A efficient semi-implicit finite volume method for blood flow simulation: from numerical modeling to clinical practice

Efficient mathematical models and numerical methods are increasingly important in hemodynamics, particularly for analyzing cardiovascular pathologies. By providing critical data for medical diagnosis, these computational tools mitigate the risks of invasive procedures and reduce healthcare costs. Within this framework, we present a staggered semi-implicit finite volume method for simulating one-dimensional blood flow in networks of elastic and viscoelastic vessels. The governing equations are split into three subsystems and discretized into four main stages, employing different numerical strategies according to the nature of each equation. Additionally, a three-dimensional approach is introduced for the treatment of junctions. This methodology is then extended to model two-dimensional blood flow in axially symmetric compliant vessels. Finally, the proposed numerical framework is validated against classical computational fluid dynamics benchmarks, and subsequently applied to study hemodynamics in patients with stable coronary artery disease, a pathological condition characterized by abnormal narrowing of the vessel wall.