Ear Deformations Give Bats a Physical Mechanism for Fast Adaptation of Ultrasonic Beam Patterns

A large number of mammals, including humans, have intricate outer ear shapes that diffract incoming sound in a direction- and frequency-specific manner. Through this physical process, the outer ear shapes encode sound-source information into the sensory signals from each ear. Our results show that horseshoe bats could dynamically control these diffraction processes through fast nonrigid ear deformations. The bats’ ear shapes can alter between extreme configurations in about 100 ms and thereby change their acoustic properties in ways that would suit different acoustic sensing tasks.

Figure 1

Beam pattern examples from HDC bats (top row) and LDC bats (bottom row). (a) Stoliczka’s trident bat (Aselliscus stoliczkanus, 104–120 kHz in steps of 2 kHz), (b) Pearson’s horseshoe bat (Rhinolophus pearsonii, 44–62 kHz in steps of 2 kHz), (c) Least horseshoe bat (Rhinolophus pusillus, 90–110 kHz in steps of 2 kHz), (d) Pomona roundleaf bat (Hipposideros pomona, 100–126 kHz in steps of 2 kHz), (e) Pratt’s roundleaf bat (Hipposideros pratti, 50–70 kHz in steps of 2 kHz), (f) Common bent-wing bat (Miniopterus schreibersii, 47–87 kHz in steps of 4 kHz), (g) Round-eared tube-nosed bat (Murina cyclotis, 40–176 kHz in steps of 8 kHz), (h) Rickett’s big-footed bat (Myotis ricketti, 30–70 kHz in steps of 4 kHz), (i) Pipistrelle (Pipistrellus sp., 35–100 kHz in steps of 5 kHz), (j) Lesser bamboo bat (Tylonycteris pachypus, 50–120 kHz in steps of 5 kHz). For each frequency, a single contour line is drawn at a gain level of $-6\mathrm{dB}$. Frequencies are coded by color from blue for the lowest frequency to red for the highest frequency analyzed.

Figure 2

Example of a typical nonrigid pinna deformation geometry in the greater horseshoe bat. (a) Upright (blue) and bent (red) state of the pinna. Black lines mark the location of the cutting planes. The arrows in the section views show the direction of movement of various portions of the pinna. (b) Corresponding change in the magnitude of the displacement as a function of time during a deformation cycle. The displacement magnitude shown is the maximum over the displacements of all landmarks. Landmark displacements and time were measured from the most upright state of the pinna. The displacement magnitude is given in absolute terms (left axis) and as a fraction of pinna height (right axis). This example is only typical in geometry of the deformation, not in the duration of the deformation cycle (which is considerably longer than average).

Figure 3

Beam pattern changes with pinna deformation. (a) Image sequence of the pinna deformations captured by a high-speed video camera with the arrows indicating the pinna tip’s approximate direction of motion in each frame. (b) Renderings of the complete digital model of the pinna at the same time instants as the video frames. (c) The normalized far-field directivity gains in different directions (beam patterns), at a resolution of 1° in azimuth and elevation, computed for each of the pinna geometries at a sound frequency of 75 kHz. The orientation of the beam pattern matches that of the shape renderings approximately; i.e., the central axis of the pinna cone points towards the North Pole.

Figure 4

Beam pattern analysis. (a) Change in total sensitivity of the main lobe (▴) and side lobes (▪) over a deformation cycle: average (▴, ▪), standard deviation (error bars), and extreme values ($+$) over frequency (60–80 kHz in 5 kHz intervals). The main lobe is defined to cover all directions inside a $-3\mathrm{dB}$ contour that contains the global maximum [inner white contour in inset (i), solid blue in inset (ii)]. The remaining directions are allocated to the side lobes [solid red in inset (ii)] as long as their gain values do not fall below $-15\mathrm{dB}$ of the global maximum. The total sensitivity of a lobe is defined as the integral of directivity gain over the lobe’s area. Values shown are normalized with respect to the mean total sensitivity value of the main lobe (taken over all pinna geometries and frequencies). (b) Comparison of the frequency dependence of main lobe and side lobe: Histograms of the average beam overlap of the main lobes (blue) and side lobes (red) in beam patterns for adjacent frequencies. The areas of main lobes and side lobes were defined by $-3\mathrm{dB}$ contours that include the lobe maxima [insets (i)–(iv)]. Only the strongest side lobe was used in this analysis. Beam overlap was used as a measure of change in beam position and shape over frequency. It was defined as the ratio of the intersection to the union of the areas of one lobe for two adjacent frequencies [inset (i)]. Average beam overlap was obtained by taking the mean over all neighboring frequencies. Only pinna geometries with significant side lobes (average total sensitivity in the side lobes greater than 3 times the average total sensitivity in the main lobe; 49 shapes met this criterion) were used in this analysis. Insets (ii)–(iv) show example lobe areas as a function of frequency where frequency is color coded such that highest frequency is the lightest.

Figure 5

Comparison of example beam patterns of pinna shapes from greater horseshoe bats in an upright (top row) and a bent pose (bottom row). (a)–(e) Five different individuals of Greater horseshoe bats (Rhinolophus ferrumequinum), upright in vivo shapes (60–80 kHz in steps of 2 kHz), and (f)–(j) in vivo bent shapes from the same Greater horseshoe bat individuals using the same frequencies.