ABSTRACT In a previous work, we developed a consistent TAC (tissue attenuation coefficient) estimator using bubble echoes. Based on temporal averaging, we can improve the estimation precision of TAC for the tissue bounded between two vessels. In this paper, we extend it to use frequency diversity for saving interrogation time by transmit multiple narrowband signals in each pulse. At first, we analyze the deterministic and stochastic properties of the diversity signals. Then a multi-band maximum likelihood diversity combiner is developed. We also provide diversity gains of different diversity estimators for comparing their estimation efficiencies. In the experimental work, we design a simplified phantom for demonstrating the performance of the purposed estimator. It is shown that the TAC estimation rate can be improved by frequency diversity. The convergence rates of single-band and multi-band estimators are compared and it is shown that the multi-band estimator is more consistent than the single-band estimator.
Cite this paper
Tsao, S. and Tsao, J. (2012) Tissue attenuation coefficient estimation using bubble harmonics with frequency diversity. Journal of Biomedical Science and Engineering, 5, 276-284. doi: 10.4236/jbise.2012.55035.
 Kuc, R. and Schwartz, M. (1979) Estimating the acoustic attenuation coefficient slope for liver from reflected ultrasound signals. IEEE Transactions on Sonics and Ultrasonics, SU-26, 353-362.
 Kuc, R. (1984) Estimating acoustic attenuation from reflected ultrasound signals: Comparison of spectral-shift and spectral-difference approaches. IEEE Transactions on Acoustics, Speech and Signal Processing, 32, 1-6.
 Tsao, S.K. and Tsao, J. (2010) A consistent tissue attenuation coefficient estimator using bubble harmonic echoes. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 57, 2654-2661.
 Shi, W.T. and Forsberg, F. (2000) Ultrasonic characte-rization of the nonlinear properties of contrast microbubbles. Ultrasound in Medicine and Biology, 26, 93-104.
 Miller, D.L. (1978) Ultrasounic detection of resonant cavitation bubbles in a flow tube by their second-harmonic emissions, Ultrasonics, 19, 217-224.
 Newhouse, V.L. and Shankar, P.M. (1984) Bubble size measurements using the nonlinear mixing of two frequencies. Journal of Acoustical Society of America, 75, 1473-1477. doi:10.1121/1.390863
 Bridal, S.L., Beyssen, B., Fornes, P., Julia, P. and Berger, G. (2000) Multiparametric attenuation and backscatter images for characterization of carotid plaque. Ultrasonic Imaging, 22, 20-34.