Instytut Podstawowych Problemów Techniki
Polskiej Akademii Nauk

Partnerzy

G. Schmitz



Ostatnie publikacje
1.  Mleczko M., Postema M., Schmitz G., Discussion of the application of finite Volterra series for the modeling of the oscillation behavior of ultrasound contrast agents, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2008.09.012, Vol.70, No.10, pp.1363-1369, 2009

Streszczenie:
Ultrasound contrast agents consist of microbubbles with diameters in the micrometer range. Excited by ultrasound, these bubbles exhibit highly nonlinear oscillation. While well developed physical models for microbubble oscillation exist, the efficiency of pulse sequences for sensitive microbubble detection is discussed based on simple mathematical models of general nonlinearity. Typically, Taylor series are used to model microbubble nonlinearity for the development of detection schemes. Recently, pulse sequences were proposed which exploit nonlinear memory of microbubbles, a property that cannot be modeled by a Taylor series but can be explained using a Volterra series. Therefore, this paper discusses and evaluates the usage of Volterra series for the modeling of the scattering behavior of contrast agent microbubbles. A numerically stable linear estimation algorithm is implemented to determine a third order Volterra model for a free gas bubble with a resting radius r0 1⁄4 1 lm. For insonification pressures up to 100 kPa, the identified model allowed for a mean-square error of less than 16 dB with respect to the reference signal. Analysis of the response to narrowband signals showed that the achievable mean-square error is further reduced for the bandwidth available to typical ultrasound transducers used for clinical diagnostics.

Słowa kluczowe:
Ultrasound contrast agent, Microbubble, Volterra series, Rayleigh–Plesset, System identification, Nonlinear oscillation

Afiliacje autorów:
Mleczko M. - inna afiliacja
Postema M. - inna afiliacja
Schmitz G. - inna afiliacja
20p.
2.  Postema M., Schmitz G., Ultrasonic bubbles in medicine: Influence of the shell, Ultrasonics Sonochemistry, ISSN: 1350-4177, DOI: 10.1016/j.ultsonch.2006.09.013, Vol.14, pp.438-444, 2007

Streszczenie:
Ultrasound contrast agents consist of microscopically small bubbles encapsulated by an elastic shell. These microbubbles oscillate upon ultrasound insonification, and demonstrate highly nonlinear behavior, ameliorating their detectability. (Potential) medical applications involving the ultrasonic disruption of contrast agent microbubble shells include release-burst imaging, localized drug delivery, and noninvasive blood pressure measurement. To develop and enhance these techniques, predicting the cracking behavior of ultra- sound-insonified encapsulated microbubbles has been of importance. In this paper, we explore microbubble behavior in an ultrasound field, with special attention to the influence of the bubble shell.
A bubble in a sound field can be considered a forced damped harmonic oscillator. For encapsulated microbubbles, the presence of a shell has to be taken into account. In models, an extra damping parameter and a shell stiffness parameter have been included, assuming that Hooke’s Law holds for the bubble shell. At high acoustic amplitudes, disruptive phenomena have been observed, such as microbubble fragmentation and ultrasonic cracking. We analyzed the occurrence of ultrasound contrast agent fragmentation, by simulating the oscillating behavior of encapsulated microbubbles with various sizes in a harmonic acoustic field. Fragmentation occurs exclusively during the collapse phase and occurs if the kinetic energy of the collapsing microbubble is greater than the instantaneous bubble surface energy, provided that surface instabilities have grown big enough to allow for break-up. From our simulations it follows that the Blake critical radius is not a good approximation for a fragmentation threshold.
We demonstrated how the phase angle differences between a damped radially oscillating bubble and an incident sound field depend on shell parameters.

Słowa kluczowe:
Ultrasound contrast agent, Shell disruption, Fragmentation threshold, Oscillation phase angle, Shell elasticity, Shell friction

Afiliacje autorów:
Postema M. - inna afiliacja
Schmitz G. - inna afiliacja
3.  Mleczko M., Wilkening W.G., Postema M., Schmitz G., Optimisation of pulse sequences for ultrasound contrast agent imaging, Biomedical Engineering-Biomedizinische Technik, ISSN: 1862-278X, Vol.52, No.S1, Supplement, pp.G2-1-2, 2007
4.  Postema M., ten Cate F.J., Schmitz G., de Jong N., van Wamel A., Generation of a droplet inside a microbubble with the aid of an ultrasound contrast agent: first result, Letters in Drug Design and Discovery, ISSN: 1570-1808, DOI: 10.2174/157018007778992847, Vol.4, pp.74-77, 2007

Streszczenie:
New ultrasound contrast agents that incorporate a therapeutic compound have become of interest. Such an ultrasound contrast agent particle might act as the vehicle to carry a drug or gene load to a perfused region of interest. The load could be released with the assistance of ultrasound. Generally, an increase in shell thickness increases the acoustic amplitude needed to disrupt a bubble. High acoustic amplitudes, however, have been associated with unwanted effects on cells. It would be interesting to incorporate a droplet containing drugs or genes inside a microbubble carrier. A liquid core surrounded by a gas encapsulation has been referred to as antibubble. In this paper, the creation of an antibubble with the aid of ultrasound has been demonstrated with high-speed photography.

Słowa kluczowe:
Antibubble, Ultrasound contrast agent, Drug delivery, High-speed photography

Afiliacje autorów:
Postema M. - inna afiliacja
ten Cate F.J. - inna afiliacja
Schmitz G. - inna afiliacja
de Jong N. - inna afiliacja
van Wamel A. - inna afiliacja
5.  Postema M., Schmitz G., Bubble dynamics involved in ultrasonic imaging, Expert Review of Molecular Diagnostics, ISSN: 1473-7159, DOI: 10.1586/14737159.6.3.493, Vol.6, No.3, pp.493-502, 2006

Streszczenie:
In clinical ultrasound, blood cells cannot be differentiated from surrounding tissue, due to the low acoustic impedance difference between blood cells and their surroundings. Resonant gas bubbles introduced in the bloodstream are ideal markers, if rapid dissolution can be prevented. Ultrasound contrast agents consist of microscopically small bubbles encapsulated by an elastic shell. These microbubbles oscillate upon ultrasound insonification. Microbubbles with thin lipid shells have demonstrated highly nonlinear behavior. To enhance diagnostic ultrasound imaging techniques and to explore therapeutic applications, these medical microbubbles have been modeled. Several detection techniques have been proposed to improve the detectability of the microbubbles. A new generation of contrast agents, with special targeting ligands attached to the shells, may assist the imaging of nonphysical properties of target tissue. Owing to microbubble-based contrast agents, ultrasound is becoming an even more important technique in clinical diagnostics.

Słowa kluczowe:
Detection, Harmonic imaging, Herring equation, Microbubble, Resonance, RPNNP equation, Scattering, Targeted imaging, Ultrasound, Ultrasound contrast agent

Afiliacje autorów:
Postema M. - inna afiliacja
Schmitz G. - inna afiliacja
6.  Postema M., Bouakaz A., ten Cate F.J., Schmitz G., de Jong N., van Wamel A., Nitric oxide delivery by ultrasonic cracking: Some limitations, Ultrasonics, ISSN: 0041-624X, DOI: 10.1016/j.ultras.2006.06.003, Vol.44, pp.e109-e113, 2006

Streszczenie:
Nitric oxide (NO) has been implicated in smooth muscle relaxation. Its use has been widespread in cardiology. Due to the effective scavenging of NO by hemoglobin, however, the drug has to be applied locally or in large quantities, to have the effect desired. We propose the use of encapsulated microbubbles that act as a vehicle to carry the gas to a region of interest. By applying a burst of high-amplitude ultrasound, the shell encapsulating the gas can be cracked. Consequently, the gas is released upon which its dissolution and diffusion begins. This process is generally referred to as (ultra)sonic cracking.
To test if the quantities of released gas are high enough to allow for NO-delivery in small vessels (ø < 200 lm), we analyzed high-speed optical recordings of insonified stiff-shelled microbubbles. These microbubbles were subjected to ultrasonic cracking using 0.5 or 1.7 MHz ultrasound with mechanical index MI > 0.6. The mean quantity released from a single microbubble is 1.7 fmol. This is already more than the NO production of a 1 mm long vessel with a 50 lm diameter during 100 ms. However, we simulated that the dissolution time of typical released NO microbubbles is equal to the half-life time of NO in whole blood due to scavenging by hemoglobin (1.8 ms), but much smaller than the extravascular half-life time of NO (>90 ms).
We conclude that ultrasonic cracking can only be a successful means for nitric oxide delivery, if the gas is released in or near the red blood cell-free plasma next to the endothelium. A complicating factor in the in vivo situation is the variation in blood pressure. Although our simulations and acoustic measurements demonstrate that the dissolution speed of free gas increases with the hydrostatic pressure, the in vitro acoustic amplitudes suggest that the number of released microbubbles decreases at higher hydrostatic pressures. This indicates that ultrasonic cracking mostly occurs during the expansion phase.

Słowa kluczowe:
Nitric oxide, Sonic cracking

Afiliacje autorów:
Postema M. - inna afiliacja
Bouakaz A. - Université François Rabelais (FR)
ten Cate F.J. - inna afiliacja
Schmitz G. - inna afiliacja
de Jong N. - inna afiliacja
van Wamel A. - inna afiliacja
7.  Postema M., de Jong N., Schmitz G., The physics of nanoshelled microbubbles, Biomedical Engineering-Biomedizinische Technik, ISSN: 1862-278X, Vol.50, No.S1, Supplement, pp.748-749, 2005

Streszczenie:
Nanoshelled microbubbles are suitable markers for perfused areas in ultrasonic imaging, and have potential applications in therapy. With radii up to 5 microns, their resonance frequencies are in the lower megahertz range. We explored the physics of nanoshelled microbubbles, with special attention to the influence of the nanoshell on the oscillation offset with respect to the driving phase. Microbubbles above resonance size oscillate π rad out of phase with respect to microbubbles under resonance size. As the damping becomes less, this transition in offset becomes more abrupt. Therefore, the damping due to the friction of the nanoshell can be derived from this abruptness. We support our results with some high-speed optical observations of oscillating microbubbles in an ultrasonic field.

Afiliacje autorów:
Postema M. - inna afiliacja
de Jong N. - inna afiliacja
Schmitz G. - inna afiliacja
8.  Mienkina M.P., Postema M., Hansen C., Schmitz G., Modelling ultrasonic backscattering of an SPIO-MRI contrast agent, Biomedical Engineering-Biomedizinische Technik, ISSN: 1862-278X, Vol.50, No.S1, Supplement, pp.750-751, 2005

Streszczenie:
The ultrasonic backscatter coefficient (BSC) of superparamagnetic iron oxide (SPIO) nanoparticles, which are used as a liver MRI contrast agent, was simulated using a Yagi backscattering model. The BSC of SPIO cores that are aggregated in the lysosomes of Kupffer cells is significantly higher (85 dB) than the BSC of non- aggregated SPIO cores. Considering in vivo concentrations, the aggregated SPIO does not elevate the BSC of the liver markedly (9x10-6 dB). Thus, the reported visibility of SPIO in clinical ultrasound cannot be explained by classical scattering theory. Other non-linear effects need to be taken into account.

Afiliacje autorów:
Mienkina M.P. - inna afiliacja
Postema M. - inna afiliacja
Hansen C. - CERN (CH)
Schmitz G. - inna afiliacja
9.  Chaudhry S.K., Khaled W., Postema M., Ermert H., Schmitz G., Accelerated block-based 2D motion estimation for pre-processing in elastography, Biomedical Engineering-Biomedizinische Technik, ISSN: 1862-278X, Vol.50, No.S1, Supplement, pp.637-638, 2005

Streszczenie:
In intravascular ultrasound, we investigate vessel motion due to pulsating blood flow. Relatively large lateral displacements are observed. To incorporate these, we propose an initially 2D displacement estimation based on an accelerated block matching algorithm for preprocessing. In this paper, an accelerated algorithm based on the Successive Elimination Algorithm is described. Furthermore, we evaluated the algorithm based on intravascular ultrasound data. The proposed algorithm is compared search time and identical motion field.

Afiliacje autorów:
Chaudhry S.K. - inna afiliacja
Khaled W. - inna afiliacja
Postema M. - inna afiliacja
Ermert H. - inna afiliacja
Schmitz G. - inna afiliacja
10.  Postema M., ten Cate F.J., Lancée C.T., Schmitz G., de Jong N., van Wamel A., Ultrasonic destruction of medical microbubbles: an overview, Ultraschall in der Medizin, ISSN: 0172-4614, Vol.26, pp.S32-S33, 2005

Streszczenie:
Purpose:
Ultrasound contrast agents consist of bubbles in the micrometer range encapsulated by nanoshells. These medical microbubbles oscillate linearly upon insonification at low acoustic amplitudes, but demonstrate highly nonlinear, destructive behavior at relatively high acoustic amplitudes. Therefore, medical microbubbles have been investigated for their potential applications in local drug and gene delivery. We used fast-framing photography at more than a million frames per second to investigate medical microbubbles in a diagnostic ultrasonic field. In this presentation, we give an overview of the physical mechanisms of medical microbubble destruction.

Methods and Materials:
Three ultrasound contrast agents were studied with high-speed photography during insonification. The agents were inserted through a cellulose capillary with a diameter of 0.2mm. The capillary was positioned below a microscope whose optical focus coincided with the ultrasonic focus. We captured images of insonified medical bubbles at higher frame rates than the ultrasonic frequency transmitted (typically 0.5MHz). The acoustic amplitudes corresponded to mechanical indices between 0.03 and 0.8. To compare theory and experiments, we simulated insonified medical microbubble behavior, based on the behavior of large, unencapsulated bubbles in an acoustic field.

Results:
At low acoustic amplitudes (mechanical index <0.1) bubbles pulsate moderately, as predicted from theory. At high amplitudes (mechanical index >0.6) their elongated expansion phase is followed by a violent collapse. Microbubbles have been observed to coalesce (merge), fragment, crack, and jet (act as a microsyringe) during one single ultrasonic cycle. From our observations of jetting through medical bubbles, we computed that the pressure at the tip of the jet is high enough to penetrate any human cell. One image sequence reveals the temporary formation of a liquid drop inside a microbubble.

Conclusions:
Medical microbubble oscillation and translation can be modeled using large, unencapsulated bubble theory. The number of fragments generated by untrasound-induced microbubble break-up has been related to the energy absorbed by the microbubble. Medical bubbles might be used as vehicles that carry a drug to a region of interest, where the release can be controlled with ultrasound. Liquid jets may act as microsyringes, injecting a drug into target tissue. Microbubble phenomena also have potential applications in imaging and noninvasive pressure measurements.

Słowa kluczowe:
Microbubble, Ultrasound

Afiliacje autorów:
Postema M. - inna afiliacja
ten Cate F.J. - inna afiliacja
Lancée C.T. - inna afiliacja
Schmitz G. - inna afiliacja
de Jong N. - inna afiliacja
van Wamel A. - inna afiliacja
11.  Postema M., van Wamel A., Schmitz G., de Jong N., Slingerende belletjes, gerichte medicijnbezorging en microïnjectienaalden, Klinische fysica, ISSN: 0168-7026, Vol.3+4, pp.6-9, 2004

Streszczenie:
Ultrasound contrast agents consist of microscopically small encapsulated bubbles that oscillate upon insonification. To enhance diagnostic ultrasound imaging techniques and to explore therapeutic applications, these medical bubbles have been studied with the aid of high-speed photography. We filmed medical bubbles at higher frame rates than the ultrasonic frequency transmitted. Microbubbles have - among others - been observed to fragment and jet during one single ultrasonic cycle. Gas was released from encapsulated microbubbles. It is concluded that bubbles might act as a vehicle to carry a drug in gas phase to a region of interest, where it has to be released by ultrasound whose amplitudes are still in the diagnostic range.

Słowa kluczowe:
Oscillating bubbles, Targeted drug delivery, Micro-injection needles

Afiliacje autorów:
Postema M. - inna afiliacja
van Wamel A. - inna afiliacja
Schmitz G. - inna afiliacja
de Jong N. - inna afiliacja

Lista rozdziałów w ostatnich monografiach
1. 
Postema M., Mleczko M., Schmitz G., ADVANCES IN MEDICAL ENGINEERING, rozdział: Mutual attraction of oscillating microbubbles, Publishing house Springer, pp.75-80, 2007
2. 
Hiltawsky K.M., Haisch C., Mienkina M.P., Postema M., Schmitz G., Health Academy, Molecular imaging: Innovationen und Visionen in der medizinischen Bildgebung, rozdział: Optoakustik in der medizinischen Bildgebung, pp.159-175, 2006
3. 
Postema M., Hiltawsky K.M., Schmitz G., Health Academy, Molecular imaging: Innovationen und Visionen in der medizinischen Bildgebung, rozdział: Ultraschallkontrastmittel - Grundlegende Überlegungen, pp.131-147, 2006

Prace konferencyjne
1.  Postema M., Mleczko M., Schmitz G., Contrast microbubble clustering at high MI, IUS 2006, IEEE Ultrasonics Symposium, 2006-10-02/10-06, Vancouver (CA), DOI: 10.1109/ULTSYM.2006.397, Vol.1, pp.1564-1567, 2006

Streszczenie:
The driving of contrast microbubbles towards a boundary by means of primary radiation (Bjerknes) forces has been of interest for ultrasound-assisted drug delivery. Secondary radiation forces, resulting from oscillating microbubbles under ultrasound insonification, may cause the mutual attraction and subsequent coalescence of contrast microbubbles. This phenomenon has been less studied. Microbubbles with a negligible shell can be forced to translate towards each other at relatively low mechanical indices (MI). Thick-shelled microbubbles would require a higher MI to be moved. However, at high MI, microbubble disruption is expected. We investigated if thick-shelled contrast agent microbubbles can be forced to cluster at high-MI. Two thick-shelled contrast agents, inserted through a cellulose capillary, were subjected to 3 MHz, high- MI pulsed ultrasound from a commercial ultrasound machine, and synchronously captured through a high numerical aperture microscope. The agent QuantisonTM did not translate, but showed a small percentage of disrupted bubbles. The agent M1639 showed the ultrasound-induced formation of bubble clusters, and the translation thereof towards the capillary boundary. It is concluded, that forced translation and clustering of thick-shelled contrast microbubbles is feasible.

Afiliacje autorów:
Postema M. - inna afiliacja
Mleczko M. - inna afiliacja
Schmitz G. - inna afiliacja
2.  Mleczko M., Postema M., Schmitz G., Identifying nonlinear characteristics for the bulk response of ultrasound contrast agent, IUS 2006, IEEE Ultrasonics Symposium, 2006-10-02/10-06, Vancouver (CA), DOI: 10.1109/ULTSYM.2006.350, Vol.1, pp.1369-1372, 2006

Streszczenie:
Ultrasound contrast agents consist of gas-filled microbubbles stabilized by a shell. Under ultrasound insonification, these bubbles oscillate nonlinearly with resonance frequencies being well within the diagnostic range. Currently, different detection methods are proposed, often with a heuristic reasoning based on the bubble nonlinearity being modeled by a time-invariant polynomial characteristic. However, it has been demonstrated [1] that microbubbles exhibit the behavior of a nonlinearity with memory. To optimize detection schemes, we propose to take this into account by ultrasound contrast agent modeling with a Wiener series. With these models, which can be identified from acoustic measurements, nonlinear system theory can be applied to improve detection methods. The feasibility of contrast agent modeling by Wiener series was evaluated on a contrast agent simulation, implemented by a modified Rayleigh-Plesset differential equation. For a sinusoidal input, the Wiener series approximated contrast agent behavior with a mean square error of 7.6% of the power of the contrast agent signal. The Wiener series approach was subsequently validated in an experimental setup where the nonlinear characteristics of a commercially available contrast agent were identified. The model obtained allowed for a mean square prediction error of 2.6% of the power of the measured signal for a pseudo-random multilevel sequence. With these experiments, it has been shown that the modeling of the oscillation behavior of ultrasound contrast agents with a Wiener series is feasible.

Afiliacje autorów:
Mleczko M. - inna afiliacja
Postema M. - inna afiliacja
Schmitz G. - inna afiliacja
3.  Postema M., de Jong N., Schmitz G., Nonlinear behavior of ultrasound-insonified encapsulated microbubbles, ISNA 17, Innovation in Nonlinear Accoustics: 17th International Symposium on Nonlinear Acoustics Including the International Sonic Boom Forum, 2005-07-18/07-22, State College (US), DOI: 10.1063/1.2210361, pp.275-278, 2006

Streszczenie:
Ultrasound contrast agents consist of small encapsulated bubbles with diameters below 10 μ m. The encapsulation influences the behavior of these microbubbles when they are insonified by ultrasound. The highly nonlinear behavior of ultrasound contrast agents at relatively high acoustic amplitudes (mechanical index>0.6) has been attributed to nonlinear bubble oscillations and to bubble destruction. For microbubbles with a thin, highly elastic nanoshell, it has been demonstrated that the presence of the nanoshell becomes negligible at high insonifying amplitudes. From our simulations it follows that the Blake critical radius is not valid for microbubble fragmentation. The low maximal excursion observed and simulated for a thick, stiff-shelled microbubble is in agreement with previous acoustic analyses. The ultrasound-induced gas release from stiff-shelled bubbles has been reported. However, we also observed gas release from microbubbles with a thin, elastic shell.

Słowa kluczowe:
Ultrasound contrast agent, Encapsulated microbubble, Nanoshell

Afiliacje autorów:
Postema M. - inna afiliacja
de Jong N. - inna afiliacja
Schmitz G. - inna afiliacja
4.  Postema M., de Jong N., Schmitz G., van Wamel A., Creating antibubbles with ultrasound, IUS 2005, IEEE International Ultrasonics Symposium, 2005-09-18/09-21, Rotterdam (NL), DOI: 10.1109/ULTSYM.2005.1603013, Vol.2, pp.977-980, 2005

Streszczenie:
Ultrasound contrast agents have been investigated for their potential applications in local drug and gene delivery. A microbubble might act as the vehicle to carry a drug or gene load to a perfused region of interest. The load has to be released with the assistance of ultrasound. We investigate the suitability of antibubbles for ultrasound-assisted local delivery. As opposed to bubbles, antibubbles consist of a liquid core surrounded by a gas encapsulation. Incorporating a liquid drop containing drugs or genes inside an ultrasound contrast agent microbubble, however, is technically challenging.
An ultrasound-insonified microbubble generates a pressure field that is inversely proportional to the distance from the microbubble. Therefore, an oscillating contrast agent microbubble may create a surface instability with a relatively big bubble at a short distance. For big enough instabilities, a drop may be formed inside the big bubble.
Three different contrast agents were subjected to 0.5 MHz ultrasound, with mechanical indices >0.6. The contrast agents were inserted through an artificial capillary which led through the acoustic focus of the transducer. High-speed photographs were captured at a speed of 3 million frames per second and higher. We observed that ultrasound contrast microbubbles below resonance size may create visible surface instabilities with bubbles above resonance size. With an albumin-shelled contrast agent, we induced a surface instability that was big enough to create an antibubble inside a free (unencapsulated) gas bubble with an 8 micron diameter. The surface instability has been attributed to the presence of a contrast microbubble with a 3 micron diameter. This instability has the form of a re-entrant jet protruding into the gas bubble. The inward protrusion grew and subsequently drained, leaving a droplet with a five micron diameter inside the bubble. In a subsequent recording after 100 ms, only the gas bubble could be detected. Thus, the life- time of the antibubble was less then 100 ms. The presence of a surfactant on the interfaces might lead to an improved stability of an antibubble.

Słowa kluczowe:
Antibubble, Ultrasound

Afiliacje autorów:
Postema M. - inna afiliacja
de Jong N. - inna afiliacja
Schmitz G. - inna afiliacja
van Wamel A. - inna afiliacja
5.  Postema M., de Jong N., Schmitz G., Shell rupture threshold, fragmentation threshold, Blake threshold, IUS 2005, IEEE International Ultrasonics Symposium, 2005-09-18/09-21, Rotterdam (NL), DOI: 10.1109/ULTSYM.2005.1603194, Vol.3, pp.1708-1711, 2005

Streszczenie:
The disruption of contrast agent microbubbles has been implicated in novel techniques for high-MI imaging and local drug delivery. At MI>0.6, microbubble fragmentation has been observed with thin-shelled agent (≈10nm), and shell rupture with thick-shelled agent (≈250nm). To predict the disruption of these nanoshelled microbubbles, destruction thresholds have been under investigation. In several studies, the Blake threshold pressure was associated with microbubble destruction. The Blake threshold pressure is the peak rarefactional acoustic pressure at which the critical Blake radius is reached, approximately twice the equilibrium radius, above which a bubble behaves like an inertial cavity. We studied the acoustic pressures at which a thin-shelled microbubble fragments and those at which a thick-shelled microbubble cracks. More specifically, we investigated the validity of the Blake threshold for these phenomena. The oscillating and fragmenting behavior of microbubbles with a 10nm shell was simulated at a driving frequency of 0.5–2 MHz, using a modified Rayleigh-Plesset equation and assuming that fragmentation occurs when the kinetic energy of the microbubble surpasses the instantaneous bubble surface energy. For microbubbles with radii between 1 and 6μm, the fragmentation thresholds lie between 20 and 200 kPa. Generally, the critical radius is much smaller than twice the equilibrium radius. The moment of break-up during the collapse phase is in agreement with high- speed optical observations that were presented previously.
Furthermore, the shell rupture behavior of microbubbles with a thick shell was analyzed for quasistatic pressure changes (relatively low ultrasonic frequencies), assuming that the shell obeys Hooke’s Law. The rupture threshold pressure of −80 kPa had been determined from acoustical data. For shells with the typical Young’s modulus 2MPa and Poisson ratio 0.5, this is in agreement with the observation that the maximal excursion upon rupture of such bubbles is smaller that 0.3μm.
In conclusion, we may state that the Blake threshold is neither a good estimator for the fragmentation, nor for the rupture of contrast agent microbubbles.

Słowa kluczowe:
Shell rupture, Fragmentation threshold, Blake threshold

Afiliacje autorów:
Postema M. - inna afiliacja
de Jong N. - inna afiliacja
Schmitz G. - inna afiliacja
6.  Postema M., Schmitz G., Ultrasonic fragmentation of microbubbles: a theoretical approach of the flash in flash-echo, 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2005-08-31/09-03, Shanghai (CN), DOI: 10.1109/IEMBS.2005.1615344, pp.4023-4026, 2005

Streszczenie:
Predicting the dynamic behavior of ultrasound insonified lipid-shelled microbubbles has been of much clinical interest. For perfusion measurements, a technique named flash- echo has been proposed. A burst of high-MI ultrasound is to destroy the contrast agent bubbles, supposedly resulting in a strong scattering signal that is visible on the B-mode image: the flash. The absence of this strong response in parts of the B-mode image indicates a (too) low perfusion. In this paper, we investigate how microbubbles collapse and fragment. An overview of fragmentation theory is given, followed by some high-speed optical observations of collapsing and fragmenting microbubbles in an ultrasonic field. Fragmentation occurs exclusively during the collapse phase. We hypothesize that fragmentation will only occur if and only if the kinetic energy of the collapsing microbubble is greater than the instantaneous bubble surface energy. In contradiction to the assumption that the Blake critical radius is a good approximation for a fragmentation threshold, our simulations show Rmax/R0 ≪2 for most microbubbles.

Słowa kluczowe:
Flash echo, Microbubble fragmentation, Ultrasound contrast agent

Afiliacje autorów:
Postema M. - inna afiliacja
Schmitz G. - inna afiliacja

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