The authors have declared that no competing interests exist.
Conceived and designed the experiments: TWC PK. Performed the experiments: TWC PK. Analyzed the data: TWC PK. Contributed reagents/materials/analysis tools: TWC PK. Wrote the paper: TWC PK.
‡ These authors contributed equally to this work.
Hearing mechanisms in baleen whales (Mysticeti) are essentially unknown but their vocalization frequencies overlap with anthropogenic sound sources. Synthetic audiograms were generated for a fin whale by applying finite element modeling tools to X-ray computed tomography (CT) scans. We CT scanned the head of a small fin whale (
Mysticete whales are the largest animals on Earth. The pelagic balaenopterids may reach 30 meters in length and produce low-frequency sounds in the range of 10–200 Hz [
The acoustic bandwidths used by mysticetes overlap with anthropogenic sound sources, raising concerns over potential deleterious effects from increasing trends in ocean noise [
To date, attempts to estimate the hearing parameters of baleen whales fall into three categories based on inferential methods:
We constructed a finite element modeling system, based on serial CT scans, that allows us to predict low-frequency hearing sensitivity and identify sound reception mechanisms in cetaceans [
On 20 November 2003 a newborn male fin whale (
This stranded fin whale was 550 cm long, weighed 1,165 kg, and was assigned a Field-ID (JEH520) by John E. Heyning at the Los Angeles County Museum of Natural History. The average length at birth for Northern Pacific fin whales is between 600–650 cm, while adults can reach 2400 cm in length [
After CT scanning, the head (in its container) was returned to a freezer until it was dissected on 21 August 2006. When the necropsy of the head was conducted, the tissue handling protocol was approved by the Graduate and Research Affairs, Institutional Animal Care and Use Committee at San Diego State University (APF#: 09-05-014B). Permission to possess the head was provided by a Letter of Authorization from the National Oceanic and Atmospheric Administration and the National Marine Fisheries Service Southwest Region (Administrative File: 151408SWR2013PROOOl). The prepared skull was accessioned by the Museum of Biodiversity at San Diego State University. The specimen now resides there under Accession-ID S-970.
Each bony ear complex in cetaceans is a conglomeration of various bones that comprise the
An incident acoustic wave of a given pressure amplitude in the sea water surrounding an animal interacts with the tissues of its head to generate traction loads on the surface of the TPC. These loadings on the TPC can be calculated from the incident sound pressure because they are, to a good approximation, driven by the amplitudes of acoustic pressure. The TPC vibrates under the action of the loads, resulting in motion of the stapes within the oval window, which produces a velocity at the center of the stapes footplate. The resulting transfer function, the Stapes Velocity Transfer Function (SVTF), is the composite of
We also consider the possibility that the ossicular chain may be set into motion by loading on the TPC that is analogous to bone conduction in humans [
We have quantified both means of loading the TPC, by pressure delivered through soft tissues and by “skull-bone conduction”, using our two-component series of finite element models specialized for propagating elastic waves through arbitrary geometries of combined fluids and solids in an acoustic medium. The CT scans were converted to a mesh of finite elements by mapping the voxel values to the material types (see
The forced harmonic vibration analysis of the TPC then resulted in the combined transfer function between the incident acoustic pressure and the stapes footplate velocity. The stapes velocity transfer function (SVTF) was then used to estimate an audiogram, for each of the loading modalities separately and also for their combination. The audiogram curve was calibrated with respect to the minimum audible pressure using measurements and estimates from two previous studies of odontocetes [
The sensitivity of the computed transfer functions to the input parameters was assessed by performing a series of forward/backward sensitivity analyses. The full details are provided in the
The mechanical response of the TPC and the vibrations of the tissues of the head, especially the skull, can be visualized with animations (as shown in the
Synthetic audiograms were generated for a fin whale head using finite element modeling simulations derived from CT scans of a small
The primary, or dominant,
Our assertion that mysticetes receive sound by a
Some display transparency has been applied to the squamosal bone so that the tympanic bulla and the dense bony ossifications or “anchors” become visible. Bony skull components that are visible in this orientation are the: occipital (yellow), parietal (white), frontal (red), maxillary (green), squamosal (magenta), tympanic bullae (green), and the “anchors” (white). The dense bony anchors fan out dorsolaterally within the squamosal bones of the skull (see also
The periotic bones (yellow) and tympanic bullae (green) are components of each TPC. The dense bony fan-like projections (cyan) are contained within the bones of the skull (salmon). Specifically, the anchors fan out as dense ossifications within the squamosal bone, from a locus at the junction with the juxtaposed periotic bones, and may function to stiffen the connection between the periotic and the skull. The mandibles (pink) are shown for context.
By contrast, the TPCs of most odontocetes tend to be separated from the skull. Odontocete TPCs are suspended from the skull by numerous ligamentous fibers that originate from an approximately hemispherical distribution on the periotic fossa and peribullary fossa, sometimes crisscrossing, to insert upon the periotic bone of each TPC. It is generally considered that this suspension system functions to acoustically isolate the TPCs from skull vibrations in odontocetes. Instead, sounds apparently reach odontocete TPCs primarily through the mandibular fat bodies [
The results of our model have been applied to a fin whale, but the same firm connection between the TPC and the skull is common to all mysticetes [
Two finite element models were required to cover the range of geometric resolution needed to accurately represent the relevant mechanisms. The first model (WP = Wave Propagation) simulated the traveling acoustic pressure waves through the water, from in front of the animal toward the head. The sound waves propagate through seawater, reach the head, continue along/within various soft tissue pathways (which have acoustic impedance values similar to water), and impinge upon the skull and the tympanic bone, the tympanic “bulla” of the TPC. The WP model could reasonably resolve the bone thicknesses of the TPC by employing cubic finite elements with dimensions of 2.7 mm on each side. This resolution was not sufficient to accurately represent the fine features of the middle ear ossicles. Therefore, the WP model was used to estimate the loading mechanisms acting on the TPC, and a second model with much higher resolution (0.684 mm) was used to compute the Forced Harmonic Vibration response of the TPC to these loads (hence the FHV model).
For the
The models that incorporate the
The
The bony projections that “anchor” the tympanoperiotic complexes to the skull are cyan. The brain is blue, the skull is salmon colored, and the mandible is pink. The periotic portions of the TPC are yellow, and each tympanic bulla is green. Note that thin bony pedicles form a fulcrum for differential vibration between the periotic bones and the large hypermineralized masses of the tympanic bulla at the distal end of each involucrum.
This lever arm construction is common to all cetacean TPCs (Archaeoceti, Odontoceti, and Mysticeti) [
For the skull-vibration induced bone conduction, the WP model yielded the amplitude of the displacements of the periotic bone and relative phase shifts between the components of displacement, while the FHV model simulated the response of the TPC to the forcing by prescribed harmonic-motion of the periotic bones.
For both the pressure and the bone conduction mechanisms, the result of the simulation was a transfer function (TF) between the amplitude of the incident sound pressure wave in the environment around the head and the magnitude of the velocity of the stapes footplate, the stapes-velocity transfer function (SVTF). Since two models were used to construct the SVTF for both loading mechanisms, the result is a composition of two TFs, WP-TF for the wave propagation model and FHV-TF for the forced vibration model.
We note that Tubelli and colleagues [
With the SVTF at hand, we can attempt to predict the audiogram. The audiogram curve needs to be calibrated with the respect to the minimum audible pressure. Since this value has never been measured for a baleen whale, our approach was to set the hearing threshold to be similar to that measured for toothed whales, the bottlenose dolphin [
The solid blue line represents the audiogram for the
Mysticete sound reception by the
This study uses the only currently available method capable of predicting relative sensitivities for sound reception in a mysticete over a broad range of frequencies, between 10 Hz and 12 kHz. Note that the lower frequencies (~20 Hz) propagate well in the ocean and are relatively less attenuated by the environment, so there may be no need for the best sensitivity to be located at those frequencies. The
Mysticete sound reception is enabled by the vibration of the relatively stiff and dense skull in response to the sound waves passing through the body of the whale. The advantage to mysticetes of using low-frequency (long-wavelength) sounds becomes evident when considering the motion or displacement of the scatterer (i.e. the skull), instead of the scattered pressure, as described by Rayleigh [
The air spaces associated with the TPCs play a minor role for the pressure forcing mechanism, but only for high frequencies (above 5 kHz). At those frequencies, the air spaces helped to establish a “resonant cavity” for the sound waves propagating through the soft tissues towards the ears. The waves in the soft tissues are much too long below 5 kHz for the air spaces to be significant contributors to the pressure-distribution calculation. The most important function for these interconnected air spaces may be to maintain sufficient air volume in the tympanic cavity around the ossicular chain to allow the ossicles to vibrate free of damping or interference by nearby soft tissues. A similar mechanism has also been proposed for the enlarged pterygoid sinuses in
Although these simulations were conducted with the skull geometry of a fin whale calf, the two basic mechanisms will not change significantly for the adult skull. The reasoning here is twofold. First, the tympanic bullae develop precocially [
Adult fin whale skulls are approximately twice as long as they are wide [
The audiogram is understood to be shaped by the external, middle, and inner ear connected in series [
Understanding the potential effects of anthropogenic noise on mysticetes is a subject that has long plagued U.S. regulatory agencies and concerned large-scale industrial users of the ocean environment. The results reported here provide a new tool for assessing these acoustic interactions.
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(A) Finite element mesh 4 (approximately 41,000 nodes, 230,000 elements). The periotic bone is trimmed off, and the red markers at the top-right of the mesh indicate nodes with prescribed displacements (as dictated by the motion or the lack of the motion of the squamosal bone of the skull). (B) Close-up of the ossicular chain and the sigmoidal process in the foreground. The joints between the ossicles are shown in color: the annular ligament between the stapes and the oval window is yellow; the incudostapedial ligament is green, and a small portion of the malleoincudal ligament is blue (most of this ligament and the malleus are obscured by the sigmoidal process).
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Mesh 4 as in
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Sound Pressure Levels (SPL) between -3 dB (pressure diminished with the respect to incident) and +6 dB (pressure amplified with respect to incident) are shown. The pressure is not displayed in the volume of the bones (gray regions) or in the volume of the air spaces or sinuses (black regions). (A) is a transverse section through the TPC with labels indicating the involucra (i) of the tympanic bulla and the expanded portion of the squamosal (sq); (B) is a coronal (horizontal) section through the TPC, at the level of the tympanic bullae (tb). Note the amplified pressure amplitude near the dorsal surface of the tympanic bullae (tb) from a reflection off of the squamosal bones (sq).
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Note that close to 1–2 kHz the incident pressure is magnified to arrive at the surface of the TPC almost doubled in amplitude.
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(A) Amplitudes of the displacements, and (B) phase shift with respect to the dorsal-ventral displacement.
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(A) SVTF(P) for two meshes: mesh 3, with 62,000 nodes, in solid line, and mesh 6, with 20,600 nodes, in dashed line. (B) Approximate error vs. the number of nodes in the model, where the smallest error is
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Amplitude magnified 20,000 times. (Animated visualization link with displacements magnified by 20,000 times).
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Amplitude magnified 20,000 times. (Animated visualization link with displacements magnified by 20,000 times).
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Amplitude magnified 20,000 times. (Animated visualization link with displacements magnified by 20,000 times).
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Amplitude magnified 20,000 times. (Animated visualization link with displacements magnified by 20,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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(Animated visualization link with displacements magnified by 5,000 times).
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Dotted line: decrease by a factor of ½, Δ = 0.159; dashed line: increase by a factor of 2, Δ = 0.084.
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Dotted line: decrease by a factor of ½, Δ = 0.65; dashed line: increase by a factor of 2, Δ = 0.85.
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Dotted line: decrease of ςmin by a factor of ½, Δ = 0.25; dashed line: increase of ςmin by a factor of 2, Δ = 0.24.
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Dotted line: decrease of
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Dotted line: decrease by a factor of ½, Δ = 0.139; dashed line: increase by a factor of 2, Δ = 0.144.
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This project included multiple daunting logistical challenges that were eventually solved by an array of individuals with diverse skill sets. We thank the following people for their support on various aspects of this project. Michael Wiese, James Eckman, and Dana Belden at the Office of Naval Research (N00014-12-1-0516); Frank Stone, Ernie Young, and Robert Gisiner at the Chief of Naval Operations (CNO45) along with Curtis Collins and John Joseph at the Naval Postgraduate School (N00244-08-1-0025). We appreciate assistance with specimen acquisition from: Judy St. Leger and Erika Nilson (Sea World, San Diego), John Heyning, David Janiger, and Jim Dines (Los Angeles County Museum of Natural History); James Mead, and Charles Potter (National Museum of Natural History, Smithsonian Institution); David Casper and Robin Dunkin (UC Santa Cruz); Joseph G. Cordaro and Sarah Wilkin, Jennifer L. Skidmore, Blair Maise, Susan Chivers, Kerri Danil, Wayne Perryman, and Debra Losey (NOAA); Eric Ekdale, Tom Deméré, and Philip Unitt (San Diego Natural History Museum). We also thank several other individuals, Jim Christmann and Dave Jablonski, Winston C. Lancaster, Jennifer Jeffress, Maureen Flannery, Kristi West, Michele Berman, Carl Schilt, William Ary, and A. Todd Newberry. Staff at the San Diego State University Research Foundation and Department of Biology provided essential logistical assistance: Frank Sweeney, Thomas Scott, Michele Goetz, Maria Ortega, Eugene Stein, Jennie Amison, Danielle Arellano-Rieger, Mary Perl, (SDSURF) Terry Frey, Medora Bratlien, Christopher Glembotski, Annalisa Berta, Bob Mangen, and Mike Van Patten (Biology). Individuals from the Scripps Institution of Oceanography were also instrumental by helping encase the specimen in a specialized container for scanning at Hill AFB: John Hildebrand, Sean Wiggins, Megan McKenna, and Jeremy Goldbogen. Michael Philcock at Analyze Direct also made valuable contributions. The staff at Hill Air Force Base provided expertise with specimen CT scanning using their industrial scanner: Sal Juarez, Barry Gould, Randy Huber, Sam Samuelson, and Art McCarty. This manuscript was improved considerably from reviews by Mats Amundin, Olav Sand, Wim Verboom, James Mead, and one anonymous reviewer.