A mathematical model for pressure-based organs behaving as biological pressure vessels

Non-invasive measurement of the internal pressure of a pressurized biological compartment using Lamb waves

In this study, we propose a mechanical analysis for estimating the internal pressure of a finitely deformed spherical compartment from Lamb wave measurements. The proposed analysis produces a dispersion relation associating Lamb wave speed with pressure using limited material parameters (only a strain stiffening term). The analysis was validated on ultrasound bladder vibrometry (UBV) experiments collected from 9 ex vivo porcine bladders before and after formalin cross-linking. Estimated pressures were compared with pressures measured directly by a pressure transducer. The proposed analysis proved broadly effective at estimating pressure from UBV based Lamb wave without calibration as demonstrated by the observed concordance between estimated and measured pressures (Lins CCC = 0.82 (0.66-0.91). Theoretical limitations and potential refinements to improve the accuracy and generality of the approach are discussed.