Scattering of ultrasound by biological tissues (continuous-inhomogeneous media) is discussed. An analytical expression for the attenuation due to scattering (αTSC) and backscatter coefficients (σT) of tissues are obtained. The results explain the variation of (αTSC) and σT with frequency for a number of tissues. The study also provides two statistical parameters, velocity fluctuation coefficient and correlation length, in terms of which the scattering of tissues can be defined quantitatively.
ChiversR. C., The scattering of ultrasound by human tissues—some theoretical models, Ultrasound Med. Biol.3, 1–13 (1977).
2.
AksS. Φ.VezzettiD. J., Ultrasonic scattering theory I: scattering by single objects, Ultrasonic Imaging2, 85–101 (1980); VezzettiD. J.AksS. Φ, Ultrasonic scattering theory II: scattering from composites, Ultrasonic Imaging2, 195–212 (1980).
3.
ReidJ. M., The Scattering of Ultrasound by Tissues, in Ultrasonic Tissue Characterization, LinzerM., ed., National Bureau of Standards Special Publication 453, pp. 29–47 (U.S. Government Printing Office, Washington, DC, 1974).
4.
HillC. R., Ultrasonic Attenuation and Scattering by Tissues, in Handbook of Clinical Ultrasound, (VliegerM.HolmesJ. H.KratochwilA.KazerE.KraussR.KossoffG.PoujolJ.StadnessD. E., eds., pp. 91–98 (John Wiley and Sons, New York, 1978).
5.
ChernovL. A., Wave Propagation in a Radom Medium. (a) Chapter IV and (b) Chapter III (Dover, New York, 1960).
6.
According to Chivers [1], scattering “may be defined as the change of amplitude, frequency, phase velocity, or direction of wave propagation of the wave as a result of spatial or temporal non-uniformity of the medium of propagation”. Due to the finite size of the scatterers as compared to the ultrasonic wavelength, some of the energy of the beam can be converted to modes of propagation other than that of the main beam. Although the energy loss due to mode conversion could be important, it is not yet possible to determine its influence quantitatively and for the present discussion, such effects will be ignored.
7.
LiebermannL., The effect of temperature inhomogeneities in the ocean on propagation of sound, J. Acoust. Soc. Am.23, 563–570 (1951).
8.
GossS. A.FrizzellL. A.DunnF., Ultrasonic absorption and attenuation in mammalian tissues, Ultrasound Med. Biol.5, 181–186 (1979).
9.
PohlhammerJ. D.EdwardsC. A.O'BrienW. D., Phase insensitive ultrasonic attenuation coefficient determination of fresh bovine liver over an extended frequency range, Med. Phys.8, 692–694 (1981).
10.
LizziF. L.LaviolaM. A.ColemanD. J., Tissue Signature Characterization Utilizing Frequency Domain Analysis, Proc. IEEE Ultrasonic Symposium714–719 (September, 1976).
11.
ShungK. K.SiglemannR. A.ReidJ. M., The Scattering of Ultrasound by Red Blood Cells, in Ultrasonic Tissue Characterization, LinzerM., ed., National Bureau of Standards Special Publication 453, pp. 207–212 (U.S. Government Printing Office, Washington, DC, 1974).
12.
O'DonnellM.MimbsJ. W.MillerJ. G., Relationship between collegen and ultrasonic backscatter in myocardial tissue, J. Acoust. Soc. Am.62, 580–588 (1981).
13.
ReidJ. M., Scattering of Sound by Tissues, in Medical Physics of CT and Ultrasound, FullertonG. D.ZagzebskiJ. A., eds., p. 388 (American Institute of Physics, 1980).
14.
FreeseM.LyonsE. A., Ultrasonic backscatter from human liver tissue: its dependence on frequency and protein/lipid composition, J. Clin. Ultrasound5, 307–312 (1977).
15.
NicholasD., Evaluation of backscattering coefficient for excised human tissues: Results interpretation and associated measurements, Ultrasound Med. Biol.8, 17–28 (1982).
16.
ShungK. K.ReidJ. M., Ultrasonic Scattering from Tissues, in Ultrasonics Symposium Proceedings, IEEE Cat. No. 77CH1264-1SU, pp. 230–233 (1977).
17.
KadabaM. P.BagatP. K.WuV. C., Attenuation and backscattering of ultrasound in freshly excised animal tissues, IEEE Trans. Biomed. Eng.27, 76–83 (1980).
18.
FoldyL. L., The multiple scattering of waves. Phys. Rev.67, 107–117 (1945); WatermanP. C.TruellR., J. Math. Phys. 2, 512 (1961); LaxM., Multiple scattering of waves, Rev. Modern Phys. 23, 287–310 (1951).
19.
Van de HulstH. C., Light Scattering by Small Particles, p. 6 (Dover Publication, Inc., New York, 1981).
20.
ShungK. K.SigelmannR. S.ReidJ. M., Scattering of ultrasound by blood, IEEE Trans. Biomed. Eng.6, 460–467 (1976).
21.
TwerskyV., On scattering of waves by random distribution: free space scatterer formulation (1), J. Math. Physics3, 700 (1962); Multiple Scattering of Waves in Dense Distributions of Large Tenuous Particles, in Electronic Scattering (Pergamon Press, New York, 1962).
22.
GossS. A.JohnstonR. L.DunnF., Comprehensive compilation of empirical ultrasonic properties of mammalian tissues, J. Acoust. Soc. Am.64, 423–457 (1978).
23.
WelsbyV. G., Scattering phenomena in acoustic wave propagation, J. Sound Vibration8, 64–96 (1968).
24.
αsc should not be confused with the term “scattering coefficient” which is a measure of the energy that is scattered in any given direction. αSC as described here is a measure of the “loss of energy” from an ultrasonic beam due to scattering. The difference between these two terms is not often emphasized in literature.
25.
PekerisC. L., Note on the scattering of radiation in an inhomogeneous medium, Phys. Rev.71, 268–269 (1947).
26.
Although this analogy between the correlation length and the mean diameter is often made and is also used in this paper, it must be pointed out that such a comparison may lead to conceptual difficulties, especially if the medium is complex and defined by more than one correlation length. For example, a point A in the medium could be correlated to two (or more) different points of space by two (or more) different correlation lengths. If one interprets correlation length as the size of the scatterer, it would mean that the same point A may be a part of two (or more) scatterers. Strictly speaking, correlation length is a concept in itself that is applicable to continuous media. Extrapolation of this concept to define discrete scatterers may at times be misleading. However, such a comparison is tremendously helpful in visualizing the complex scattering processes. So, even though the comparison may not strictly hold true, it is beneficial to use it as long as it is borne in mind that correlation length is a “continuum” concept whereas scatterer sizes and their separation from one another are “discrete” concepts.
27.
EdmondsP. D.DunnF., Introduction: Physical Description of Ultrasonic Fields, in Methods of Experimental Physics: Ultrasonics, EdmondsP. D., ed. (Academic Press, New York, 1981).
28.
WellsP. N. T., Physical Principles of Ultrasonic Diagnosis (Academic Press, New York, 1969).
29.
FieldsS.DunnF., Correlation of echographic visualizability of tissue with biological composition and physiological state, J. Acoust. Soc. Am.54, 809–812 (1973).
30.
PohlhammerJ.O'BrienW. D.Jr., Dependence of the ultrasonic scatter coefficient on collagen concentration in mammalian tissue, J. Acoust. Soc. Am.69, 283–285 (1981).
31.
SehgalC. M.GreenleafJ. F., Ultrasonic absorption and dispersion in biological media: a postulated model, J. Acoust. Soc. Am.72, 1711–1718 (1982).
