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Coronary arteries have high curvatures, and hence, flow through them causes disturbed flow patterns, resulting in stenosis and atherosclerosis. This in turn decreases the myocardial flow perfusion, causing myocardial ischemia and infarction. Therefore, in order to understand the mechanisms of these phenomena caused by high curvatures and branching of coronary arteries, we have conducted elaborate hemodynamic analysis for both (i) idealized coronary arteries with geometrical parameters representing realistic curvatures and stenosis and (ii) patient-specific coronary arteries with stenoses. Firstly, in idealized coronary arteries with approximated realistic arterial geometry representative of their curvedness and stenosis, we have computed the hemodynamic parameters of pressure drop, wall shear stress (WSS) and wall pressure gradient (WPG), and their association with the geometrical parameters of curvedness and stenosis. Secondly, we have similarly determined the wall shear stress and wall pressure gradient distributions in four patient-specific curved stenotic right coronary arteries (RCAs), which were reconstructed from medical images of patients diagnosed with atherosclerosis and stenosis; our results show high WSS and WPG regions at the stenoses and inner wall of the arterial curves. This paper provides useful insights into the causative mechanisms of the high incidence of atherosclerosis in coronary arteries. It also provides guidelines for how simulation of blood flow in patient's coronary arteries and determination of the hemodynamic parameters of WSS and WPG can provide a medical assessment of the risk of development of atherosclerosis and plaque formation, leading to myocardial ischemia and infarction. The novelty of our paper is in our showing how in actual coronary arteries (based on their CT imaging) curvilinearity and narrowing complications affect the computed WSS and WPG, associated with risk of atherosclerosis. This is very important for cardiologists to be able to properly take care of their patients and provide remedial measures before coronary complications lead to myocardial infarctions and necessitate stenting or coronary bypass surgery. We want to go one step further and provide clinical application of our research work. For that, we are offering to cardiologists worldwide to carry out hemodynamic analysis of the medically imaged coronary arteries of their patients and compute the values of the hemodynamic parameters of WSS and WPG, so as to provide them an assessment of the risk of atherosclerosis for their patients. Graphical abstract Theme and aims: Coronary arteries have high curvatures, and hence flow through them causes disturbed flow patterns, resulting in stenosis and atherosclerosis. This in turn decreases the myocardial flow perfusion, causing myocardial ischemia and infarction. Therefore, in order to understand the mechanisms of these phenomena caused by high curvatures and branching of coronary arteries, we have conducted elaborate hemodynamic analysis for both (i) idealized coronary arteries with geometrical parameters representing curvatures and stenosis, and (ii) patient-specific coronary arteries with stenoses. Methods and results: Firstly, in idealized coronary arteries with approximated realistic arterial geometry representative of their curvedness and stenosis, we have computed the hemodynamic parameters of pressure drop, wall shear stress (WSS) and wall pressure gradient (WPG), and their association with the geometrical parameters of curvedness and stenosis. Then, we have determined the wall shear stress and wall pressure gradient distributions in four patient-specific curved stenotic right coronary arteries (RCAs), that were reconstructed from medical images of patients diagnosed with atherosclerosis and stenosis, as illustrated in Figure 1, in which the locations of the stenoses are highlighted by arrows. Figure 1: Three-dimensional CT visualization of arteries in patients with suspected coronary disease. The arteries can be seen as a combination of various curved segments with stenoses at unspecific locations highlighted by arrows. Our results show high WSS and WPG regions at the stenoses and inner wall of the arterial curves, as depicted in Figure 2. Therein, the encapsulations show (i) high WSS, and (ii) high WPG regions at the stenosis and inner wall of the arterial curves. Figure 2: WSS and WPG surface plot of realistic arteries (a), (b), (c) and (d), wherein the small squared parts are enlarged to show the detailed localized contour plots at the stenotic regions. Therein, the circular encapsulations show (i) high WSS and (ii) high WPG regions at the stenosis and inner wall of the arterial curves. Conclusion and novelty: This paper provides useful insights into the causative mechanisms of the high incidence of atherosclerosis in coronary arteries. It also provides guidelines for how simulation of blood flow in patient coronary arteries and determination of the hemodynamic parameters of WSS and WPG can provide a medical assessment of the risk of development of atherosclerosis and plaque formation, leading to myocardial ischemia and infarction. The novelty of our paper is our showing how in actual coronary arteries (based on their CT imaging), curvilinearity and narrowing complications affect the computed WSS and WPG associated with risk of atherosclerosis. This is very important for cardiologists to be able to properly take care of their patients and provide remedial measures before coronary complications lead to myocardial infarctions and necessitate stenting or coronary bypass surgery.

In this paper, we have analysed pulsatile flow through partially occluded elastic arteries, to determine the haemodynamic parameters of wall shear stress (WSS), wall pressure gradient and pressure drops (ΔP), contributing to enhanced flow resistance and myocardial ischaemic regions which impair cardiac contractility and cause increased work load on the heart. In summary, it can be observed that stenoses in an artery significantly influence the haemodynamic parameters of wall shear stress and pressure drop in contrast to dilatations case. This deduces that stenosis plays a more critical role in plaque growth and vulnerability in contrast to dilatation, and should be the key element in cardiovascular pathology and diagnosis. Through quantitative analysis of WSS and ΔP, we have provided a clearer insight into the haemodynamics of atherosclerotic arteries. Determination of these parameters can be helpful to cardiologists, because it is directly implicated in the genesis and development of atherosclerosis. [ABSTRACT FROM AUTHOR]