Recent studies have shown that high intensity focused ultrasound (HIFU) accelerates thrombolysis for ischemic stroke. Although the mechanisms are not fully understood, cavitation is thought to play an important role. The goal of this paper is to investigate the potential for cavitation to cause mechanical damage to a blood clot. The amount of damage to the fiber network caused by a single bubble expansion and collapse is estimated by two independent approaches: One based on the stretch of individual fibers and the other based on the energy available to break individual fibers. The two methods yield consistent results. The energy method is extended to the more important scenario of a bubble outside a blood clot that collapses asymmetrically creating an impinging jet. This leads to significantly more damage compared to a bubble embedded within the clot structure. Finally, as an example of how one can apply the theory, a simulation of the propagation of HIFU waves through model calvaria of varying density is explored. The maximum amount of energy available to cause damage to a blood clot increases as the density of the calvaria decreases.

1.
V. L.
Roger
,
A. S.
Go
,
D. M.
Lloyd-Jones
,
R. J.
Adams
,
J. D.
Berry
,
T. M.
Brown
,
M. R.
Carnethon
,
S.
Dai
,
G.
de Simone
,
E. S.
Ford
,
C. S.
Fox
,
H. J.
Fullerton
,
C.
Gillespie
,
K. J.
Greenlund
,
S. M.
Hailpern
,
J. A.
Heit
,
P. M.
Ho
,
V. J.
Howard
,
B. M.
Kissela
,
S. J.
Kittner
,
D. T.
Lackland
,
J. H.
Lichtman
,
L. D.
Lisabeth
,
D. M.
Makuc
,
G. M.
Marcus
,
A.
Marelli
,
D. B.
Matchar
,
M. M.
McDermott
,
J. B.
Meigs
,
C. S.
Moy
,
D.
Mozaffarian
,
M. E.
Mussolino
,
G.
Nichol
,
N. P.
Paynter
,
W. D.
Rosamond
,
P. D.
Sorlie
,
R. S.
Stafford
,
T. N.
Turan
,
M. B.
Turner
,
N. D.
Wong
, and
J.
Wylie-Rosett
, “
Heart disease and stroke statistics—2011 update: A report from the American Heart Association
,”
Circulation
123
(
4
),
e18
209
(
2011
).
2.
A.
Barreto
, “
Intravenous thrombolytics for ischemic stroke
,”
Neurotherapeutics
8
,
388
399
(
2011
).
3.
G. J.
del Zoppo
,
J. L.
Saver
,
E. C.
Jauch
, and
H. P.
Adams
, “
Expansion of the time window for treatment of acute ischemic stroke with intravenous tissue plasminogen activator
,”
Stroke
40
(
8
),
2945
2948
(
2009
).
4.
I. L.
Katzan
,
M. D.
Hammer
,
E. D.
Hixson
,
A. J.
Furlan
,
A.
Abou-Chebl
, and
D. M.
Nadzam
, “
Utilization of intravenous tissue plasminogen activator for acute ischemic stroke
,”
Arch. Neurol.
61
(
3
),
346
350
(
2004
).
5.
D.
Kleindorfer
,
B.
Kissela
,
A.
Schneider
,
D.
Woo
,
J.
Khoury
,
R.
Miller
,
K.
Alwell
,
J.
Gebel
,
J.
Szaflarski
,
A.
Pancioli
,
E.
Jauch
,
C.
Moomaw
,
R.
Shukla
, and
J. P.
Broderick
, “
Eligibility for recombinant tissue plasminogen activator in acute ischemic stroke
,”
Stroke
35
(
2
),
e27
29
(
2004
).
6.
A.
Blinc
,
C. W.
Francis
,
J. L.
Trudnowski
, and
E. L.
Carstensen
, “
Characterization of ultrasound-potentiated fibrinolysis in vitro
,”
Blood
81
(
10
),
2636
2643
(
1993
).
7.
C. W.
Francis
,
P. T.
Onundarson
,
E. L.
Carstensen
,
A.
Blinc
,
R. S.
Meltzer
,
K.
Schwarz
, and
V. J.
Marder
, “
Enhancement of fibrinolysis in vitro by ultrasound
,”
J. Clin. Invest.
90
(
5
),
2063
2068
(
1992
).
8.
V.
Frenkel
,
J.
Oberoi
,
M. J.
Stone
,
M.
Park
,
C.
Deng
,
B. J.
Wood
,
Z.
Neeman
,
M.
Horne
, and
K. C.
Li
, “
Pulsed high-intensity focused ultrasound enhances thrombolysis in an in vitro model
,”
Radiology
239
(
1
),
86
93
(
2006
).
9.
C. K.
Holland
,
S. S.
Vaidya
,
S.
Datta
,
C. C.
Coussios
, and
G. J.
Shaw
, “
Ultrasound-enhanced tissue plasminogen activator thrombolysis in an in vitro porcine clot model
,”
Thromb. Res.
121
(
5
),
663
673
(
2008
).
10.
C. G.
Lauer
,
R.
Burge
,
D. B.
Tang
,
B. G.
Bass
,
E. R.
Gomez
, and
B. M.
Alving
, “
Effect of ultrasound on tissue-type plasminogen activator-induced thrombolysis
,”
Circulation
86
(
4
),
1257
1264
(
1992
).
11.
U.
Rosenschein
,
V.
Furman
,
E.
Kerner
,
I.
Fabian
,
J.
Bernheim
, and
Y.
Eshel
, “
Ultrasound imaging guided noninvasive ultrasound thrombolysis: Preclinical results
,”
Circulation
102
(
2
),
238
245
(
2000
).
12.
S.
Westermark
,
H.
Wiksell
,
H.
Elmqvist
,
K.
Hultenby
, and
H.
Berglund
, “
Effect of externally applied focused acoustic energy on clot disruption in vitro
,”
Clin. Sci.
97
(
1
),
67
71
(
1999
).
13.
A. V.
Alexandrov
,
A. M.
Demchuk
,
W. S.
Burgin
,
D. J.
Robinson
, and
J. C.
Grotta
, “
Ultrasound-enhanced thrombolysis for acute ischemic stroke: Phase I. Findings of the clotbust trial
,”
J. Neuroimag.
14
(
2
),
113
117
(
2004
).
14.
A. V.
Alexandrov
,
C. A.
Molina
,
J. C.
Grotta
,
Z.
Garami
,
S. R.
Ford
,
J.
Alvarez-Sabin
,
J.
Montaner
,
M.
Saqqur
,
A. M.
Demchuk
,
L. A.
Moy
,
M. D.
Hill
, and
A. W.
Wojner
, “
Ultrasound-enhanced systemic thrombolysis for acute ischemic stroke
,”
New Eng. J. Med.
351
(
21
),
2170
2178
(
2004
).
15.
J.
Eggers
,
B.
Koch
,
K.
Meyer
,
I.
Konig
, and
G.
Seidel
, “
Effect of ultrasound on thrombolysis of middle cerebral artery occlusion
,”
Ann. Neurol.
53
(
6
),
797
800
(
2003
).
16.
J.
Eggers
,
G.
Seidel
,
B.
Koch
, and
I. R.
Knig
, “
Sonothrombolysis in acute ischemic stroke for patients ineligible for rt-pa
,”
Neurology
64
(
6
),
1052
1054
(
2005
).
17.
A.
Kashyap
,
A.
Blinc
,
V. J.
Marder
,
D. P.
Penney
, and
C. W.
Francis
, “
Acceleration of fibrinolysis by ultrasound in a rabbit ear model of small vessel injury
,”
Thromb. Res.
76
(
5
),
475
485
(
1994
).
18.
R.
Kornowski
,
R. S.
Meltzer
,
A.
Chernine
,
Z.
Vered
, and
A.
Battler
, “
Does external ultrasound accelerate thrombolysis? Results from a rabbit model
,”
Circulation
89
(
1
),
339
344
(
1994
).
19.
M. J.
Stone
,
V.
Frenkel
,
S.
Dromi
,
P.
Thomas
,
R. P.
Lewis
,
K. C.
Li
,
M.
Horne
, and
B. J.
Wood
, “
Pulsed-high intensity focused ultrasound enhanced tpa mediated thrombolysis in a novel in vivo clot model, a pilot study
,”
Thromb. Res.
121
(
2
),
193
202
(
2007
).
20.
V. N.
Suchkova
,
R. B.
Baggs
, and
C. W.
Francis
, “
Effect of 40-kHz ultrasound on acute thrombotic ischemia in a rabbit femoral artery thrombosis model: Enhancement of thrombolysis and improvement in capillary muscle perfusion
,”
Circulation
101
(
19
),
2296
2301
(
2000
).
21.
T.
Hoelscher
,
D.
Fisher
,
R.
Raman
,
K.
Ernstrom
,
E.
Zadicario
,
W. G.
Bradley
, and
A.
Voie
, “
Noninvasive transcranial clot lysis using high intensity focused ultrasound
,”
J. Neurol. Neurophysiol.
S1
,
1
6
(
2011
).
22.
F.
Xie
,
J. M.
Tsutsui
,
J.
Lof
,
E. C.
Unger
,
J.
Johanning
,
W. C.
Culp
,
T.
Matsunaga
, and
T. R.
Porter
, “
Effectiveness of lipid microbubbles and ultrasound in declotting thrombosis
,”
Ultrasound Med. Biol.
31
(
7
),
979
985
(
2005
).
23.
E. C.
Everbach
and
C. W.
Francis
, “
Cavitational mechanisms in ultrasound-accelerated thrombolysis at 1 MHz
,”
Ultrasound Med. Biol.
26
(
7
),
1153
1160
(
2000
).
24.
S.
Datta
,
C. C.
Coussios
,
L. E.
McAdory
,
J.
Tan
,
T.
Porter
,
G.
De Courten-Myers
, and
C. K.
Holland
. “
Correlation of cavitation with ultrasound enhancement of thrombolysis
,”
Ultrasound Med. Biol.
32
(
8
),
1257
1267
(
2006
).
25.
A. F.
Prokop
,
A.
Soltani
, and
R. A.
Roy
, “
Cavitational mechanisms in ultrasound-accelerated fibrinolysis
,”
Ultrasound Med. Biol.
33
(
6
),
924
933
(
2007
).
26.
J. W.
Weisel
, “
The mechanical properties of fibrin for basic scientists and clinicians
,”
Biophys. Chem.
112
(
2-3
),
267
276
(
2004
).
27.
J. P.
Collet
,
H.
Shuman
,
R. E.
Ledger
,
S.
Lee
, and
J. W.
Weisel
, “
The elasticity of an individual fibrin fiber in a clot
,”
Proc. Natl. Acad. Sci. U.S.A.
102
(
26
),
9133
9137
(
2005
).
28.
E. A.
Ryan
,
L. F.
Mockros
,
J. W.
Weisel
, and
L.
Lorand
, “
Structural origins of fibrin clot rheology
,”
Biophys. J.
77
(
5
),
2813
2826
(
1999
).
29.
C. R.
Carlisle
,
C.
Coulais
,
M.
Namboothiry
,
D. L.
Carroll
,
R. R.
Hantgan
, and
M.
Guthold
, “
The mechanical properties of individual, electrospun fibrinogen fibers
,”
Biomaterials
30
(
6
),
1205
1213
(
2009
).
30.
C. R.
Carlisle
,
E. A.
Sparks
,
C.
Der Loughian
, and
M.
Guthold
, “
Strength and failure of fibrin fiber branchpoints
,”
J. Thrombo. Haemost.
8
(
5
),
1135
1138
(
2010
).
31.
W.
Liu
,
C. R.
Carlisle
,
E. A.
Sparks
, and
M.
Guthold
, “
The mechanical properties of single fibrin fibers
,”
J. Thromb. Haemost.
8
(
5
),
1030
1036
(
2010
).
32.
W.
Liu
,
L. M.
Jawerth
,
E. A.
Sparks
,
M. R.
Falvo
,
R. R.
Hantgan
,
R.
Superfine
,
S. T.
Lord
, and
M.
Guthold
, “
Fibrin fibers have extraordinary extensibility and elasticity
,”
Science
313
(
5787
),
634
(
2006
).
33.
W. W.
Roberts
,
O.
Kramer
,
R. W.
Rosser
,
F. H.
Nestler
, and
J. D.
Ferry
, “
Rheology of fibrin clots. I. Dynamic viscoelastic properties and fluid permeation
,”
Biophys. Chem.
1
(
3
),
152
160
(
1974
).
34.
C.
Gerth
,
W. W.
Roberts
, and
J. D.
Ferry
, “
Rheology of fibrin clots. II: Linear viscoelastic behavior in shear creep
,”
Biophys. Chem.
2
(
3
),
208
217
(
1974
).
35.
C. C.
Huang
,
C. C.
Shih
,
T. Y.
Liu
, and
P. Y.
Lee
, “
Assessing the viscoelastic properties of thrombus using a solid-sphere-based instantaneous force approach
,”
Ultrasound Med. Biol.
37
(
10
),
1722
1733
(
2011
).
36.
F. G.
Mitri
and
Z. E.
Fellah
, “
Instantaneous axial force of a high-order bessel vortex beam of acoustic waves incident upon a rigid movable sphere
,”
Ultrasonics
51
(
6
),
719
724
(
2011
).
37.
P
Riha
,
X.
Wang
,
R.
Liao
, and
J. F.
Stoltz
, “
Elasticity and fracture strain of whole blood clots
,”
Clin. Hemorheol. Microcirc.
21
(
1
),
45
49
(
1999
).
38.
X.
Yang
and
C. C.
Church
, “
A model for the dynamics of gas bubbles in soft tissue
,”
J. Acoust. Soc. Am.
118
(
6
),
3595
3606
(
2005
).
39.
J. B.
Keller
and
M.
Miksis
, “
Bubble oscillations of large amplitude
,”
J. Acoust. Soc. Am.
68
(
2
),
628
633
(
1980
).
40.
K. C.
Gersh
,
K. E.
Edmondson
, and
J. W.
Weisel
, “
Flow rate and fibrin fiber alignment
,”
J. Thromb. Haemost.
8
(
12
),
2826
2828
(
2010
).
41.
A. E.
Brown
,
R. I.
Litvinov
,
D. E.
Discher
,
P. K.
Purohit
, and
J. W.
Weisel
, “
Multiscale mechanics of fibrin polymer: Gel stretching with protein unfolding and loss of water
,”
Science
325
(
5941
),
741
744
(
2009
).
42.
A. J.
Szeri
and
L. G.
Leal
, “
A new computational method for the solution of flow problems of microstructured fluids. Part 1. Theory
,”
J. Fluid Mech.
242
,
549
576
(
1992
).
43.
R. B.
Bird
,
R. C.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymeric Liquids. Fluid Dynamics
, 2nd ed. (
Wiley and Sons
,
New York
,
1987
), Vol.
1
, pp.
1
624
.
44.
M. L.
Calvisi
,
J. I.
Iloreta
, and
A. J.
Szeri
, “
Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies non-spherical cavitation collapse
,”
J. Fluid Mech.
616
,
63
97
(
2008
).
45.
A.
Pearson
,
J. R.
Blake
, and
S. R.
Otto
, “
Jets in bubbles
,”
J. Eng. Math.
48
,
391
412
(
2004
), doi 10.1023/B:engi. 0000018172.53498.a2.
46.
J. I.
Iloreta
,
Y.
Zhou
,
G. N.
Sankin
,
P.
Zhong
, and
A. J.
Szeri
, “
Assessment of shock wave lithotripters via cavitation potential
,”
Phys. Fluids
19
(
8
),
086103
(
2007
).
47.
M. L.
Calvisi
,
O.
Lindau
,
J. R.
Blake
, and
A. J.
Szeri
, “
Shape stability and violent collapse of microbubbles in acoustic traveling waves
,”
Phys. Fluids
19
(
4
),
047101
(
2007
).
48.
K.
Okita
,
S.
Takagi
,
K.
Ono
, and
Y.
Matsumoto
, “
Development of high intensity focused ultrasound simulator for large–scale computing
,”
Int. J. Numer. Methods Fluids
65
(
1-3
),
43
66
(
2011
).
49.
E.
Hairer
,
C.
Lubich
, and
G.
Wanner
,
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
(
Springer Series in Computational Mathematics. Springer
,
Berlin
,
2006
), pp.
1
644
.
50.
F. J.
Fry
and
J. E.
Barger
, “
Acoustical properties of the human skull
,”
J. Acoust. Soc. Am.
63
(
5
),
1576
1590
(
1978
).
51.
B.
Martin
and
J. H.
McElhaney
, “
The acoustic properties of human skull bone
,”
J. Biomed. Mater. Res.
5
(
4
),
325
333
(
1971
).
52.
T. G.
Leighton
,
The Acoustic Bubble
(
Academic
,
London
,
1997
), pp.
1
613
.
53.
W.
Lauterborn
and
E.
Cramer
, “
Subharmonic route to chaos observed in acoustics
,”
Phys. Rev. Lett.
47
,
1445
1448
(
1981
).
54.
H. L.
Weiss
, “
Mechanical damage from cavitation in high intensity focused ultrasound accelerated thrombolysis
,” Ph.D. thesis,
University of California
, Berkeley,
2012
.
You do not currently have access to this content.