Damage mechanisms for ultrasound-

induced cavitation in tissue 2014 April 4

International Symposium for Therapeutic Ultrasound, Las Vegas NV

Matt Warnez1 and Eric Johnsen2

In collaboration with Eli Vlaisavljevich3 and Zhen Xu3

1 Engineering Physics, 2 Mechanical Engineering, 3 Biomedical Engineering

Background • Cavitation occurs in various ultrasound therapies (e.g.,

histotripsy, lithotripsy)

• High-amplitude pressure oscillations cause violent bubble response

and potentially damage

• Many cavitation bioeffect mechanisms have been proposed

• Tissue is viscoelastic, which significantly effects bubble behavior

• Numerical models allow insight into high-speed bubble dynamics

• Objective: to understand cavitation damage

mechanisms in viscoelastic media using

numerical simulations

Micro- and macroscopic histotripsy-induced ablation –

University of Michigan Therapeutic Ultrasound Group

Large gas bubble in tissue-mimicking gel –

University of Michigan Therapeutic Ultrasound Group

1 mm

Possible damage mechanisms

Minimum radius

Collapse phase

• High temperatures

• High pressures

• Shockwaves, free radicals, microjets

• Large strain rates, viscous stresses

Maximum radius

Growth phase

• Large strains, elastic stresses

Theoretical model Assumptions:

• Spherical bubble

• Uniform bubble pressure

• Zero mass transfer

• Incompressible near field with compressible correction

𝜏

Governing equations • Generalized Keller-Miksis equation

• Energy equations, solved via Chebyshev collocation (Kamath et al. 1989)

• Internal bubble pressure

Constitutive model • Past approaches include: Allen & Roy (2000), Yang & Church (2005)

• The Zener (standard linear solid) model is the simplest viscous- elastic model to include relaxation effects

• A Chebyshev spectral method was developed to solve for the stresses and temperatures in the entire domain

• Model agrees well with experimental data:

• Laser-induced cavitation experiments in water

• Histotripsy experiments in gels (see presentation by Eli Vlaisavljevich)

Sinusoidal forcing:

Viscoelasticity reduces the violence of the collapse (and thus pressure)

Water

Zener tissue properties

Water properties

Zener tissue

Radius versus time Pressure

External temperature

Water

Temperatures external to bubble remain cool, despite viscous heating

Zener tissue

Internal temperature

Finite strain rate dγθθ/dt

Water

Deformation and deformation rates large, but similar between media

Zener tissue

Finite strain γθθ

Stress at particle

Water

Geometrical effects amplify stresses experienced at Lagrangian points

Zener tissue

Radial stress τrr

Stress at particle

Viscoelastic properties induce higher stress even for low forcing amplitudes

Zener tissue

Radial stress τrr

Water

Causes for increased stress • Viscoelastic properties amplify stress values; relaxation

effects allow for large oscillations

• Out-of-equilibrium oscillations means Lagrangian points are nearer to bubble wall at collapse

Viscoelastic collapse

Bubble at maximum

radius

Bubble at collapse

Newtonian collapse

Conclusions • In tissue, viscoelastic stresses may be important damage mechanisms

in therapeutic ultrasound

• Large stresses may be an important bioeffect mechanisms due to:

• Viscoelastic properties

• Geometry

• Future work:

• Simulating more complex constitutive models for tissue

• Studying resilience of cells to viscoelastic stresses

• High time-resolution ultrasound-induced cavitation experiments (collaboration with Zhen Xu, U-Michigan)

Matt Warnez (mwarnez@umich.edu)

Eric Johnsen (ejohnsen@umich.edu)

Azimuthal strain γθθ

Water

Comparison of radial and azimuthal finite strain

Zener tissue

Radial strain γrr

Azimuthal stress τθθ

Water

Comparison of radial and azimuthal stress

Zener tissue

Radial stress τrr