A shaped-based ultrasound tomography method is proposed to reconstruct ellipsoidal objects using a linearized scattering model. The method is motivated by the desire to detect the presence of lesions created by high intensity focused ultrasound (HIFU) in applications of cancer therapy. The computational size and limited view nature of the relevant three-dimensional inverse problem renders impractical the use of traditional pixel-based reconstruction methods. However, by employing a shape-based parametrization it is only necessary to estimate a small number of unknowns describing the geometry of the lesion, in this paper assumed to be ellipsoidal. The details of the shape-based nonlinear inversion method are provided. Results obtained from a commercial ultrasound scanner and a tissue phantom containing a HIFU-like lesion demonstrate the feasibility of the approach where a 20mm×5mm×6mm ellipsoidal inclusion was detected with an accuracy of around 5%.

1.
L.
Poissonnier
,
A.
Gelet
,
J.
Chapelon
,
R.
Bouvier
,
O.
Rouviere
,
C.
Pangaud
,
D.
Lyonnet
, and
J.
Dubernard
, “
Results of transrectal focused ultrasound for the treatment of localized prostate cancer (120 patients with PSA <or+10ngml)
,”
Prog. Urol.
13
,
60
72
(
2003
).
2.
T. A.
Gardner
,
M. O.
Koch
,
A.
Shalhav
,
R.
Bihrle
,
R. S.
Foster
,
C.
Steidle
,
I.
Grunberger
,
A. S. M.
Resnick
,
J.
Cochran
,
V.
Rao
, and
N. T.
Sanghvi
, “
Minimally invasive treatment of benign prostatic hyperplasia with high intensity focused ultrasound using the SonablateTM system: An updated report of phase III clinical studies conducted in the USA
,”
Proc. SPIE
4609
,
107
114
(
2002
).
3.
N. T.
Sanghvi
,
J.
Syrus
,
R. S.
Foster
,
R.
Bihrle
,
R.
Casey
, and
T.
Uchida
, “
Noninvasive surgery of prostate tissue by high intensity focused ultrasound: An updated report
,”
Proc. SPIE
3907
,
194
200
(
2000
).
4.
S.
Madersbacher
,
C.
Kratzik
, and
M.
Marberger
, “
Prostatic tissue ablation by transrectal high intensity focused ultrasound: Histological impact and clinical application
,”
Ultrason. Sonochem.
4
,
175
179
(
1997
).
5.
K.
Nakamura
,
S.
Baba
,
S.
Saito
,
M.
Tachibana
, and
M.
Murai
, “
High-intensity focused ultrasound energy for benign prostatic hyperplasia: Clinical response at 6 months to treatment using sonablate 200
,”
J. Endourol
11
,
197
201
(
1997
).
6.
E. D.
Mulligan
,
T. H.
Lynch
,
D.
Mulvin
,
D.
Greene
,
J. M.
Smith
, and
J. M.
Fitzpatrick
, “
High-intensity focused ultrasound in the treatment of benign prostatic hyperplasia
,”
Br. J. Urol.
79
,
177
180
(
1997
).
7.
C.
Chaussy
,
S.
Thuroff
,
F.
Lacoste
, and
A.
Gelet
, “
HIFU and prostate cancer: The European experience
,” in
Proceedings of the Second International Symposium on Therapeutic Ultrasound
, July 29–Aug. 1; Seattle, WA (
2002
).
8.
J.
Kennedy
,
G. T.
Haar
, and
D.
Cranstron
, “
High intensity focused ultrasound: Surgery of the future?
,”
Br. J. Radiol.
76
,
590
599
(
2003
).
9.
F.
Wu
,
W.
Chen
,
J.
Bai
,
Z.
Zou
,
Z.
Wang
,
H.
Zhu
, and
Z.
Wang
, “
Pathological changes in human malignant carcinoma treated with high-intensity focused ultrasound
,”
Ultrasound Med. Biol.
27
,
1099
1106
(
2001
).
10.
F.
Wu
,
Z.
Wang
,
W.
Chen
,
W.
Wang
,
Y.
Gui
,
M.
Zhang
,
G.
Zheng
,
Y.
Zhou
,
G.
Xu
,
M.
Li
,
C.
Zhang
,
H.
Ye
, and
R.
Feng
, “
Extracorporeal high intensity focused ultrasound ablation in the treatment of 1038 patients with solid carcinomas in China: An overview
,”
Ultrason. Sonochem.
11
,
149
154
(
2004
).
11.
G. T.
Clement
, “
Perspectives in clinical uses of high-intensity focused ultrasound
,”
Ultrasonics
42
,
1087
1093
(
2004
).
12.
Z.
Wang
,
J.
Bai
,
F.
Li
,
Y.
Du
,
S.
Wen
,
K.
Hu
,
G.
Xu
,
P.
Ma
,
N.
Yin
,
W.
Chen
,
F.
Wu
, and
R.
Feng
, “
Study of a ‘biological focal region’ of high-intensity focused ultrasound
,”
Ultrasound Med. Biol.
29
,
749
754
(
2003
).
13.
G.
ter Haar
,
D.
Sinnett
, and
I.
Rivens
, “
High intensity focused ultrasound—A surgical technique for the treatment of discrete liver tumors
,”
Phys. Med. Biol.
34
,
1743
1750
(
1989
).
14.
H.
Cline
,
K.
Hynynen
,
C.
Hardy
,
R.
Watkins
,
F.
Schenck
, and
F.
Jolesz
, “
MR temperature mapping of focused ultrasound surgery
,”
Magn. Reson. Med.
31
,
628
636
(
1994
).
15.
N.
McDannold
,
L.
King
,
F.
Jolesz
, and
K.
Hynynen
, “
Usefulness of MR imaging-derived thermometry and dosimetry in determining the threshold for tissue damage induced by thermal surgery in rabbits
,”
Radiology
216
,
517
523
(
2000
).
16.
K.
Hynynen
,
O.
Pomeroy
,
D.
Smith
,
P.
Huber
,
N.
McDannold
,
J.
Kettenbach
,
J.
Baum
,
S.
Singer
, and
F.
Jolesz
, “
MR imaging-guided focused ultrasound surgery of fibroadenomas in the breast: A feasibility study
,”
Radiology
219
,
176
185
(
2001
).
17.
J. C.
Bamber
and
C. R.
Hill
, “
Ultrasonic attenuation and propagation speed in mammalian tissues as a function of temperature
,”
Ultrasound Med. Biol.
5
,
149
157
(
1979
).
18.
N. L.
Bush
,
I.
Rivens
,
G. R.
ter Haar
, and
J. C.
Bamber
, “
Acoustic properties of lesions generated with an ultrasound therapy system
,”
Ultrasound Med. Biol.
19
,
789
801
(
1993
).
19.
C. A.
Damianou
,
N. T.
Sanghvi
,
F. J.
Fry
, and
R.
Maass-Moreno
, “
Dependence of ultrasonic attenuation and absorption in dog soft tissues on temperature and thermal dose
,”
J. Acoust. Soc. Am.
102
,
628
634
(
1997
).
20.
S. H.
Bloch
,
M. R.
Bailey
,
L.
Crum
,
P.
Kaczkowski
,
G.
Keilman
, and
P.
Mourad
, “
Measurements of sound speed in excised tissue over temperature expected under high-intensity focused ultrasound conditions
,”
J. Acoust. Soc. Am.
,
103
(5), pp.
2868
(
1998
).
21.
A. E.
Worthington
and
M. D.
Sherar
, “
Changes in ultrasound properties of porcine kidney tissue during heating
,”
Ultrasound Med. Biol.
27
,
673
682
(
2001
).
22.
U.
Techavipoo
,
T.
Varghese
,
Q.
Chen
,
T. A.
Stiles
,
J. A.
Zagzebski
, and
G. R.
Frank
, “
Temperature dependence of ultrasonic propagation speed and attenuation in excised canine liver tissue measured using transmitted and reflected pulses
,”
J. Acoust. Soc. Am.
116
,
2859
2865
(
2004
).
23.
P. D.
Tyréus
and
C.
Diederich
, “
Two-dimensional acoustic attenuation mapping of high-temperature interstitial ultrasound lesions
,”
Phys. Med. Biol.
49
,
533
546
(
2004
).
24.
C.
Simon
,
P.
VanBaren
, and
E. S.
Ebbini
, “
Two-dimensional temperature estimation using diagnostic ultrasound
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
45
,
1088
1099
(
1998
).
25.
M.
Pernot
,
M.
Tanter
,
J.
Bercoff
,
K.
Waters
, and
M.
Fink
, “
Temperature estimation using ultrasonic spatial compound imaging
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
51
,
606
615
(
2004
).
26.
L. A. S.
Baker
and
J. C.
Bamber
, “
Effect of dynamic receive focusing on reflex transmission imaging (RTI)
,”
Proc.-IEEE Ultrason. Symp.
2
,
1581
1584
(
2002
)
27.
A.
Anand
and
P. J.
Kaczkowski
, “
Monitoring formation of high intensity focused ultrasound (HIFU) induced lesions using backscattered ultrasound
,”
ARLO
5
,
88
94
(
2004
).
28.
H.
Zhong
,
M.
Xi Wan
,
Y.-F.
Jiang
, and
S.
Pin Wang
, “
Monitoring imaging of lesions induced by high intensity focused ultrasound based on differential ultrasonic attenuation and integrated backscatter estimation
,”
Ultrasound Med. Biol.
33
,
82
94
(
2007
).
29.
N.
Duric
,
P.
Littrup
,
A.
Babkin
,
D.
Chambers
,
S.
Azevedo
,
A.
Kalinin
,
R.
Pevzner
,
M.
Tokarev
,
E.
Holsapple
,
O.
Rama
, and
R.
Duncan
, “
Development of ultrasound tomography for breast imaging: Technical assessment
,”
Med. Phys.
32
,
1375
1386
(
2005
).
30.
R. G.
Pratt
,
L.
Huang
,
N.
Duric
, and
P.
Littrup
, “
Sound-speed and attenuation imaging of breast tissue using waveform tomography of transmission ultrasound data
,”
Proc. SPIE
6510
,
65104S
(
2007
).
31.
K. W. A.
van Dongen
and
W. M. D.
Wright
, “
A full vectorial contrast source inversion scheme for three-dimensional acoustic imaging of both compressibility and density profiles
,”
J. Acoust. Soc. Am.
121
,
1538
1549
(
2007
).
32.
G.
Dassios
, “
The inverse scattering problem for the soft ellipsoid
,”
J. Math. Phys.
28
,
2858
2862
(
1987
).
33.
R. J.
Lucas
, “
An inverse problem in low-frequency scattering by a rigid ellipsoid
,”
J. Acoust. Soc. Am.
95
,
2330
2333
(
1994
).
34.
R. J.
Lucas
, “
The inverse problem for scattering by an ellipsoidal boss
,”
J. Acoust. Soc. Am.
97
,
2645
2650
(
1995
).
35.
G.
Dassios
and
R. J.
Lucas
, “
An inverse problem in low-frequency scattering by an ellipsoidally embossed surface
,”
Wave Motion
20
,
33
39
(
1994
).
36.
T. S.
Angell
and
R. E.
Kleinman
, “
Polarizability tensors in low-frequency inverse scattering
,”
Radio Sci.
22
,
1120
1126
(
1987
).
37.
M. E.
Kilmer
,
E. L.
Miller
,
A.
Barbaro
, and
D.
Boas
, “
Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography
,”
Appl. Opt.
42
,
3129
3144
(
2003
).
38.
M.
Kilmer
,
E. L.
Miller
,
A.
Barbaro
, and
D. A.
Boas
, “
3d shape-based imaging for diffuse optical tomography
,”
Appl. Opt.
42
,
3129
3144
(
2003
).
39.
P. M.
Morse
and
K. U.
Ingard
,
Theoretical Acoustics
(
Princeton University Press
, Princeton, NJ,
1986
).
40.
B. U.
Karbeyaz
,
E. L.
Miller
,
R. O.
Cleveland
, and
R. A.
Roy
, “
Adaptive linearized modeling and inversion for 3d tissue characterization
,”
J. Acoust. Soc. Am.
114
,
2379
2380
(
2003
).
41.
B. U.
Karbeyaz
, “
Modeling and shape based inversion for frequency domain ultrasonic monitoring of cancer treatment
,” Ph.D. thesis,
Northeastern University
, Boston, MA,
2005
.
42.
J. A.
Jensen
, “
A model for the propagation and scattering of ultrasound in tissue
,”
J. Acoust. Soc. Am.
89
,
182
190
(
1991
).
43.
M.
Arditi
,
F.
Foster
, and
J.
Hunt
, “
Transient fields of concave annular arrays
,”
Ultrason. Imaging
3
,
37
61
(
1981
).
44.
E.
Madsen
,
M.
Insana
, and
J. A.
Zagzebski
, “
Method of data reduction for accurate determination of acoustic backscatter coefficients
,”
J. Acoust. Soc. Am.
76
,
913
923
(
1984
).
45.
T. L.
Szabo
,
B. U.
Karbeyaz
,
R. O.
Cleveland
, and
E. L.
Miller
, “
Determining the pulse-echo electromechanical characteristic of a transducer using flat plates and point targets
,”
J. Acoust. Soc. Am.
116
,
90
96
(
2004
).
46.
S. J.
Osher
and
R. P.
Fedkiw
,
Level Set Methods and Dynamic Implicit Surfaces
(
Springer
, New York,
2002
).
47.
G.
Ter Haar
, “
Acoustic surgery
,”
Phys. Today
54
,
29
34
(
2001
).
48.
W. F.
,
W.-Z.
Chen
,
J.
Bai
,
J.-Z.
Zou
,
Z.-L.
Wang
,
H.
Zhu
, and
Z.-B.
Wang
, “
Pathological changes in human malignant carcinoma treated with high-intensity focused ultrasound
,”
Ultrasound Med. Biol.
27
,
1099
1106
(
2001
).
49.
P. E.
Gill
,
W.
Murray
, and
M. H.
Wright
,
Practical optimization
(
Academic
, New York,
1981
).
50.
C.
Lafon
,
P. J.
Kaczkowski
,
S.
Vaezy
,
M.
Noble
, and
O. A.
Sapozhnikov
, “
Development and characterization of an innovative synthetic tissue-mimicking material for high intensity focused ultrasound (HIFU) exposures
,”
Proc.-IEEE Ultrason. Symp.
2
,
1295
1298
(
2001
).
51.
B. U.
Karbeyaz
,
E. L.
Miller
, and
R. O.
Cleveland
, “
Semi-analytical computation of the acoustic field of a segment of a cylindrically concave transducer in lossless and attenuating media
,”
J. Acoust. Soc. Am.
121
,
1226
1237
(
2007
).
52.
J.
Stalnaker
and
E.
Miller
, “
Particle swarm optimization as an inversion tool for a nonlinear uxo model
,” IEEE International Geoscience and Remote Sensing Symposium, IGARSS
23-28 July 2007
,
432
435
.
53.
B.
Durning
,
R. O.
Cleveland
, and
E. L.
Miller
, “
Parametric study of a shape based inversion for detecting high-intensity focused ultrasound lesions
,”
J. Acoust. Soc. Am.
121
,
3082
(
2007
).
54.
G.
Boverman
and
E. L.
Miller
, “
Estimation-theoretic algorithms and bounds for three-dimensional polar shape-based imaging in diffuse optical tomography
,”
Proceedings of the 2006 IEEE International Symposium on Biomedical Imaging: From Nano to Macro
, Arlington, VA, April 6–9,
1132
1135
(
2006
).
55.
G.
Boverman
,
Q.
Fang
,
E.
Miller
,
D. H.
Brooks
,
R. H.
Moore
,
D. B.
Kopans
, and
D. A.
Boas
, “
Estimation and statistical bounds for three-dimensional polar shapes in diffuse optical tomography
,” IEEE Trans. Med. Imaging (in press).
56.
A.
Zacharopoulos
,
S.
Arridge
,
O.
Dorn
,
V.
Kolehmainen
, and
J.
Sikora
, “
3d shape reconstruction in optical tomography using spherical harmonics and bem
,”
J. Electromagn. Waves Appl.
20
,
1827
1836
(
2006
).
57.
O.
Dorn
,
E.
Miller
, and
C.
Rappaport
, “
A shape reconstruction method for electromagnetic tomography using adjoint elds and level sets
,”
Inverse Probl.
16
,
1119
1156
(
2000
).
58.
M. K.
Ben Hadj Miled
, and
E. L.
Miller
, “
A projection-based level-set approach to enhance conductivity anomaly reconstruction in electrical resistance tomography
,”
Inverse Probl.
23
,
2375
2400
(
2007
).
59.
M.
Soleimani
,
O.
Dorn
, and
W. R. B.
Lionheart
, “
A narrow-band level set method applied to eit in brain for cryosurgery monitoring
,”
IEEE Trans. Biomed. Eng.
53
,
2257
2264
(
2006
).
60.
M.
Soleimani
,
W. R. B.
Lionheart
, and
O.
Dorn
, “
Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data
,”
Inverse Probl.
14
,
193
210
(
2006
).
61.
O.
Dorn
and
D.
Lesselier
, “
Level set methods for inverse scattering
,”
Inverse Probl.
22
,
R67
R131
(
2006
).
62.
D.-L.
Liu
and
R. C.
Waag
, “
Correction of ultrasonic wavefront distortion using back-propagation and a reference waveform method for time-shift compensation
,”
J. Acoust. Soc. Am.
96
,
649
660
(
1994
).
63.
S.-E.
Masoy
,
T.
Varslot
, and
B.
Angelsen
, “
Iteration of transmit-beam aberration correction in medical ultrasound imaging
,”
J. Acoust. Soc. Am.
117
,
450
461
(
2005
).
64.
N. M.
Ivancevich
,
J. J.
Dahl
,
G. E.
Trahey
, and
S. W.
Smith
, “
Phase-aberration correction with a 3-d ultrasound scanner: Feasibility study
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
53
,
1432
1439
(
2006
).
65.
Y.
Fei
and
A. J.
Devaney
, “
Inverse scattering for real-valued scattering potentials
,”
Inverse Probl.
21
,
L7
L12
(
2005
).
66.
M. L.
Dennison
and
A. J.
Devaney
, “
Inverse scattering in inhomogeneous background media: II. Multi-frequency case and svd formulation
,”
Inverse Probl.
20
,
1307
1324
(
2004
).
67.
A. J.
Devaney
and
M.
Dennison
, “
Inverse scattering in inhomogeneous background media
,”
Inverse Probl.
19
,
855
870
(
2003
).
68.
G.
Boverman
,
E. L.
Miller
,
A.
Li
,
Q.
Zhang
,
T.
Chaves
,
D. H.
Brooks
, and
D. A.
Boas
, “
Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information
,”
Phys. Med. Biol.
50
,
3941
3956
(
2005
).
You do not currently have access to this content.