Parameter estimation in fluid flow models from aliased velocity measurements

Abstract

Parameter estimation in blood flow models from measured velocity data—as e.g. velocity-encoded MRI—is a key step for patient-specific hemodynamic analysis. However, velocity encoding suffers from competing noise and aliasing artifacts, which negatively impact the parameter estimation results. The aim of this work is to propose a new inverse problem formulation capable of tackling aliased and noisy velocity MRI measurements in parameter estimation in flows. The formulation is based on a modification of the quadratic cost function for velocity measurements. This allows for a correct parameter estimation when they have influence on the whole measurement domain, in spite of aliasing artifacts. The new inverse problem can be solved numerically using any standard solver, and we show how a popular sequential approach can be applied. Numerical results in an aortic flow show robust parameter estimation for velocity encoding ranges until 30% of the maximal velocity of the problem, while the standard inverse problem fails already for any encoding velocity smaller than the true one. Moreover, the parameter estimation results are even improved for reduced velocity encoding ranges when using the new cost function. The presented approach allows therefore for great flexibility in personalization of blood flows models from MRI data commonly encountered in the clinical context.