Martynov, Sergey

Saffari, Nader

Stride, Eleanor

English

UCL Discovery

MODELLING  OF THE DYNAMICS OF A COATED MICROBUBBLE CONFINED IN A BLOOD VESSELSergey Martynov, Eleanor Stride and Nader SaffariDepartment of Mechanical Engineering, UCL, Torrington Place, London, WC1E 7JE, UKObjectivesSolution MethodAcknowledgementsResults of studies of the effects of bubble encapsulation and confinementAssumptions and Governing Equations•To develop the numerical model for the dynamics of a bubble, encapsulated in a shell, and located in a narrow elastic vessel filled with a viscous fluid•To study the effects of bubble coating and vessel stiffness, on the bubble-vessel deformations, radiated pressure, amplitude and frequency spectra of oscillationsFluidVessel wallBubble shellConclusionsThe resonance frequency of a bubble is shown to be strongly affected by the vessel wall stiffness, and the membrane (bulk) stiffness of the bubble coating, while the influence of the coating bending stiffness is relatively small. The resonance frequency is shown to increase with the vessel wall stiffness.The wall deformation pattern is mainly influenced by the vessel wall stiffness and liquid viscosity; the amplitude of wall deformations and wall stresses depends on the membrane stiffness of the bubble coating.The development of a buckling instability in the bubble shell is governed by the shell bending stiffness, and also depends on the pressure field in the liquid around the bubble, which is strongly affected by the vessel and bubble stiffness, and the vessel diameter.(Pa) opp ds=50nm, Es=23.6MPa; Ev= 1MPads=300nm, Es=3.93MPa; Ev= 1MPads=50nm, Es=23.6MPa; Ev=10MPaThe effect of the bubble shell bending stiffness Bs on the resonance frequency of bubbles with radius R1o=3mm confined in vessels with Rv=4mm and Ev= 1MPa and 10 MPads=15nm, Es=78.7MPa; Ev= 1MPa* The bubble and vessel deformations are shown magnified by 10 times012345670.01 0.1 1 10 100Ev  (MPa)Resonant  frequency (MHz) .FEM coated bubbleFEM uncoated bubbleUnconfined coated Unconfined uncoated Elastic vessel modeGasUltrasound waveMicro-bubbleR1o ~ 3 mmBlood capillary (wall thickness dv ~1mm)Shell thicknessds~ 0 - 300nm~ 8 mm- a long elastic membrane-type tube of a thickness dv ~1mm, radius Rv ~4-100mm, and elastic modulus Ev ~ 0.1-10 MPa vovvvvaivvv RRRdEppRd 22 )1(  )sin( tppp acoexternal - an incompressible homogenous Newtonian liquid with properties similar to water0 u     0 Tlll ptuuIuuumUltrasound wave:- a finite-thickness linear elastic structure, undergoing small deformations022t,211 ijkkijijEjkkiijjixxxx21VVppeqeqgg ,grant  EP/E029310/1                          Gas inside the bubble• Dynamics of a spherical (unconfined) coated bubble (Hoff, et al, 2000);• Resonance frequency of oscillations of uncoated bubble confined in:– a rigid vessel (Oguz and Proseperetti, 1998), and– an elastic vessel (Qin and Ferarra, 2007);• Free non-spherical oscillations of uncoated bubbles (Hao and Prosperetti, 1999);• Static buckling of a hollow spherical shell (Koiter, 1969)Validation CasesThe governing equations subject to boundary conditions are solved using the FEM package COMSOL MultiPhysics v. 3.4. The fluid-structure interaction is calculated using the  ALE method on the non-uniform moving mesh.0 0.2 0.4 0.6 0.8 1.0 1.2 time (ms)Forced bubble oscillations (f = 2.3MHz,  pac = 10kPa) – shape deformations* and radiated pressure frequency spectraThe results of analysis of free and forced oscillations are shown for bubbles with the internal radius R1o = 3mm and shell thickness ds = 0 – 300 nm, placed in vessels with radius Rv = 4mm, length Lv = 200 mm, wall thickness dv = 1mm, and elastic modulus Ev = 0.1 - 50 MPaThe effect of the vessel wall stiffness Ev on the forced oscillations ofcoated bubbles (ds = 50 nm, Es = 23.6 MPa) The effect of the bubble shell bending stiffness Bs on the forced oscillations of bubbles with radius R1o=3mm confined in vessels with Rv=4mm and Ev=1 MPaThe effect of the vessel stiffness Ev on the resonance frequency of coated bubbles (ds = 50 nm, Es = 23.6 MPa) and uncoated bubbles (0.0643 Pa m)Resonance frequency of confined bubbles0 0.2 0.4 0.6 0.8 1.0 1.2 time (ms)2.02.53.03.54.00 1 10 100 1000 10000 100000Shell bending stiffness, Bs   (Pa mm 3̂)Resonant frequency (MHz) .Confined (Ev=10 MPa)Confined (Ev= 1 MPa)   Unconfined bubble )mm(Pa   112323sssdE0  1  Frequency (MHz)      10Spectral power density .0  1  Frequency (MHz)      10Spectral power density .0  1  Frequency (MHz)      10Spectral power density .Unconfined bubble0  1  Frequency (MHz)      10Spectral power density. 0  1  Frequency (MHz)      10Spectral power density .

Modelling of the dynamics of a coated microbubble in a blood vessel

https://discovery.ucl.ac.uk/id/eprint/10153018/1/MicroBubble_A0.pdf

Modelling of the dynamics of a coated microbubble in a blood vessel

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