Focused ultrasound (FUS) is an established technique for non-invasive surgery and has recently attracted considerable attention as a potential method for non-invasive neuromodulation. While the pressure waves in FUS procedures have been extensively studied in this context, the accompanying shear waves are often neglected due to the relatively high shear compliance of soft tissues. However, in bony structures such as the skull, acoustic pressure can also induce significant shear waves that could propagate outside the ultrasound focus. Here, we investigate wave propagation in the human cranium by means of a finite-element model that accounts for the anatomy, elasticity, and viscoelasticity of the skull and brain. We show that, when a region on the scalp is subjected to FUS, the skull acts as a waveguide for shear waves that propagate with a speed close to 1500 m/s, reaching off-target structures such as the cochlea. In particular, when a sharp onset of FUS is introduced in a zone proximal to the intersection of the parietal and temporal cranium, the bone-propagated shear waves reach the inner ear in about 40 μs, leading to cumulative displacements of about 1 μm. We further quantify the effect of ramped and sharp application of FUS on the cumulative displacements in the inner ear. Our results help explain the off-target auditory responses observed during neuromodulation experiments and inform the development of mitigation and sham control strategies.

2.
K.
Hynynen
and
F. A.
Jolesz
,
Ultrasound Med. Biol.
24
,
275
(
1998
).
3.
M.
Tanter
,
J.-L.
Thomas
, and
M.
Fink
,
J. Acoust. Soc. Am.
103
,
2403
(
1998
).
4.
K.
Hynynen
,
N.
McDannold
,
N.
Vykhodtseva
, and
F. A.
Jolesz
,
Radiology
220
,
640
(
2001
).
5.
S.
Mitragotri
,
Nat. Rev. Drug Discovery
4
,
255
(
2005
).
6.
T.
Deffieux
,
J.-L.
Gennisson
,
M.
Tanter
,
M.
Fink
, and
A.
Nordez
,
Appl. Phys. Lett.
89
,
184107
(
2006
).
7.
Y.
Li
,
H.
Zhang
,
C.
Kim
,
K. H.
Wagner
,
P.
Hemmer
, and
L. V.
Wang
,
Appl. Phys. Lett.
93
,
011111
(
2008
).
8.
Y.-S.
Tung
,
F.
Marquet
,
T.
Teichert
,
V.
Ferrera
, and
E. E.
Konofagou
,
Appl. Phys. Lett.
98
,
163704
(
2011
).
9.
J.
Ylitalo
,
J.
Koivukangas
, and
J.
Oksman
,
IEEE Trans. Biomed. Eng.
37
,
1059
(
1990
).
10.
A.
Fenster
,
D. B.
Downey
, and
H. N.
Cardinal
,
Phys. Med. Biol.
46
,
R67
(
2001
).
11.
Y.
Younan
,
T.
Deffieux
,
B.
Larrat
,
M.
Fink
,
M.
Tanter
, and
J.-F.
Aubry
,
Med. Phys.
40
,
082902
(
2013
).
12.
S.-S.
Yoo
,
A.
Bystritsky
,
J.-H.
Lee
,
Y.
Zhang
,
K.
Fischer
,
B.-K.
Min
,
N. J.
McDannold
,
A.
Pascual-Leone
, and
F. A.
Jolesz
,
Neuroimage
56
,
1267
(
2011
).
13.
Y.
Tufail
,
A.
Matyushov
,
N.
Baldwin
,
M. L.
Tauchmann
,
J.
Georges
,
A.
Yoshihiro
,
S. I. H.
Tillery
, and
W. J.
Tyler
,
Neuron
66
,
681
(
2010
).
14.
P. P.
Ye
,
J. R.
Brown
, and
K. B.
Pauly
,
Ultrasound Med. Biol.
42
,
1512
(
2016
).
15.
W.
Legon
,
T. F.
Sato
,
A.
Opitz
,
J.
Mueller
,
A.
Barbour
,
A.
Williams
, and
W. J.
Tyler
,
Nat. Neurosci.
17
(
2
),
322
(
2014
).
16.
R. L.
King
,
J. R.
Brown
, and
K. B.
Pauly
,
Ultrasound Med. Biol.
40
(
7
),
1512
(
2014
).
17.
R. L.
King
,
J. R.
Brown
,
W. T.
Newsome
, and
K. B.
Pauly
,
Ultrasound Med. Biol.
39
(
2
),
312
(
2013
).
18.
W.
Lee
,
H. C.
Kim
,
Y.
Jung
,
I. U.
Song
,
Y. A.
Chung
, and
S. S.
Yoo
,
Sci. Rep.
5
,
8743
(
2015
).
19.
W.
Lee
,
H. C.
Kim
,
Y.
Jung
,
Y. A.
Chung
,
I. U.
Song
,
J. H.
Lee
, and
S. S.
Yoo
,
Sci. Rep.
6
(
1
),
34026
(
2016
).
20.
N.
Wattiez
,
C.
Constans
,
T.
Deffieux
,
P. M.
Daye
,
M.
Tanter
,
J. F.
Aubry
, and
P.
Pouget
,
Brain Stimul.
10
(
6
),
1024
(
2017
).
21.
L.
Verhagen
,
C.
Gallea
,
D.
Folloni
,
C.
Constans
,
D. E.
Jensen
,
H.
Ahnine
,
L.
Roumazeilles
,
M.
Santin
,
B.
Ahmed
,
S.
Lehéricy
, and
M. C.
Klein-Flügge
,
eLife
8
,
e40541
(
2019
).
22.
D.
Folloni
,
L.
Verhagen
,
R. B.
Mars
,
E.
Fouragnan
,
C.
Constans
,
J. F.
Aubry
,
M. F.
Rushworth
, and
J.
Sallet
,
Neuron
101
(
6
),
1109
(
2019
).
23.
J.
Blackmore
,
S.
Shrivastava
,
J.
Sallet
,
C. R.
Butler
, and
R. O.
Cleveland
,
Ultrasound Med. Biol.
45
(
7
),
1509
(
2019
).
24.
T.
Sato
,
M. G.
Shapiro
, and
D. Y.
Tsao
,
Neuron
98
,
1031
(
2018
).
25.
H.
Guo
,
M.
Hamilton
 II
,
S. J.
Offutt
,
C. D.
Gloeckner
,
T.
Li
,
Y.
Kim
,
W.
Legon
,
J. K.
Alford
, and
H. H.
Lim
,
Neuron
98
,
1020
(
2018
).
26.
V.
Braun
,
J.
Blackmore
,
R. O.
Cleveland
, and
C. R.
Butler
, “
Transcranial ultrasound stimulation in humans is associated with an auditory confound that can be effectively masked
,” bioRxiv (
2020
).
27.
J. L.
Robertson
,
B. T.
Cox
,
J.
Jaros
, and
B. E.
Treeby
,
J. Acoust. Soc. Am.
141
,
1726
(
2017
).
28.
A.
Jerusalem
,
Z.
Al-Rekabi
,
H.
Chen
,
A.
Ercole
,
M.
Malboubi
,
M.
Tamayo-Elizalde
,
L.
Verhagen
, and
S.
Contera
,
Acta Biomater.
97
,
116
(
2019
).
29.
J.
Weickenmeier
,
C.
Butler
,
P.
Young
,
A.
Goriely
, and
E.
Kuhl
,
Comput. Methods Appl. Mech. Eng.
314
,
180
(
2017
).
30.
Y.-C.
Lu
,
N. P.
Daphalapurkar
,
A.
Knutsen
,
J.
Glaister
,
D.
Pham
,
J.
Butman
,
J. L.
Prince
,
P.
Bayly
, and
K.
Ramesh
,
Ann. Biomed. Eng.
47
,
1923
(
2019
).
31.
S.
Ganpule
,
N. P.
Daphalapurkar
,
K. T.
Ramesh
,
A. K.
Knutsen
,
D. L.
Pham
,
P. V.
Bayly
, and
J. L.
Prince
,
J. Neurotrauma
34
,
2154
(
2017
).
32.
R. T.
Miller
,
S. S.
Margulies
,
M.
Leoni
,
M.
Nonaka
,
X.
Chen
,
D. H.
Smith
, and
D. F.
Meaney
, in
SAE Transactions
(
1998
), p.
2798
.
33.
T. E.
Sayed
,
A.
Mota
,
F.
Fraternali
, and
M.
Ortiz
,
J. Biomech.
41
,
1458
(
2008
).
34.
T. E.
Sayed
,
A.
Mota
,
F.
Fraternali
, and
M.
Ortiz
,
Comput. Methods Appl. Mech. Eng.
197
,
4692
(
2008
).
35.
L. A.
Mihai
,
L.
Chin
,
P. A.
Janmey
, and
A.
Goriely
,
J. R. Soc. Interface
12
,
20150486
(
2015
).
36.
S.
Budday
,
T. C.
Ovaert
,
G. A.
Holzapfel
,
P.
Steinmann
, and
E.
Kuhl
,
Arch. Comput. Methods Eng.
(published online
2019
).
37.
S.
Budday
,
G.
Sommer
,
C.
Birkl
,
C.
Langkammer
,
J.
Haybaeck
,
J.
Kohnert
,
M.
Bauer
,
F.
Paulsen
,
P.
Stein- mann
,
E.
Kuhl
 et al.,
Acta Biomater.
48
,
319
(
2017
).
38.
S.
Budday
,
G.
Sommer
,
G.
Holzapfel
,
P.
Steinmann
, and
E.
Kuhl
,
J. Mech. Behav. Biomed. Mater.
74
,
463
(
2017
).
39.
S.
Chatelin
,
A.
Constantinesco
, and
R.
Willinger
,
Biorheology
47
,
255
(
2010
).
40.
A. P.
Sarvazyan
,
O. V.
Rudenko
,
S. D.
Swanson
,
J. B.
Fowlkes
, and
S. Y.
Emelianov
,
Ultrasound Med. Biol.
24
,
1419
(
1998
).
41.
E. H.
Clayton
,
G. M.
Genin
, and
P. V.
Bayly
,
J. R. Soc. Interface
9
,
2899
(
2012
).
42.
J.
Achenbach
,
Wave Propagation Elastic Solids
(
Elsevier
,
2012
), Vol.
16
.
43.
K.
Nightingale
,
S.
McAleavey
, and
G.
Trahey
,
Ultra-sound Med. Biol.
29
,
1715
(
2003
).
44.
J.
Ophir
,
I.
Cespedes
,
H.
Ponnekanti
,
Y.
Yazdi
, and
X.
Li
,
Ultrasonic Imaging
13
,
111
(
1991
).
45.
J.
Bercoff
,
M.
Tanter
, and
M.
Fink
,
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
51
,
396
(
2004
).
46.
A.
Warner
,
J.
Tate
,
B.
Burton
, and
C. R.
Johnson
, “
A high-resolution head and brain computer model for forward and inverse EEG simulation
,” bioRxiv, 552190 (
2019
).
47.
H.
Mao
,
L.
Zhang
,
B.
Jiang
,
V. V.
Genthikatti
,
X.
Jin
,
F.
Zhu
,
R.
Makwana
,
A.
Gill
,
G.
Jandir
,
A.
Singh
 et al.,
J. Biomech. Eng.
135
,
111002
(
2013
).
48.
J. D.
Stitzel
,
S. M.
Duma
,
J. M.
Cormier
, and
I. P.
Herring
, “
A nonlinear finite element model of the eye with experimental validation for the prediction of globe rupture
,” Technical Report (The Stapp Association,
2002
).
49.
A. S.
Wineman
and
K. R.
Rajagopal
,
Mechanical Response of Polymers: An Introduction
(
Cambridge University Press
,
2000
).
50.
J.
Newman
,
C.
Barr
,
M. C.
Beusenberg
,
E.
Fournier
,
N.
Shewchenko
,
E.
Welbourne
, and
C.
Withnall
, in
Proceedings of the International Research Council on the Biomechanics of Injury Conference
(
International Research Council on Biomechanics of Injury
,
2000
), Vol.
28
.
51.
L.
Zhang
,
K. H.
Yang
, and
A. I.
King
,
J. Biomech. Eng.
126
,
226
(
2004
).
52.
C.
Deck
and
R.
Willinger
,
Int. J. Crashworthiness
13
,
667
(
2008
).
53.
R. M.
Wright
and
K.
Ramesh
,
Biomech. Model. Mechanobiol.
11
,
245
(
2012
).
54.
T.
Deffieux
,
Y.
Younan
,
N.
Wattiez
,
M.
Tanter
,
P.
Pouget
, and
J. F.
Aubry
,
Curr. Biol.
23
(
23
),
2430
2433
(
2013
).
55.
J.
Kubanek
,
J.
Brown
,
P.
Ye
,
K. B.
Pauly
,
T.
Moore
, and
W.
Newsome
,
Sci. Adv.
6
(
21
),
eaaz4193
(
2020
).
56.
S.
Sharabi
,
D.
Daniels
,
D.
Last
,
D.
Guez
,
Z.
Zivli
,
D.
Castel
,
Y.
Levy
,
A.
Volovick
,
J.
Grinfeld
,
I.
Rachmilevich
, and
T.
Amar
,
Brain Stimul.
12
,
1
8
(
2019
).
57.
M.
Mohammadjavadi
,
P. P.
Ye
,
A.
Xia
,
J.
Brown
,
G.
Popelka
, and
K. B.
Pauly
,
Brain Stimul.
12
(
4
),
901
910
(
2019
).
58.
G.
Von Békésy
and
E. G.
Wever
,
Experiments in Hearing
(
McGraw-Hill
,
New York
,
1960
).
59.
P. M.
Morse
and
K. U.
Ingard
,
Theoretical Acoustic
(
Princeton University Press
,
1986
).

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