A reduced order model formulation for left atrium flow: an atrial fibrillation case

Abstract

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier-Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.

Keywords: Cardiovascular flows; Data-driven models; Hemodynamics; Left atrium; Patient-specific configurations; Reduced order model.

Fig. 1

Left: LA patient-specific geometry; the green surfaces are the PV inlets, while the red region is the MV outlet. Right: boundary conditions for MV flow for different scaling factors ranging in [0.5, 1.5] (the dashed line corresponds to 1)

Algorithm 1

Description of the main steps of the Offline/Online framework

Fig. 2

Sketch of the mesh. The red portion corresponds to LAA

Fig. 3

Variation of the number of modes and of the relative error with respect to the cumulative energy threshold $\epsilon$ for the Newtonian (first column) and non-Newtonian (second column) case for all the variables involved

Fig. 4

Variation in time of the relative error corresponding to the test parameters values for the Newtonian (first column) and non-Newtonian (second column) case for $m_1$, $m_2$ and $\phi$

Fig. 5

Newtonian case: qualitative comparison between FOM (top) and ROM (bottom) solutions at different times for $m_1$

Fig. 6

Casson’s case: qualitative comparison between FOM (top) and ROM (bottom) solutions, different times for $m_1$

Fig. 7

Newtonian case: qualitative comparison between FOM (top) and ROM (bottom) solutions at different times for $m_2$

Fig. 8

Casson’s case: qualitative comparison between FOM (top) and ROM (bottom) solutions at different times for $m_2$

Fig. 9

Newtonian case: qualitative comparison between FOM (top) and ROM (bottom) solutions at different times for $\phi$

Fig. 10

Casson’s case: qualitative comparison between FOM (top) and ROM (bottom) solutions at different times for $\phi$

Fig. 11

Newtonian case: qualitative comparison between FOM and ROM solutions for $\text{TAWSS}$ (panels A and B) and $\text{OSI}$ (panels D and E)

Fig. 12

Casson’s case: qualitative comparison between FOM and ROM solutions for $\text{TAWSS}$ (panels A and B) and $\text{OSI}$ (panels D and E)

Fig. 13

Description of validation experiment taken from Dueñas-Pamplona et al. (2021). A: Isometric view of the in vitro LA with inflows ${\mathcal{Q}}_{PV,i}$, mitral valve outflow ${\mathcal{Q}}_{\mathit{MV}}$ and LAA volume highlighted; B: Front view of the in vitro LA; C: Detailed view of the measurement section and plane at the in vitro LAA

Fig. 14

Comparison of mean velocity field obtained by experimental measurements (PIV, Dueñas-Pamplona et al. (2021)) Vs. OpenFOAM simulation data (top) and boundary conditions (bottom)