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Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 156094, 10 pages
Research Article

A Numerical Method of Reduced Complexity for Simulating Vascular Hemodynamics Using Coupled 0D Lumped and 1D Wave Propagation Models

1Department of Surgery, Maastricht University Medical Center, 6202 AZ Maastricht, The Netherlands
2Department of Biomedical Engineering, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
3Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

Received 31 August 2011; Revised 11 December 2011; Accepted 13 January 2012

Academic Editor: Akira Amano

Copyright © 2012 Wilco Kroon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A computational method of reduced complexity is developed for simulating vascular hemodynamics by combination of one-dimensional (1D) wave propagation models for the blood vessels with zero-dimensional (0D) lumped models for the microcirculation. Despite the reduced dimension, current algorithms used to solve the model equations and simulate pressure and flow are rather complex, thereby limiting acceptance in the medical field. This complexity mainly arises from the methods used to combine the 1D and the 0D model equations. In this paper a numerical method is presented that no longer requires additional coupling methods and enables random combinations of 1D and 0D models using pressure as only state variable. The method is applied to a vascular tree consisting of 60 major arteries in the body and the head. Simulated results are realistic. The numerical method is stable and shows good convergence.