粘弾性液体中の被膜気泡の分岐解析(ND)

【共著論文】超音波造影剤など、薄い膜で覆われたマイクロバブルは、血液や組織のような粘弾性媒質中で超音波により駆動され、画像診断や薬剤輸送に用いられます。本研究では、この膜付き気泡の非線形振動を、粘弾性液体（Oldroyd-Bモデル）中の音響定在波下で、Rayleigh-Plesset方程式を界面と粘弾性応力の釣り合いと連成させた縮約力学系として定式化し、分岐解析・位相空間解析・エネルギー収支解析を用いて調べました。音圧の増加に伴い、気泡振動は周期振動 → 多周期振動 → カオス的振動という分岐カスケードを経ますが、膜の存在によって、その入口にあたる最初の周期倍分岐の音圧閾値が約80%（1.0 MPa → 1.8 MPa）上昇し、カオス領域も縮小することがわかりました。エネルギー収支解析から、この安定化は、膜の弾性が界面と周囲粘弾性応力との間で弾性エネルギーを再分配することに由来することが示されました。膜の弾性と気泡周囲液体の粘弾性のバランスを表す安定化指標を導入し、超音波造影剤（Definity, SonoVue, BR14など）を含む複数のシェル材料に対し、振動レジームを統一的に分類しました。

これは、エジプト・メヌフィア大学の応用数学者との共同研究成果であり、Nonlinear Dynamics (top 10%ジャーナル, JCR 2024, JIF percentile: 93% (Mechanics), IF: 6.0) から出版されました。

Abu-Nab, A.K., Kanagawa, T. and Fedorov, Y.V., “Shell–polymer coupling reorganizes nonlinear bifurcation thresholds of ultrasound-driven encapsulated microbubbles in Oldroyd-B fluids,” Nonlinear Dynamics, Vol.~114 (2026.5), 725.

A paper has been published from Nonlinear Dynamics (a top 10% journal; JCR 2024, JIF percentile: 93% in Mechanics; IF: 6.0).

Abu-Nab, A.K., Kanagawa, T. and Fedorov, Y.V., “Shell–polymer coupling reorganizes nonlinear bifurcation thresholds of ultrasound-driven encapsulated microbubbles in Oldroyd-B fluids,” Nonlinear Dynamics, Vol.~114 (2026.5), 725.

Microbubbles, including those used as ultrasound contrast agents, are gas bubbles a few micrometers in diameter, coated with a thin shell, and applied in viscoelastic media such as blood or tissue for medical imaging and targeted drug delivery. This work investigates the nonlinear radial oscillations of such a shell-coated bubble driven by an acoustic standing wave in an Oldroyd-B viscoelastic liquid. The generalized Rayleigh-Plesset equation was coupled with the interfacial stress balance and the polymeric stress evolution, giving a reduced dynamical-systems formulation, which was analyzed using bifurcation diagrams, phase-space portraits, and an energy budget. As the acoustic pressure is increased, the bubble undergoes a cascade from regular periodic oscillations to multi-periodic and eventually chaotic regimes. The presence of the shell shifts the entry of this cascade, namely the first period-doubling bifurcation, from about 1.0 MPa to 1.8 MPa, an increase of about 80%, and also contracts the chaotic regions. The energy budget analysis shows that this stabilization originates from a redistribution of elastic energy between the interfacial shell and the bulk polymeric stresses. A stabilization parameter representing the balance between shell elasticity and the surrounding viscoelasticity is introduced, and the oscillation regimes are classified for representative ultrasound contrast agents (Definity, SonoVue, BR14) and a laboratory-prepared lipid shell within a single consistent model.

This work was carried out as collaborative research with applied mathematicians at Menoufia University, Egypt.