Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

Xinyang Ge; Youjun Liu; Zhaofang Yin; Shengxian Tu; Yuqi Fan; Yuri Vassilevski; Sergey Simakov; Fuyou Liang

doi:10.1155/2020/4094121

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

Ge, Xinyang;Liu, Youjun;Yin, Zhaofang;Tu, Shengxian;Fan, Yuqi;Vassilevski, Yuri;Simakov, Sergey;Liang, Fuyou 2020-05-12 00:00:00 Hindawi Journal of Interventional Cardiology Volume 2020, Article ID 4094121, 12 pages https://doi.org/10.1155/2020/4094121 Research Article Comparison of Instantaneous Wave-Free Ratio (iFR) and FractionalFlowReserve(FFR)withrespecttoTheirSensitivitiesto Cardiovascular Factors: A Computational Model-Based Study 1 2 3 4 3 5,6,7 Xinyang Ge, Youjun Liu, Zhaofang Yin, Shengxian Tu, Yuqi Fan, Yuri Vassilevski, 5,6 1,5 Sergey Simakov, and Fuyou Liang School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100124, China Department of Cardiology, Shanghai Ninth People’s Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200011, China Med-X Research Institute, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China Institute for Personalized Medicine, Sechenov University, Moscow 119991, Russia Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia Correspondence should be addressed to Fuyou Liang; fuyouliang@sjtu.edu.cn Received 8 November 2019; Revised 18 January 2020; Accepted 27 February 2020; Published 12 May 2020 Academic Editor: Piotr Musiałek Copyright © 2020 Xinyang Ge et al. /is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. While coronary revascularization strategies guided by instantaneous wave-free ratio (iFR) are, in general, noninferior to those guided by fractional ﬂow reserve (FFR) with respect to the rate of major adverse cardiac events at one-year follow-up in patients with stable angina or an acute coronary syndrome, the overall accuracy of diagnosis with iFR in large patient cohorts is about 80% compared with the diagnosis with FFR. So far, it remains incompletely understood what factors contribute to the discordant diagnosis between iFR and FFR. In this study, a computational method was used to systemically investigate the respective eﬀects of various cardiovascular factors on FFR and iFR. /e results showed that deterioration in aortic valve disease (e.g., regurgitation or stenosis) led to a marked decrease in iFR and a mild increase in FFR given ﬁxed severity of coronary artery stenosis and that increasing coronary microvascular resistance caused a considerable increase in both iFR and FFR, but the degree of increase in iFR was lower than that in FFR. /ese ﬁndings suggest that there is a high probability of discordant diagnosis between iFR and FFR in patients with severe aortic valve disease or coronary microcirculation dysfunction. the hypothesis that there is a diastolic “wave-free” period 1. Introduction (WFP) during the heartbeat period when coronary micro- vascular resistance is inherently stable and minimized [3]. In Fractional ﬂow reserve (FFR), deﬁned as the ratio between mean poststenosis coronary arterial and aortic blood comparison with the measurement of FFR, measuring iFR is pressures under a vasodilator-induced hyperemic condition quicker and cheaper, and more importantly, it can avoid the [1], has been used as a gold standard for assessing the potential side eﬀects (e.g., breathlessness and chest tightness) functional severity of epicardial coronary artery lesions in associated with vasodilator infusion [3]. Clinical studies have the past decades [2]. Recently, the instantaneous wave-free shown that iFR is comparable to FFR with respect to di- ratio (iFR), which can be measured without the need for agnostic categorization [4] and that revascularization vasodilator administration, has emerged as an alternative strategies guided by iFR are noninferior to those guided by index of stenosis severity [3]. /e concept of iFR is based on FFR with respect to the risk of major adverse cardiac events 2 Journal of Interventional Cardiology among patients and have considerable inﬂuence on systemic at 12 months in patients with stable angina or acute coronary syndrome [5, 6]. A study comparing FFR and iFR with a and/or coronary hemodynamics and, based on this, identify the speciﬁc conditions under which iFR and FFR are most third ischemic test (e.g., positron emission tomography myocardial perfusion imaging) as the arbiter showed that likely to give discordant diagnostic results. iFR did not perform diﬀerently from FFR in identifying hemodynamically signiﬁcant ischemic coronary lesions [7]. 2. Materials and Methods On the other hand, some studies have revealed that iFR only correlated weakly with FFR in patients whose FFRs were in 2.1. Conﬁguration of the Computational Model. /e com- the clinically important range for decision making of 0.60 to putational model was adapted from the models developed in 0.90 [8] and that the overall diagnostic accuracy of iFR our previous studies [21, 22] where the modeling methods (using a ROC-determined cutoﬀ value of 0.90) was about and associated numerical schemes have been described in 80% when FFR was used as the reference index for diagnosis detail. In brief, a zero-one-dimensional (0-1-D) multiscale (i.e., discordant diagnosis with iFR and FFR occurred in over modeling method was employed to represent the coronary 20% patients) [9]. So far, reasons underlying the discordant circulation coupled to the global cardiovascular system. 1-D diagnosis between iFR and FFR remain incompletely elu- modeling was applied to large epicardial coronary arteries cidated. /e study by Lee et al. [10] found that patients with and systemic arteries to describe pulse wave propagation and discordant iFR and FFR (i.e., negative iFR while positive pressure/ﬂow waveforms, while 0-D modeling was applied FFR) usually had higher hyperemic myocardial blood ﬂow to intramyocardial vessels and the rest of the global car- and CFR (coronary ﬂow reserve) and higher resting mi- diovascular system to describe intramyocardial and systemic crovascular resistance while there was greater reduction of hemodynamics. Coupling of the 1-D and 0-D models coronary microvascular resistance at hyperemia compared yielded a closed-loop model capable of describing both to patients with concordant iFR and FFR, which implies that coronary and systemic hemodynamics as well as their in- the resting state and hyperemic response of coronary mi- teraction (see Figure 1). More importantly, the model crovasculature may be important factors related to the di- provided a ﬂexible platform for simulating iFR and FFR agnostic agreement between iFR and FFR [11]. In addition, under various pathophysiological conditions through the functional status of the aortic valve has also been modifying the values of model parameters that represent demonstrated to aﬀect the diagnostic performance of iFR various cardiovascular properties. compared with FFR [12, 13]. For instance, it was found that the diagnostic accuracy of iFR in predicting an FFR of ≤0.8 was poor (65%) for coronary lesions in patients with severe 2.2. Parameter Assignment and Model Calibration. Model aortic valve obstruction and tended to improve after parameters were initially assigned based on population- transcatheter aortic valve implantation (TAVI) [13]. Despite averaged data reported in the literature [23, 24] to let model the valuable insights from these clinical studies, a systemic predictions fall in the ranges of in vivo hemodynamic data analysis of the relationship between iFR and FFR under acquired from healthy subjects. It is noted that parameter various pathophysiological conditions with identical severity assignment was implemented for nonhyperemic resting and of coronary artery disease remains absent due to the diﬃ- hyperemic conditions, respectively, in order to meet the culties in completely removing the eﬀects of interpatient requirement for simulating iFR and FFR. Comparisons of variability and measuring all cardiovascular and hemody- model predictions and in vivo measurements under resting namic parameters necessary for analysis in general clinical and hyperemic conditions are summarized in Table 1. In settings. cases when aortic valve diseases (e.g., stenosis and regur- In comparison with in vivo measurements, computa- gitation) were present, model parameters such as resting tional modeling methods provide a more convenient ap- intramyocardial vascular resistance and systemic vascular proach to quantifying the impacts of any pathophysiological resistance were further adjusted so that model-predicted factors of interest on iFR and FFR at ﬁxed severities of coronary arterial ﬂow and systemic arterial pressure were coronary artery disease and thereby establishing a basis for comparable to those measured in patients with aortic valve exploring mechanisms underlying the discordant diagnosis disease [25, 26] (refer to [21] for more details). between iFR and FFR. Computational modeling methods have been widely applied in conjunction with medical im- 2.3. Deﬁnitions of iFR and FFR. iFR was deﬁned as the ratio age-based model reconstruction techniques to predict iFR between the mean values of poststenosis coronary arterial and/or FFR [14–20]. While most model-based studies have and aortic blood pressures (herein denoted by P and demonstrated the ability of computational models to predict d,wf P , respectively) during the diastolic wave-free period iFR and/or FFR with good accuracy in comparison with their a,wf (WFP) under the nonhyperemic resting condition [3]. in vivo counterparts, few studies have been dedicated to Herein, WFP was set to begin in 25% of the way into diastole addressing the relationship between iFR and FFR over a wide and end 5 ms before the end of diastole in accordance with range of pathophysiological conditions. the general deﬁnition of iFR in clinical practice [3]: In the present study, a computational modeling method was employed to quantitatively investigate the respective d,wf iFR � . (1) sensitivities of iFR and FFR to various cardiovascular factors a,wf whose pathophysiological states are expected to diﬀer Journal of Interventional Cardiology 3 0-D model of heart and pulmonary circulation 1-D model of coronary arterial tree 1-D model of systemic arterial tree Systemic arteries Pulmonary circulation Right heart Le h ft ear t L L L L L pua L L LCx B pv R puc R av B LM tv R B pua puv R mv B R R tv pv puc av tv pv puv mv mv av LAD C C C E E E E pua puc puv ra rv la lv RCA S S S S ra rv la lv pc it 0-D model of intramyocardial vessels Subepicardium L R L R L R R 3 3 2 2 1 1 c Intramyocardial Layer no. 1 vessels C C C 3 2 1 P d Midwall im v Layer no. 2 Stenosis im Layer no.3 Subendocardium Systemic distal im vessels 0-D model of small arteries/arterioles /capillaries/venules/veins Figure 1: Schematic description of 0-1-D multiscale modeling of the coronary circulation coupled to the global cardiovascular system. Note that coronary branch arteries in the RCA and LCx territories were modeled but are not presented in the ﬁgure in order to save space. A stenosis was introduced in the middle segment of LAD, with blood pressure immediately distal to it (P ) being monitored along with blood pressure at the aortic root (P ) for the purpose of calculating iFR or FFR. More details of model development, parameter assignment, and numerical methods have been described in our previous studies [21, 22]. Abbreviations: LM, left main artery; LAD, left anterior descending coronary artery; LCx, left circumﬂex coronary artery; RCA, right coronary artery. Notations of main parameters: L, vascular inductance; R, vascular resistance; C, vascular compliance; E, elastance of cardiac chamber; P , intrathoracic pressure; P , intramyocardial tissue pressure. it im Table 1: Comparisons of model simulations and in vivo measurements in terms of main systemic and coronary hemodynamic variables. Resting Hyperemic In vivo measurement Simulation In vivo measurement Simulation Q (mL/min) 76.15± 33.41 [24] 86.60 256.15± 110.84 [24] 264.91 LAD Q (mL/min) 54.62± 24.59 [24] 64.40 163.85± 67.18 [24] 171.26 LCx Q (mL/min) 68.46± 31.87 [24] 72.00 217.69± 76.70 [24] 232.54 RCA P (mmHg) 113.0± 5.0 [23] 121.30 113.00± 6.0 [23] 111.68 as P (mmHg) 74.0± 8.0 [23] 79.70 70.00± 5.0 [23] 74.93 ad CO (L/min) 5.19± 0.83 [23] 5.14 7.6± 1.19 [23] 7.49 Q, mean ﬂow rate over a cardiac cycle; P /P , aortic systolic/diastolic pressure; CO, cardiac output. as ad FFR was deﬁned as the ratio between the mean post- descending coronary artery (LAD) (see Figure 1 for the stenosis coronary arterial and aortic blood pressures (herein location), with its length being ﬁxed at 10 mm while the denoted by P and P , respectively) during the entire diameter stenosis rate (SR) varied from 0% (i.e., no stenosis) d,hp a,hp cardiac cycle under the hyperemic condition [1]: to 70% (i.e., severe stenosis). Heart rate (HR) was set to 66 beats/minute and 90 beats/minute for normal resting and d,hp FFR � . (2) hyperemic conditions, respectively. a,hp 2.5. Sensitivity Analyses of iFR and FFR with respect to Car- 2.4. Baseline Computation Conditions. A stenosis was in- diovascular Factors. Physiologically, iFR and FFR could be troduced in the middle segment of the left anterior aﬀected by any cardiovascular factors involved in the 4 Journal of Interventional Cardiology regulation of coronary and/or systemic hemodynamics changed the value (values) of the model parameter (pa- irrespective of whether they are related to the severity of rameters) corresponding to the factor while ﬁxing other coronary artery disease or not. In the present study, we model parameters at their reference states. In other words, considered six representative factors and categorized them we performed a one-at-a-time parametric study using the into three groups: (1) cardiac factors, which include aortic computational model to evaluate the sensitivity of iFR/FFR valve function, the systolic and diastolic functions of the left with respect to each individual cardiovascular factor. /e ventricle, and heart rate (HR) that aﬀects the magnitude and range of variations in each model parameter was estimated shape of aortic/cardiac blood pressure wave, as well as the based on clinical data measured under the nonhyperemic extravascular tissue pressure of intramyocardial coronary resting condition [22, 27–40] and is listed along with its vessels; (2) systemic vascular factors, which include the reference value in Table 2. It is noted that for the purpose of stiﬀness of the aorta and total systemic vascular resistance simplicity, we assumed that the ranges of parameter vari- that aﬀects the amplitude and mean value of aortic pressure ations relative to their reference values under the hyperemic wave, respectively; and (3) coronary vascular factors, which condition were the same as those assigned for the resting mainly include coronary microvascular resistance, a major condition. In all the sensitivity analyses, the severity of the determinant of trans-stenosis blood ﬂow rate and pressure mid-LAD stenosis was ﬁxed at 50% or 70%. drop given coronary perfusion pressure and severity of /e percentage diﬀerence of computed iFR/FFR relative stenosis. to its reference value (computed with all parameters being held at their reference states) was then calculated to evaluate the impact of varying each model parameter on iFR/FFR. It 2.5.1. Parametric Representations of Cardiovascular Factors is noted that due to the diﬀerential physiological conditions in the Model. All the aforementioned cardiovascular factors under which iFR and FFR are measured, there were two sets were represented in the model with parameters that can be of reference values of model parameters: (1) one set cor- quantitatively modiﬁed to reﬂect the variations in the responding to the intact resting condition, and (2) the other pathophysiological states of the factors. set corresponding to the hyperemic condition. /e status of aortic valve function was controlled by the eﬀective oriﬁce areas of the aortic valve during diastole and 3. Results systole (herein denoted by EOA and EOA , respectively). dia sys Assigning a value of >0 cm to EOA represents the dia 3.1. Changes in iFR and FFR with the Severity of Coronary presence of aortic valve regurgitation (AR), whereas Artery Stenosis and Typical Hemodynamic Characteristics assigning a value lower than 4 cm (i.e., the normal value of during iFR Measurement. Numerical simulations were EOA ) to EOA represents the presence of aortic valve sys sys ﬁrstly carried out to simulate iFR and FFR, respectively, with stenosis (AS). Accordingly, progressively increasing EOA dia the severity of the mid-LAD stenosis being increased in- 2 2 (from 0 to 0.3 cm ) and reducing EOA (from 4 to 1.0 cm ) sys crementally from 0% (no stenosis) to 70% (severe stenosis) represent the increasing severities of AR and AS, respec- while other cardiovascular factors ﬁxed at their reference tively. /e systolic and diastolic functions of the left ventricle resting or hyperemic states. /e simulated values of iFR and were parametrically represented by the peak systolic ela- FFR both decreased monotonously with the severity of stance (E ) and baseline diastolic elastance (E ), respec- lva lvb stenosis (see Figure 2). If a FFR of 0.8 was taken as the tively. Increasing E represents the enhancement in lva threshold for identifying a physiologically signiﬁcant lesion myocardial contractility during systole, whereas increasing [41], the corresponding iFR was 0.913, a value close to the E represents the stiﬀening of the ventricular chamber (or lvb cutoﬀ value (0.89–0.93) established in previous clinical impairment in myocardial relaxation) during diastole. HR studies [12, 42, 43]. /ese results indicate that our model can was assigned directly in the model. reasonably predict the general relationship between iFR and /e stiﬀness of the aorta was controlled by the value FFR in the context of various severities of coronary artery assigned to the elastic modulus of the aortic wall in the stenosis. model. Since the elastic modulus of the aortic wall is the Figure 3 shows the model-simulated pressure waves in main determinant of the aortic pulse wave velocity (aPWV), the ascending aorta and those immediately distal to a 50% we herein took aPWV as a measure of aortic stiﬀness. An stenosis in mid-LAD under the control condition (i.e., all increase in aPWV corresponds to an increase in aortic model parameters were at the reference state) and under two stiﬀness. /e total systemic vascular resistance (R ) and sys altered physiological conditions characterized by a 67% coronary microvascular resistance (R ) are holistic de- cmv increase in HR and a 200% elevation in aPWV, respectively. scriptions of vascular resistances distributed in systemic /e wave-free pressure portions used to calculate iFR are tissues/organs and myocardium, respectively, and were highlighted by the gray shadows. Figure 3 also shows the modiﬁed by simultaneously varying all the corresponding corresponding time histories of wave intensity (WI) in the vascular resistances. LAD (Figures 3(d)–3(f)) and total resistance of coronary vessels distal to the stenosis (Figures 3(g)–3(i)). As expected, 2.5.2. Quantiﬁcation of the Sensitivities of iFR and FFR to the variations in HR and aPWV both led to considerable Cardiovascular Factors. In order to investigate how iFR/FFR changes in pressure waveform and time history of WI via is aﬀected by varying the pathophysiological state of each their inﬂuence on pressure wave propagation and reﬂection aforementioned cardiovascular factor, we incrementally in the systemic arterial system, but they had little inﬂuence Journal of Interventional Cardiology 5 Table 2: Reference values of model parameters involved in the sensitivity analyses for iFR and FFR under resting and hyperemic conditions. Model parameter Reference value (resting/hyperemic) Range of variation (resting) EOA (cm ) 0.0/0.0 (0.0∼0.3) [27] dia EOA (cm ) 4.0/4.0 (4.0∼1.0) [28, 29] sys E (mmHg/ml) 2.87/2.87 (1.435∼6.601) [30] lva E (mmHg/ml) 0.056/0.056 (0.028∼0.112) [30] lvb HR (beats/min) 66/90 (48∼111) [31, 32] aPWV (m/s) 4.7/4.7 (3.478∼10.011) [33–35] R (mmHg·s/ml) 1.14/0.98 (0.456∼1.824) [36, 37] sys R (mmHg·s/ml) 196.97/45.94 (157.58∼433.33) [38–40] cmv Note that the ranges of parameter variations under resting condition were estimated based on available clinical data reported in the literature. 1.0 1.0 mildly aﬀected by the variations in EOA or EOA . dia sys Moreover, varying EOA or EOA induced opposite dia sys changes in iFR and FFR. For instance, increasing EOA 0.9 0.9 dia (representing a progressive deterioration in AR) or de- iFR = 0.913 creasing EOA (representing a progressive deterioration in 0.8 0.8 sys AS) remarkably reduced iFR whilst it elevated FFR mildly. When the results of the sensitivity analyses were further 0.7 0.7 investigated with respect to the severity of coronary artery stenosis, an increase in stenosis rate (i.e., from 50% to 70%) 0.6 0.6 was observed to considerably augment the sensitivities of iFR and FFR to EOA and EOA . Relatively, both iFR and dia sys 0.5 0.5 FFR were insensitive to the systolic and diastolic functions of SR = 51% the left ventricle (represented by E and E ) and HR. lva lvb 0.4 0.4 Varying the systemic vascular factors (i.e., aortic stiﬀness –10 0 1020304050607080 represented by aPWV and total systemic vascular resistance Stenosis rate (%) (R )) induced detectable while only mild changes in iFR sys iFR and FFR (see Figures 4(f) and 4(g)). As is diﬀerent from FFR systemic vascular factors, increasing coronary microvascular resistance (R ) under the resting or hyperemic condition cmv Figure 2: Model-simulated changes in iFR/FFR with the increase tended to signiﬁcantly elevate iFR and FFR, although the in the severity (i.e., the diameter stenosis rate is increased from 0% degree of elevation in FFR was larger than that in iFR (see to 70% at an interval of 10%) of a stenosis present in mid-LAD Figure 4(h)). under the control resting/hyperemic condition. When FFR is at the cutoﬀ value (i.e., 0.8), the corresponding stenosis rate (SR) is 51% In summary, if a maximal percentage change in iFR or and iFR is 0.913. FFR of >10% in response to the variations in a model pa- rameter was set as the threshold for judging high sensitivity, iFR was observed to be highly sensitive to EOA , EOA dia sys on iFR. In the wave-free period (WFP), WI was close to zero, (aortic valve function), and R (state of coronary mi- cmv proving that the “wave-free” assumption in the deﬁnition of crovasculature), whereas FFR was solely sensitive to R . cmv iFR is reasonable; however, the poststenosis coronary vas- cular resistance was not constant during WFP. Nevertheless, the relatively low value of poststenosis vascular resistance 3.3. Hemodynamic Characteristics Underlying the Diﬀerential during WFP compared with that in systole can still partly Sensitivities of iFR and FFR to Aortic Valve Function and support the clinical hypothesis that iFR is an index derived Coronary Microvascular Resistance. In order to explore under the condition of low coronary vascular resistance. hemodynamic characteristics underlying the diﬀerential sensitivities of iFR and FFR to aortic valve function and coronary microvascular resistance, taking the 50% mid-LAD 3.2. Sensitivities of iFR and FFR to Variations in the State of stenosis as an example, we plotted the model-simulated Each Cardiovascular Factor. /e sensitivities of iFR and FFR aortic pressure wave and poststenosis coronary arterial to variations in each of the eight model parameters that pressure/ﬂow waves and poststenosis coronary microvas- represent various cardiac or vascular factors are presented in cular resistance under the control condition (i.e., all model the form of percentage changes relative to the reference parameters were ﬁxed at their reference states) against those values of iFR and FFR in Figure 4. under the condition characterized by the presence of severe As for the sensitivities of iFR and FFR to cardiac factors aortic valve stenosis (AS) (represented by setting (represented by EOA , EOA , E , E , and HR in the dia sys lva lvb EOA � 1.0 cm ) or increased coronary microvascular re- sys model) (see Figures 4(a)–4(e)), iFR was observed to be sistance (represented by increasing R by 120%) in Fig- cmv highly sensitive to both EOA and EOA that represent dia sys ure 5. It is noted that the numerical simulations were the status of the aortic valve function, whereas FFR was only performed under the resting and hyperemic conditions, iFR FFR 6 Journal of Interventional Cardiology 140 140 140 WFP WFP WFP 120 120 120 100 100 100 iFR = 0.932 iFR = 0.920 80 80 80 iFR = 0.922 Control 67% increase in HR 200% increase in aPWV 60 60 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) P P P a a a P P P d d d (a) (b) (c) 1.0 1.0 1.0 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) (d) (e) (f) 300 300 300 200 200 200 100 100 100 0 0 0 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) (g) (h) (i) Figure 3: Model-simulated aortic and poststenosis coronary arterial pressure waves (a∼c), wave intensity in mid-LAD (d∼f), and poststenosis coronary microvascular resistance (g∼i) during iFR measurement under the control and two altered physiological conditions (one with a 67% increase in HR and the other with a 200% increase in aPWV). /e wave-free period (WFP) during a cardiac cycle is highlighted by the gray shadow. /e stenosis was present in mid-LAD, with the stenosis rate being ﬁxed at 50% in all the simulations. respectively, in consideration of the diﬀerential physiological comparable to or even slightly lower than that under the conditions corresponding to iFR and FFR measurements. control condition (which is consistent with previous Under the resting condition, although the presence of clinical observations [44]), leading to a mild increase in severe AS induced a marked decrease in both aortic and FFR. poststenosis coronary pressures, the degree of decrease in In contrast to AS, increasing coronary microvascular poststenosis pressure was larger than that of aortic pres- resistance under the resting or hyperemic condition had an sure, resulting in an evident decrease in iFR. /e enhanced overall small inﬂuence on the aortic pressure, but signiﬁ- decrease in poststenosis pressure was caused mainly by the cantly elevated the poststenosis coronary pressure primarily increased resting coronary blood ﬂow (which augments the due to its role in reducing trans-stenosis ﬂow rate. Such pressure drop across the stenosis) as a consequence of eﬀects were particularly pronounced under the hyperemic coronary microvascular adaptive responses to increased condition when the ﬂow rate was higher and more sensitive myocardial stress and oxygen demand in the presence of AS to the variation in poststenosis coronary vascular resistance [21]. Under the hyperemic condition, the simulated cor- (see Figure 5(h)) compared with the resting condition, onary blood ﬂow rate in the presence of AS was however thereby leading to a larger increase in FFR than in iFR. R (mmHg/mL/s) 5 Blood pressure (mmHg) cmv WI (W·10 ) R (mmHg/mL/s) 5 Blood pressure (mmHg) cmv WI (W·10 ) R (mmHg/mL/s) Blood pressure (mmHg) cmv WI (W·10 ) Journal of Interventional Cardiology 7 40 40 40 20 20 20 0 0 0 –20 –20 –20 –40 –40 –40 0.0 0.1 0.2 0.3 4321 0.4 0.8 1.2 1.6 2.0 2.4 2 2 EOA (cm ) EOA (cm ) E (normalized) dia sys lva iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (a) (b) (c) 40 40 40 20 20 20 0 0 0 –20 –20 –20 –40 –40 –40 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 0.8 1.2 1.6 2.0 E (normalized) HR (normalized) aPWV (normalized) lvb iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (d) (e) (f) 40 40 20 20 0 0 –20 –20 –40 –40 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.8 1.2 1.6 2.0 2.4 R (normalized) R (normalized) sys cmv iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (g) (h) Figure 4: Percentage changes of iFR and FFR relative to their reference values upon the variations of each model parameter. /e variations of all parameters except for EOA and EOA are expressed in normalized form relative to their reference values to facilitate the dia sys comparisons of the eﬀects on iFR/FFR among diﬀerent parameters. /e stenosis is present in mid-LAD with its stenosis rate being set at 50% and 70%, respectively, and the corresponding reference values (computed with all model parameters being ﬁxed at their reference states) of iFR/FFR are 0.920/0.813 and 0.677/0.534, respectively. (a) EOA . (b) EOA . (c) E . (d) E . (e) HR. (f) aPWV. (g) R . (h) R . dia sys lva lvb sys cmv Notations: EOA /EOA , eﬀective oriﬁce area of aortic valve during diastole/systole (an increase in EOA represents an increase in the dia sys dia severity of aortic valve regurgitation, whereas a decrease in EOA represents an increase in the severity of aortic valve stenosis); E /E , sys lva lvb peak systolic elastance/baseline diastolic elastance of the left ventricle; HR, heart rate; aPWV, aortic pulse wave velocity; R , total systemic sys vascular resistance; R , total coronary microvascular resistance. cmv and FFR to various cardiovascular factors involved in the 4. Discussion regulation of systemic and/or coronary hemodynamics. /e In the present study, we employed a computational model to results revealed that iFR and FFR diﬀered considerably with respect to the cardiovascular factors to which they are simulate the processes of iFR and FFR measurements and quantitatively investigated the respective sensitivities of iFR sensitive and the degree and/or pattern of changes in Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) 8 Journal of Interventional Cardiology Resting Hyperemic Resting Hyperemic 125 125 125 100 100 100 75 75 75 iFR = 0.920 iFR = 0.960 FFR = 0.832 FFR = 0.917 iFR = 0.852 FFR = 0.813 iFR = 0.920 FFR = 0.813 50 50 50 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 Time (s) Time (s) Time (s) Time (s) P (control) P (control) P (control) P (control) a a a P (control) P (control) P (control) P (control) d d P (severe AS) P (severe AS) P (120% increase in R ) P (120% increase in R ) a cmv a cmv P (severe AS) P (severe AS) P (120% increase in R ) P (120% increase in R ) d d cmv d cmv (a) (b) (c) (d) Resting Hyperemic Resting Hyperemic 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 Time (s) Time (s) Time (s) Time (s) Q (control) Q (control) Q (control) Q (control) dis dis dis dis Q (severe AS) Q (severe AS) Q (120% increase in R ) Q (120% increase in R ) dis dis dis cmvr dis cmvr (e) (f) (g) (h) Resting Hyperemic Resting Hyperemic 300 300 600 300 200 200 400 200 100 100 200 100 0 0 0 0 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) Time (s) control control control control severe AS severe AS 120% increase in R 120% increase inR cmv cmv (i) (j) (k) (l) Figure 5: Comparisons of model-simulated aortic pressure wave and coronary arterial pressure wave distal to a 50% stenosis in mid-LAD and iFR/FFR (a∼d), ﬂow wave in mid-LAD (e∼h), and poststenosis coronary microvascular resistance (i∼l) under control resting/hyperemic condition with those in the presence of severe AS (EOA � 1.0 cm ) or increased coronary microvascular resistance (increased by 120% sys relative to the reference value). response to the variations in the state of each cardiovascular consistent with relevant clinical observations reported in the factor. literature. For instance, it was found that in patients with /e model-predicted marked decrease in iFR while mild severe AS, the conventional iFR cutoﬀ value had lower increase in FFR following increasing severity of AS (simu- diagnostic agreement with FFR in the classiﬁcation of lated by reducing the value of EOA in the model) implies coronary lesions and that a lower iFR cutoﬀ value (e.g., sys shifting the cutoﬀ value from 0.89 to 0.83) should be used in that in patients with severe AS, the measured iFRs may be much lower than those in patients with equivalent severity of order to better predict a positive FFR [12, 13, 45, 46]. In the coronary artery disease while normal aortic valve function, case of increasing severity of AR (simulated by increasing the although the measured FFRs in the two patient cohorts value assigned to EOA in the model), our study revealed dia might be comparable, which may consequently lead to in- similar patterns of diﬀerential changes in iFR and FFR to creased probability of discordant diagnosis between iFR and those found in the case of increasing severity of AS and FFR in the former patient cohort if cutoﬀ values of iFR and would cause a similar trend of discordant diagnosis between FFR established based on clinical data acquired from the iFR and FFR, although relevant clinical evidence from latter patient cohort were used. /ese theoretical ﬁndings are studies focused on patients with AR is rare, probably due to R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) Journal of Interventional Cardiology 9 the low prevalence of AR in patients with coronary artery 0.98 disease [47]. 0.96 Unlike aortic valve disease which aﬀects iFR and FFR in opposite ways, increasing coronary microvascular resistance Reference iFR 0.94 led to a considerable increase in both iFR and FFR, although the degree of increase in iFR was lower than that in FFR. /e 0.92 diﬀerential eﬀects of coronary microvascular resistance on 0.90 iFR and FFR would become more evident when the resting coronary microvascular resistance is preserved while the 0.88 hyperemic counterpart is higher than the normal value due to impaired vasodilation function, which may explain why 0.86 Decrease in iFR with low iFR and high FFR (i.e., iFR+/FFR−) were more fre- increasing severity of AS 0.84 quently observed in patients with diabetes mellitus who 1.0 1.2 1.4 1.6 1.8 2.0 2.2 usually have increased coronary microvascular resistance R (normalized) and low coronary ﬂow at hyperemia due to microcirculation cmv dysfunction [48, 49]. EOA = 4.0 (cm ) (no AS) sys Relatively, varying left ventricular systolic and diastolic functions and HR and systemic vascular factors (i.e., aortic EOA = 2.0 (cm ) (moderate AS) sys stiﬀness and systemic vascular resistance) over large ranges EOA = 1.0 (cm ) (severe AS) sys only had mild inﬂuences on iFR and FFR, which indicates (a) that iFR and FFR would both perform well in assessing the functional severity of coronary artery lesions irrespective of 0.94 potential high interpatient variability in these cardiac or 0.92 vascular properties. In summary, the present study demonstrates the general 0.90 trend that iFR and FFR are more likely to give discordant Increase in FFR with increasing diagnostic results in the presence of severe aortic valve 0.88 severity of AS disease (stenosis or regurgitation) or increased coronary microvascular resistance. /erefore, special caution should 0.86 be taken in the interpretation of measured iFR and FFR or 0.84 the use of general cutoﬀ values for diagnosis in patients with these speciﬁc cardiovascular conditions. Furthermore, given Reference FFR 0.82 the diﬀerential eﬀects on iFR and FFR of aortic valve disease and increased coronary microvascular resistance, the 0.80 changes in iFR and FFR would become more complex in the 1.0 1.2 1.4 1.6 1.8 2.0 2.2 presence of aortic valve disease combined with increased R (normalized) cmv coronary microvascular resistance. Our additional numer- EOA = 4.0 (cm ) (no AS) ical tests revealed that increasing coronary microvascular sys resistance could counteract or even reverse the decrease in EOA = 2.0 (cm ) (moderate AS) sys iFR whilst augmenting the increase in FFR caused by aortic EOA = 1.0 (cm ) (severe AS) sys valve stenosis (see Figure 6). In this sense, in patients suf- fering from concomitant aortic valve disease and coronary (b) microcirculation dysfunction, the diagnostic agreement Figure 6: Eﬀects of diﬀerent combinations of AS (with its severity between iFR and FFR could be highly complex and should be being controlled by the value of EOA ) and increased coronary sys carefully interpreted in the context of patient-speciﬁc microvascular resistance (R , herein normalized by its reference cmv conditions. normal value) on (a) iFR and (b) FFR. Increasing the severity of AS leads to a marked decrease in iFR and moderate increase in FFR, 5. Limitations whereas increasing R causes a progressive increase in both iFR and cmv FFR. As a consequence, increasing R counteracts or even reverses cmv While our study, through quantifying the respective sensi- the decrease in iFR while augments the increase in FFR caused by AS. tivities of iFR and FFR to the variations in the patho- Note that the coronary stenosis is present in mid-LAD with its severity physiological state of each individual cardiovascular factor, being ﬁxed at 50% in all the simulations and that the values of iFR and provided useful insights for exploring mechanisms under- FFR highlighted by the ﬁlled circles indicate their reference values computed under the condition that only the 50% coronary stenosis is lying the clinically observed discordant diagnosis between present while AS and increased R are absent. iFR and FFR in some patient cohorts, the study is limited by cmv its theoretical nature and the focus on single-factor sensi- tivity analyses that render the ﬁndings unable to be applied may deviate signiﬁcantly from those represented by the directly to explain the measurements in individual patients model. In addition, the numerical simulations tailored to whose cardiovascular conditions are highly complex and single-factor sensitivity analyses were not suﬃcient to Increase in iFR with increasing R cmv Increase in FFR with increasing R cmv FFR iFR 10 Journal of Interventional Cardiology generate a large database for statistical determination of the References cutoﬀ values of iFR or FFR under speciﬁc pathological [1] N. H. J. Pijls, B. De Bruyne, K. Peels et al., “Measurement of conditions (e.g., various types and severities of aortic valve fractional ﬂow reserve to assess the functional severity of disease combined with other cardiovascular abnormalities). coronary-artery stenoses,” New England Journal of Medicine, For this purpose, large-scale stochastic numerical simula- vol. 334, no. 26, pp. 1703–1708, 1996. tions (similar to those reported in [50]) that cover a wide [2] T. Force, S. Windecker, P. Kolh et al., “ESC/EACTS guidelines range of various pathophysiological conditions would be on myocardial revascularization: the task force on myocardial needed. /e 0-1-D multiscale model employed in the present revascularization of the European society of cardiology (ESC) study is however computationally costly and therefore not and the European association for cardio-thoracic surgery well suited to such a study. /e problem might be solved by (EACTS) developed with the special contribution of the developing a lumped-parameter model that contains the European association of percutaneous cardiovascular inter- ventions (EAPCI),” European Heart Journal, vol. 35, no. 37, main components of the present model whilst is compu- pp. 2541–2619, 2014. tationally much cheaper, which would be addressed in our [3] S. Sen, J. Escaned, I. S. Malik et al., “Development and val- future studies. idation of a new adenosine-independent index of stenosis severity from coronary wave-intensity analysis,” Journal of the 6. Conclusion American College of Cardiology, vol. 59, no. 15, pp. 1392–1402, A computational model-based numerical study has been [4] S. Sen, K. N. Asrress, S. Nijjer et al., “Diagnostic classiﬁcation carried out to compare the sensitivities of iFR and FFR to of the instantaneous wave-free ratio is equivalent to fractional variations in the pathophysiological states of various car- ﬂow reserve and is not improved with adenosine adminis- diovascular factors. It was found that aortic valve disease and tration,” Journal of the American College of Cardiology, vol. 61, increased coronary microvascular resistance had consider- no. 13, pp. 1409–1420, 2013. able while diﬀerential inﬂuences on iFR and FFR, which [5] J. E. Davies, S. Sen, H. M. Dehbi et al., “Use of the instan- provides theoretical evidence for explaining the increased taneous wave-free ratio or fractional ﬂow reserve in PCI,” <e New England Journal of Medicine, vol. 376, no. 376, risk of discordant diagnosis between iFR and FFR in patients pp. 1824–1834, 2017. with aortic valve disease or coronary microcirculation [6] M. Gotberg, ¨ E. H. Christiansen, I. J. Gudmundsdottir et al., dysfunction. “Instantaneous wave-free ratio versus fractional ﬂow reserve to guide PCI,” New England Journal of Medicine, vol. 376, Data Availability no. 19, pp. 1813–1823, 2017. [7] G. A. de Waard, I. Danad, R. Petraco et al., “Fractional ﬂow All clinical data used in the present study have been reported reserve, instantaneous wave-free ratio, and resting P /P d a in the corresponding references and the values of most compared with [ O]H O positron emission tomography model parameters not provided in the manuscript have been myocardial perfusion imaging: a PACIFIC trial sub-study,” reported in a previous study of ours [21] (https:// European Heart Journal, vol. 39, no. 46, pp. 4072–4081, 2018. onlinelibrary.wiley.com/doi/full/10.1002/cnm.3257). [8] C. Berry, M. van’t Veer, N. Witt et al., “VERIFY (VERiﬁcation of instantaneous wave-free ratio and fractional ﬂow reserve for the assessment of coronary artery stenosis severity in Conflicts of Interest EverydaY practice),” Journal of the American College of Cardiology, vol. 61, no. 13, pp. 1421–1427, 2013. /e authors have no conﬂicts of interest to declare. [9] A. Jeremias, A. Maehara, P. Gen ´ ereux ´ et al., “Multicenter core laboratory comparison of the instantaneous wave-free ratio Authors’ Contributions and resting P /P with fractional ﬂow reserve,” Journal of the d a American College of Cardiology, vol. 63, no. 13, pp. 1253–1261, Xinyang Ge built the computational model, performed numerical simulations, and drafted the manuscript. Youjun [10] J. M. Lee, D. Hwang, J. Park, Y. Tong, and B.-K. Koo, Liu and Shengxian Tu analyzed the data and revised the “Physiologic mechanism of discordance between instanta- manuscript. Zhaofang Yin and Yuqi Fan interpreted the data neous wave-free ratio and fractional ﬂow reserve: insight from from the clinical point of view. Sergey Simakov and Yuri 13 N-ammonium positron emission tomography,” Interna- tional Journal of Cardiology, vol. 243, pp. 91–94, 2017. Vassilevski optimized the computational model and revised [11] H. Matsuo, Y. Kawase, and I. Kawamura, “FFR and iFR,” the manuscript. Fuyou Liang designed the study, interpreted Annals of Nuclear Cardiology, vol. 3, no. 1, pp. 53–60, 2017. the data, and revised the manuscript. All authors have read [12] R. Scarsini, G. Pesarini, C. Zivelonghi et al., “Coronary and approved the ﬁnal manuscript. physiology in patients with severe aortic stenosis: comparison between fractional ﬂow reserve and instantaneous wave-free Acknowledgments ratio,” International Journal of Cardiology, vol. 243, pp. 40–46, /e study was supported in part by the National Natural [13] R. Scarsini, G. Pesarini, C. Zivelonghi et al., “Physiologic Science Foundation of China (Grant nos. 11832003, evaluation of coronary lesions using instantaneous wave-free 11972231, and 81611530715) and the SJTU Medical-Engi- ratio (iFR) in patients with severe aortic stenosis undergoing neering Cross-cutting Research Project (Grant no. transcatheter aortic valve implantation,” EuroIntervention, YG2016MS09). vol. 13, no. 13, pp. 1512–1519, 2018. Journal of Interventional Cardiology 11 [14] C. A. Taylor, T. A. Fonte, and J. K. Min, “Computational ﬂuid [27] M. Enriquez-Sarano and A. J. Tajik, “Aortic regurgitation,” dynamics applied to cardiac computed tomography for New England Journal of Medicine, vol. 351, no. 15, pp. 1539–1546, 2004. noninvasive quantiﬁcation of fractional ﬂow reserve,” Journal [28] D. Garcia, P. G. Camici, L.-G. Durand et al., “Impairment of of the American College of Cardiology, vol. 61, no. 22, coronary ﬂow reserve in aortic stenosis,” Journal of Applied pp. 2233–2241, 2013. Physiology, vol. 106, no. 1, pp. 113–121, 2009. [15] Y. Ma, H. Liu, Y. Hou et al., “Instantaneous wave-free ratio [29] P. Pibarot and J. G. Dumesnil, “Improving assessment of derived from coronary computed tomography angiography in aortic stenosis,” Journal of the American College of Cardiology, evaluation of ischemia-causing coronary stenosis: feasibility vol. 60, no. 3, pp. 169–180, 2012. and initial clinical research,” Medicine, vol. 96, no. 4, p. e5979, [30] F. Liang, H. Senzaki, C. Kurishima, K. Sughimoto, R. Inuzuka, and H. Liu, “Hemodynamic performance of the Fontan cir- [16] L. Calmac, R. Niculescu, E. Badila et al., “TCT-40 image-based culation compared with a normal biventricular circulation: a computation of instantaneous wave-free ratio from routine computational model study,” American Journal of Physiology- coronary angiography-initial validation by invasively mea- Heart and Circulatory Physiology, vol. 307, no. 7, sured coronary pressures,” Journal of the American College of pp. H1056–H1072, 2014. Cardiology, vol. 66, no. 15, pp. B17–B18, 2015. [31] J. M. Mangrum and J. P. Dimarco, “/e evaluation and [17] W. Wang, B. Mao, B. Li et al., “Numerical simulation of management of bradycardia,” New England Journal of Med- instantaneous wave-free ratio of stenosed coronary artery,” icine, vol. 342, no. 10, pp. 703–709, 2000. International Journal of Computational Methods, vol. 16, [32] A. F. Chu, E. Zado, and F. E. Marchlinski, “Atrial arrhythmias no. 3, Article ID 1842009, 2019. in patients with arrhythmogenic right ventricular cardio- [18] J. M. Carson, S. Pant, C. Roobottom et al., “Non-invasive myopathy/dysplasia and ventricular tachycardia,” <e coronary CT angiography-derived fractional ﬂow reserve: a American Journal of Cardiology, vol. 106, no. 5, pp. 720–722, benchmark study comparing the diagnostic performance of four diﬀerent computational methodologies,” International [33] P. V. Vaitkevicius, J. L. Fleg, J. H. Engel et al., “Eﬀects of age Journal for Numerical Methods in Biomedical Engineering, and aerobic capacity on arterial stiﬀness in healthy adults,” vol. 35, no. 10, p. e3235, 2019. Circulation, vol. 88, no. 4, pp. 1456–1462, 1993. [19] L. O. Muller, ¨ F. E. Fossan, A. T. Braten, ˚ A. Jørgensen, [34] R. P. Wildman, G. N. Farhat, A. S. Patel et al., “Weight change R. Wiseth, and L. R. Hellevik, “Impact of baseline coronary is associated with change in arterial stiﬀness among healthy ﬂow and its distribution on Fractional Flow Reserve pre- young adults,” Hypertension, vol. 45, no. 2, pp. 187–192, 2005. diction,” International Journal for Numerical Methods in [35] Z. Dhakam, Yasmin, C. M. McEniery, T. Burton, M. J. Brown, Biomedical Engineering, p. e3246, 2019. and I. B. Wilkinson, “A comparison of atenolol and nebivolol [20] J. Carson, C. Roobottom, R. Alcock, and P. Nithiarasu, in isolated systolic hypertension,” Journal of Hypertension, “Computational instantaneous wave-free ratio (IFR) for pa- vol. 26, no. 2, pp. 351–356, 2008. tient-speciﬁc coronary artery stenoses using 1D network [36] W. G. Haynes, C. J. Ferro, K. P. J. O’Kane, D. Somerville, models,” International Journal for Numerical Methods in C. C. Lomax, and D. J. Webb, “Systemic endothelin receptor Biomedical Engineering, vol. 35, no. 11, p. e3255, 2019. blockade decreases peripheral vascular resistance and blood [21] X. Ge, Y. Liu, S. Tu, S. Simakov, Y. Vassilevski, and F. Liang, pressure in humans,” Circulation, vol. 93, no. 10, pp. 1860– “Model-based analysis of the sensitivities and diagnostic 1870, 1996. implications of FFR and CFR under various pathological [37] T. Linde, B. Sandhagen, A. Hagg, ¨ C. Morlin, ¨ B. Wikstrom, ¨ and conditions,” International Journal for Numerical Methods in B. G. Danielson, “Blood viscosity and peripheral vascular Biomedical Engineering, p. e3257, 2019. resistance in patients with untreated essential hypertension,” [22] X. Ge, Z. Yin, Y. Fan, Y. Vassilevski, and F. Liang, “A multi- Journal of Hypertension, vol. 11, no. 7, pp. 731–736, 1993. scale model of the coronary circulation applied to investigate [38] S. E. Reis, R. Holubkov, J. S. Lee et al., “Coronary ﬂow velocity transmural myocardial ﬂow,” International Journal for Nu- response to adenosine characterizes coronary microvascular merical Methods in Biomedical Engineering, vol. 34, no. 10, function in women with chest pain and no obstructive cor- p. e3123, 2018. onary disease,” Journal of the American College of Cardiology, [23] N. Watzinger, G. K. Lund, M. Saeed et al., “Myocardial blood vol. 33, no. 6, pp. 1469–1475, 1999. ﬂow in patients with dilated cardiomyopathy: quantitative [39] M. Fineschi, A. Bravi, and T. Gori, “/e “slow coronary ﬂow” assessment with velocity-encoded cine magnetic resonance phenomenon: evidence of preserved coronary ﬂow reserve imaging of the coronary sinus,” Journal of Magnetic Reso- despite increased resting microvascular resistances,” Inter- nance Imaging, vol. 21, no. 4, pp. 347–353, 2005. national Journal of Cardiology, vol. 127, no. 3, pp. 358–361, [24] H. Wieneke, C. Von Birgelen, M. Haude et al., “Determinants of coronary blood ﬂow in humans: quantiﬁcation by intra- [40] R. F. Wilson, K. Wyche, B. V. Christensen, S. Zimmer, and coronary Doppler and ultrasound,” Journal of Applied D. D. Laxson, “Eﬀects of adenosine on human coronary ar- Physiology, vol. 98, no. 3, pp. 1076–1082, 2005. terial circulation,” Circulation, vol. 82, no. 5, pp. 1595–1606, [25] A. Nitenberg, J.-M. Foult, I. Antony, F. Blanchet, and M. Rahali, “Coronary ﬂow and resistance reserve in patients [41] D.-Y. Kang, J.-M. Ahn, Y. W. Kim et al., “Impact of coronary with chronic aortic regurgitation, angina pectoris and normal lesion geometry on fractional ﬂow reserve: data from inter- coronary arteries,” Journal of the American College of Car- ventional cardiology research in-cooperation society-frac- diology, vol. 11, no. 3, pp. 478–486, 1988. tional ﬂow reserve and intravascular ultrasound registry,” [26] P. Meimoun, A. L. Germain, F. Elmkies et al., “Factors as- Circulation: Cardiovascular Imaging, vol. 11, no. 6, Article ID sociated with noninvasive coronary ﬂow reserve in severe e007087, 2018. aortic stenosis,” Journal of the American Society of Echocar- [42] L. Itu, T. Passerini, E. Badila et al., “Image-based computation diography, vol. 25, no. 8, pp. 835–841, 2012. of instantaneous wave-free ratio from routine coronary 12 Journal of Interventional Cardiology angiography: evaluation of a hybrid decision making strategy with ﬀr,” Journal of the American College of Cardiology, vol. 67, no. 13, p. 328, 2016. [43] R. Scarsini, G. Pesarini, M. Lunardi et al., “Observations from a real-time, iFR-FFR “hybrid approach” in patients with se- vere aortic stenosis and coronary artery disease undergoing TAVI,” Cardiovascular Revascularization Medicine, vol. 19, no. 3, pp. 355–359, 2018. [44] F. R. Eberli, M. Ritter, J. Schwitter et al., “Coronary reserve in patients with aortic valve disease before and after successful aortic valve replacement,” European Heart Journal, vol. 12, no. 2, pp. 127–138, 1991. [45] F. Yamanaka, K. Shishido, T. Ochiai et al., “Instantaneous wave-free ratio for the assessment of intermediate coronary artery stenosis in patients with severe aortic valve stenosis: comparison with myocardial perfusion scintigraphy,” JACC: Cardiovascular Interventions, vol. 11, no. 20, pp. 2032–2040, [46] R. Scarsini, R. Cantone, G. Venturi et al., “Correlation be- tween intracoronary physiology and myocardial perfusion imaging in patients with severe aortic stenosis,” International Journal of Cardiology, vol. 292, pp. 162–165, 2019. [47] A.-H. Hakki, D. Kimbiris, A. S. Iskandrian, B. L. Segal, G. S. Mintz, and C. E. Bemis, “Angina pectoris and coronary artery disease in patients with severe aortic valvular disease,” American Heart Journal, vol. 100, no. 4, pp. 441–449, 1980. [48] C. M. Cook, A. Jeremias, R. Petraco et al., “Fractional ﬂow reserve/instantaneous wave-free ratio discordance in angio- graphically intermediate coronary stenoses,” JACC: Cardio- vascular Interventions, vol. 10, no. 24, pp. 2514–2524, 2017. [49] J. M. Lee, E.-S. Shin, C.-W. Nam et al., “Discrepancy between fractional ﬂow reserve and instantaneous wave-free ratio: clinical and angiographic characteristics,” International Journal of Cardiology, vol. 245, pp. 63–68, 2017. [50] T. Wang, F. Liang, Z. Zhou, and X. Qi, “Global sensitivity analysis of hepatic venous pressure gradient (HVPG) mea- surement with a stochastic computational model of the he- patic circulation,” Computers in Biology and Medicine, vol. 97, pp. 124–136, 2018. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Interventional Cardiology Hindawi Publishing Corporation http://www.deepdyve.com/lp/hindawi-publishing-corporation/comparison-of-instantaneous-wave-free-ratio-ifr-and-fractional-flow-cM6elq50T7

Loading next page...

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2020 Xinyang Ge et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 1540-8183
eISSN: 0896-4327
DOI: 10.1155/2020/4094121
Publisher site: See Article on Publisher Site

Abstract

Hindawi Journal of Interventional Cardiology Volume 2020, Article ID 4094121, 12 pages https://doi.org/10.1155/2020/4094121 Research Article Comparison of Instantaneous Wave-Free Ratio (iFR) and FractionalFlowReserve(FFR)withrespecttoTheirSensitivitiesto Cardiovascular Factors: A Computational Model-Based Study 1 2 3 4 3 5,6,7 Xinyang Ge, Youjun Liu, Zhaofang Yin, Shengxian Tu, Yuqi Fan, Yuri Vassilevski, 5,6 1,5 Sergey Simakov, and Fuyou Liang School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100124, China Department of Cardiology, Shanghai Ninth People’s Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200011, China Med-X Research Institute, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China Institute for Personalized Medicine, Sechenov University, Moscow 119991, Russia Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia Correspondence should be addressed to Fuyou Liang; fuyouliang@sjtu.edu.cn Received 8 November 2019; Revised 18 January 2020; Accepted 27 February 2020; Published 12 May 2020 Academic Editor: Piotr Musiałek Copyright © 2020 Xinyang Ge et al. /is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. While coronary revascularization strategies guided by instantaneous wave-free ratio (iFR) are, in general, noninferior to those guided by fractional ﬂow reserve (FFR) with respect to the rate of major adverse cardiac events at one-year follow-up in patients with stable angina or an acute coronary syndrome, the overall accuracy of diagnosis with iFR in large patient cohorts is about 80% compared with the diagnosis with FFR. So far, it remains incompletely understood what factors contribute to the discordant diagnosis between iFR and FFR. In this study, a computational method was used to systemically investigate the respective eﬀects of various cardiovascular factors on FFR and iFR. /e results showed that deterioration in aortic valve disease (e.g., regurgitation or stenosis) led to a marked decrease in iFR and a mild increase in FFR given ﬁxed severity of coronary artery stenosis and that increasing coronary microvascular resistance caused a considerable increase in both iFR and FFR, but the degree of increase in iFR was lower than that in FFR. /ese ﬁndings suggest that there is a high probability of discordant diagnosis between iFR and FFR in patients with severe aortic valve disease or coronary microcirculation dysfunction. the hypothesis that there is a diastolic “wave-free” period 1. Introduction (WFP) during the heartbeat period when coronary micro- vascular resistance is inherently stable and minimized [3]. In Fractional ﬂow reserve (FFR), deﬁned as the ratio between mean poststenosis coronary arterial and aortic blood comparison with the measurement of FFR, measuring iFR is pressures under a vasodilator-induced hyperemic condition quicker and cheaper, and more importantly, it can avoid the [1], has been used as a gold standard for assessing the potential side eﬀects (e.g., breathlessness and chest tightness) functional severity of epicardial coronary artery lesions in associated with vasodilator infusion [3]. Clinical studies have the past decades [2]. Recently, the instantaneous wave-free shown that iFR is comparable to FFR with respect to di- ratio (iFR), which can be measured without the need for agnostic categorization [4] and that revascularization vasodilator administration, has emerged as an alternative strategies guided by iFR are noninferior to those guided by index of stenosis severity [3]. /e concept of iFR is based on FFR with respect to the risk of major adverse cardiac events 2 Journal of Interventional Cardiology among patients and have considerable inﬂuence on systemic at 12 months in patients with stable angina or acute coronary syndrome [5, 6]. A study comparing FFR and iFR with a and/or coronary hemodynamics and, based on this, identify the speciﬁc conditions under which iFR and FFR are most third ischemic test (e.g., positron emission tomography myocardial perfusion imaging) as the arbiter showed that likely to give discordant diagnostic results. iFR did not perform diﬀerently from FFR in identifying hemodynamically signiﬁcant ischemic coronary lesions [7]. 2. Materials and Methods On the other hand, some studies have revealed that iFR only correlated weakly with FFR in patients whose FFRs were in 2.1. Conﬁguration of the Computational Model. /e com- the clinically important range for decision making of 0.60 to putational model was adapted from the models developed in 0.90 [8] and that the overall diagnostic accuracy of iFR our previous studies [21, 22] where the modeling methods (using a ROC-determined cutoﬀ value of 0.90) was about and associated numerical schemes have been described in 80% when FFR was used as the reference index for diagnosis detail. In brief, a zero-one-dimensional (0-1-D) multiscale (i.e., discordant diagnosis with iFR and FFR occurred in over modeling method was employed to represent the coronary 20% patients) [9]. So far, reasons underlying the discordant circulation coupled to the global cardiovascular system. 1-D diagnosis between iFR and FFR remain incompletely elu- modeling was applied to large epicardial coronary arteries cidated. /e study by Lee et al. [10] found that patients with and systemic arteries to describe pulse wave propagation and discordant iFR and FFR (i.e., negative iFR while positive pressure/ﬂow waveforms, while 0-D modeling was applied FFR) usually had higher hyperemic myocardial blood ﬂow to intramyocardial vessels and the rest of the global car- and CFR (coronary ﬂow reserve) and higher resting mi- diovascular system to describe intramyocardial and systemic crovascular resistance while there was greater reduction of hemodynamics. Coupling of the 1-D and 0-D models coronary microvascular resistance at hyperemia compared yielded a closed-loop model capable of describing both to patients with concordant iFR and FFR, which implies that coronary and systemic hemodynamics as well as their in- the resting state and hyperemic response of coronary mi- teraction (see Figure 1). More importantly, the model crovasculature may be important factors related to the di- provided a ﬂexible platform for simulating iFR and FFR agnostic agreement between iFR and FFR [11]. In addition, under various pathophysiological conditions through the functional status of the aortic valve has also been modifying the values of model parameters that represent demonstrated to aﬀect the diagnostic performance of iFR various cardiovascular properties. compared with FFR [12, 13]. For instance, it was found that the diagnostic accuracy of iFR in predicting an FFR of ≤0.8 was poor (65%) for coronary lesions in patients with severe 2.2. Parameter Assignment and Model Calibration. Model aortic valve obstruction and tended to improve after parameters were initially assigned based on population- transcatheter aortic valve implantation (TAVI) [13]. Despite averaged data reported in the literature [23, 24] to let model the valuable insights from these clinical studies, a systemic predictions fall in the ranges of in vivo hemodynamic data analysis of the relationship between iFR and FFR under acquired from healthy subjects. It is noted that parameter various pathophysiological conditions with identical severity assignment was implemented for nonhyperemic resting and of coronary artery disease remains absent due to the diﬃ- hyperemic conditions, respectively, in order to meet the culties in completely removing the eﬀects of interpatient requirement for simulating iFR and FFR. Comparisons of variability and measuring all cardiovascular and hemody- model predictions and in vivo measurements under resting namic parameters necessary for analysis in general clinical and hyperemic conditions are summarized in Table 1. In settings. cases when aortic valve diseases (e.g., stenosis and regur- In comparison with in vivo measurements, computa- gitation) were present, model parameters such as resting tional modeling methods provide a more convenient ap- intramyocardial vascular resistance and systemic vascular proach to quantifying the impacts of any pathophysiological resistance were further adjusted so that model-predicted factors of interest on iFR and FFR at ﬁxed severities of coronary arterial ﬂow and systemic arterial pressure were coronary artery disease and thereby establishing a basis for comparable to those measured in patients with aortic valve exploring mechanisms underlying the discordant diagnosis disease [25, 26] (refer to [21] for more details). between iFR and FFR. Computational modeling methods have been widely applied in conjunction with medical im- 2.3. Deﬁnitions of iFR and FFR. iFR was deﬁned as the ratio age-based model reconstruction techniques to predict iFR between the mean values of poststenosis coronary arterial and/or FFR [14–20]. While most model-based studies have and aortic blood pressures (herein denoted by P and demonstrated the ability of computational models to predict d,wf P , respectively) during the diastolic wave-free period iFR and/or FFR with good accuracy in comparison with their a,wf (WFP) under the nonhyperemic resting condition [3]. in vivo counterparts, few studies have been dedicated to Herein, WFP was set to begin in 25% of the way into diastole addressing the relationship between iFR and FFR over a wide and end 5 ms before the end of diastole in accordance with range of pathophysiological conditions. the general deﬁnition of iFR in clinical practice [3]: In the present study, a computational modeling method was employed to quantitatively investigate the respective d,wf iFR � . (1) sensitivities of iFR and FFR to various cardiovascular factors a,wf whose pathophysiological states are expected to diﬀer Journal of Interventional Cardiology 3 0-D model of heart and pulmonary circulation 1-D model of coronary arterial tree 1-D model of systemic arterial tree Systemic arteries Pulmonary circulation Right heart Le h ft ear t L L L L L pua L L LCx B pv R puc R av B LM tv R B pua puv R mv B R R tv pv puc av tv pv puv mv mv av LAD C C C E E E E pua puc puv ra rv la lv RCA S S S S ra rv la lv pc it 0-D model of intramyocardial vessels Subepicardium L R L R L R R 3 3 2 2 1 1 c Intramyocardial Layer no. 1 vessels C C C 3 2 1 P d Midwall im v Layer no. 2 Stenosis im Layer no.3 Subendocardium Systemic distal im vessels 0-D model of small arteries/arterioles /capillaries/venules/veins Figure 1: Schematic description of 0-1-D multiscale modeling of the coronary circulation coupled to the global cardiovascular system. Note that coronary branch arteries in the RCA and LCx territories were modeled but are not presented in the ﬁgure in order to save space. A stenosis was introduced in the middle segment of LAD, with blood pressure immediately distal to it (P ) being monitored along with blood pressure at the aortic root (P ) for the purpose of calculating iFR or FFR. More details of model development, parameter assignment, and numerical methods have been described in our previous studies [21, 22]. Abbreviations: LM, left main artery; LAD, left anterior descending coronary artery; LCx, left circumﬂex coronary artery; RCA, right coronary artery. Notations of main parameters: L, vascular inductance; R, vascular resistance; C, vascular compliance; E, elastance of cardiac chamber; P , intrathoracic pressure; P , intramyocardial tissue pressure. it im Table 1: Comparisons of model simulations and in vivo measurements in terms of main systemic and coronary hemodynamic variables. Resting Hyperemic In vivo measurement Simulation In vivo measurement Simulation Q (mL/min) 76.15± 33.41 [24] 86.60 256.15± 110.84 [24] 264.91 LAD Q (mL/min) 54.62± 24.59 [24] 64.40 163.85± 67.18 [24] 171.26 LCx Q (mL/min) 68.46± 31.87 [24] 72.00 217.69± 76.70 [24] 232.54 RCA P (mmHg) 113.0± 5.0 [23] 121.30 113.00± 6.0 [23] 111.68 as P (mmHg) 74.0± 8.0 [23] 79.70 70.00± 5.0 [23] 74.93 ad CO (L/min) 5.19± 0.83 [23] 5.14 7.6± 1.19 [23] 7.49 Q, mean ﬂow rate over a cardiac cycle; P /P , aortic systolic/diastolic pressure; CO, cardiac output. as ad FFR was deﬁned as the ratio between the mean post- descending coronary artery (LAD) (see Figure 1 for the stenosis coronary arterial and aortic blood pressures (herein location), with its length being ﬁxed at 10 mm while the denoted by P and P , respectively) during the entire diameter stenosis rate (SR) varied from 0% (i.e., no stenosis) d,hp a,hp cardiac cycle under the hyperemic condition [1]: to 70% (i.e., severe stenosis). Heart rate (HR) was set to 66 beats/minute and 90 beats/minute for normal resting and d,hp FFR � . (2) hyperemic conditions, respectively. a,hp 2.5. Sensitivity Analyses of iFR and FFR with respect to Car- 2.4. Baseline Computation Conditions. A stenosis was in- diovascular Factors. Physiologically, iFR and FFR could be troduced in the middle segment of the left anterior aﬀected by any cardiovascular factors involved in the 4 Journal of Interventional Cardiology regulation of coronary and/or systemic hemodynamics changed the value (values) of the model parameter (pa- irrespective of whether they are related to the severity of rameters) corresponding to the factor while ﬁxing other coronary artery disease or not. In the present study, we model parameters at their reference states. In other words, considered six representative factors and categorized them we performed a one-at-a-time parametric study using the into three groups: (1) cardiac factors, which include aortic computational model to evaluate the sensitivity of iFR/FFR valve function, the systolic and diastolic functions of the left with respect to each individual cardiovascular factor. /e ventricle, and heart rate (HR) that aﬀects the magnitude and range of variations in each model parameter was estimated shape of aortic/cardiac blood pressure wave, as well as the based on clinical data measured under the nonhyperemic extravascular tissue pressure of intramyocardial coronary resting condition [22, 27–40] and is listed along with its vessels; (2) systemic vascular factors, which include the reference value in Table 2. It is noted that for the purpose of stiﬀness of the aorta and total systemic vascular resistance simplicity, we assumed that the ranges of parameter vari- that aﬀects the amplitude and mean value of aortic pressure ations relative to their reference values under the hyperemic wave, respectively; and (3) coronary vascular factors, which condition were the same as those assigned for the resting mainly include coronary microvascular resistance, a major condition. In all the sensitivity analyses, the severity of the determinant of trans-stenosis blood ﬂow rate and pressure mid-LAD stenosis was ﬁxed at 50% or 70%. drop given coronary perfusion pressure and severity of /e percentage diﬀerence of computed iFR/FFR relative stenosis. to its reference value (computed with all parameters being held at their reference states) was then calculated to evaluate the impact of varying each model parameter on iFR/FFR. It 2.5.1. Parametric Representations of Cardiovascular Factors is noted that due to the diﬀerential physiological conditions in the Model. All the aforementioned cardiovascular factors under which iFR and FFR are measured, there were two sets were represented in the model with parameters that can be of reference values of model parameters: (1) one set cor- quantitatively modiﬁed to reﬂect the variations in the responding to the intact resting condition, and (2) the other pathophysiological states of the factors. set corresponding to the hyperemic condition. /e status of aortic valve function was controlled by the eﬀective oriﬁce areas of the aortic valve during diastole and 3. Results systole (herein denoted by EOA and EOA , respectively). dia sys Assigning a value of >0 cm to EOA represents the dia 3.1. Changes in iFR and FFR with the Severity of Coronary presence of aortic valve regurgitation (AR), whereas Artery Stenosis and Typical Hemodynamic Characteristics assigning a value lower than 4 cm (i.e., the normal value of during iFR Measurement. Numerical simulations were EOA ) to EOA represents the presence of aortic valve sys sys ﬁrstly carried out to simulate iFR and FFR, respectively, with stenosis (AS). Accordingly, progressively increasing EOA dia the severity of the mid-LAD stenosis being increased in- 2 2 (from 0 to 0.3 cm ) and reducing EOA (from 4 to 1.0 cm ) sys crementally from 0% (no stenosis) to 70% (severe stenosis) represent the increasing severities of AR and AS, respec- while other cardiovascular factors ﬁxed at their reference tively. /e systolic and diastolic functions of the left ventricle resting or hyperemic states. /e simulated values of iFR and were parametrically represented by the peak systolic ela- FFR both decreased monotonously with the severity of stance (E ) and baseline diastolic elastance (E ), respec- lva lvb stenosis (see Figure 2). If a FFR of 0.8 was taken as the tively. Increasing E represents the enhancement in lva threshold for identifying a physiologically signiﬁcant lesion myocardial contractility during systole, whereas increasing [41], the corresponding iFR was 0.913, a value close to the E represents the stiﬀening of the ventricular chamber (or lvb cutoﬀ value (0.89–0.93) established in previous clinical impairment in myocardial relaxation) during diastole. HR studies [12, 42, 43]. /ese results indicate that our model can was assigned directly in the model. reasonably predict the general relationship between iFR and /e stiﬀness of the aorta was controlled by the value FFR in the context of various severities of coronary artery assigned to the elastic modulus of the aortic wall in the stenosis. model. Since the elastic modulus of the aortic wall is the Figure 3 shows the model-simulated pressure waves in main determinant of the aortic pulse wave velocity (aPWV), the ascending aorta and those immediately distal to a 50% we herein took aPWV as a measure of aortic stiﬀness. An stenosis in mid-LAD under the control condition (i.e., all increase in aPWV corresponds to an increase in aortic model parameters were at the reference state) and under two stiﬀness. /e total systemic vascular resistance (R ) and sys altered physiological conditions characterized by a 67% coronary microvascular resistance (R ) are holistic de- cmv increase in HR and a 200% elevation in aPWV, respectively. scriptions of vascular resistances distributed in systemic /e wave-free pressure portions used to calculate iFR are tissues/organs and myocardium, respectively, and were highlighted by the gray shadows. Figure 3 also shows the modiﬁed by simultaneously varying all the corresponding corresponding time histories of wave intensity (WI) in the vascular resistances. LAD (Figures 3(d)–3(f)) and total resistance of coronary vessels distal to the stenosis (Figures 3(g)–3(i)). As expected, 2.5.2. Quantiﬁcation of the Sensitivities of iFR and FFR to the variations in HR and aPWV both led to considerable Cardiovascular Factors. In order to investigate how iFR/FFR changes in pressure waveform and time history of WI via is aﬀected by varying the pathophysiological state of each their inﬂuence on pressure wave propagation and reﬂection aforementioned cardiovascular factor, we incrementally in the systemic arterial system, but they had little inﬂuence Journal of Interventional Cardiology 5 Table 2: Reference values of model parameters involved in the sensitivity analyses for iFR and FFR under resting and hyperemic conditions. Model parameter Reference value (resting/hyperemic) Range of variation (resting) EOA (cm ) 0.0/0.0 (0.0∼0.3) [27] dia EOA (cm ) 4.0/4.0 (4.0∼1.0) [28, 29] sys E (mmHg/ml) 2.87/2.87 (1.435∼6.601) [30] lva E (mmHg/ml) 0.056/0.056 (0.028∼0.112) [30] lvb HR (beats/min) 66/90 (48∼111) [31, 32] aPWV (m/s) 4.7/4.7 (3.478∼10.011) [33–35] R (mmHg·s/ml) 1.14/0.98 (0.456∼1.824) [36, 37] sys R (mmHg·s/ml) 196.97/45.94 (157.58∼433.33) [38–40] cmv Note that the ranges of parameter variations under resting condition were estimated based on available clinical data reported in the literature. 1.0 1.0 mildly aﬀected by the variations in EOA or EOA . dia sys Moreover, varying EOA or EOA induced opposite dia sys changes in iFR and FFR. For instance, increasing EOA 0.9 0.9 dia (representing a progressive deterioration in AR) or de- iFR = 0.913 creasing EOA (representing a progressive deterioration in 0.8 0.8 sys AS) remarkably reduced iFR whilst it elevated FFR mildly. When the results of the sensitivity analyses were further 0.7 0.7 investigated with respect to the severity of coronary artery stenosis, an increase in stenosis rate (i.e., from 50% to 70%) 0.6 0.6 was observed to considerably augment the sensitivities of iFR and FFR to EOA and EOA . Relatively, both iFR and dia sys 0.5 0.5 FFR were insensitive to the systolic and diastolic functions of SR = 51% the left ventricle (represented by E and E ) and HR. lva lvb 0.4 0.4 Varying the systemic vascular factors (i.e., aortic stiﬀness –10 0 1020304050607080 represented by aPWV and total systemic vascular resistance Stenosis rate (%) (R )) induced detectable while only mild changes in iFR sys iFR and FFR (see Figures 4(f) and 4(g)). As is diﬀerent from FFR systemic vascular factors, increasing coronary microvascular resistance (R ) under the resting or hyperemic condition cmv Figure 2: Model-simulated changes in iFR/FFR with the increase tended to signiﬁcantly elevate iFR and FFR, although the in the severity (i.e., the diameter stenosis rate is increased from 0% degree of elevation in FFR was larger than that in iFR (see to 70% at an interval of 10%) of a stenosis present in mid-LAD Figure 4(h)). under the control resting/hyperemic condition. When FFR is at the cutoﬀ value (i.e., 0.8), the corresponding stenosis rate (SR) is 51% In summary, if a maximal percentage change in iFR or and iFR is 0.913. FFR of >10% in response to the variations in a model pa- rameter was set as the threshold for judging high sensitivity, iFR was observed to be highly sensitive to EOA , EOA dia sys on iFR. In the wave-free period (WFP), WI was close to zero, (aortic valve function), and R (state of coronary mi- cmv proving that the “wave-free” assumption in the deﬁnition of crovasculature), whereas FFR was solely sensitive to R . cmv iFR is reasonable; however, the poststenosis coronary vas- cular resistance was not constant during WFP. Nevertheless, the relatively low value of poststenosis vascular resistance 3.3. Hemodynamic Characteristics Underlying the Diﬀerential during WFP compared with that in systole can still partly Sensitivities of iFR and FFR to Aortic Valve Function and support the clinical hypothesis that iFR is an index derived Coronary Microvascular Resistance. In order to explore under the condition of low coronary vascular resistance. hemodynamic characteristics underlying the diﬀerential sensitivities of iFR and FFR to aortic valve function and coronary microvascular resistance, taking the 50% mid-LAD 3.2. Sensitivities of iFR and FFR to Variations in the State of stenosis as an example, we plotted the model-simulated Each Cardiovascular Factor. /e sensitivities of iFR and FFR aortic pressure wave and poststenosis coronary arterial to variations in each of the eight model parameters that pressure/ﬂow waves and poststenosis coronary microvas- represent various cardiac or vascular factors are presented in cular resistance under the control condition (i.e., all model the form of percentage changes relative to the reference parameters were ﬁxed at their reference states) against those values of iFR and FFR in Figure 4. under the condition characterized by the presence of severe As for the sensitivities of iFR and FFR to cardiac factors aortic valve stenosis (AS) (represented by setting (represented by EOA , EOA , E , E , and HR in the dia sys lva lvb EOA � 1.0 cm ) or increased coronary microvascular re- sys model) (see Figures 4(a)–4(e)), iFR was observed to be sistance (represented by increasing R by 120%) in Fig- cmv highly sensitive to both EOA and EOA that represent dia sys ure 5. It is noted that the numerical simulations were the status of the aortic valve function, whereas FFR was only performed under the resting and hyperemic conditions, iFR FFR 6 Journal of Interventional Cardiology 140 140 140 WFP WFP WFP 120 120 120 100 100 100 iFR = 0.932 iFR = 0.920 80 80 80 iFR = 0.922 Control 67% increase in HR 200% increase in aPWV 60 60 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) P P P a a a P P P d d d (a) (b) (c) 1.0 1.0 1.0 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) (d) (e) (f) 300 300 300 200 200 200 100 100 100 0 0 0 0.0 0.3 0.6 0.9 0.00 0.18 0.36 0.54 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) (g) (h) (i) Figure 3: Model-simulated aortic and poststenosis coronary arterial pressure waves (a∼c), wave intensity in mid-LAD (d∼f), and poststenosis coronary microvascular resistance (g∼i) during iFR measurement under the control and two altered physiological conditions (one with a 67% increase in HR and the other with a 200% increase in aPWV). /e wave-free period (WFP) during a cardiac cycle is highlighted by the gray shadow. /e stenosis was present in mid-LAD, with the stenosis rate being ﬁxed at 50% in all the simulations. respectively, in consideration of the diﬀerential physiological comparable to or even slightly lower than that under the conditions corresponding to iFR and FFR measurements. control condition (which is consistent with previous Under the resting condition, although the presence of clinical observations [44]), leading to a mild increase in severe AS induced a marked decrease in both aortic and FFR. poststenosis coronary pressures, the degree of decrease in In contrast to AS, increasing coronary microvascular poststenosis pressure was larger than that of aortic pres- resistance under the resting or hyperemic condition had an sure, resulting in an evident decrease in iFR. /e enhanced overall small inﬂuence on the aortic pressure, but signiﬁ- decrease in poststenosis pressure was caused mainly by the cantly elevated the poststenosis coronary pressure primarily increased resting coronary blood ﬂow (which augments the due to its role in reducing trans-stenosis ﬂow rate. Such pressure drop across the stenosis) as a consequence of eﬀects were particularly pronounced under the hyperemic coronary microvascular adaptive responses to increased condition when the ﬂow rate was higher and more sensitive myocardial stress and oxygen demand in the presence of AS to the variation in poststenosis coronary vascular resistance [21]. Under the hyperemic condition, the simulated cor- (see Figure 5(h)) compared with the resting condition, onary blood ﬂow rate in the presence of AS was however thereby leading to a larger increase in FFR than in iFR. R (mmHg/mL/s) 5 Blood pressure (mmHg) cmv WI (W·10 ) R (mmHg/mL/s) 5 Blood pressure (mmHg) cmv WI (W·10 ) R (mmHg/mL/s) Blood pressure (mmHg) cmv WI (W·10 ) Journal of Interventional Cardiology 7 40 40 40 20 20 20 0 0 0 –20 –20 –20 –40 –40 –40 0.0 0.1 0.2 0.3 4321 0.4 0.8 1.2 1.6 2.0 2.4 2 2 EOA (cm ) EOA (cm ) E (normalized) dia sys lva iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (a) (b) (c) 40 40 40 20 20 20 0 0 0 –20 –20 –20 –40 –40 –40 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 0.8 1.2 1.6 2.0 E (normalized) HR (normalized) aPWV (normalized) lvb iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (d) (e) (f) 40 40 20 20 0 0 –20 –20 –40 –40 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.8 1.2 1.6 2.0 2.4 R (normalized) R (normalized) sys cmv iFR, DSR = 50% iFR, DSR = 70% iFR, DSR = 50% iFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% FFR, DSR = 50% FFR, DSR = 70% (g) (h) Figure 4: Percentage changes of iFR and FFR relative to their reference values upon the variations of each model parameter. /e variations of all parameters except for EOA and EOA are expressed in normalized form relative to their reference values to facilitate the dia sys comparisons of the eﬀects on iFR/FFR among diﬀerent parameters. /e stenosis is present in mid-LAD with its stenosis rate being set at 50% and 70%, respectively, and the corresponding reference values (computed with all model parameters being ﬁxed at their reference states) of iFR/FFR are 0.920/0.813 and 0.677/0.534, respectively. (a) EOA . (b) EOA . (c) E . (d) E . (e) HR. (f) aPWV. (g) R . (h) R . dia sys lva lvb sys cmv Notations: EOA /EOA , eﬀective oriﬁce area of aortic valve during diastole/systole (an increase in EOA represents an increase in the dia sys dia severity of aortic valve regurgitation, whereas a decrease in EOA represents an increase in the severity of aortic valve stenosis); E /E , sys lva lvb peak systolic elastance/baseline diastolic elastance of the left ventricle; HR, heart rate; aPWV, aortic pulse wave velocity; R , total systemic sys vascular resistance; R , total coronary microvascular resistance. cmv and FFR to various cardiovascular factors involved in the 4. Discussion regulation of systemic and/or coronary hemodynamics. /e In the present study, we employed a computational model to results revealed that iFR and FFR diﬀered considerably with respect to the cardiovascular factors to which they are simulate the processes of iFR and FFR measurements and quantitatively investigated the respective sensitivities of iFR sensitive and the degree and/or pattern of changes in Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) Relative change in iFR/FFR (%) 8 Journal of Interventional Cardiology Resting Hyperemic Resting Hyperemic 125 125 125 100 100 100 75 75 75 iFR = 0.920 iFR = 0.960 FFR = 0.832 FFR = 0.917 iFR = 0.852 FFR = 0.813 iFR = 0.920 FFR = 0.813 50 50 50 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 Time (s) Time (s) Time (s) Time (s) P (control) P (control) P (control) P (control) a a a P (control) P (control) P (control) P (control) d d P (severe AS) P (severe AS) P (120% increase in R ) P (120% increase in R ) a cmv a cmv P (severe AS) P (severe AS) P (120% increase in R ) P (120% increase in R ) d d cmv d cmv (a) (b) (c) (d) Resting Hyperemic Resting Hyperemic 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 Time (s) Time (s) Time (s) Time (s) Q (control) Q (control) Q (control) Q (control) dis dis dis dis Q (severe AS) Q (severe AS) Q (120% increase in R ) Q (120% increase in R ) dis dis dis cmvr dis cmvr (e) (f) (g) (h) Resting Hyperemic Resting Hyperemic 300 300 600 300 200 200 400 200 100 100 200 100 0 0 0 0 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 0.000 0.125 0.250 0.375 0.500 0.625 0.0 0.3 0.6 0.9 Time (s) Time (s) Time (s) Time (s) control control control control severe AS severe AS 120% increase in R 120% increase inR cmv cmv (i) (j) (k) (l) Figure 5: Comparisons of model-simulated aortic pressure wave and coronary arterial pressure wave distal to a 50% stenosis in mid-LAD and iFR/FFR (a∼d), ﬂow wave in mid-LAD (e∼h), and poststenosis coronary microvascular resistance (i∼l) under control resting/hyperemic condition with those in the presence of severe AS (EOA � 1.0 cm ) or increased coronary microvascular resistance (increased by 120% sys relative to the reference value). response to the variations in the state of each cardiovascular consistent with relevant clinical observations reported in the factor. literature. For instance, it was found that in patients with /e model-predicted marked decrease in iFR while mild severe AS, the conventional iFR cutoﬀ value had lower increase in FFR following increasing severity of AS (simu- diagnostic agreement with FFR in the classiﬁcation of lated by reducing the value of EOA in the model) implies coronary lesions and that a lower iFR cutoﬀ value (e.g., sys shifting the cutoﬀ value from 0.89 to 0.83) should be used in that in patients with severe AS, the measured iFRs may be much lower than those in patients with equivalent severity of order to better predict a positive FFR [12, 13, 45, 46]. In the coronary artery disease while normal aortic valve function, case of increasing severity of AR (simulated by increasing the although the measured FFRs in the two patient cohorts value assigned to EOA in the model), our study revealed dia might be comparable, which may consequently lead to in- similar patterns of diﬀerential changes in iFR and FFR to creased probability of discordant diagnosis between iFR and those found in the case of increasing severity of AS and FFR in the former patient cohort if cutoﬀ values of iFR and would cause a similar trend of discordant diagnosis between FFR established based on clinical data acquired from the iFR and FFR, although relevant clinical evidence from latter patient cohort were used. /ese theoretical ﬁndings are studies focused on patients with AR is rare, probably due to R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) R (mmHg/mL/s) Blood pressure (mmHg) cmv Flow rate (mL/s) Journal of Interventional Cardiology 9 the low prevalence of AR in patients with coronary artery 0.98 disease [47]. 0.96 Unlike aortic valve disease which aﬀects iFR and FFR in opposite ways, increasing coronary microvascular resistance Reference iFR 0.94 led to a considerable increase in both iFR and FFR, although the degree of increase in iFR was lower than that in FFR. /e 0.92 diﬀerential eﬀects of coronary microvascular resistance on 0.90 iFR and FFR would become more evident when the resting coronary microvascular resistance is preserved while the 0.88 hyperemic counterpart is higher than the normal value due to impaired vasodilation function, which may explain why 0.86 Decrease in iFR with low iFR and high FFR (i.e., iFR+/FFR−) were more fre- increasing severity of AS 0.84 quently observed in patients with diabetes mellitus who 1.0 1.2 1.4 1.6 1.8 2.0 2.2 usually have increased coronary microvascular resistance R (normalized) and low coronary ﬂow at hyperemia due to microcirculation cmv dysfunction [48, 49]. EOA = 4.0 (cm ) (no AS) sys Relatively, varying left ventricular systolic and diastolic functions and HR and systemic vascular factors (i.e., aortic EOA = 2.0 (cm ) (moderate AS) sys stiﬀness and systemic vascular resistance) over large ranges EOA = 1.0 (cm ) (severe AS) sys only had mild inﬂuences on iFR and FFR, which indicates (a) that iFR and FFR would both perform well in assessing the functional severity of coronary artery lesions irrespective of 0.94 potential high interpatient variability in these cardiac or 0.92 vascular properties. In summary, the present study demonstrates the general 0.90 trend that iFR and FFR are more likely to give discordant Increase in FFR with increasing diagnostic results in the presence of severe aortic valve 0.88 severity of AS disease (stenosis or regurgitation) or increased coronary microvascular resistance. /erefore, special caution should 0.86 be taken in the interpretation of measured iFR and FFR or 0.84 the use of general cutoﬀ values for diagnosis in patients with these speciﬁc cardiovascular conditions. Furthermore, given Reference FFR 0.82 the diﬀerential eﬀects on iFR and FFR of aortic valve disease and increased coronary microvascular resistance, the 0.80 changes in iFR and FFR would become more complex in the 1.0 1.2 1.4 1.6 1.8 2.0 2.2 presence of aortic valve disease combined with increased R (normalized) cmv coronary microvascular resistance. Our additional numer- EOA = 4.0 (cm ) (no AS) ical tests revealed that increasing coronary microvascular sys resistance could counteract or even reverse the decrease in EOA = 2.0 (cm ) (moderate AS) sys iFR whilst augmenting the increase in FFR caused by aortic EOA = 1.0 (cm ) (severe AS) sys valve stenosis (see Figure 6). In this sense, in patients suf- fering from concomitant aortic valve disease and coronary (b) microcirculation dysfunction, the diagnostic agreement Figure 6: Eﬀects of diﬀerent combinations of AS (with its severity between iFR and FFR could be highly complex and should be being controlled by the value of EOA ) and increased coronary sys carefully interpreted in the context of patient-speciﬁc microvascular resistance (R , herein normalized by its reference cmv conditions. normal value) on (a) iFR and (b) FFR. Increasing the severity of AS leads to a marked decrease in iFR and moderate increase in FFR, 5. Limitations whereas increasing R causes a progressive increase in both iFR and cmv FFR. As a consequence, increasing R counteracts or even reverses cmv While our study, through quantifying the respective sensi- the decrease in iFR while augments the increase in FFR caused by AS. tivities of iFR and FFR to the variations in the patho- Note that the coronary stenosis is present in mid-LAD with its severity physiological state of each individual cardiovascular factor, being ﬁxed at 50% in all the simulations and that the values of iFR and provided useful insights for exploring mechanisms under- FFR highlighted by the ﬁlled circles indicate their reference values computed under the condition that only the 50% coronary stenosis is lying the clinically observed discordant diagnosis between present while AS and increased R are absent. iFR and FFR in some patient cohorts, the study is limited by cmv its theoretical nature and the focus on single-factor sensi- tivity analyses that render the ﬁndings unable to be applied may deviate signiﬁcantly from those represented by the directly to explain the measurements in individual patients model. In addition, the numerical simulations tailored to whose cardiovascular conditions are highly complex and single-factor sensitivity analyses were not suﬃcient to Increase in iFR with increasing R cmv Increase in FFR with increasing R cmv FFR iFR 10 Journal of Interventional Cardiology generate a large database for statistical determination of the References cutoﬀ values of iFR or FFR under speciﬁc pathological [1] N. H. J. Pijls, B. De Bruyne, K. Peels et al., “Measurement of conditions (e.g., various types and severities of aortic valve fractional ﬂow reserve to assess the functional severity of disease combined with other cardiovascular abnormalities). coronary-artery stenoses,” New England Journal of Medicine, For this purpose, large-scale stochastic numerical simula- vol. 334, no. 26, pp. 1703–1708, 1996. tions (similar to those reported in [50]) that cover a wide [2] T. Force, S. Windecker, P. Kolh et al., “ESC/EACTS guidelines range of various pathophysiological conditions would be on myocardial revascularization: the task force on myocardial needed. /e 0-1-D multiscale model employed in the present revascularization of the European society of cardiology (ESC) study is however computationally costly and therefore not and the European association for cardio-thoracic surgery well suited to such a study. /e problem might be solved by (EACTS) developed with the special contribution of the developing a lumped-parameter model that contains the European association of percutaneous cardiovascular inter- ventions (EAPCI),” European Heart Journal, vol. 35, no. 37, main components of the present model whilst is compu- pp. 2541–2619, 2014. tationally much cheaper, which would be addressed in our [3] S. Sen, J. Escaned, I. S. Malik et al., “Development and val- future studies. idation of a new adenosine-independent index of stenosis severity from coronary wave-intensity analysis,” Journal of the 6. Conclusion American College of Cardiology, vol. 59, no. 15, pp. 1392–1402, A computational model-based numerical study has been [4] S. Sen, K. N. Asrress, S. Nijjer et al., “Diagnostic classiﬁcation carried out to compare the sensitivities of iFR and FFR to of the instantaneous wave-free ratio is equivalent to fractional variations in the pathophysiological states of various car- ﬂow reserve and is not improved with adenosine adminis- diovascular factors. It was found that aortic valve disease and tration,” Journal of the American College of Cardiology, vol. 61, increased coronary microvascular resistance had consider- no. 13, pp. 1409–1420, 2013. able while diﬀerential inﬂuences on iFR and FFR, which [5] J. E. Davies, S. Sen, H. M. Dehbi et al., “Use of the instan- provides theoretical evidence for explaining the increased taneous wave-free ratio or fractional ﬂow reserve in PCI,” <e New England Journal of Medicine, vol. 376, no. 376, risk of discordant diagnosis between iFR and FFR in patients pp. 1824–1834, 2017. with aortic valve disease or coronary microcirculation [6] M. Gotberg, ¨ E. H. Christiansen, I. J. Gudmundsdottir et al., dysfunction. “Instantaneous wave-free ratio versus fractional ﬂow reserve to guide PCI,” New England Journal of Medicine, vol. 376, Data Availability no. 19, pp. 1813–1823, 2017. [7] G. A. de Waard, I. Danad, R. Petraco et al., “Fractional ﬂow All clinical data used in the present study have been reported reserve, instantaneous wave-free ratio, and resting P /P d a in the corresponding references and the values of most compared with [ O]H O positron emission tomography model parameters not provided in the manuscript have been myocardial perfusion imaging: a PACIFIC trial sub-study,” reported in a previous study of ours [21] (https:// European Heart Journal, vol. 39, no. 46, pp. 4072–4081, 2018. onlinelibrary.wiley.com/doi/full/10.1002/cnm.3257). [8] C. Berry, M. van’t Veer, N. Witt et al., “VERIFY (VERiﬁcation of instantaneous wave-free ratio and fractional ﬂow reserve for the assessment of coronary artery stenosis severity in Conflicts of Interest EverydaY practice),” Journal of the American College of Cardiology, vol. 61, no. 13, pp. 1421–1427, 2013. /e authors have no conﬂicts of interest to declare. [9] A. Jeremias, A. Maehara, P. Gen ´ ereux ´ et al., “Multicenter core laboratory comparison of the instantaneous wave-free ratio Authors’ Contributions and resting P /P with fractional ﬂow reserve,” Journal of the d a American College of Cardiology, vol. 63, no. 13, pp. 1253–1261, Xinyang Ge built the computational model, performed numerical simulations, and drafted the manuscript. Youjun [10] J. M. Lee, D. Hwang, J. Park, Y. Tong, and B.-K. Koo, Liu and Shengxian Tu analyzed the data and revised the “Physiologic mechanism of discordance between instanta- manuscript. Zhaofang Yin and Yuqi Fan interpreted the data neous wave-free ratio and fractional ﬂow reserve: insight from from the clinical point of view. Sergey Simakov and Yuri 13 N-ammonium positron emission tomography,” Interna- tional Journal of Cardiology, vol. 243, pp. 91–94, 2017. Vassilevski optimized the computational model and revised [11] H. Matsuo, Y. Kawase, and I. Kawamura, “FFR and iFR,” the manuscript. Fuyou Liang designed the study, interpreted Annals of Nuclear Cardiology, vol. 3, no. 1, pp. 53–60, 2017. the data, and revised the manuscript. All authors have read [12] R. Scarsini, G. Pesarini, C. Zivelonghi et al., “Coronary and approved the ﬁnal manuscript. physiology in patients with severe aortic stenosis: comparison between fractional ﬂow reserve and instantaneous wave-free Acknowledgments ratio,” International Journal of Cardiology, vol. 243, pp. 40–46, /e study was supported in part by the National Natural [13] R. Scarsini, G. Pesarini, C. Zivelonghi et al., “Physiologic Science Foundation of China (Grant nos. 11832003, evaluation of coronary lesions using instantaneous wave-free 11972231, and 81611530715) and the SJTU Medical-Engi- ratio (iFR) in patients with severe aortic stenosis undergoing neering Cross-cutting Research Project (Grant no. transcatheter aortic valve implantation,” EuroIntervention, YG2016MS09). vol. 13, no. 13, pp. 1512–1519, 2018. Journal of Interventional Cardiology 11 [14] C. A. Taylor, T. A. Fonte, and J. K. Min, “Computational ﬂuid [27] M. Enriquez-Sarano and A. J. Tajik, “Aortic regurgitation,” dynamics applied to cardiac computed tomography for New England Journal of Medicine, vol. 351, no. 15, pp. 1539–1546, 2004. noninvasive quantiﬁcation of fractional ﬂow reserve,” Journal [28] D. Garcia, P. G. Camici, L.-G. Durand et al., “Impairment of of the American College of Cardiology, vol. 61, no. 22, coronary ﬂow reserve in aortic stenosis,” Journal of Applied pp. 2233–2241, 2013. Physiology, vol. 106, no. 1, pp. 113–121, 2009. [15] Y. Ma, H. Liu, Y. Hou et al., “Instantaneous wave-free ratio [29] P. Pibarot and J. G. Dumesnil, “Improving assessment of derived from coronary computed tomography angiography in aortic stenosis,” Journal of the American College of Cardiology, evaluation of ischemia-causing coronary stenosis: feasibility vol. 60, no. 3, pp. 169–180, 2012. and initial clinical research,” Medicine, vol. 96, no. 4, p. e5979, [30] F. Liang, H. Senzaki, C. Kurishima, K. Sughimoto, R. Inuzuka, and H. Liu, “Hemodynamic performance of the Fontan cir- [16] L. Calmac, R. Niculescu, E. Badila et al., “TCT-40 image-based culation compared with a normal biventricular circulation: a computation of instantaneous wave-free ratio from routine computational model study,” American Journal of Physiology- coronary angiography-initial validation by invasively mea- Heart and Circulatory Physiology, vol. 307, no. 7, sured coronary pressures,” Journal of the American College of pp. H1056–H1072, 2014. Cardiology, vol. 66, no. 15, pp. B17–B18, 2015. [31] J. M. Mangrum and J. P. Dimarco, “/e evaluation and [17] W. Wang, B. Mao, B. Li et al., “Numerical simulation of management of bradycardia,” New England Journal of Med- instantaneous wave-free ratio of stenosed coronary artery,” icine, vol. 342, no. 10, pp. 703–709, 2000. International Journal of Computational Methods, vol. 16, [32] A. F. Chu, E. Zado, and F. E. Marchlinski, “Atrial arrhythmias no. 3, Article ID 1842009, 2019. in patients with arrhythmogenic right ventricular cardio- [18] J. M. Carson, S. Pant, C. Roobottom et al., “Non-invasive myopathy/dysplasia and ventricular tachycardia,” <e coronary CT angiography-derived fractional ﬂow reserve: a American Journal of Cardiology, vol. 106, no. 5, pp. 720–722, benchmark study comparing the diagnostic performance of four diﬀerent computational methodologies,” International [33] P. V. Vaitkevicius, J. L. Fleg, J. H. Engel et al., “Eﬀects of age Journal for Numerical Methods in Biomedical Engineering, and aerobic capacity on arterial stiﬀness in healthy adults,” vol. 35, no. 10, p. e3235, 2019. Circulation, vol. 88, no. 4, pp. 1456–1462, 1993. [19] L. O. Muller, ¨ F. E. Fossan, A. T. Braten, ˚ A. Jørgensen, [34] R. P. Wildman, G. N. Farhat, A. S. Patel et al., “Weight change R. Wiseth, and L. R. Hellevik, “Impact of baseline coronary is associated with change in arterial stiﬀness among healthy ﬂow and its distribution on Fractional Flow Reserve pre- young adults,” Hypertension, vol. 45, no. 2, pp. 187–192, 2005. diction,” International Journal for Numerical Methods in [35] Z. Dhakam, Yasmin, C. M. McEniery, T. Burton, M. J. Brown, Biomedical Engineering, p. e3246, 2019. and I. B. Wilkinson, “A comparison of atenolol and nebivolol [20] J. Carson, C. Roobottom, R. Alcock, and P. Nithiarasu, in isolated systolic hypertension,” Journal of Hypertension, “Computational instantaneous wave-free ratio (IFR) for pa- vol. 26, no. 2, pp. 351–356, 2008. tient-speciﬁc coronary artery stenoses using 1D network [36] W. G. Haynes, C. J. Ferro, K. P. J. O’Kane, D. Somerville, models,” International Journal for Numerical Methods in C. C. Lomax, and D. J. Webb, “Systemic endothelin receptor Biomedical Engineering, vol. 35, no. 11, p. e3255, 2019. blockade decreases peripheral vascular resistance and blood [21] X. Ge, Y. Liu, S. Tu, S. Simakov, Y. Vassilevski, and F. Liang, pressure in humans,” Circulation, vol. 93, no. 10, pp. 1860– “Model-based analysis of the sensitivities and diagnostic 1870, 1996. implications of FFR and CFR under various pathological [37] T. Linde, B. Sandhagen, A. Hagg, ¨ C. Morlin, ¨ B. Wikstrom, ¨ and conditions,” International Journal for Numerical Methods in B. G. Danielson, “Blood viscosity and peripheral vascular Biomedical Engineering, p. e3257, 2019. resistance in patients with untreated essential hypertension,” [22] X. Ge, Z. Yin, Y. Fan, Y. Vassilevski, and F. Liang, “A multi- Journal of Hypertension, vol. 11, no. 7, pp. 731–736, 1993. scale model of the coronary circulation applied to investigate [38] S. E. Reis, R. Holubkov, J. S. Lee et al., “Coronary ﬂow velocity transmural myocardial ﬂow,” International Journal for Nu- response to adenosine characterizes coronary microvascular merical Methods in Biomedical Engineering, vol. 34, no. 10, function in women with chest pain and no obstructive cor- p. e3123, 2018. onary disease,” Journal of the American College of Cardiology, [23] N. Watzinger, G. K. Lund, M. Saeed et al., “Myocardial blood vol. 33, no. 6, pp. 1469–1475, 1999. ﬂow in patients with dilated cardiomyopathy: quantitative [39] M. Fineschi, A. Bravi, and T. Gori, “/e “slow coronary ﬂow” assessment with velocity-encoded cine magnetic resonance phenomenon: evidence of preserved coronary ﬂow reserve imaging of the coronary sinus,” Journal of Magnetic Reso- despite increased resting microvascular resistances,” Inter- nance Imaging, vol. 21, no. 4, pp. 347–353, 2005. national Journal of Cardiology, vol. 127, no. 3, pp. 358–361, [24] H. Wieneke, C. Von Birgelen, M. Haude et al., “Determinants of coronary blood ﬂow in humans: quantiﬁcation by intra- [40] R. F. Wilson, K. Wyche, B. V. Christensen, S. Zimmer, and coronary Doppler and ultrasound,” Journal of Applied D. D. Laxson, “Eﬀects of adenosine on human coronary ar- Physiology, vol. 98, no. 3, pp. 1076–1082, 2005. terial circulation,” Circulation, vol. 82, no. 5, pp. 1595–1606, [25] A. Nitenberg, J.-M. Foult, I. Antony, F. Blanchet, and M. Rahali, “Coronary ﬂow and resistance reserve in patients [41] D.-Y. Kang, J.-M. Ahn, Y. W. Kim et al., “Impact of coronary with chronic aortic regurgitation, angina pectoris and normal lesion geometry on fractional ﬂow reserve: data from inter- coronary arteries,” Journal of the American College of Car- ventional cardiology research in-cooperation society-frac- diology, vol. 11, no. 3, pp. 478–486, 1988. tional ﬂow reserve and intravascular ultrasound registry,” [26] P. Meimoun, A. L. Germain, F. Elmkies et al., “Factors as- Circulation: Cardiovascular Imaging, vol. 11, no. 6, Article ID sociated with noninvasive coronary ﬂow reserve in severe e007087, 2018. aortic stenosis,” Journal of the American Society of Echocar- [42] L. Itu, T. Passerini, E. Badila et al., “Image-based computation diography, vol. 25, no. 8, pp. 835–841, 2012. of instantaneous wave-free ratio from routine coronary 12 Journal of Interventional Cardiology angiography: evaluation of a hybrid decision making strategy with ﬀr,” Journal of the American College of Cardiology, vol. 67, no. 13, p. 328, 2016. [43] R. Scarsini, G. Pesarini, M. Lunardi et al., “Observations from a real-time, iFR-FFR “hybrid approach” in patients with se- vere aortic stenosis and coronary artery disease undergoing TAVI,” Cardiovascular Revascularization Medicine, vol. 19, no. 3, pp. 355–359, 2018. [44] F. R. Eberli, M. Ritter, J. Schwitter et al., “Coronary reserve in patients with aortic valve disease before and after successful aortic valve replacement,” European Heart Journal, vol. 12, no. 2, pp. 127–138, 1991. [45] F. Yamanaka, K. Shishido, T. Ochiai et al., “Instantaneous wave-free ratio for the assessment of intermediate coronary artery stenosis in patients with severe aortic valve stenosis: comparison with myocardial perfusion scintigraphy,” JACC: Cardiovascular Interventions, vol. 11, no. 20, pp. 2032–2040, [46] R. Scarsini, R. Cantone, G. Venturi et al., “Correlation be- tween intracoronary physiology and myocardial perfusion imaging in patients with severe aortic stenosis,” International Journal of Cardiology, vol. 292, pp. 162–165, 2019. [47] A.-H. Hakki, D. Kimbiris, A. S. Iskandrian, B. L. Segal, G. S. Mintz, and C. E. Bemis, “Angina pectoris and coronary artery disease in patients with severe aortic valvular disease,” American Heart Journal, vol. 100, no. 4, pp. 441–449, 1980. [48] C. M. Cook, A. Jeremias, R. Petraco et al., “Fractional ﬂow reserve/instantaneous wave-free ratio discordance in angio- graphically intermediate coronary stenoses,” JACC: Cardio- vascular Interventions, vol. 10, no. 24, pp. 2514–2524, 2017. [49] J. M. Lee, E.-S. Shin, C.-W. Nam et al., “Discrepancy between fractional ﬂow reserve and instantaneous wave-free ratio: clinical and angiographic characteristics,” International Journal of Cardiology, vol. 245, pp. 63–68, 2017. [50] T. Wang, F. Liang, Z. Zhou, and X. Qi, “Global sensitivity analysis of hepatic venous pressure gradient (HVPG) mea- surement with a stochastic computational model of the he- patic circulation,” Computers in Biology and Medicine, vol. 97, pp. 124–136, 2018.

Journal

Journal of Interventional Cardiology – Hindawi Publishing Corporation

Published: May 12, 2020

References

Measurement of fractional flow reserve to assess the functional severity of coronary-artery stenoses,

N. H. J. Pijls, B. De Bruyne, K. Peels et al.
ESC/EACTS guidelines on myocardial revascularization: the task force on myocardial revascularization of the European society of cardiology (ESC) and the European association for cardio-thoracic surgery (EACTS) developed with the special contribution of the European association of percutaneous cardiovascular interventions (EAPCI),

T. Force, S. Windecker, P. Kolh et al.
Development and validation of a new adenosine-independent index of stenosis severity from coronary wave-intensity analysis,

S. Sen, J. Escaned, I. S. Malik et al.
Diagnostic classification of the instantaneous wave-free ratio is equivalent to fractional flow reserve and is not improved with adenosine administration,

S. Sen, K. N. Asrress, S. Nijjer et al.
Use of the instantaneous wave-free ratio or fractional flow reserve in PCI,

J. E. Davies, S. Sen, H. M. Dehbi et al.
Instantaneous wave-free ratio versus fractional flow reserve to guide PCI,

M. Götberg, E. H. Christiansen, I. J. Gudmundsdottir et al.
Fractional flow reserve, instantaneous wave-free ratio, and resting Pd/Pa compared with [15O]H2O positron emission tomography myocardial perfusion imaging: a PACIFIC trial sub-study,

G. A. de Waard, I. Danad, R. Petraco et al.
VERIFY (VERification of instantaneous wave-free ratio and fractional flow reserve for the assessment of coronary artery stenosis severity in EverydaY practice),

C. Berry, M. van’t Veer, N. Witt et al.
Multicenter core laboratory comparison of the instantaneous wave-free ratio and resting Pd/Pa with fractional flow reserve,

A. Jeremias, A. Maehara, P. Généreux et al.
Physiologic mechanism of discordance between instantaneous wave-free ratio and fractional flow reserve: insight from 13 N-ammonium positron emission tomography,

J. M. Lee, D. Hwang, J. Park, Y. Tong, and B.-K. Koo
FFR and iFR,

H. Matsuo, Y. Kawase, and I. Kawamura
Coronary physiology in patients with severe aortic stenosis: comparison between fractional flow reserve and instantaneous wave-free ratio,

R. Scarsini, G. Pesarini, C. Zivelonghi et al.
Physiologic evaluation of coronary lesions using instantaneous wave-free ratio (iFR) in patients with severe aortic stenosis undergoing transcatheter aortic valve implantation,

R. Scarsini, G. Pesarini, C. Zivelonghi et al.
Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve,

C. A. Taylor, T. A. Fonte, and J. K. Min
Instantaneous wave-free ratio derived from coronary computed tomography angiography in evaluation of ischemia-causing coronary stenosis: feasibility and initial clinical research,

Y. Ma, H. Liu, Y. Hou et al.
TCT-40 image-based computation of instantaneous wave-free ratio from routine coronary angiography-initial validation by invasively measured coronary pressures,

L. Calmac, R. Niculescu, E. Badila et al.
Numerical simulation of instantaneous wave-free ratio of stenosed coronary artery,

W. Wang, B. Mao, B. Li et al.
Non‐invasive coronary CT angiography‐derived fractional flow reserve: a benchmark study comparing the diagnostic performance of four different computational methodologies,

J. M. Carson, S. Pant, C. Roobottom et al.
Impact of baseline coronary flow and its distribution on Fractional Flow Reserve prediction,

L. O. Müller, F. E. Fossan, A. T. Bråten, A. Jørgensen, R. Wiseth, and L. R. Hellevik
Computational instantaneous wave‐free ratio (IFR) for patient‐specific coronary artery stenoses using 1D network models,

J. Carson, C. Roobottom, R. Alcock, and P. Nithiarasu
Model‐based analysis of the sensitivities and diagnostic implications of FFR and CFR under various pathological conditions,

X. Ge, Y. Liu, S. Tu, S. Simakov, Y. Vassilevski, and F. Liang
A multi-scale model of the coronary circulation applied to investigate transmural myocardial flow,

X. Ge, Z. Yin, Y. Fan, Y. Vassilevski, and F. Liang
Myocardial blood flow in patients with dilated cardiomyopathy: quantitative assessment with velocity-encoded cine magnetic resonance imaging of the coronary sinus,

N. Watzinger, G. K. Lund, M. Saeed et al.
Determinants of coronary blood flow in humans: quantification by intracoronary Doppler and ultrasound,

H. Wieneke, C. Von Birgelen, M. Haude et al.
Coronary flow and resistance reserve in patients with chronic aortic regurgitation, angina pectoris and normal coronary arteries,

A. Nitenberg, J.-M. Foult, I. Antony, F. Blanchet, and M. Rahali
Factors associated with noninvasive coronary flow reserve in severe aortic stenosis,

P. Meimoun, A. L. Germain, F. Elmkies et al.
Aortic regurgitation,

M. Enriquez-Sarano and A. J. Tajik
Impairment of coronary flow reserve in aortic stenosis,

D. Garcia, P. G. Camici, L.-G. Durand et al.
Improving assessment of aortic stenosis,

P. Pibarot and J. G. Dumesnil
Hemodynamic performance of the Fontan circulation compared with a normal biventricular circulation: a computational model study,

F. Liang, H. Senzaki, C. Kurishima, K. Sughimoto, R. Inuzuka, and H. Liu
The evaluation and management of bradycardia,

J. M. Mangrum and J. P. Dimarco
Atrial arrhythmias in patients with arrhythmogenic right ventricular cardiomyopathy/dysplasia and ventricular tachycardia,

A. F. Chu, E. Zado, and F. E. Marchlinski
Effects of age and aerobic capacity on arterial stiffness in healthy adults,

P. V. Vaitkevicius, J. L. Fleg, J. H. Engel et al.
Weight change is associated with change in arterial stiffness among healthy young adults,

R. P. Wildman, G. N. Farhat, A. S. Patel et al.
A comparison of atenolol and nebivolol in isolated systolic hypertension,

Z. Dhakam, Yasmin, C. M. McEniery, T. Burton, M. J. Brown, and I. B. Wilkinson
Systemic endothelin receptor blockade decreases peripheral vascular resistance and blood pressure in humans,

W. G. Haynes, C. J. Ferro, K. P. J. O’Kane, D. Somerville, C. C. Lomax, and D. J. Webb
Blood viscosity and peripheral vascular resistance in patients with untreated essential hypertension,

T. Linde, B. Sandhagen, A. Hägg, C. Mörlin, B. Wikström, and B. G. Danielson
Coronary flow velocity response to adenosine characterizes coronary microvascular function in women with chest pain and no obstructive coronary disease,

S. E. Reis, R. Holubkov, J. S. Lee et al.
The “slow coronary flow

M. Fineschi, A. Bravi, and T. Gori
Effects of adenosine on human coronary arterial circulation,

R. F. Wilson, K. Wyche, B. V. Christensen, S. Zimmer, and D. D. Laxson
Impact of coronary lesion geometry on fractional flow reserve: data from interventional cardiology research in-cooperation society-fractional flow reserve and intravascular ultrasound registry,

D.-Y. Kang, J.-M. Ahn, Y. W. Kim et al.
Image-based computation of instantaneous wave-free ratio from routine coronary angiography: evaluation of a hybrid decision making strategy with ffr,

L. Itu, T. Passerini, E. Badila et al.
Observations from a real-time, iFR-FFR “hybrid approach

R. Scarsini, G. Pesarini, M. Lunardi et al.
Coronary reserve in patients with aortic valve disease before and after successful aortic valve replacement,

F. R. Eberli, M. Ritter, J. Schwitter et al.
Instantaneous wave-free ratio for the assessment of intermediate coronary artery stenosis in patients with severe aortic valve stenosis: comparison with myocardial perfusion scintigraphy,

F. Yamanaka, K. Shishido, T. Ochiai et al.
Correlation between intracoronary physiology and myocardial perfusion imaging in patients with severe aortic stenosis,

R. Scarsini, R. Cantone, G. Venturi et al.
Angina pectoris and coronary artery disease in patients with severe aortic valvular disease,

A.-H. Hakki, D. Kimbiris, A. S. Iskandrian, B. L. Segal, G. S. Mintz, and C. E. Bemis
Fractional flow reserve/instantaneous wave-free ratio discordance in angiographically intermediate coronary stenoses,

C. M. Cook, A. Jeremias, R. Petraco et al.
Discrepancy between fractional flow reserve and instantaneous wave-free ratio: clinical and angiographic characteristics,

J. M. Lee, E.-S. Shin, C.-W. Nam et al.
Global sensitivity analysis of hepatic venous pressure gradient (HVPG) measurement with a stochastic computational model of the hepatic circulation,

T. Wang, F. Liang, Z. Zhou, and X. Qi

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

Comparison of Instantaneous Wave-Free Ratio (iFR) and Fractional Flow Reserve (FFR) with respect to Their Sensitivities to Cardiovascular Factors: A Computational Model-Based Study

References

Abstract

Journal

Recommended Articles

References

Our policy towards the use of cookies