Evaluation of the adjoint equation based algorithm for elasticity imaging.

Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient-based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.

[1]  Paul E. Barbone,et al.  Elastic modulus imaging: On the uniqueness and nonuniqueness of the elastography inverse problem in , 2004 .

[2]  Assad A. Oberai,et al.  INVERSE PROBLEMS PII: S0266-5611(03)54272-1 Solution of inverse problems in elasticity imaging using the adjoint method , 2003 .

[3]  J. Bamber,et al.  Quantitative elasticity imaging: what can and cannot be inferred from strain images. , 2002, Physics in medicine and biology.

[4]  J M Rubin,et al.  Triplex ultrasound: elasticity imaging to age deep venous thrombosis. , 2002, Ultrasound in medicine & biology.

[5]  Y. Y. Belov,et al.  Inverse Problems for Partial Differential Equations , 2002 .

[6]  Paul M. Meaney,et al.  Progress in Freehand Elastography of the Breast , 2002 .

[7]  K D Paulsen,et al.  Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion. , 2001, Medical physics.

[8]  N Bom,et al.  Characterization of plaque components with intravascular ultrasound elastography in human femoral and coronary arteries in vitro. , 2000, Circulation.

[9]  D B Plewes,et al.  Two-dimensional MR elastography with linear inversion reconstruction: methodology and noise analysis. , 2000, Physics in medicine and biology.

[10]  M. Doyley,et al.  Evaluation of an iterative reconstruction method for quantitative elastography. , 2000, Physics in medicine and biology.

[11]  J. Bishop,et al.  Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography. , 2000, Physics in medicine and biology.

[12]  P. Serruys,et al.  Characterization of plaque components and vulnerability with intravascular ultrasound elastography. , 2000, Physics in medicine and biology.

[13]  A F van der Steen,et al.  Intraluminal ultrasonic palpation: assessment of local and cross-sectional tissue stiffness. , 2000, Ultrasound in medicine & biology.

[14]  K D Paulsen,et al.  An overlapping subzone technique for MR‐based elastic property reconstruction , 1999, Magnetic resonance in medicine.

[15]  T. Krouskop,et al.  Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues , 1999, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[16]  R. Howe,et al.  Breast Tissue Stiffness in Compression is Correlated to Histological Diagnosis , 1999 .

[17]  C. D. de Korte,et al.  Influence of catheter position on estimated strain in intravascular elastography , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[18]  A F van der Steen,et al.  Intravascular ultrasound elastography. , 2008, Ultraschall in der Medizin.

[19]  S Y Emelianov,et al.  Elasticity reconstructive imaging by means of stimulated echo MRI , 1998, Magnetic resonance in medicine.

[20]  C. D. de Korte,et al.  Intravascular ultrasound elastography in human arteries: initial experience in vitro. , 1998, Ultrasound in medicine & biology.

[21]  T. Hall,et al.  2-D companding for noise reduction in strain imaging , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[22]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[23]  V. Isakov.  Appendix -- Function Spaces , 2017 .

[24]  F. Foster,et al.  Ultrasonic Measurement of Differential Displacement and Strain in a Vascular Model , 1997, Ultrasonic imaging.

[25]  B. Garra,et al.  Elastography of breast lesions: initial clinical results. , 1997, Radiology.

[26]  C T Lancée,et al.  Intravascular elasticity imaging using ultrasound: feasibility studies in phantoms. , 1997, Ultrasound in medicine & biology.

[27]  Faouzi Kallel,et al.  Tissue elasticity reconstruction using linear perturbation method , 1996, IEEE Trans. Medical Imaging.

[28]  A.R. Skovoroda,et al.  Tissue elasticity reconstruction based on ultrasonic displacement and strain images , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[29]  C. Sumi,et al.  Estimation of shear modulus distribution in soft tissue from strain distribution , 1995, IEEE Transactions on Biomedical Engineering.

[30]  K. R. Raghavan,et al.  Forward and inverse problems in elasticity imaging of soft tissues , 1994 .

[31]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[32]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[33]  G. Golub.  Matrix computations , 1983 .

[34]  Philip E. Gill,et al.  Practical optimization , 1981 .