Modeling the musculoskeletal system of an insect thorax for flapping flight.

Indirect actuation of the wings via thoracic deformation is a unique mechanism widely observed in flying insect species. The physical properties of the thorax have been intensively studied in terms of their ability to efficiently generate wingbeats. The basic mechanism of indirect wing actuation is generally explained as a lever model on a cross-sectional plane, where the dorsoventral movement of the mesonotum (dorsal exoskeleton of the mesothorax) generated by contractions of indirect muscles actuates the wing. However, the model considers the mesonotum as an ideal flat plane, whereas the mesonotum is hemispherical and becomes locally deformed during flight. Furthermore, the conventional model is two-dimensional; therefore, three-dimensional wing kinematics by indirect muscles have not been studied to date. In this study, we develop structural models of the mesonotum and mesothorax of the hawkmothAgrius convolvuli, reconstructed from serial cross-sectional images. External forces are applied to the models to mimic muscle contraction, and mesonotum deformation and wing trajectories are analyzed using finite element analysis. We find that applying longitudinal strain to the mesonotum to mimic strain by depressor muscle contraction reproduces local deformation comparable to that of the thorax during flight. Furthermore, the phase difference of the forces applied to the depressor and elevator muscles changes the wing trajectory from a figure eight to a circle, which is qualitatively consistent with the tethered flight experiment. These results indicate that the local deformation of the mesonotum due to its morphology and the thoracic deformation via indirect power muscles can modulate three-dimensional wing trajectories.