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Abstract
There is considerable interest in using shelled microbubbles as a transportation mechanism for localised drug delivery, specifically in the treatment of various cancers. In this paper a theoretical model is proposed which predicts the dynamics of an oscillating shelled microbubble. A neoHookean, compressible strain energy density function is used to model the potential energy per unit volume of the shell. The shell is stressed by applying a series of small radially directed stress steps to the inner surface of the shell whilst the outer surface is traction free. Once a certain radial deformation is reached, the stress load at the inner radius is switched off causing the shell to collapse and oscillate about its equilibrium (stress free) position. The inflated shell configuration is used as an initial condition to model the time evolving collapse phase of the shell. The collapse phase is modelled by applying the momentum balance law and mass conservation. The dynamical model which results is then used to predict the collapse time of the shelled microbubble as it oscillates about its equilibrium position. A linear approximation is used in order to gain analytical insight into both the quasistatic inflationary and the oscillating phases of the shelled microbubble. Results from the linearised model are then analysed which show the influence of the shell's thickness, Poisson ratio and shear modulus on the rate of oscillation of the shelled microbubble. The nonlinear model for the quasistatic state is solved numerically and compared to the linearised quasistatic solution. At present, there is no solution to the nonlinear collapsed state. This is a future area of research for the current authors.
Original language  English 

Pages (fromto)  781801 
Number of pages  21 
Journal  IMA Journal of Applied Mathematics 
Volume  82 
Issue number  4 
Early online date  18 May 2017 
DOIs  
Publication status  Published  31 Aug 2017 
Keywords
 shelled microbubbles
 transportation mechanism
 drug delivery
 cancer
 deformation
 quasistatic
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Profiles
Projects
 1 Finished

EPSRC Doctoral Training Grant  DTA, University of Strathclyde
EPSRC (Engineering and Physical Sciences Research Council)
1/10/13 → 30/09/17
Project: Research  Studentship
Datasets

Data for: "A nonlinear elasticity approach to modelling the collapse of a shelled microbubble"
COWLEY, J. (Creator), University of Strathclyde, 16 Jun 2017
DOI: 10.15129/752714cd35b74d96a1bc9f2536deed88
Dataset