Image illustrating the simulated propagation of ultrasonic wave in a suspension of ultrasound contrast agents. The curved separation represents an arbitrary split of the simulation domain. In the upper part of the figure, the gray scale codes the amplitude of the displacement as a function of position at a given time. In the lower part, the figure displays the random distribution of the particles. On the right hand side, an isolated particle is shown where black and gray pixels correspond, respectively, to elastic PLGA and liquid PFOB.
Typical simulated rf signals. (a) The signal in water (in black) is identical in shape to the signal generated by the emitter. In gray, the rf signal transmitted in an ultrasound contrast agent solution. The particle concentration is C = 60.41 mg/ml. Each particle is surrounded by a PLGAR capsule (see Table I). The capsule thickness tomicrosphere radius ratio T/R = 0.35. The value of the corresponding velocity (respectively, attenuation coefficient at 50 MHz) is equal to 1440 m/s (respectively, 45.1 dB/cm). (b) Backscattered rf signal obtained with the same UCA solution. The corresponding value of the relative backscattering intensity is equal to −18.4 dB/cm.
Scattering cross-section obtained with the shell model (dashed lines) and the numerical simulation (solid lines) at angles of 180° (thick lines) and 90° (thin lines) from the incident beam.
Variation of the total scattering cross-section γsca as a function of frequency between 0 and 100 MHz predicted by the shell scattering model. A resonance is obtained around 77 MHz.
Total scattering cross-section predicted by the shell model for different values of membrane thicknesses. The results are given in logarithmic scale.
Total scattering cross-section predicted by the shell model for different values of material properties. The results are given in logarithmic scale. The solid gray line corresponds to the reference material properties given in Table I. The solid black line corresponds to the material properties denoted the PLGAL in Table I. The dashed black line corresponds to the material properties denoted the PLGAT in Table I. The dashed gray line corresponds to the material reference material properties indicated in Table I with a value of PLGA mass density equal to 1.215 g/ml.
(a) Mean attenuation coefficient and (b) apparent backscattering cross-section obtained when averaging the results obtained with 15 solutions with C = 60.41 mg/ml and T/R = 0.35. The two dashed lines in (a) and (b) represent the sum and the subtraction of the mean and of the standard deviation of each quantity.
(a) Mean attenuation coefficient at 50 MHz, (b) modified backscattered intensity I B, and (c) speed of sound and as a function of UCA concentration for a ratio T/R = 0.35. The black solid lines correspond to numerical results. The two dashed lines in (a) and (b) represent the sum and the subtraction of the mean and of the standard deviation of each quantity. The gray line in (c) indicates the results obtained with a shell effective medium model. The triangles in (b) correspond to the corresponding experimental results published in Pisani et al. (2008).
(a) Mean attenuation coefficient at 50 MHz, (b) relative backscattered intensity I B, and (c) speed of sound and as a function T/R for UCA concentration C = 60.4 mg/ml. The black solid lines correspond to numerical results. The two dashed lines in (a) and (b) represent the sum and the subtraction of the mean and of the standard deviation of each quantity. The gray line in (c) indicates the results obtained with the shell effective medium model.
Density, stiffness coefficients and corresponding wave longitudinal and transverse propagation velocities (VL and VT ) of the different materials of interest. For PLGA, the first line corresponds to the reference properties (see text for details).
Number N of particles accounted for in the simulation domain, of the corresponding ultrasound contrast agent concentration, of the particle volume fraction and of the mean inter-particule distance (D 2 ).
Values of the membrane thickness and of the concentration as a function of the T/R values. Here, R = 3 μm, the number of particle N is equal to 1000 and D 2 = 25 μm.
UCA solution ultrasonic properties at C = 60.41 mg/ml for different properties of PLGA capsule (see Table I).
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