Velocity and attenuation of shear waves in the phantom of a muscle–soft tissue matrix with embedded stretched fibers


We develop a theory of the elasticity moduli and dissipative properties of a composite material: a phantom simulating muscle tissue anisotropy. The model used in the experiments was made of a waterlike polymer with embedded elastic filaments imitating muscle fiber. In contrast to the earlier developed phenomenological theory of the anisotropic properties of muscle tissue, here we obtain the relationship of the moduli with characteristic sizes and moduli making up the composite. We introduce the effective elasticity moduli and viscosity tensor components, which depend on stretching of the fibers. We measure the propagation velocity of shear waves and the shear viscosity of the model for regulated tension. Waves were excited by pulsed radiation pressure generated by modulated focused ultrasound. We show that with increased stretching of fibers imitating muscle contraction, an increase in both elasticity and viscosity takes place, and this effect depends on the wave propagation direction. The results of theoretical and experimental studies support our hypothesis on the protective function of stretched skeletal muscle, which protects bones and joints from trauma.

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  1. 1.

    O. V. Rudenko and A. P. Sarvazyan, Acoust. Phys. 60, 710 (2014).

    ADS  Article  Google Scholar 

  2. 2.

    A. Sarvazyan, O. Rudenko, S. Aglyamov, and S. Emelianov, Med. Hypotheses 83, 6 (2014).

    Article  Google Scholar 

  3. 3.

    O. V. Rudenko, S. Tsyurupa, and A. Sarvazyan, Acoust. Phys. 62 (4), 1 (2016).

    Article  Google Scholar 

  4. 4.

    L. D. Landau and E. M. Lifshits, Course of Theoretical Physics. Vol. 7. The Theory of Elasticity (Nauka, Moscow, 1965; Elsevier, Oxford, 1986).

    Google Scholar 

  5. 5.

    Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Ed. by M. Abramowits and I. A. Stegun, (Dover, New York, 1968).

  6. 6.

    S. M. Rytov, Akust. Zh. 2, 71 (1956).

    MathSciNet  Google Scholar 

  7. 7.

    E. Behrens, J. Acoust. Soc. Am. 42, 378 (1967).

    ADS  Article  Google Scholar 

  8. 8.

    A. Sarvazyan, S. Tsyuryupa, and O. Rudenko, POMA 23, 1121 (2015).

    Google Scholar 

  9. 9.

    E. J. Chen, J. Novakofski, W. K. Jenkins, and W. D. O’Brien, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 191 (1996).

    Article  Google Scholar 

  10. 10.

    J. R. Basford, T. R. Jenkyn, A. Kai-Nan, R. L. Ehman, G. Heers, and K. R. Kaufman, Arch. Phys. Med. Rehabil. 83, 1530 (2002).

    Article  Google Scholar 

  11. 11.

    O. V. Rudenko and A. P. Sarvazyan, Acoust. Phys. 52, 720 (2006).

    ADS  Article  Google Scholar 

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Correspondence to O. V. Rudenko.

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Original Russian Text © O.V. Rudenko, S.N. Tsyuryupa, A.P. Sarvazyan, 2016, published in Akusticheskii Zhurnal, 2016, Vol. 62, No. 5, pp. 609–615.

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Rudenko, O.V., Tsyuryupa, S.N. & Sarvazyan, A.P. Velocity and attenuation of shear waves in the phantom of a muscle–soft tissue matrix with embedded stretched fibers. Acoust. Phys. 62, 608–614 (2016).

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  • radiation force
  • ultrasound
  • muscle phantom
  • anisotropic muscle
  • elasticity modulus
  • viscosity tensor
  • stretching of fibers