# A Computational Analysis of the Influence of a Pressure Wire in Evaluating Coronary Stenosis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{s}

^{max}) to the maximal myocardial blood flow in that same territory in the hypothetical case that the stenosis were removed and the epicardial vessel were completely normal (Q

_{n}

^{max}) [5]. In hyperemia conditions, the resistance is assumed to be constant and equivalent. The venous pressure is small and could be negligible. FFR therefore equals the distal pressure (P

_{d}) divided by the aortic pressure (P

_{a}).

_{a}in the coronary ostium, and a 0.014-inch (≈0.36 mm) pressure wire is introduced to record the value of P

_{d}at the distal end of a stenosis [6].

_{CTA}) was predicted via computational fluid dynamics (CFD) study (HeartFlow, Inc., Redwood City, CA, USA) [7]. The lumped-parameter coronary artery model was prescribed at the outlet for an unsteady simulation. A high diagnostic performance of FFR

_{CTA}was concluded compared with invasively measured FFR [12]. FFR presents a proportion of the averaged flow or pressure over the cardiac cycle. Virtual FFR computed from steady state was proposed and compared with invasively measured data in 21 patients [11]. It was found that the computational burden reduced to 1/16 in comparison to unsteady flow simulation and the accuracy maintained to be high. The non-CFD method of angiography derived FFR (FFR

_{angio}) was generated according to rapid flow analysis (CathWorks Ltd., Kefar Sava, Israel), and a high concordance between FFR

_{angio}and wire-based FFR was concluded [10]. Although good agreements are indicated in the previous studies, one major inconsistency between clinically measured FFR and numerically predicted FFR is the presence of the pressure wire.

## 2. Methods

#### 2.1. Modeling Geometry

_{wire}= 0.36 mm) pressure wire was inserted and positioned 10 times D distal to the minimal lumen area (MLA) [18]. The value of P

_{d}is captured at the central point at the tip of pressure wire. FFR is calculated as the pressure ratio (Equation (1)):

^{2}, and the area reduction of this case is 79% (DS% of about 54%). The lesion length is 13.14 mm, and the total length is 63.24 mm. The pressure wire was introduced along the centerline in the position of 2 cm distal to the narrowest area. The value of P

_{d}is captured at the central point at the tip of pressure wire, and FFR is calculated by Equation (1).

#### 2.2. Numerical Assumptions and Boundary Condition

^{3}and a viscosity of 0.0035 Pa∙s [19,20]. In practice, the vasodilator is injected to maintain the maximal hyperemic condition and the vessels expand to the maximum, vessels are therefore considered as rigid conduits with a non-slip wall boundary in the simulation. A mean blood pressure of 93 mmHg was applied at the inlet for the steady flow simulation, which denotes the value of P

_{a}in our study. Based on the load independence principle of FFR [21], a resistance boundary is considered to represent the downstream arterial system [22]. The pressure in the artery is a function of the flow rate and resistance. At the outlet, a user-defined function of the resistance was applied, which couples the blood pressure and flow rate. The value of resistance in maximal hyperemia reduced to 0.24 of that in resting condition from the clinical data of Wilson et al. [23]. In this study, the resistance of the downstream microcirculatory was set as 4 × 10

^{9}Pa∙s/m

^{3}in the predicting models according to the published data [22]. The relative tolerance was set to be 10

^{−4}for the converged results.

#### 2.3. Navier–Stokes Equation

#### 2.4. Grid Independence Study

^{4}and 2 × 10

^{5}elements, respectively. The minimum element quality was greater than 0.5 in each case. For the patient-specific model, 1.5 million- and 3 million-element meshes were generated. The parameter of P

_{d}is sensitive and significant in our study, and it is selected to determine an appropriate element size. The difference in the value of P

_{d}generated by the normal and fine grids was observed to be less than 0.1% for the idealized models and patient-specific case alike. Hence, the 5 × 10

^{4}and 1.5 million element grids were deemed to be appropriate to use in the remaining ideal and patient-specific model studies, respectively.

## 3. Results and Discussion

#### 3.1. Blockage Ratio and Flow Obstructive Effect

_{wire}) divided by the MLA (Equation (3)):

#### 3.2. Pressure

_{d}are 11,927 and 11,563 Pa in the models without and with a pressure wire, respectively. In the model with 30% DS, the value of P

_{d}is 11,789 Pa without the presence of the pressure wire, while it drops to 11,379 Pa after the insertion (Figure 3B). In 40% and 50% DS models, the values of Pd decrease slightly as well in wire-absent and wire-included conditions (11,575 vs. 11,129; 11,013 vs. 10,504) (Figure 3C,D). When a stenosis increases to 60%, the value of Pd reduces from 9645 to 8994 Pa after inserting a pressure wire (Figure 3E). In the severe model (70% DS), the pressure drops significantly, and the presence of a wire leads to a decrease of P

_{d}from 7106 to 6032 Pa (Figure 3F). In summary, a growth of the narrowing contributes to the decrease of pressure, and the insertion of pressure wire in the simulations accelerates the (measured) pressure drop.

_{d}in the non-wire model is 10,927 Pa, while it decreases to 8855 Pa in the wire-included model, respectively (Figure 4). A larger pressure drop between wire-absent and wire-included models is observed in the patient-specific case compared with the ideal models. There are two causes. Firstly, in the cardiovascular system, the downstream arterial diameter usually becomes smaller even though a stenosis is not present and the individual is healthy, as can be demonstrated in the geometry in Figure 2—the outlet diameter is smaller than the upstream arterial diameter. A reduced diameter downstream of the vessel may accelerate the decrease of the pressure [24]. Secondly, pressure reduces due to the aforementioned flow obstructive effect caused by the pressure wire.

#### 3.3. FFR

_{d}to P

_{a}. P

_{d}is obtained at the central point at the tip of pressure wire, while P

_{a}is assumed to be 93 mmHg at the inlet in our study. The value of FFR in the non-stenosed (pipe) model is 0.96 when the wire is not inserted, while it dropped by 0.03 due to the insertion of the wire. Figure 5 shows the value of FFR in various ideal stenosis models. In mild stenosis cases (30, 40, 50% DS), the values of FFR are 0.95, 0.93 and 0.89 in the models without a pressure wire, respectively, while they decrease to 0.92, 0.90 and 0.85 in those with a wire. The presence of the pressure wire contributes to a relatively slight overestimation of around 4%. In the stenotic model of 60% DS, the value of FFR reduces from 0.78 to 0.73 in the two comparative models, and it drops significantly in the 70% DS model from 0.57 to 0.49 with an overestimation rate of 15%.

## 4. Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ohman, E.M.; Bhatt, D.L.; Steg, P.G.; Goto, S.; Hirsch, A.T.; Liau, C.-S.; Mas, J.-L.; Richard, A.-J.; Röther, J.; Wilson, P.W. The REduction of Atherothrombosis for Continued Health (REACH) Registry: An international, prospective, observational investigation in subjects at risk for atherothrombotic events-study design. Am. Heart J.
**2006**, 151, 786.e1–786.e10. [Google Scholar] [CrossRef] [PubMed] - Pijls, N.H.; Van Son, J.A.; Kirkeeide, R.L.; De Bruyne, B.; Gould, K.L. Experimental basis of determining maximum coronary, myocardial, and collateral blood flow by pressure measurements for assessing functional stenosis severity before and after percutaneous transluminal coronary angioplasty. Circulation
**1993**, 87, 1354–1367. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Tonino, P.A.L.; Fearon, W.F.; De Bruyne, B.; Oldroyd, K.G.; Leesar, M.A.; Ver Lee, P.N.; MacCarthy, P.A.; van’t Veer, M.; Pijls, N.H.J. Angiographic versus functional severity of coronary artery stenoses in the FAME study: Fractional flow reserve versus Angiography in Multivessel Evaluation. J. Am. Coll. Cardiol.
**2010**, 55, 2816–2821. [Google Scholar] [CrossRef] [PubMed] [Green Version] - De Bruyne, B.; Pijls, N.H.; Kalesan, B.; Barbato, E.; Tonino, P.A.; Piroth, Z.; Jagic, N.; Möbius-Winkler, S.; Rioufol, G.; Witt, N. Fractional flow reserve–guided PCI versus medical therapy in stable coronary disease. N. Engl. J. Med.
**2012**, 367, 991–1001. [Google Scholar] [CrossRef] [PubMed] [Green Version] - De Bruyne, B.; Sarma, J. Fractional flow reserve: A review. Heart
**2008**, 94, 949–959. [Google Scholar] [CrossRef] [PubMed] - Toth, G.G.; Johnson, N.P.; Jeremias, A.; Pellicano, M.; Vranckx, P.; Fearon, W.F.; Barbato, E.; Kern, M.J.; Pijls, N.H.; De Bruyne, B. Standardization of fractional flow reserve measurements. J. Am. Coll. Cardiol.
**2016**, 68, 742–753. [Google Scholar] [CrossRef] - Taylor, C.A.; Fonte, T.A.; Min, J.K. Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve: Scientific basis. J. Am. Coll. Cardiol.
**2013**, 61, 2233–2241. [Google Scholar] [CrossRef] [Green Version] - Itu, L.; Rapaka, S.; Passerini, T.; Georgescu, B.; Schwemmer, C.; Schoebinger, M.; Flohr, T.; Sharma, P.; Comaniciu, D. A machine-learning approach for computation of fractional flow reserve from coronary computed tomography. J. Appl. Physiol.
**2016**, 121, 42–52. [Google Scholar] [CrossRef] [Green Version] - Lee, K.E.; Lee, S.H.; Shin, E.-S.; Shim, E.B. A vessel length-based method to compute coronary fractional flow reserve from optical coherence tomography images. Biomed. Eng. Online
**2017**, 16, 83. [Google Scholar] [CrossRef] [Green Version] - Pellicano, M.; Lavi, I.; De Bruyne, B.; Vaknin-Assa, H.; Assali, A.; Valtzer, O.; Lotringer, Y.; Weisz, G.; Almagor, Y.; Xaplanteris, P.; et al. Validation study of image-based fractional flow reserve during coronary angiography. Circ. Cardiovasc. Interv.
**2017**, 10. [Google Scholar] [CrossRef] - Zhang, J.-M.; Zhong, L.; Luo, T.; Lomarda, A.M.; Huo, Y.; Yap, J.; Lim, S.T.; Tan, R.S.; Wong, A.S.L.; Tan, J.W.C. Simplified models of non-invasive fractional flow reserve based on CT images. PLoS ONE
**2016**, 11, e0153070. [Google Scholar] [CrossRef] [Green Version] - Rizvi, A.; Hyun Lee, J.; Han, D.; Park, M.W.; Roudsari, H.M.; Lu, B.; Lin, F.Y.; Min, J.K. Fractional flow reserve measurement by coronary computed tomography angiography: A review with future directions. Cardiovasc. Innov. Appl.
**2016**, 2, 125–135. [Google Scholar] [CrossRef] - De Bruyne, B.; Paulus, W.J.; Vantrimpont, P.J.; Sys, S.U.; Heyndrickx, G.R.; Pijls, N.H. Transstenotic coronary pressure gradient measurement in humans: In vitro and in vivo evaluation of a new pressure monitoring angioplasty guide wire. J. Am. Coll. Cardiol.
**1993**, 22, 119–126. [Google Scholar] [CrossRef] [Green Version] - Ashtekar, K.D.; Back, L.H.; Khoury, S.F.; Banerjee, R.K. In vitro quantification of guidewire flow-obstruction effect in model coronary stenoses for interventional diagnostic procedure. J. Med. Devices
**2007**, 1, 185–196. [Google Scholar] [CrossRef] - Peelukhana, S.V.; Effat, M.; Kolli, K.K.; Arif, I.; Helmy, T.; Leesar, M.; Kerr, H.; Back, L.H.; Banerjee, R. Lesion flow coefficient: A combined anatomical and functional parameter for detection of coronary artery disease—A clinical study. J. Invasive Cardiol.
**2015**, 27, 54–64. [Google Scholar] - Siouffi, M.; Deplano, V.; Pélissier, R. Experimental analysis of unsteady flows through a stenosis. J. Biomech.
**1997**, 31, 11–19. [Google Scholar] [CrossRef] - Douglas, P.S.; Fiolkoski, J.; Berko, B.; Reichek, N. Echocardiographic visualization of coronary artery anatomy in the adult. J. Am. Coll. Cardiol.
**1988**, 11, 565–571. [Google Scholar] [CrossRef] - Solecki, M.; Kruk, M.; Demkow, M.; Schoepf, U.J.; Reynolds, M.A.; Wardziak, Ł.; Dzielińska, Z.; Śpiewak, M.; Miłosz-Wieczorek, B.; Małek, Ł. What is the optimal anatomic location for coronary artery pressure measurement at CT-derived FFR? J. Cardiovasc. Comput. Tomogr.
**2017**, 11, 397–403. [Google Scholar] [CrossRef] - Kenner, T. The measurement of blood density and its meaning. Basic Res. Cardiol.
**1989**, 84, 111–124. [Google Scholar] [CrossRef] [PubMed] - Mayer, G.A. Blood viscosity in healthy subjects and patients with coronary heart disease. Can. Med. Assoc. J.
**1964**, 91, 951. [Google Scholar] [PubMed] - Pijls, N.H.; Van Gelder, B.; Van der Voort, P.; Peels, K.; Bracke, F.A.; Bonnier, H.J.; El Gamal, M.I. Fractional flow reserve: A useful index to evaluate the influence of an epicardial coronary stenosis on myocardial blood flow. Circulation
**1995**, 92, 3183–3193. [Google Scholar] [CrossRef] - Bulant, C.; Blanco, P.; Talou, G.M.; Bezerra, C.G.; Lemos, P.; Feijóo, R. A head-to-head comparison between CT-and IVUS-derived coronary blood flow models. J. Biomech.
**2017**, 51, 65–76. [Google Scholar] [CrossRef] [PubMed] - Wilson, R.F.; Wyche, K.; Christensen, B.V.; Zimmer, S.; Laxson, D.D. Effects of adenosine on human coronary arterial circulation. Circulation
**1990**, 82, 1595–1606. [Google Scholar] [CrossRef] [Green Version] - Park, S.-J.; Kang, S.-J.; Ahn, J.-M.; Shim, E.B.; Kim, Y.-T.; Yun, S.-C.; Song, H.; Lee, J.-Y.; Kim, W.-J.; Park, D.-W. Visual-functional mismatch between coronary angiography and fractional flow reserve. JACC Cardiovasc. Interv.
**2012**, 5, 1029–1036. [Google Scholar] [CrossRef] [Green Version] - Pijls, N.H.; De Bruyne, B. Coronary Pressure; Springer: Berlin/Heidelberg, Germany, 2000; Volume 195. [Google Scholar]
- Pijls, N.H.; De Bruyne, B.; Peels, K.; Van Der Voort, P.H.; Bonnier, H.J.; Bartunek, J.; Koolen, J.J. Measurement of fractional flow reserve to assess the functional severity of coronary-artery stenoses. N. Engl. J. Med.
**1996**, 334, 1703–1708. [Google Scholar] [CrossRef] [PubMed] - Fearon, W.F.; Tonino, P.A.; De Bruyne, B.; Siebert, U.; Pijls, N.H.; Investigators, F.S. Rationale and design of the fractional flow reserve versus angiography for multivessel evaluation (FAME) study. Am. Heart J.
**2007**, 154, 632–636. [Google Scholar] [CrossRef] [PubMed] - Morris, P.D.; van de Vosse, F.N.; Lawford, P.V.; Hose, D.R.; Gunn, J.P. “Virtual” (computed) fractional flow reserve: Current challenges and limitations. JACC Cardiovasc. Interv.
**2015**, 8, 1009–1017. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**A schematic illustration of ideal models inserted with a pressure wire. (

**B**–

**F**) are zoom-in views of stenosis locating at −2D to 2D in the coordinate. (

**A**) represents the non-stenosed (pipe) case, while (

**B**–

**F**) represent the stenotic domains of 30, 40, 50, 60, 70% DS models, respectively.

**Figure 2.**A patient-specific model with a 79% area reduction inserted with a pressure wire along the centerline. The resistance prescribed at the outlet denotes the downstream mircocirculatory resistance.

**Figure 3.**Pressure contours of the ideal models in a cross section. (

**A**) denotes a healthy model, while (

**B**–

**F**) denote the stenotic model with 30–70% DS in the increment of 10%, respectively. (

**1**) and (

**2**) denote the paired model without and with a pressure wire. In order to visualize the variations more easily, different legends are performed in different cases.

**Figure 5.**The value of FFR in the idealized models with 30% to 70% DS in the increment of 10%. The red region denotes the “gray zone” of FFR from 0.75 to 0.80.

Model | DS% | Blockage Ratio | Flow Obstructive Rate |
---|---|---|---|

Ideal | 0% | 1.4% | 3.4% |

30% | 3.0% | 3.8% | |

40% | 4.0% | 4.5% | |

50% | 5.8% | 5.8% | |

60% | 9.0% | 9.8% | |

70% | 16.0% | 20.3% | |

Patient-specific | 54% | 17.8% | 18.7% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yi, J.; Tian, F.-B.; Simmons, A.; Barber, T.
A Computational Analysis of the Influence of a Pressure Wire in Evaluating Coronary Stenosis. *Fluids* **2021**, *6*, 165.
https://doi.org/10.3390/fluids6040165

**AMA Style**

Yi J, Tian F-B, Simmons A, Barber T.
A Computational Analysis of the Influence of a Pressure Wire in Evaluating Coronary Stenosis. *Fluids*. 2021; 6(4):165.
https://doi.org/10.3390/fluids6040165

**Chicago/Turabian Style**

Yi, Jie, Fang-Bao Tian, Anne Simmons, and Tracie Barber.
2021. "A Computational Analysis of the Influence of a Pressure Wire in Evaluating Coronary Stenosis" *Fluids* 6, no. 4: 165.
https://doi.org/10.3390/fluids6040165