An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

Abstract

In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

Methods of Blood Flow Modelling

“…Other dependencies [2,53,75,82,100] provide good results for arteries. The most advanced in silico studies of elastic vascular response use complex fiber reinforced material models [61,90].…”

“…In a simplified form, such models were used for studying the impacts of endovascular implants or atherosclerotic plaques to the p(A) dependence [142]. Aneurysm model was developed in [82] by parameterising pressure-to-area function along the length of the diseased vessel. Other generalizations of the elastic vessel wall model are visco-elastic wall models [2,16,25,102].…”

“…, k N } are the indices of the incident vessels, ε k = 1,x k = 0 for incoming vessels, ε k = −1,x k = L k for outgoing vessels. The other boundary conditions are N pressure drop conditions 9) or N Bernoulli integral conservation conditions expressing the total pressure continuity [3,16,82,91,100,102,120,121] 10) where p l and P l are the pressure and the total pressure at the junction point with index l, respectively. A modification of this condition accounts the angle of the vessel bifurcation [52].…”

“…For its numerical solution diverse methods have been reported. The incomplete list contains Discontinuous Galerkin and Taylor-Galerkin methods [121], second-order local conservative Galerkin method [82,95], high-order Finite Volume method [91,92], Finite Differences with artificial viscosity method [1], characteristic methods [52,67,120,124,141].…”

Robust Finite Element Approaches to Systemic Circulation Using the Locally Conservative Galerkin (LCG) Method

“…Since the width of the pressure wave produced by the heart is much greater than any vessel diameter, the one-dimensional assumption is valid for studying systemic circulation (Avolio, 1980;Alastruey et al, 2007;Steele et al, 2007;Mynard and Nithiarasu, 2008;Raines et al, 1974;Wan et al, 2002;Low et al, 2012;Stergiopulos et al, 1992;Chen et al, 2013;Blanco et al, 2012;Kufahl and Clark, 1985;Urquiza et al, 2006;Franke et al, 2002;Watanabe et al, 2013). Some of the recent publications in this area adopted Locally Conservative Galerkin (LCG) technique, which was developed in (Nithiarasu, 2004, Thomas et al, 2008 using an explicit Taylor-Galerkin method along with the characteristic variables.…”