One-dimensional modeling of blood flow: A comprehensive yet concise review

Abstract

One-dimensional (1D) blood flow simulations are extensively used in cardiovascular research due to their computational efficiency and effectiveness in analyzing pulse wave dynamics. Despite their versatility and simplicity, there is a lack of a unified, step-by-step guide integrating theoretical derivations with practical implementation details. In this work, we summarize key components for comprehensive 1D blood flow simulations, including the derivation of reduced-order governing equations, the method of characteristics (Riemann invariants), a finite volume-based numerical scheme, boundary conditions (application of Riemann invariants for reflective/non-reflective and 3-element Windkessel outlet boundaries), junction treatments, verification of presented methodologies, and relevant practical applications. Additionally, we provide detailed step-by-step instructions for implementing the numerical scheme, applying boundary conditions, and treatment of junctions. By integrating rigorous theory with practical guidance for implementation, we seek to improve accessibility of 1D blood flow simulations. We anticipate that this guide will serve as a valuable resource and foundational reference for both novice and experienced researchers in cardiovascular modeling.