Multi-scale 0D-1D, 0D-3D, 1D-3D coupling for cardiovascular simulation and modelling applications: A review

Mathematical modelling of systemic haemodynamics plays a crucial role in contemporary biomedical research. Clinical tasks, such as surgical planning, require a personalised and patient-specific approach for a precise mathematical formulation of problems covering all significant physiological phenomena. Application of multi-scale models assumes development of methods to couple low-dimensional and high-dimensional models, which describe interaction between local and systemic processes. Thus, it is necessary to systematise existing approaches to couple 0D, 1D and 3D blood flow models to reveal optimal techniques corresponding to specific clinical and research tasks. The aim of the present work is to classify contemporary methods for coupling multi-scale models for computational haemodynamics applications. To achieve this aim, a systematic analysis of scientific publications was performed. The publications were selected from the electronic databases Google Scholar, PubMed, ScienceDirect, ResearchGate and Scopus using the following keywords: 'coupling', '3d/0d', '1d/0d', '3d/1d', 'computational haemodynamics', 'numerical simulations', 'blood flow', 'mathematical model', 'FSI', 'CFD', 'boundary conditions', 'multiscale model', 'multidimensional model'. As a result of the analysis, the main coupling approaches were systematised and their key features, advantages and limitations were identified. The obtained results allow the most relevant coupling methods for the solution of various cardiovascular problems to be determined. This contributes to the optimisation of computational processes and enhances the reliability of predictive models in personalised medicine.