Surrogate Modelling and Simulation Approaches for Renal Artery Haemodynamics: Balancing Symmetry in Computational Cost and Accuracy

Finite element analysis (FEA)-based computational fluid dynamics (CFD) simulations are essential in biomedical engineering for studying haemodynamics, yet their high computational cost limits large-scale parametric studies. This paper presents a comparative analysis of FEA and surrogate modelling techniques applied to renal artery haemodynamics. The aortic–renal bifurcation strongly influences renal perfusion, affecting conditions such as hypertension, infarction, and transplant rejection. This study evaluates GPU-accelerated voxel simulations (Ansys 2024 R2 Discovery), 2D and 3D FEA simulations (COMSOL Multiphysics 6.3), finite volume CFD (Ansys 2020 R2 Fluent), and deep neural networks (DNNs) as surrogate models. Branching angles and blood pressure were systematically varied, and their effects on velocity, pressure, and turbulent kinetic energy were assessed in a time-dependent framework. Fluent provided accurate baseline results, while COMSOL 2D gave sufficient accuracy with much lower runtimes. In contrast, COMSOL 3D required over 160 times longer, making it prohibitive. Surrogate models trained on 6500 or more FEA-derived samples achieved high predictive accuracy (R2 > 0.98 for velocity and pressure), balancing training cost and result quality. Cost analysis showed surrogate models become advantageous after 76–93 simulations. Symmetry is expressed in balancing model fidelity and computational efficiency, providing a resource-effective methodology with broad potential in vascular applications.