NUMERICAL MODELING OF ULTRASOUND IMAGING USING CONTRAST AGENTS FOR PARTICLE IMAGE VELOCIMETRY IN VIVO O.M. Mukdadi 1 , H.B. Kim 1 , J.R. Hertzberg 1 , and R. Shandas 1,2 1 Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309 2 Department of Pediatric Cardiology, The Children’s Hospital, Denver, CO 80218 ABSTRACT Non-invasive in vivo medical ultrasound imaging using contrast agents requires further physical understanding of ultrasound wave propagation phenomenon in tissue and scattering from microbubbles. Cumulative nonlinearity exhibited by wave motion in tissue and local nonlinearity by microbubble dynamics are strongly influence the imaging technique and microbubble detectability. The wave propagation in tissue is studied using KZK-type parabolic evolution equation. This model considers ultrasound beam diffraction, attenuation, and tissue nonlinearity. Pressure-wave scattering from microbubbles, seeded in the blood stream, is modeled using Rayleigh-Plesset-type equation. The continuity and the radial-momentum equations of encapsulated microbubbles are employed to account for the lipid layer surrounding the microbubble. Numerical results show the effects of tissue and microbubble nonlinearities on pressure-wave propagation and scattering. These nonlinearities have a strong influence on the waveform distortion and harmonic generation. Results also show that microbubbles have stronger nonlinearity than that of tissue, and thus improves signal-to-noise ratio. 1. INTRODUCTION Non-invasive ultrasound imaging offers a means for characterizing blood flow [1], arterial-wall shear stresses [2], macro and micro opaque flows [3], and tissue imaging [4]. Nonlinear effects accompanying the propagation of intense ultrasound beam are known to distort the wave profile and generate harmonic components. Earlier work [5], we assumed linear wave propagation in tissue to investigate the non-linear wave scattering from encapsulated microbubbles. This work accounts for tissue and microbubbles nonlinearities and their influence on the wave propagation and scattering features. Modeling of wave motion in soft tissue using a parabolic approximate KZK-model is adopted. This model, which was derived by Zabolotskaya and Khokhlov [6] and Kuznetsov [7], accounts for diffraction, nonlinearity, and thermo-viscous absorption in tissue. To take advantage of nonlinear imaging technique of contrast agents, it is vital to distinguish between cumulative and local nonlinear effects. Cumulative effects arise from variation in propagation speed over the waveform, causing distortion to develop with distance, such as ultrasound propagation in tissue [8-13]. Whereas, local effects exhibited by large displacements of vibrating sources such as acoustically driven microbubbles used in contrast agents [14-17]. The focus of this work is to determine the effects of both cumulative and local nonlinearities generated from tissue and ultrasound contrast agents, respectively, and how the tissue harmonics influence the pressure scattering from microbubbles used for echo particle imaging velocimetry in vivo. Numerical treatment of KZK-equation is based on the time-domain algorithm originally developed to model plane wave propagation in thermo-viscous fluids [9]. Implicit backward finite difference (IBFD) scheme is employed to compute the pressure field propagation from a circular focused transducer. To characterize the nonlinear microbubble dynamics, a Rayleigh-Plesset-type equation is derived to account for the shell and blood properties. The extensional (breathing) mode is analyzed by considering both the continuity and the radial- momentum equations [14-17]. Adaptive time step-size is used to solve the equation of radial oscillation of a coated microbubble. The scattering pressure is thus determined by the volumetric oscillation in the domain. These microbubbles play an important role in emitting significant pressure components. The tissue-microbubble model is investigated to quantitatively compare the tissue harmonic components versus the harmonic emission from contrast agents. 2. MATHEMATICAL MODELING We consider an axi-symmetric model for single array ultrasound transducer having a circular cross-section with radius a. The transducer is perfectly placed on the body skin with no air gap. Single array excitation and scattering detector is modeled by KZK-equation for wave propagation in tissue. Pressure wave scattering from 504 0-7803-8388-5/04/$20.00 ©2004 IEEE