Stress Field Formation for Multifrequency Vibro-acoustography Matthew W. Urban, Randall R. Kinnick, Mostafa Fatemi, James F. Greenleaf Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine Rochester, Minnesota USA Corresponding email: urban.matthew@mayo.edu Glauber T. Silva Departamento de Tecnologia da Informação, Universidade Federal de Alagoas Maceió, Alagoas, Brazil Corresponding email: glauber@tci.ufal.br Abstract —A multifrequency vibro-acoustography method is proposed that uses a multifrequency radiation stress produced by an array transducer driven with N ultrasound frequencies. The N ultrasound beams interfere at the system focus producing up to N(N-1)/2 unique difference frequencies in the radiation stress. The objective of this paper is to present the image formation theory in multifrequency vibro-acoustography systemswith experimental validation. The radiation stress generated by sector array and annular array transducersystems is analyzed theoretically. We also used a computer phantomwith small spheres to demonstrate the usefulness of multifrequency vibro- acoustography for microcalcification detection in breast imaging. The proposed method holds the potential for a large gain of information with no increase in scanning time when applied to conventional vibro-acoustography systems. Keywords-vibro-acoustography, stress field, multifrequency, ultrasound, imaging I. I NTRODUCTION Vibro-acoustography is an ultrasound based method that uses the dynamic acoustic radiation force to vibrate objects at low frequency [1, 2]. When the object vibrates it creates a sound field called acoustic emission. An image is formed by moving the localized force over an object and measuring the acoustic emission with a sensitive hydrophone. To date we have used a dual frequency excitation with two ultrasound beams at frequencies f 0 and f 0 + ∆ f, where ∆ f is typically in the kilohertz range, to create the radiation stress where the beams intersect at the system focus. Because the beams only intersect at the system focus this makes the excitation localized to a small region. Many different configurations have been studied for this dual frequency case including amplitude modulation, confocal, X-focal, sector and linear arrays [3, 4, 5]. Imagecontrast in vibro-acoustography is intrinsically linked to the value of ∆ f, and to obtain images at different values of ∆ f multiple scans are necessary. We propose an extension to the current method that uses an array transducer and creates a multifrequency stress field using N ultra sources. The resulting radiation stress can have up to N(N-1)/2 low frequency ∆ f components. Because we can acquire information at multiple values of ∆ f, the information yield per scan will increase by a factor of N(N-1)/2. In this paperwe will present the theoryfor image formation using a multifrequency stress field, specifically fo focused sector array and flat annular array transducer will compare experimental and theoretical results for the point-spread function for the sector array and show the abi to extract the information for eachof the multifrequency components. Lastly, we explore a simulation phantom provides motivation for use in vibro-acoustic mammograph II. M ETHODS A. Image Formation Theory We will analyze the multifrequency stress field formatio for sector and annular array transducers. We conside ultrasound waves in a lossless fluid with density ρ and speed of sound c. We describe the ultrasound waves in terms of t velocity potential, φ (r,t), where r is the position vector and t is time. The multifrequency dynamic radiation stress is form with N intersecting ultrasound beams focused at the s point in space. Each ultrasound beam has frequency ω n where n = 1, 2,…, N and we assume that ω m > ω n when m > n. The difference frequency produced by two beams of freque ω m and ω n is ∆ω mn = ω m - ω n . The total velocity potential of the N ultrasound beams is ( ) () 1 ˆ r, r n N j t n n t e ω φ φ = = ∑ . (1) We can calculate the dynamic radiation force at ∆ω mn on a small sphere as () ( ) 2 * 1 ˆˆ ˆ mn mn N j t m n m n m n f t a k k y e ω ω π φ φ ∆ ∆ ≠ = = ∑ , (2) where a is the radius of the sphere [6], k m = ω m /c is the m- wavenumber, ˆ mn y ω ∆ is the dynamic radiation force function for the sphere, and the symbol * denotes the complex conjugat This study was supported in part by grants EB002640, EB002167, and EB00535-03 from National Institutes of Health, and DCR2003.013 from FAPEAL/CNPq, Brazil. 2005 IEEE Ultrasonics Symposium 0-7803-9383-X/05/$20.00 (c) 2005 IEEE 2275