The Cramér-Rao Lower Bounds (CRLB) are derived for the displacement and strain estimation in directions orthogonal to the ultrasonic beam axis, using a previously-described recorrelation method of axial, lateral and elevational motion estimation. We also compare it to the lateral tracking method that involves the sole use of the axial signal in the transverse direction. Our theoretical results, verified with simulations and phantom experiments, show that elastography is capable of measuring axial and transverse strain at up to 10% axially applied compression. Finally, we predict the performance of the estimation of the Poisson's ratio using decoupled axial and lateral estimates that result from the recorrelation method.
OphirJ.CéspedesI.PonnekantiH.YazdiY.LiX., Elastography: a quantitative method for imaging the elasticity of biological tissues, Ultrasonic Imaging13, 111–134 (1991).
2.
KallelF.VargheseT.OphirJ.BilgenM.The nonstationary strain filter in elastography, Part II: Lateral and elevational decorrelation, Ultrasound Med. Biol.23, 1357–1369 (1997).
3.
KonofagouE.E.OphirJ., A new elastographic method for estimation and imaging of lateral strains, corrected axial strains and poison's ratios in tissues, Ultrasound Med. Biol.24, 1183–1199 (1998).
4.
VargheseT.OphirJ.CéspedesE. I., Noise reduction in elastography using temporal stretching with multicompression averaging, Ultrasound Med. Biol.22, 1042–1053 (1996).
5.
KonofagouE.E., Estimation and imaging of 3D motion and Poisson's ratio in elastography, Ph.D. dissertation (University of Houston, 1999).
6.
CéspedesI.OphirJ., Reduction of image noise in elastography, Ultrasonic Imaging15, 89–102 (1993).
7.
SarvazyanA.P., Low frequency acoustic properties of biological tissues, Mech. Polymers4, 691–695 (1975).
8.
SkovorodaAREmelianovSYLubinskiAMSarvazyanA.P.O'DonnellM., Theoretical analysis and verification of ultrasound displacement and strain imaging. IEEE Trans. Ultras., Ferroel. Freq. Control41, 302–313 (1994).
9.
SumiC.SuzukiA.NakayamaK., Estimation of shear modulus distribution in soft tissue from strain distribution, IEEE Trans. Biomed. Eng.42, 193–212 (1995).
10.
KallelF.BertrandM.OphirJ., Advances in tissue elasticity reconstruction using linear perturbation method, in Acoustical Imaging, pp. 267–277, JonesJ.P., ed. (Plenum Press, New York, 1996).
11.
MridhaM.ÖdmanS.Noninvasive method for assessment of subcutaneous edema, Med. Biol. Eng. Comp.24, 393–398 (1986).
12.
FungY.C., Connecting incremental shear modulus and Poisson's ratio of lung tissue with morphology and rheology of microstructure, Biorheology26, 279–289 (1989).
13.
JurvelinJ.S.BuschmannM.D.HunzikerE.B., Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage, J. Biomech.30, 235–241 (1997).
WalkerW.F.TraheyG.E.A Fundamental Limit on the performance of correlation-based phase correction and flow correction and flow estimation techniques, IEEE Trans. Ultrason. Ferroel. Freq. Cont.41, 644–654 (1994).
16.
WagnerR.F.SmithS.W.SandrikJ.M.LopezH., Statistics of speckle in ultrasound B-Scans. IEEE Trans. Sonics Ultras.30, 156–163 (1983).
17.
BonnefousO., Measurement of the complete (3D) velocity vector of blood flows, in Proc. IEEE Ultrason. Symp., pp. 795–799 (1988).
18.
VargheseT.OphirJ.A theoretical framework for performance characterization of elastography: the Strain Filter, IEEE Trans. Ultrason. Ferroel. Freq. Cont.44, 164–172, (1997).
ZagarB.G.FornarisR.J.FerraraK.W., Ultrasonic mapping of the microvasculature, signal alignment, Ultras. Med Biol., 809–824 (1998).
21.
BendatJ.S.PiersolA.G., Random Data, Analysis and Measurement Procedures, (John Wiley & Sons, New York, 2nd edition, 1986).
22.
JensenJ.A.Estimation of Blood Velocities Using Ultrasound (Cambridge University Press, Cambridge, U.K., 1996).
23.
MallartR.FinkM., The Van Cittert-Zernike theorem in pulse echo measurements, J. Acous. Soc. Amer.90, 2718–2727 (1991).
24.
NgG.C.WorrellS.S.FreiburgerP.D.TraheyG.E., A comparative evaluation of several algorithms for phase aberration correction, IEEE Trans. Ultras., Ferroel. Freq. Control41, 631–643 (1994).
25.
CéspedesI.InsanaM.OphirJ.Theoretical bounds on strain estimation in elastography, IEEE Trans Ultras., Ferroel. Freq. Control42, 969–972 (1995).
26.
BilgenM.InsanaM.F.Error analysis in acoustic elastography, II. Strain estimation and SNR analysis, J. Acoust. Soc. Am.101, 1147–1154 (1997).
27.
KonofagouE.E.OphirJ.KallelF.VargheseT., Elastographic dynamic range expansion using variable applied strains, Ultrasonic Imaging19, 145–166 (1997).
PapoulisA., Probability, Random Variables and Stochastic Processes (McGraw Hill, New York, 1st edition, 1965).
30.
WeinsteinE.WeissA., Fundamental limitations in passive time delay estimation — Part I, Narrow-band systems, IEEE Trans. Acoust, Speech, Sig. Proc.31, 472–485 (1983).
31.
CarterG.C., Coherence and time delay estimation, IEEE Proc.75, 236–255 (1987).
32.
WalkerW.F.TraheyG.E., A fundamental limit on delay estimation using partially correlated speckle signals, IEEE Trans. Ultras. Ferroel. Freq. Cont.42, 301–308 (1995).
33.
BilgenM.InsanaM.F., Deformation models and correlation analysis in elastography, J. Acoust. Soc. Am.99, 3212–3224 (1996).
