TY - JOUR
T1 - A fast algorithm for the simulation of arterial pulse waves
AU - Du, Tao
AU - Hu, Dan
AU - Cai, David
N1 - Funding Information:
This work was supported by grants National Natural Science Foundation of China 91230202 , 11471213 , 11071161 , 31571071 , and National Science Foundation DMS-1009575 , Shanghai 14JC1403800 , 15JC1400104 , the NYU Abu Dhabi Institute under grant G1301 , and HPC π at Shanghai Jiao Tong University .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - One-dimensional models have been widely used in studies of the propagation of blood pulse waves in large arterial trees. Under a periodic driving of the heartbeat, traditional numerical methods, such as the Lax-Wendroff method, are employed to obtain asymptotic periodic solutions at large times. However, these methods are severely constrained by the CFL condition due to large pulse wave speed. In this work, we develop a new numerical algorithm to overcome this constraint. First, we reformulate the model system of pulse wave propagation using a set of Riemann variables and derive a new form of boundary conditions at the inlet, the outlets, and the bifurcation points of the arterial tree. The new form of the boundary conditions enables us to design a convergent iterative method to enforce the boundary conditions. Then, after exchanging the spatial and temporal coordinates of the model system, we apply the Lax-Wendroff method in the exchanged coordinate system, which turns the large pulse wave speed from a liability to a benefit, to solve the wave equation in each artery of the model arterial system. Our numerical studies show that our new algorithm is stable and can perform ~15 times faster than the traditional implementation of the Lax-Wendroff method under the requirement that the relative numerical error of blood pressure be smaller than one percent, which is much smaller than the modeling error.
AB - One-dimensional models have been widely used in studies of the propagation of blood pulse waves in large arterial trees. Under a periodic driving of the heartbeat, traditional numerical methods, such as the Lax-Wendroff method, are employed to obtain asymptotic periodic solutions at large times. However, these methods are severely constrained by the CFL condition due to large pulse wave speed. In this work, we develop a new numerical algorithm to overcome this constraint. First, we reformulate the model system of pulse wave propagation using a set of Riemann variables and derive a new form of boundary conditions at the inlet, the outlets, and the bifurcation points of the arterial tree. The new form of the boundary conditions enables us to design a convergent iterative method to enforce the boundary conditions. Then, after exchanging the spatial and temporal coordinates of the model system, we apply the Lax-Wendroff method in the exchanged coordinate system, which turns the large pulse wave speed from a liability to a benefit, to solve the wave equation in each artery of the model arterial system. Our numerical studies show that our new algorithm is stable and can perform ~15 times faster than the traditional implementation of the Lax-Wendroff method under the requirement that the relative numerical error of blood pressure be smaller than one percent, which is much smaller than the modeling error.
KW - Blood pulse wave
KW - Fast algorithm
KW - Large wave speed
KW - Lax-Wendroff method
KW - Riemann variables
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U2 - 10.1016/j.jcp.2016.03.036
DO - 10.1016/j.jcp.2016.03.036
M3 - Article
AN - SCOPUS:84961785324
VL - 314
SP - 450
EP - 464
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -