Does rotation increase the acoustic field of view? Comparative models based on CT data of a live dolphin versus a dead dolphin

Rotational behaviour has been observed when dolphins track or detect targets, however, its role in echolocation is unknown. We used computed tomography data of one live and one recently deceased bottlenose dolphin, together with measurements of the acoustic properties of head tissues, to perform acoustic property reconstruction. The anatomical configuration and acoustic properties of the main forehead structures between the live and deceased dolphins were compared. Finite element analysis (FEA) was applied to simulate the generation and propagation of echolocation clicks, to compute their waveforms and spectra in both near- and far-fields, and to derive echolocation beam patterns. Modelling results from both the live and deceased dolphins were in good agreement with click recordings from other, live, echolocating individuals. FEA was also used to estimate the acoustic scene experienced by a dolphin rotating 180° about its longitudinal axis to detect fish in the far-field at elevation angles of −20° to 20°. The results suggest that the rotational behaviour provides a wider insonification area and a wider receiving area. Thus, it may provide compensation for the dolphin’s relatively narrow biosonar beam, asymmetries in sound reception, and constraints on the pointing direction that are limited by head movement. The results also have implications for examining the accuracy of FEA in acoustic simulations using recently deceased specimens.


Introduction
Dolphins, like all odontocetes, utilize a biosonar (echolocation) system for navigation and foraging (Au 1993). Series of echolocation clicks are produced by a set of phonic lips and propagate through the forehead to shape a biosonar beam in the forward direction (Au and Simmons 2007). Dolphins have some control over the acoustic parameters (e.g. source level and peak frequency) of their echolocation clicks (Moore and Pawloski 1990), depending on the echolocation task and environment (Houser et al 1999). They can further adjust the properties of the outgoing beam (e.g. beamwidth and direction), possibly through muscular reshaping of the forehead and inflation of the air sacs (Moore et al 2008, Wisniewska et al 2012. Our understanding of echolocation signal characteristics and biosonar performance is based in part on signal measurements in the wild and in the laboratory (under controlled experimental tasks), as well as on anatomical and acoustical modelling using finite element analysis (FEA).
FEA is a numerical, computer-based technique that allows us to model how an object with complex geometry and material properties (such as a dolphin's head with complex anatomical structures) responds to physical forces (e.g. as a result of acoustic pressure). The object is simulated as a finite set of connected elements. Physical properties of the objects determine the strength of the connections (e.g. the bulk modulus of bones and other tissues). The connections between elements are analogous to 'springs' of various stiffnesses interconnecting the objects, each element of which may have a different mass. Mathematical equations then determine how the object responds to sound, vibration, or other physical situations. For example, FEA has been used to develop hypotheses about the physical mechanisms underlying dolphin target detection and discrimination (Feng et al 2018, Wei et al 2021. The numerical models are constructed based on computed tomography (CT) images of dolphin heads (which reveal the anatomical structures) and physical property measurements (e.g. sound speed and density) of head tissues. The specimens are typically dead, either fresh (e.g. recently deceased after stranding) or older, frozen, then thawed (Aroyan et al 1992, Cranford et al 2014. There might be differences in morphology (e.g. shape of air sacs) and properties (sound speed and density of tissues) between live, fresh, and frozen-then-thawed samples (Mckenna et al 2007, Cranford et al 2014, and hence comparisons are needed. Ultimately, any model needs to be able to replicate the echolocation click features (waveforms, spectra, beam patterns, etc.) of those recorded from live, echolocating dolphins .
Bottlenose dolphin (Tursiops truncatus) echolocation signals are characterized by a short duration, relatively high peak frequency, wide bandwidth, and high source level. Mean durations of individual clicks of 18-23 µs have been reported (Wahlberg et al 2011). Mean peak frequencies may be as high as 84-124 kHz (Au 1993, Akamatsu et al 1998, Wahlberg et al 2011, de Freitas et al 2015, Ladegaard et al 2019. Mean bandwidths (3-dB) greater than 85 kHz have been measured (Au 1993, Houser et al 1999, de Freitas et al 2015. Mean peak-to-peak source levels can be in excess of 220 dB re 1 µPa (Au 1993. The echolocation beam is relatively narrow with a mean 3-dB beamwidth of approximately 10 • for both the vertical and horizontal planes (Au 1993). While such highly directional biosonar features have advantages in long-range echolocation, there can be situations when a wider field of view is beneficial-wider than what biosonar muscular adjustments allow in the vertical plane (the horizontal beamwidth can exceed 26 • according to Moore et al 2008). This raises the question of whether dolphins can enhance performance through additional fine-or gross-motor behaviours.
Behavioural adaptations that might enhance sensory functions include the lateralized behaviour accompanying foraging in several dolphin species. Dusky dolphins (Lagenorhynchus obscurus) keep the right side of their body and the right eye towards the targeted prey while circling their prey clockwise (Vaughn-Hirshorn et al 2013). Atlantic bottlenose dolphins create and swim through a plume of mud while keeping the right side of their bodies towards the water-borne prey (Lewis et al 2003). This rightside bias might be a result of right-eye supremacy in visual discrimination and visuospatial processing in dolphins (Kaplan et al 2019). Alternatively or additionally, these lateralized behaviours with right-side bias might always be associated with echolocation behaviour and be a direct result of the echolocation clicks being produced by the dolphin's right set of phonic lips (Madsen et al 2010(Madsen et al , 2013. Another gross-motor behaviour that might enhance echolocation performance is rotation about the body's longitudinal axis. Wild and captive bottlenose dolphins have demonstrated rotational behaviour. They rotated their body along the longitudinal axis by a certain degree (e.g. 90 • , 180 • ) when tracking or searching for targets (supplementary material). Whether this rotation serves a communication function, or, in fact, enhances echolocation performance has not been studied to date. In this article, our hypothesis is that rotational behaviour during echolocation increases the acoustic field of view (i.e. both the ensonified field and the field from which echoes are received). To test our hypothesis, we constructed CT-image-based 2D finite element (FE) models to numerically estimate the acoustic scene experienced by an echolocating dolphin rotating 180 • about its longitudinal axis. Using CT data of one live and one recently deceased bottlenose dolphin, we were able to compare model outputs. These outputs, specifically, were the waveforms and spectra in both near-and far-fields, as well as the echolocation beam patterns, all of which we ultimately compared with acoustic measurements from live, echolocating individuals.

CT data acquisition and analysis
The specimens were all adult bottlenose dolphins. The CT scan data of the live bottlenose dolphin were provided by the U.S. Navy Marine Mammal Program (MMP) located at the Navy Information Warfare Center (NIWC) Pacific in San Diego, CA. CT data were collected at the Balboa Navy Medical Center in San Diego, CA on a GE Optima CT580 as part of a veterinary procedure. The male dolphin was 21 year old during the scanning, it was scanned in a prone position using a 2.5 mm spiral acquisition at 120 kV and 125 mA. Scans collected by the MMP were performed in accordance with approved protocols of the NIWC Pacific Institutional Animal Care and Use Committee (IACUC) and followed all applicable U.S. Department of Defense guidelines for the care and use of laboratory animals. The CT scan data of the fresh, recently deceased bottlenose dolphin (male, 10 year old) were provided by the Woods Hole Oceanographic Institution (WHOI) Biology Department. The head of the specimen was cut and then CTscanned in a prone position using a Siemens Volume Zoom helical CT scanner, using 1 mm spiral acquisition at 120 kV × 125 mA. Images were formatted in the transaxial plane at 0.1-1 mm slice increments. Raw acquisition data and all DICOM images were archived. Approval for the research from IACUC for handling and examining the cadaveric specimens was granted by the Animal Use Committee of the WHOI after reviewing the research protocol. Specimens scanned were obtained postmortem from freshly stranded animals under NMFS and NOAA permits to D. R. Ketten.
Two sets of DICOM images were imported into Horos™ (Horos Project, Geneva, Switzerland) for analysis and 3D geometrical model reconstruction, as shown in figure 1. The anatomical configuration of the main structures of the live and deceased dolphins, such as the melon, connective tissues, air sacs, brain, etc. were carefully compared slice-by-slice in the sagittal plane, transverse plane, and frontal plane. To better compare with the live dolphin beam formation experiment results, we rotated the head of the dolphin until the maxilla was roughly parallel to the ground. After carefully checking the CT data, we found that the fiducial markers on the melon did not affect the CT image of the underlying tissues.

Acoustic property reconstruction
The HU is a calibrated measure of radio density used in the interpretation of CT images. The HU values of tissues can be automatically obtained from CT data. We exported the distribution of HU of the animal's entire head to a text file, which contained the information about coordinates and corresponding HU values.
Since the acoustic properties of tissues cannot be measured on a live animal, we used the relationships of HU-to-sound speed and HU-to-density from previous tissue measurements (Wei et al 2015) to convert the HU distributions to the distributions of sound speed and density. More details can be found in our earlier studies , in which the same procedures were used to reconstruct acoustic impedance models for the heads of a harbour porpoise (Phocoena phocoena) and Atlantic bottlenose dolphin based on CT data and measurements of the physical properties of tissues. Moreover, 3D acoustic property reconstruction was used to compare the anatomical structures of the live and deceased specimens.

FE model construction
We selected a sagittal slice closest to the midline of the head that cut through the right set of phonic lips to create a 2D impedance model, which was imported into COMSOL Multiphysics modelling software (Stockholm, Sweden) for FEA. The FE models simulated click generation and propagation from the head into the water. Three main parts were included in the models: the head of an echolocating dolphin, surrounding seawater, and the target fish located in the acoustic far-field.
The reflecting fish was simulated by an oval swim bladder (axis ratio 1:1.93), which is responsible for Figure 2. Setup of the FE model to estimate the acoustic scene experienced by a dolphin rotating 180˚about its longitudinal axis. The fishes (grey points) were located along a circle with a 0.6 m radius from −20 • to 20 • elevation. Two ovals represent the simulated fish orientated longitudinally and perpendicularly in the far-field. the main echo when dolphins echolocate on fish (Au et al 2010a). Two orientations of the fish were modelled: (1) in line with the radius vector from the tip of the rostrum (i.e. horizontal at 0 • elevation) and (2) perpendicular to the radius vector from the tip of the rostrum (i.e. vertical at 0 • elevation). We further created a model by flipping the head of the dolphin upside down to simulate a dolphin rotating 180 • about its longitudinal axis. The model setups are shown in figure 2, in which the grey points at ±1 • , • , and ±20 • elevation display the locations of the fish in each test. The fish was moved from −20 • to 20 • at a constant radius of 0.6 m (i.e. range). The centre of the circle was set as a receiving point located right in front of the tip of the rostrum. The acoustic fields of returning echoes, when the fish was located at each elevation, were computed. The COMSOL results were imported into OriginPro software (Origin-Lab, Northampton, MA, USA) for data analysis and plotting. This procedure was applied to the models of both the live and deceased dolphins.
Based on the CT data, the heads of both the live and deceased dolphins in the models contained internal structures such as the right set of phonic lips, melon, connective tissue, vestibular sac, nasal passage, premaxillary sac, maxilla, mandible, blubber, musculature, mandibular fat, brain, etc. The sound speed and density of the structures in the head of the live dolphin were input according to the acoustic property reconstruction results. Whereas the sound speed and density of the structures of the deceased dolphin were referenced from the previous study , the sound speed and density of seawater outside of the animals' heads were set as 1483 m s −1 and 998 kg m −3 , respectively. The material properties of air were used to model the gas-filled swim bladders of fish.
We used COMSOL's free mesher to map the entire model into second-order triangular elements. The element size was set as a grid spacing of 1/10th of a wavelength λ at the centre frequency f c of the excitation signal at the source (λ = c water /f c , where c water is the sound speed in water). With f c = 60 kHz, the grid spacing was ∼0.25 cm. To simulate click propagation in free space with minimal reflections from the map's boundaries, a low-reflecting boundary condition (Bérenger 1994) was applied in the models.
A transient time domain FE computation was performed with a time step set at 0.8 µs. We set the sound source at the right phonic lips based on previous acoustic measurements (Madsen et al 2010(Madsen et al , 2013. In the selected sagittal slice, the length of the right phonic lip (∼3 mm) was significantly smaller than the wavelength (at least 16.4 mm); therefore, a point source was used to model the source. A shortduration pulse with wide bandwidth  was used as click excitation. It modelled the physical process that the right phonic lips open and close rapidly to generate a short pulse of the form: where A is the pulse amplitude (Pa), f 0 is the centre frequency (Hz), t p is the time from the onset of the pulse to its peak amplitude (s), and t is time (s).
The time of the pulse in equation (1) has to satisfy equation (2). The waveform and spectra of the pulse can be found in Wei et al (2018).

FE model validation
The FE model that was based on the live dolphin CT data was compared to the FE model that was based on the deceased specimen. Specifically, the waveforms in the acoustic near-field along the animal's forehead, and the waveforms, spectra, and echolocation beam patterns in the acoustic far-field were compared. Both near-and far-field predictions from both live and deceased dolphin FE models were further compared to click recordings from live, echolocating dolphins using published data from earlier studies (Au 1993 The vertical far-field beam pattern can be predicted from the FEA results by calculating the peakto-peak sound pressure of an echolocation click spreading from the source (phonic lips) over a circle of 1 m radius. The predicted beam pattern of the FE model from live dolphin CT scans was compared with that previously modelled from dead dolphin CT scans . Both modelled beam patterns were further compared to direct beam pattern measurements from live, echolocating dolphins (Au 1993).

Morphology differences between live and fresh, deceased specimen
The CT data of the live and deceased bottlenose dolphins were compared based on three planes (sagittal, transverse, and frontal). Figure 3 displays one of the images from each plane. Panels A, B, C of the live dolphin show greater air volume in the naris, vestibular sac, and spiracular cavity than panels D, E, F of the dead dolphin, where air sacs were partially collapsed. Some air was visible in the brain of the deceased dolphin (D, E) but was clearly absent from the live dolphin's brain (A, B). The melon of the live dolphin was slightly longer than that of the deceased dolphin. Thus a bigger region between the forehead apex and the most anterior projection of the melon in the head of the deceased dolphin was observable in D than in A, which might be due to individual anatomical differences.

Acoustic property reconstruction results between live and fresh deceased specimens
The grayscale in the CT scan data can only show the difference when the HU values of structures are significantly different (e.g. bones vs. soft tissues), therefore figure 4 was plotted to display the anatomical features in colours corresponding to the derived acoustic properties. The lines with different colours were located at approximately the same positions on the 2D slices of the live and deceased dolphins ( figure 4). The values of sound speed and density along the lines were extracted for quantitative comparison.
In the sagittal plane (figures 4(A) and (B)), the position of the melon of the deceased dolphin (purple line vs. blue line) was shifted about 30 mm compared to that of the live dolphin and a marginally larger forehead apex was observed. In the selected sagittal slices in figures 4(A) and (B), the distances between the forehead apex and the most anterior projection of the melon in the live and decreased dolphins' heads were approximately 50 and 65 mm, respectively. In the frontal plane (figures 4(C) and (D)), the sound speed and density of the connective tissues around the terminal region of the melon in the deceased dolphin's head were slightly higher than those in the live dolphin's head. These differences in the melon might be due to individually different anatomy or variation in positioning of the two specimens during scanning, rather than caused by death.
In both the sagittal and frontal planes, the melons of the live and deceased dolphins showed a similar trend, where both sound speed and density gradually increased from the inner core to the outer layer. The results agreed well with the measurements by Norris and Harvey (1974) using a diseased specimen, who demonstrated an inhomogeneous melon. The melon is embraced by the connective tissue, which has significantly greater values of sound speed and density. Therefore, the inhomogeneous melon combines with the connective tissue to form a distinct acoustic impedance gradient in the forehead of the dolphin (figures 4(C) and (D)). The melon thus plays an important role in sound propagation through the forehead by guiding the sound and matching acoustic impedance.
In general, the sound speeds and densities of the structures of the live and deceased dolphins in both the sagittal and frontal planes (including the melon, connective tissues, muscles, and bony structures) are very similar, supporting the previous conclusion by Mckenna et al (2007) and Soldevilla et al (2005), who suggested the variations of the sound speed and density values between live and postmortem specimens were insignificant.

FE modelling results
The comparisons of the click waveforms in the nearfield are shown in figure 5(A) for the live dolphin FE model, deceased dolphin FE model, and live echolocating dolphin recordings. The major axis of the outgoing beam for both live and deceased specimens was in the region between points a and c, in all three cases. The comparisons of the click waveforms and spectra in the far-field are shown in figure 5(B). Both the simulated clicks showed the typical broadband signal characteristics and were similar to the live measurements, albeit somewhat lower in peak frequency.
It should be noted that the click comparison between the FEA results and live dolphin measurements in figure 5 is qualitative rather than quantitative since the clicks produced by a live, echolocating dolphin are dynamic and may change with individual and task. A click-by-click analysis of clicks produced by an echolocating dolphin can have a lot of variability in waveform and spectra, which is likely accomplished through manipulation of the sacs and muscular control of the melon. The CT data used to build the FE models were static in the sense that they were not collected as a time series during actual echolocation behaviour. Therefore, the FEA results do not capture the click dynamics of a dolphin echolocating underwater. Moreover, a small discrepancy was found in terms of the polarity of the simulated clicks between the live and dead dolphins. The live dolphin's click was consistent with TRO's measurement results (the same individual) from Finneran et al (2014), and the dead dolphin's click was consistent with Au's recording data. The clicks were formed by the reflected and direct signal components in the forehead transmission. Different anatomical configurations could reflect the signals differently and result in different click waveforms in the far-field. Figure 6 compares the vertical far-field beam patterns: (1) calculated from FEA of live dolphin CT scans, (2) calculated from FEA of dead dolphin CT scans , and (3) measured from live, echolocating dolphins (Au 1993). Shapes, widths, and elevations of the two simulated and one measured beams were similar. The major axis of the simulated, live dolphin's beam was elevated 5.3 • , almost identical to the elevation angles of the main beams from the dead dolphin model and measurements by Au (1993). The vertical 3-dB beamwidth computed from the live dolphin FEA was 8.5 • (the averaged horizontal 3-dB beamwidth of the same individual 'TRO' was 7.5 • , measured by Finneran et al 2014), slightly narrower than those from the dead dolphin FEA (11.1 • ) and measurements (10.2 • ; Au 1993). This is attributed to the different head sizes.
The diameter at the blowhole of the live dolphin was ∼31.5 cm, larger than that of the dead dolphin (∼28 cm), and no measurements of the size of the live dolphin in the acoustic recording by Au (1993) were available. The width of the beam pattern has been shown inversely proportional to the size of an animal's head (Au et al 1999, Wei et al 2016, Jensen et al 2018. In addition, the simulated far-field beam based on the live dolphin CT data had significantly less energy in the side lobes than the FEA results from the dead dolphin CT data, suggesting that the model results based on live dolphin CT data may match the live recordings slightly better in terms of the energy loss into the side lobes.

Dolphin rotation simulation
We simulated the acoustic scene of an echolocating dolphin rotated 180 • about its longitudinal body axis to detect a fish in the far-field (figure 2). Two fish orientations are shown in figure 7: perpendicular (A&B) and longitudinal (C&D) to the radius vector from the tip of the rostrum. Examples of the echo wavefronts received at the tip of the dolphin's rostrum when the fish was located at +10 • elevation are plotted. The dolphin's outgoing beam pointed upwards (+5.3 • ) in the upright position (see section 3 above), but pointed downward (−5.3 • ) when the animal rotated 180 • . The location of the fish relative to the beam axis was thus not symmetrical in the upright and upside-down cases. The dolphin's rotation to 180 • led to a longer propagation path for the echo and an altered arrival waveform (figures 7(E) and (F)).
The acoustic fields at the moment when the echoes reached the tips of the rostrums in both the live and deceased dolphin models were computed and derived for each case. Correlation analysis was performed between the echo acoustic fields from the numeric positions (e.g. +1 • vs. −1 • , +2 • vs. −2 • , etc.), the results are shown in figure 8. In the 2D models, rotating 180 • along the body axis created a mirror-image relationship between the geometries of the unrotated and rotated models (see figure 7). For example, when the fish was located at the elevation angle +10 • , rotating 180 • along the dolphin's body axis would be equivalent to only moving the fish to −10 • . Therefore, the correlation coefficient between the echo acoustic fields in the position +10 • and −10 • can serve as a qualitative measure of the different acoustic fields that dolphins experience after body rotation. In particular, a low signal correlation value combined with sharply different signal spectra can be used as a qualitative measure of the different acoustic fields that dolphins experience after body rotation.
It should be noted that correlation coefficients in the longitudinal cases of both the live and dead dolphin models are scattered compared to those in the perpendicular cases (figure 8). Differences in the significance of the correlations between the models was due to the orientation of the oval (simulated fish). When the simulated fish was orientated Figure 6. Comparison of vertical far-field beam patterns: modelled based on CT data from a live dolphin, modelled based on CT data from a deceased dolphin , and measured from a live, echolocating dolphin (Au 1993). perpendicularly, the length of the reflection arc was ∼0.1 m, however, the length of the reflection arc reduced to ∼0.01 m when the oval was orientated longitudinally. The nearly ten-fold difference in the length of the reflection arc and the different shapes of reflection boundaries caused variations in the returning echoes (see the distinct difference in the amplitude between echoes A&B vs. C&D in figures 7(E) and (F). In other words, the aspect-dependence of the target greatly affected the spread of the echo reception field of view. Nevertheless, the trends of the two dead dolphin cases closely resembled those of the live dolphin suggesting that FE modelling of dolphin biosonar transmissions can effectively be performed using freshly deceased specimens.
As an example, figure 9 shows comparisons of received echo waveform and spectra between the unrotated and 180 • rotated models. When the simulated fish was located at 1 • elevation, regardless of perpendicular or longitudinal orientation (figures 9(A) and (C)), the variations in the echo characteristics were limited. However, when the simulated fish was located at 20 • elevation (figures 9(B) and (D)), significant variations were visible.

Discussion
Our understanding of dolphin biosonar behaviour and performance is informed both through measurements and modelling. In this article, we present a FE model for dolphin echolocation click production and propagation based on CT scans of a live dolphin. Model outputs were compared to those based on CT scans of a recently deceased dolphin and to acoustic recordings of clicks in both near-and far-fields from live, echolocating dolphins.
Training live odontocetes for CT imaging is challenging (Houser et al 2004) and a method has not yet been developed to measure the physical properties of dolphin tissues in vivo. Therefore, FE acoustic models are usually based on CT scans and tissue measurements using specimens that are recently deceased (e.g. after live stranding) or thawed after having been frozen. The accuracy of the morphological descriptions extracted from the scans and tissue measurements is essential. Mckenna et al (2007) examined the post-mortem changes in geometry, density, and sound speed of anatomical structures based on a comparison between CT scans of a live and a post-mortem Atlantic bottlenose dolphin. Limited post-mortem differences were found in the morphology of the forehead structures. However, whether these limited differences would affect FE modelling results was not examined. Cranford et al (2014) found general similarities in forehead sound propagation between the FE models from a live and a carefully preserved post-mortem specimen. However, their simulated beam patterns (both vertical and horizontal beam patterns) were wider than the beam measurements from live, echolocating animals. More importantly, no data were presented about the signal characteristics of the modelled click for comparison with previously recorded clicks.
Our study filled these gaps and further demonstrated that the FEA results of the live and dead dolphins were similar in terms of the near-and far-field waveforms and spectra, as well as the beam pattern. Moreover, the simulated results of the two FE models were similar to echolocation click recordings from live dolphins (Au 1993, Au et al 2010b, Finneran et al 2014, suggesting the two FE models can simulate certain aspects of the echolocation system of a live dolphin. Our results provide evidence that 2D FE acoustic models based on fresh, deceased specimens are sufficiently accurate that CT scans of live animals are not necessarily needed (depending on the goals of the simulation). We hypothesise, however, that FE We presented a simplified, 2D model of dolphin rotational behaviour during echolocation. The correlation coefficients of the returning echo acoustic Live-perpendicular and dead-perpendicular represent the simulated data from the live dolphin and deceased dolphin when the fish was placed perpendicularly, respectively; live-longitudinal and dead-longitudinal represent the simulated data from the live dolphin and deceased dolphin when the fish was placed longitudinally, respectively. Note that all of x-axes here are scaled logarithmically. Linear regression lines were drawn to indicate trends. fields in figure 8 suggested that the rotation may provide additional information in the vertical plane about the targeted fish. When the targeted fish was moving away from the dolphin's main beam axis in each test, we found strong tendencies for the correlation of the echo acoustic fields to decline (see figure  8). Because of the relatively narrow biosonar beam (Au 1993), the farther the targeted fish is away from the main beam, the greater the differences in the echo acoustic fields during rotation (see figure 9). Thus, the advantage of rotational behaviour should be relatively limited if a fish is close to the main response axis of the echolocation beam. However, if a fish is located off of the main response axis, the rotational behaviour could provide a wider insonification area and provide more acoustic information about the fish, thus compensating for both the relatively narrow echolocation beam and the constraints imposed by the limited head movement of the dolphin.
Rotation not only increases the insonified field but also the area of reception. Dolphins' hearing thresholds are asymmetrical in both the vertical and horizontal planes (Au and Moore 1984, Aroyan 2001, Accomando et al 2020. In the vertical plane, dolphins tend to be more sensitive to sounds arriving from below, which is likely the result of specialized acoustic pathways for echolocation beginning in the lower jaw (Brill et al 1988, Supin and Popov 1993, Aroyan 2001, Cranford et al 2010. When the dolphin is stationed, the receiving windows are located in the two areas around the lower jaws (labelled in figure 2). Thus, rotation of the lower jaws with the body during rotational behaviour could potentially compensate for the dolphin's asymmetries (Aroyan 2001) in sound reception by orienting the most sensitive sound reception path towards the insonified target. It should be noted that we used an ellipse to represent a fish in this study. With acoustically reflective bone structures and swimbladders, fishes would have even more details in the echo and a greater difference between echoes at different angles. Therefore the reality is likely to be an even stronger argument for our hypothesis. The next logical step is to conduct experiments and model dolphin rotation in 3D to test the hypothesis. We cannot exclude the possibility that rotational behaviour may serve other biological functions or that dolphins only rotate for fun. Therefore, controlled acoustic experiments would be critical for us to further understand this behaviour. Our 2D study was only able to consider two positions of the dolphin: 0 • and 180 • rotated. Our 2D FE model provides the starting point to understanding the possible role of the frequently Figure 9. Comparisons of the received echo waveforms and spectra between unrotated and rotated models. When the fish was located at (A) 1 • elevation and in a perpendicular orientation, (B) 20 • elevation in a perpendicular orientation, (C) 1 • elevation in a longitudinal orientation, and (D) 20 • elevation in a longitudinal orientation. The relative amplitude values were normalized according to the maximum peak-to-peak sound pressure of the received waveform in (A). observed dolphin rotational behaviour. However, dolphins live in a 3D environment and their rotational behaviour exploits this dimensionality. Indeed, the creation of 3D acoustic fields for dolphin echo-location beams and returning echoes could provide more information on not only the question of how rotational behaviour might benefit an echolocating dolphin, but on biosonar behaviour in general.

Conclusions
We constructed numerical models based on both live and fresh deceased Atlantic bottlenose dolphin CT scan data to estimate the acoustic scene of an echolocating dolphin rotating 180 • about its longitudinal axis while detecting a fish at elevation angles of −20 • to 20 • . The models suggest that dolphins experience different echo acoustic fields when in rotation, which may provide extra information about the insonified fish, particularly when a fish is located out of the main response axis of the echolocation beam. The rotational behaviour not only provides a wider insonification area but also a wider receiving area to compensate for the dolphin's relatively narrow biosonar beam and asymmetries in sound reception. This paper represents the first step towards understanding how the dolphin's rotational behaviour could contribute to its echolocation performance.
This study also compared the anatomical configuration and acoustic properties of the forehead structures between the live and fresh deceased dolphins, as well as examining the accuracy of FEA in acoustic simulations using freshly deceased specimens. Our results suggest that freshly deceased specimens, if handled properly, may be sufficient alternatives for FE acoustic modelling when live specimens are not available. This has important implications for the study of acoustic mechanisms for biosonar production and hearing in species only accessible after stranding (i.e. most species of echolocating whales are unavailable for experimental measurements).

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors