Computed Fractional Flow Reserve
(FFTCT) Derived from Coronary CT
Christopher K. Zarins, Charles A. Taylor
& James K. Min
Journal of Cardiovascular
J. of Cardiovasc. Trans. Res. (2013)
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J. of Cardiovasc. Trans. Res. (2013) 6:708-714
Computed Fractional Flow Reserve (FFTCT) Derived
from Coronary CT Angiography
Christopher K. Zarins & Charles A. Taylor & James K. Min
Received: 29 May 2013 / Accepted: 7 July 2013 / Published online: 10 August 2013
© The Author(s) 2013. This article is published with open access at Springerlink.com
Abstract Recent advances in image-based modeling and
computational fluid dynamics permit the calculation of cor-
Coronary artery disease
onary artery pressure and flow from typically acquired cor-
Coronary computed tomographic angiography
onary computed tomography (CT) scans. Computed frac-
Invasive coronary angiography
tional flow reserve is the ratio of mean coronary artery
pressure divided by mean aortic pressure under conditions
Fractional flow reserve
of simulated maximal coronary hyperemia, thus providing a
FFR derived from coronary computed tomography
noninvasive estimate of fractional flow reserve (FFRCT) at
Percutaneous coronary intervention
every point in the coronary tree. Prospective multicenter
Area under the receiver operating characteristic
clinical trials have shown that computed FFRCT improves
diagnostic accuracy and discrimination compared to CT
stenosis alone for the diagnosis of hemodynamically signif-
icant coronary artery disease (CAD), when compared to
invasive FFR as the reference gold standard. This promising
new technology provides a combined anatomic and physio-
Invasive coronary angiography (ICA) has served as the
logic assessment of CAD in a single noninvasive test that can
cornerstone for the diagnosis of patients with known or
help select patients for invasive angiography and revascular-
suspected coronary artery disease (CAD) and provides a
ization or best medical therapy. Further evaluation of the
roadmap for interventional and surgical treatment. Decisions
clinical effectiveness and economic implications of nonin-
regarding coronary revascularization are typically made on
vasive FFRCT are now being explored.
an ad hoc basis from visual estimates of the severity of
coronary artery luminal narrowing . However, it is well
known that coronary angiography has limited value in deter-
Keywords Fractional flow reserve · Computational fluid
mining the hemodynamic, or physiologic, significance of
dynamics · Coronary computed tomographic angiography ·
coronary lesions, particularly for moderate coronary stenosis
Noninvasive cardiac imaging
. This determination prior to coronary revascularization
has been demonstrated as the most important factor to influ-
ence clinical outcome in patients with CAD [2, 3]. Patients
with ischemia-causing stenoses benefit from revasculariza-
Associate Editor Angela Taylor oversaw the review of this article.
tion [4, 5] whereas patients with hemodynamically insignif-
C. K. Zarins (✉) ·C. A. Taylor
icant stenoses require no intervention and experience favor-
HeartFlow, Inc., Redwood City, CA, USA
able outcomes on medical therapy alone, with myocardial
infarction and mortality rates of <1 % per year [6, 7]. Thus,
J. K. Min
determination of the hemodynamic significance of coronary
Weill Cornell Medical College and New York Presbyterian
lesions is of paramount importance in guiding treatment
Hospital, New York, NY, USA
strategy, and this can be readily accomplished during ICA
by measurement of fractional flow reserve (FFR) . De-
C. K. Zarins · C. A. Taylor
Stanford University, Stanford, CA, USA
spite remarkable advances in noninvasive cardiac imaging
J. of Cardiovasc. Trans. Res. (2013) 6:708-714
capabilities, no currently available noninvasive imaging test
of the coronary arteries, each of which underscores the need for
can reliably diagnose the presence or absence of ischemia-
a noninvasive method to determine the functional significance
causing stenoses on a lesion-specific basis. The recent intro-
of individual coronary lesions.
duction of a novel computational method has enabled the
calculation of fractional flow reserve (FFRCT) from cardiac
(CT) imaging data without the
Noninvasive Evaluation of CAD
need for additional imaging, medication, or modification
of CT acquisition protocols
. This manuscript
Noninvasive evaluation of coronary artery disease can be
will review the rationale of FFR and the scientific basis
readily performed using multidetector row CT scanners
for noninvasive computational FFR and discuss its clin-
which provide high-resolution anatomic imaging of the cor-
onary arteries and obstructive atherosclerotic plaques . A
number of prospective, multicenter studies have demonstrat-
ed high diagnostic performance for the identification and
Invasive FFR Measurement
exclusion of anatomically obstructive coronary artery dis-
ease compared to ICA [20-22]. However, CT cannot deter-
Fractional flow reserve measurement is based on the rela-
mine the hemodynamic significance of coronary lesions and
tionship between coronary artery pressure and blood flow.
frequently overestimates the severity of stenosis. Even
Although this relationship is quite variable at rest, during
among high-grade stenoses identified by CT and confirmed
maximal hyperemia, there is a linear relationship between
by angiography, less than half are ischemia causing when
coronary pressure and flow because peripheral resistance is
compared to FFR [23, 24]. This unreliable relationship be-
minimal and therefore constant . FFR is thus defined as
tween stenosis severity and functional significance has raised
the ratio of maximal achievable blood flow through a stenot-
concerns that the use of coronary computed tomographic
ic artery to maximal flow in the hypothetical case that the
angiography (CCTA) may precipitate unnecessary invasive
artery is normal and is determined by the ratio of pressures
angiography and unneeded revascularization procedures
across the stenosis during maximal coronary hyperemia [12,
. Revascularization of nonischemic lesions provides no
13]. FFR is measured during cardiac catheterization using a
clinical benefit in terms of improvement of blood flow but
guide wire with a pressure-sensing transducer that is placed
nonetheless exposes the patient to the risks of the procedure.
across the stenotic lesion. After induction of maximal hyper-
Recent randomized trials have shown no survival benefit in
emia using a vasodilating agent such as intravenous or intra-
patients undergoing angiographically guided coronary revas-
arterial adenosine, the pressure gradient across the lesion is
cularization compared to medical treatment alone [26, 27]
recorded, and FFR is calculated as the mean distal coronary
and have highlighted the need for physiologic testing prior to
pressure divided by mean aortic pressure. FFR takes into
account the contribution of collaterals and provides a thresh-
A number of noninvasive imaging studies provide func-
old of cutoff values for discriminating lesions that do vs. do
tional assessment of CAD by identifying regional differences
not cause ischemia . Coronary stenoses with FFR <0.75
in coronary flow reserve or wall motion abnormalities. While
are almost always functionally significant whereas lesions
these serve as useful surrogates for ischemia, they do not
with FFR >0.80 are rarely associated with inducible ische-
directly visualize coronary stenoses or assess the hemody-
mia . Prospective, multicenter, randomized clinical trials
namic significance of individual coronary lesions. Further-
have shown that FFR-guided revascularization provides a
more, noninvasive stress testing misclassifies a significant
sustained clinical benefit with improved event-free survival
number of patients as low risk and has significant false-
and reduced health-care expenditures compared with the
positive and false-negative rates resulting in many patients
traditional strategy of angiographic stenosis guidance [6,
having no evidence of obstructive CAD when studied by
14, 15]. FFR is now considered to be the standard of care
ICA [28, 29]. Accordingly, some have advocated for hybrid
for guiding percutaneous coronary revascularization with
imaging with physiologic and anatomic evaluation of CAD
class IA European Society of Cardiology and class IIA
by stress testing and CT . However, this approach re-
American Heart Association practice guideline recommen-
quires two tests and is associated with higher costs and a
dations [16, 17]. Nonetheless, despite unequivocal evidence
greater radiation burden for the patient. A long-standing goal
supporting the use of FFR to guide clinical decision making,
of noninvasive imaging of CAD has been to provide physi-
adoption into daily clinical practice has been limited, and
cians with a single test that identifies high-grade stenosis and
FFR is currently used in less than 10 % of coronary revas-
determines the functional significance of identified lesions.
cularization procedures in the USA . This may be due in
This has been described as the elusive “holy grail” of non-
part to the invasive nature of the procedure, the need for
invasive CAD imaging . The addition of computational
pharmacologic vasodilation, and risks related to instrumentation
FFR analysis to the anatomic imaging capabilities of CT
J. of Cardiovasc. Trans. Res. (2013) 6:708-714
provides such a combined anatomic-physiologic assessment
blood vessels are properly sized and adapt to the amount of
of CAD from a single imaging test.
flow they carry. The third principle states that the coronary
microcirculation has a predictable vasodilatory response to
adenosine . When the myocardium lacks oxygen, ATP
Computational Analysis of Blood Flow Based on CT
breaks down with a resulting release of endogenous adeno-
sine. Exogenous administration of adenosine elicits an in-
While computational analysis of airflow has been a mainstay
crease in coronary blood flow with a maximum hyperemic
of aircraft and automotive design for more than 50 years,
response by producing complete relaxation of smooth mus-
computational fluid dynamics has only recently been applied
cle cells lining the resistance arterioles. This predictable
to the human circulatory system for evaluation of blood flow.
response allows simulation of maximum hyperemia in the
Initial applications involved the study of flow characteristics
computational model. Thus, FFR is computed by applying a
in the carotid bifurcation , followed by image-based
dynamic physiologic model of coronary flow to patient-
modeling of pulsatile blood flow in the abdominal aorta
specific coronary anatomy as revealed by the coronary CT
and aortic aneurysms . The key element for the realistic
scan. This coronary CT scan can be performed in the usual
modeling of human blood flow is precise 3D anatomic
manner, using standard acquisition protocols, with no need
imaging of the vasculature that can now be readily provided
for additional imaging or radiation exposure and no need for
by contrast-enhanced computed tomography. In addition,
numerical methods which incorporate physiologic boundary
conditions of the circulation are needed in order to construct
patient-specific computational blood flow . The intro-
Computation of FFR from Coronary CT
duction of 64-detector row CT scanners provided accurate
anatomic images of the moving heart that made it possible to
Computation of FFR from coronary CT involves three basic
build patient-specific 3D computational models of the coro-
elements: (1) constructing an accurate patient-specific ana-
nary vasculature. The calculation of coronary blood flow
tomic model of the epicardial coronary arteries, (2) specify-
required development of specific methods appropriate to
ing inflow and outflow boundary conditions reflecting
the unique physiologic boundary conditions of the coronary
patient-specific coronary physiology during maximal hyper-
circulation [35, 36]. This allowed the computation of coro-
emia, and (3) performing a numerical solution of the laws of
nary velocity and pressure under a variety of conditions
physics governing fluid dynamics. This combination of anat-
including rest, exercise, and physiologically induced coro-
omy, physiology, and computational fluid dynamics enables
nary hyperemia flow by modification of the boundary con-
the calculation of coronary artery blood flow and pressure
ditions. Thus, fractional flow reserve could be calculated as
under conditions of maximum hyperemia .
the ratio of distal coronary pressure divided by the proximal
Computation of coronary flow and pressure is based on
aortic pressure under simulated conditions of maximal hy-
the governing equations of fluid dynamics, which are
peremia, much the same as when measured FFR is deter-
founded in the relationship between conservation of mass
mined during invasive coronary angiography .
and momentum balance. These equations are known as the
“Navier Stokes equations” and have existed in their current
form for more than 150 years. The equations are solved for
Scientific Basis for Computation of FFR
coronary flow and pressure as a function of three spatial
coordinates and time. The physical properties of blood (fluid
The scientific basis for noninvasive quantification of FFR
density and fluid viscosity) are assumed, and blood is treated
from coronary CT has been described in detail by Taylor
as an incompressible Newtonian fluid with a constant vis-
et al. . It is based on three underlying principles for the
cosity in the coronary arteries. Since the governing equations
generation of physiologic models of coronary blood flow.
of blood flow are nonlinear partial differential equations
The first principle is that baseline coronary blood flow is
which can only be solved analytically under highly idealized
proportional to myocardial oxygen demand at rest. This
circumstances, solutions for realistic patient-specific models
enables calculation of total resting coronary blood flow
of the coronary tree require a numerical approximation for
relative to patient-specific myocardial mass that can be quan-
velocity and pressure at a finite, but very large, number of
tified on the CT scan. The second principle is that the
points . This requires the computation of millions of
resistance of the microcirculatory vascular bed at rest is
nonlinear equations simultaneously and repeating this pro-
inversely, but not linearly, proportional to the size of the
cess for thousands of time intervals in a single cardiac cycle.
feeding vessel, as has been demonstrated in prior morphom-
In addition, it is necessary to define the boundary conditions
etry, shear stress autoregulation, and compensatory remod-
that interface the modeled domain to the remainder of the
eling research [37-39]. In other words, healthy and diseased
circulation; this represents the biggest challenge in blood
J. of Cardiovasc. Trans. Res. (2013) 6:708-714
flow modeling. Realistic modeling of coronary flow requires
ischemia-producing stenoses from those lesions not producing
coupling of lumped parameter models of the heart, systemic
ischemia was significantly improved with an increase in the
circulation, and coronary circulation to a patient-specific
area under the curve (AUC) of the receiver operating charac-
model of the root of the aorta and epicardial coronary arteries
teristics curve (0.90) compared to CCTA (0.75) [difference
extracted from CCTA data . These lumped parameter
0.15, p<0.001] .
models combine peripheral resistance, blood vessel compli-
Subsequently, the Determination of Fractional Flow Re-
ance, and other factors into distinct elements dependent on
serve by Anatomic Computed Tomographic Angiography
the specific parameters of each circulatory bed. Importantly,
(DeFACTO) study—an international multicenter study in-
neither pressure nor flow rate is directly specified at the
volving 252 stable patients with suspected or known CAD
boundaries of the 3D model, but instead arises naturally from
from 17 centers in five countries—was performed. The di-
the interaction between the 3D model and the lumped pa-
agnostic accuracy of FFRCT plus CT for the diagnosis of
rameter models representing cardiac output, aortic pressure,
hemodynamically significant coronary stenosis was assessed
and microcirculatory resistance . As a final step, the
using measured FFR as the reference standard . Among
boundary condition of maximum coronary hyperemia is
(54 %) had evidence of coronary
modeled by simulating the effect that adenosine has on
ischemia with a measured FFR of ≤0.80. FFRCT demonstrat-
reducing the peripheral resistance of the downstream micro-
ed improved accuracy for the diagnosis of ischemia com-
circulatory coronary bed.
pared to CT alone—73 % (95 % CI 67-78 %) for FFRCT vs.
64 % (95 % CI 58-70 %) for CT—but did not satisfy the
prespecified primary endpoint of diagnostic accuracy of
Clinical Validation of Computed FFR
greater than 70 % of the lower-bound one-sided 95 % con-
fidence interval. When FFRCT was compared to CT for the
Clinical validation of computed FFR is based on a direct
ability to discriminate patients with and without ischemia,
comparison to measured FFR during invasive coronary an-
FFRCT demonstrated superior discrimination with the AUC
giography. The diagnostic accuracy of noninvasive FFRCT to
in the ROC analysis of 0.81 compared to 0.68 for CT alone
identify or exclude functionally significant coronary steno-
(difference 0.13, p<0.001). Similarly, FFRCT demonstrated
ses has been evaluated in two prospective, multicenter stud-
superior discrimination of ischemia on a per-vessel basis
ies using measured FFR as the reference standard. The first
(AUC for FFRCT 0.81 vs. 0.75 for CT, p<0.001) .
of these—the Diagnosis of Ischemia-Causing Stenosis
Obtained via Non-invasive Fractional Flow Reserve (DIS-
Two case examples from the DeFACTO study demonstrate
COVER-FLOW) study—evaluated the diagnostic perfor-
the benefit of FFRCT in differentiating functional significance
mance of FFRCT compared to CT stenosis severity using
in vessels with anatomically obstructive stenoses .
measured FFR as the reference standard . The study was
Case 1: CCTA demonstrates significant CAD with >50 %
conducted at four clinical sites in the USA, Europe, and Asia
lumen stenosis in the left anterior descending
and included 103 stable patients with known or suspected
(LAD) artery. This is confirmed by quantitative
CAD who underwent CCTA, ICA, measurement of FFR,
angiography with a stenosis of 57 %. The compu-
and computation of FFRCT. Lesion-specific ischemia was
tational model based on the CT data demonstrates
defined as measured FFR ≤0.8 in accord with prior invasive
a hemodynamically significant lesion with FFRCT
FFR trials . Obstructive coronary artery disease was de-
in the distal LAD of 0.62. The measured FFR
fined as stenosis ≥50 % on CCTA as measured by a CT core
during invasive angiography is 0.65.
laboratory. Diagnostic performance of FFRCT was superior
to CT, and the primary endpoint was met with a per-vessel
diagnostic accuracy for FFRCT of 84 % (95 % CI 78-90 %)
compared to 59 % (95 % CI 50-66 %) for CT alone. This
42 % improvement was primarily due to a 70 % reduction of
false positives. Among the 159 vessels studied, the sensitiv-
ity, specificity, positive predictive value, negative predictive
value, and accuracy of FFRCT were 88, 82, 74, 92, and 84 %,
respectively. While CT alone had a high sensitivity (91 %)
and negative predictive value (89 %), CCTA suffered from a
low specificity (40 %) and low positive predictive value
(47 %). FFRCT increased the specificity of identifying hemo-
dynamically significant stenoses to 82 % compared to 40 %
for CT alone. Further, the ability of FFRCT to discriminate
J. of Cardiovasc. Trans. Res. (2013) 6:708-714
CCTA demonstrates >50 % stenosis in the mid
calcification, and increased image noise. These issues can be
right coronary artery
(RCA). The angiogram
minimized by close adherence to CCTA image acquisition
demonstrates a significant lesion in the RCA
guidelines , in particular by use of beta blockers to reduce
which measured 62 % stenosis by quantitative
heart rate and heart rate variability as well as administration of
coronary angiography. Computed FFRCT is 0.87
sublingual nitrates to dilate the coronary arteries. In the clin-
indicating a nonfunctionally significant stenosis.
ical studies of FFRCT, CT image quality was evaluated by
This was confirmed by a measured FFR of
independent core laboratories, and all patients judged to have
0.86. Such nonfunctionally significant lesions
evaluable images were included for FFRCT analysis. In the
have a favorable outlook when treated medically
DeFACTO study, 11 % of patients were judged by the core
laboratory to have nonevaluable CT images and were excluded
from the study. Given the dependence of FFRCT on accurate
coronary segmentation for proper image-based modeling,
excellent image quality should remain a primary goal of
cardiac CT imaging.
In addition, diagnostic performance of FFRCT compared
to measured FFR may be affected by patient-specific differ-
ences in responsiveness of the microcirculation to vasodila-
tors and physiologic conditions which may affect assumed
parameters such as fluid density and viscosity. Viscosity is
assumed from hematocrit/hemoglobin concentration and,
when in the normal range, has minimal influence on FFRCT.
However, under conditions of severe anemia, reduced vis-
cosity may impact calculation of FFRCT. The magnitude of
such an impact is not yet known.
To date, evaluation of FFRCT has been limited to a
population of stable patients with known or suspected
coronary artery disease who were undergoing coronary
angiography. Patients with prior CABG or PCI with
suspected in-stent restenosis were excluded from the
studies as were patients with acute coronary syndrome
Intermediate-severity coronary stenoses often cause ische-
or within 30 days of myocardial infarction . Thus,
mia, but differentiating between hemodynamically signifi-
generalizability to broader populations of patients with
cant and nonfunctional intermediate lesions is challenging,
CAD is unknown. Finally, outcomes data are not yet
both for noninvasive imaging as well as for invasive angi-
available, and it is unknown whether revascularization
ography. Among 103 patients in the DISCOVER-FLOW
of the ischemic lesions identified by FFRCT will achieve
study, 60 patients (58 %) had intermediate stenosis of 40-
reduction in ischemia from revascularization.
69 % by quantitative coronary angiography. Computation of
FFRCT improved the accuracy of identifying functionally
significant lesions to 86 % compared to 56 % for CT alone.
This was primarily due to a threefold improvement in spec-
ificity (83 % compared to only 26 % for CT alone). There
was a marked improvement in the ability to discriminate
Noninvasive assessment of the functional significance of
ischemia-causing stenosis with an AUC in the receiver op-
coronary stenoses is now possible using computationally
erating characteristics curve of 0.95 for FFRCT (p<0.0001
derived fractional flow reserve from anatomic coronary CT
compared to CT alone) .
data. This promising new technology provides a combined
anatomic-functional assessment of coronary artery disease
using a single noninvasive test with the goal of helping
physicians appropriately select patients for medical therapy
or invasive angiography to improve clinical outcomes while
reducing health-care costs.
A number of potential limitations exist that may influence the
diagnostic performance of FFRCT, most notably impaired
coronary CT image quality. Significant CT imaging artifacts
Conflict of Interest CKZ and CAT are employees of HeartFlow, Inc.;
include misalignment, motion, beam hardening from coronary
JKM has a consulting relationship with HeartFlow, Inc.
J. of Cardiovasc. Trans. Res. (2013) 6:708-714
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