Closed-form weak-wave propagation pressure amplitudes for arbitrary power-law attenuation

Biological tissues exhibit power-law frequency dependence of the attenuation coefficient. We derive closed-form weak-wave expressions for fundamental, second-, and third-harmonic pressure amplitudes of monochromatic acoustic plane waves in homogeneous media with arbitrary power-law attenuation to extend classical expressions for quadratic attenuation. For linear frequency dependence of attenuation, one-dimensional simulations using the k-Wave k-space pseudospectral solver yielded 35%-42% (classical) and 0%-2% (proposed) normalized root mean square errors for fundamental-band depletion. This extension supports improved fundamental-band B/A estimation for quantitative ultrasound tissue characterization. A proof-of-concept through-transmission application in phantoms with nearly linear attenuation yielded experimental B/A estimation errors of 23.7%-52.7% (classical) and 4.0%-5.9% (proposed).