Zero‐dimensional lumped approach to incorporate the dynamic part of the pressure at vessel junctions in a 1D wave propagation model. (7th August 2018)

• Record Type: Journal Article
• Authors: van den Boom, Tim; Stevens, Raoul; Delhaas, Tammo; van de Vosse, Frans; Huberts, Wouter
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 34:Number 9(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-08-07
• Subjects: arterial network -- dynamic pressure -- junctions -- lumped approach -- 1D wave propagation; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3116
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: A benchmark study by Boileau et al tested 6 commonly used numerical schemes for 1D wave propagation, for their ability to capture the main features of pressure, flow, and area waveforms in large arteries. While all numerical schemes showed good agreement in pressure and flow waveforms for smaller arterial networks, the simplified trapezium rule method proposed by Kroon et al showed an overestimation for the systolic pressure of 1% in proximal regions and an underestimation of 3% in distal regions in comparison with the 5 other schemes when using a larger arterial network, published as the ADAN56 model. The authors attributed this difference to the neglection of the dynamic part of the pressure at vessel junctions. Carson et al resolved these differences by proposing 2 methods to implement the dynamic part of the pressure in the simplified trapezium rule method scheme. In the present study, an alternative method is introduced extending the work by Kroon et al. This alternative method consists of a new 0D element, which is placed at vessel junctions. The strength of this new element is the ease of implementation and its flexible coupling with other elements, without introducing additional degrees of freedom or the need of a penalty function. This new approach is compared with 5 other numerical schemes, which already have the dynamic part of the pressure incorporated. The new method shows excellent agreement with these schemes for the ADAN56 model. Abstract : The implementation of a new 0D junction element that incorporates the dynamic part of the pressure at junctions in 1D wave propagation models. The new 0D junction element allows for flexible coupling between 1D and 0D elements, and nonlinear pressure‐flow equations are easily incorporated, while maintaining excellent computational speed and efficiency.