### Abstract

Original language | English |
---|---|

Place of Publication | Glasgow |

Publisher | University of Strathclyde |

Number of pages | 60 |

Volume | 1 |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

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

### Cite this

*Mathematical modelling of the collapse time of an unfolding shelled microbubble*. Glasgow: University of Strathclyde.

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*Mathematical modelling of the collapse time of an unfolding shelled microbubble*. vol. 1, University of Strathclyde, Glasgow.

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

Research output: Book/Report › Other report

TY - BOOK

T1 - Mathematical modelling of the collapse time of an unfolding shelled microbubble

AU - Cowley, James

AU - Mulholland, Anthony J.

AU - Stewart, Iain W.

AU - Gachagan, Anthony

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - ultrasound contrast agents

KW - UCAs

KW - drug delivery

KW - theoretical models

KW - shelled microbubbles

M3 - Other report

VL - 1

BT - Mathematical modelling of the collapse time of an unfolding shelled microbubble

PB - University of Strathclyde

CY - Glasgow

ER -