Theoretical Analysis of Shear Wave Interference Patterns by Means of Dynamic Acoustic Radiation Forces

Authors

  • K Hoyt

DOI:

https://doi.org/10.1260/1750-9548.5.1.9

Abstract

Acoustic radiation forces associated with high intensity focused ultrasound stimulate shear wave propagation allowing shear wave speed and shear viscosity estimation of tissue structures. As wave speeds are meters per second, real time displacement tracking over an extend field-of-view using ultrasound is problematic due to very high frame rate requirements. However, two spatially separated dynamic external sources can stimulate shear wave motion leading to shear wave interference patterns. Advantages are shear waves can be imaged at lower frame rates and local interference pattern spatial properties reflect tissue's viscoelastic properties. Here a theoretical analysis of shear wave interference patterns by means of dynamic acoustic radiation forces is detailed. Using a viscoelastic Green's function analysis, tissue motion due to a pair of focused ultrasound beams and associated radiation forces are presented. Overall, this paper theoretically demonstrates shear wave interference patterns can be stimulated using dynamic acoustic radiation forces and tracked using conventional ultrasound imaging.

References

Sarvazyan, A.P., Rudenko, O.V., Swanson, S.D., Fowlkes, J.B. and Emelianov, S.Y., Shear wave elasticity imaging: A new ultrasonic technology of medical diagnostics, Ultrasound in Medicine and Biology, 1998, 24, 1419-1435. https://doi.org/10.1016/s0301-5629(98)00110-0

Krouskop, T.A., Wheeler, T.M., Kallel, F., Garra, B.S. and Hall, T., Elastic moduli of breast and prostate tissues under compression, Ultrasonic Imaging, 1998, 20 260-274. https://doi.org/10.1177/016173469802000403

Sandrin, L., Fourquet, B., Hasquenoph, J.M., Yon, S., Fournier, C., Mal, F., Christidis, C., Ziol, M., Poulet, B., Kazemi, F., Beaugrand, M. and Palau, R., Transient elastography: A new noninvasive method for assessment of hepatic fibrosis, Ultrasound in Medicine and Biology, 2003, 29 1705-1713. https://doi.org/10.1016/j.ultrasmedbio.2003.07.001

Phipps, S., Yang, T.H.J., Habib, F.K., Reuben, R.L., McNeill, S.A., Measurement of tissue mechanical characteristics to distinguish between benign and malignant prostatic disease, Journal of Urology, 2005, 66, 447-450. https://doi.org/10.1016/j.urology.2005.03.017

Zhang, M., Nigwekar, P., Castaneda, B., Hoyt, K., Sant'Agnese, A., Joseph, J.V., Messing, E.M., Rubens, D.J. and Parker, K.J., Quantitative characterization of viscoelastic properties of human prostate correlated with histology, Ultrasound in Medicine and Biology, 2007, 34, 1033-1042. https://doi.org/10.1016/j.ultrasmedbio.2007.11.024

DeLoach, S.S. and Townsend, R.R., Vascular stiffness: Its measurement and significance for epidemiologic and outcome studies, Clinical Journal of the American Society of Nephrology, 2008, 3, 184-192. https://doi.org/10.2215/cjn.03340807

Hoyt, K., Castaneda, B., Zhang, M., Nigwekar, P., di Sant' Agnese, P.A., Joseph, J.A., Strang, J., Rubens, D.J. and Parker, K.J., Tissue elasticity properties as biomarkers for prostate cancer, Cancer Biomarkers, 2008, 4, 213-225. https://doi.org/10.3233/cbm-2008-44-505

Hagan, J.J., and Samani, A., Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples, Physics in Medicine and Biology, 2009, 54, 2557-2569. https://doi.org/10.1088/0031-9155/54/8/020

Gao, L., Parker, K.J., Lerner, R.M. and Levinson, S.F., Imaging of the elastic properties of tissue: A review, Ultrasound in Medicine and Biology, 1996, 22, 959-977. https://doi.org/10.1016/s0301-5629(96)00120-2

Ophir, J., Alam, S.K., Garra, B., Kallel, F., Konofagou, E., Krouskop, T. and Varghese, T. Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues, Proceedings of the Institution of Mechanical Engineers, 1999, 213, 203-233. https://doi.org/10.1243/0954411991534933

Greenleaf, J.F., Fatemi, M. and Insana, M., Selected methods for imaging elastic properties of biological tissues, Annual Review of Biomedical Engineering, 2003, 5, 57-78. https://doi.org/10.1146/annurev.bioeng.5.040202.121623

Walker, W.F., Fernandez, F.J. and Negron, L.A., A method of imaging viscoelastic parameters with acoustic radiation force, Physics in Medicine and Biology, 2000, 45, 1437-1447. https://doi.org/10.1088/0031-9155/45/6/303

Catheline, S., Gennisson, J.L., Delon, G., Fink, M., Sinkus, R., Abouelkaram, S. and Culioli, J., Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: An inverse problem approach, Journal of the Acoustical Society of America, 116, 3734-3741. https://doi.org/10.1121/1.1815075

Chen, S., Fatemi, M. and Greenleaf, J.F., Quantifying elasticity and viscosity from measurement of shear wave speed dispersion, Journal of the Acoustical Society of America, 2004, 115, 2781-2785. https://doi.org/10.1121/1.1739480

McLaughlin, J. and Renzi, D., Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts, Inverse Problems, 2006, 22, 681-706. https://doi.org/10.1088/0266-5611/22/2/018

Palmeri, M.L., Wang, M.H., Dahl, J.J., Frinkley, K.D. and Nightingale, K.R., Quantifying hepatic shear modulus in vivo using acoustic radiation force, Ultrasound in Medicine and Biology, 2008, 34, 546-558. https://doi.org/10.1016/j.ultrasmedbio.2007.10.009

Wu, Z., Taylor, L.S., Rubens, D.J. and Parker, K.J., Sonoelastographic imaging of interference patterns for estimation of the shear velocity of homogeneous biomaterials, Physics in Medicine and Biology, 2004, 49, 911-922. https://doi.org/10.1088/0031-9155/49/6/003

Wu, Z., Hoyt, K., Rubens, D.J., and Parker, K.J., Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials, Journal of the Acoustical Society of America, 2006, 120, 535-545. https://doi.org/10.1121/1.2203594

McLaughlin, J., Renzi, D., Parker, K. and Wu, Z., Shear wave speed recovery using moving interference patterns obtained in sonoelastography experiments, Journal of the Acoustical Society of America, 2007, 121 2438-2446. https://doi.org/10.1121/1.2534717

Hoyt, K., Parker, K.J. and Rubens, D.J., Real-time shear velocity imaging using sonoelastographic techniques, Ultrasound in Medicine and Biology, 2007, 33, 1086-1097. https://doi.org/10.1016/j.ultrasmedbio.2007.01.009

Hoyt, K., Castaneda, B. and Parker, K.J., Two-dimensional sonoelastographic shear velocity imaging, Ultrasound in Medicine and Biology, 2008, 34, 276-288. https://doi.org/10.1016/j.ultrasmedbio.2007.07.011

Torr, G.R., The acoustic radiation force, American Journal of Physics, 1984, 52, 402-408.

Nightingale, K.R., Palmeri, M.L., Nightingale, R.W. and Trahey, G.E., On the feasibility of remote palpation using acoustic radiation force, Journal of the Acoustical Society of America, 2001, 110, 625-634. https://doi.org/10.1121/1.1378344

Landau, L.D. and Lifshitz, E.M., Theory of elasticity, Elsevier Butterworth-Heinemann, New York, 1986.

Oestreicher, H.L., Field and impedance of an oscillating sphere in a viscoelastic medium with an application to biophysics, Journal of the Acoustical Society of America, 1951, 23, 707-714. https://doi.org/10.1121/1.1906828

Bercoff, J., Tanter, M. and Fink, M., Supersonic shear imaging: A new technique for soft tissue elasticity mapping, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 2004, 51, 396-409. https://doi.org/10.1109/tuffc.2004.1295425

Bercoff, J., Tanter, M., Muller, M. and Fink, M., The role of viscosity in the impulse diffraction field of elastic waves induced by the acoustic radiation force, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 2004, 51, 1523-1536. https://doi.org/10.1109/tuffc.2004.1367494

Sandrin, L., Cassereau, D. and Fink, M., The role of the coupling term in transient elastography, Journal of the Acoustical Society of America, 2004, 115, 73-83. https://doi.org/10.1121/1.1635412

Hoyt, K., Kneezel, T., Castaneda, B. and Parker, K.J., Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticity, Physics in Medicine and Biology, 2008, 53 4063-4080. https://doi.org/10.1088/0031-9155/53/15/004

Jensen, J.A. and Svendsen, N.B., Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 1992, 39, 262-267. https://doi.org/10.1109/58.139123

Palmeri, M.L., Sharma, A.C., Bouchard, R.R., Nightingale, R.W. and Nightingale, K.R., A finite-element method model of soft tissue response to impulsive acoustic radiation force, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 2005, 52, 1699-1712. https://doi.org/10.1109/tuffc.2005.1561624

Céspedes, E.I., Huang, Y., Ophir, J. and Spratt, S., Methods for the estimation of subsample time-delays of digitized echo signals, Ultrasonic Imaging, 1995, 17, 142-171. https://doi.org/10.1177/016173469501700204

Huang, S.R., Lerner, R.M., and Parker, K.J., On estimating the amplitude of harmonic vibration from the Doppler spectrum of reflected signals, Journal of the Acoustical Society of America, 1990, 88, 2702-2712. https://doi.org/10.1121/1.399673

Yamakoshi, Y., Sato, J., and Sato, T., Ultrasonic imaging of internal vibration of soft tissue under forced vibration, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 1990, 37, 45-53. https://doi.org/10.1109/58.46969

Dahl, J.J., Gianmarco, F.P., Palmeri, M.L., Agrawal, V., Nightingale, K.R. and Trahey, G.E., A parallel tracking method for acoustic radiation force impulse imaging, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 2007, 54, 301-312. https://doi.org/10.1109/tuffc.2007.244

Palmeri, M.L. and Nightingale, K.R., On the thermal effects associated with radiation force imaging of soft tissue, IEEE Transactions on. Ultrasonics, Ferroelectrics and Frequency Control, 2004, 51, 551-565. https://doi.org/10.1109/tuffc.2004.1320828

Published

2011-03-31

How to Cite

Hoyt, K. (2011). Theoretical Analysis of Shear Wave Interference Patterns by Means of Dynamic Acoustic Radiation Forces. The International Journal of Multiphysics, 5(1), 9-24. https://doi.org/10.1260/1750-9548.5.1.9

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Articles