Fractional Scattering at Imperfect Ultrasonic Bio-Interfaces: Mechanical Flux, Thermochemical Proxies, and Calibration Pathways
Year: 2026
Type: article
Abstract: 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.
Source: Mathematics
DOI: 10.3390/math14162955
Authors: Amr M. Y. Abdelaty, Ibrahim S. Elshazly
Institution: King Saud University
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: King Saud University
OpenAlex ID: W7203602348