Inuence of the position of the distal pressure measurement point on the Fractional Flow Reserve using in-silico simulations

Coronary stenosis is largely responsible of severe heart failure as they can stop the blood ow to the myocardial. The Fractional Flow Reserve, the ratio of the mean distal coronary pressure to mean aortic pressure, is the most usual functional assessment of the severity of the coronary stenosis. In most cases, its value dictates the clinical decision to set a stent to restore the ow. Therefore, a correct measurement of this variable is crucial. The objective of this work is to evaluate how the Fractional Flow Reserve value is altered depending on the point where the distal pressure is measured. This information can be very important to prevent cardiologists from making the wrong clinical decisions. From the data taken from anonymous patients who underwent Coronary Computed Tomographic Angiography and cardiac catheterization, a comparison was made with the results of a computational simulation of the model reconstructed from the angiography. The results of the Fractional Flow Reserve obtained by simulation (0.834) agree with those obtained experimentally (0.830), difference less than 0.8%, which indicates that with simulation more results can be obtained than experimentally would be impossible to achieve. The actual invasive procedure to measure the Fractional Flow Reserve is being executed with a protocol that do not consider the inuence of the location on the distal pressure value. The new procedure would avoid false results related to the point where the distal pressure is measured.


Introduction
The rst cause of death in the world is the coronary disease. A recent report shows an alarming number of more than 16 million Americans over 20 years old are affected by this illness [1]. An elevated level of cholesterol and apolipoprotein B increase the risk of developing atherosclerosis and cardiovascular events [2]. The accumulation lipoproteins inside the artery wall leads to a series of events that conclude in an atheromatous plaque formation. The plaque presence reduces the vessel lumen. This particular case of lumen narrowing is called stenosis. A coronary stenosis modi es not only the type of blood ow but also its amount. This is important because coronary ow irrigates the myocardium and an important reduction could lead to an ischemic heart disease.
Of the two existing procedures to evaluate coronary stenosis, the traditional anatomical one is becoming obsolete compared to the functional one [3]. The anatomic lies on a visual inspection of the lumen narrowing in images from an angiography. Nevertheless, its assessment may lead to false positives of ischemia [4,5]. The alternative is a hemodynamic or functional assessment. Among the different techniques, the FFR measurement is the most widely accepted [6]. FFR was de ned as the ratio between the maximum blood ow through a stenosis in hyperemia conditions and the same value in the ideal case of a healthy artery [7]. As it is impossible to know the ow rate in the original geometry of a vessel when it already has a stenosis, a different procedure is followed. This procedure is a catheterization to measure the pressure in two points distal and proximal to the stenosis. Then, FFR is de ned as the minimum value of the ratio P d /P a in several cardiac cycles, being P d and P a the mean values over a cardiac cycle as de ned in [8]. The FAME (Fractional Flow Reserve vs Angiography for Multivessel Evaluation) [9] and FAME II [10] trials have proved that, in critical lesions (FFR < 0.80), a substantial reduction in urgent revascularizations is achieved performing FFR-guided PCI plus the best medical therapy in contrast to applying only the best medical therapy. Although these studies have proved the validity of this technique, it is applied in a very reduced percentage of patients [11]. A recent study over 60,000 ICA cases has reported a tiny 6.1% of cases where the invasive FFR was employed [6]. Several reasons such as the use of adenosine, the need of an experienced interventionist, the economic costs and the risk of an invasive intervention have encouraged the shift to a non-invasive alternative [11].
The use of in-silico simulations combining medical imaging (e.g. CCTA), digital image processing and computational uid dynamics (CFD) has been proposed as a non-invasive alternative to calculate hemodynamical parameters in coronaries [12]. The early years of the 2010 decade brought the calculation of non-invasive FFR values [13][14][15]. Since them, several techniques have been introduced to perform this task: rotational angiography plus zero order Windkessel boundary conditions [16], 3D-QCA [17], 3D-QCA plus the TIMI frame [18], allometric laws combined with estimates of coronary microvascular resistance [19], lumped parameter models [20,21], and machine learning algorithms [22,23]. The result is a non-invasive FFR named in different ways (FFR angio , FFR CFD , FFR ML , FFR CT , etc.). As these techniques continue developing, several trials have been employed to compare the non-invasive FFR CT against CTA taking invasive FFR as the standard [24][25][26]. The performance of the FFR CT is superior to that of the CTA [6], and according to the PLATFORM trial, has resulted in a drastic reduction of the scheduled ICA procedures and their associated costs [6,27]. The future seems bright for these technologies. The computation time is reducing continuously from days to several hours, using the complete transient simulation, and to a few minutes if the CFD analysis is reduced [27]. A company has commercially offered these calculations and several institutions declare safe this technology [6]. There are new techniques emerging such as MPI to calculate the MBF and its authors claim to obtain better results in ow limiting stenoses [29]. Nevertheless, all these models estimate the FFR value with an accuracy that ranges from ± 0.15 to ± 0.10 in the best scenario and several authors point that a calculation will never match invasive FFR [28].
So, there is a fundamental question: what does it happen if a FFR CT value of 0.75-0.85 is obtained? In those cases, invasive FFR remains as the gold standard as the pressure wires limit the error to a ± 0.03 (PressureWire® Aeris manual [30]). There are several references which argue about the location where the distal pressure should be measured. Toth et al. [31] suggested the measurement 2-3 cm downstream the stenosis, Ihdayhid et al. [32] and Matsumura et al. [33] proposed to measure as distal as possible and, just a short time ago, Renard et al. [34] found that the distance suggested by [31] reduce measurement errors.
As there is a growing debate about the distance at which the sensor should be placed, this paper uses the FFR CT to examine the issue of the location. As FFR CT provides computed values along the affected coronary, the variation of this parameter in space from the lesion will be checked. The 3D coronary tree of an anonymous patient will be reconstructed from CCTA images. The CFD will be used to simulate the coronary stenosis performing a transient simulation with a constant increase of pressure at the inlet of the model. Rather than using a constant time, a constant increase of pressure makes it possible to run the boundary condition function with absolute delity. The results will be validated with invasive data acquired to this patient. Then the analysis will be extended to three more cases.

Methods
As mentioned in the introduction, a CCTA and a cardiac catheterization were performed in four anonymous patients, having the rst patient a stenosis grade of 68% in the right branch of the coronary artery.

In vivo measurements
These tests were performed at the Cardiology Service of University Hospital using an ACIST Navvus Rapid Exchange FFR MicroCatheter [35]. This catheter utilizes ber-optic based sensor technology instead of piezoresistive (electrical) sensor technology. The elliptically-shaped crossing pro le of the catheter has a dimension of 0.51 mm × 0.64 mm. These dimensions are comparable to the circularshaped wire diameter (0.56 mm). The wire effect on vessels whose diameter changes is negligible. Before each test, the probes were calibrated to ensure that the results obtained were reproducible with differences below 0.1%. During the tests, rst of all, intracoronary nitroglycerin (200 µg) was introduced inside the coronary. Then maximal hyperemia was induced by introducing a bolus of adenosine (240 µg/kg min). The guide catheter was introduced through the radial artery to reach the right coronary artery and to measure the P a . The microcatheter was then moved, crossing the stenosis, and its position was xed 2 cm downstream of it to control the P d . Once it was veri ed that both pressures were in the correct range, their values were recorded throughout several cardiac cycles, being displayed in a monitor (Fig. 1). These values correspond to the rst patient.

In silico simulation
The construction of the numerical model begins with the 3D geometry reconstruction. A set of images taken from the CCTA were exported to the DICOM format. The region exported covers the coronary tree and the area of the ascending aorta (Fig. 2).
The available resolution of the DICOM images is 512 x 512 pixels, being 640 µm the pixel size. Each pixel has a gray intensity value according to the scale of Houns eld [36]. As it is known, there is a direct relationship between the density of each anatomical structure and the gray value assigned to each pixel in the image. The 3D Slicer software [37], was used to group similar gray values, identifying the threshold between the different tissues. In this case, a pixel mask was de ned in the region of interest with a threshold range of 190-250 HU to extract the coronary tree [38]. A 3D model was implemented from the created dynamic region (Fig. 3) and a design tool was employed to adapt it for the numerical simulation. Slights adjustments and a smooth process were performed using this tool. We expected a negligible effect in the calculations as a result of the tiny deviation between the original geometry and the resulting model.
Before the geometry was set, we did an additional simpli cation. In these problems it is usual to take the volumetric ow at the inlet of the aorta. This ow is obtained from allometric approximations of the volume pumped by the heart [39]. However, in our rst patient, the P a is known, so this variable can be imposed as an inlet boundary condition. Therefore, the 3D numerical model can be simpli ed, reducing the analysis to the right coronary artery, where the stenosis is located (Fig. 3). This simpli cation will considerably reduce the number of cells in the numerical model and, therefore, the computational time.
The same simpli cation will be applied to the remaining patients but in those cases, we will take into account the brachial pressure.
The imported geometry was meshed using the code ANSYS version 18.2 [40]. According to the conclusions shown in [41], the combination of virtual topology and the patch-independent algorithm was employed. The mesh has two parts, an inner unstructured portion and an outer one.
Tetrahedral cells (Fig. 4) covered the inner part of the duct because they adapt better to complex geometries and require less calculation time. The structured portion, composed of eight in ation layers close to the wall, is necessary to correctly capture the ow behavior in the boundary layer. The y + values were kept below 0.5, which means that the centers of the cells next to the wall are inside the laminar sublayer. The total number of cells was approximately 1.8x10 6 , with a size range between 2.83x10 − 12 m 3 and 2.39x10 − 16 m 3 . An analysis of the quality of the mesh yielded a very satisfactory result. A 99.99% of the cells in the mesh had an equisized skew value under 0.6.
The dependence of the results against the size of the mesh was also analyzed. Three additional grids (one coarser, 1.2x10 6 cells and two ner grids, 2.4x10 6 and 3.0x10 6 cells) were built to check the change in the predicted ow characteristics with the cell number. The simulations were carried out by imposing a constant ow rate at the coronary inlet. The static pressure drop between the inlet to the coronary artery and the farthest outlet was employed as a reference variable. This variable quanti es the resistance to ow on the way. The obtained results differed less than 2.2% against the nest mesh. A 5.2% difference was found if the coarsest mesh is taken into account. Therefore, the chosen mesh was the one with 1.8x10 6 cells, since the required calculation time is signi cantly shorter than those with a larger number of cells. The URANS equations, mass and momentum conservation laws, that describe a uid in movement [42] were solved with the Fluent solver of the ANSYS code. The solver was set to pressurebased and implicit with an absolute formulation for the velocity eld. The discretization of the spatial and temporal derivatives in the equations was carried out by means of second-order schemes. The discretization of the pressure was a standard centred scheme. The SIMPLE algorithm was used to solve the coupling between pressure and velocity elds.
On the other hand, these equations must be solved using turbulence models. The turbulence is de ned as a phenomenon of intrinsic instability of the ow that causes its movement to become chaotic, appearing eddies. These eddies appear and disappear without a solution of continuity: the large eddies are divided into smaller ones, and so on. When the eddies become small enough, they dissipate due to their viscosity. Turbulence appears when the Reynolds number exceeds a certain value (between 400 and 2,000). We conducted simulations in four patients. The patient, whose in-vivo measurements were used to validate the simulation, has a Reynolds number value of 1,554. The remaining patients have 5,300, 1,200 and 1,820 respectively. The ow is both laminar and turbulent with transition zones in the coronary arteries we are studying. The turbulence model that best adapts to these conditions is the SST k-omega [43,44], which is a combination of the standard models k-epsilon and k-omega. The k-omega model is used for the ow close to the walls while the k-epsilon is used in the far eld to the wall. More details of this type of simulation can be found in [45]. The working uid was blood with a constant density of 1,060 kg/m 3 and a dynamic viscosity of: and Carreau models, respectively). Finally, one of the most critical parts in any simulation is the choice of boundary conditions. Concerning the inlet, the pressure value is known (Fig. 1) as stated in Sect.2. Moreover, a vascular resistance model using allometric laws was employed (the output diameters are proportional to the ow resistance) to calculate the outlet boundary conditions. Additionally, we have to take into account that the ow is a pulsatile one, so our inlet boundary condition is the pressure value during a cardiac cycle (Fig. 5). To reproduce this temporal variation of pressure, a UDF was designed. We needed to choose an appropriate time step. It depends on the number of CFL, which is the ratio between the time interval and the residence time in a nite volume:  Since in this case the most relevant variable is aortic pressure instead of time, a uniform step will be used in the dependent variable aortic pressure rather than a uniform step in the independent variable time. This procedure [8,46,47] uses a constant pressure increase, being determined the corresponding time increase. An algorithm, that is incorporated into the program by means of an UDF, determines the appropriate constant aortic pressure variation and calculates the corresponding variable time steps. For example, if with a constant time step of 0.005 s for a cardiac cycle of 0.97 s, 194 steps are necessary, following the described procedure, with a pressure range between 54 and 102 mm in the cardiac cycle, if pressure increments of 0.5 mm are taken, 96 steps will be required, 50% less. The advantage of this method is that the whole range of the aortic pressure dependent variable will be covered with absolute delity, gaining convergence security and computational time. To verify that the solution converges properly, the pressure difference variable between the inlet and the outlet is controlled, which reaches an almost stationary   downstream of the stenosis. It increases its velocity, which causes its pressure drop suddenly, and consequently the FFR CT value. The Fig. 7.c shows how the vortexes disappear downstream with slight crossings between streamlines. In that section, the ow is reorganizing itself and the pressure is increasing, and consequently the FFR CT . Starting from this region, the ow is relaminarized and the value of the pressure, and the FFR, decreases linearly. This situation will remain until a new geometrical alteration is reached (e. g. a new stenosis or a bifurcation).
Additional calculations were done for three more patients. Figures  In the remaining patients, the ow is not so altered. Patient 2 shows more disturbances before the stenosis than patient 3 but these disturbances are not reinforced after the stenosis. In patient 2 case, the streamlines are not relaminarized quickly after the stenosis due to the presence of a rami cation. The ow is laminar in case 3 for several reasons, the stenosis is not as severe as in case 2, the artery geometry does not favor turbulence arising and the branch appearing downstream of the stenosis is slightly further.

Discussion
Previous sections have shown how the FFR can be determined in a non-intrusive way employing CFD in the reconstructed coronary artery from CT images. Patient 1 and 3 in vivo measurements coincide with the simulation results. It has also been veri ed that the current invasive procedure to measure the FFR is being executed with a protocol that do not consider the in uence of the location on the P d value.
Concerning the patient 1, if Toth et al. [31] and Renard et al. [34] criterion is followed, a catheterization could be avoided as the FFR is 0.83. However, this catheterization would be suggested according Ihdayhid et al. [32] and Matsumura et al. [33] indications. If the sensor is placed 4 cm downstream, the FFR value would be under 0.8.
In this paper, we present relevant information that could be helpful to assist in the invasive procedure. It is necessary to study the graphs of both the evolution of the FFR CT value from the stenosis and the streamlines behavior.
In the rst case, streamlines are reorganized 2.8 cm after the stenosis (see arrow in Fig. 7). This should be the point where the sensor should be located and that would mean an FFR value of 0.81. That location is close to the suggested in the medical protocols (2 cm) but as seen in the remaining patients, the types and severities of the stenosis are quite different between different individuals and the pressure eld distribution is variable. For example, patient 2 streamlines are not reorganized (Fig. 8). We could measure right after the stenosis but the presence of a branch does not help the stabilization of the ow. It is not recommendable to place a pressure sensor just in the vicinities of a rami cation. For this reason, if one pays attention to the FFR CT value evolution, after a slight increase in 2.5 cm, the slope of the FFR CT is constant and stable and this place should be chosen to place the sensor. The location chosen (arrow placed in both gures), would differ signi cantly from Toth et al. [31] and Renard et al. [34] suggestions and would approximate better to Ihdayhid et al. [32] and Matsumura et al. [33] criterion. The behavior of patient 3 (Fig. 9) seems similar to that of patient 2, although there are differences concerning the geometry. The ow is much more stable before the stenosis and the severity of the stenosis is not as acute as in patient 2. For this reason, as the ow is very stable, we recommend to place the pressure sensor before the branch is reached. In this case this rami cation would not mean an important in uence in the ow because of its position and origin from the principal artery. Finally, patient 4 ( Fig. 10) resembles to patient 1. The gure shows clearly the place where the streamlines are reorganized. This point is located 3 cm downstream of the stenosis and as it is clearly seen, the slope is almost constant since this location is reached.
All these cases, show that new non-invasive technologies are quite helpful when performing an invasive FFR. The previous studies about the location of the probe, are quite useful but its validity depends on the coronary geometry. One possibility would be to move the pressure probe downstream of the stenosis to take more distal pressure values until it is veri ed that these pressures values are independent of the position of the probe. This procedure should include a veri cation process to check that there are no pressure uctuations downstream of the stenosis and would avoid false results related to the point where the distal pressure is measured. The result would be taking different clinical decisions because P d1 and P d2 values differ signi cantly from the P d3 value. However, this procedure would imply to add more adenosine to the patient to perform all these pressure measurements. Here we propose a method based on the information provided by the CFD simulation. This method would indicate the cardiologist the best angle to visualize the intervention and a limited region where the sensor should be set.

Conclusion
Coronary stenosis is largely responsible of severe heart failure as they can stop the blood ow to the myocardial. The FFR, ratio of the P d to P a , is the most usual functional assessment of the severity of the coronary stenosis. The numerical results of the FFR CT are in good agreement with those obtained experimentally (FFR) in multiple references in the bibliography. Nevertheless, the invasive protocol would be recommended in limiting cases (0.75 < FFR CT < 0.85).
In this paper we have performed simulations that match the invasive measurements taken in two different patients. Once our method is validated, we have taken advantage of the simulation technology and obtained useful information that it is quite helpful to the invasive procedure. The present paper, assess with Fluid Dynamics principles, the best region to place the sensor in an invasive pressure measurement. This region is not xed and it depends on the patient. This procedure would avoid false results related to the pressure variations concerning the point where the distal pressure is measured.
Additionally, would help the cardiologist with the intervention planning. As the measurement area is constrained and the location is known, the interventionist could indicate the best position for the visualization of the coronary and could limit duration of the procedure. Badajoz, which provided the images for this study, and the University of Oviedo in the framework of the Projects "Desarrollo de nuevo material docente para prácticas de Anatomía Humana (PINN-18-A-069)" and "Uso de juegos y vídeos en las prácticas de anatomía humana (PINN-19-A-004)".
Funding: Authors acknowledge that this work was partially funded by Junta de Extremadura through Grants GR18175 and IB16119 (partially nanced by FEDER), and by the Spanish Ministry of Economy, Industry and Competitiveness -Instituto de Salud Carlos III under Project "Estudio de la in uencia de la geometría de las vías respiratorias en las patologías pulmonares obstructivas (PI17/01639)".
Compliance with ethical standards: The study was approved by the Badajoz Clinical Research Committee, belonging to the Extremadura Health Service, in accordance with the ethical standards. The need of informed consent for this study was waived by Badajoz Clinical Research Committee, belonging to the Extremadura Health Service.
Con ict of interest: The authors are not aware of any a liations, memberships, funding, or nancial holdings that might be perceived as affecting the objectivity of this review.
Author contributions: R.A. has developed and designed the paper, being the general responsible. R.A. and C.F. have written the paper. R.G. and J.N. have carried out the analysis and interpretation of the results.