Fast Virtual Fractional Flow Reserve Based Upon Steady-State Computational Fluid …basictranslational.onlinejacc.org/content/btr/2/4/434... · 2017-12-06 · CLINICAL RESEARCH Fast

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C O L L E G E O F C A R D I O L O G Y F O UN DA T I O N . T H I S I S A N O P E N A C C E S S A R T I C L E U N D E R

T H E C C B Y L I C E N S E ( h t t p : / / c r e a t i v e c o mm o n s . o r g / l i c e n s e s / b y / 4 . 0 / ) .

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CLINICAL RESEARCH

Fast Virtual Fractional Flow ReserveBased Upon Steady-State ComputationalFluid Dynamics AnalysisResults From the VIRTU-Fast Study

Paul D. Morris, PHD,a,b,c Daniel Alejandro Silva Soto, PHD,a,c Jeroen F.A. Feher, MSC,a Dan Rafiroiu, PHD,d

Angela Lungu, PHD,a,c Susheel Varma, PHD,a,c Patricia V. Lawford, PHD,a,c D. Rodney Hose, PHD,a,c

Julian P. Gunn, MDa,b,c

VISUAL ABSTRACT

FrombDepcInsi

tech

Morris, P.D. et al. J Am Coll Cardiol Basic Trans Science. 2017;2(4):434–46.

the aDepartment of Infection, Immunity and Cardiovascular Disease, University of She

artment of Cardiology, Sheffield Teaching Hospitals National Health Service Foundation

gneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom

nics and Electrical Measurements, Technical University of Cluj-Napoca, Cluj-Napoca, Ro

HIGHLIGHTS

� Computed vFFR promises the benefits of

physiological lesion assessment without

the drawbacks limiting use of the invasive

method.

� Sophisticated, zero-dimension–coupled,

transient, 3-dimensional CFD models

provide high degrees of accuracy but are

typically slow to compute, and models are

sensitive to unknown physiological

parameters such as myocardial resistance.

� Based on paired steady-state CFD ana-

lyses, 2 mathematical methods (“steady”

and “pseudotransient”) were developed

that accelerate the computation of vFFR

from >36 h to <4 min.

� The pseudotransient method computed

transient results, without the need for

complex, and computationally expensive,

full transient CFD analysis.

� Sensitivity analysis demonstrated that

the hyperemic myocardial resistance

is the dominant influence on vFFR and

not the geometry of the lesion itself.

ffield, Sheffield, United Kingdom;

Trust, Sheffield, United Kingdom;

; and the dDepartment of Electro-

mania. This independent research

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R E V I A T I O N S

J A C C : B A S I C T O T R A N S L A T I O N A L S C I E N C E V O L . 2 , N O . 4 , 2 0 1 7 Morris et al.A U G U S T 2 0 1 7 : 4 3 4 – 4 6 Fast Virtual Fractional Flow Reserve

435

SUMMARYAB B

AND ACRONYM S

CAD = coronary artery disease

CAG = coronary angiography

CFD = computational fluid

dynamics

CMV = coronary

microvasculature

FFR = fractional flow reserve

mFFR = invasively measured

fractional flow reserve

PCI = percutaneous coronary

intervention

wa

of

De

au

dy

Mo

All

ins

vis

Ma

Fractional flow reserve (FFR)-guided percutaneous intervention is superior to standard assessment but

remains underused. The authors have developed a novel “pseudotransient” analysis protocol for computing

virtual fractional flow reserve (vFFR) based upon angiographic images and steady-state computational fluid

dynamics. This protocol generates vFFR results in 189 s (cf >24 h for transient analysis) using a desktop PC,

with <1% error relative to that of full-transient computational fluid dynamics analysis. Sensitivity analysis

demonstrated that physiological lesion significance was influenced less by coronary or lesion anatomy

(33%) and more by microvascular physiology (59%). If coronary microvascular resistance can be

estimated, vFFR can be accurately computed in less time than it takes to make invasive measurements.

(J Am Coll Cardiol Basic Trans Science 2017;2:434–46) © 2017 The Authors. Published by Elsevier on behalf

of the American College of Cardiology Foundation. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).
= rotational coronary
graphy

RoCA

angio

vFFR = virtual fractional flow

reserve

vFFRsteady = virtual fractional

flow reserve computed with

steady-state CFD analysis and

cycle mean values

vFFRtrns = virtual fractional


full transient CFD

vFFRps-trns = virtual fractional


the pseudotransient steady-

state method

F ractional flow reserve (FFR) has become thestandard of care for assessment of the physio-logical significance of coronary artery disease

(CAD) (1,2). When FFR is used to guide percutaneouscoronary intervention (PCI), clinical outcomes areimproved, fewer stents are deployed, and costs arereduced (3–5). However, even in countries whereFFR is most frequently used, FFR is used in < 10%of PCI procedures and far fewer diagnostic cases(6,7). This is due to a combination of factors relatedto practicality, time, and cost. Using computationalfluid dynamics (CFD) to compute a “virtual” FFR(vFFR) from the coronary angiogram (CAG) is a wayof making coronary physiology available to manymore patients. vFFR can assess lesion significancewithout the insertion of a pressure-sensitive wireand without the induction of hyperemia. vFFR there-fore offers the benefits of physiologically guided PCI

SEE PAGE 447

without the drawbacks which limit the invasive tech-nique. Although early results have been promising, 2fundamental problems currently limit the usefulnessof vFFR. The first problem is the time required togenerate a result, which can be in excess of 24 h,due to the complexity of CFD solutions. Second, theprecision of vFFR computation is limited by the

s commissioned by the Health Innovation Challenge Fund (R/135171-11-1),

Health. The views expressed in this publication are those of the authors

partment of Health. Dr. Morris was supported by a British Heart Found

thors have reported that they have no relationships relevant to the conten

namics acceleration techniques described in this article are the subject of

rris and Silva Soto contributed equally to this work and are to be consid

authors attest they are in compliance with human studies committe

titutions and Food and Drug Administration guidelines, including patien

it the JACC: Basic to Translational Science author instructions page.

nuscript received October 29, 2016; revised manuscript received April 2,

accuracy by which the model represents thecoronary and lesion geometry (imaging andreconstruction) and the physiological param-eters (boundary condition tuning) on an indi-vidual patient basis (8). The current studyresolves the former and sheds new light onthe latter.

Our group has previously described a CFD-based method for computing vFFR frominvasive CAG with good diagnostic accuracy(97%) (9). This method incorporated fully
transient, 3-dimensional (3D) CFD analysis which re-quires substantial computing resources and typicallytook >24 h to produce a result. This approach is notappropriate for use in the cardiac catheter laboratorywhere on-table results are desirable.
Coronary blood flow follows a well-known pulsatilepattern. Modeling time-varying pulsatility requires“transient” (time-dependent) CFD analysis. However,FFR is calculated from mean pressure (and, by infer-ence, flow) differences over time. This study hy-pothesized that complex transient CFD analysismight not be necessary. Steady-state CFD analysisruns several orders of magnitude more quickly thantransient CFD analysis. However, it has yet to bedetermined whether an adequate estimation of thetransient pressure and flow distributions could be

a partnership of the Wellcome Trust and Department

and not necessarily those of the Wellcome Trust or

ation clinical training fellowship (R/134747-11-1). All

ts of this paper to disclose. The computational fluid

a UK patent application (PCT/GB2016/053942). Drs.

ered joint first authors.

es and animal welfare regulations of the authors’

t consent where appropriate. For more information,

2017, accepted April 4, 2017.

http://creativecommons.org/licenses/by/4.0/

http://www.basictranslational.onlinejacc.org/content/instructions-authors

Morris et al. J A C C : B A S I C T O T R A N S L A T I O N A L S C I E N C E V O L . 2 , N O . 4 , 2 0 1 7

Fast Virtual Fractional Flow Reserve A U G U S T 2 0 1 7 : 4 3 4 – 4 6

436

made based on steady-state analysis results, partic-ularly in the context of vFFR estimation. Predictingpulsatile vascular physiology on the basis of steadyflow assumptions is not without precedent. In 1951,Gorlin and Gorlin (10) validated an equation whichpredicted cardiovascular orifice area from mean(steady) flow and disregarded flow pulsatility.More recently, both Tu et al. and Papafaklis et al.described systems capable of estimating coronaryphysiology, which are based upon steady-state CFDanalysis (11–13).

The outputs of any model are determined by vari-ations in input parameters which may occur due tonatural biological variability or error in measurement.In the context of vFFR, these errors include a variety ofgeometric and physiological parameters. PromisingvFFR results have been produced despite limitationsin coronary imaging and segmentation and in the waysin which physiological parameters are used in modeltuning (9,14). It is important to understand the relativesensitivity of computed FFR to individual model inputparameters. Sensitivity analysis is a formal mathe-matical process which allows the influence and in-terdependencies of individual model inputs to bedecomposed and quantified in terms of their effects onmodel outputs, which in this case is the vFFR result.

The aims of the current study were first, to developand validate a method which accelerated thecomputation of vFFR to a point which made it prac-tical for use in the cardiac catheter laboratory; andsecond, to quantify the principal, accuracy-definingmodel features and parameters.

METHODS

STUDY DESIGN. This was an observational, analyt-ical, single-center study in which a novel “pseudo-transient” analysis protocol for computing vFFR wasdeveloped and validated relative to both invasiveFFR measurement and fully transient CFD analysis.All work was approved by the local ethics committee,and all participating patients gave informed consent.

PATIENTS. Patients were eligible for recruitment ifthey had proven CAD and were awaiting assessmentfor elective PCI. Apart from chronic total occlusion,all patterns and severity levels of stable CAD wereeligible for recruitment. Exclusion criteria were acutepresentation within 60 days; intolerance to intrave-nous nitrate, adenosine, or iodine-based contrastmedium; coronary artery bypass graft surgery; orobesity which precluded CAG. Ethical approval andformal patient consent were obtained.

CLINICAL PROTOCOL. Rotational coronary angiog-raphy (RoCA) was performed after isocentering in

posterior-anterior and lateral planes after adminis-tration of glyceryl trinitrate, during a breath hold,with a hand injection of 10 to 20 ml of contrast.Fractional flow reserve was measured in the standardway (15), across all lesions with >50% vessel diameterby visual estimation, under baseline and hyperemicconditions, using intravenous adenosine, 140 mg/kg/min(Volcano Corp., San Diego, California) with the pres-sure transducer positioned at least 4 reference vesseldiameters distal to the end of the lesion. Percuta-neous coronary intervention proceeded according tothe operator’s normal practice, guided by the angio-gram and the measured FFR. To ensure a diverse andwide-ranging case mixture, RoCA and physiologicalmeasurements were repeated post PCI and underbaseline and hyperemic conditions.

SEGMENTATION AND MESHING. Vessels werereconstructed from the angiogram images (Allura 3D-RA system, Philips Healthcare, Best, the Netherlands)by a cardiologist experienced in such methods(Figure 1). A 1- to 2-million element volumetric meshwas fabricated in ICEM (ANSYS, Canonsburg, Penn-sylvania) for each unique arterial geometry (Figure 2).Depending on the size of the segmented vesselsegment, the volumetric meshing process tookbetween 1 and 4 min. Computation and all simula-tions were performed using ANSYS CFX (ANSYS, Inc.,Cannonsburg, Pennsylvania) on a Precision T5600computer (Intel Xeon processor, 32GB RAM, Dell,Round Rock, Texas).

FULLY TRANSIENT vFFR MODEL. Our gold standardreference method was vFFR computed by fully tran-sient 3D CFD. It was computed in a method consistentwith the methods described in the VIRTU-1 (VIRTUalFractional Flow Reserve From Coronary Angiography)trial (9). Catheter pressure was applied at the proximalboundary. The distal boundary of the 3D domain wascoupled to a 7-element, modified Windkessel model,applying the coronary microvasculature (CMV) pa-rameters derived by the optimization processdescribed below. The pressures were uniform at theboundaries, and no velocity profiles were imposed.

PSEUDOTRANSIENT vFFR ANALYSIS PROTOCOL. Apseudotransient vFFR protocol (virtual fractionalflow reserve computed with the pseudotransientsteady-state method [vFFRps-trns]) was developed sothat transient results could be approximated withoutperforming fully transient CFD analysis. A transientanalysis of a 2-compartment model, consisting of acompartment representing the diseased arterialsegment and a compartment representing the distalmicrovasculature, was performed. The proximalcompartment was represented by a quadratic

FIGURE 1 Processing Raw Clinical Data

Angiograms of a diseased right coronary artery (left) have been segmented, and the reconstructed vessel is shown (middle) alongside the

processed pressure data (right) within the VIRTUheart workflow environment.


437

equation relating the instantaneous pressure drop tothe instantaneous flow. The coefficients of thisequation, z1 and z2, for the linear and quadratic terms,respectively, were determined from 2 steady-state 3DCFD analyses of the arterial geometry with prescribedflow rates, with a plug velocity profile and a uniform

FIGURE 2 Sample Finite Element Mesh Used for Simulations

Mesh shown is produced from the angiogram shown in Figure 1. Details o

refined using prism elements.

zero-pressure outlet (see Supplemental Appendix Afor derivation). A range spanning sub- to supra-physiological flow rates was evaluated (0.5, 1, 2, 3, 4, 5ml/s) in order to identify the 2 flow rates whichoptimally characterized the terms z1 and z2 over thecohort investigated. vFFRps-trns was a function of 9

f the wall (blue) and inlet (green) are shown. The near-wall region is


FIGURE 3 Models for Computing vFFR

The imaging and pressure input data for both novel models are those collected during routine coronary angiography (image data in yellow and

aortic pressure data in green). The parameters of CMV physiology must be estimated (red). The type of simulation used to calculate vFFR

values are shown in the blue boxes. vFFRps-trns is a function of 9 parameters, whereas vFFRsteady is a function of 4. Pseudotransient flow can be

reconstructed using a 1D flow model representing the 3D vessel geometry coupled to the 0-dimensional Windkessel model. C ¼ compliance;

CMV ¼ coronary microvasculature; R ¼ resistance; vFFR ¼ virtual fractional flow reserve; Z ¼ impedance.



438

parameters: the proximal pressure trace, terms z1 andz2, CMV resistance, CMV compliance, and the pa-rameters describing the myocardial systolic contrac-tion including pressure generation, plateau, decay,and amplitude (see Supplemental Appendix B for thederivation of vFFRps-trns).

STEADY vFFR MODEL. The pseudotransient analysisprotocol computed an approximation of the temporalvariation of pressure distal to the lesion from which,together with the proximal pressure, the vFFR wascalculated. The transient waveforms have valuebeyond the computation of vFFR, but given that FFRis a measurement computed from average pressure, itwas interesting also to investigate whether vFFR canbe computed from a single steady flow analysis at themean pressure. The protocol was further simplified tocalculate “steady” vFFR (vFFRsteady). In the compu-tation of vFFRsteady, all distal parameters of CMVphysiology were reduced to a single, time-averaged

value of resistance. vFFRsteady was therefore a func-tion of just 4 parameters: mean proximal pressure,terms z1 and z2, and total distal resistance. Thismethod does not require (or allow) accurate recon-struction of the aortic pressure wave because themean pressure is used. The major advantage of thismethod is that it requires far fewer parameters;however, there is little advantage in computationalspeed over the pseudotransient analysis. Derivationof the equation for calculating vFFRsteady is describedin Supplemental Appendix C. A comparison of thedata used in each model is demonstrated in Figure 3.

BOUNDARY DATA. The proximal physiologicalboundary condition was the patient-specific pressuremeasured from the guiding catheter which sits at thecoronary ostium (i.e., aortic pressure). The distalcompartment requires a characterization of distalimpedance. This was computed for each individualfrom the invasive pressure measurements at the



TABLE 1 Baseline Characteristics

Baseline characteristics

Age, yrs 66 (51–87)

Male 70%

Body mass index, kg/m2 29.6 (3.4)

Comorbidities

Hypertension 60%

Hyperlipidemia 90%

Diabetes 30%

Current smoker 0%

Prior myocardial infarction 45%

Stroke 0%

Peripheral vascular disease 15%

Medication

Aspirin 90%

Beta-blocker 65%

Nitrate 60%

Statins 90%

ACE inhibitors 45%

Calcium-channel blockers 25%

Clopidogrel 75%

ARBs 20%

Values are mean (range), %, or mean (%).

ACE ¼ angiotensin-converting enzyme; ARB ¼ angiotensin receptor blocker.


439

proximal and distal boundaries by using the guidingcatheter and pressure wire (Volcano Corp.), respec-tively. The outlet of the reconstructed vessel corre-sponded to the location of the pressure wiretransducer, the location of which was specificallyrecorded during CAG. This is consistent with standardFFR measurement. Because the distal boundary con-dition was based upon measured values, thecomputed vFFR was expected to be accurate. Thefocus of this study was not a clinical trial of vFFR butrather an analysis of the speed and accuracy of thenovel CFD acceleration techniques described below.The challenge of tuning the parameters of the distalimpedance model to the individual is discussed indetail elsewhere (8). The important result in thisstudy is, therefore, not whether vFFR matches mFFRbut rather, can the accelerated methods generate re-sults which do not sacrifice accuracy relative to thefully transient 3D analysis. A semiautomatic optimi-zation algorithm was developed within Matlab(Mathworks Inc., Natick, Massachusetts) to derive theparameters of the CMV from invasively measuredvalues. This method was based on the method byLungu et al. (16), who provided a full description.These parameters included CMV impedance, resis-tance, and compliance, along with 4 parametersreflecting the amplitude and timing of intra-myocardial systolic pressure.

SENSITIVITY ANALYSIS. A formal sensitivity analysiswas performed using the Sobol decompositionmethod(17,18). The input parameters examined were CMVresistance, geometry parameters (z1 and z2), andproximal pressure (Pa). This variation-based methodcan be used to determine the magnitude of effect ofindividual input parameters on the output of a model,in this case vFFR. The main sensitivity indices provideinformation about the reduction in model outputvariation if an input factor would be accuratelyapplied. Therefore, the main sensitivity indices canprovide a ranking of the individual input parametersresponsible for proportions of the model output vari-ation (i.e., the inputs are ranked in order of the level ofinfluence on the vFFR result that they have). Addi-tionally, total sensitivity indices can be used to iden-tify parameters that have little or even negligible effecton model output and can therefore be fixed to popu-lation averages. For the current study, the main andtotal sensitivity indices were determined over param-eter ranges derived from the patient cohort by usingthe vFFRsteady method. Definitions of the sensitivityindices can be found in Supplemental Appendix D.

STATISTICAL ANALYSIS. The diagnostic accuracy ofthe workflow (ability of vFFR to predict FFR <0.80 or

>0.80) was assessed by calculating the sensitivity,specificity, positive predictive value, and negativepredictive value. Overall accuracy was calculated asthe true positive-to-true negative results ratio to thetotal number of cases. Agreeability between vFFR andFFR was assessed by calculating the bias, mean delta,and standard deviation of the mean delta and wasdemonstrated graphically as a Bland-Altman plot (19).Time-dependent error between transient and pseu-dotransient results is expressed as the normalizedroot mean square (RMS) norm (i.e., the measuredtransient distal pressure vector is subtracted from thecomputed pseudotransient one, normalizing bydividing by the mean transient pressure andcomputing the 2-norm [RMS]) of this vector. BecauseFFR is calculated using cycle mean values, the errorbetween the means is also expressed. The intraclasscorrelation coefficient is reported as a measurementof agreeability between the vFFR metrics. Unlessstated otherwise, data are mean � SD. Comparison ofmeans was performed using a Mann-Whitney U test.Statistical analysis was performed using SPSS Statis-tics version 22 (IBM Analytics, Armonk, New York).

RESULTS

PATIENT AND CLINICAL CHARACTERISTICS. Datawere collected from 20 patients. Their baseline char-acteristics are summarized in Table 1. In total, 73unique arterial datasets were studied (Table 2), which


TABLE 2 Comparison Among Pseudotransient and Steady vFFR Methods Relative to

Measured Translesional Pressure Ratio Values

N Error Bias Max Error Range*

All cases

Pseudotransient 73 0.0070 � 0.0045 �0.0051 � 0.0065 �0.018 to þ0.013

Steady 73 0.0044 � 0.0044 �6e�4 � 0.0062 �0.011 to þ0.022

FFR <0.90


Steady 37 0.0050 � 0.0049 �9.7e�5 � 0.0070 �0.011 to þ0.022

FFR 0.70–0.90


Steady 29 0.0048 � 0.0045 �3.1e�4 � 0.0067 �0.011 to þ0.022

Values are mean � SD unless otherwise indicated. *Indicates worst underestimation to worst overestimation.

vFFR ¼ virtual fractional flow reserve.

FIGURE 4 A Pseud

Invasively measured

transient result close

despite no transient

abbreviations as in F



440

consisted of 34 left anterior descending, 21 rightcoronary, 3 diagonal, 7 left circumflex, and 8 left maincoronary arteries. A total of 39 cases were pre PCI,25 cases were post PCI, and 9 cases did not receive astent; 41 cases were under hyperemic conditions, and32 cases were baseline measurements. Mean SYNTAX(Synergy between PCI with TAXUS drug-eluting stentand Cardiac Surgery) score was 10.45 (20), and meanNew York PCI Risk Score was 0.22 (21).

SELECTION OF STEADY FLOW RATES FOR

CHARACTERIZATION. We performed 438 steady-state simulations (73 cases, each at 0.5, 1, 2, 3, 4,and 5 ml/s), and a quadratic pressure-drop versusflow relationship was computed from each pair offlow rates (Supplemental Appendix B). When we

otransient Pressure Result From an LAD Arterial Case

FFR was 0.350 and the computed vFFR was 0.346. The pseudo-

ly matches the invasively measured result (RMS norm: 0.026),

data being used in its computation. RMS ¼ root mean square; other

igure 3.

compared the errors between the steady-statemethod (pseudotransient) and measured FFR, thebest overall accuracy was produced when z1 and z2were derived from steady-state flows simulated at 0.5and 5 ml/s (vFFR mean error vs. measured values:�0.0043 [0.004]). However, neither of these flowrates are physiological in the context of stable CAD.Furthermore, at a flowrate of 5 ml/s, 1 steady-stateanalysis became unstable and failed to converge to asatisfactory result due to an excessively high Rey-nold’s number (i.e., unrealistic physics for biologicalflow through a tight stenosis). For this reason, flowrates of 1 and 3 ml/s were selected as the bases for thecharacterizations. This pairing is more representativeof the prevailing underlying physiology, converged toa satisfactory result expediently in all cases, and wasassociated with an error which was only mildly higherthan that of the 1 and 5 ml/s pairing (mean error:�0.0069 [0.005]). The 1 and 3 ml/s pairing wastherefore adopted for subsequent analysis.

STEADY-STATE CFD ANALYSIS TIME. Using the 1 and3 ml/s flow pairings, all 73 steady-state flow pairingsconverged successfully at the first attempt with noalteration to the protocol. The mean total time for1 pair of steady-state analyses (the basis for thepseudotransient and steady vFFR workflows) was189.3 � 34.0 s.

ACCURACY OF PSEUDOTRANSIENT vFFR. Anexample of a pseudotransient result plotted relativeto measured data is demonstrated in Figure 4. Thehigh accuracy compared with measured FFR wasbecause the distal impedance was tuned using the(measured) distal pressure. The primary challenge inusing the analysis protocol for accurate computationin the clinical setting to replace measured FFR is inthe prior and independent estimation of the distalimpedance (17), but the focus of this paper was toshow that a computationally inexpensive analysisprotocol based on steady flow analyses can replace afully transient CFD study. A Bland-Altman plot isshown in Figure 5A. Agreement between vFFRps-trns

and measured data was also high (Table 3). In per-centage terms, relative to measured values, meanerror was �0.86% (0.60). The intraclass correlationcoefficient between vFFRps-trns and mFFR was 0.999(95% confidence interval [CI]: 0.998 to 0.999;p < 0.001). vFFRps-trns achieved 100% sensitivity,specificity, positive predictive accuracy, negativepredictive accuracy, and overall diagnostic accuracyfor diagnosing physiological lesion significance(FFR <0.80 or >0.80). Pseudotransient results werecompared with those derived from values measuredfor goodness-of-fit. An example of a measured


FIGURE 5 Bland-Altman Plots Demonstrating Agreement Between vFFR and

Measured FFR

The solid line indicates bias (mean delta), and the interrupted lines represent the upper

and lower limits of agreement (SD: �1.96). (A) Agreement for vFFRps-trns, and (B)

agreement for vFFRsteady. Note the high number of cases in the clinically important FFR

range from 0.7 to 0.9.


441

transient versus pseudotransient result is demon-strated in Figure 4. Over all 73 datasets, the RMS normbetween the pseudotransient results and measureddata was 0.37 � 0.49. However, this was significantlybetter in the cases where FFR was <0.90 (RMS norm0.15 � 0.34).

ACCURACY OF vFFRsteady. Agreement betweenvFFRsteady and measured FFR was also high (Table 2).A Bland-Altman plot is shown in Figure 5B. In per-centage terms, relative to measured values, meanerror was �0.50% (0.40). The intraclass correlationcoefficient between vFFRsteady and mFFR was 0.999(95% CI: 0.998 to 0.999; p < 0.001). vFFRsteady alsoachieved 100% sensitivity, specificity, positive pre-dictive accuracy, negative predictive accuracy, andoverall diagnostic accuracy when we diagnosedphysiological lesion significance (FFR #0.80 or>0.80).

COMPARISON WITH TRANSIENT RESULTS. Forcomparison, the complex, zero-dimension–coupled,fully transient method was compared with thevFFRps-trns and vFFRsteady methods. The mean timefor the completion of the fully transient CFD analyseswas 26 h,48 min (range: 6 to 48 h). The steady-statemethod therefore was processed more than 500times faster than the fully transient analysis. Unlikethe steady-state analyses, the transient CFD analysesbecame repeatedly unstable, necessitating reductionsin the simulation time-step (at the expense ofincreasing computation time). Mean error for thetransient method (�1.0%) was not statisticallysignificantly different from vFFRps-trns and vFFRsteady

methods in a small subset of 6 transient cases.

AREAS OF CLINICAL INTEREST. According to pub-lished studies, the ischemic threshold correspondsto an FFR of #0.80. FFR is typically used to helpdetermine the best course of action in angio-graphically significant or borderline cases. Accuracyof both of the steady-state vFFR methods wastherefore also assessed in subgroups of caseswhere FFR was <0.90 (n ¼ 37) and more border-line cases where FFR was 0.70 to 0.90 (n ¼ 29)(Table 2). There were no statistically significantdifferences in accuracy of either method whendeployed in either subgroup or when deployed inall cases (Table 2).

SENSITIVITY ANALYSIS. Figure 6 provides a rankingof the main sensitivity indices and demonstratesthat the principal influence on the variation ofvFFR values was the total distal CMV resistance, ac-counting for 59.1% of the variation. Coronary anatomyand stenosis geometry (characterized by z1 and z2)were of secondary importance in the study

population, accounting for 33.2% of vFFR variation. Aheatmap of the FFR sensitivity indices is displayed inFigure 7. Only 7.5% of the model output variation wascaused by higher order interaction effects. Interaction(indirect) effects are defined as the difference be-tween the total effect and the direct (main) effect of aninput parameter. The magnitude of the interactioneffects is demonstrated in Figure 8, which displays thetotal sensitivity indices divided into the main effects(Si) and the remainder accounting for higher-orderinteraction effects. A relatively small proportion ofthe total effect of the individual input parameters canbe attributed to interaction effects. The total variationin vFFR caused by proximal pressure (Pa) is <1%, asdemonstrated by the total sensitivity index value of0.0038. Therefore, average proximal pressure hadnegligible effect upon vFFR result.

TABLE 3 Effect of Applying Generic (Averaged) Boundary Conditions on Quantitative and Diagnostic Errors

Basis Upon Which Subgroupings Were Averaged (CMVRtotal) N Datasets Error of vFFR Result Bias (Mean Delta) Diagnostic Accuracy

All cases 73 0.11 � 0.12 0.11 � 0.12 75%

Baseline and hyperemic conditions 73 0.096 � 0.096 0.088 � 0.104 52.1%

Right and left coronary arteries (under hyperemic conditions) 40 0.078 � 0.079 0.046 � 0.102 80%

Artery-specific (LAD, RCA, DX, LMCA, LCX) (under hyperemic conditions) 40 0.0050 � 0.0046 �2.6 e�5 � 0.0068 82%

Case-specific (no averaging) 73 0.0044 � 0.0044 �6.0 e�4 � 0.0062 100%

Values are mean � SD unless otherwise indicated.

CMVRtotal ¼ total coronary microvascular resistance; DX ¼ diagonal artery; LAD ¼ left anterior descending artery; LCX ¼ left circumflex artery; LMS ¼ left main coronary artery; RCA ¼ rightcoronary artery; other abbreviations as in Table 2.

FIGURE 6 Pie Chart Demonstrates Relative Effect of Each

Individual Model Input Parameter on Model Output (vFFR)

Variance

See Supplemental Appendix D.



442

GENERIC BOUNDARY CONDITIONS. The influenceof CMV resistance was further demonstrated byreanalyzing all cases, applying a generic value of CMVresistance as the distal boundary condition. Thisuniversal value was the mean resistance from allincluded cases. The effect this had upon vFFR error isdemonstrated in Table 3. Accuracy improved as theaveraged value for CMV applied at the distal bound-ary better and more specifically reflected the coronaryarterial subgrouping.

DISCUSSION

We have developed a pseudotransient analysis pro-tocol for the fast and accurate computation of vFFR.It requires 2 steady-state CFD analyses to derive thelinear and quadratic terms which characterize therelationship between pressure and flow for eachunique arterial case. The computational executiontime is approximately 3 min on a standard desktopPC, and given an accurate measure of distal imped-ance, the protocol quantified FFR with <1% error andwas 100% accurate in diagnosing physiologicallesion significance, relative to the gold standardreference of fully transient CFD analysis. An evensimpler, fully steady protocol also gave similar resultsfor FFR but at almost the same computationalexpense and without the benefit of representation ofthe transient waveforms. These results suggest thattime-consuming, high-powered computer processingfor complex transient CFD analysis is not necessaryfor the computation of vFFR. Furthermore, steady-state analysis was more robust and reliable thanfully transient analysis, which proved unstable in anumber of cases. We applied a rigid wall simulationwhich simplified the CFD solution. Although thisdisregards coronary vascular compliance, thisapproach has previously been demonstrated to beacceptable in coronary hemodynamic modeling (22)and appears appropriate in the current study.

The pseudotransient protocol runs in 0.2% of thetime taken for fully transient CFD analysis. Themagnitude of this acceleration means it is nowfeasible that vFFR can be computed in less time thanit takes to measure FFR invasively with a pressure-sensitive wire. Computational fluid dynamics anal-ysis is now no longer the rate-limiting step in vFFRcomputation. Instead, segmentation, meshing, andpre-processing protocols are now the time-criticalprocesses. At the current stage of development,these additional components of the workflow (whichare not the focus of this study) run in approximately2 to 4, 2, and 2 min, respectively.

Aside from system acceleration, the sensitivityanalysis performed in this study has demonstrated therelative importance of each input parameter in theprecision of vFFR computation. The fact that vFFRwas insensitive to variations in Pa is consistent withthe original clinical FFR studies by Pijls et al. (15) and


FIGURE 7 Sensitivity Index Heatmap

The main sensitivity indices (Si), total sensitivity indices (SiT), and interaction effects are

displayed for the 4 input parameters: RCMV, geometry parameters (z1 and z2), and

average proximal pressure (Pa). The axis on the right indicates the magnitude of the in-

fluence on output (vFFR) result, with higher values having a stronger influence on result.

CMV resistance is the dominant influence on vFFR result. CMV ¼ coronary microvas-

cular; RCMV ¼ CMV resistance; other abbreviations as in Figure 3.


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De Bruyne et al. (23). For many years, angiographicassessment of CAD focused solely upon lesion anat-omy. More recently, it has been demonstrated thatphysiological assessment (e.g., FFR) correlates moreclosely with clinical outcome than lesion anatomyalone. Several groups have tried, largely unsuccess-fully, to infer physiological lesion significance purelyfrom lesion anatomy by using 2D and 3D quantitativecoronary angiography (QCA) (24–26). The sensitivityanalysis presented in this study explains this collec-tive failure: the aforementioned studies did notincorporate any measurement of CMV resistance intheir processing. This study of a population of patientswith stable coronary artery disease demonstrates thatvariability in CMV resistance had a greater influenceon the vFFR result than variability in epicardial coro-nary and lesion anatomy. This highlights how criticalit is to include an accurate estimate of CMV resistanceinto any virtual FFR model. This also explains thestrength and success of FFR over standard and quan-titative CAG, because invasive FFR measurementautomatically incorporates the magnitude of CMVresistance (15). It also explains why other publishedwork in this area has been able to report reasonablevFFR accuracy, despite using relatively impreciseimaging and segmentation protocols (9,12,14). Ifmodelers wish to construct workflows which accu-rately compute FFR, without wire insertion andwithout the induction of hyperemia, tuning the modelparameters of CMV resistance on an individual casebasis now represents the single greatest challenge toovercome (17). The application of completely genericboundary conditions yielded inferior accuracy. Whenwe applied subcategorized averages based uponarterial subtype, accuracy improved, supporting thenotion that the precision of the CMV resistance iscritical to computing physiological lesion significance.

The ability to predict transient values withoutperforming transient analysis is also a significantdevelopment. The quality of the fit between pseu-dotransient and actual values was dependent uponthe accuracy of the Windkessel parameters applied(CMV resistance, impedance, compliance and intra-myocardial systolic pressure). Although the accuracyof both of the novel methods was high across a widerange of FFR values tested (Table 2), for methodo-logical reasons, parameter derivation is improvedwhen the translesional pressure gradient is greater.This explains why accuracy appears to be slightlyimproved for cases where the FFR was lower(Figure 5). Not only is this effect subtle, it is notrelated to the accuracy of the computational modelbut, separately, of the parameterization strategyused. The accuracy and value of the pseudotransient

method are impressive and applicable to a wide rangeof engineering applications (along with but notnecessarily limited to models with scales of similarlength and Reynold’s numbers) beyond the cardio-vascular system and even beyond biologicalmodeling. The pseudotransient method retains thehigh temporal and spatial resolution of the transientanalysis but relies upon faster and more robuststeady-state analysis. In the current study, theNavier-Stokes equations of fluid flow were solvedusing CFX (ANSYS). The drawback of the pseudo-transient method is that, in addition to z1 and z2, itrequires the application of 7 parameters (impedance,resistance, compliance, and 4 parameters describingthe timing and amplitude of intramural myocardialsystolic pressure), whereas the steady method onlyrequires resistance (Figure 3). This may be simple innonbiological modeling, but deriving these parame-ters noninvasively remains a significant challenge forthe current application.

The accuracy of the steady analysis protocol(vFFRsteady) demonstrates how simple the computa-tion of vFFR can be. This protocol requires only thevessel geometry (to derive z1 and z2) and the totaldistal resistance of the CMV (Figure 3).

Apart from lesions causing chronic total obstruc-tion, all patterns and severities of CAD, including leftmain coronary artery disease were included in this

FIGURE 8 Total and Interaction Model Input Effects

Bar chart demonstrating the magnitude of the total (direct and interactions) effect on

vFFR caused by the input parameters CMV resistance (RCMV), geometry parameters

(z1 and z2) and average proximal pressure (Pa). Abbreviations as in Figure 7.



444

study. The current study therefore reflects “realworld” working practice and is widely applicable. Afurther strength of the current methods is thatthey can be applied to any arterial geometric recon-struction including CAG and coronary computed to-mography angiography (CCTA).

Other authors have used steady-state analysis in asimilar context. Papafaklis et al. (12) used pairedsteady-state analysis to compute “virtual functionalassessment index” (vFAI) for fast functional assess-ment of intermediate coronary lesions, which was alsobased upon steady-state analysis. vFAI was computedin 7 min, based on the distal pressure-to-proximalpressure ratios over the lesion for flows in the rangeof 0 to 4 ml/s, normalized by the ratio over this rangefor a normal artery. vFAI is numerically equal to theaverage of the computed pressure ratio over this flowrange. Although this is likely to be superior to QCA-derived functional lesion assessment (because thegeometric description is transformed into a morephysiologically relevant measurement, namely pres-sure ratio, by the computation of the relationship

between pressure ratio and flow), vFAI is entirely afunction of the geometry of the stenosis. The resultsof the current sensitivity analysis demonstrated thecritical importance of distal resistance. Because vFAIignores this parameter, it cannot be a surrogate forFFR. vFAI will indicate the need for intervention if thelesion is geometrically significant, whereas the FFRmight be high or low for the same lesion depending onthe overall physiology and, particularly, on the statusof the coronary microvasculature.

Tu et al. (11) developed a 3D steady-state model topredict vFFR. Arterial segmentation was from CAGimages. Computational fluid dynamic simulation wascompleted in approximately 5 min. Mean hyperemiccoronary flow was estimated from Thrombolysis InMyocardial Infarction (TIMI) frame counting of therapidity of the contrast wave front within the coronaryarteries during injection. This approach is advanta-geous because it can be estimated during routineangiography and is computed in a similar time scale.However, a disadvantage is that it requires inductionof hyperemia (another potential factor contributing toFFR underuse); and because it is only an estimation ofmean flow, the method cannot generate transient (orpseudotransient data). More recently, Tu et al. (11)described a method for computing quantitative flowratio (QFR). Not only is QFR quick to compute buttuning can be performed based upon contrast flow(cQFR) without inducing hyperemia. Compared withmFFR, QFR identified physiological lesion signifi-cance with 86% overall accuracy (13).

STUDY LIMITATIONS. First and most importantly, inthis study, we inferred the parameters of the CMVfrom invasive measurement. In a truly predictivestudy, where invasive measurement is avoided, thesewould not be known. However, the aim of this studywas to develop and validate a method of vFFRcomputation which could operate within time scaleswhich are practical for real-time use in the cardiaccatheter laboratory. Tuning the boundary conditionsto reflect CMV physiology remains a challenge for allgroups working in this area and represents a work inprogress for the study team. Second, the simplifiedapproach applied in this study ignored the influenceof side branches proximal and distal to a lesion. Aschema for distributing pressure and flow amongbranches is currently under development. Third, theimage segmentation protocol used is based uponRoCA, which is not widely available and producesaxis-symmetrical coronary lumen segmentations.However, this study demonstrates that when vFFR iscomputed, geometric precision is of secondaryimportance to the precision of the CMV resistance.

PERSPECTIVES

COMPETENCY IN MEDICAL KNOWLEDGE: The

gold-standard assessment of physiological lesion significance is

the invasive measurement of FFR, but clinical uptake remains

low. Investigators have attempted to compute vFFR by using

CFD modeling to provide the benefits of physiological lesion

assessment without the drawbacks limiting the invasive method.

The novel mathematical methods described in this article reduce

vFFR computation time from >36 h to <4 min on a standard

desktop computer, without compromising clinical accuracy or

transient (time-dependent) physiology. Sensitivity analysis

demonstrates that myocardial resistance, not lesion geometry, is

the dominant influence on vFFR results.

TRANSLATIONAL OUTLOOK: The final major barrier to a

reliable vFFR tool is the application of a patient-specific tuning

strategy to represent either hyperemic flow or myocardial

resistance.


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Furthermore, the methods developed in this study areapplicable to any coronary segmentation. Fourth, thecurrent sensitivity analysis examines the sensitivityof the model to interpatient variability (leading tovariability in vFFR prediction). The variation of allvFFR values has been decomposed and attributed tothe individual model parameters (or combinations ofthese parameters). This study did not address intra-patient sensitivity and uncertainty of vFFR pre-dictions due to measurement uncertainties. This issomething we intend to develop for future iterationsof the vFFR workflow and will be formally examinedon a patient-by-patient basis.

CONCLUSIONS

Given an accurate value for CMV resistance, vFFR canbe accurately computed from CAG in <4 min, withoutthe insertion of a pressure wire and without inductionof hyperemia. Transient results can be predictedwithout performing time-consuming transient CFDanalysis. Accuracy of vFFR computation is influencedless by geometric accuracy and more upon the tuningof the model to accurately represent distal CMVresistance.

ACKNOWLEDGMENTS The authors thank Dr. RolandBullens (Philips Healthcare, Best, the Netherlands) forproviding a console enabling 3D rotational angiog-raphy data download and segmentation, Tina Hook(Sheffield Teaching Hospitals) for help and expertisecollecting invasive physiological data, and James

Heppenstall (Sheffield Teaching Hospitals) for sup-porting the export of angiographic data.

ADDRESS FOR CORRESPONDENCE: Dr. Paul D. Morris,Mathematical Modelling in Medicine Group, Departmentof Infection, Immunity and Cardiovascular Disease, Uni-versity of Sheffield, The Medical School, Beech Hill Road,Sheffield S102RX, United Kingdom. E-mail: [email protected].

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KEY WORDS computational fluid dynamics,coronary artery disease, coronarymicrovascular physiology, coronarymodelling, coronary physiology, fractionalflow reserve, virtual fractional flow reserve

APPENDIX For supplemental material,please see the online version of this paper.









































































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