In the last decade, different computational models have been published to simulate blood hemodynamic phenomena in coronary arteries by means of Computational Fluid Dynamics (CFD) and Fluid-Solid Interaction (FSI) simulations [1]. Considering only the fluid, CFD models are less computationally demanding and are used to simulate these phenomena. FSI models describe the coupling between arterial wall mechanics and the blood flow. Consequently, the complexity and the difficulty of convergence of these models increase [2].

The development of FSI computational models for simulating the fully coupled interaction between the blood flow and the wall of a coronary artery implies handling the geometrical representation of the domains, the blood flow profile, the rheology, the representation of the arterial wall and the validation of the results.

The geometry of the coronary artery has been considered as a simple pipeline of constant diameter which implies a significant simplification of the problem [3, 4] and facilitates the convergence of various tests performed with different rheological models [3, 4]. More complex geometries are generated by means of 3D reconstructions of CT (computer tomography), CTA (computed tomography angiography) [5], IVUS (intravascular ultrasound) [6], MRI (magnetic resonance imaging), angiogram images, and software, such as MIMICS® (Materialise, Ann Arbor, MI, USA) [2, 7], SimVascular (open-source)[8, 9] and non-commercial open-source reconstruction software [10, 11].

Blood flow in a healthy right coronary artery (RCA) has a Reynolds number of about 200 in resting conditions [12]. The corresponding laminar profile is distorted into a jet flow profile when the RCA lumen decreases in diameter [13, 14]. Under these new conditions of higher speeds in the RCA some authors have resorted to the Large Eddy Simulation (LES)[4] and Reynolds Averaged Navier Stokes (RANS) equations [13]. Blood has been modeled as a Newtonian fluid because under high shear and large lumen diameter like the RCA, the viscosity of the blood is approximately constant [15]. More detailed approaches model blood as a non-Newtonian shear-thinning fluid with rheological models such as the Bird-Carreau model [2, 3, 15, 16], Power Law model[10] and Generalized Power Law model [11, 17].

Modeling RCA arterial wall mechanical behavior is described as an elastic isotropic [7, 18] or an isotropic highly [19] hyperelastic material [2, 9, 10]. The Mooney-Rivlin equations have been used to represent the hyperelastic behavior of the RCA arterial wall with satisfactory results [2, 10].

Comparison of computed and measured hemodynamic parameters, like the wall shear stress (WSS), is the preferred route to validate the computational simulation of blood flow through the coronary artery [10, 17, 20–22]. The WSS is also the base parameter with which other hemodynamic descriptors such as the Time Average Wall Shear Stress (TAWSS), the Oscillatory Shear Index (OSI) and the Relative Residence Time (RRT) are calculated [2]. The experimental determination of these parameters presents significant challenges because determining local velocity and pressure profiles within the artery require access to the patients [2–5, 7–9, 11, 13, 16–18, 20–30].

Chaichana *et al.* [31] quantified the effects on WSS generated by plaque formation on coronary arterial walls with a CFD computational analysis. It was noted that plaque usually is located in the bifurcated regions [32, 33]. High WSS are located in the zones of greatest reduction of the lumen diameter, while the low WSS zones are located in the zones before and after the reduction [31].

Li *et al*. [21] indicate that the low WSS regions (≤ 4 Pa) occurred at the inner wall opposite to the flow divider while high WSS (≥ 40 Pa) were located on the opposite side. Pinto *et al.* [3] reported WSS values up to 45 Pa for RCA located near of the flow separation (bifurcation) region.

Gholipour *et al.* [10] calculated the time dependent variation of WSS at the location of maximum WSS for a complete cardiac cycle. They reported a range of values between 6 to 50 Pa for an RCA, without flow separation for a patient that presented ST-Elevation Myocardial Infarction.

Claes *et al*. [34] reported circumferential tensile strength values of coronary wall specimens of 1.5 MPa for 20 years old patients and up to 0.5 MPa for patients older than 30 years old. Liu *et al.* [24] simulated the von Mises stresses (VMS) of the RCA of 12 patients, in one case, they found von Mises stress magnitudes of up to 95 kPa in the main branch of this artery and up to 110 kPa in the areas near the flow separations (bifurcations). Similarly, Liu *et al.* [24] concluded that baseline low VMS was associated with decrease in plaque volume and decrease in minimal lumen area whereas baseline high VMS was associated with increase in plaque volume and MLA. Dong *et al.* [35] used the first principal stress for stress distribution analysis in the bifurcation of a coronary artery. This article showed the maximum value of first principal stresses occurred at the bifurcation vertex, followed by the bifurcation shoulders. The maximum value of first principal stress, located at the angulation, was found to negatively correlate with magnitude of the bifurcation angle.