A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

Abstract

One-dimensional (1D) hemodynamic models of arteries have increasingly been applied to coronary circulation. In this study, we have adopted flow and pressure profiles in Olufsen's 1D structured tree as coronary boundary conditions, with terminals coupled to the dynamic pressure feedback resulting from the intra-myocardial stress because of ventricular contraction. We model a trifurcation structure of the example coronary tree as two adjacent bifurcations. The estimated results of blood pressure and flow rate from our simulation agree well with the clinical measurements and published data. Furthermore, the 1D model enables us to use wave intensity analysis to simulate blood flow in the developed coronary model. Six characteristic waves are observed in both left and right coronary flows, though the waves' magnitudes differ from each other. We study the effects of arterial wall stiffness on coronary blood flow in the left circumflex artery (LCX). Different diseased cases indicate that distinct pathological reactions of the cardiovascular system can be better distinguished through Wave Intensity analysis, which shows agreement with clinical observations. Finally, the feedback pressure in terminal vessels and measurement deviation are also investigated by changing parameters in the LCX. We find that larger feedback pressure increases the backward wave and decreases the forward one. Although simplified, this 1D model provides new insight into coronary hemodynamics in healthy and diseased conditions. We believe that this approach offers reference resources for studies on coronary circulation disease diagnosis, treatment and simulation.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid–Structure Interaction Simulation

“…Although this 3-element Windkessel model has limitations to predict spatially distributed flow quantities, it is simple and accurate to predict the ventricular after-load as discussed by Westerhof et al ( 2008 ). There are many blood flow models ranging from the zero-dimensional models (lumped-parameter models) (Liu et al, 2020 ), the one-dimensional models (Olufsen et al, 2000 ; Chen et al, 2016 ; Duanmu et al, 2019 ), and the three-dimensional models (Lee et al, 2016 ). Interested reader can refer to Shi et al ( 2011 ); Morris et al ( 2016 ) for reviews on blood flow modeling.…”

“…For example, Chen et al ( 2016 ) reported a coupled LV-systemic arteries model to study the effects of the arterial wall stiffness and vascular rarefaction on ventricular function. Using a similar 1-D arterial model, Duanmu et al ( 2019 ) studied the coupling between the LV and the coronary blood flow. In this study, we do not intend to simulate patient-specific AV dynamics with detailed flow predictions in the systemic circulation, thus a 3-element Windkessel model is used.…”

A poroelastic immersed finite element framework for modelling cardiac perfusion and fluid–structure interaction

“…We note that throughout this paper, the solid may be referred to as either the skeleton or the myocardium, the pore fluid is the coronary flow while the chamber flow is the cavity blood fluid. Techniques for explicitly modelling the coronary vascular network have been refined over several decades, [2][3][4][5][6] but models accounting for interactions within the micro vascular network, 1 where clinical perfusion is typically assessed, 7 remain scarce. Further, despite continued improvement in the spatial resolution of clinical imaging, a fully detailed representation of the coronary vessels within the ventricular wall remains unachievable.…”

Input Impedance of an Arterial Tree Model

“…In the literature, one of the computational models used to represent truncated arterial districts is a tree generated based on fractal laws (COUSINS; GREMAUD, 2012;DUANMU et al, 2019;OLUFSEN, 1998;STEELE;TAYLOR, 2007;XU et al, 2018). According to (OLUFSEN, 1998), the model reproduces characteristics of the pulse wave in hemodynamic simulations.…”