α-Cut PDE-Constrained Optimization for Patient-Specific Pulse-Wave Propagation in Elastic Arteries

Abstract

Pulse-wave analysis underpins vascular diagnosis and endovascular planning, yet patient-specific calibration is hampered by epistemic uncertainty in vessel properties, boundary data, and afterload. We present an α-cut PDE-constrained optimization framework that fits a 1D elastic-artery hemodynamic model to clinical waveforms while propagating uncertainty from fuzzy priors on wall stiffness, geometry, viscosity, and Windkessel elements. At each α-level, the feasible set U_α defines nested parameter boxes; a simultaneous multi-scenario program is solved with adjoint-based gradients and projected quasi-Newton/SQP, yielding nominal estimates and α-indexed prediction bands for pressure/flow, wall-shear surrogates, and pulse-wave velocity (PWV). A worked, physiologic example demonstrates the pipeline: automated diastolic-tail fitting recovers afterload time constant τ and R_1 -C-R_2; geometry-derived Moens–Korteweg PWV falls within 5.37–5.94 m/s along a 30 cm segment; inlet pressure is reproduced with RMSE = 3.61 mmHg and peak-timing error = 9 ms. α-robust calibration tightens uncertainty envelopes as α increases (e.g., ±10% → ±3% amplitude bands from α = 0.2 to 0.8) and stabilizes parameters that are otherwise weakly identifiable. The method is computationally tractable (forward + adjoint per scenario), seamlessly integrates with standard vascular modeling tools, and produces clinician-interpretable bands that support threshold-based decisions (e.g., PWV cut-offs, peri-procedural pressure limits). Extensions to viscoelastic walls, type-2 fuzzy sets, and 3D–1D coupling are straightforward within the same α-cut/adjoint structure.