Reconstruction of echoes reaching bats in flight from arbitrary targets by acoustic simulation Open Access

The echolocating bat is an example of a species that performs active sensing. Echolocating bats perceive their environment by emitting ultrasound pulses from their mouth or nose and listening to the echoes reflected from their surroundings. Bats have species-specific auditory systems and pulse characteristics that are adapted to their foraging environment (Denzinger , 2018; Neuweiler, 1984, 1990). For instance, some bat species (Rhinolophidae, Hipposideridae, and Pteronotus parnellii) emit complex sounds that combine constant-frequency (CF) and frequency-modulated (FM) sounds with a high-duty cycle (HDC) (Fenton , 2012; Neuweiler and Fenton, 1988). The pulse has a harmonic structure, with the second harmonic of CF (CF₂) being the maximum sound pressure. Bats emitting CF–FM pulses at HDC are also known to exhibit Doppler shift compensation (DSC) behavior, which cancels the Doppler effect caused by flight by lowering the frequency of the pulses (Schnitzler, 1968). The DSC behavior exhibited by bats adjusts the CF₂ of the echo (F_echo) in the auditory fovea, a region on the basilar membrane of the cochlea, with an extended frequency representation centered around a reference frequency and an over-representation of neurons tuned around the reference frequency occurs at all stations in the auditory pathway from the peripheral to the central auditory system (Bruns, 1976; Henson , 1980; Schuller and Pollak, 1979; Suga, 1984). During the bat's flight, the reference frequency is in good agreement with the average F_echoes (Schuller , 1974) and is approximately 200 Hz higher than the CF₂ of the pulse at rest (rest frequency) in the case of Rhinolophus ferrumequinum (Schnitzler, 1973). This makes it possible to detect a glint (the modulation of the CF component of the echo by insect flutter) with high accuracy and to detect foraging targets (von der Emde and Schnitzler, 1990; Koselj , 2011). A telemetry microphone mounted on the back of the bat during flight was used to measure the echoes from the wall in front of the bat, and the echoes were found to be highly accurate and constant owing to the DSC behavior exhibited by the bats (Hiryu , 2016).

Previous studies have observed that bats do not exhibit DSC on echoes from moving prey, but on echoes from immobile walls ahead of them (Mantani , 2012; Trappe , 1982). Bats hear multiple echoes from their surroundings with a single pulse emission and choose one of them to exhibit the DSC behavior. To understand the function of DSC and to study their attention process during navigation, it is important to identify the echoes that are selected by the bat to exhibit the DSC. Herein, we hypothesize that bats switch their attention to different echoes (targets) during flight and exhibit DSC. To address this hypothesis, it is essential to measure the echoes; however, the telemetry microphones that are currently in use cannot measure all the echoes reaching a bat in flight, and even if they could, it would be difficult to analyze each echo independently and identify the target that is the source of the reflection due to the temporal overlap of multiple echoes. Furthermore, to understand the echolocation behavior of bats, it is crucial to analyze the echoes that reach the bat, as represented by the DSC behavior. Nevertheless, currently there is no suitable method that can acquire all the echoes that reach the bats during flight.

In this study, using the finite-difference time-domain (FDTD) method, which implements a moving source and a moving receiver point, we propose a new approach that enables reproduction of all the echoes reaching bats during flight, including the Doppler effect, from flight paths and sound data of the emitted pulses obtained from behavioral experiments. The FDTD method is a numerical method developed to solve the Maxwell's equations, which are the governing equations of electromagnetic waves (Yee, 1966). It is now widely used in the field of sound propagation analysis. In addition, the FDTD method allows for the flexible setting of reflective walls, so that the echoes from each wall and object can be acquired independently. We allowed a bat equipped with a telemetry microphone on its back to fly in a particular direction and measured the bat's broadcasts and flight paths. The measured sound was used as the source for the FDTD method, and the echoes from all the walls reaching the bats were calculated independently as echoes specific to each wall, and the reflections from individual walls were calculated separately. As a result, the direction of the bat's attention in DSC was clarified by examining the spatiotemporal changes in the specific wall to which the bat exhibited the DSC behavior.

In this study, we first measured a bat flying in a straight line toward a wall and compared the echo CF₂s from the wall recovered by the FDTD simulation with those of the actual echoes measured by the telemetry microphone mounted on the bat, which confirmed the usefulness of the simulation. Using this method, we also investigated how the circling bats switch their attention to different walls, where they exhibit DSC behaviors, by flying freely in the flight chamber, and the spatiotemporal changes in the walls to which the bats pay attention.

Four adult Japanese horseshoe bats (Rhinolophus ferrumequinum nippon, three males and one female) were used in this study. The bats were captured from a wild colony in a cave in the Fukui Prefecture. All bats were housed in a dedicated colony room (4 m long × 6 m wide ×  2 m high) at Doshisha University in Kyoto. The temperature and humidity in the colony room were maintained at approximately 21 °C and above 80%, respectively. In the colony room, the bats were able to fly freely and allowed to have mealworms and water without restriction. The lighting in the room was also controlled to provide a 12-h light/dark cycle. All the necessary licenses for capturing and rearing bats were obtained, and these activities were conducted correctly in accordance with the Japanese Animal Experimentation Law. Prior approval was obtained from the Animal Experiment Committee of Doshisha University. All experimental procedures were performed in accordance with the Principles of Animal Care published by the U.S. National Institutes of Health (Pub. No. 86-23, revised 1985).

The bat species, R. ferrumequinum nippon, is known to exhibit DSC behavior during flight (Hiryu , 2008; Schnitzler, 1973). They emit a composite pulse with harmonics, which consist of a CF component and a FM component before and after it. The CF₂ is approximately 68–70 kHz and has the highest sound pressure (Hiryu , 2008).

Two types of experimental setups were constructed for behavioral experiments. The first experimental setup consisted of a corridor [6.0 m (L) × 1.0 m (W) × 2.5 m (H)] covered with a net inside a flight chamber [9 m (L) × 4.5 m (W) × 2.5 m (H)] so as to direct the flight path of the bats in a straight line toward the front wall. Sound-absorbing materials were installed on the sidewalls of the corridor, except for the front wall. The experimenter carefully placed the bat at the starting position at the end of the corridor and allowed it to fly towards the front wall of the corridor. In the second experimental setup, two nets were used to separate the flight chamber to construct a space 3.5 m long × 4.5 m wide × 2.5 m high. The experimenter carefully placed the bats at the corner of the space and allowed them to fly into the flying space.

The flight of the bats was measured by two high-speed video cameras (IDT Japan, Inc., MotionXtra NX8-S1, Tokyo, Japan, 90 fps) located in the corners of the flight chamber. To prevent the light from affecting the bats' behavior during experiment, the chamber was illuminated with red-filtered light (>650 nm) The video data were analyzed in frames using motion capture software (Ditect Corporation, Dipp-Motion version 1.1.31, Tokyo, Japan) to reconstruct the three-dimensional (3D) positions of the flying bat. In addition, a custom-made miniature telemetry microphone (Hiryu , 2008) was attached to the back of the bat using double-sided adhesive tape to record the bat's broadcasts and echoes during flight. The telemetry microphone was set to face forward and was positioned approximately 1 cm from the nose leaf of the bat so as to measure the bat's emitted pulse without being affected by sound attenuation or the Doppler effect. The telemetry microphone can also receive high-intensity echoes, such as those reflected from the front wall toward which the bat is directed. The emitted pulses and echoes received by the telemetry microphone were stored on a personal computer (PC) via a bandpass filter (NF Corporation, model 3625, Yokohama, Japan, 20–150 kHz) and digitized using a high-speed data acquisition card (National Instruments, model NI PXI-6358, 16 bit, fs = 500 kHz). The recorded sounds were analyzed using matlab and Python scripts. The echo delay between the pulses and echoes was calculated using the start time of each terminal FM component after converting the spectrogram using the matlab script. The CF₂ frequencies of the pulses and echoes were then calculated from the extracted sound using the Python script by only cutting out the CF components. The fast Fourier transform (FFT) window length was set to 16 384 points (frequency resolution of 30.5 Hz) by zero-packing, and the peak frequency was set as the CF₂.

The method used in this study is known as the compact explicit finite-difference time-domain (CE-FDTD) method (Kowalczyk and van Walstijn, 2010, 2011; Tsuchiya , 2019; Yamashita , 2015) in two-dimensional (2D) space. The CE-FDTD method not only considers the discretization along the coordinate axis but also the diagonal direction, which allows for a more accurate simulation than the standard FDTD method. To determine the echoes that reach a bat during flight, it is necessary to implement a moving acoustical source and receiving point in the simulation of the CE-FDTD method. This method has been proposed in the previous studies (Tsuchiya , 2022; Tsuchiya and Kanamori, 2021) and is outlined herein.

The source value is multiplied by the respective weight function and further distributed into four points to drive the source. At the receiving point, the received waveform (echo) is estimated by multiplying the waveforms of the surrounding four grid points by a weight function and summing them [Fig. 1(c)].

Because the Doppler effect of the directly reflected wave from each reflecting surface is determined by the vertically reflected wave, the simulation in a 2D plane does not affect the accuracy of the Doppler effect calculation. Therefore, in this study, FDTD simulations were performed by appropriately transforming the three-dimensional space of the flight space into the necessary 2D planes considering the memory limit of the PC and with an aim to shorten the computation time. In the first experiment, the bats flew in the corridor in a straight path toward the front wall with minimum diversion to the left or right side; therefore, the simulation of echoes from the front wall was performed in the y–z plane, which included the ceiling, floor, and front wall [see Fig. 2(a)]. In the second experimental space, the bats flew in circles with little change in altitude; therefore, simulations in the x–y plane that included the four surrounding walls were also performed. Except for the size of the space, the parameters of the simulations in these two experimental spaces are the same, and the parameters used for the FDTD simulations are listed in Table I. For the surrounding walls, Higdon's second-order absorption boundary was applied (Higdon, 1986). The reflection coefficient was set to 0.98, only for the reflective surfaces, and the echoes from each surface were acquired independently. The sound source was moved along the flight path obtained in the behavioral experiment, and each receiving point was set 1 cm away from the source. The simulation programs used in this study were written in C and are available online (https://github.com/tsmyu/Reconstruction-of-echoes-reaching-bats-in-flight-from-arbitrary-targets-by-acoustic-simulation).

The echoes from the walls of the flight chamber were simulated by introducing the flight paths and sound data obtained from the behavioral experiments. In the simulation, a sound source, which is an omnidirectional point source, transmits the waveform recorded by the telemetry microphone, which was mounted on the bat in the behavioral experiment. Although the sound recorded by telemetry microphones occasionally contains echoes with weak sound pressure, the sound pressure of the pulses emitted by the bats is sufficiently high compared to the sound pressure of the echoes (≳40 dB); therefore, using the recorded sounds as source data does not affect the simulation results.

We first simulated the environment with all the boundaries set as absorbing boundaries and calculated a reference waveform (arrival wave directly from the transmission point to the reception point) at each location of the moving receiver, which corresponded to the flight path of the bat, which was obtained from the behavioral experiment. Then, the waveform returning from the wall at the sound receiving point was calculated (calculated waveform) by changing from the sound absorption boundary of the specific wall [the first experimental setup (ceiling, floor, and front wall) and the second experimental setup (four surrounding walls)] to the reflective surface. Second, the echoes from a specific wall can be obtained by subtracting the calculated waveform from the reference waveform. The moving speed of the sound source and receiver points corresponds to each plane component of the flight path data of the bat measured in the behavioral experiment. In this study, the echoes were simulated assuming that both the source and receiver were omnidirectional.

To verify the accuracy of the simulation, we compared the CF₂s of the echoes (reference frequency) acquired from the telemetry microphone in the first experimental setup, a behavioral experiment, wherein a corridor was constructed, and the echoes from the front wall were acquired in the simulation. If the difference in the echo delay between the measured echoes and the echoes from the front wall obtained by simulation was less than 1 ms (allowable limit of error), the measured echoes were considered to be from the front wall, and their CF₂s were compared.

In the second experimental setup, the attended wall was determined by extracting echoes in the reference frequency band from the CF₂ frequencies of the simulated echoes from the surrounding walls. The spatiotemporal change in the attended wall of the Doppler shift compensation behavior during flight was examined.

In the first experimental setup, the bat flew in a straight line down the corridor and landed on the front wall at the end of the corridor [Fig. 2(a)]. The telemetry microphone attached to the back of the bat clearly recorded the pulses emitted by the bat [Fig. 2(b)]. After the flight began, the bats decreased the CF₂ frequency of the pulse, and after landing, it remained constant at approximately 67 kHz (67.1 kHz ± 0.02 kHz, rest frequency), thus confirming the DSC behavior of bats in this flight experiment. On the other hand, the echoes that could be observed with the telemetry microphone were limited to the case where the bat approached the front wall, indicating that it is not feasible to obtain all the echoes that reach the bat in flight by actual measurement. This is due to the microphone sensitivity and dynamic range of the telemetry microphones, and because the sound pressure of the pulses is very high.

Next, we used acoustic simulation to determine the echoes from the ceiling, floor, and front wall that reached the bats during this flight (Fig. 3). Figure 4(a) shows the change in echo delay for the 22 echoes acquired by the telemetry microphone before the bat landed in the flight, as shown in Fig. 2. Among these measured echoes, we examined the CF₂s of six echoes that matched the echo delay of the echoes from the front wall, which were acquired in the simulation below the allowable limit of error. For all six echoes, the measured and simulated CF₂s were found to be in good agreement, indicating that the simulation can be adapted to bat echo recovery [Fig. 4(b)]. Figure 4(c) shows the CF₂ of the echoes from each wall obtained by simulation in addition to the measured pulses and echoes, indicating that the simulation can supplement the echoes that could not be measured in the behavioral experiment. The CF₂ of the simulated echoes from the front wall between −2.5 s and −1.0 s, when the bats seemed to be exhibiting the DSC behavior against the front wall, was 138 Hz ± 57 Hz, higher than the rest frequency which was determined from the pulses immediately after landing [Fig. 4(d)].

In the second experimental setup, all four individual bats (A, B, C, and D) performed circling flights. The emitted pulses from the bats were measured using telemetry microphones placed on their backs, and the echoes were simulated independently from each of the four surrounding walls (wall1, wall2, wall3, and wall4) using the measured pulses. The CF₂s of the measured pulses and simulated echoes are shown in the left column of Fig. 5. The rest frequencies were A: 68.4 ± 0.04 kHz, B: 68.2 ± 0.02 kHz, C: 68.1 ± 0.02 kHz, and D: 68.9 ± 0.01 kHz (from 10 pulses), respectively. Considering the experimental results of straight flight [Fig. 4(d)],the reference frequency range was set to be in between −33 and 309 Hz (=138 ± 3 × 57 Hz) from each of the individual rest frequencies. The echoes in the range of the reference frequency were defined as echoes from attended wall to which the bats paid attention during DSC and visualized by superimposing different colors for each wall on the flight path. The results showed that the bats always had one attended wall for each pulse, and that they smoothly switched the attended wall for DSC during the circling flight and paid attention to the wall in front of the flight direction.

To understand the echolocation behavior of bats, it is crucial to analyze the pulses that bats emit as well as the echoes that get reflected back. These factors are the input information used to determine their behavior. However, due to technical problems, it was not feasible to practically measure the echoes in real space, especially those reaching bats during flight. Based on the information that can be measured in behavioral experiments, we propose a new method, the FDTD method, which allows us to independently calculate the echoes reaching bats in flight, including the Doppler effect from arbitrary targets, by adapting this method with moving sources and implemented receiver points. First, we demonstrated its usefulness by confirming that the measured CF₂ of echoes from the front wall matched those of the simulated echoes. From the echoes acquired in the simulations, it was found that the reference frequency range of bats during straight flight was 138 ± 57 Hz from the rest frequency. It has been reported that the reference frequency of R. ferrumequinum is approximately 200 Hz above the rest frequency (Schnitzler, 1973) and our results of the simulated echoes are considered to be reasonable. Then, by applying this method to the behavioral data of circling flight, we tested the hypothesis that bats in free flight may spatiotemporally switch the attended wall targeted by DSC depending on their flight. The results show that the bats smoothly switch the attended wall for DSC during their circling flight and pay attention to the wall ahead of them in the direction of flight.

The F_echoes values from each of the four walls were such that no more than two of them fell into the reference frequency range, demonstrating that the bats always used one of the walls as a reference (attended wall) to exhibit their DSC behavior during this circling flight (note that the F_echoes from all the walls overlap around −4 s in Bat B, because the bat is about to land on the ceiling). Furthermore, the point where the two echoes were at the same frequency was at a frequency lower than the reference frequency range. Next, the bat controlled the pulse CF₂ so that only the frequency of the echo from the wall ahead of the direction of flight would be in the reference frequency range during the next broadcast. Considering the DSC behavior, which selects one echo CF₂ to determine the pulse CF₂, it would be reasonable to coordinate the of pulse and flight control so that only one echo is within the reference frequency.

The finite element method has been adapted for the analysis of the effect of the bat's ears on its echo characteristics (Gao , 2011; Müller, 2004), and acoustic simulations have proven useful for analyzing echoes that cannot be measured. In contrast, the FDTD method used in this study can be implemented with less memory and can be adapted to a larger space with the same amount of PC memory. Another crucial aspect of understanding echolocation is that the echoes reaching bats in flight always include the Doppler effect. For example, echolocation behavior in FM bats, which do not exhibit DSC behavior, has also been discussed in relation to the Doppler effect that bats experience during flight (Boonman , 2003; Holderied , 2006; Masters and Raver, 2000). Therefore, to verify how bats perceive their environment from the echoes, it is necessary to use the method proposed in this paper to recover the echoes, including the Doppler effect. Our proposed approach can reproduce the echoes of a bat in flight in an obstacle space, or to verify how a bat listens to the pulses and echoes belonging to other bats during group flight, which allows us to understand the decision-making process of bat sonar behavior.

In this paper, we propose a method for recovering bat echoes by combining the FDTD method and introducing the Doppler effect with behavioral experiments. We confirmed the usefulness of the method and introduced it to study the shifting of the attended wall of DSC behavior because the method can recover echoes from each target independently. As a result, it was possible to clarify the spatiotemporal shifting of the attended wall of the DSC behavior exhibited by bats during flight. If the echoes of bats can be precisely reconstructed based on this method, it will be possible to study the nature of information obtained from the echoes and what kind of space bats perceive.

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Nos. 18H03786 and 21H05295). Y.T. and Y.H. contributed equally to this work.