Visco-Elastic Models for Soft Tissues
The simplest, and much utilized (despite its numerous shortcomings), model for soft tissue is based on the assumption of a linear elastic medium, although there is substantial evidence to suggest that soft tissue is, in fact, visco-elastic in nature. Here we discuss the simple and direct inclusion of visco-elastic concepts into descriptions of soft tissue. The two most elementary linear visco-elastic mechanical models (Maxwell and Kelvin-Voigt) are discussed. The wave equations for pressure propagation in these media are derived and their absorption and velocity dispersion characteristics are examined. One interesting feature is that explicit pulsed wave solutions may be derived in some cases. Another finding is that absorptive behavior may be characterized in a relative efficient manner, without recourse to the usual frequency-dependent description. The extent to which these media can be regarded as suitable for tissue modeling purposes is investigated. The incorporation of scattering into these models may be effected in the usual manner, except that scattering by absorption fluctuations is also predicted.
Key wordsVisco-elasticity Kelvin-Voigt model Maxwell model Absorption scattering
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- 1.Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissue, 2nd ed., Springer-Verlag (1993).Google Scholar
- 3.L. Hutchins, S. Leeman, & J. P. Jones, “Bounded Pulse Propagation,” in Acoustical Imaging, 10, P. Alais & A. Metherell (eds), Plenum Press, 427 (1981).Google Scholar
- 4.S. Leeman & A. Peyman, “The Maxwell Model as a Soft Tissue Descriptor,” in Acoustical Imaging , 25, M. Halliwell & P. N. T. Wells (eds), Kluwer/ Plenum, 357 (2000).Google Scholar
- 5.P. M. Morse & K. U. Ingard, Theoretical Acoustics, McGraw-Hill, 400 (1968).Google Scholar
- 6.S. Leeman, R. Leeks, & P. Sutton, “Information Processing in Medical Imaging,” in Les Colloques de I’INSERM, 88, R. Di Paola & E. Kahn (eds), INSERM, 35, (1979).Google Scholar
- 7.E. Nolan, Reflection of Acoustic Waves From a Discontinuity in Absorption, MS Thesis, University of California Irvine (1988).Google Scholar