^{1,a)}, Romain Berti

^{2,b)}, Belfor Galaz

^{2,b),c)}, Nicolas Taulier

^{2,b)}, Jean-Jacques Amman

^{3}and Wladimir Urbach

^{4,b),d)}

### Abstract

A generation of tissue-specific stable ultrasound contrast agent (UCA) composed of a polymeric capsule with a perfluorocarbone liquid core has become available. Despite promising uses in clinical practice, the acoustical behavior of such UCA suspensions remains unclear. A simulation code (2-D finite-difference time domain,FDTD) already validated for homogeneous particles [Galaz Haiat, Berti, Taulier, Amman and Urbach, (2010). J. Acoust. Soc. Am.127, 148–154] is used to model the ultrasound propagation in such UCA suspensions at 50 MHz to investigate the sensitivity of the ultrasonic parameters to physical parameters of UCA. The FDTD simulation code is validated by comparison with results obtained using a shell scatterer model. The attenuation coefficient (respectively, the sound velocity) increases (respectively, decreases) from 4.1 to 58.4 dB/cm (respectively, 1495 to 1428 m/s) when the concentration varies between 1.37 and 79.4 mg/ml, while the backscattered intensity increases non-linearly, showing that a concentration of around 30 mg/ml is sufficient to obtain optimal backscattering intensity. The acoustical parameters vary significantly as a function of the membrane thickness, longitudinal and transverse velocity, indicating that mode conversions in the membrane play an important role in the ultrasonic propagation. The results may be used to help manufacturers to conceive optimal liquid-filled UCA suspensions.

The authors B.G., R.B., N.T., and W.U. acknowledge the financial support from ANR (Agence Nationale de la Recherche, ACUVA n° NT05-3_42548) and from EC-FP6-project DiMI, LSHB-CT-2005-512146.

I. INTRODUCTION

II. MATERIALS AND METHODS

A. Two-dimensional (2-D) numerical modeling

B. Simulation domain

C. Comparison between numerical approach and experiments

D. Determination of the ultrasonic parameters

III. RESULTS AND DISCUSSION

A. Analytical validation

B. Scattering response of an isolated particle

C. Ultrasound contrast agent solutions

1. Effect of concentration

2. Influence of capsule thickness

3. Effect of polymerproperties

D. Limitation of the study

### Key Topics

- Ultrasonics
- 32.0
- Backscattering
- 22.0
- Materials properties
- 18.0
- Particle scattering
- 15.0
- Suspensions
- 15.0

## Figures

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.

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 PLGA_{R} 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.

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 PLGA_{R} 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.

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 γ_{sca} as a function of frequency between 0 and 100 MHz predicted by the shell scattering model. A resonance is obtained around 77 MHz.

Variation of the total scattering cross-section γ_{sca} 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 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 PLGA_{L} in Table I. The dashed black line corresponds to the material properties denoted the PLGA_{T} 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.

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 PLGA_{L} in Table I. The dashed black line corresponds to the material properties denoted the PLGA_{T} 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 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) 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.

(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.

## Tables

Density, stiffness coefficients and corresponding wave longitudinal and transverse propagation velocities (*V _{L} * and

*V*) of the different materials of interest. For PLGA, the first line corresponds to the reference properties (see text for details).

_{T}Density, stiffness coefficients and corresponding wave longitudinal and transverse propagation velocities (*V _{L} * and

*V*) of the different materials of interest. For PLGA, the first line corresponds to the reference properties (see text for details).

_{T}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 }).

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.

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).

UCA solution ultrasonic properties at *C* = 60.41 mg/ml for different properties of PLGA capsule (see Table I).

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