CIRCULATION
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assistance; and to Ruth
of the manuscript.
M. Harris, who assisted in the preparation
References
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1. Geffers H, Adam WE, Bitter F, Sigel H, Kampmann H: Data
processing and functional imaging in radionuclide ventriculography. Proceedings of the Fifth International Conference on
Review of Information Processing in Medical Imaging, Nashville, 1977, Oak Ridge National Laboratory, ORNL/
BCTIC/2, p 322
2. Verba JW, Bornstein I, Alazraki NP, Taylor A, Bhargava V,
Shabetai R, Le Winter M: Computer program for behavior of
all four cardiac chambers. (abstr) J Nucl Med.20: 655, 1979
3. Byrom E, Pavel DG: Algorithm for quantification of regional
wall motion abnormalities, using the phase image of the ECGsynchronized cardiac study. (abstr) J Nucl Med 21: P47, 1980
4. Vos PH, Vossepoel AM, Beekhuis H, Pauwels EKJ: Characterization of the ventricular function by temporal Fourier transform of gated blood pool studies. Nucl Med Comm 1: 11, 1980
5. De Graff. CN, Van Rijik PP: Improved cardiac phase/amplitude imaging. Nucl Med Comm 1: 19, 1980
6. Links JM, Douglass=KH, Wagner HN: Patterns of ventricular
emptying by Fourier analysis of gated blood pool studies. J
Nucl Med 21: 978, 1980
7. Von Behren PL, Turner DA, Groch MW: Least-square fitting
of sinusoidal functions to pixel time-activity curves in nuclear
medicine cardiac blood pool studies. (abstr) J Nucl Med 21:
P46, 1980
8. Green MV, Ostrow HG, Douglas MA, Myers RW, Scott RN,
Bailey JJ, Johnston GS: High temporal resolution ECG-gated
Should
VOL 65, No 7, JUNE 1982
scintigraphic angiocardiography. J Nucl Med 16: 95, 1975
9. Pavel DG, Zimmer AM, Patterson VN: In vivo labeling of red
blood cells with "mTc: a new approach to blood pool visualization. J Nucl Med 18: 305, 1977
10. Parker AJ, Secker-Walker R, Hill R, Siegel BA, Potchen JE:
A new technique for the calculation of left ventricular ejection
fraction. J Nucl Med 13: 649, 1972
11. Josephson ME, Horowitz LN, Farshidi A, Spear JF, Kastor
JA, Moore EN: Recurrent sustained ventricular tachycardia.
Endocardial mapping. Circulation 57: 440, 1978
12. Rosenbush SW, Ruggie NT, Turner DA, Von Behren PL,
Denes P, Messer JV, Hauser RG, Fordham EW, Groch MW:
Radionuclide cineangiographic analysis of ventricular wall motion in patients with abnormal excitation and conduction.
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Phase analysis of radionuclide cardiac gated studies in patients
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Fixed External Reference System Be Used
to Analyze Left Ventricular Wall Motion?
a
PAUL D. CLAYTON, PH.D., GARY M. JEPPSON, M.S.,
AND
STEVEN C. KLAUSNER, M.D.
SUMMARY To investigate whether a fixed external reference system should be used to most accurately
describe regional left ventricular wall motion, we used vectors to analyze a simple model of ventricular contraction. If measured in a fixed external reference system, motion of implanted radiopaque midwall markers may
contain translational as well as contractile components. Therefore, comparisons of different reference systems
that use marker motion measured in a fixed reference system as a standard will be biased unless proper corrections are included. We conclude that evidence to date does not indicate that the use of a fixed reference system
is superior to other methods for analyzing regional ventricular wall motion.
THE USE of contrast, ventriculography to quantify
left ventricular segmental wall motion has resulted in
the development of methods to measure regional
endocardial movement. As the methods have proliferated, the accuracy of these alternative approaches in
separating abnormal, from normal wall motion has
been compared.1 These comparisons are difficult to
evaluate for the same reasons that have led to the
From the Departments of Medical Biophysics and Computing
and Medicine, LDS Hospital and the University of Utah, Salt Lake
City, Utah.
Supported in part by grant HL-24137, NHLBI, and RCDA
1K04LM00044-01, the National Library of Medicine.
Address for correspondence: Paul D. Clayton, LDS Hospital, 325
8th Avenue, Salt Lake City, Utah 84143.
Received June 8, 1981; revision accepted September 23, 1981.
Circulation 65, No. 7, 1982.
development of multiple methods of analysis: (1) By
examining a two-dimensional silhouette of the threedimensional ventricle, one cannot determine with certainty which segments exhibit truly abnormal motion
and to what extent the motion is abnormal. (2) There
is a choice between external and internal reference
systems. (3) The ventricle has multiple landmarks that
may be used to superimpose a reference grid system.
(4) There are choices between measurements (segmental area, hemiaxial lengths, and radial lengths),
the number of radii, chords or regions to be measured,
and the frequency of the measurement (end-diastole
and end-systole or frame-by-frame).
Ingels and co-workers" reported that left ventricular midwall dynamics were measured most accurately in the 300 right anterior oblique plane by a
fixed external reference system using polar coor-
1519
REFERENCE SYSTEM FOR LV WALL MOTION/Clayton et al.
dinates. Their conclusions were based on a study in
which five methods for describing wall motion were
evaluated for measurement accuracy. To assess differences between fixed and internal reference systems,
they used the motion of surgically implanted midwall
radiopaque markers as a standard. They compared
the magnitude of "error" between measurements of
marker motion obtained in a fixed external reference
system and measurements of marker motion defined
by the alternative systems. However, measurements of
marker movement using internal reference systems
were not corrected for translation of that reference
system within the fixed system. We feel that this
procedure added an extra component to the calculated
error for all internal systems and biased the results of
their study.
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Methods and Results
To facilitate understanding of the issues involved,
we will use an example to show that marker motion
measured in a fixed external coordinate system may
not agree with marker motion due to contraction if
there is movement of the entire ventricle. Then, we
will show how the error defined by Ingels et al. includes (rather than excludes) any motion of the
reference system that is being evaluated. We will use
vectors to illustrate the concept that marker motion
measured in a fixed external coordinate system consists of contractile and translational components.
Figure 1 is a simplified model of ventricular contraction, with four markers at specific locations
around two circles. In this model, there is contraction
(r2 = O.90r,) as well as translation (the center of the
circle moves from P(1) to P(2)). Using a fixed external
reference system, the motion of the four markers is
represented by the vectors a, b, c and d, and the motion of the center of the circle is denoted by the vector
p If there is no translation of the circle, then p = 0,
and the points P(1) and P(2) coincide. If there is
translation of the circle, the magnitudes of the vectors
representing marker motion in the fixed external
reference system are not equal (e.g., i
"I)
However, since both contours are circles, actual contractile motion for each marker must be equal.
Figure 2 illustrates an approach which may be used
to reconcile this discrepancy. The vector a, which
represents the motion of marker A in the fixed external coordinate system, can be represented with respect
to two alternative reference systems: the origin of the
fixed external reference system or a reference point
(such as the center of the circle) that is defined internally using ventricular landmarks that may move with
respect to the fixed coordinate system. Using the fixed
external reference system, the marker motion may be
expressed as
a = A2 - A1
(1)
where the vectors A2 and A1 are drawn from the origin
/Center
II
of larger circle or reference
point at "End Diastole"
End Diastole
--- Center of smaller circle or
reference point at "End
Systole"
ORIGIN
FIGURE 1. A simple model of ventricular contraction in which there is also translation of the entire ventricle with respect to the laboratory. The radius of the smaller circle is 10% less than that of the larger circle.
The center of the circle moves from P(1) ("end-diastole") to P(2) ("end-systole") in thefixed external coordinate system. The motion offour markers in the fixed system is represented by vectors d , c2and 3'Although the contractile motion for each marker should be equal, the magnitudes of the four vectors are
different when measured in the fixed reference system. These differences are attributable to the translation
and can be resolved by subtracting the vector p from each marker vector.
CI RCULATION
1520
VOL 65, No 7, JUNE 1982
FIGURE 2. The vector approach for
measuring marker motion using different
reference systems. When measured using the
center of the circle as the origin of an internal reference system, the measured marker
motion is t2 - L,. In the external system the
marker motion is equal to the vector
difference A4 - AT1 and is represented by the
vector a. These two measurements give unequal results unless the vector 'is subtracted
from
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to the marker position at end-systole and end-diastole.
The location of the marker in the fixed reference
system can also be specified by drawing a vector from
its o'rigin to the internal reference point, and then from
the internal reference point to the marker:
A2 =P2 + L2
(2a)
and
+
A1 = P1 + L1.
(2b)
The magnitude of the vector L1 is the distance from
the internal reference point P(1) to the position of
marker A at end-diastole and the magnitude of the
vector L2 is the distance from the internal reference
point at end-systole to the marker position at endsystole. When an internal reference system is used instead of a fixed external reference system, the difference between t2 and Y1 is the measured marker motion.
The equation for the motion of the internal
reference point is p = P2 - P1. Combining this equation with equations 2a and 2b, equation 1 may be
rewritten as:
a =
L2
-
L1
+ p
(3)
which also can be written
+
_+
-0
(4)
p = a (L2-Lj).
In the work of Ingels and co-workers," "error (E)
was defined as the absolute value of the difference
between standard marker motion (marker motion
measured in a fixed external '[laboratory] reference
system) and marker motion measured by each
method." Using the nomenclature applied to figure 2,
the absolute magnitude of vector a (designated
I)
is the standard marker motion, and the difference in
length between vectors from an internal reference
point to the marker is measured marker motion
- L1I . Their definition of the magnitude
_+
-
t2i
a.
of error due to measurements for a single marker is
thus written
E = la - IL2 - ILI 1 I .
(5)
By comparing the scalar equation 5 with the vector
equation 4, one can see that if there is motion of the
internal reference system with reference to the fixed
external reference system (p 7 0), there will
automatically be a contribution to the error term (E)
that was defined by Ingels et al. This contribution will
be equal to the magnitude of p and will be added to
other components which originate because' scalar
rather than vector quantities are used. Therefore,
measurements of marker motion made when using an
internal reference system will contain an added component of "error" when they are compared to
measurements made with a fixed external reference
system; the magnitude of this contribution to the
''error" term will be equal to the movement of the
origin of the internal system measured in the external
system. Ingels et al. compared angiographic measurements to those of the markers made with the external
system; thus, it is not surprising that the angiographic
measurements made with the external system'had the
smallest total error and those made with internal
reference systems had larger total errors.
Discussion
Using a simple spherical model of contraction, we
have attempted to show that marker motion measured
in a fixed external reference system does not correspond to actual contractile motion if there is
translation of the entire ventricle in the fixed external
coordinate system. Using vector notation, we have
also illustrated that any motion of an internal
reference system was directly added to the error term
when Ingels et al. compared different reference
systems using Imeasurements with a fixed external
REFERENCE SYSTEM FOR LV WALL MOTION/Clayton et al.
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system as their standard. Because one of the primary
purposes of ventriculography is to examine contraction and relaxation of the ventricle, we think it is appropriate to judge alternative methods by their ability
to describe the contractile component of motion
rather than total motion. Therefore, translational motion of the ventricle should be compensated for. We
conclude that Ingels et al. have not shown that fixed
external reference systems are superior to internal
moving reference systems.
We have used a simple circular model of the ventricle to illustrate the concepts discussed in this paper.
Such a model, although not suitable for actually
describing segmental wall motion, was used because it
provides an easy means of identifying a reference
point. However, all of the models for internal reference systems used to describe segmental ventricular
wall motion do define (implicitly or explicitly) a
reference point. This reference point generally moves
to some extent, as the ventricular landmarks move due
to translation, rotation and contraction or relaxation.
In previous studies that compared alternative
reference systems,1-6 the goal was to determine which
scheme (if any) for defining the reference point
provides the most accurate measurement of contractile motion.
Aside from some additional issues (rotation in and
out of the silhouette plane) originally discussed by
Ingels et al.,6 we feel that the implanted marker approach provides some clearcut advantages for a comparison study. Equations 3 and 4 are exact vector
equations that introduce no measurement errors,
because translation of the ventricle is taken into account. A substantial proportion of measurement error
apparently occurs when scalar quantities representing
the magnitudes of vectors are added or subtracted
without regard to the direction of the vectors. If vector
equations were used, there would be no preferred point
for the origin of a fixed external reference system. We
speculate that Ingels' choice of 69% of the distance
along the long axis of the end-systolic frame as the optimal origin for a fixed reference system7 resulted
because this location happened to minimize the
differences between the scalar and vector descriptions
of motion. Because the definition of error used to find
this optimum reference point was the same as was
used in the comparison paper of Ingels et al.,6 we
believe that the original results regarding optimal
reference points7 should be reevaluated.
We believe that the scalar quantity IL2
as the measured motion in any reference
L,
system is appropriate because, by definition, one must
always compare measurements for a specific chord,
radius or hemiaxis. Because of this constraint, the vectors L2 and i, should be in the same direction, and
scalar subtraction would be justified. Ingels et al.
1521
noted that when the vectors are constrained to be in
the same direction, some error is encountered because
the vectors will not always exactly follow the markers.
Given that the use of scalars may be appropriate to
define the measured marker motion (with respect to a
given reference system), we will discuss what Ingels et
al.f characterized as standard marker motion. The
motion of the markers as measured in the fixed external system is a combination of contractile and translational motion. To separate translational from contractile motion, standard marker motion should be
redefined as the vector difference a - p. If this convention were adopted, the resulting formula for error
would beE= Va-p - a112| - i1|
.If
were subtracted from each of the four vectors (T, b, c
and d) in our model, the result would be four vectors
of equal magnitude equivalent to the amount of radial
contraction. A comparison of reference systems using
this correction would be based primarily on the contractile component of standard marker motion.
Another problem of using measured marker motion
as a standard is caused by rotation of the ventricle in
the plane of the angiogram. If the smaller circle in
figure 1 were rotated clockwise through a large angle,
the true contractile motion of the markers would not
be represented by the magnitude of the vectors alone.
Rotation out of the plane of the silhouette presents
similar problems. Even though both types of rotations
may cause error, these errors were discussed by Ingels
et al.,6 and it is not evident that they could
systematically bias a comparison study to the extent
caused by the problems discussed in this paper.
In summary, conclusive evidence is not available
that indicates that any particular reference system is
superior to others.
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EL: A new method for assessment of left ventricular segmental
wall motion. Comput Cardiol IEEE, 57, 1978
Should a fixed external reference system be used to analyze left ventricular wall motion?
P D Clayton, G M Jeppson and S C Klausner
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Circulation. 1982;65:1518-1521
doi: 10.1161/01.CIR.65.7.1518
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