Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents

Garashchuk, Ivan R.; Kazakov, Alexey O.; Sinelshchikov, Dmitry I.

doi:10.1007/s11071-020-05864-4

Cited by 9 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We would also like to note that the attractor we are studying here is relatively stable to symmetry breaking in model ( 1), corresponding to the transition from two identical bubbles to a pair of slightly different. Let us introduce a small parameter that characterizes this transition as follows [12] 1) are no longer symmetrical with respect to R 1 ←→ R 2 transformation. Now we study the influence of symmetry breaking on several attractors representing typical stages of the bubbling transition process.…”

Section: Implementation Of the Bubbling Transition Scenariomentioning

confidence: 99%

“…On the other hand, in a number of works it was shown that the contrast agents dynamics may be complicated and strongly depend on both control parameters and initial conditions (see, e.g. [6][7][8][9][10][11][12]). In works [6][7][8][9] the case of one microbubble was studied and it was demonstrated that the dynamics may be either regular or chaotic and multistable in both cases, while, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In works [6][7][8][9] the case of one microbubble was studied and it was demonstrated that the dynamics may be either regular or chaotic and multistable in both cases, while, e.g. in [10][11][12], interactions between bubbles were taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…[11] demonstrated that oscillations of bubbles may be both synchronous and asynchronous. It is worth noting that a synchronization manifold exist only in the case of two identical bubble, when the governing system of equations possesses a symmetry [11,12]. Thus, complete synchronization is possible only in the symmetrical case.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, complete synchronization is possible only in the symmetrical case. In [12] authors studied how symmetry breaking affects various synchronous and asynchronous attractors. However, the destructions of synchronous oscillations without symmetry breaking in the model of two interacting contrast agents has not been studied previously.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents

Garashchuk,

Sinelshchikov

2021

Preprint

View full text Add to dashboard Cite

We study the process of destruction of synchronous oscillations in a model of two interacting microbubble contrast agents exposed to an external ultrasound field. Completely synchronous oscillations in this model are possible in case of identical bubbles, when the governing system of equations possess a symmetry leading to the existence of a synchronization manifold. Such synchronous oscillations can be destructed without breaking the corresponding symmetry of the governing dynamical system. Here we describe the phenomenological mechanism responsible for such destruction of synchronization and demonstrate its implementation in the studied model. We show that the appearance and expansion of transversally unstable areas in the synchronization manifold leads to transformation of a synchronous chaotic attractor into a hyperchaotic one. We also demonstrate that this bifurcation sequence is stable with respect to symmetry breaking perturbations.

show abstract

Section: Implementation Of the Bubbling Transition Scenariomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents

Garashchuk,

Sinelshchikov

2021

Preprint

View full text Add to dashboard Cite

show abstract

Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactions on oversaturation and enhancement of the subharmonic signal

et al. 2021

View full text Add to dashboard Cite

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

Nguyen

Kanagawa

2023

Nonlinear Dyn

View full text Add to dashboard Cite

With promising applications in medical diagnosis and therapy, the behavior of shell-encapsula-ted ultrasound contrast agents (UCAs) has attracted considerable attention. Currently, second-generation contrast agents stabilized by a phospholipid membrane are widely used and studies have focused on the dynamics of single phospholipid shell-encapsulated microbubbles. To improve the safety and the efficiency of the methods using the propagation or targeted ultrasound, a better understanding of the propagation of ultrasound in liquids containing multiple encapsulated microbubbles is required. By incorporating the Marmottant–Gompertz model into the multiple scale analysis of two-phase model, this study derived a Korteweg–de Vries–Burgers equation as a weakly nonlinear wave equation for one-dimensional ultrasound in bubbly liquids. It was found that the wave propagation characteristics changed with the initial surface tension, highlighting two notable features of the phospholipid shell: buckling and rupture. These results may provide insights into the suitable state of microbubbles, and better control of ultrasound for medical applications, particularly those that require high precision.

show abstract

Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents

Cited by 9 publications

References 27 publications

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents

Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactions on oversaturation and enhancement of the subharmonic signal

Nonlinear ultrasound in liquid containing multiple coated microbubbles: effect of buckling and rupture of viscoelastic shell on ultrasound propagation

Contact Info

Product

Resources

About