Escobar-thesis-presentation-2

Prob Statement Motivation Numerical App Modeling App Results Conclusion References
Sound reception mechanism analysis of a Cuvier’s
beaked whale (Ziphius cavirostris)
Ivana Escobar
May 27, 2016
Department of Structural Engineering

Overview
Problem Statement
Motivation
Numerical Approach
Modeling Approach
Boundary Conditions
Relative Velocity
Results
Stapes Velocity Transfer Function
Mesh Reﬁnement
Parametric Study
Audiogram
Conclusion

Problem statement
Simulate sound reception of the Ziphius ear complex with two
mechanisms that enable hearing; pressure loading from
surrounding soft tissues and bone conduction from skull
vibration4. (Software: MATLab with FinEALE, an open
source program) [4]
Compare mesh discretization and parametric values of
amplitudes and phase shifts, used in loading, and material
damping coeﬃcients.
Generate a synthetic audiogram from the stapes velocity
transfer function (SVTF) based on relative displacement of
the hearing structure.
4
T.W. Cranford and P. Krysl (2015)

Motivation
Anthropogenic sound in the ocean,
such as sonar, has been related to
mass strandings of marine life, in
particular the Cuvier’s beaked
whale (Ziphius cavirostris).
Provide insight on the auditory
sensitivity of the Cuvier’s beaked
whale and its ability to capture
sound in the known range of
mid-frequency sonar2. [2]
2
T. M. Cox et al. (2006) Source: 2015 c Nat’l Resources Defense
Council / Int’l Fund for Animal Welfare

Numerical approach
Matrix form
M¨u + C ˙u + Ku = F
Force vector composed of applied body loads and tractions.
F = F¯b + F¯t
Harmonic behavior applied to loading and nodal displacement
F = ˜Feiωt
and u = ˜ueiωt
Reducing the equation to time-independent components
−ω2
M˜u + iωC˜u + K˜u = ˜F

Numerical approach
Assumed-strain formulation weakly enforcing the kinematic
equation6 [6]
= Bu
After spacial discretization with linear tetrahedrals, the strain
energy is approximated as
Ψe =
i,j=1 q=1
1
2
[uT
i (BNi (xq))T
D(BNj(xq))uj].
Nodally integrated continuum elements (NICE)5 [5]
Nk(xq) = e
Nk(ξ(xq)) adj(J(xq))J (xq)Wq
e
J (xq)Wq
5
P. Krysl and H. Kagey (2012)
6
P. Krysl and B. Zhu (2008)

Ziphius tympanoperiotic complex (TPC)
Skull view from bottom without the mandible3
[3]
3
T.W. Cranford and P. Krysl (2012) Source: 2012 c Springer
Science+Business Media, LLC

Two applied loading mechanisms
Pressure loading (P)
From mandibular fat body
branches interacting with the
tympanic bone
t = Peiφp
· n
blabla
hihihi
one more
TPC pressure transfer
function (TPTF)4 [4]
Bone conduction (U)
From skull-vibration through
the periotic bone
¯b = [¯bx
¯by
¯bz]T
¯bx = −ω2
ρboneUx ,
¯by = −ω2
ρboneUy eiφy
,
¯bz = −ω2
ρboneUzeiφz
.
Periotic-bone displacement
transfer function (PDTF)4 [4]
4
T.W. Cranford and P. Krysl (2015)

From VibroAcoustic toolkit (VATk) simulations

Boundary Conditions
Body load applied on all volume elements in the domain for
bone conduction.
Nodes are fixed at the connection of the periotic bone to the
rest of the skull.
Traction applied on specified surface elements where the
mandibular fat bodies connect with the tympanic bone for
pressure loading.
Soft tissue surrounding the tympanic bone dissipates energy
as ramped damping, 0 Hz to 2, 000 Hz and held constant
after, on a prescribed surface.
The stapes footplate in contact with the cochlear fluid, which
is modeled as damping along the footplate surface.

Boundary Conditions

Boundary Conditions
Using cochlear impedance reported for humans1 [1]
Z ≈ 95, 488 [Pa · m−1 · s].
1
R. Aibara et al. (2001)

Relative velocity of stapes footplate
Model solution
Displacement found at points,
˜ust and umean = (
4
i=1
˜ui )/4.
Relative displacement,
ur = ˜ust − umean.
In normal direction of footplate,
m, as ust = |ur · m|.
Relative velocity,
vst = ωust.

Stapes Velocity Transfer Function (SVTF)
Relates output from stapes motion to cochlear input from sound
occuring underwater.
SVTF = vst
Pinc

SVTF
Isolating each mechanism to only bone conduction (U) and only
pressure loading (P).

SVTF

Visualization

Parameters studied
Mesh reﬁnement
Seven discretization levels with volume and surface smoothing
applied at each increment.
Phase shifts
Turned oﬀ phase shifts incrementally.
Amplitudes
Uniform scaling of all amplitudes.
Rayleigh system damping
Minimum damping ratio
Baseline frequency

Mesh reﬁnement study
Mesh 1:
527,725 elements,
39,193 mm3
Mesh 7:
27,297 elements,
37,617 mm3
you go Glenn Coco
Total volume change: 4.02% decrease

Mesh reﬁnement study

Toggling phase shifts
Bone conduction Pressure loading
∆ = SVTFi −SVTFbase
SVTFbase
(U):
∆ = 0.520
(UP):
∆ = 0.168
(P):
∆ = 0.000
(UP):
∆ = 0.194

Toggling phase shifts
(UP): ∆ = 0.194

Amplitude scaling
Uniform factor applied on all amplitudes at once.

Viscous damping proportional to a linear combination of mass and
stiﬀness matrices
C = amM + akK.
am and as, were determined by a minimum damping ratio,
ζmin = 1
2(akω + am/ω) as
am = ζminωmin [1/s] and ak = ζmin
ωmin
[s].
The base model has
ζmin = 0.025 and
ωmin = 2π · 25000 [rad].

Varying minimum damping ratio, ζmin.
1/4: ∆ = 0.612, 1/2: ∆ = 0.325, 2: ∆ = 0.334, 4: ∆ = 0.648.

Varying baseline frequency, ωmin.
1/4: ∆ = 0.540, 1/2: ∆ = 0.245, 2: ∆ = 0.126, 4: ∆ = 0.161.

Audiogram
An audiogram is a graph used to visualize audible sound for a
given range of frequencies, typically determined with behavioral
experiments.
Sound pressure levels
Calibrated to the minimal audible pressure of a Blainville’s beaked
whale7, 50dB re 1µPa.
Threshold pressure
pth = max[SVTF(ω)]
SVTF(ω) pmin.
Sound pressure levels
SPL = 20 log pth(ω)/pref.
[7]
7
A. Pacini et al. (2011)

Audiogram
Known mid-frequency sonar emits sound between 3 − 10 kHz.
Ziphius has an estimated hearing range of 40 dB.

Conclusion
Optimal hearing occurs at higher frequencies, 40 − 60 kHz,
but still shows hearing response dominated by bone
conduction at lower frequencies.
Based on this work, the Ziphius has a potential ability to
receive sound at known mid-frequency sonar ranges 3 − 10
kHz.
Future work
Considering asymmetry of skull, simulate both ears.
Vary planar wave direction and angle hitting the skull.
Study other marine life using the combined loading technique.

Questions?
Acknowledgements
Dr. Petr Krysl, Dr. Michael Todd, Dr. Joel Conte, Poorya
Mirkhosravi, Alireza Pakravan, Phi Nguyen, Marco Pasetto
SE Admin and others

References I
[1] R. Aibara, J. T. Welsh, S. Puria, and R. L. Goode. Human
middle-ear sound transfer function and cochlear input
impedance. Hearing research, 152(1):100–109, 2001.
[2] T. M. Cox, T. Ragen, A. Read, E. Vos, R. Baird, K. Balcomb,
J. Barlow, J. Caldwell, T. Cranford, and L. Crum.
Understanding the impacts of anthropogenic sound on beaked
whales. Technical report, DTIC Document, 2006.
[3] T. W. Cranford and P. Krysl. Acoustic function in the
peripheral auditory system of cuvier’s beaked whale (Ziphius
cavirostris). In The Eﬀects of Noise on Aquatic Life, pages
69–72. Springer, 2012.

References II
[4] T. W. Cranford and P. Krysl. Fin whale sound reception
mechanisms: skull vibration enables low-frequency hearing.
PloS one, 10(1):e0116222, 2015.
[5] P. Krysl and H. Kagey. Reformulation of nodally integrated
continuum elements to attain insensitivity to distortion.
International Journal for Numerical Methods in Engineering, 90
(7):805–818, 2012.
[6] P. Krysl and B. Zhu. Locking-free continuum displacement
ﬁnite elements with nodal integration. International Journal for
Numerical Methods in Engineering, 76(7):1020–1043, 2008.

References III
[7] A. F. Pacini, P. E. Nachtigall, C. T. Quintos, T. D. Schoﬁeld,
D. A. Look, G. A. Levine, and J. P. Turner. Audiogram of a
stranded blainville’s beaked whale (Mesoplodon densirostris)
measured using auditory evoked potentials. Journal of
Experimental Biology, 214(14):2409–2415, 2011. ISSN
0022-0949. doi: 10.1242/jeb.054338. URL
http://jeb.biologists.org/content/214/14/2409.

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