Numerical investigation of acoustic cavitation and viscoelastic tissue deformation

Abstract

Acoustic cavitation and tissue deformation are studied by modifying a level-set method for compressible two-phase flows to consider viscoelastic tissue deformation. The numerical simulations performed using different shear moduli and bubble-tissue distances demonstrate various interactions between bubble and viscoelastic tissue, including inverted cone-shape bubbles, bubble migration, liquid jet formation, compressive and expansive tissue deformation, and tissue perforation. The bubble is observed to grow larger with increasing tissue bulk modulus and density. The maximum tissue deformation generally increases with decreasing initial bubble-tissue distance and with increasing tissue bulk modulus and density. The tissue shear modulus conditions that maximize tissue deformation are in the range of 1-10 MPa, unless the tissue density is very large.

Keywords: Acoustic cavitation; Bubble collapse; Bubble growth; Bubble-tissue interaction; Tissue deformation.

Fig. 1

Schematic for analysis of acoustic cavitation and viscoelastic tissue deformation.

Fig. 2

Liquid velocity field with direction vectors (left) and pressure field (right) associated with acoustic bubble motion without including nearby tissue at $A_u=0.3\mathrm{MPa},f_u=1\mathrm{MHz}$. Here, the white area represents the bubble.

Fig. 3

Acoustic bubble growth without including nearby tissue compared with the Keller-Miksis prediction at $A_u=0.3\mathrm{MPa},f_u=1\mathrm{MHz}$.

Fig. 4

Liquid velocity field with direction vectors (left) and pressure field (right) associated with acoustic cavitation and tissue deformation at $l_o=5\mathrm{\mu }\mathrm{m}$ and $G=1\mathrm{MPa}$. The gray and white regions represent the tissue and bubble, respectively.

Fig. 5

Detailed bubble motion and tissue deformation during three different periods at $l_o=5\mathrm{\mu }\mathrm{m}$ and $G=1\mathrm{MPa}$: (a) bubble growth, (b) contraction, and (c) rebound.

Fig. 6

Liquid velocity field with direction vectors (left) and pressure field (right) associated with acoustic cavitation and tissue deformation at $l_o=4\mathrm{\mu }\mathrm{m}$ and $G=1\mathrm{MPa}$.

Fig. 7

Influence of $l_o$ on acoustic cavitation bubble and tissue behavior at $G=1\mathrm{MPa},{\mathrm{\Pi }}_s={\mathrm{\Pi }}_w$ and ${\rho }_s={\rho }_w$: (a) temporal change of $R_b$ and (b) tissue deformation $y_{\mathit{sc}}$ at the central axis ($r=0$).

Fig. 8

Liquid velocity field with direction vectors (left) and pressure field (right) associated with acoustic cavitation and tissue deformation at $l_o=4\mathrm{\mu }\mathrm{m},{\mathrm{\Pi }}_s={\mathrm{\Pi }}_w,{\rho }_s={\rho }_w$ and two different shear moduli: (a) $G=10\mathrm{MPa}$ and (b) $G=0.1\mathrm{MPa}$.

Fig. 9

Combined effects of $l_o$ and G on bubble growth and tissue deformation at ${\mathrm{\Pi }}_s={\mathrm{\Pi }}_w$ and ${\rho }_s={\rho }_w$.

Fig. 10

Instantaneous liquid pressure field without including bubble motion (two figures on the left) and instantaneous flow fields associated with acoustic cavitation and tissue deformation at $l_o=5\mathrm{\mu }\mathrm{m},G=1\mathrm{MPa},{\rho }_s={\rho }_w$ and different bulk moduli: (a) ${\mathrm{\Pi }}_s=0.5{\mathrm{\Pi }}_w$ and (b) ${\mathrm{\Pi }}_s=2{\mathrm{\Pi }}_w$.

Fig. 11

Effect of tissue bulk modulus on acoustic cavitation bubble and tissue behavior at $l_o=5\mathrm{\mu }\mathrm{m},G=1\mathrm{MPa}$, and ${\rho }_s={\rho }_w$: (a) temporal change of $R_b$ and (b) tissue deformation $y_{\mathit{sc}}$ at the central axis ($r=0$).

Fig. 12

Combined effects of tissue bulk modulus and shear modulus on bubble growth and tissue deformation at $l_o=5\mathrm{\mu }\mathrm{m}$ and ${\rho }_s={\rho }_w$.

Fig. 13

Effect of tissue density on acoustic cavitation bubble and tissue deformation at $l_o=5\mathrm{\mu }\mathrm{m}$ ,$G=1\mathrm{MPa}$, and ${\mathrm{\Pi }}_s={\mathrm{\Pi }}_w$: (a) temporal change of $R_b$ and (b) tissue deformation $y_{\mathit{sc}}$ at the central axis ($r=0$).

Fig. 14

Combined effects of tissue density and shear modulus on bubble growth and tissue deformation at $l_o=5\mathrm{\mu }\mathrm{m}$ and ${\mathrm{\Pi }}_s={\mathrm{\Pi }}_w$.