When acoustic waves propagate through a nonlinear reactive medium, they can generate a variety of secondary waves. This generation depends on the magnitude of the nonlinear parameter β of the medium. Large variations of β in biological tissue (from 3.5 to 6.5) are reported in the literature. Tomographic imaging of the nonlinear parameter β in human organs is currently being proposed as a potentially powerful tool in medical diagnosis. The magnitude of the generated secondary waves can be described by a line integral of the distribution of along the propaga-tion path. We analyze two types of tomographic image reconstruction of the nonlinear parameter. In one case, two primary waves of different frequencies are used to parametrically excite a difference-frequency secondary wave, which is then detected. In the other case, a single-frequency primary wave produces a second-harmonic wave, which is then detected. In this paper, we present the underlying mathematics and physical assumptions which describe the generation of the secondary waves in the above two cases. The approximations and simplifications used in image reconstruction are justified. The experimental results we have thus far obtained are stated, and possible modifications in the reconstruction algorithm and imaging system are considered.
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