58
CIRCULATION RESEARCH
lasting one and two cardiac cycles. Circ Res 35: 702-712, 1974
23. Olsson RA, Gregg DE: Myocardial reactive hyperemia in the unanesthetized dog. Am J Physiol 208: 224-230, 1965
24. Khouri EM, Gregg DE, Lowensohn HS: Flow in the major branches
of the left coronary artery during experimental coronary insufficiency
in the unanesthetized dog. Circ Res 23: 99-109, 1968
25. Ross G, Mulder DG: Effects of right and left cardiosympathetic nerve
stimulation on blood flow in the major coronary' arteries of the anesthetized dog. Cardiovasc Res 3: 22-29, 1969
26. Brown AM, Malliani A: Spinal sympathetic reflexes initiated by coronary receptors. J Physiol (Lond) 212: 685-705, 1971
27. Malliani A, Recordati G, Schwartz PJ: Nervous activity of afferent
cardiac sympathetic fibres with atrial and ventricular endings. J Physiol
(Lond) 229: 457-469, 1973
28. Malliani A, Schwartz PJ, Zanchetti A: A sympathetic reflex elicited
by experimental coronary occlusion. Am J Physiol 217: 703-708,
1969
29. Schwartz PJ, Foreman RD, Stone HL, Brown AM: Effect of dorsal
root section on the arrhythmias associated with coronary occlusion.
Am J Physiol 231: 923-928, 1976
VOL. 41, No. 1, JULY 1977
30. Szentivanyi M, Juhasz-Nagy A: Physiological role of coronary' constrictor fibres. II. The role of coronary vasomotoers in metabo, adaptation of the coronaries. Q J Exp Physiol 48: 105-118, 1963
31. Becker LC, Ferreira R, Thomas M: Mapping of left ventricular blood
flow with radioactive microspheres in experimental coronary artery
occlusion. Cardiovasc Res 7: 391-400, 1973
32. Donemech RJ, Hoffman JIE, Noble MIM, Saunders KB, Henson JR,
Subijanto S: Total and regional coronary blood flow measured by
radioactive microspheres in conscious and anesthetized dogs. Circ Res
25: 581-596, 1969
33. Fortuin NJ, Kaihara S, Becker LC, Pitt B: Regional myocardial blood
flow in the dog studied with radioactive microspheres. Cardiovasc Res
5:331-336, 1971
34. Feigl EO: Sympathetic control of coronary circulation. Circ Res 20:
262-271, 1967
35. Pitt B, Elliot EC, Gregg DE: Adrenergic receptor activity in the
coronary arteries of the unanesthetized dog. Circ Res 21: 75-84, 1967
36. Feigl EO: Control of myocardial oxygen tension by sympathetic coronary vasoconstriction in the dog. Circ Res 37: 88-95, 1975
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The Canine Heart As an Electrocardiographs
Generator
Dependence on Cardiac Cell Orientation
L. VINCENT CORBIN, II, AND ALLEN M.
SCHER
SUMMARY Traditionally it is assumed that during cardiac depolarization the macroscopic current generators that
produce electrocardiographic voltages can be represented as a uniform double-layer source, coincident with the
macroscopic boundary between resting and depolarized cardiac fibers as measured with extracellular electrodes
("uniform" hypothesis). A segment of this boundary is thus considered as a current dipole oriented perpendicular to
the boundary. We present evidence that, contrary to the above, the effective dipoles largely parallel the long
axes of cardiac fibers ("axial" hypothesis). Calculated potentials in volume conductors differ markedly in the two
cases. The magnitudes of rapid local "intrinsic" deflections also differ markedly. In our experiments, potential fields
produced by stimulation at several cardiac sites and measured magnitudes of intrinsic deflections during normal
depolarization and that caused by stimulation support the axial hypothesis and are incompatible with the uniform
hypothesis. Our results suggest that axial orientation of sources is sufficiently strong so that predictions assuming the
uniform hypothesis would be seriously in error, although the axial theory alone does not exactly describe all the
measured potentials. Axial orientation of current generators must be considered in quantitative prediction of
electrocardiographic potentials. Further study of the geometry of the intracellular depolarization boundary and its
relation to fiber direction and to the frequency of lateral intercellular junctions is required to describe the generators
exactly.
THE ELECTROCARDIOGRAM (ECG) is of great utility in physiology and in cardiac diagnosis, but its shape has
not been quantitatively predictable from a knowledge of
intracardiac events. Such prediction, known as the electrocardiographic "forward" problem (usually dealing with
ventricular depolarization and the QRS complex), has
appeared feasible on the basis of available knowledge of
(1) cellular electrical changes associated with depolarization of cardiac cells:1"3 (2) the sequence of these changes
in the heart (pathway of depolarization);4-8 (3) geometry
and conductivity of the torso and its contents; and (4) the
physical theory describing current flow in three-dimenFrom the Department of Physiology and Biophysics, University of
Washington School of Medicine, Seattle, Washington.
Supported by U.S. Public Health Service Research Grant HL 0131522.
Received June 28, 1976; accepted for publication December 21, 1976.
sional, bounded, inhomogeneous conductors like the
torso.9-" If the forward problem were solved, it would
greatly strengthen the scientific basis of electrocardiography. Although all necessary information seems available,
past attempts to solve the forward problem during ventricular depolarization6' 18~23 appear to us either qualitative
and very difficult to evaluate or, when body surface maps
that can be compared with real body surface maps have
been produced, the studies do not show good agreement
between the two. An explanation for failure to solve the
forward problem may, we believe, be found in myocardial
cellular anatomy, the electrophysiology of cardiac cell-tocell conduction, and the manner in which cardiac cells
generate external currents. These are the subject of this
paper.
Cardiac cells are long and narrow (about 15 /im in
diameter by 70 /im in length, with considerable variabil-
ECG DEPENDENCE ON CELL ORIENTATION/Corfcm and Scher
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ity)24- 25 and form a complex anatomical network through
bifurcations and interconnections. The direction of the
cells rotates smoothly with depth, although cells remain
approximately parallel to each other within a plane parallel to the nearest heart surface.26 The ventricular depolarization process in humans and dogs is initiated by endocardial and subpapillary Purkinje fiber terminations, and
travels from cell to cell*"8 via low resistance junctions
(called nexuses or gap junctions) associated with the intercalated disks.27 Cellular geometry and cell-to-cell contacts
influence velocity of conduction, which is faster along than
across the axes of the groups of cells by about 2:1 to
3:1 1-3,28-30 Electrotonic current spread is similarly anisotropic.31
As depolarization propagates from cell to cell, currents
are generated within the myocardium which give rise to
electrocardiographic potentials at the torso surface. The
ECG forward problem attempts to calculate these potentials in order to test our understanding of the total electrocardiographic system. Traditionally, calculations of extracellular potentials from depolarizing excitable tissue have
been approached in two very different manners. Those
dealing with nerves or single strands of muscle develop an
analytic solution for potential within and around a long
single cell and assume boundary conditions at the cell
membrane approximating those for an experimentally
measured action potential.14"17-32-33 It is usually assumed
that membrane current is symmetric with respect to rotation around the cell axis and thus the resulting potential
field is also axially symmetric. (Rail33 has calculated time
constants of approach to equilibrium in the radial, angular, and longitudinal dimensions for passive currents. He
shows that for long cells, symmetry about the cell axis is
reached very rapidly.) The axially symmetric "core conductor model"34-35 is used to derive membrane current
from experimentally measured intracellular action potentials. Potentials external to a cell are then calculated by
integrating, over the entire cell, the membrane current
divided by the distance to the observation point. Spach
and co-workers32 demonstrate that this formulation accurately predicts measured extracellular potentials around
dog Purkinje fibers from simultaneously measured intracellular action potentials. They find that the magnitudes of
the extracellular potentials are proportional to Vmax, the
maximal rate of rise of the intracellular action potential.
The potentials are also directly proportional to <rUm, the
intracellular-extracellular conductivity ratio. When multiple cells are considered, the quantity of extracellular fluid
becomes important.17-36 At a distance, these three-dimensional fields from single cardiac fibers are roughly dipolar
in shape, as if a current dipole source were located on the
cell axis at the location of Vmax, pointing along the cell
axis, with polarity such that positive potentials would be
seen ahead of the wavefront* and negative potentials behind it.
* The wavefront (isochrone) is here considered to be the region of the
cells which is undergoing depolarization, i.e., the region which is neither
resting nor depolarized. In this study, we treat the wavefront as a voltage
step or discontinuity, while realizing that it actually is a distributed boundary and that the depolarizing process spans several cells simultaneously.
We do not feel that this approximation influences our conclusions as
discussed below.
59
Although effective for a single cell, this approach is not
directly applicable to predicting torso ECG's, but it indicates that where cells do not branch extensively the potentials can be modeled as though they were produced by
current dipoles oriented along the cell axes. Effective
dipole strength may vary as conductivities, fluid spaces,
and action potentials change.37
Investigators concerned with directly relating cardiac
depolarization to torso electrocardiographic potentials
have used a much different approach, that of a uniform
macroscopic dipole-sheet approximation rather than a microscopic cellular approach. In this approximation ("uniform" hypothesis), a sharply defined, smooth, and continuous boundary between resting and depolarized myocardial tissue is assumed and is taken a priori to behave as a
uniform double-layer current source.38 That is, an element
of this surface behaves as a current dipole pointing perpendicular to that surface (in the direction of propagation), with strength proportional to the area of each surface element. (This representation of the boundary ignores the presence of cells or of any structure smaller than
about 1 mm.) Excitation maps can thus be converted into
electrical generators by substituting dipoles for segments
of wavefront.22-39 If the strength per unit area of this
uniform double-layer source surface is constant, the potentials produced are directly proportional to the solid
angle which that surface subtends7-15-40 (Appendix A). All
that is important for determining the solid angle are the
edges and holes of the wavefront (that is, where it terminates on endocardium, epicardium, or inactive tissue), and
the exact description of activity at other positions is irrelevant.
Although the uniform hypothesis has been useful to
provide a rough qualitative visualization of the origin of
the ECG, we and others, as indicated earlier, have been
generally unsuccessful in quantitative predictions of ECG
potential maps using the solid angle approach, even when
corrections for inhomogeneities and boundaries are
made.20-21 Spach and co-workers have abandoned the use
of the isochrones (boundaries between resting and active
tissues) as potential sources and this implies abandonment
of the uniform double-layer concept. They have questioned,8-41 as did Frank,38 the assumption that all parts of
an isochrone (wavefront) generate equal current per unit
area, and have advocated the use of potential fields as
volume-conductor sources.
The validity of the uniform hypothesis is questionable
unless all cells are identical in terms of the action potential
they generate and unless conductivity and extracellular
space are identical along the wavefront. Its validity will
also depend on the geometry of cardiac cells and the
relative frequency of branching and side-to-side intercellular junctions. If lateral junctions were infinitely frequent
and if gaps between cells did not exist, then depolarizing
regions within adjacent cells would join coherently to form
a hole-free macroscopic wavefront of uniform strength, as
illustrated in Figure 1A. Conversely, if lateral junctions
were relatively infrequent, then the wavefront within each
cell would tend to lie in a plane perpendicular to the cell
axis, as hypothetically illustrated in Figure IB. Each cell
would then act as a dipole current source pointed along the
cell axis. The effective strength per unit area of the result-
CIRCULATION RESEARCH
60
B
\7
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FIGURE 1 A schematic of possible cellular current generator orientation. A represents the case when adjacent intracellular excitation boundaries (heavy lines) join to form a coherent, hole-free
macroscopic wave (dotted line), as when lateral intercellular contacts are infinitelyfrequent(uniform hypothesis). Arrows represent
direction and magnitude of resulting dipolar current sources. B
represents the case in which intercellular contacts are infrequent
enough that cellular excitation is symmetrical about the cell axis
(axial hypothesis). Gaps in the wave are now present along lateral
cell walls. In B the effective electrical strength per unit area of the
macroscopic wave is reduced by cos y because of the reduced
effective source area of each cell.
ant macroscopic wavefront would then be reduced by cos y
because the wavefront is no longer continuous but has
gaps along lateral cell borders. For certain idealized cases
(Appendices C and D), the components of axial dipoles
tangential to the macroscopic wavefront (Fig. IB) cancel,
giving another cos y reduction in effective wavefront
strength. In general, however, fields must be calculated by
the full numerical technique of Appendix B, which does
not ignore tangential components. Aspects of this model
have been discussed by Plonsey.42
The configuration of Figure 1A is not likely to be the
general case within the ventricular wall because anisotropy
of conduction velocity and electrotonic spread, as well as
results of anatomical studies,27 indicate relatively infrequent branching and side-to-side cellular junctions. Yet, it
is also unlikely that pure axial symmetry will be the general case, and typically the truth will lie somewhere between Figures 1A and I B . But we thus have raised the
possibility that effective wavefront strength may be highly
variable, although all cells are electrophysiologically identical—merely because of differences in orientation of intracellular depolarization gradients.
Thus, we determined to examine the validity of the
uniform hypothesis using stimulation experiments in which
simple, well localized excitation wavefronts are produced
and resulting potentials are recorded from many points
close to the wave. We wished to predict potentials close to
a wavefront as a prerequisite for later predicting potentials
at a greater distance. In these experiments, we accurately
mapped the position of the wavefront in three dimensions,
and compared actual measured potentials with potentials
derived from the measured wavefront by the solid angle
formulation. We also calculated potentials from the wavefront position via a new approach, a macroscopic exten-
VOL. 41, No.
1, JULY
1977
sion of the axially symmetric single cell theory. We call this
the "axial" hypothesis. It treats the partially depolarized
portion of a myocardial fiber as an ideal dipole source
pointing along the axis of that fiber. The boundary between resting and active tissue, as in the solid angle approach, is considered to be macroscopically smooth, and
cells are assumed to be electrophysiologically identical and
locally parallel, with uniform extracellular space (Appendix B).
The axial and uniform hypotheses not only predict very
different shapes and magnitudes of fields, but also predict
different electrical changes as a depolarization wave passes
a recording electrode. When a wavefront surface passes a
recording point within the myocardium, the solid angle
subtended by that surface changes by 477 steradians; when
the recording point is on an epicardial or endocardial
surface, the change is 2TT steradians. The "discontinuity"
in potential should then be either K,AV or KiAV/2, where
AV is the cellular plateau voltage minus resting voltage,
and K, = 0.5 6 - 7 ' 42 (for AV = 120 mV, then K,AV = 60
mV). Thus, although the wave is not actually infinitesimally thin, we would expect from solid angle predictions
to observe rapid changes in potential, referred to as "intrinsic deflections," with magnitudes clustering near K,AV
and K,AV/2 (that is, 60 mV and 30 mV). In contrast, as
developed in the Appendix, the axial theory predicts a
continuous variability of intrinsic deflections, equal to
K,AVcos2y, where y is the angle between cell axes and
wave propagation direction.
Methods
PREDICTION OF POTENTIAL SHAPES FROM
DEPOLARIZATION
Five dogs were studied by two different techniques. In
the first study, three dogs were anesthetized with pentobarbital, 30 mg/kg, iv, and the heart was exposed through
a left-lateral thoracotomy. Multiterminal needle electrodes (terminals at 1-mm distance) were inserted in a
close array into the lateral left ventricular wall. Two or
more rings of electrodes were inserted around a central
electrode, all perpendicular to the epicardium, such that a
total of 15-20 electrodes were placed within a 3-cm diameter. The heart was covered with 400 fi-cm sucrose-saline
to a depth of several centimeters during the recording to
approximate an infinite homogeneous medium. Depolarization was initiated by stimulation along the central electrode either at the epicardium or within the wall. The time
of local depolarization at each of the multiple recording
electrodes was determined as the instant of most rapid
negative-going change of the unipolar potential. After
each experiment, the position of each electrode was carefully measured and the anatomy of the block of tissue with
electrodes was reconstructed. The tissue was then grossly
dissected to determine the orientation of cardiac muscle
fibers. The recorded potentials could be compared with
those predicted from the solid angle or axial theory.
In a second study we used a brushlike electrode consisting of single tungsten wires (0.125 mm in diameter),
insulated except for the sharpened tips. Eight parallel
wires 6 mm long protruded at right angles from a plastic
block around a 6-mm diameter circle. An additional elec-
ECG DEPENDENCE ON CELL ORIENTATION/Corb/n and Scher
trode in the center was used for stimulation. This brush
electrode was inserted into the left ventricular wall so that
all nine wire tips lay 5 mm deep in a plane parallel to the
epicardium. Stimulation currents just above threshold
were applied to the central electrode, and the potentials
were measured on the surrounding wires. The object was
to examine potentials very close to a closed excitation
surface at points where the local wavefront moved in many
directions relative to cell orientation.
In the third study, two dogs were anesthetized as above
and the heart exposed as before. Two multiple electrodes
were placed into the left anterior papillary muscle, one
near the tip and one in the body of the muscle. We
stimulated at various points and observed potentials on the
other electrodes. By stimulating near the muscle tip, we
were able to generate a simple wave which initially traveled nearly along cell axes.
61
tions are always much less positive than predicted from the
uniform theory.) Note that there cannot be superposition
from distant wavefronts here because we know the location of all depolarizing tissue.
MIDWALL STIMULATION
Figure 3, from a study using the brush electrode, shows
the potentials observed around an expanding, closed excitation wave (one which has not intersected endocardial or
epicardial surfaces) which is schematized as though the
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MEASUREMENTS OF INTRINSIC DEFLECTION
MAGNITUDES
During extensive mapping of myocardial depolarization
sequence in studies on the isolated, perfused dog heart, we
had recorded unipolar potentials from hundreds of intramyocardial locations. For this study, we retrieved these
records and tabulated the magnitudes of the rapid intrinsic
deflections (slopes greater than about 10 mV/msec)
which, for small recording electrodes, approximate the
voltage difference across the local wavefront as it passes
the electrode. In these studies, 71-terminal plunge electrodes were used (0.9-mm shaft diameter, with 0.05-mm
wire tips exposed at 1-mm intervals). Recordings were
made with 1-kHz band-width amplifiers and recorder,
with an AC coupling constant of 0.3 seconds.
Results
EPICARDIAL STIMULATION
Figure 2 shows the isopotential contours expected according to the solid angle (A) and axial (B) formulations
for a hemispherical boundary between depolarized and
resting myocardium. Assumed fiber directions are described in the caption. All calculations are within an infinite, homogeneous medium. (Details are in Appendices A
and B.) Figure 2C shows contours drawn from potentials
recorded from a cup-shaped interface after stimulation 2
mm below the epicardium. The measured field shows
regions of strong positivity ahead of the wave only in the
direction of the cell axes, as predicted by the axial theory
but not by the uniform hypothesis. In addition, negativity
precedes the central part of the wave, which is traveling
transversely to the fibers, also as predicted by the axial
theory. This is clear evidence that the depolarization
wavefront behaves as if cellular dipole current sources are
oriented preferentially along the cell axes rather than
normal to the wavefront.
From the uniform theory, we had previously thought
that for such a simple wave (without superposition from
other distant waves) one must always see positivity ahead
of a wave. Here, however, we see negativity ahead of a
wave when it is traveling transversely to the fibers, as
predicted from the axial hypothesis. (This negativity is not
always so striking, but the potentials in transverse direc-
FIGURE 2 Three potential fields from a hemispherical boundary
(isochrone) of excitation (heavy dashed line) within cardiac muscle
and bounded by the epicardium (dotted line) in fluid of muscle
conductivity. A and B are the potential fields predicted from
uniform and axial hypotheses, respectively. C is the measured field
from electrodes whose tracks are shown. For A, B, or C, longitudinal cell axes lie left to right in the illustrated plane for subepicardial
cells, and slowly rotate counterclockwise about a vertical axis as
depth increases. Maximal rotation is about 90° at the deepest point
of the hemisphere. Contour lines are labeled in millivolts. The steep
gradients close to the wavefronts have been spread out for clarity.
(In regions ofC not near electrodes, contour lines are not uniquely
determined and could perhaps be drawn differently.) The measured field C resembles the axial theory B in all major features,
especially in the positive contours found in the direction of the
subepicardial cell axes. We believe these positive areas are created
by cardiac cells acting as dipole current sources preferentially
oriented along the cell axes. Also, C resembles B in the negative
region preceding the wave. (In A, cell axis orientation is irrelevant.
In B, the predictions with rotating axes differ only slightly from
predictions with all axes left to right, because only a small area of
the wavefront intersects rotated fibers. Thus, the exact description
of fiber rotation is not critical here.) Electrode terminals in C are 1
mm apart.
CIRCULATION RESEARCH
62
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X.
10 msec.
FIGURE 3 A wave of depolarization has been initiated in the
middle of the ventricular wall. The depolarizing tissue forms a
closed three-dimensional shell which becomes roughly ellipsoidal
because of faster propagation along the cell axes. Current sources
(the central figure) are illustrated as oriented along the cell axes as a
hypothesis to explain the results. (The central figure is a cross
section of the depolarized region as viewed from the epicardial
direction.) Single small tungsten wires were used to record potentials roughly at the symmetrical points labeled L, B, and T in a 6mm-diameter circle lying in a plane parallel to the epicardium,
halfway between endocardium and epicardium. Potentials shown
in the insets are as predicted, assuming uniform source density
along the boundary (U), assuming the axial hypothesis (A) (see
Appendix D), and as measured (M). Other unlabeled curves are as
measured. The existence of potential changes (arrows), positive at
points L and negative at points T, preceding local depolarization
(rapid negative intrinsic deflection) supports axial orientation of
cellular sources. Axial orientation of cellular dipoles, as illustrated
by the terraced elliptical figure, causes points L to "see" positivity
as depolarization approaches, whereas points T "see" the negative
side of each source as the wave approaches. The depolarization
boundary is not actually sharp, but is about 0.5-1 mm thick, which
is significant compared to the electrode spacing. But a thick "uniform" wave could not produce the positivity seen at L and the
negativity seen at T. Rather, it would merely prolong the intrinsic
deflection.
VOL. 41, NO. 1, JULY
1977
pendix D). The positive spike in both "measured" and
"axial" potentials and the lack of positive spike in potentials predicted by the solid angle calculation again confirm
a preferential axial orientation of cellular dipoles.
In contrast, as the wave approaches electrodes T transversely, a negative dip is seen (arrows), as predicted from
axial dipole orientation. Then, as the wave passes the
electrode, a sharper negative deflection occurs. This major
negative deflection is slower and shows a more variable
rate of change than is seen on the longitudinal electrodes.
It is less than that predicted by the uniform theory, but
much greater than that predicted by the axial theory. The
presence of this intrinsic deflection at the transverse electrodes is possibly due to (1) some laterally oriented cellular dipoles, or the fact that (2) the wavefront near the
electrode is not coherent, or (3) the wavefront at the
electrode is not traveling exactly transversely to cell axes.
Electrodes B at intermediate angles record potentials intermediate between L and T.
Although the electrodes are only 3 mm from the stimulation point, the distributed nature of the wavefront would
not, we believe, account for the contrasting positive and
negative potentials preceding local depolarization at L and
T.
The consistent differences between potentials at longitudinal and transverse electrodes are more evidence for
rejecting the uniform double-layer assumption and for
considering fiber direction in understanding potentials
generated during myocardial depolarization.
PAPILLARY MUSCLE STUDY
Figure 4 illustrates results of the papillary muscle study.
Those electrodes where the wave arrived first (wave traveling directly from stimulus along the cell axes) experienced the largest intrinsic deflections (up to 57 mV) and
the largest pre-arrival positive spikes (up to 1 2 mV). Later
arrival times (wave arriving by oblique propagation) were
accompanied by reduced intrinsic deflections (about 25
60-
r30
40-
•25.
20-
•20
LAP
15
dipoles were oriented along the cell axes. (The electrodes,
including the central stimulation electrode, are in the middle of the left wall in a plane parallel to the epicardium.)
Both the central figure and the egg-shaped figure in the
upper left are hypothetical, but fiber direction is as indicated. As the wave travels along the cell axes toward both
longitudinal electrodes marked L, a sharply rising positive
potential ("spike") is seen (arrows), followed by a strong,
sharply negative deflection as the wave passes the electrode . The two upper curves in the left insert of Figure 3
are predictions by the uniform and axial approaches (Ap-
15
10
5
DEPTH (mm)
FIGURE 4 The canine left anterior papillary muscle is stimulated
near the tip at S on electrode 1, creating a simple open wave
traveling roughly along cell axes (arrows). As the wave arrives at
points along multiterminal electrode 2, arrival times (O), intrinsic
deflection amplitudes (A), and pre-arrival positive spike amplitudes (O) are shown. For the earliest arrival (wave traveling directly along the cell axes) the largest intrinsic deflections (55-57
mV) are seen, accompanied by the largest positive spikes (12 mV).
Later arrivals, via oblique propagation, have lower intrinsic deflections (20-25 mV) and insignificant positive spikes.
ECG DEPENDENCE ON CELL ORIENTATION/0>/*m and Seller
63
tissue viability surrounding the electrode. Since axial conduction would account for the potential magnitudes in
Figure 6 as well as the other findings reported above, it
appears unnecessary at present to invoke these other factors, but they should be investigated.
w
cell
oxes
time-
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FIGURE 5 Potentials predicted at point P for an expanding, closed
spherical depolarization wavefront W, assuming that all cellular
sources are oriented exactly along the cell axes. For propagation
along the cell axes (tji = 0°), an initial pre-arrival positive deflection
occurs, followed by a strong negative-going discontinuity, A (the
intrinsic deflection), equal to K,AV. As propagation becomes more
transverse to the cell axes (<\> increases toward 90°), the positive prearrival deflection decreases and then becomes negative. Also, the
intrinsic deflection (equal to K^Vcos2^) is reduced, disappearing
completely for I/I = 90°. (See Appendix D.)
mV) and little or no positive spike. This agrees with axial
predictions in which intrinsic deflections should be equal
to K,AV = 60 mV for propagation along cell axes with a
positive spike, and smaller intrinsic deflections with no
spikes would be seen for large oblique angles of approach.
(Figure 5 illustrates these features for an expanding,
closed spherical wave.)
INTRINSIC DEFLECTION MAGNITUDES
Figure 6 shows histograms of rapid intrinsic deflection
magnitudes for three dog hearts. The distributions are
smooth and singly peaked, with means of 15-23 mV, and
tail off between 50 mV and 70 mV. No significant differences were found between right wall, left wall, and septum.
Also, because over 80% of these electrodes were deep
in myocardium, according to the solid angle theory one
would expect nearly 80% of the values to cluster near
K,AV = 60 mV. The axial theory, however, predicts a
distribution related to the distribution of angles between
fibers and wavefronts, with an absolute upper limit of
around K,AV = 60 mV, which occurs for purely longitudinal propagation. The measured distributions do, in
fact, tail off at about 60 mV and have the mean one would
expect if the average angle between fibers and wavefront
direction were about 60 degrees. Since cardiac excitation
generally proceeds from endocardium to epicardium
roughly transversely to the cells, a mean angle between
wavefront direction and cell axes of about 60 degrees is
reasonable. One might argue that what Figure 6 is really
showing, however, is a variation of such other factors as
the conductivity factor K,, extracellular fluid space, or
Discussion
Several findings invalidate the hypothesis that the
boundary between resting and active myocardial tissue
behaves as a uniform dipolar-sheet current source. First,
there are strong positive potentials in the direction of the
cell axes around cup-shaped waves that indicate strong
preferential axial orientation of the cellular electrical
sources rather than orientation normal to the wavefront.
Second, potential changes occur before local depolarization external to closed-surface depolarization waves.
These potentials are incompatible with a uniform dipolarsheet representation, but are again consistent with a preferential orientation of generators along the cell axes.
Third, magnitudes of rapid intrinsic deflections are
highly variable, in contrast to predictions of the uniform
hypothesis, and are related to the angle between the wavefront and the fiber direction, again as predicted from
assuming a preferential axial orientation. We believe that
the magnitudes of the rapid components of the intrinsic
deflection are approximately proportional to the effective
strength of the wave in the immediate vicinity of the
electrode. The wide variation in these measured magnitudes, as illustrated in Figure 6, thus indicates in itself a
wide variation in effective wavefront strength. If this variation is systematic and due to fiber orientation, as we
believe, it must be considered in quantitative predictions
of electrocardiographic potentials.
These results are not (with hindsight) particularly unexpected considering the longstanding knowledge of cardiac
excitation velocity anisotropy,28"30 anistropy of electrotonic spread,31 a knowledge of cardiac cell geometry,24-25
and the frequency of intercellular contacts in the rabbit
heart,27 as well as a knowledge of the behavior of
electrical fields within and around long cylindrical
cells.14~17i32'33 The widespread use of the uniform theory
by ourselves and by others thus appears to be a failure
to consider the effects of cell-to-cell conduction and
cell geometry on extracellular potentials. Plonsey42 has
made a beginning toward considering these and similar
matters in depth.
25
SO 7S
(mv)
2S
SO 7S
(mv)
2S
SO 7S
(mv)
FIGURE 6 Histograms of rapid intrinsic deflection magnitudes
observed during extensive mapping of excitation in three isolated,
blood-perfused dog hearts. These serve as an indication of variation in local wavefront source strength. Discussion in text.
64
CIRCULATION RESEARCH
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Vander Ark and Reynolds43 measured voltage variations on the epicardium. They found that the largest voltages occurred when propagation was parallel to the muscle
fibers and that for cross-fiber propagation the waveforms
were prolonged, with multiple notching and a lack of sharp
intrinsic deflections.* The mean voltages (total peak-topeak changes) in this latter case were 29.5% less than with
parallel movement, even without distinction between
rapid and slow phases and without correction for distant
superposition. Conduction velocity was also reduced by
51.8%. They did not, however, conclude that this difference implied a variability in effective wavefront strength
with fiber direction, probably because of their study of the
closed-surface wave. It is our opinion that their closedsurface wave study was insufficient to resolve the question
of uniformity of wavefront strength for two reasons. First,
they did not show how much voltage would be expected at
various distances from the wave if the wave were not
uniform (we present such an analysis in Appendix D).
Thus, there is no reason to believe that their choice of
electrode position and amplifier gain was adequate for
testing uniformity. Second, they recorded with bipolar
endocardial-epicardial electrode pairs which, according to
the analysis in Appendix D, both would measure the same
voltage, even for a nonuniform wave. Also, our own study
of a closed-surface wave (Fig. 3) shows external potentials
for electrodes within the muscle only briefly in advance of
local depolarization. These potentials fall off so rapidly
with distance that it probably would be impossible to
measure them from electrodes on heart surfaces, but they
nevertheless result from significant wavefront strength
nonuniformities. (There may be some small voltage
changes preceding local depolarization in Figure 7 in their
paper.)
To supplement the voltage vs. fiber direction study of
Vander Ark and Reynolds,43 we studied epicardial unipolar potentials, utilizing 50 measurements with poststimulus
propagation parallel to muscle fiber direction and 100
measurements for propagation not parallel to fiber direction. We measured rapid intrinsic deflections and total
(peak-to-peak) voltage changes. These are summarized in
Table 1. They indicate that there are substantial differences in potentials between parallel and nonparallel propagation, especially in the rapid deflections.
The data presented above indicate that a macroscopic
wavefront cannot be considered a uniform double-layer
source and that systematic changes in effective wavefront
strength and direction are determined by cellular geometry and by interconnections between cells. We believe that
this accounts for the fact that the forward problem remains
largely unsolved. We see no reason why the clear improvement in qualitative prediction of potentials external to a
wavefront, as seen in Figures 2 and 3 (from the axial
hypothesis), will not apply equally to body surface potentials.
The assumption of purely axial orientation of cellular
dipoles is an improvement over the uniform dipole-sheet
assumption, but it may not always be adequate. A com* The notching seen in transverse (T) and intermediate (B) recording
locations in Figure 3 supports the finding of Vander Ark and Reynolds.43
VOL. 41, No. 1, JULY
1977
,w
(P-r)
FIGURE 7 A description of the geometry for calculating potentials
from an infinite plane depolarization wave, for cellular sources
oriented along the cell axis direction a. P is the observation point; n
is the normal to the wave W. The wave lies in the x-y plane; O is the
origin. (See Appendix C.)
promise must be developed, and tested experimentally,
that allows for some lateral orientation of current sources,
depending on the geometry of cells and the frequency of
intercellular junctions. Also, more direct information is
needed about the occurrence of branching and lateral
intercellular junctions.
In addition, the concept of a "coherent macroscopic
wavefront" should be examined experimentally, especially
in regions of Purkinje fiber penetration and in trabeculated regions. The question of uniform packing of myocardial cells and of intracellular-extracellular volume ratios
may need exploration. Finally, fiber directions must be
measured everywhere in the heart and described in some
way appropriate for numerical processing.
We hope that we and other investigators can then proceed toward a solution of the electrocardiographic forward
problem by incorporating a knowledge of cell-to-cell conduction and myocardial fiber direction.
TABLE 1 Magnitude in Millivolts of the Rapid Intrinsic
Deflection and Total Voltage Drop Recorded on Unipolar Electrodes following Epicardial Stimulation
Magnitude (mV)
Parallel
Nonparallel
Intrinsic
Total
46.2 (8.4)
26.6 (8.4)
52.2 (5.9)
42.7 (3.6)
Results are given as mean (SD).
Differences in voltage between parallel and nonparallel propagation are
significant at the 0.1% level. Discussion in text.
Appendix
A. DESCRIPTION OF THE UNIFORM THEORY
The uniform theory considers the wavefront a uniform
double-layer current source and gives the potential V at
the point P within an infinite homogeneous conducting
medium as the following integral over all points r on the
macroscopic depolarization interface W:
V(P) =
47TO-
dA m(r) n • (P - r)
P~^ i
(1)
where n is the outward surface normal, cr is the conductiv-
ECG DEPENDENCE ON CELL ORIENTATION/Cor6/« and Scher
ity, and m(r) is the dipole source strength per unit area at
r. (Units follow Plonsey.15) If it is assumed that m is a
constant and is equal to K.crAV, where AV is the cellular
V p l a ,eau- V r e s l , then
V(P) = -
(2)
477
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where fl(P) is the solid angle subtended at P by the
depolarization wave, and K, =0.5 is a correction due to
unequal intracellular and extracellular resistivites.6-7'41
The field of Figure 2A was calculated in two different
ways, each yielding the same result. The first was to find
off-axis solid angles for Equation 2 using an expansion in
spherical harmonics. The second was to do a numerical
integration of Equation 1 over the hemispherical wave.
The wave was broken into small area elements, and each
was replaced by a dipole source at the element center,
pointing normal to that element and having strength proportional to the area of the element. The potential at any
point was then obtained by summing potentials produced
by all the dipoles. Elements were progressively subdivided
until no further change in the potentials occurred.
B. DESCRIPTION OF THE AXIAL THEORY
until no further change in calculated potential occurred, (y
is the angle between wave propagation direction and fiber
direction at the wavefront element. The sign of fiber
direction is always taken so that cos y is positive.)
By this same method, axial model calculations can be
performed for any shape d wavefront and for any fiber
configuration, as long as the. area elements are small
enough that fiber direction does not change significantly
over any individual element.
C. PREDICTIONS OF POTENTIALS BY THE AXIAL
THEORY FOR INFINITE PLANE WAVE
EXCITATION
The following calculations give some insight into axial
model behavior when the wave is planar and very extensive compared to its thickness, at locations where edge
effects need not be considered.
Equation 3, for an infinite plane wave traveling in the z
direction at an angle y to the cell axes (all cells parallel and
in direction a) (Fig. 7), becomes
V(P) = ^ ~ cosy a
f f* dxdy(P- r)
)L
I P - if
which integrates out as
Both Equations 1 and 2 assume a cellular picture as in
Figure 1A. If, instead, one assumes axial symmetry of
cellular membrane currents as in Figure IB, and assumes
uniform locally parallel cell packing and, as before, that a
smooth microscopically continuous surface can be drawn
connecting the transitional regions of myocardium, then
the potential is given as in Equation 1, except that the
dipole sources now point along the local cell axis instead of
normal to the surface, and the strength per unit area is
reduced by cos y because of the "holes" now present in the
wave (Fig. IB). If we also assume that the maximum
magnitude of m is K,o-AV, then the potential becomes
V(P) =
65
K.AV
dAa(r)-(P - r)cosy
4TT
IP-r|3
'
'
J
'
where a(r) is a unit vector pointing in the axial direction of
the cells located at r. (This integral does not simplify, as
does Equation 1, and thus for most applications it must be
evaluated numerically.)
Equation 3 describes the "axial" calculation for an infinite homogeneous medium. Equation 3 can be extended
to a bounded homogeneous solution (as can Equations 1
and 2) by using it as the source term in the numerical
computer algorithm of Barnard et al.10
The field of Figure 2B for a hemispherical wavefront,
with current generators assumed parallel to cell axes, was
calculated by a numerical integration of Equation 3. As in
Appendix A, the wavefront was subdivided into small area
elements, and potentials were calculated by substituting
for each element a dipolar source located at the center of
the element. The strength and direction of each dipole,
however, as indicated by Equation 3, are different than in
Appendix A. The strength becomes the area of the element multiplied by cos y, and the dipole points in the local
fiber direction rather than normal to the wave surface. As
before, elements were progressively further subdivided
z K,AV
,
V(z) = - j ^ y - ^ — cos2y.
This is constant on either side of the wave, +AVK,cos2-y
ahead of the wave and -AVK,cos2y behind it, and thus
the "discontinuity" in crossing the wave is
At/) = K,AV cos2y.
(4)
For small electrodes in intimate contact with active myocardium, this discontinuity is seen as a rapid negative
deflection, the intrinsic deflection. Thus, when the depolarization wave in myocardium is extensive compared to its
thickness, the axial model would predict a large variation
in measured intrinsic deflections, depending on the angles
between wavefront and fibers.
D. PREDICTIONS OF POTENTIALS BY THE AXIAL
THEORY FOR A CLOSED SPHERICAL WAVE
OF EXCITATION
The following development leads to the axial model
predictions for closed waves as illustrated in Figure 3.
Consider a closed spherical excitation wave of radius R,
centered on the origin, immersed in an infinite bed of
homogeneous cell fibers oriented parallel to the z axis
(Fig. 8).
Equation 3 can be rewritten as
V(P) =
K.AV
IL
dA cos y a • Vr
- r|J'
where Vr is the vector gradient operating on the r variable.
This is solved by expanding 1/| P - r| in an infinite series of
spherical harmonics,44 then expressing Vr in spherical coordinates, applying the derivatives in Vr to the series
expansion and then integrating term by term. (The resulting solution is symmetric with respect to rotations about
the z axis, and thus is a function only of the distance P and
66
CIRCULATION RESEARCH
VOL. 41, No. 1, JULY
1977
2. Weidmann S: Resting and action potentials of cardiac muscle. Ann
NY Acad Sci 65: 663-678, 1957
3. Woodbury JW: Cellular electrophysiology of the heart. In Handbook
of Physiology, section 2, Circulation, vol 1, edited by WF Hamilton, P
Dow. Washington D.C., American Physiological Society, 1962, pp
237-286
4. Boineau JP, Spach MS: The relationship between the electrocardiogram and the electrical activity of the heart. J Electrocardiol 1: 117124, 1968
5. Durrer D, van Dam RT, Freud GE, Janse MJ, Meijler FL, Arzbaecher RC: Total excitation of the isolated human heart. Circulation
cell
41: 899-912, 1970
oxes
6. Scher AM, Young AC: Ventricular depolarization and the genesis of
QRS. Ann NY Acad Sci 65: 768-778, 1957
7. Scher AM, Young AC: The pathway of ventricular depolarization in
the dog. Circ Res 4: 461-469, 1956
8. Spach MS, Barr RC: Ventricular intramural and epicardial potential
distributions during ventricular activation and repolarization in the
intact dog. Circ Res 37: 243-257, 1975
9. Barnard ACL, Duck IM, Lynn MS: The application of electromagFIGURE 8 A spherical wave W of radius R is propagating within
netic theory to electrocardiology. I. Derivation of the integral equations. Biophys J 7: 443-462, 1967
an infinite bed of cells which are all oriented in direction a, parallel
10. Barnard ACL, Duck IM, Lynn MS, Timlake WP: The application of
to the Z axis. The sphere is centered on the origin; n is the outward
electromagnetic theory to electrocardiology. II. Numerical solution of
surface normal; Band <j> (<t> not shown) are the angular variables of
the integral equations. Biophys J 7: 463-491, 1967
spherical coordinates for the vector r; <j> is the angle between the Z
11. Craib WH: A study of the electrical field surrounding active heart
muscle. Heart 14: 71-109, 1927
axis and the vector to P. The small arrows show the orientation of
12. Gelernter HL, Swihart JC: A mathematical-physical model of the
the cellular dipole sources. (See Appendix D.)
genesis of the electrocardiogram. Biophys J 4: 285-301, 1964
13. Helmholtz H: Ober einige Gesetze der Verteilung elektrischer Strome
in korperlichen Leitern mit Anwendung auf die thierischelektrischen
Versuche. Ann Physik Chemie 89: 211-233 and 353-377, 1853
the azimuthal angle i//.) The solution for P inside the
14. Lorente de No R: A study of nerve physiology; analysis of the distribution of action currents of nerve in volume conductors. Stud. Rockefelspherical wavefront becomes
ler Inst Med Res 132: 384-477, 1947
15. Plonsey R: Bioelectric Phenomena. New York, McGraw-Hill, 1969
2
V(P^) = - ^
[l + I (|-) (3cos> - 1)], (5a)
16. Plonsey R: Volume conductor fields of action currents. Biophys J 4:
317-328, 1964
17. Rosenfalck P: Intra- and Extracellular Potential Fields of Active
and for P outside the sphere,
Nerve and Muscle Fibres: A Physico-Mathematical Analysis of Different Models. Copenhagen, Akademisk Forlag, 1969
18. Arntzenius AC: A geometrical model of successive stages in excitation
- 1).
(5*)
of the human heart; its value as a link between excitation and clinical
vectorcardiography. Cardiovasc Res 3: 198-208, 1969
19. Boineau JP, PilkingtonTC, Rogers CL, Spach MS: Simulation of body
At the wavefront surface, <p is equal to y, the wave-fiber
surface equipotential distribution (abstr 31-6). In Proceedings of the
angle, so that the discontinuity in crossing the wave, as in
7th International Conference on Medical and Biological Engineering.
Stockholm, Institute of Electrical and Electronics Engineers 1967, p
the infinite plane wave case (Eq. 4), is again equal to
412
K.AVcosV
20. d'Alche P. Ducimetiere P, Lacombe J: Computer model of cardiac
Also, the potential V outside the sphere goes to zero
potential distribution in an infinite medium and on the human torso
during ventricular activation. Circ Res 34: 719-729, 1974
rapidly, as an inverse cubic, as shown in Equation 5b. In
21. Scher AM, Corbin LV: Origin of the electrocardiogram from the
addition, the external potential is exactly zero for all
perfused dog heart (abstr). Circulation 48 (suppl IV): 61, 1973 [Note:
2
angles i|< such that cos )// = 1/3 (e.g.,i/; = 54.7°), becoming
Sentence 5 of this abstract is in error and should be changed to read:
"Prediction appears good early and late, is more accurate for the
negative for larger <<
| (cross-fiber propagation) and positive
extrasystolic beat than for the normal beat, but is poor during midfor smaller t// (longitudinal propagation). Because of the
normal QRS."]
22. Selvester RH, Collier CR, Pearson RB: Analog computer model of
rapid falloff and this (Scos^/i - 1) dependence of Equation
the vectorcardiogram. Circulation 31: 45-53, 1965
5b, easily measurable potentials would be found only very
23. Selvester RH, Solomon JC, Gillespie TL: Digital computer model of a
near the wave, and only for i// nearly 0° or 90°.
total body electrocardiographic surface map; an adult male-torso simulation with lungs. Circulation 38: 684-690, 1968
We have measured potentials near closed wavefronts, as
24. Laks MM, Nisenson MJ, Swan HJC: Myocardial cell and sarcomere
described in Figure 3. The time curves illustrated there for
lengths in the normal dog heart. Circ Res 21: 671-678, 1967
25. Truex RC, Copenhaver WM: Histology of the moderator band in man
the axial model were obtained from Equations 5a and 5b
and other mammals with special reference to the conduction system.
by allowing the sphere radius R to expand from zero at a
Am 1 Anat 80: 173-197, 1947
constant rate, while holding P and <|/ constant. The curves
26. Streeter DD, Spotnitz HM, Patel DP, Ross J Jr, Sonnenblick EH:
Fiber orientation in the canine left ventricle during diastole and sysof Figure 5 were obtained in the same way. Equation 5 is
tole. Circ Res 24: 339-347, 1969
for a sphere, and the wave of Figure 3 is elliptical, but the
27. Johnson EA, Sommer JR: A strand of cardiac muscle; its ultrastrucqualitative results from the sphere are also valid for the
ture and the electrophysiological implications of its geometry. J Cell
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ellipse.
28. Draper MH, Mya-Tu M: A comparison of the conduction velocity in
cardiac tissues of various mammals. Q J Exp Physiol 44: 91-109, 1959
Acknowledgments
29. Kriebel ME: Wave front analyses of impulses in tunicate heart. Am J
Physiol 218: 1194-1200, 1970
We are grateful to Dr. Allan C. Young for his advice and encourage30. Sano T, Takayama N, Shimamoto T: Directional difference of conducment.
tion velocity in the cardiac ventricular syncytium studied by microelectrodes. Circ Res 7: 262-267, 1959
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constants fora membrane cylinder. Biophys J 9: 1509-1541, 1969
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sodium, and chloride in canine Purkinje and ventricular tissues. Circ
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heart currents and body surface potentials. In The Theoretical Basis of
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38. Frank E: A comparative analysis of the eccentric double-layer representation of the human heart. Am Heart J 46: 364-378, 1953
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multiple dipole electrical source. Circulation 40: 687-718, 1969
40. Panofsky WKH, Phillips M: Classical Electricity and Magnetism, ed 2.
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Downloaded from http://circres.ahajournals.org/ by guest on June 15, 2017
Renal Blood Flow, Afferent Vascular Resistance,
and Estimated Glomerular Capillary Pressure in the
Nonexposed Rat Kidney
ISAO ISHUCAWA AND NORMAN K .
HOLLENBERG
SUMMARY Much of our detailed understanding of renal function has come from studies, such as micropuncture,
which require exposure of the kidney. In this study we have utilized a new method for assessing afferent arteriolar
resistance in vivo to assess the influence of renal exposure on renal blood flow and preglomerular resistance in the rat.
Exposure of the kidney did not reduce arterial pressure (111 ± 5.4 vs. 110 ± 5.5 mm Hg), but did reduce cardiac
output (298 ± 32 vs. 235 ± 6 ml/kg per min; P < 0.02), and renal blood flow in the exposed kidney (5.90 ± 0.26 vs.
4.55 ± 0.19 ml/g per min; P < 0.001). Afferent arteriolar resistance, estimated from the size of microspheres
reaching the glomeruli, was increased more strikingly (40%) than total renal resistance (29%), suggesting a
quantitatively important influence of the surgery on glomerular capillary pressure. Equations, developed to allow the
calculation of glomerular capillary pressure, suggested that glomerular capillary pressure was in the range of 50-60
mm Hg in the unexposed kidney, and fell to 45 mm Hg in response to trauma. We conclude that the surgery required
to expose the kidney reduces renal blood flow and has a quantitatively important influence on glomerular capillary
pressure —a response which must be considered when interpreting experiments which require surgery. The reduction
in flow and capillary pressure may well be a useful part of the renal response to volume deficits and trauma.
SURGICAL trauma exerts a striking influence on renal
perfusion and function, which has been well documented
in several species.1"3 Several lines of evidence suggest, at
least in the dog, that the renal vascular response is due to
activation of the renin-angiotensin system.3
We recently have devised a modification of the microsphere technique which makes it possible to assess afferent
vascular dimensions and resistance without exposing the
kidney.4 The known effects of surgical trauma on renal
perfusion led us to examine the effect of the surgery
required to expose the kidney on renal hemodynamics in
the rat, and to explore the implications of the renal
From the Departments of Medicine and Radiology, Peter Bent Brigham
Hospital and Harvard Medical School, Boston, Massachusetts.
Supported by National Institutes of Health Grants HL 14944, GM
18674, HL 11668, HE 05832 and the U.S. Army Research and Development Command (DAMD 17 74 4023). Dr. Ishikawa was the Samuel
Levine Research Fellow of the American Heart Association, Greater
Boston Massachusetts Chapter.
Address for reprints: Norman K. Hollenberg, M.D., Ph.D., Peter Bent
Brigham Hospital, 721 Huntington Avenue, Boston, Massachusetts
02115.
Received August 2,1976; accepted for publication December 15,1976.
vascular response for glomerular dynamics. Our working
hypothesis was that the surgery required to expose the
kidney for micropuncture in the rat may have influenced
the results of many experiments in which this maneuver is
unavoidable. The results, moreover, provide further insight
into the renal vascular and functional response to trauma.
Methods
GENERAL TECHNIQUES AND PROTOCOLS
Studies were performed in 46 male Sprague-Dawley rats
weighing approximately 300 g. Standard laboratory chow
and tap water were provided. Anesthesia was induced with
pentobarbital sodium (40 mg/kg, ip) and maintained with
occasional supplements of 5-6 mg/kg as required for surgical anesthesia with spontaneous respiration. Tracheostomy provided an airway. Rectal temperature (Yellow
Springs Instrument) was kept between 36°C and 37°C with
a lamp. Ventricular catheterization was achieved from the
right carotid artery with a tapered, polyethylene (ClayAdams PE 50) catheter. An identical catheter was placed
into the aorta below the renal arteries from the femoral
The canine heart as an electrocardiographic generator. Dependence on cardiac cell
orientation.
L V Corbin, 2nd and A M Scher
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Circ Res. 1977;41:58-67
doi: 10.1161/01.RES.41.1.58
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