Amin Jafari Sojahrood

Surface modes and acoustic scattering of microspheres and ultrasound contrast agents.

Surface modes of spherical objects subject to ultrasound excitation have been recently proposed to explain experimental measurements of scattering from microspheres and ultrasound contrast agents (UCAs). In this work, the relationship between surface modes and resonance frequencies of microspheres and UCAs is investigated. A finite-element model, built upon the fundamentals of wave propagation and structural mechanics, was introduced and validated against analytical solutions (error <5%). Numerical results showed the existence of a systematic relationship between resonance frequencies and surface modes of a 30 μm microsphere driven at 1-70 MHz. On the contrary, for a 100 nm shelled, 4 μm diameter UCA, no clear relationship between the resonance frequencies and the surface modes was found in the frequency range examined. Instead, the UCA exhibited a collection of complex oscillations, which appear to be a combination of various surface modes and displacements. A study of the effects of varying the shell properties on the backscatter showed the presence of peaks in the backscatter of thick-shelled UCAs, which are not predicted by previous models. In summary, this work presents a systematic effort to examine scattering and surface modes from ultrasound contrast agents using finite-element models.

Numerical investigation of the subharmonic response of a cloud of interacting microbubbles

Microbubbles (MBs) usually exist in polydisperse populations and often strongly interact with each other. Accurate investigation of the dynamics of the MBs requires considering the interaction between Microbubbles. We have developed an efficient method for numerically simulating N interacting MBs. The subharmonic (SH) responses of a polydispersions of 3-52 microbubbles with sizes between 2-5 microns, excited with ultrasound with a frequency and pressure of 1.8-8 MHz and 1-500 kPa were investigated. We show that if the frequency is set to the SH resonance of the larger MBs, the smaller MBs oscillations are controlled by the larger MB and the SH amplitude of the population of MBs increases. For small enough distances between MBs, one large MB may control the oscillations of the rest. If the excitation frequency is equal to the SH resonance of the smaller MBs, there exists two pressure regions. For lower pressures, the oscillations of the larger MB are out of phase with the smaller MBs and the resulting SH a...

Towards the accurate characterization of the shell parameters of microbubbles based on attenuation and sound speed measurements

Measurements of microbubble (MB) shell parameters is a challenging task because of the nonlinear dynamics of MBs. Shell parameter estimations that are typically based on solving linear models will generate inaccurate results, especially at higher pressure excitations. These approaches also often ignore the analysis of sound speed which provides useful information about the bulk modulus of the medium. In addition, the effect of MB-MB interaction is neglected. In this work, the attenuation and sound speed of monodisperse MB populations with mean diameters of 4 to 6 micron and peak concentrations of 1000 to 15000 bubbles/ml are measured for a pressure range of 10 to 100 kPa. The subharmonic pressure threshold of the solution was measured by narrowband excitations spanning from 1 to 4 MHz. The subharmonic generation pressure threshold was used to estimate an initial guess for shell viscosity and surface tension. The experimental results were fitted using numerical simulations of the Marmottant model and our r...

Numerical investigation of the nonlinear dynamics of interacting microbubbles

The successful application of MBs requires detailed understanding of the nonlinear behavior of microbubbles (MBs), especially in polydisperse clouds, where the dynamic of every individual MB affects the other MBs. However, there is not enough information on how the nonlinear oscillations of one MB influences the other and vice versa. In this work the dynamics of 2 and 3 interacting MBs of initial radii of 1μm<R0<4 μm are studied by investigating the pressure dependent resonance curves and the bifurcation diagrams of the MBs (1 MHz<f<15 MHz, 1 kPa<p<1 MPa) for cases of no interaction and interaction with varying MB-MB distances. Results show that, for small enough distances, the pressure dependent resonance frequencies (fr) and the pressure threshold for harmonic and SH fr decreases. The larger MB may force new peaks in the resonance curves of the smaller MB at fr, harmonic fr and SH fr of the larger MB. The larger MB can control the dynamics of the smaller MB and force the smaller MB to exhibit the same n...

Nonlinear model of acoustical attenuation and speed of sound in a bubbly medium

The presence of microbubbles (MBs) in a medium changes the mediums acoustic properties and increases the attenuation of the bubbly medium. Current models of ultrasound attenuation in a bubbly medium are based on linear approximations; that is MB undergoes very small amplitude oscillations. Thus linear models of attenuation are not valid in many regimes used in diagnostic and therapeutic ultrasound applications. In this study, a model is developed that incorporates the nonlinear attenuation and sound speed by deriving the complex wave number from the Calfish model for the propagation of acoustic waves in a bubbly medium. Using the methods of nonlinear dynamics, we have classified the behavior of MBs for a wide range of frequencies and applied pressures. The results of the bubble oscillations are visualized using the bifurcation diagrams of the radial oscillations of the MBs as a function of the incident pressure. It is shown that depending on the frequency of the ultrasound wave, the nonlinear oscillations of the MBs can be classified into 5 main categories in which the MBs oscillations exhibit: 1. Linear resonance (fr), 2. Pressure-dependent resonance (fs), 3. Sub Harmonic (SH) resonance (fSH), 4. Pressure-dependent SH resonance (fpSH) and 5. Higher order SH resonance oscillations (fn). Results show that when MBs are sonicated by their fr, the effective attenuation of the medium can potentially decrease as the pressure increases, which is in good agreement with experimental observations. When sonicated with their fs, the effective attenuation of the medium is smaller than in the case of fr. This happens only below a pressure threshold that corresponds to the saddle node bifurcation in the corresponding bifurcation diagram. Above this pressure, the effective attenuation and sound speed increase abruptly by ~5 and ~2 folds, respectively. In the other classified sonication regimes (fSH, fsSH and fn) (3-5), the attenuation and sound speed changes are negligible below the pressure threshold corresponding to the SH oscillations. As soon as the pressure increases above the threshold for SH oscillations (e.g. period doubling in the bifurcation diagram), the effective attenuation increases abruptly (~ up to 3 fold), however the maximum exhibited attenuation is ~10 to 50 folds smaller than the maximum attenuation in case of sonication with fr and fs.

Numerical and experimental classification of the oscillations of single isolated microbubbles: Occurrence of higher order subharmonics

Imaging and therapeutic applications of micro bubbles (MBs) in medical ultrasound are rapidly increasing. Despite the many theoretical and experimental investigations of MB dynamics, the MB behavior is considered to be very complex and difficult to control. The optimization of microbubble composition and ultrasound exposure parameters requires detailed knowledge of the behavior of MBs over a large range of the control parameters of the system (e.g. pressure, frequency, MB size, MB shell composition). In this work, the dynamics of microbubbles consisting of viscoelastic shells were studied both numerically and experimentally. Polydisperse dilute solutions of Artenga MBs (Artenga Inc.) were sonicated at the frequency of 25 MHz using pulse trains of 30 cycles with a Vev0770 ultrasonic machine. For each sonication the driving pressure were varied between 100 kPa to 3.8 MPa. The backscatter signals from single MBs were isolated and analyzed further. The Hoff model for viscoelastic shell MBs was numerically solved for a wide range of MB sizes and driving acoustic pressures at 25 and 55 MHz. The results of the numerical simulations were visualized using bifurcations diagrams (MB expansion ratio versus MB size and acoustic pressure). The bifurcation structure of the viscoelastic MBs, to our best knowledge for the first time, classified the dynamics over a large range of exposure parameters, predicting the existence of higher order subharmonics. In agreement with experimental observations, simulations predict the generation of oscillations including period 2, period 3, period 4 and period 5 in the case of the sonication of polydisperse MB sizes at pressure values above specific thresholds. Another interesting finding is the differentiation between different regimes of period 4 oscillations, observed both experimentally and numerically. Numerical simulations reveal that depending on the MB size, an increase in acoustic pressure can result in oscillations that can undergo two successive period doublings from period two to period 4 or directly from period one to period 4. The dynamic characteristics of these two types of oscillations are for the first time studied in detail. In addition, frequency analysis of the ring-down oscillations of the MBs in experiments is in good agreement with the size predictions of the numerical simulations. The higher period oscillations from bigger MBs at higher frequencies may provide significant advantages for imaging, drug delivery and clot lysis ultrasound applications. These include stronger SHs or UHs signals which are closer to the transducer resonant frequency and higher and longer lasting shear stresses on the nearby cells.

On amplification of radial oscillations of microbubbles due to bubble-bubble interaction in polydisperse microbubble clusters under ultrasound excitation

Optimizing the performance of microbubbles (MBs) in applications not only requires a good understanding of the dynamics of individual MBs, but also knowledge of their interactions with each other within polydisperse clusters. However, the behavior of acoustically driven MB clusters is not well understood. Most studies have been limited to cases of a few interacting MBs for a limited range of acoustical parameters. We use a numerical method to simulate the dynamics of clusters of (20–50 MBs) randomly distributed MBs. MBs with the size distribution of 2–8 micron were sonicated with pressures between 1 and 250 kPa, frequencies between 0.5 and 10 MHz and concentrations between 2e3 and 2.5e6 MBs/mL. Bifurcation structures of radial oscillations of each MB within a cluster were studied. Results show that in a polydisperse MB cluster, larger MBs (even in small numbers) can amplify the radial oscillations of smaller MBs. Amplification occurs if the resonance peaks of larger MBs coincide with the resonance peaks of smaller MBs. Additionally, there is an optimum number density at which amplification is maximized. Results suggest that the presence of bigger MBs may enhance the superharmonic oscillations of the smaller MBs which can be applied in superhamonic ultrasound imaging using MBs.Optimizing the performance of microbubbles (MBs) in applications not only requires a good understanding of the dynamics of individual MBs, but also knowledge of their interactions with each other within polydisperse clusters. However, the behavior of acoustically driven MB clusters is not well understood. Most studies have been limited to cases of a few interacting MBs for a limited range of acoustical parameters. We use a numerical method to simulate the dynamics of clusters of (20–50 MBs) randomly distributed MBs. MBs with the size distribution of 2–8 micron were sonicated with pressures between 1 and 250 kPa, frequencies between 0.5 and 10 MHz and concentrations between 2e3 and 2.5e6 MBs/mL. Bifurcation structures of radial oscillations of each MB within a cluster were studied. Results show that in a polydisperse MB cluster, larger MBs (even in small numbers) can amplify the radial oscillations of smaller MBs. Amplification occurs if the resonance peaks of larger MBs coincide with the resonance peaks o...

Effect of ultrasound pressure and bubble-bubble interaction on the nonlinear attenuation and sound speed in a bubbly medium

The presence of bubbles changes the attenuation and sound speed of a medium. These changes in medium properties depend on the nonlinear behavior of bubbles which are not well understood. Previous studies employed linear models for the calculation of the attenuation and sound speed of bubbly mediums. These predictions are not valid in the regime of nonlinear oscillations. In addition, bubble-bubble interactions are often neglected. In this work, we have numerically simulated the attenuation and sound speed of a bubbly medium by solving a recently developed nonlinear model and considering the bubble-bubble interactions. A cluster of 52 interacting bubbles was simulated, with sizes derived from experimental measurements. Broadband attenuation measurements of monodisperse solutions were performed with peak pressures ranging within 10-100 kPa. The bubble solutions had mean diameters of 4-6 micron and peak concentrations of 1000 to 15000 bubbles/ml. At lower concentrations (with minimal microbubble interactions...

Development of a nonlinear model for the pressure dependent attenuation and sound speed in a bubbly liquid and its experimental validation

Presence of the MBs in the sound field increases the attenuation of the medium and changes the sound speed. A detailed knowledge about the attenuation of the medium is critical for controlling and optimizing the behavior of the MBs in applications. However, existing models of ultrasound attenuation in bubbly mediums are based on linear approximations (low amplitude MB oscillations) and thus are not valid in many regimes used in applications. A model to calculate the nonlinear attenuation and sound speed is developed by deriving the complex and real part of the wave number from the Calfish model. The predictions of the model were validated by measuring the attenuation and sound speed of dilute monodisperse MB solutions (5000 microbubbles/ml) with median diameter of 5.2 and 9.8 µm using acoustic pressure range of 10–130 kPa. The attenuation of the medium was calculated by numerically solving the radial oscillations of the MB and incorporating it in the attenuation model. Predictions of the model were in goo...

Pressure dependence of the attenuation and sound speed in a bubbly medium: Theory and experiment

Existence of bubbles in a medium changes the attenuation and sound speed (Cs) of the medium. The relationship between the nonlinear oscillations of the MBs and acoustical parameters of the medium is not fully understood. In this work, monodisperse solutions of lipid coated bubbles with mean diameter of 5.2 micron and peak concentration of (5000 microbubbles/ml) were sonicated with a broadband pulse with center frequency of 2.25 MHz. The attenuation and Cs, were measured over a pressure range of 10-100 kPa. Using our recent nonlinear model and by solving the Marmattont Model, the attenuation and Cs of the solution were numerically analyzed. Experimental results showed that as the pressure increased, the attenuation peak increased by ~7-8 dB while its frequency decreased from 2.05 to 1.55 MHz. The maximum Cs of the medium increased with pressure (1521 to 1529 m/s) and shifted towards lower frequencies (2.34 to 1.95 MHz). At a fixed frequency (e.g., 1.65 MHz) the Cs increased by ~14%. The Cs of the bubbly me...