Poster U5 - ROLE OF CORONARY FLOW REGULATION: A COMPARISON OF LUMPED, DISTRIBUTIVE AND 1D NAVIER-STOKES MODEL

Introduction: Coronary artery disease (CAD) is a cardiovascular disease which has been found to be the leading cause of death in the U.S. Although the development of some clinical indices has helped improve the prognosis of patients suffering from CAD, the underlying mechanisms that cause CAD remain unclear. In addition to extravascular loading and hemodynamics boundary conditions, coronary blood flow regulation, including myogenic, shear and metabolic responses, controls the vessel lumen radius in response to changes in perfusion pressure. The lack of understanding of these mechanisms arises largely because it is difficult/challenging to measure blood flow and pressures in the coronary vessels embedded in deep layer of the myocardium (Fig. 1A). Computational modeling of the coronary vascular system thus provides an alternative approach to understand the pressure-flow relationship in coronary circulation with flow regulation. The 0D lumped parameter model (LM) and distributive model (DM) based on mass conservation of each vessel, have been applied to predict the pressure and flow rate in coronary vessels. The 1D Naiver-Stokes (NS) equation based on conservation of both mass and momentum considers the wave propagation in the elastic vessels, and thus provides more physiological predictions of pressure and flow rate. The goal of this work is to develop LM, DM, and 1D NS models to predict the spatial distribution of coronary flow waveform with flow regulation, which can be potentially applied to understand the mechanisms of CAD.

Materials and

Methods: The three-element Windkessel LM has been developed in our previous work [1-2]. Each vessel is described by two nonlinear resistances and a nonlinear capacitor. The mass conservation is imposed in a three-vessel network (Fig. 1B). The DM is based on conservation of mass in a short temporal period and spatial length. In DM, changing cross-sectional area in time and changing flow in distance are considered equal. The governing equation of 1D NS model based on momentum conservation develops the results from regulation DM. To model flow regulation mechanism, myogenic response is controlled by a sigmoidal function corresponding to transvascular pressure. Shear regulation is modelled by a Hill function of mean shear stress. Metabolic response is determined by a vessel dilator signal, Fmeta. These three methods are used to solve the pressure and coronary flow rate in a three-vessel network (Fig. 1B) using hemodynamics measurments of a swine model. Perfusion presssure and IMP in the model are imposed using the difference between arterial and venous pressure waveforms, and the left ventricular pressure, respectively (Fig. 1C). LM is implemented in MATLAB to compare agaisnt the developed DM and 1D NS model that are implemented using finite element method in FEniCS. In DM and NS model, each vessel is discretized using 32 elements.

Results, Conclusions, and Discussions: Fig. 2 shows the pressure at middle of each vessel ( P_mid ), radius, coronary flow rate under fully-dilated condition, and regulated condition (Fmeta = 0), predicted by three models are comparable (Fig. 2A-D). The relative percentage difference of P_mid is 8% between DM and LM, and 8% between 1D NS model and LM (Fig. 2A). The largest difference occurs when the IMP gradient is the largest. The percentage difference of radian is 8% between DM and LM, and 8% between 1D NS model and LM (Fig. 2A). The percentage difference of coronary flow rate under fully-dilated and regulated conditions is 7% and 9% between DM and LM, and 6% and 9% between LM and 1D NS model (Fig. 2C-D), respectively. Fig. 2E shows that when perfusion pressure increase from 16 to 250 mmHg, passive coronary flow rate increases linearly whereas regulated coronary flow rate maintains a slight change at lower perfusion pressure then increases linearly at higher perfusion pressure. Fig. 2F-G show the pressure and flow rates are continuously reduced from source vessel to terminal vessel.
In this project, we compared the model predicted coronary flow with regulation using LM, DM and 1D NS models in a three-vessel coronary network. The model predictions in terms of pressure in the middle of each vessel, radius in the middle of each vessel, inlet flow rate and outlet flow rate using DM and 1D NS are comparable with those predicted by LM. Compared to LM, the DM and 1D NS models can provide pressure and flow rate at any point of the vessel. In the future, we will extend the coronary vessel network and apply the developed model to investigate the pressure and flow rate distribution under physiological and pathological conditions.

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