Quantitative elastography techniques have recently been developed to estimate the shear modulus μ of soft tissues in vivo. In the case of isotropic and quasi-incompressible media, the Young’s modulus E is close to 3μ, which is not true in transverse anisotropic tissues such as muscles. In this letter, the transverse isotropic model established for hexagonal crystals is revisited in the case of soft solids. Relationships between elastic constants and Young’s moduli are derived and validated on experimental data found in the literature. It is shown that and that E// cannot only be determined from the measurements of μ// and μ⊥
REFERENCES
1.
S. F.
Levinson
, “Ultrasound propagation in anisotropic soft tissues: The application of linear elastic theory
,” J. Biomech.
20
(3
), 251
–260
(1987
).2.
B. K.
Hoffmeister
, S. M.
Handley
, S. A.
Wickline
, and J. G.
Miller
, “Ultrasonic determination of the anisotropy of Young’s modulus of fixed tendon and fixed myocardium
,” J. Acoust. Soc. Am.
100
(6
), 3933
–3940
(1996
).3.
P. L.
Kuo
, P. C.
Li
, and M. L.
Li
, “Elastic properties of tendon measured by two different approaches
,” Ultrasound Med. Biol.
27
(9
), 1275
–1284
(2001
).4.
H. S.
Yoon
and J. L.
Katz
, “Ultrasonic wave propagation in human cortical bone. I. Theoretical considerations for hexagonal symmetry
,” J. Biomech.
9
, 407
–412
(1976
).5.
D.
Royer
and E.
Dieulesaint
, Elastic Waves in Solids. I. Free and Guided Propagation
(Springer
, Berlin
, 1999
), Chap. 4.6.
L.
Sandrin
, M.
Tanter
, J. L.
Gennisson
, S.
Catheline
, and M.
Fink
, “Shear elasticity probe for soft tissue with 1D transient elastography
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
49
(4
), 436
–446
(2002
).7.
J. L.
Gennisson
, S.
Catheline
, S.
Chaffaï
, and M.
Fink
, “Transient elastography in anisotropic medium: Application to the measurement of slow and fast shear waves velocities in muscles
,” J. Acoust. Soc. Am.
114
(1
), 536
–541
(2003
).8.
J.
Bercoff
, M.
Tanter
, and M.
Fink
, “Supersonic shear imaging: A new technique for soft tissues elasticity mapping
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
51
(4
), 396
–409
(2004
).9.
J. L.
Gennisson
, T.
Deffieux
, E.
Macé
, G.
Montaldo
, M.
Fink
, and M.
Tanter
, “Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by Supersonic Shear Imaging
,” Ultrasound Med. Biol.
36
(5
), 789
–801
(2010
).10.
A.
Ballato
, “Poisson’s ratio of auxetic and other technological materials
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
57
(1
), 7
–15
(2010
).11.
S.
Levinson
, S.
Catheline
, and M.
Fink
, “Anisotropy elasticity and viscosity deduced from supersonic shear imaging in muscle
,” in International Society of Biomechanics, XXth Congress, 29th Annual Meeting of the American Society of Biomechanics
, Cleveland, OH
(2005
), p. 101
.© 2011 Acoustical Society of America.
2011
Acoustical Society of America
You do not currently have access to this content.