Numerical Investigation of the Radial Behavior and Scattered Pressure from the Encapsulated Microbubble in Vicinity of the Boundaries with Different Elasticities

Document Type : Original Article

Authors

1 department of mechanical engineering, shahid rajaee theacher training university

2 shahid rajaee teacher training university

Abstract

One of the best methods for improving quality and clarity of the ultrasound imaging is the use of coated bubbles. In this paper, the dynamics of an encapsulated bubble near the wall is simulated with different elasticity for the ultrasound imaging. For this purpose, a computer program has been developed in MATLAB software, in which the modified Rayleight-Plesset differential equation is solved numerically using by the fourth-order Runge Kutta method. Initially, the results were compared with experimental data, then the radial behavior of the encapsulated bubble (UCA) was investigated for two adjacent states with rigid and elastic wall and the scattered pressure from the bubble was simulated. In addition, the effect of the shell viscosity (Ks), the initial radius of the bubble and the distance between the bubble and the wall on the dynamic behavior of the bubble and the amount of scattered pressure therefrom are investigated. The results are presented in the form of table and graphs. The results show that the bubble shell's viscosity and the initial bubble radius have a significant effect on the bubble dynamics. Finally, the frequency response of the encapsulated bubble has been investigated and the effect of the initial radius of the bubble, the shell material and the elastic modulus of the wall on the strength of the fundamental spectrum has been presented. The results show that by increasing the elastic modulus of the wall, the strength of the fundamental spectrum reach the limit state and does not change.

Keywords


  1. Brennen, C. E. “Cavitation and Bubble Dynamics”, Oxford University Press, New York, 1995.##
  2. Leighton, T. G. “The Acoustic Bubble”, Academic Press, University of Southampton, England, 1994.##
  3. Blake, J. R. and Gibson, D. C. “Cavitation Bubbles Near Boundaries”, J. of Annual Review Fluid Mechanics, Vol. 19, pp. 99–123, 1987.##
  4. Brujan, E. A., Nahen, K., Schmidt, P., and Vogel, A. “Dynamics of Laser-induced Cavitation Bubbles Near an Elastic Boundary”, J. Fluid Mech., Vol. 433, pp. 251-281, 2001.##
  5. Brujan, E. A., Nahen, K., Schmidt, P., and Vogel, A. “Dynamics of Laser-Induced Cavitation Bubbles Near Elastic Boundaries: Influence of the Elastic Modulus”, J. Fluid Mech., Vol. 433, pp. 283–314, 2001.##
  6. Brujan, E. A., Pearson, A., and Blake, J. R. “Pulsating Buoyant Bubbles Close to a Rigid Boundary and Near the Null Final Kelvin Impulse State” Int. J. Multiphas. Flow, Vol. 31, no. 3, pp. 302–317, 2005.##
  7. Kodama, T. and Tomita, Y. “Cavitation Bubble Behavior and Bubble-shock Wave Interaction Near a Gelatin Surface as a Study of in Vivo Bubble Dynamics” Appl. Phys. B, Vol. 70,no. 1, pp.139–149, 2000.##
  8. Zhao, S., Kruse, D. E., Ferrara, K. W., and Dayton, P. A. “Acoustic Response from Adherent Targeted Contrast Agents” J. Acoust. Soc. Am., Vol. 120, no. 6, pp. 63–69, 2006.##
  9. Fong, S. W., Klaseboer, E., Turangan, C. K., Khoo, B. C., and Hung, K. C. “Numerical Analysis of a Gas Bubble Near Bio-Materials in an Ultrasound Field” Ultrasound Med. Biol., Vol. 32, no. 6, pp. 925-942, 2006.##
  10. Bettinger, T. and Tranquart, F “Design of Microbubbles for Gene and Drug Delivery” Therapeutic Ultrasound, Advances in Experimental Medicine and Biology Vol. 880, pp.191-204, 2016.##
  11. Doinikov, A. A., Aired, L. and Bouakaz, A. “Acoustic Scattering From a Contrast Agent Microbubble Near An Elastic Wall Of finite thickness” Physics in Medicine & Biology Vol. 56, no. 21, pp. 6951-6967, 2011.##
  12. Herring, C. “Theory of the Pulsations of the Gas Bubble Produced by an Underwater Explosion” Technical report, New London, Conn. Columbia Univ., Div. of National Defense Research, OSRD report 236, 1941.##
  13. Strasberg, M. “The pulsation frequency of nonspherical gas bubbles in liquids” J. Acoust Soc. Am., Vol. 25, pp. 536-537,1953.##
  14. Blue, J. E. “Resonance of a Bubble on an Infinite Rigid Boundary” J. Acoust. Soc. Am., Vol. 41, pp. 369–372, 1967.##
  15. Illesinghe, S., Ooi, A., and Manasseh, R. “Eigenmodal resonances of polydisperse bubble systems on a rigid boundary” J. Acoust. Soc. Am., Vol. 126, pp. 2929-2938, 2009.##
  16. Doinikov, A., Zhao, S., and Dayton, P.  “Modeling of the acoustic response from contrast agent microbubbles near a rigid wall” J. of Ultrasonics, Vol. 49, pp. 195-20, 2009.##
  17. Shima, A. and Tomita, Y. “The behavior of a spherical bubble near a solid wall in a compressible liquid” Ing. Arch, Vol. 51, pp. 243–255, 1981.##
  18. Doinikov, A., Aired, L., and Bouakaz, A. “Acoustic response from a bubble pulsating near a fluid layer of finite density and thickness” J. Acoust. Soc. Am., Vol. 129, pp. 616-621, 2011.##
  19. Garbin, V., Cojoc, D., Ferrari, E., Fabrizio, E., Overvelde, M. L. J., Van Der Meer, S. M., De Jong, N., Lohse, D., and Versluis, M. “Changes in microbubble dynamics near a boundary revealed by combined optical micromanipulation and high-speed imaging” Applied physics letters, Vol. 90, pp. 114103-1-114103-3, 2007.##
  20. Marmottant, P., Van Der Meer, S., Emmer, M., Versluis, M., De Jong, N., Hilgenfeldt, S., and Lohse, D. “A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture” J. Acoust. Soc. Am., Vol. 118, pp. 3499-3505, 2005.##
  21. Martynov, S., Stride, E., and Saffari, N. “The natural frequencies of microbubble oscillation in elastic vessels” J. Acoust. Soc. Am., Vol. 126, pp. 2963-2972, 2009.##
  22. Der Meer, S. M., Dollet, B., Voormolen, M. M., Chin, C. T., Bouakaz, A, De Jong, N., Versluis, M., and Lohse, D. ”Microbubble spectroscopy of ultrasound contrast agents” J. Acoust. Soc. Am., Vol. 121, pp. 648-656, 2007.##
  23. Garbin V, Cojoc D, Ferrari E, Di Fabrizio E, Overvelde M L J, van der Meer S M, de Jong N, Lohse D and Versluis M “Changes in microbubble dynamics near a boundary revealed by combined optical micromanipulation and high-speed imaging” Appl. Phys. Lett. Vol. 90, pp.114103-1-114103-3, 2007.##

 

 

 

 

 

 

 

 

  1. Shirshendu, P., Amit, K., and Kausik S., "Material Characterization of the Encapsulation of an Ultrasound Contrast Microbubble and its Subharmonic Response: Strain-Softening Interfacial Elasticity Model", J. Acoust. Soc. Am., Vol. 127, no. 6, pp. 3846–3857, 2010.##
  2. Doinikov, A. A.,  Aired, L., and Bouakaz, A. "Modeling and experiments on the far-field scattering of a bubble pulsating near a wall with finite density and thickness," IEEE International Ultrasonics Symposium, San Diego, CA, 2010.##
  3. Doinikov, A. A., Aired, L., and Bouakaz, A. “Effect of an Elastic Wall on the Dynamics of an Encapsulated Microbubble: A Simulation Study”, Ultrasonics, Vol. 53, pp. 23-28, 2013.##
  4. Sarkar, K., Paul, S., and Katiyar, A. “Material Characterization of the Encapsulation of an Ultrasound Contrast Microbubble and its Subharmonic Response” J. Acoust. Soc. Am., Vol. 127, pp. 3846-3857, 2010.##
  5. Tu, J., Guan, J., Qui, Y., and Matula, T. J. “Estimating the Shell Parameters of Sonovue Microbubbles Using Light Scattering”
    J. Acoust. Soc. Am., Vol. 126, no. 6, pp. 2954-295462, 2009.##
  6. Kumar, K. and Sarkar, K. “Effects of Ambient Hydrostatic Pressure on the Material Properties of the Encapsulation of an Ultrasound Contrast Microbubble” J. Acoust. Soc. Am., Vol. 138, no. 2, 624–634, 2015.##
  7. Garashchuk, I., Sinelshchikov, D., and Kudryashov, N. “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall” Regular and Chaotic Dynamics, Vol. 23, pp. 257–272, 2018.##
  8. Garashchuk, I., Sinelshchikov, D. and Kudryashov, N. “General Solution of the Rayleigh Equation for Description of Bubble Oscillations Near a Wall” Mathematical Modeling and Computational Physics 2017 (MMCP 2017), Dubna, Russia, EPJ Web of Conferences, Vol. 173.##
  9. Doinikov, A.A., Novell, A.,  Escoffre, JM. And  Bouakaz, A. “Encapsulated Bubble Dynamics in Imaging and Therapy” Bubble Dynamics and Shock Waves, Vol. 8 , pp. 259-289, 2013.##