Construction of hybrid 1D‐0D networks for efficient and accurate blood flow simulations

• Published in: International journal for numerical methods in fluids 2023-02, Vol.95 (2), p.262-312
• Main Authors: Ghitti, Beatrice, Blanco, Pablo J., Toro, Eleuterio F., Müller, Lucas O.
• Format: Article
• Language: English
• Subjects: Accuracy; a‐priori model selection criteria; Blood; Blood flow; Blood vessels; Complexity; Computational efficiency; Computer applications; Coupling; Criteria; Flow simulation; high‐order numerical schemes/couplings; hybrid 1D‐0D networks; Mechanical properties; Methods; Modelling; Networks; reduced‐order blood flow models; Simulation
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.5149

The one‐dimensional (1D) modeling of blood flow in complex networks of vessels and cardiovascular models can result in computationally expensive simulations. The complexity of such networks has significantly increased in the last years, in terms of both enhanced anatomical detail and modeling of physiological mechanisms and mechanical characteristics. To address such issue, the main goal of this work is to present a novel methodology to construct hybrid networks of coupled 1D and 0D vessels and to perform computationally efficient and accurate blood flow simulations in such networks. Departing from both the 1D and lumped‐parameter (0D) nonlinear models for blood flow, we propose high‐order numerical coupling strategies to solve the 1D, 0D, and hybrid coupling of vessels at junctions. To effectively construct hybrid networks, we explore different a‐priori model selection criteria focusing in obtaining the best possible trade‐off between computational cost of the simulations and accuracy of the computed solutions for the hybrid network with respect to the 1D network. The achievement of the expected order of accuracy is verified in several test cases. The novel methodology is applied to two different arterial networks, the 37‐artery network and the reduced ADAN56 model, where, in order to identify the best performing a‐priori model selection criteria, the quantitative assessment of CPU times and errors and the qualitative comparison between results are carried out and discussed. A set of coupling equations to appropriately couple nonlinear 1D and lumped‐parameter (0D) models for blood flow in compliant vessels is defined. Then, a methodology for the high‐order numerical coupling between 1D and 0D vessels through hybrid junctions is proposed. Finally, an effective methodology to construct hybrid 1D‐0D networks of vessels is developed, where different a‐priori model selection criteria are explored, focusing on obtaining the best possible trade‐off between computational cost of the simulations and accuracy of the computed solutions for the hybrid network with respect to the reference 1D network.