Mathematical modelling of the collapse time of an unfolding 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 collapse time of an unfolding shelled microbubble. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. This is achieved by considering a reference configuration (stress free) consisting of a shelled microsphere with a hemispherical cap removed. This is then displaced angularly and radially by applying a stress load to the free edge of the shell. This forms a deformed open sphere possessing a stress. This is then used as an initial condition to model the unfolding of the shell back to its original stress free configuration. Asymptotic expansion along with the conservation of mass and energy are then used to determine the collapse times for the unfolding shell and how the material parameters influence this. The theoretical model is compared to published experimental results.
LanguageEnglish
Place of PublicationGlasgow
PublisherUniversity of Strathclyde
Number of pages60
Volume1
Publication statusPublished - 2016

Fingerprint

Microbubbles
Unfolding
Mathematical Modeling
Shell
Theoretical Models
Microspheres
Theoretical Model
Unit of volume
Strain Energy Density
Drug Delivery
Configuration
Strain energy
Potential energy
Energy
Energy Function
Drug delivery
Density Function
Pharmaceutical Preparations
Probability density function
Asymptotic Expansion

Keywords

  • ultrasound contrast agents
  • UCAs
  • drug delivery
  • theoretical models
  • shelled microbubbles

Cite this

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title = "Mathematical modelling of the collapse time of an unfolding 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 collapse time of an unfolding shelled microbubble. A neo-Hookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. This is achieved by considering a reference configuration (stress free) consisting of a shelled microsphere with a hemispherical cap removed. This is then displaced angularly and radially by applying a stress load to the free edge of the shell. This forms a deformed open sphere possessing a stress. This is then used as an initial condition to model the unfolding of the shell back to its original stress free configuration. Asymptotic expansion along with the conservation of mass and energy are then used to determine the collapse times for the unfolding shell and how the material parameters influence this. The theoretical model is compared to published experimental results.",
keywords = "ultrasound contrast agents, UCAs, drug delivery, theoretical models, shelled microbubbles",
author = "James Cowley and Mulholland, {Anthony J.} and Stewart, {Iain W.} and Anthony Gachagan",
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language = "English",
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}

Mathematical modelling of the collapse time of an unfolding shelled microbubble. / Cowley, James; Mulholland, Anthony J.; Stewart, Iain W.; Gachagan, Anthony.

Glasgow : University of Strathclyde, 2016. 60 p.

Research output: Book/ReportOther report

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AU - Gachagan, Anthony

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