114
JACC Vol 7, No I
January 1986 114-5
Editorial Comment
Efforts Toward Quantitation of
Coronary Artery Functional
Capacity*
EDMUND M. HERROLD, MD, PHD,
JEFFREY S. BORER, MD, FACC
New York, New York
The concept that a measure of coronary flow reserve should
provide an accurate and clinically useful index of the ana•
tomic severity of a coronary artery stenosis is both theo•
retically attractive and of potentially great clinical impor•
tance. If validated, this concept could lead to important
refinement in the manner in which angiographic data are
employed in decision making in patients with coronary ar•
tery disease, with additional important implications with
regard to the potential role of noninvasive modalities.
Derivation of coronary flow reserve. In the article by
Kirkeeide et al. (l) published in this issue of the Journal,
the authors have endeavored to provide an experimental
basis for the use of coronary flow reserve as an index of
lesion severity. Their work is of intrinsic interest and merit.
In approaching the problem, the authors have coupled equa•
tions characterizing fluid flow through a stenotic region,
first derived by Young et al. (2-4) and simplified by Gould
and coworkers (5-7), with the familiar fluid flow equation
originally derived by Poiseuille (8). In fact, these equations
are intrinsically related, in that all are derived by applying
simplifying assumptions to the Navier-Stokes equations, wh.ich
describe the manner in which Newton's law of conservation
of momentum applies to fluid flow. To analogize from elec•
trical circuitry, Kirkeeide et al. have applied the Young•
Gould and Poiseuille equations' 'in series," in that the equa•
tions of Young-Gould were used to predict the mean flow
through a discrete proximal stenosis, whereas the Poiseuille
equation (simplified to Ohm's law of electricity) was used
to predict the distal coronary (microvascular) pressure-flow
relation. By requiring as boundary conditions in their ex-
*Editorials published in Journal of the AmericanCollege ofCardio!ogy
reflect the views of the authors and do not necessanly represent the views
of JACC or the American College of Cardiology.
From the CardIOlogy Division, The New York HospItal-Cornell Med•
Ical Center, New York, New York.
Address for reprints: Jeffrey S. Borer, MD, Division of Cardiology,
The New York Hospital-Cornell Medical Center, 525 East 68th Street,
New York, New York 10021.
© 1986 by the Amencan College of Cardiology
perimental system that poststenosis pressure and premicro•
vascular perfusion pressure are equal (a situation that obtains
only when a single stenosis is present), Kirkeeide et al.
could derive a series of two equations with three unknowns:
I) mean coronary flow at rest, 2) mean coronary flow post•
dilation in the stenosed coronary artery, and 3) poststenosis
perfusion pressure. By assuming that the ratio of flow rate
after maximal dilation to flow rate at rest is relatively con•
stant in normal arteries, and that flow rates at rest in normal
and stenotic vessels are similar, Kirkeeide et al. were able
to reduce this series to a solvable series of two equations
with two unknowns. While not explicitly stated, this series
can be solved to produce a single quadratic equation with
one unknown (coronary flow reserve) as a function of ste•
nosis length and cross-sectional area:
o=
where X = coronary flow reserve (CFR); all other variables
are defined as by Kirkeeide et al (l).
Correlation with clinical coronary stenotic lesions.
The validity of these simplifying assumptions within the
context of the experiments of Kirkeeide et al. has been
verified by the results of the experiments. ~owever, ex•
trapolation of these results to conditions not bound by the
experimental constraints must be performed with caution.
The equations solved simultaneously for a single discrete
lesion resulted in good correlation between the predicted
and actual flow reserve. However, it is unclear the extent
to which this correlation would persist if additional stenoses
were present, a common clinical situation. Thus, the pre•
dictability of the hemodynamic consequences of multiple
lesions from quantitative radiographic measurements of
stenoses remains to be determined. Moreover, it is to be
expected that the relative severity of multiple lesions also
would markedly affect the mathematical determination of
the hemodynamic effects of the lesions. For example, a
I severe proximal lesion in series with a mild distal lesion
I would have different hemodynamic consequences than would
I a mild proximal lesion in series with a severe distal lesion;
thus, the two situations might require solutions not involving
Jthe simplifying assumptions employed by Kirkeeide.
Other potential problems also exist in the formulation of
Kirkeeide et al. Previously, in a similar experimental prep•
aration, Gould et al. (6) reported that the angle of post•
stenosis wall expansion did not change after coronary artery
dilation. However, other investigators (9) found that the
angle of expansion strongly influences the pressure gradient
0735-1097/86/$3.50
HERROLD AND BORER
EDITORIAL COMMENT
JACC Vol 7, No I
January 1986,114-5
across stenoses in rigid tube models. The resolution of this
apparent paradox may be that the compliant vessel walls in
the experiments of Gould et al. had reached dynamic equi•
librium between the energy distribution of the blood and
the arterial wall such that the length of the expansion region,
and not the angle itself, changed as the arteries dilated
proximally and distally; in contrast, in the case of rigid
tubes, possibly more analogous to arteriosclerotic vessel
walls, the expansion angle would not necessarily conform
to the fluid flow and the resultant separation of flow from
the wall could strongly influence the flow rate (2). Thus,
the influence of expansion angle on flow rate and pressure
gradient will require further investigation for clarification.
Although Gould et al. (7) did not find the relative asym•
metry of stenoses to influence the pressure gradient in an
experimental preparation similar to that in the present study
(1), Young and coworkers (2-4) found that asymmetry clearly
and directly influenced pressure gradient in rigid vessel
models. The importance of stenosis asymmetry was further
suggested by the results of flow studies performed in ex•
cised, arteriosclerotic human coronary arteries where ste•
nosis severity varied with flow when stenoses were asym•
metric whereas severity of symmetric stenoses remained
constant throughout the flow range used (10). Presumably,
the relative lack of elasticity of the vessel walls associated
with symmetric stenoses may cause resulting flow to differ
from that observed with asymmetric stenoses of the same
severity (10).
Clinical application. As Kirkeeide et al. (I) state, their
efforts were directed toward elucidating the influence of a
specific discrete lesion in a fluid system. It would be er•
roneous to extrapolate from the results of their equations to
the global perfusion in an effort to evaluate the importance
of a coronary artery lesion in a specific patient. However,
when methods for measuring the actual flow rate in a coro•
nary artery become clinically applicable (11-17), the ana•
lytical methods of Kirkeeide et al. potentially may be applied
to discrete lesions to better understand the relative influence
of these lesions on arterial flow, thus leading to a more
accurate prediction of the effect of therapeutic modalities.
115
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