Dynamical model of an oscillating shelled microbubble

Research output: Book/ReportOther report

Abstract

There is considerable interest at the moment on using shelled microbubbles as a transportation mechanism for localised drug delivery, specifically in the treatment of various cancers. In this report a theoretical model is proposed which predicts the dynamics of an oscillating shelled microbubble. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. The shell is then stressed by applying a series of small radially directed stress steps to the inner surface of the shell whilst setting the outer surface’s stress to zero. The spatial profiles of the Cauchy radial and angular (hoop) stresses that are created within the shell during this quasistatic inflationary process are then stored as the shelled microbubble is inflated. The shelled microbubble is then allowed to collapse by setting the stress at the inner surface to zero. The model which results is then used to predict the dynamics of the shelled microbubble as it oscillates about its equilibrium state. A linear approximation is then used to allow analytical insight into both the quasistatic inflationary and oscillating phases of the shelled microbubble. Numerical results from the full nonlinear model are produced which show the influence of the shell’s thickness, Poisson ratio and shear modulus on the rate of oscillation of the shelled microbubble and these are compared to the approximate analytical solution. The theoretical model’s collapse time is compared to published experimental results.
LanguageEnglish
Place of PublicationGlasgow
PublisherUniversity of Strathclyde
Number of pages110
Volume15
Publication statusPublished - 2015

Fingerprint

Microbubbles
Dynamical Model
Shell
Theoretical Model
Unit of volume
Strain Energy Density
Predict
Drug Delivery
Poisson's Ratio
Theoretical Models
Zero
Poisson ratio
Linear Approximation
Strain energy
Potential energy
Energy Function
Drug delivery
Equilibrium State
Density Function
Probability density function

Keywords

  • oscillating shelled microbubble
  • drug delivery
  • oncology
  • ultrasound imaging contrast agents

Cite this

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title = "Dynamical model of an oscillating shelled microbubble",
abstract = "There is considerable interest at the moment on using shelled microbubbles as a transportation mechanism for localised drug delivery, specifically in the treatment of various cancers. In this report a theoretical model is proposed which predicts the dynamics of an oscillating shelled microbubble. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. The shell is then stressed by applying a series of small radially directed stress steps to the inner surface of the shell whilst setting the outer surface’s stress to zero. The spatial profiles of the Cauchy radial and angular (hoop) stresses that are created within the shell during this quasistatic inflationary process are then stored as the shelled microbubble is inflated. The shelled microbubble is then allowed to collapse by setting the stress at the inner surface to zero. The model which results is then used to predict the dynamics of the shelled microbubble as it oscillates about its equilibrium state. A linear approximation is then used to allow analytical insight into both the quasistatic inflationary and oscillating phases of the shelled microbubble. Numerical results from the full nonlinear model are produced which show the influence of the shell’s thickness, Poisson ratio and shear modulus on the rate of oscillation of the shelled microbubble and these are compared to the approximate analytical solution. The theoretical model’s collapse time is compared to published experimental results.",
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author = "James Cowley and Mulholland, {Anthony J.} and Stewart, {Iain W.} and Anthony Gachagan",
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Dynamical model of an oscillating shelled microbubble. / Cowley, James; Mulholland, Anthony J.; Stewart, Iain W.; Gachagan, Anthony.

Glasgow : University of Strathclyde, 2015. 110 p.

Research output: Book/ReportOther report

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