International Journal of Cardiology 73 (2000) 237–242
www.elsevier.com / locate / ijcard
True shape and area of proximal isovelocity surface area (PISA) when
flow convergence is hemispherical in valvular regurgitation
a,b ,
b
a,b
Darrel P. Francis MB, MRCP *, Keith Willson MSc, MIPEM , L. Ceri Davies BSc, MRCP ,
Viorel G. Florea PhD, DSc a , Andrew J.S. Coats DM, FRCP b , Derek G. Gibson FRCP, FESC b
a
National Heart and Lung Institute, Imperial College of Science, Technology and Medicine, London, UK
b
Royal Brompton Hospital, London, UK
Received 19 October 1999; received in revised form 20 December 1999; accepted 28 January 2000
Abstract
The proximal isovelocity surface area (PISA) method for quantifying valvular regurgitation uses an echocardiographic image with
superimposed colour Doppler mapping to visualise the contours of velocity in the blood travelling towards the regurgitant orifice. The flux
of blood through the regurgitant orifice is obtained as the product of the area of one of these (presumed hemispherical) contours and the
speed of the blood passing through it. However, colour Doppler mapping measures the velocity component towards the echo probe
(v cos u ) rather than speed (v), so that the contours of equal Doppler velocity (isodoppler velocity contours) differ from isospeed contours.
We derive the shape of the isodoppler contour surface obtainable by colour Doppler mapping, and show that its area is much less than that
of the hemispherical isospeed contour. When regurgitant flux is derived from an appropriate single measure of contour dimension, an
appropriate result may be obtained. However, if the true echocardiographic surface area is measured directly, the regurgitant flux will be
substantially underestimated. Indeed, the conditions necessary for isodoppler velocity contours to be hemispherical are extraordinary. We
should not therefore make deductions from the apparent shape for the convergence zone without considering the principles by which the
image is generated. The discrepancy will assume practical significance when increased resolution of colour Doppler technology makes
measurement of apparent surface area feasible. Assuming the flow contours are indeed hemispherical, a ‘correction’ factor of 1.45 would
be required.  2000 Published by Elsevier Science Ireland Ltd. All rights reserved.
Keywords: Hemispherical; Proximal isovelocity surface area (PISA); Flow convergence region (FCR); Valvular regurgitation
1. Introduction
The proximal isovelocity surface area (PISA)
method [1,2] is a non-invasive technique for quantifying the severity of valvular regurgitation by
echocardiography. A two- or three-dimensional
image with superimposed colour Doppler is used,
*Corresponding author. Heart Function Unit, Royal Brompton Hospital, National Heart & Lung Institute, Sydney Street, London SW3 6NP,
UK. Tel.: 144-171-351-8700; fax: 144-171-351-8733.
E-mail address: [email protected] (D.P. Francis)
ostensibly to visualise nested hemispheres of blood
travelling at ever-greater speeds towards the orifice.
The area of one such hemisphere (in cm 2 ) multiplied
by the speed of the blood passing through it (in cm / s)
equals the total flux of blood through the regurgitant
orifice (in cm 3 / s).
However, Doppler echocardiography measures not
speed but the velocity component towards the echo
probe, which is dependent on the cosine of the angle
between the probe and the direction of flow. This has
two important consequences. Firstly, if blood flow
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D.P. Francis et al. / International Journal of Cardiology 73 (2000) 237 – 242
truly forms hemispherical shells of increasing speed,
their shape and area may be severely misrepresented
by Doppler echocardiography, leading to seriously
misleading calculations of regurgitant flow. Secondly,
the scarcity of hemispherical shells in routine clinical
practice (in contrast to their ubiquitous appearance in
exemplary cases in the literature) may thus be
explained; hemispherical contours on Doppler echo
may represent a different phenomenon that would
require a separate explanation.
2. Methods
2.1. Model of blood flow at regurgitant orifice
The PISA concept observes that blood must accelerate as it approaches the regurgitant orifice. Ideally,
there is radial symmetry and the speed is dependent
only on the distance from the valve orifice, so for any
given speed v there will be a hemisphere of blood
travelling at that speed (Fig. 1a). The surface area of
the hemisphere with radius r is 2p r 2 . If the speed of
blood travelling towards the orifice is v, the flux of
blood through the hemisphere is Q~ 5 2p vr 2 , so that
v 5 Q~ /(2p r 2 )
(1)
2.2. Velocity obtained by Doppler mapping
The Doppler map indicates not the speed v (Fig.
1a) but vy , the velocity component directed towards
the probe (Fig. 1b). Using u to represent the angle
away from the axis of regurgitation, the magnitude of
this component is
vy
5 v 3 cos u
5 Q~ cos u /(2p r 2 )
(2)
The contour for velocity vy is therefore defined by
]]]]]
r iso-vy 5œQ~ cos u /(2p vy ).
This asymmetrically prolate spheroid shape (or ‘urchinoid’, Fig. 1b) is far closer to being a sphere than
a hemisphere.
3. Results
3.1. Consequences of hemispherical isospeed
contours
The conventional assumption with the PISA tech-
Fig. 1. Assumption of hemispherical shells of increasing speed. Speed, represented by length of arrows in (a) and greyscale in (b), increases towards the
orifice. The velocity component towards the probe also increases towards the orifice, but is additionally dependent on the cosine of the angle between the
ultrasound beam and the direction of blood flow, and so decreases as this angle moves away from zero, as shown by the arrows in (c) and the greyscale in
(d). Note that while the isospeed contours of (b) are hemispherical, the isodoppler velocity contours of (d) are distinctly non-hemispherical.
D.P. Francis et al. / International Journal of Cardiology 73 (2000) 237 – 242
nique is that the isospeed contours are hemispherical
(Fig. 1a). The areas of the corresponding isodoppler
velocity contours (Fig. 1b) can be determined by
integration (see Fig. 2).
p/2
A iso-vy 5
E
]]]]2
dr
2p (r sin u ) r 2 1 ] ? du
du
œ S D
0
]]]]
Q~
]] cos u sin u
2p vy
p/2
5
E 2pSœ
0
D
]]]]]]]]]
Q~
1
3 ]] cos u 1 ] sin u tan u ? du
2p vy
4
]
Q~ 1 Œ3
]
5 ] ] 1 ] ln(2 1Œ3)
vy 2
12
œ
S
S
D
D
This area, numerically |0.69Q~ /vy , is more than 30%
below the true isospeed shell area, and thus at least a
30% underestimate of blood flow will be obtained.
It may be tempting from the diagrammatic representation to speculate that this surface is a sphere of
diameter r. However, isodoppler velocity surface area
is greater than that of such a sphere by about 38%.
The isodoppler velocity surface may therefore be
considered to be midway between a hemisphere and a
sphere, for not only does it give the visual impression
of being spherical near its perivalvular pole, but near
239
its opposite pole it approximates extremely closely to
the hemisphere.
The practical implication is that, if the area of the
surface is inferred using the formula 2p r 2 from a
single echocardiographic measurement of r taken
parallel to the direction of flow (where cos u 51), as
is currently standard practice with 2D echocardiography [3], then the calculated flux will be correct.
However, should the resolution of 3D echocardiography ever become capable of discerning the part of
the surface immediately adjacent to the regurgitant
orifice itself, the calculated regurgitant flux would be
underestimated by more than 30%, necessitating a
‘correction’ factor of 1.45. Of course, this correction
factor would only be appropriate in the specific
condition of true hemispherical flow contours.
In vivo, the instantaneous flow rate and velocity
contours will vary during the cardiac cycle. Nevertheless, as long as the isospeed surface is hemispherical,
the isodoppler velocity surface will underestimate its
area by the same scale factor throughout the cardiac
cycle.
3.2. Conditions necessary for observation of
hemispherical contours on Doppler
echocardiography
The literature reports Doppler contours that are not
Fig. 2. Calculation of isodoppler velocity surface area.
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D.P. Francis et al. / International Journal of Cardiology 73 (2000) 237 – 242
Fig. 3. Conditions necessary for the observation of hemispherical shells on Doppler echocardiography (i.e., isodoppler velocity hemispheres) shown in
panel (d). For angles away from the axis of the beam, blood speed must be increasingly fast (a,b) to maintain the size of the component towards the
Doppler probe (c,d).
the closed loops that would be expected from the
analysis above, but hemispheres [1,4], as illustrated
in Fig. 3b. For this to occur with blood travelling
radially towards the orifice, its speed at any given
distance from the orifice must be progressively
greater at angles increasingly far from the axis of
regurgitation (Fig. 3a) with v~1 / cos u. At the edges
of the hemisphere, the speeds required become
infinitely large.
have described may become a serious obstacle to
quantification of regurgitant flow unless this error
factor is taken into account.
How can the implausibility of such speeds be
reconciled with the repeated appearance of hemispherical contours in the literature? We suggest three
4. Discussion
Assessment of valvular regurgitation has principally been semi-quantitative or indirect because of the
difficulties in developing an accurate quantitative
method. The PISA method is being developed to
improve quantification of regurgitant flow. This
theoretical study shows that the isodoppler velocity
surface area, is substantially different from the area
of the postulated isospeed hemisphere, because of the
effect of cos u, as illustrated in Fig. 4. As 3D
echocardiographic techniques develop [5–7], formal
measurement of isodoppler velocity surface areas will
become more widely available. The discrepancy we
Fig. 4. Graphical cut-section comparing isospeed hemisphere (outer
structure) and its corresponding isodoppler velocity ‘urchinoid’ surface
(inner structure).
D.P. Francis et al. / International Journal of Cardiology 73 (2000) 237 – 242
possibilities. The first is that the finite size of real
regurgitant orifices (in contrast to the pinhole assumed in the hemispherical model) leads to some
transverse spread of the contours. However, this
effect is only prominent at distances from the valve
orifice that are smaller than the orifice width; PISA
hemisphere measurements are typically considerably
larger, and so ought not to be greatly affected. A
second factor is the constrained space in the proximal
chamber which, in the case of aortic regurgitation,
leads to enhanced speeds near the walls of the aortic
root and consequently wider isodoppler velocity
shells. Ring movement parallel to the Doppler beam
adds an equal increment to velocities at all points,
and therefore does not change the shape of the
contours.
A final possible explanation for the appearance of
hemispherical Doppler contours in the literature is the
preference, in the minds of authors, reviewers and
readers alike, for pleasing imagery. Thus the majority
of cases, whose Doppler contours are clearly nonhemispherical, may be rejected as ‘unrepresentative’,
in favour of isolated examples of hemispherical
contours, which are then presented as ‘typical’. Once
such patterns become widely accepted and soughtafter, subsequent authors may hesitate before showing pictures more reflective of real clinical practice.
4.1. Study limitations
This study concentrates on the simple case where
the axis of regurgitation is parallel to the ultrasound
beam and the region surrounding the orifice is flat
rather than funnel-shaped in either direction. If the
flow convergence region subtends more than a hemisphere, then the area of the urchinoid will not
increase correspondingly, because blood flowing
towards the orifice from angles greater than 908 from
the axis of the beam will have a negative velocity. If
the flow convergence region subtends less than a
hemisphere (i.e., the blood funnels in towards the
orifice), then the area of the hemisphere will fall more
rapidly than the area of the urchinoid, so that the
correspondence between them will improve.
Second, this study considers the case of a probe
that is positioned far from the regurgitant orifice
(compared to the size of the orifice and the radius of
the contour). If the probe position is, in contrast,
241
close to the valve, then the appearance will be more
hemispherical. However, it is notable that cos u is
close to 1.0 for a wide range of u ; thus the probe
need not be very far from the orifice for the isospeed
contour to have the appearance shown in Fig. 4.
Third, the theoretical assumption that flow contours are hemispherical has been demonstrated by
some MRI studies to be valid only away from the
immediate vicinity of the orifice, where they are
flatter. However, the PISA technique is applied at
sufficient distance from the orifice for the shape to be
hemispherical.
5. Conclusions
The primary assumption of the PISA technique is
that blood approaching a regurgitant orifice accelerates in a series of nested hemispherical shells of equal
speed, and that the surface area of one such shell
(determined by colour Doppler echocardiography)
multiplied by the speed of the blood passing through
it gives the flux of blood through the orifice. We
demonstrate that the surface area of such a shell (and
thus regurgitant flux) can be underestimated by over
30% by echocardiography. Secondly, we show that
the appearance of true hemispherical shells on a 2D
colour Doppler echocardiogram, generally soughtafter as an ideal for the PISA technique, would
require a particular flow pattern that may (at best)
occur only rarely. Thirdly, the best measurement to
make may be the maximum distance of the isospeed
contour from the orifice, since cos u cannot ever be
greater than 1. This assumes that the flow towards the
orifice is indeed hemispherical in contour. If this is
the case, then a single measurement suffices. If,
however, these contours are non-hemispherical, this
analysis suggests that attempting to compensate for
this by measurement of the contour will tend to lead
to further errors which may be unquantifiable, at least
in the clinical setting.
Acknowledgements
Dr Francis is supported by the British Heart
Foundation (FS 98005) and the Royal Brompton
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D.P. Francis et al. / International Journal of Cardiology 73 (2000) 237 – 242
Clinical Research Committee (CRC 9716). Dr Davies
is supported by the Robert Luff Fellowship.
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