The Auditory Mechanics of the Outer Ear of the Bush-Cricket: A Numerical Approach

Bush-crickets have tympanal ears located in the forelegs. Their ears are elaborated as they have outer, middle and inner ear components. The outer ear comprises an air-filled tube derived from the respiratory trachea, the acoustic trachea (AT), which transfers sound from the prothoracic acoustic spiracle to the internal side of the ear drums in the legs. A key feature of the AT is its capacity to reduce the velocity of sound propagation and alter the acoustic driving forces of the tympanum (the ear drum), producing differences in sound pressure and time between the left and right sides, therefore aiding the directional hearing of the animal. It has been demonstrated experimentally that the tracheal sound transmission generates a gain of approximately 15 dB and a propagation velocity of 255 m/s, an approximately 25% reduction from free-field propagation. However the mechanism responsible for this change in sound pressure level and velocity remains elusive. In this study, we investigate the mechanical processes behind the sound pressure gain in the AT by numerically modelling the tracheal acoustic behaviour using the finite element method and real 3D geometries of the tracheae of the bush-cricket Copiphora gorgonensis. Taking into account the thermoviscous acoustic-shell interaction on the propagation of sound, we analyse the effects of the horn-shaped domain, material properties of the tracheal wall and the thermal processes on the change in sound pressure level in the AT. Through the numerical results obtained it is discerned that the tracheal geometry is the main factor contributing to the observed pressure gain

A numerical approach to investigating the mechanisms behind tonotopy in the bush-cricket inner-ear

Bush-crickets (or katydids) have sophisticated and ultrasonic ears located in the tibia of their forelegs, with a working mechanism analogous to the mammalian auditory system. Their inner-ears are endowed with an easily accessible hearing organ, the crista acustica (CA), possessing a spatial organisation that allows for different frequencies to be processed at specific graded locations within the structure. Similar to the basilar membrane in the mammalian ear, the CA contains mechanosensory receptors which are activated through the frequency dependent displacement of the CA. While this tonotopical arrangement is generally attributed to the gradual stiffness and mass changes along the hearing organ, the mechanisms behind it have not been analysed in detail. In this study, we take a numerical approach to investigate this mechanism in the Copiphora gorgonensis ear. In addition, we propose and test the effect of the different vibration transmission mechanisms on the displacement of the CA. The investigation was carried out by conducting finite-element analysis on a three-dimensional, idealised geometry of the C. gorgonensis inner-ear, which was based on precise measurements. The numerical results suggested that (i) even the mildest assumptions about stiffness and mass gradients allow for tonotopy to emerge, and (ii) the loading area and location for the transmission of the acoustic vibrations play a major role in the formation of tonotopy

Beyond the exponential horn:a bush-cricket with ear canals which function as coupled resonators

Bush-crickets have dual-input, tympanal ears located in the tibia of their forelegs. The sound will first of all reach the external sides of the tympana, before arriving at the internal sides through the bush-cricket’s ear canal, the acoustic trachea (AT), with a phase lapse and pressure gain. It has been shown that for many bush-crickets, the AT has an exponential horn-shaped morphology and function, producing a significant pressure gain above a certain cut-off frequency. However, the underlying mechanism of different AT designs remains elusive. In this study, we demonstrate that the AT of the duetting Phaneropterinae bush-cricket Pterodichopetala cieloi function as coupled resonators, producing sound pressure gains at the sex-specific conspecific calling song frequency, and attenuating the remainder—a functioning mechanism significantly different from an exponential horn. Furthermore, it is demonstrated that despite the sexual dimorphism between the P. cieloi AT, both male and female AT have a similar biophysical mechanism. The analysis was carried out using an interdisciplinary approach, where micro-computed tomography was used for the morphological properties of the P. cieloi AT, and a finite-element analysis was applied on the precise tracheal geometry to further justify the experimental results and to go beyond experimental limitations

A narrow ear canal reduces sound velocity to create additional acoustic inputs in a micro-scale insect ear

Located in the forelegs, katydid ears are unique among arthropods in having outer, middle and inner components, analogous to the mammalian ear. Unlike mammals, sound is received externally via two tympanic membranes in each ear, and internally via a narrow ear canal (EC) derived from the respiratory tracheal system. Inside the EC sound travels slower than in free air, causing temporal and pressure differences between external and internal inputs. The delay was suspected to arise as a consequence of the narrowing EC geometry. If true, a reduction in sound velocity should persist independently of the gas composition in the EC (e.g. air, CO2). Integrating laser Doppler vibrometry, micro-CT scanning, and numerical analysis on precise 3D geometries of each experimental animal EC, we demonstrate that the narrowing radius of the EC is the main factor reducing sound velocity. Both experimental and numerical data also show that sound velocity is reduced further when excess CO2 fills the EC. Likewise, the EC bifurcates at the tympanal level (one branch for each tympanic membrane) creating two additional narrow internal sound paths and imposing different sound velocities for each tympanic membrane. Therefore, external and internal inputs total to four sound paths for each ear (only one for the human ear). New research paths, and implication of findings in avian directional hearing are discussed

Ear pinnae in a neotropical katydid (Orthoptera: Tettigoniidae) function as ultrasound guides for bat detection

Early predator detection is a key component of the predator-prey arms race, and has driven the evolution of multiple animal hearing systems. Katydids (Insecta) have sophisticated ears, each consisting of paired tympana on each foreleg that receive sound both externally, through the air, and internally via a narrowing ear canal running through the leg from an acoustic spiracle on the thorax. These ears are pressure-time difference receivers capable of sensitive and accurate directional hearing across a wide frequency range. Many katydid species have cuticular pinnae which form cavities around the outer tympanal surfaces, but their function is unknown. We investigated pinnal function in the katydid Copiphora gorgonensis by combining experimental biophysics and numerical modelling using 3D ear geometries. We found that the pinnae in C. gorgonensis do not assist in directional hearing for specific call frequencies, but instead act as ultrasound detectors. Pinnae induced large sound pressure gains (20–30 dB) that enhanced sound detection at high ultrasonic frequencies (> 60 kHz), matching the echolocation range of co-occurring insectivorous bats. These findings were supported by behavioural and neural audiograms and tympanal cavity resonances from live specimens, and comparisons with the pinnal mechanics of sympatric katydid species, which together suggest that katydid pinnae primarily evolved for the enhanced detection of predatory bats

On the fourth-order accurate approximations of the solution of the Dirichlet problem for Laplace’s equation in a rectangular parallelepiped

An interpolation operator is proposed using the cubic grid solution of order 0 (h(4)), h is the mesh size, of the Dirichlet problem for Laplace's equation in a rectangular paralellepiped. It is proved that when the boundary functions on the faces of the rectangular parallelepiped are from the Holder classes C-4,C-lambda, lambda is an element of (0, 1), and their second and fourth derivatives obey compatibility conditions implied by Laplace's equation on the edges, the solution obtained by the constructed operator also has fourth-order accuracy with respect to mesh size