| The spectral analysis of echo signals from linear and non-linear scatterers is important for understanding ultrasound contrast microbubble (MB) behavior and assisting pulse design. Most pulse designs assume a theoretical MB behavior instead of using experimental data despite it being accepted that theoretical models have not succeeded in describing MB behavior. Fourier transform (FT) based non-parametric spectral analysis methods are widely used but have limitations. This study is the first to incorporate receiver characteristics and to introduce a parametric model for the estimation of temporal and spectral content of experimental echo signals. This study improves spectral analysis performance and helps understand MB behavior. A modified scanner (Sonos5500 Philips Medical Systems, MA, USA) is used to acquire echo signals from linear scattering copper spheres. The transmit pulses are 6-cycle sinusoidal signals with fundamentals 1.28 to 3.7MHz. The receiver characteristic is accounted by deconvolving the received signals with the receiver response; the deconvolution filter is designed by analyzing the theoretical and experimental solid sphere echo signals. The filtered echo signal is then modeled as a sum of sinusoids embedded in noise. Bayesian inference is used to obtain the posterior density of the frequencies present, and numerical estimates are obtained using reversible jump Markov chain Monte Carlo techniques. The performance of our algorithm is compared with a ground truth by analyzing synthetic data. Evaluated over many Monte Carlo runs the average error is just 0.01%. Our method is then applied to real experimental data generated with a transmit pulse with fundamental f0=1.28MHz and peak negative pressure 300kPa. The Bayesian method also detects subharmonics at 0.5f0 and ultraharmonics at 1.5f0 or 2.5f0; this is important for the analysis of MB behavior. When the receiver response is not taken into account, frequency estimation errors result; if f0 lies in a region where the receiver attenuates the signal, f0 is not correctly identified: the largest peak occurs at 2.52MHz and is misidentified as the f0 rather than a harmonic. Incorporating the receiver response into the analysis results in correct detection of f0. The frequency content of the received MB signal using the FT results in peaks at 2.60, 2.98, 3.25, 3.52 and 3.75MHz. Some of these peaks are spurious, whereas our method produces three frequencies at 2.52, 3.13 and 3.78MHz. These are the 2nd, 2.5th and 3rd harmonics, consistent with the transmitted pulse. This study presents a robust temporal and spectral estimation algorithm and accounts for the receiver response. The superiority of our new method over the FT is demonstrated and the method will help with understanding MB behavior. This may also progress to the automatic classification of echo signals and is intended to be used for adaptive pulse sequence design. |