Ph.D Scholarship Programme "Heraclitus II"

PhD thesis description:

Microbubbles with elastic integument (a.k.a. Contrast Agents or CA) are widely used in biomedical applications for better perfusion imaging¹ in regions around vital organs (e.g. Heart, Liver) where it's difficult to be done with the conventional methods. Furthermore, it has been found out² that lipids, which usually form the shell of the microbubble, can be covered by proteins or antibiotics to reach specific targets in tissues through the microcirculation.

These microbubbles are non-linear oscillators when are insonated by acoustic disturbances and they can be used in different ways:

1. They enhance the contrast between the blood circulation and the adjacent tissues in the backscatter signal. Thus, the distribution of microbubbles in space is correlated with the tissue morphology and is used, for example, in tumor detection or monitoring abdominal walls, amongst others¹.
2. Combining acoustic disturbances of small Mechanical Index MI=p_Ac/√ƒ, where ƒ: the forcing frequency and p_Ac: its amplitude, for activation and detection of bubbles with pulses of large MI for their destruction, one can estimate their replacement rate and therefore to quantify the perfusion of a region through the blood circulation (Contrast Perfusion Imaging)³.
3. Ultrasounds are useful in accelerating the release of macromolecules from the surface of the microbubbles and their subsequent connection with the targeted tissues, e.g. detection of inflammation of blood vessels (angiogenesis) and atheromatous plaque⁴. Furthermore, due to the local microcirculation, the nearby tissues open and become more receptive to transported drugs which are also released from the microbubbles (targeted drug delivery & sonoporation)⁵.

The effect of nearby tissues or adjacent bubbles has already theoretically^6,7,8 and computationally^9,10 been studied in the literature for the case of bubbles without elastic integument. These studies mainly concern the secondary Bjerknes force and whether it varies depending on the distance, the phase difference, the amplitude and the viscosity of the surrounding fluid. The theoretical studies are valid for relatively large distances between microbubbles or bubble - wall while the computational ones mainly use the Boundary Element Method (boundary integral method) which is based on potential flow theory for the computation of movement and deformation of the microbubbles, when viscous forces can be neglected. The main finding of these studies concern to the attraction or repulsion between two bubbles or a bubble and the adjacent wall, depending on whether there are oscillations in phase or out of phase. On the interaction of microbubble - rigid wall or microbubble - free surface, earlier studies^11,12, via Boundary Element Method, have shown that in the first case the microbubble always approaches the rigid wall while in the second case it may move away from the free surface depending on the initial distance. Recently, the boundary element method is used to calculate the bubble interaction with a material exhibiting elastic behavior¹³ and showed that the latter significantly affects the stability of the bubble and its collapse mechanism.

The present research effort studies the interaction between a microbubble (of order 2.5 - 4 μm) surrounded by elastic shell and an adjacent wall. The microbubble performs oscillations due to acoustic disturbance in the frequence range of ultrasounds (1 - 10 MHz), while the adjacent wall may exhibit elastic behavior. This research aims to predict the backscatter signal taking into account the effect of:

1. the parameters that define the non-linearity in the viscoelastic behavior of the material of the shell,
2. the distance from adjacent surfaces and the properties of the latter and
3. the viscous stresses that develop in relatively thin blood vessels (of order 5 - 10 μm) where bubbles intrude.

This approach will be theoretical/computational using the Boundary Element Method as a first step for assessment of the interaction between the microbubble and the adjacent surface and as a second step Finite Element Method will be used to estimate the effect of the viscous stresses when distance between the bubble and the wall becomes very small. The result will be collated with existing theoretical approaches and available experimental measurements of the collaborating laboratories.

References:

1. Kaufmann B. A., Wei K. & Lindner J. R., 2007, "Contrast Echocardiography", Curr. Probl. Cardiol. 32, 51-96.
2. Klibanov A. L., 2005, "Ligand-carrying gas-filled microbubbles: ultrasound contrast agents for targeted molecular imaging", Bioconjugate Chem. 16, 9-17.
3. Wei K., Jayaweera A. R., Firoozan S., Linka A., Skyba D. M., & Kaul S., 1998, "Quantification of myocardial blood flow with ultrasound-induced destruction of microbubbles administered as a constant venous infusion", Circulation 97, 473-483.
4. Lindner J. R., Song J., Christiansen J., Klibanov A. L., Xu G. & Lay K., 2001, "Ultrasound assessment of inflammation and renal tissue injury with microbubbles targeted to p-selectin" Circulation 104, 2107-12.
5. Dijkmans A., 2004, "Microbubbles and ultrasound: from diagnosis to therapy", Eur. Journal of Echocardiography 5 (4), 245-246.
6. Oguz H. & Prosperetti A., 1990, "A generalization of the impulse and virial theorems with an application to bubble oscillations", J. Fluid Mech. 218, 143-162.
7. Doinikov A. A. & Zavtrak S. T., 1995, "On the mutual interaction of two gas bubbles in a sound field", Phys. Fluids 7 (8), 1923-1930.
8. Pelekasis N. A., Gaki A., Doinikov A. & Tsamopoulos J. A., 2004, "Secondary Bjerknes forces and the phenomenon of acoustic streamers", J. Fluid Mech., 500, 313-347.
9. Pelekasis N. A., Tsamopoulos J. A., 1993, "Bjerknes forces between two bubbles. Part I: Response to a step chance in pressure", J. Fluid Mech. 254, 467-499.
10. Pelekasis N. A., Tsamopoulos J. A., 1993, "Bjerknes forces between two bubbles. Part II: Response to an oscillatory pressure field", J. Fluid Mech. 254, 501-527.
11. Blake J. R. & Gibson D. C., 1987, "Growth and collapse of a vapour cavity near a free surface", J. Fluid Mech. 111, 123-140.
12. Shima A. Tomita Y., Gibson D. C. & Blake J. R., 1989, "The growth and collapse of cavitation bubbles near composite surfaces", J. Fluid Mech. 203, 199-214.
13. Klaseboer E. & Khoo B. C., 2004, "An oscillating bubble near an elastic material", J. Applied Physics, 96 (10), 5808-5818.

Παραδοτέα έργου δημοσίως προσβάσιμα: 

Ph.D Thesis

9th EUROMECH Fluid Mechanics Conference, 9-13 September 2012, Rome, Italy

Published in 9th EUROMECH Fluid Mechanics Conference, 9-13 September 2012, Rome, Italy

8th National Conference "Fluid flow phenomena", 16-17 November 2012, Volos, Greece

Published in 8th National Conference "Fluid flow phenomena", 16-17 November 2012, Volos, Greece

5th BIFD International Symposium, 7-11 July 2013, Haifa, Israel

Published in 5th BIFD International Symposium, 7-11 July 2013, Haifa, Israel

1st International Conference FLOW14, 18-21 May 2014, Twente, The Netherlands

Published in 1st International Conference FLOW14, 18-21 May 2014, Twente, The Netherlands

9th National Conference "Fluid flow phenomena", 12-13 December 2014, Athens, Greece

Published in 9th National Conference "Fluid flow phenomena", 12-13 December 2014, Athens, Greece

20th European Symposium on Ultrasound Contrast Imaging, 22-23 January 2015, Rotterdam, The Netherlands

Published in 20th European Symposium on Ultrasound Contrast Imaging, 22-23 January 2015, Rotterdam, The Netherlands

8th International Congress on Computational Mechanics, 12-15 July 2015, Volos, Greece

Published in 8th International Congress on Computational Mechanics, 12-15 July 2015, Volos, Greece