotypical neuronal control pattern, which is in agreement with previous studies for cockroaches (Schmitt et al., 2014) and the locust (Blaney and Chapman, 1970). In contrast, bite cycles are shorter than in cockroaches and the locust (Blaney and Chapman, 1970; Schmitt et al., 2014). Measured bite force for S. vulgatum is in the range of bite force results for cockroaches (Weihmann et al., 2015) or stag beetles (Cyclommatus metallifer) (Goyens et al., 2014; Wheater and Evans, 1989). Successive bite cycles typically lasted between 30 and 59 s with some of the strongest bite cycles occurring during the end of the measurements (Fig. S1). Given the duration of the bite cycles, fatigue may not play a role in the biting process, which would in turn suggest that the muscles are neuronally probably not stimulated to their respective maximum force outputs even when the specimen is heavily stressed. Again, this points towards a stereotypical neuronal control pattern for the biting process, which is in agreement with studies investigating, for example, insect leg movement (Bässler, 1988; Büschges et al., 2008). In this context, non optimal pre-stretching and resting lengths of the muscles could be another factor influencing maximum force output. Under isometric conditions, it was shown that pre-stretching effects account for ∼1% of the total muscle output (Blümel et al., 2012a) and affect total muscle output during the first 0.1–0.5 s. Although we have to assume concentric loading conditions in our case, muscle activity modelling was done only for the time steps after contact with the force plate. We therefore hypothesize that non-optimal pre-stretching is negligible for the time frames we measured but has to be accounted for where initial muscle activation during the beginning of a given movement is modelled.

Muscle activation patterns showed that muscle 0md1 acts as the main adductor under all biting scenarios. This was to be expected given that 0md1 is by far the largest muscle in the dragonfly head (Beutel et al., 2013; von Kéler, 1963). During the strongest bite cycle analysed (Figs 2B, 4A), we could also record the characteristic additional activation of the so-called ‘slower muscle fibres’ already reported in, for example, ants (Paul and Gronenberg, 1999), which can produce higher forces at slower activation speeds (Paul and Gronenberg, 2002). The temporal activation pattern simulated by the AnyBody Modeling System™ model thus corresponds to earlier in vivo measurements of muscle neuronal control and activation (Paul and Gronenberg, 2002). The conspicuous pattern of the strongest recorded bite cycles shows that our simulation can account for slight variations in bite geometry and model muscle activation patterns accordingly. A higher recording frequency (1000 Hz in our case) may be advantageous in order to resolve bite force variations within a single bite cycle compared with previous studies (Goyens et al., 2014; Weihmann et al., 2015).

With the musculoskeletal model developed here, the role of the other smaller mandibular adductors 0md5–8 during biting could be assessed. Data for intermediate and weak bites show that during the initial bite phase the intramandibular muscles 0md5–8 account for nearly 50% (IB) or 30% (WB) of the total activation, while during later parts of the bite cycle the activation increase is much lower than for 0md1 (Fig. 4B,C).

Given these results, it can be expected that 0md5–8 do not play a significant role during biting in dicondylic insects, while their input in more basal insects with loose mandibular joints such as Zygentoma (silverfish) and Archaeognatha (jumping bristletails) may be more significant. Indeed, our artificial setup with only 0md5–8 present as adductors (Fig. 4D–F) resulted in muscle overload if the same initial force was assumed. The initial force of each muscle fibre therefore had to be increased fivefold in order to generate the same bite force. These results correspond to the configuration of these muscles in more ‘basal’ insects like silverfish, bristletails and even two-pronged bristletails: in these groups, 0md5–8 have a larger volume, 0md6+8 nearly fill out the lumen of the mandibles completely, while 0md1 is comparably smaller (Bitsch, 1963; Blanke et al., 2014,, 2015; Staniczek, 2000). In many ‘higher’ insects such as certain Grylloblattodea, Mantodea and Orthoptera, a part or all of muscles 0md5–8 are absent (Blanke et al., 2012). We therefore suggest that muscles 0md5–8 do not play a crucial role during biting in winged insects like Ephemeroptera, Odonata and Polyneoptera and accordingly were reduced in some higher lineages of insects [see character matrices in, for example, Blanke et al. (2012, 2013a,,c) and Wipfler et al. (2011) for presence/absence of these muscles within winged insect orders].

The spatial activation of the fibre groups within 0md1 (Figs 5, 6) shows a distinct pattern according to the origin and insertion of each fibre group. Fibre groups 1–4 most probably show lower activities as they are in a suboptimal position for optimal force output (Siemienski, 1992). The activation pattern moreover reflects observations made for the spatial composition in higher insects. In Mantodea (Wipfler et al., 2012) and Neuroptera (Beutel et al., 2010), 0md1 shows a division into distinct bundles, and even in Odonata other than the one studied here, this muscle splits into several distinct bundles (Blanke et al., 2013c). Given our data, these divisions most probably reflect a development towards optimization of fibre quantity and spatial configuration, i.e. the use of less muscle mass to generate similar overall force outputs. Functional requirements of muscle organization may therefore play a crucial role and the phylogenetic value of different spatial muscle configurations of 0md1 (such as multiple attachments at the head capsule) is probably questionable. However, we cannot rule out that other effects such as fibre density optimization, fibre combination, properties of surrounding tissues or passive forces of joints might influence muscle configuration as well. For example, different muscle fibre-type combinations were reported for several ant species (Paul, 2001), and tissue properties in insects seem to be species and body part dependent, varying sometimes by several orders of magnitude (Hillerton, 1980; Hillerton et al., 1982; Vincent, 2002; Vincent and Wegst, 2004). Compared with musculoskeletal research in vertebrates, knowledge of insect muscle characteristics is only fragmentary and needs to be studied on a systematic level by investigating a range of species from different orders. Influences of joint geometries have up to now been impossible to model because of the small size of insect joints (∼200 µm diameter for the ball-and-socket joint in Sympetrum); however, μCT methods will allow modelling of different joint geometries in insects in the near future.

The in vivo measurement of muscle parameters in insects has been done for model insects like Carausius morosus in order to study patterns of neuronal control, muscle activation and among-animal variation of muscle activation (Blümel et al., 2012a,,b,,c). Comparable in vivo measurements have not been done for insect heads so far because of the difficulty of assessing motor neurons and the whole range of muscle fibres and fibre types. So far, only comparably simple unipinnate muscles have been assessed experimentally (Blümel et al., 2012a,,b,,c) and the results suggest that large animal-to-animal variations in muscle parameters can occur for the measured muscle groups, which might affect force predictions of single muscles. In contrast, MDA case studies investigating simulated bite force against measured values show that muscle geometry and force orientation as well as realistic muscle wrapping have the highest influence on the accuracy of MDA models (Curtis et al., 2010a; Gröning et al., 2013). Regarding initial muscle activation, it was demonstrated that this does not depend critically on muscle model parameters (van Bolhuis and Gielen, 1999) but that activation is most probably a function of a stereotypical neuronal control pattern.

A potential avenue for validation of muscle activation patterns in millimetre-sized insects would be time-resolved μCT investigations of the internal anatomy (Schmitt et al., 2014; Walker et al., 2014). However, current image resolutions are too low to accurately model muscle geometries and obtain force–length curves and variations in cross-sectional areas.

Although it was shown that muscle model parameters do vary even between single individuals, our setup provides a useful toolbox for assessing general muscle activation patterns in extremely small specimens with complicated muscle geometries, where direct measurements are currently impossible. Information about muscle activation and force output is an invaluable basis for future studies on the head mechanics of insects. It will allow the study of optimization patterns across insects concerning structural design, material usage and more generally the evolution of insect mouthparts from a mechanical view.

We thank Christof Sonderegger of Kistler Instrumente AG for kindly providing the force sensor. We furthermore thank Jürgen Geiermann (German Sports University) who designed and constructed the fixation device. Susanne Duengelhoef, Björn M. von Reumont and Karen Meusemann are thanked for assistance during the SR-µCT experiments. Felix Beckmann and Fabian Wilde [both Helmholtz-Zentrum Geesthacht (HZG)/Deutsches Elektronen-Synchrotron DESY] provided excellent support at the synchrotron facilities. The useful discussions with Bernhard Misof and Benjamin Wipfler during the preparation of the manuscript are gratefully acknowledged.