Filip Bělík

Henry Crandall, Tyler Schuessler, Filip Bělík et al.

Wearable technologies have the potential to transform ambulatory and at-home hemodynamic monitoring by providing continuous assessments of cardiovascular health metrics and guiding clinical management. However, existing cuffless wearable devices for blood pressure (BP) monitoring often rely on methods lacking theoretical foundations, such as pulse wave analysis or pulse arrival time, making them vulnerable to physiological and experimental confounders that undermine their accuracy and clinical utility. Here, we developed a smartwatch device with real-time electrical bioimpedance (BioZ) sensing for cuffless hemodynamic monitoring. We elucidate the biophysical relationship between BioZ and BP via a multiscale analytical and computational modeling framework, and identify physiological, anatomical, and experimental parameters that influence the pulsatile BioZ signal at the wrist. A signal-tagged physics-informed neural network incorporating fluid dynamics principles enables calibration-free estimation of BP and radial and axial blood velocity. We successfully tested our approach with healthy individuals at rest and after physical activity including physical and autonomic challenges, and with patients with hypertension and cardiovascular disease in outpatient and intensive care settings. Our findings demonstrate the feasibility of BioZ technology for cuffless BP and blood velocity monitoring, addressing critical limitations of existing cuffless technologies.

Filip Bělík, Jesse Chan, Akil Narayan

In many applications, one seeks to approximate integration against a positive measure of interest by a positive discrete measure: a numerical quadrature rule with positive weights. One common desired discretization property is moment preservation over a finite dimensional function space, e.g., bounded-degree polynomials. Carathéodory's theorem asserts that if there is any finitely supported quadrature rule with more nodes than the dimension of the given function space, one can form a smaller (and hence more efficient) positive, nested, quadrature rule that preserves the moments of the original rule. We describe an efficient streaming procedure for Carathéodory-Steinitz pruning, a numerical procedure that implements Carathéodory's theorem for this measure compression. The new algorithm makes use of Givens rotations and on-demand storage of arrays to successfully prune very large rules whose storage complexity only depends on the dimension of the function space. This approach improves on a naive implementation of Carathéodory-Steinitz pruning whose runtime and storage complexity are quadratic and linear, respectively, in the size of the original measure. We additionally prove mathematical stability properties of our method with respect to a set of admissible, total-variation perturbations of the original measure. Our method is compared to two alternative approaches with larger storage requirements: non-negative least squares and linear programming, and we demonstrate comparable runtimes, with improved stability and storage robustness. Finally, we demonstrate practical usage of this algorithm to generate quadrature for discontinuous Galerkin finite element simulations on cut-cell meshes.