Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions. Application to short‐term transient and stationary hemodynamic simulation of postural changes

• Published in: International journal for numerical methods in biomedical engineering Vol. 39; no. 11; pp. e3751 - n/a
• Main Authors: Murillo, Javier, García‐Navarro, Pilar
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.11.2023; Wiley Subscription Services, Inc
• Subjects: 0D‐1D coupling; Blood vessels; Boundary conditions; Coupling; Hemodynamic responses; Hemodynamics; HUT; junctions; Maneuvers; mathematical modeling; Mathematical models; Microvasculature; Numerical models; One dimensional models; Posture; short‐term transient; Simulation; sonic flow; Subsonic flow; Supersonic flow; Transient response; Transonic flow
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.3751

When modeling complex fluid networks using one‐dimensional (1D) approaches, boundary conditions can be imposed using zero‐dimensional (0D) models. An application case is the modeling of the entire human circulation using closed‐loop models. These models can be considered as a tool to investigate short‐term transient and stationary hemodynamic responses to postural changes. The first shortcoming of existing 1D modeling methods in simulating these sudden maneuvers is their inability to deal with rapid variations in flow conditions, as they are limited to the subsonic case. On the other hand, numerical modeling of 0D models representing microvascular beds, venous valves or heart chambers is also currently modeled assuming subsonic flow conditions in 1D connecting vessels, failing when transonic and supersonic flow conditions appear. Therefore, if numerical simulation of sudden maneuvers is a goal in closed‐loop models, it is necessary to reformulate the current methodologies used when coupling 0D and 1D models, allowing the correct handling of flow evolution for both subsonic and transonic conditions. This work focuses on the extension of the general methodology for the Junction Riemann Problem (JRP) when coupling 0D and 1D models. As an example of application, the short‐term transient response to head‐up tilt (HUT) from supine to upright position of a closed‐loop model is shown, demonstrating the potential, capability and necessity of the presented numerical models when dealing with sudden maneuvers. In this work, for the first time, the limitation in the prediction and simulation in 1D network models coupled with 0D models to the subsonic flow condition, is avoided by extending the methodologies in junctions in subsonic, sonic, and supersonic flow conditions to valve modeling, vascular and heart 0D modeling. The short‐term effect of HUT in an integrated closed model of the CVS has been computed for the first time proving the potential and capability of the numerical techniques presented in the manuscript.