Oscillating microbubbles within microvessels could induce stresses that lead to bioeffects or vascular damage. Previous work has attributed vascular damage to the vessel expansion or bubble jet. However, ultra-high speed images of recent studies suggest that it could happen due to the vascular invagination. Numerical simulations of confined bubbles could provide insight into understanding the mechanism behind bubble–vessel interactions. In this study, a finite element model of a coupled bubble/fluid/vessel system was developed and validated with experimental data. Also, for a more realistic study viscoelastic properties of microvessels were assessed and incorporated into this comprehensive numerical model. The wall shear stress (WSS) and circumferential stress (CS), metrics of vascular damage, were calculated from these simulations. Resultant amplitudes of oscillation were within 15% of those measured in experiments (four cases). Among the experimental cases, it was numerically found that maximum WSS values were between 1.1–18.3 kPa during bubble expansion and 1.5–74 kPa during bubble collapse. CS was between 0.43–2.2 MPa during expansion and 0.44–6 MPa while invaginated. This finding confirmed that vascular damage could occur during vascular invaginations. Predicted thresholds in which these stresses are higher during vessel invagination were calculated from simulations.

1.
D. L.
Miller
,
A. R.
Williams
,
J. E.
Morris
, and
W. B.
Chrisler
, “
Sonoporation of erythrocytes by lithotripter shockwaves in vitro
,”
Ultrasonics
36
,
947
952
(
1998
).
2.
K.
Hynynen
,
N.
McDannold
,
N.
Vykhodtseva
, and
F.
Jolesz
, “
Noninvasive MR imaging-guided focal opening of the blood-brain barrier in rabbits
,”
Radiology
220
,
640
646
(
2001
).
3.
E. C.
Unger
,
T. O.
Matsunaga
,
T.
McCreery
,
P.
Schumann
,
R.
Sweitzer
, and
R.
Quigley
, “
Therapeutic applications of microbubbles
,”
Eur. J. Radiol.
42
,
160
168
(
2002
).
4.
D. M.
Skyba
,
R. J.
Price
,
A. Z.
Linka
,
T. C.
Skalak
, and
S.
Kaul
, “
Direct in vivo visualization of intravascular destruction of microbubbles by ultrasound and its local effects on tissue
,”
Circulation
98
,
290
293
(
1998
).
5.
D. L.
Miller
and
J.
Quddus
, “
Diagnostic ultrasound activation of contrast agent gas bodies induces capillary rupture in mice
,”
Proc. Natl. Acad. Sci. U.S.A.
18
,
10179
10184
(
2000
).
6.
D. L.
Miller
and
R. A.
Gies
, “
Gas-body-based contrast agent enhances vascular bioeffects of 1.09 MHz ultrasound on mouse intestine
,”
Ultrasound Med. Biol.
24
,
1201
1208
(
1998
).
7.
S.
Bao
,
B. D.
Thrall
,
R. A.
Gies
, and
D. L.
Miller
, “
In vivo transfection of melanoma cells by lithotripter shock waves
,”
Cancer Res.
58
,
219
221
(
1998
).
8.
K.
Kooiman
,
M.
Harteveld
,
N.
de Jong
, and
A.
van Wamel
, “
Transiently increased endothelial layer permeability by ultrasound-activated microbubbles
,”
Proc.-IEEE Ultrason. Symp.
2006
,
529
531
(
2006
).
9.
J. H.
Hwang
,
A. A.
Brayman
,
M. A.
Reidy
,
T. J.
Matula
,
M. B.
Kimmey
, and
L. A.
Crum
, “
Vascular effects induced by combined 1-MHz ultrasound and microbubble contrast agent treatments in vivo
,”
Ultrasound Med. Biol.
31
,
553
564
(
2005
).
10.
C. F.
Caskey
,
S. M.
Stieger
,
S.
Qin
,
P. A.
Dayton
, and
K. W.
Ferrara
, “
Direct observations of ultrasound microbubble contrast agent interaction with the microvessel wall
,”
J. Acoust. Soc. Am.
122
,
1191
1200
(
2007
).
11.
P.
Zhong
,
Y.
Zhou
, and
S.
Zhu
, “
Dynamics of bubble oscillation in constrained media and mechanisms of vessel rupture in SWL
,”
Ultrasound Med. Biol.
27
,
119
134
(
2001
).
12.
S.
Qin
and
K. W.
Ferrara
, “
Acoustic response of compliable microvessels containing ultrasound contrast agents
,”
Phys. Med. Biol.
51
,
5065
5088
(
2006
).
13.
H.
Chen
,
A. A.
Brayman
,
M. R.
Bailey
, and
T. J.
Matula
, “
Direct observation of microbubble interactions with ex vivo microvessels
,”
J. Acoust. Soc. Am.
125
,
2680
(
2009
).
14.
H.
Chen
,
A. A.
Brayman
, and
T. J.
Matula
, “
Microbubble dynamics in microvessels: Observations of microvessel dilation, invagination and rupture
,”
Proc.-IEEE Ultrason. Symp.
2008
,
1163
1166
(
2008
).
15.
E.
VanBavel
, “
Effects of shear stress on endothelial cells: Possible relevance for ultrasound applications
,”
Prog. Biophys. Mol. Biol.
93
,
374
383
(
2007
).
16.
J.
Song
,
J. C.
Chappell
,
M.
Qi
,
E. J.
VanGieson
,
S.
Kaul
, and
R. J.
Price
, “
Influence of injection site, microvascular pressure and ultrasound variables on microbubble-mediated delivery of microspheres to muscle
,”
J. Am. Coll. Cardiol.
39
,
726
731
(
2002
).
17.
K.
Hynynen
,
N.
McDannold
,
H.
Martin
,
F. A.
Jolesz
, and
N.
Vykhodtseva
, “
The threshold for brain damage in rabbits induced by bursts of ultrasound in the presence of an ultrasound contrast agent (Optison®)
,”
Ultrasound Med. Biol.
29
,
473
481
(
2003
).
18.
S. M.
Stieger
,
C. F.
Caskey
,
R. H.
Adamson
,
S.
Qin
,
F. E.
Curry
,
E. R.
Wisner
, and
K. W.
Ferrara
, “
Enhancement of vascular permeability with low frequency contrast-enhanced ultrasound in the chorioallantoic membrane model
,”
Radiology
243
,
112
121
(
2007
).
19.
H. N.
Ogũz
and
A.
Prosperetti
, “
The natural frequency of oscillation of gas bubbles in tubes
,”
J. Acoust. Soc. Am.
103
,
3301
3308
(
1998
).
20.
H.
Miao
,
S. M.
Gracewski
, and
D.
Dalecki
, “
Ultrasonic excitation of a bubble inside a deformable tube: Implications for ultrasonically induced hemorrhage
,”
J. Acoust. Soc. Am.
124
,
2374
2384
(
2008
).
21.
S.
Qin
and
K. W.
Ferrara
, “
The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels
,”
Ultrasound Med. Biol.
33
,
1140
1148
(
2007
).
22.
H.
Chen
,
A. A.
Brayman
,
M. R.
Bailey
, and
T. J.
Matula
, “
Blood vessel rupture by cavitation
,”
Urol. Res.
38
,
321
326
(
2010
).
23.
Y. C.
Fung
, “
Structure and stress-strain relationship of soft tissues
,”
Am. Zool.
24
,
13
22
(
1984
).
24.
G. T.
Swayne
,
L. H.
Smaje
, and
D. H.
Bergel
, “
Distensibility of single capillaries and venules in the rat and frog mesentery
,”
Int. J. Microcirc.: Clin. Exp.
8
,
25
42
(
1989
).
25.
R.
Skalak
,
N.
Ozkaya
, and
T. C.
Skalak
, “
Biofluid mechanics
,”
Annu. Rev. Fluid Mech.
21
,
167
204
(
1989
).
26.
H.
Chen
,
W.
Kreider
,
A. A.
Brayman
,
M. R.
Bailey
, and
T. J.
Matula
, “
Blood vessel deformations on microsecond time scales by ultrasonic cavitation
,”
Phys. Rev. Lett.
106
,
034301
(
2011
), supplementary material.
27.
H.
Chen
,
A. A.
Brayman
, and
T. J.
Matula
, “
Characteristic microvessel relaxation timescales associated with ultrasound-activated microbubbles
,”
Appl. Phys. Lett.
101
,
163704
(
2012
).
28.
Y. C.
Fung
,
Biomechanics: Mechanical Properties of Living Tissues
(
Springer
,
New York
,
1993
), Chap. 2, pp.
23
65
.
29.
L. H.
Smaje
,
P. A.
Fraser
, and
G.
Clough
, “
The distensibility of single capillaries and venules in the cat mesentery
,”
Microvasc. Res.
20
,
358
370
(
1980
).
30.
S.
Girnyk
,
A.
Barannik
,
E.
Barannik
,
V.
Tovstiak
,
A.
Marusenko
, and
V.
Volokhov
, “
The estimation of elasticity and viscosity of soft tissues in vitro using the data of remote acoustic palpation
,”
Ultrasound Med. Biol.
32
,
211
219
(
2006
).
31.
F. A.
Duck
,
Physical Properties of Tissue: A Comprehensive Reference Book
(
Academic
,
London
,
1990
), pp.
1
336
.
32.
S.
van der Meer
,
B.
Dollet
,
M. M.
Voormolen
,
C. T.
Chin
,
A.
Bouakaz
,
N.
de Jong
,
M.
Versluis
, and
D.
Lohse
, “
Microbubble spectroscopy of ultrasound contrast agents
,”
J. Acoust. Soc. Am.
121
,
648
656
(
2007
).
33.
N.
de Jong
,
R.
Cornet
, and
C. T.
Lancée
, “
Higher harmonics of vibrating gas filled microspheres. Part one: Simulations
,”
Ultrasonics
32
,
447
453
(
1994
).
34.
M. A.
Walkley
,
P. H.
Gaskell
,
P. K.
Jimack
,
M. A.
Kelmanson
, and
J. L.
Summers
, “
Finite element simulation of three-dimensional free-surface flow problems
,”
J. Sci. Comput.
24
,
147
162
(
2005
).
35.
P.
Marmottant
,
S.
van der Meer
,
E.
Emmer
,
M.
Versluis
,
N.
de Jong
,
S.
Hilgenfeldt
, and
D.
Lohse
, “
A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture
,”
J. Acoust. Soc. Am.
118
,
3499
3505
(
2005
).
36.
J.
Tu
,
J. E.
Swalwell
,
D.
Giraud
,
W.
Cui
,
W.
Chen
, and
T. J.
Matula
, “
Microbubble sizing and shell characterization using flow cytometry
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control.
58
,
955
963
(
2011
).
37.
H. G.
Flynn
, “
Cavitation dynamics. I. A mathematical formulation
,”
J. Acoust. Soc. Am.
57
,
1379
1396
(
1975
).
38.
A. K.
Srivastava
and
P. C.
Gope
,
Strength of Materials
(
Prentice-Hall of India Private Limited
,
New Delhi
,
2007
), pp.
127
148
.
39.
S.
Qin
,
D. E.
Kruse
, and
K. W.
Ferrara
, “
Transmitted ultrasound pressure variation in micro blood vessel phantoms
,”
Ultrasound Med. Biol.
34
,
1014
1020
(
2008
).
40.
N.
Hosseinkhah
and
K.
Hynynen
, “
A three-dimensional model of an ultrasound contrast agent gas bubble and its mechanical effects on microvessels
,”
Phys. Med. Biol.
57
,
785
808
(
2012
).
41.
H.
Yamada
and
F. G.
Evans
,
Strength of Biological Materials
(
Williams and Wilkins
,
Baltimore, MD
,
1970
), pp.
1
297
.
42.
A. J.
Rowe
,
H. M.
Finlay
, and
P. B.
Canham
, “
Collagen biomechanics in cerebral arteries and bifurcations assessed by polarizing microscopy
,”
J. Vasc. Res.
40
,
406
415
(
2003
).
43.
P. B.
Snowhill
and
F. H.
Silver
, “
A mechanical model of porcine vascular tissues: Part II. Stress–strain and mechanical properties of juvenile porcine blood vessels
,”
Cardiovasc. Eng.
5
,
157
169
(
2005
).
44.
J. A.
Rooney
, “
Hemolysis near an ultrasonically pulsating gas bubble
,”
Science
169
,
869
871
(
1970
).
45.
H.
Chen
,
A. A.
Brayman
,
A. P.
Evan
, and
T. J.
Matula
, “
Preliminary observations on the spatial correlation between short-burst microbubble oscillations and vascular bioeffects
,”
Ultrasound Med. Biol.
38
,
2151
2162
(
2012
).
You do not currently have access to this content.