Fractional Scattering at Imperfect Ultrasonic Bio-Interfaces: Mechanical Flux, Thermochemical Proxies, and Calibration Pathways

The biological interfaces encountered by ultrasound are rarely welded in the ideal elastic sense. Around tissue–implant contacts, fibrotic capsules, thin membranes, hydrated layers, and tissue-mimicking phantoms, a weak boundary may involve finite mechanical compliance, viscoelastic memory, and local thermo-diffusive exchange. Here, we develop a forward scattering model for a plane P-wave incident from an elastic half-space onto a fractional bio-thermo-diffusive viscoelastic half-space through such an imperfect interface. Caputo-type memory is used in the viscoelastic moduli and the thermal and diffusive relaxation terms, while normal and tangential spring-layer laws describe the mechanical weakness of the contact. The formulation gives a coupled longitudinal dispersion matrix and a reduced six-amplitude interface system. In the revised flux calculation, mechanical reflection and transmission are obtained from the signed total stress–velocity work of the complete reflected and transmitted fields, so modal cross-contributions are retained. The accepted computational population contains 1326 paths and 131,361 points from sub-kilohertz frequencies to ten megahertz, with high-precision recomputation and reliability grades used where conditioning requires caution. Thermochemical quantities remain separate diagnostic channels because a physical absorption coefficient cannot be identified from the present source model. The results show parameter-dependent associations with fractional order, interface stiffness, and frequency, but they do not establish single-parameter causation. The model is therefore intended as a verification-oriented framework for future calibrated studies of weak biological interfaces, not as an experimentally validated or patient-specific predictor.