Data-driven cardiovascular flow modeling: examples and opportunities

Abstract

High-fidelity modeling of blood flow is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low spatiotemporal resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Datadriven modeling techniques have the potential to overcome these challenges and transform cardiovascular flow modeling. In this paper, we review several data-driven modeling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modeling for cardiovascular flows, including the dynamic mode decomposition (DMD), and the sparse identification of nonlinear dynamics (SINDy). All of these techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modeling techniques have the potential to transform computational and experimental cardiovascular flow research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modeling.

Sparse Identification of Variable Star Dynamics

“…We use the sparse identification of nonlinear dynamics (SINDy; Brunton et al 2016) method, which discovers equations that accurately reproduce the observed dynamics with as small a number of terms as possible. SINDy is now available as a Python module (de Silva et al 2020) and applied to numerous fields (e.g., Arzani & Dawson 2020;Guan et al 2021;Horrocks & Bauch 2020). Unlike three-dimensional hydrodynamical simulations, concise systems of governing equations are easily interpretable, similarly to those derived by a simple physical model.…”