“…At the molecular level, PDE systems (e.g., advection-diffusion-reaction equations) are broadly implemented in the vascular field to describe the transport of molecular species (e.g., low density lipoproteins, inflammatory cytokines and other pro-atherogenic species ( Silva et al, 2020 )). In addition to transport phenomena, equation-based models are adopted to evaluate the mechanical behavior or the fluid dynamics at tissue/organ scale (e.g., to quantify stresses and strains in the arterial wall or the hemodynamic variables following endovascular procedures as percutaneous transluminal angioplasty (PTA) with/without stenting ( Chiastra et al, 2021a ; Chiastra et al, 2021b ; Colombo et al, 2021a ; Colombo et al, 2021b )). Usually, given the complex geometry of the vascular segments, numerical methods, such as finite difference method, finite element method (FEM) or finite volume method, are needed to solve PDE systems associated to solid mechanics or fluid dynamics problems ( Walpole et al, 2013 ).…”