Discrete echo signal modeling of ultrasound imaging systems

Abstract

In this paper, a discrete model representing the pulse-tissue interaction in the medical ultrasound scanning and imaging process is developed. The model is based on discretizing the acoustical wave equation and is in terms of convolution between the input ultrasound pulses and the tissue mass density variation. Such a model can provide a useful means for ultrasound echo signal processing and imaging. Most existing models used for ultrasound imaging are based on frequency domain transform. A disadvantage of the frequency domain transform is that it is only applicable to shift-invariant models. Thus it has ignored the shift-variant nature of the original acoustic wave equation where the tissue compressibility and mass density distributions are spatial-variant factors. The discretized frequency domain model also obscures the compressibility and mass density representations of the tissue, which may mislead the physical understanding and interpretation of the image obtained. Moreover, only the classical frequency domain filtering methods have been applied to the frequency domain model for acquiring some tissue information from the scattered echo signals. These methods are non-parametric and require a prior knowledge of frequency spectra of the transmitted pulses. Our proposed model technique will lead to discrete, multidimensional, shift-variant and parametric difference or convolution equations with the transmitted pulse pressure as the input, the measurement data of the echo signals as the output, and functions of the tissue compressibility and mass density distributions as shift-variant parameters that can be readily identified from input-output measurements. The proposed model represents the entire multiple scattering process, and hence overcomes the key limitation in the current ultrasound imaging methods.