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Broadband finite-element modeling codes have proven effective in the hands of medical ultrasound transducer designers. Similar modeling advantages have not yet been realized by image processing engineers concerned with aberrating media. Their principal difficulty is the much larger physical scale of bioacoustic models for imaging, e.g., a 20-cm round trip at 5 MHz is 600 wavelengths. Conventional (low order) finite-element/finite-difference wave solvers are inadequate at this scale because of cumulative numerical errors and computer limits. The solution is more accurate algorithms, based on spectral methods or high-order finite differences, in conjunction with parallel processing. The modeling problem is described, starting from a detailed transducer section, coupled to the heterogeneous abdominal wall and deeper tissue, to the scattering object(s) and back. Computed examples illustrate fundamental modeling and phenomenological issues. Solving the bioacoustic equations in the time domain is essential, and comprehensive models include both frequency-dependent absorption and second-order nonlinearity (B/A parameter). Algorithmic issues involve balanced, high-order space and time differential operators, treatment of discontinuities, radiation boundary conditions, and parallelization. The key is maintaining consistent, high-order accuracy throughout the analysis. An overall capability is demonstrated. [Work supported by DARPA, ONR, NSF, and NIH.]

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