- Email: [email protected]
The magnetic heart vector
The magnetic
heart
vector
Gerhard M. Baule, Ph.D.* Richard McFee, Ph.D. Syracuse, N. Y.
E
lectromotive forces (EMF) in the heart produce currents in the torso which set up a weak external magnetic field. This field can be measured by the use of pickup coils. l-3 A major problem has been the presence of interfering fields from motors and other electrical equipment hundreds of times stronger than the peak field due to the heart (about one millionth of the earth’s field). However, by the use of additional coils fairly distant from the heart, this interference can be cancelled out to a considerable extent. With our present “magnetocardiograph” we are able to measure the heart’s magnetic field in a hospital environment (New York State Upstate Medical Center) without the use of a magnetically shielded room. These records are several times noisier than average conventional electrocardiograms (ECG’s). Averaging 2.5 to 100 complexes provides records comparable in “cleanliness” to ECG’s. Fig. 1 shows an unaveraged magnetocardiogram along with the noise reduction achieved by averaging. We have been using a coil arrangement intended to provide magnetocardiograms similar in form to conventional x- and y-lead ECG’s. This was done primarily to establish that the magnetic records were
not artifacts. A great deal of experimentation has now shown beyond doubt that the magnetocardiographic records reflect variations in the magnetic fields set up by currents induced by the heart’s EMF’s. Magnetocardiograms obtained on persons without heart disease do roughly mimic the appropriate ECG’s. However, in many subjects with heart disease (LVE’s, RVE’s, infarcts) gross differences between the two types of records have been observed. This and studies of the effect of differences in conductivity between heart and lung lead us to believe that with a different coil arrangement, magnetocardiograph y might furnish diagnostic data not present in the ECG. The heart is almost surrounded by lung, whose electrical resistivity considerably exceeds that of the cardiac muscle and enclosed blood masses. Reported resistivity values are 2,000 ohms per centimeter for lung tissue, 400 ohms per centimeter for ventricular muscle,t and 160 ohms per centimeter for blood.4*5 One result of these differences is that the heart and blood offer relatively low electrical resistance paths to “tangential” EMF’s, i.e., electromotive surfaces so oriented that a vector perpendicular to them is directed tangentially
From the Department of Electrical Engineering. Syracuse This work was supported by Research Grant HE-06971 of Received for publication April 10. 1969. *Reprint requests to: Dr. Baule. Department of Electrical N. Y. 13210. tVentricular muscle resistivity is anisotropic. being about per centimeter across the fibers. The t%we, 400 ohms
Vol. 79, No. 2, pp. 223-236
February, 1970
University. the National Engineering,
Syracuse. N. Y. 13210. Heart Institute, National Syracuse
250 ohms per centimeter per centimeter, ia used
University,
Institutes
131 Hinds
in the fiber direction aa a rough “lumped”
Hall,
of Health. Syracuse.
and 550 ohms average.
American Heart Journal
223
224
Bade und .McFee
.4nter. Heart 1. Fcbrmwy. 1970
Fig. 1. Signal averaging. The top record shows three unaveraged complexes. The photograph on the bottom shows 25 and 128 averaged complexes. These records were obtained in a room in the New York State Upstate Medical Center some 20 meters from 30 large electric motors. The output of the coils has been integrated so the deflections register the magnetic flux and not the rate change of flux.
elemental
dipole
layers
Fig. 2. A tangential and a radial EMF. Each elemental electromotive surface is represented by a vector perpendicular to its surface. The terms tangential and radial refer to the vector direction. The vector for a radial EMF is coincidentwith a line from the heart’s center to its periphery. The vector for a tangential EMF is perpendicular to such a line.
with respect to the heart’s outer surface (Fig. 2). Thus large circulating currents and magnetic fields will be produced by such tangential EMF’s. In contrast, current flow from radial EMF components will be inhibited by the high resistance
of the lung. Given equal radial and tangential components, the latter will cause the larger magnetic field. This situation is the opposite to that found in conventional ECG leads where, because of the low resistivity of blood relative to heart muscle, radial EMF’s are emphasized (“Brody” effect).6 The net result is that magnetocardiographic leads tend to emphasize the tangentially oriented EMF’s, which are usually masked in conventional electrocardiographic leads by the radial EMF’s. In addition, the magnetic measurements can be expressed as a “magnetic heart vector” analogous to the “heart vector” of vectorcardiography, but radically different in interpretation. The latter part of the paper discusses magnetocardiography from the reciprocal or “lead field” point of view. Here the concept of ideal magnetovectorcardiographic leads, analogous to ideal electrovectorcardiographic leads, is introduced. A magnetic apparatus design suitable for mag-
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225
Quadripalar Magnetic Flux Distribution (bl
(a) Fig. 3. Magnetic flux distributions in one plane only.
HOMOGENEOUS MODEL
for one and two current loops. The magnetic flux distribution
INSULATING LUNG MODEL
is sketched
HIGH RESISTIVIT Y LUNG MODEL
enters chest (a)
(b)
Fig. 4. Current flow and magnetic field distributions. Each model shows a tangential electromotive surface. For the homogeneous model on the top of a the current flow consists of oppositely directed pairs of loops and the magnetic flux will be of the form shown in Fig. 3, b. This magnetic field is sketched in relation to the torso in (4) (bottom). If the lung is assumed to be an insulator, the tangential EMS will cause unidirectional current loops resulting in magnetic flux of the form shown in Fig. 3, a, and again sketched in (b).
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netovectorcardiography is shown. Magnetovectorcardiograms will share one of the clinically important features of vectorcardiograms, namely that given a welldesigned lead system, accurate knowledge of the anatomical location of the heart is unnecessary. Elementary
theory
of magnetic
leads
The elementary source of magnetic flux is a current loop. Fig. 3, a, shows such a loop and its magnetic field. At distances large compared to the size of the loop (in practice, one or two loop diameters), the shape of the magnetic field follows the well-known “dipole” formula. For example, the magnitude of the magnetic flux goes down with the cube of the distance from the loop. As a magnetic dipole source, the exact shape of the current loop is unimportant and its dipole strength is IA where I is the loop current and A is the area enclosed by the loop. Two current loops in close proximity, equal in magnitude of strength but with opposing current directions, form a quadripole source of magnetic flux. Such a configuration is shown in Fig. 3, b, along with a sketch of the quadripole magnetic field. At remote points this field diminishes with the fourth power of the distance to the loops. Consider two extremes of simplified heart-lung models. In the first, all resistivities are considered equal, and in the second the lung is considered to be a perfect insulator. The difference in resistivity between muscle and blood will be ignored. Fig. 4, a and b, illustrate these two cases, and in each is shown an electromotive surface located in the outer part of the heart and perpendicular to the heart’s periphery. For the homogeneous model (Fig. 4, a), the electromotive surface (EMS) causes a dipolar electric current flow throughout the heart and torso. This current distribution is a “smeared” form of the two current loops shown in Fig. 3, b, and the resulting magnetic field will be of the magnetic quadripolar type. For the orientations of Fig. 4, a, magnetic flux will leave the chest on the left side of the heart, and re-enter on the right side. In Fig. 4, b, all current flow is within the heart, since the lung is assumed to be an insulator. There will be no voltage drops
anywhere on the body surface,* i.e., the ECG will be silent. This current flow distribution resembles that of the single current loop of Fig. 3, a, and will give rise to a dipolar magnetic field. Magnetic flux will leave the chest over the heart and re-enter the chest in a circular region around the heart. When the lung resistivity is higher than heart and blood resistivities, but not infinite, the current distribution and magnetic field distributions can be considered, as a first approximation, to be a mixture of the two extreme case distributions. This is illustrated in Fig. 4, c. The electromotive surface in the ventricular walls is seldom purely tangential. It is often oblique, as shown in Fig. 5, a, with a radial component parallel to the epicardial surface, as well as a tangential component from endocardium to epicardium. Such an EMS can be replaced by an equivalent surface consisting of a radial component and a tangential component, as is shown in Fig. 5, b.t The component coincident with the heart-lung boundary will not cause currents to circulate within the heart, and will not give rise to the dipolar form of magnetic field. Note also that an EMS whose entire boundary lies on the epicardium (Fig. 5, c) has no tangential component since it can be replaced by an equivalent surface entirely coincident with the heart-lung boundary. An EMS in the center of the heart, as might arise for example from septal depolarization, will cause a quadripolar rather than a dipolar magnetic field even assuming the lung to be an insulator (Fig. 6, a). As the EMS is moved from the center to the periphery of the heart maintaining an orientation perpendicular to the periphery, the opposing loop pairs of current flow change to unidirectional loops. The magnetic field will change from the quadripolar to the dipolar form. In Fig. 6, b, where the EMS lies to the right of center, the current circulates clockwise, and the magnetic field is directed into the paper. In Fig. 6, C, the EMS lies to the left of center, the current circulates counterclockwise, and the mag*Assuming the muscle layer around the torso is not an insulator. tThe complete equivalency of the two surfaces follows from a theorem by Gauss. A completely closed uniform electromotive surface causes no current flow. This is true even for a nonhomogeneous and nonisotropic volume conductor.
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(b)
(al obliqye
ems
Fig. 5. The decomposition of a typical activation shown in (c) has no tangential component.
front
radial
and tangential
components.
(b)
(a) Fig. 6. Current flow located in the center,
into
wave
front
(cl
in the heart, when the lung conductivity right side, and left side of the heart.
netic field points out of the paper. Thus the EMS to the right of center will give a deflection opposite to that left of center. This is in contrast to a vectorcardiographic lead (ideally sensitive only to strength and orientation of an EMS) which will give the same deflection for the EMS illustrating the three cases. It is possible to build a magnetic pickup system sensitive to. the dipole magnetic field but not to the quadripole field. From the previous considerations, it is seen that such a pickup configuration will be sensitive primarily to the tangential components of the heart’s electromotive surfaces, and that this sensitivity will be in proportion to the distance of the EMS from the center of the heart. Such a magnetocardiograph should provide information that differs substantially from that found with electrocardiography, where the tangential com-
The
is considered
negligible
for elemental
EMF’s
ponents of the EMS are suppressed and the radial components are accentuated due to the intracavitary blood resistivity being lower than the ventricular muscle resistivity (“Brady” effect). We parenthetically note one other difference, The voltage induced in electric leads is strongly influenced by the low resistivity muscle layer around the torso.’ This is not true for magnetic leads. Fig. 7 shows one possible apparatus for picking up the magnetic dipole and rejecting the magnetic quadripole due to current loops lying in the frontal plane. The subject lies between two fairly large high permeability disks. The disks are magnetically connected by the remainder of the high permeability structure. The two pickup coils are wound in the same direction. In Fig. 7, b, a single current loop is used to represent a magnetic dipole source and the
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high permeobility ( iron or ferrite
moteriol
magnetic flux lines
1
single current loop in frontal plan+!
I
two
opposing
current
loops
\
d (b) Fig. 7. An example of a magnetic pickup assembly that will register a dipolar magnetic field and not register a quadripolar magnetic field. For clarity, the coils have been omitted from (b) and (c). The single loop of (a) causes flux through coils causing an output voltage. For two opposing loops there is no flux through the coils.
(a)
(b)
VCG reference
system
(cl
current loop circulating about Y axis ( in horizontal plane )
(e)
z
current loop circulating about Z axis (in frontal plane 1
current loop circulating about X axis (in sagittal plane 1
(f)
-?
(d)
(91
7
Y vector I of loop
Y to plane
components vector V
3
of
components of loop
3
Fig. 8. The magnetic heart vector. Parts (b), (c), and (d) show current loops in three orthogonal planes. Each is represented by a vector directed along the axis of circulation. The vector direction is determined using the “right-hand rule.” The vector strength is proportional to the current strength times its distance from the axis of circulation (analogous to torque in mechanics). Part (e) shows a spatial current loop (taken 45 degrees to each axis) and its vector representation. The components, vector and loop, are shown in (f) and (g).
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Magnetic
(0) r Fig.
9. An
example
illustrating
the use of reciprocity
lines of magnetic flux due to this source as they travel through the magnetic structure are sketched. Flux travels through the cores of the two coils and induces additive voltages. In Fig. 7, c, two loops of current are used to represent a magnetic quadripole source. The lines of magnetic flux are again sketched. No flux passes through the windings and hence there is no output. the magnetic
heart
vector
The heart vector of electrovectorcardiography has three components; one along the x axis (right side to left side), one along the y axis (head to foot), and one along the z axis (front to back). The magnetic heart vector may also be viewed qualitatively as arising from three components: a current circulating in the heart about the x axis and two other currents circulating about the y and z axes, respectively, where each of the circulating currents is established by tangential components of the heart’s EMF’s. This is shown in Fig. 8, b through d. These three circulating currents may each be represented by a vector along the axis of circulation with a magnitude proportional to the strength of the circulation and a polarity determined according to the right-hand rule.* The sum of these three vector components is the total spatial magnetic heart vector. For example, Fig. 8, e, shows a current loop 45 degrees to all *Curl
the fingers of the right hand and extend the thumb. Consider the fingernails to be arrowheads. When the curled fingers point in the direction of current flow. the thumb points in the direction of the loop vector.
heart vector
229
(bl for an electrocardiographic
lead.
axes and its representative vector V. Fig. 8, f, shows the three components of vector V, namely V,, 1/‘,, and Irl. These components represent current flows around the x, y, and z axes, respectively. Since vector V was chosen to have equal lengths on all three axes, the three component current loops are of equal strength as shown in Fig. 8, g. As in vectorcardiography, the vector representing the magnetic dipole current will change in direction and strength throughout the depolarization and repolarization cycle. Any of the display systems of vectorcardiography can be applied to magnetovectorcardiography. Magnetic heart vector lead jields. The interpretation of magnetocardiograms, and the design of appropriate magnetic pickup configurations, is greatly simplified by the use of the reciprocal or “lead field” method.s-10 The extension of the electrocardiographic lead field method to magnetocardiography is given in reference 9. A brief nonmathematical review is given here. To illustrate the lead field concept as used in electrocardiography, consider a y-lead ECG (Fig. 9). Fig. 9, a, shows the electromotive surface of the heart across which there is a uniform potential difference e. Due to this EMS, there is a voltage v across the two wires which go to the recorder input. Because of the complicated boundary conditions the visualization of how voltage v is related to the EMS and the location of the electrodes upon the body is not always easy. Fig. 8, b, illustrates the reciprocal or lead field method. The
230
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Bade and MC Fee
potential
across
ems
Heart
February,
magnetic flux due to current I 1 The body is “transparent” to this flux )
1. 1970
current flow induced by magnetic flux I current intercepted by the ems is i
+r -1
v -=e
(a) Fig. would
10. An example be magnetically
i
I
(b 1 illustrating induced
(cl
the use of reciprocity for a magnetic lead. The lead field is the current that in the torso if a fluctuating current I were passed through the pickup windings.
potential e across the electromotive surface is first set to zero. A current I is then injected into the lead that was previously labeled “minus” and a current I removed from the lead that was previously labeled “plus.” The distribution of this current as it flows through the body is the lead field. A certain percentage of the injected current, denoted by i, is intercepted by the electromotive surface. By the reciprocity theorem it can be shown that the ratio of the intercepted current to the injected current is identical to the ratio of the voltage at the recorder input to the voltage across the EMS, that is, v-=- i e I The advantage to this method of attack is that it is easy to visualize the lines of current flow or “lead field” within the body. In magnetocardiography we are interested in the voltage produced across the pickup coil winding as a result of the EMS of the heart. This relation can be obtained by putting a current I into the pickup coil and finding the resultant current i intercepted by the electrotiotive surface under consideration. The magnetic assembly of Fig. 7 is used as an example. To mqke a direct evaluation of the voltage across the coil winding, one must first find the current field in the body
which is produced by the electromotive surface, then find the magnetic field due to this current, taking into account the fact that it will be distorted by the high permeability iron of the pickup assembly. The portion of the magnetic field passing through the winding will induce a voltage in it which is proportional to the rate change of the field. In the reciprocal method we go through a sequence of steps illustrated in Fig. 10. The electromotive potential e of the heart (Fig. 10, a) is first set equal to zero. A fluctuating current I is (conceptually) injected into the pickup winding. This current causes a magnetic flux to emanate from the disk above the chest, to flow through the torso, and enter the disk beneath the back.* This flow of magnetic flux through the torso induces “eddy” currents therein, as shown by the circular flow lines in Fig. 10, c. (The secondary magnetic field caused by the eddy currents is negligible for typical tissue resistivities.) These induced currents are proportional to the rate change of flux through the torso and thus require that the initial injected current I be changing with time, if there is not to be a zero result. Some of this induced current, denoted by i, is in*The
permeability of the body tissues (space. i.e.. the torsa is “transparent”
differs little to magnetic
from flux.
. free
Magnetic
Volume 79 Number 2
. ZiEg
ideal x vcg lead
heart vector
231
cross section
ideol mvcg leod
(b)
ideal y vcg lead (0)
Fig. 11. Ideal magnetovectorcardiographic leadfields.For comparison, (a) showsthe uniform leadfieldsassociated with idealelectrovectorcardiographic leads.The leadfield of an idealmagnetovectorcardiographic lead (b) consistsof circularcurrent flow aroundan axis and confinedto planesperpendicular to that axis.The lead field strength is zero at the axis and increases in proportion to the distancefrom it. The strength doesnot dependon the directionfrom the axis,i.e., it is the samefor A, B, C, andD of (bf.
tercepted by the electromotive surface. By use of the reciprocity theorem the ratio of the intercepted current i to the current I fed into the pickup coil is the same as the ratio of the voltage w measured across the pickup coil due to the potential e across the electromotive surface of the heart. The induced currents then constitute the lead field which is produced magnetically. This lead field is determined by anatomical boundaries between tissues of different resistivities (including the outside torso-air boundary), and by the magnetic pickup configuration. This statement is analogous to the statement that the lead field in electrocardiography is determined by the torso boundaries and the number and location of electrodes placed on the torso. Because of this close analogy, the disks of the pickup units from which magnetic flux leaves or enters might well be called “magnodes”; thus the number and location of the magnodes and the torso geometry determine the lead field. Both arrangements of electrodes and arrangements of magnodes can be characterized completely by the lead field which they produce. There is one major difference between
the lead field which can be produced by magnetic electrodes (magnodes) and those which can be produced by conventional electrodes. For electrodes, the lines of current flow must begin and end on electrodes. In contrast to this, the magnetic lead field consists of currents which swirl around without starting at surface electrodes. ‘LIdeal” lead field for magnetmectorcardiography. Since the electromotive surface representing the activation boundaries lies in the heart, electrocardiographic or magnetocardiographic lead fields need only be known within this region. The ideal electrovectorcardiographic lead is one which is uniform throughout the heart region. Three such leads, orthogonal and of equal strength, are required. Ideal x and y vectorcardiographic leads are illustrated in Fig. 11, a. Due to their uniformity, they are sensitive only to the strength and orientation of an elemental electromotive surface, but not to its position, i.e., there are no “proximity effects.” A magnetovectorcardiographic lead field will be considered ideal if it consists of essentially circular flow lines, zero on an axis through the center of the heart, and
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magnetic field in the heart region. Note that this was the case for the example of Figs. 7 and 10. In the presence of a uniform (time-varying) magnetic field, the heartlung boundary will result in circular lead field flow lines centered in the heart, and lying in planes perpendicular to the magnetic flux. Using Faraday’s law that the line integral of the electric force around a closed loop is equal to the rate change of the enclosed flux f E . de = d/dt f JB * dA, it can be seen that the lead field strength increases in proportion to the distance from the heart center. Since B is constant (Fig. 13), the enclosed flux for a loop of radius a is (?ra2)P,and thus:
2
X
Y v?
12. Three
Fig. heart
x
orthogonal
leads
for
the
magnetic
vector.
UNIFORM MAGNETIC FLUX x x x Y x
(6) x
x x Y
x Y Fig. ideal
x
x
x
x
13. A uniform magnetic magnetovectorcardiographic
x flux
x will induce lead field.
an
increasing linearly in strength towards the periphery (Fig. 11, b). This lead is sensitive only to tangentially oriented elemental electromotive surfaces. There are no proximity effects in the sense that the output due to a tangential EMS will depend only on its distance from the axis, e.g., surfaces A, B, C, and D of Fig. 11, b, will give equal outputs. For a complete magnetovectorcardiogram, three such lead fields are needed, mutually orthogonal and of equal strength. This is illustrated in Fig. 12. To the extent that the heart can be represented by a homogeneous sphere imbedded in a high resistivity lung, there is a simple criterion for generating ideal magnetovectorcardiographic leads. Considered reciprocally, current into the coils of the magnetic pickup should produce a uniform
where p is the resistivity of the “heart.” Note that the exact anatomical location of the heart need not be known for the lead field to center itself. Self-centering will occur so long as the lung conductivity is negligible and the heart may be considered to be spherically homogeneous and to lie within the region of uniformity of the magnetic flux produced by the reciprocally energized coils. This is analogous to the case for ideal vectorcardiographic leads, where lead design can make the location of the heart noncritical by insuring a sufficiently large region of uniform lead field current. Design of a magnetic pickup suitable for magnetovectorcardiography. The magnetic pickup configuration previously discussed (Fig. 7) is suitable for inducing an ideal magnetovectorcardiographic lead field in the frontal plane, and by turning the subject on his side, the sagittal plane. It would be difficult to implement for the horizontal plane. Fig. 14 shows a structure suitable for all 3 planes. It consists of 6 “magnodes,” 3 above the chest and 3 beneath the back. The distal ends of the upper magnetic pickup units are connected by a “magnetic shorting” bar. The same is true for the bottom units. The 4 corner coils, A, B, C, and D are connected in series, and the winding directions are such that when energized magnetic flux will leave magnodes A and C and enter mag-
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bar (a)
IIIn\Lametic
1
(b) Fig. 14. A coil configuration capable of measuring all 3 components of the magnetic heart vector. The subject is lying on a nonmagnetic bed (not shown). From the reciprocal point of view, energizing coils A, B, C, and D in part (a) will result in a uniform magnetic flux in the heart region directed from foot to head and inducing the y magnetovectorcardiographic lead. With an appropriate pivot on the bed, the subject can be rotated 90 degrees so the magnetic flux passes from right to left, inducing an x directed lead. Energizing coils E and F will result in a z directed lead, as shown in (b).
nodes B and D. Magnodes E and F are not energized. The resulting magnetic flux distribution is sketched in Fig. 14, a. At the structure’s center the magnetic field distribution is directed from head to foot and is quite uniform. The induced lead field current flows in planes perpendicular to the magnetic flux, i.e., the subject’s
“horizontal” plane. By rotating the subject 90 degrees, still lying on his back, the lead field current will lie in sagittal planes. A magnetic flux distribution directed from front to back and uniform in the heart region is generated by energizing coils E and F such that flux leaves E and enters F. This induces lead field current in the
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pick-up 0
(b)
Fig. 15. The “single coil lead” of our present magnetocardiograph. (a), The lead field current for a single pickup unit flows in circles centered under the pickup. The lead field strength is zero at the center and increases with radius a so long as a is less than 4 2 d. (b), The present magnetccardiograph has two pickup units 20 cm. apart. In the records of Fig. 16, coil A is placed over the heart region (fifth intercostal space and 2 cm. left of the sternal margin) and coil B is beyond the left boundary of the torso. Here the influence of coil B on the lead field in the heart region is small and the lead field will be approximately that described in (a). This lead is sensitive primarily to tangential EMF’s.
Fig. 16. A test of the influence of coil B. Coil A remains centered over the heart, while B is moved from the left side location to a location over the neck, right side, and abdomen. The magnetocardiogram obtained at each position for a normal subject shows little change. This was true for all persons (5) so tested. In every subject a record taken with coil B over the right side was compared to that obtained with coil B over the left side. There were no large discrepancies. The S-T segment depression is due to the poor (0.3 cycle per second) low frequency response of the magnetocardiogram.
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Fig. 17. Magnetocardiograms obtained with a magnetic lead that emphasizes tangential EMF’s. The first column shows 4 subjects from a series of 20 with the magnetocardiograms ordered from smallest to largest. The second column shows the 4 (out of 20) subjects with heart disease for whom the single coil lead deflections were most abnormal. The ECG’s were obtained with the axial lead system. All records are at 50 mm. per second and the ECG’s are at 10 mm. per millivolt. All magnetocardiograms are taken at the same gain as determined by a calibration coil.
frontal plane. If desired, all 3 leads could be obtained simultaneously by the use of ten coils. The arrangement of these 10 coils is shown schematically in Fig. 14, c. Some preliminary measurements of tangential EMF’s. A pickup unit in our present magnetocardiograph consists of a 1.6 cm. diameter ferrite rod 30 cm. long, capped on each end with a ferrite disk 6 cm, in diameter. A pickup coil of 5,000 turns is wrapped around the ferrite rod. Fig. 1.5,a, shows such a unit over a homogeneous resistive slab with a top boundary (“chest”) and a bottom boundary (“back”), but no side boundaries. It is easily shown” that the induced lead fieId current will flow in circles around an axis perpendicular to the front (and back) boundaries and centered underneath the pickup unit. The circular lead field shape is but little altered
by the boundaries corresponding to the torso sides, top and bottom,12 or consideration of the resistivity differences between heart and lung. This “magnetic lead” thus measures tangential EMF components lying in frontal planes. The present magnetocardiograph,13 designed primarily to duplicate ECG’s, has two such pickup units 20 cm. apart.* The above “single coil lead” is approximated by placing the heart under one of the two coils (labeled A in Fig. 15, b) with the other (labeled B in Fig. 15, b) positioned beyond *There are actually four units. Two of these are used only to cancel interfering fields and are suilidentl~ far from the heart that they can he ignored with regard to the cardiac magnetic field. The need to cancel interference also explains why the “tingle coil lead” ie not realized by removing coil B of Fig. 15. b, entirely. When the heart is centered between the two coils it lies in a roughly uniform lead field and hence the magnetocardiograms should be comparable to ECG’s obtained with vectorcardiographic leads.
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the left side of the torso. Fig. 16 shows a test of the influence of coil B, made by rotating the subject (the specially made bed had a pivot point for this purpose) such that coil A remained fixed over the heart, and coil B assumed positions over the left side, the head, the right side, and the abdomen. If the influence of coil B were completely negligible, the magnetocardiograms for the four positions would be identical. The observed change was on the order of 5 to 15 per cent. Fig. 17 shows magnetocardiograms obtained for the “single coil lead,” i.e., frontal plane tangential EMF’s, along with x, y, and z lead ECG’s (axial system). The first column of four records are from a group of 20 normal subjects. Fifteen normal subjects had entirely upright QRS deflections, with 5 having a small negative terminal deflection (e.g., F. B.). The smallest amplitude normal magnetocardiogram was from subject B. C. and the largest from F. B. From a group of 20 subjects with heart disease, 4 had strikingly abnormal deflections for the single coil lead. These are shown in the second column of Fig. 17. The magnetocardiogram for subject M. Pf. with right ventricular enlargement shows a large negative terminal deflection in addition to a larger than normal upright deflection. Subjects J. F. and R. C. have aortic insufficiency (LVE). Here the magnetic record amplitude has increased much more markedly than the electrocardiographic voltages. For infarct subject C. G., the magnetic deflection was entirely negative. Summary
Records of the magnetic field due to the heart can be obtained in a hospital environment without the use of a magnetically shielded room. It is possible to build a magnetocardiograph sensitive primarily to the tangential components of the heart’s EMF’s. This is in contrast to ECG’s where the radial component is emphasized and usually masks any tangential components. Tangential EMF components lying in frontal planes cause current to circulate around the front-to-back (z) axis, and can be assigned a vector direction along this axis. Similarly, tangential EMF’s in sagittal and horizontal planes can be associated
February,
I.
1970
with x and y directed vectors. The vector sum of these three components is the spatial “magnetic heart vector.” The magnetic heart vector is conceptually similar to, and can be displayed using the same techniques as, the “heart vector” of electrovectorcardiography but is of radically different interpretation. Ideal magnetocardiographic leads, analogous to ideal electrovectorcardiographic leads, are defined in terms of the lead fields produced. Our present magnetocardiograph, while not specifically designed to implement the ideas of this paper, does give evidence that there are some tangentially oriented EMF components in persons without heart disease, and often much larger tangential EMF’s in persons with heart disease. REFERENCES 1. Baule, G., and McFee, R.: Detection of the magnetic field of the heart, AM. HEART J. 55:95, 1963. 2. Safonov, Y. D., and Provotorov, V. M.: Method of recording the magnetic field of the heart (magnetocardiography), Bull. Exper. Biol. Med. 64:1022, 1967. 3. Cohen, D.: Magnetic fields around the torso: Production by electrical activity of the human heart, Science 156:652, 1967. 4. Rush, S., Abildskov, J. A., and McFee, R.: Resistivity of body tissues at low frequencies, Circulation Res. 12:40, 1963. L. A., and Baker, L. E.: The specific 5. Geddes, resistance of biological material, Med. & Biol. Eng. 5:271, 1967. 6. Brady, D. A.: A theoretic analysis of intercavitary blood mass influence on the electrocardiogram. Circulation Res. 4:731. 1956. 7. McFee, R.,‘and Rush,‘S.: Qualitative effects of thoracic resistivity variations on the interpretation of electrocardiograms: The low resistance surface layer, AM. HEART J. 76:48, 1968. 8. McFee, R., and Johnston, F. D.: Electrocardiographic leads. I. Introduction, Circulation 8:554, 1953. 9. McFee, R., and Johnston, F. D.: Electrocardiographic leads. II. Analysis, Circulation 9:255, 1954. R., and Johnston, F. D.: Electrocardio10. McFee, graphic leads. III. Synthesis, Circulation 9:868, 1954. 11. Baule, G., and McFee, R.: Theory of magnetic detection of the heart’s electrical activity, J. Appl. Phys. 36:2066, 196.5. 12. Rov._ T. K.: Experimental study on the magnetic field of the- human heart, Master’s the& Syracuse University, Department of Electrical Engineering, March, 1969. 13. Baule, G.: Instrumentation for measuring the heart’s magnetic field, Trans. New York Acad. SC. 27:689, 1965.
heart
vector
Gerhard M. Baule, Ph.D.* Richard McFee, Ph.D. Syracuse, N. Y.
E
lectromotive forces (EMF) in the heart produce currents in the torso which set up a weak external magnetic field. This field can be measured by the use of pickup coils. l-3 A major problem has been the presence of interfering fields from motors and other electrical equipment hundreds of times stronger than the peak field due to the heart (about one millionth of the earth’s field). However, by the use of additional coils fairly distant from the heart, this interference can be cancelled out to a considerable extent. With our present “magnetocardiograph” we are able to measure the heart’s magnetic field in a hospital environment (New York State Upstate Medical Center) without the use of a magnetically shielded room. These records are several times noisier than average conventional electrocardiograms (ECG’s). Averaging 2.5 to 100 complexes provides records comparable in “cleanliness” to ECG’s. Fig. 1 shows an unaveraged magnetocardiogram along with the noise reduction achieved by averaging. We have been using a coil arrangement intended to provide magnetocardiograms similar in form to conventional x- and y-lead ECG’s. This was done primarily to establish that the magnetic records were
not artifacts. A great deal of experimentation has now shown beyond doubt that the magnetocardiographic records reflect variations in the magnetic fields set up by currents induced by the heart’s EMF’s. Magnetocardiograms obtained on persons without heart disease do roughly mimic the appropriate ECG’s. However, in many subjects with heart disease (LVE’s, RVE’s, infarcts) gross differences between the two types of records have been observed. This and studies of the effect of differences in conductivity between heart and lung lead us to believe that with a different coil arrangement, magnetocardiograph y might furnish diagnostic data not present in the ECG. The heart is almost surrounded by lung, whose electrical resistivity considerably exceeds that of the cardiac muscle and enclosed blood masses. Reported resistivity values are 2,000 ohms per centimeter for lung tissue, 400 ohms per centimeter for ventricular muscle,t and 160 ohms per centimeter for blood.4*5 One result of these differences is that the heart and blood offer relatively low electrical resistance paths to “tangential” EMF’s, i.e., electromotive surfaces so oriented that a vector perpendicular to them is directed tangentially
From the Department of Electrical Engineering. Syracuse This work was supported by Research Grant HE-06971 of Received for publication April 10. 1969. *Reprint requests to: Dr. Baule. Department of Electrical N. Y. 13210. tVentricular muscle resistivity is anisotropic. being about per centimeter across the fibers. The t%we, 400 ohms
Vol. 79, No. 2, pp. 223-236
February, 1970
University. the National Engineering,
Syracuse. N. Y. 13210. Heart Institute, National Syracuse
250 ohms per centimeter per centimeter, ia used
University,
Institutes
131 Hinds
in the fiber direction aa a rough “lumped”
Hall,
of Health. Syracuse.
and 550 ohms average.
American Heart Journal
223
224
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.4nter. Heart 1. Fcbrmwy. 1970
Fig. 1. Signal averaging. The top record shows three unaveraged complexes. The photograph on the bottom shows 25 and 128 averaged complexes. These records were obtained in a room in the New York State Upstate Medical Center some 20 meters from 30 large electric motors. The output of the coils has been integrated so the deflections register the magnetic flux and not the rate change of flux.
elemental
dipole
layers
Fig. 2. A tangential and a radial EMF. Each elemental electromotive surface is represented by a vector perpendicular to its surface. The terms tangential and radial refer to the vector direction. The vector for a radial EMF is coincidentwith a line from the heart’s center to its periphery. The vector for a tangential EMF is perpendicular to such a line.
with respect to the heart’s outer surface (Fig. 2). Thus large circulating currents and magnetic fields will be produced by such tangential EMF’s. In contrast, current flow from radial EMF components will be inhibited by the high resistance
of the lung. Given equal radial and tangential components, the latter will cause the larger magnetic field. This situation is the opposite to that found in conventional ECG leads where, because of the low resistivity of blood relative to heart muscle, radial EMF’s are emphasized (“Brody” effect).6 The net result is that magnetocardiographic leads tend to emphasize the tangentially oriented EMF’s, which are usually masked in conventional electrocardiographic leads by the radial EMF’s. In addition, the magnetic measurements can be expressed as a “magnetic heart vector” analogous to the “heart vector” of vectorcardiography, but radically different in interpretation. The latter part of the paper discusses magnetocardiography from the reciprocal or “lead field” point of view. Here the concept of ideal magnetovectorcardiographic leads, analogous to ideal electrovectorcardiographic leads, is introduced. A magnetic apparatus design suitable for mag-
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225
Quadripalar Magnetic Flux Distribution (bl
(a) Fig. 3. Magnetic flux distributions in one plane only.
HOMOGENEOUS MODEL
for one and two current loops. The magnetic flux distribution
INSULATING LUNG MODEL
is sketched
HIGH RESISTIVIT Y LUNG MODEL
enters chest (a)
(b)
Fig. 4. Current flow and magnetic field distributions. Each model shows a tangential electromotive surface. For the homogeneous model on the top of a the current flow consists of oppositely directed pairs of loops and the magnetic flux will be of the form shown in Fig. 3, b. This magnetic field is sketched in relation to the torso in (4) (bottom). If the lung is assumed to be an insulator, the tangential EMS will cause unidirectional current loops resulting in magnetic flux of the form shown in Fig. 3, a, and again sketched in (b).
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netovectorcardiography is shown. Magnetovectorcardiograms will share one of the clinically important features of vectorcardiograms, namely that given a welldesigned lead system, accurate knowledge of the anatomical location of the heart is unnecessary. Elementary
theory
of magnetic
leads
The elementary source of magnetic flux is a current loop. Fig. 3, a, shows such a loop and its magnetic field. At distances large compared to the size of the loop (in practice, one or two loop diameters), the shape of the magnetic field follows the well-known “dipole” formula. For example, the magnitude of the magnetic flux goes down with the cube of the distance from the loop. As a magnetic dipole source, the exact shape of the current loop is unimportant and its dipole strength is IA where I is the loop current and A is the area enclosed by the loop. Two current loops in close proximity, equal in magnitude of strength but with opposing current directions, form a quadripole source of magnetic flux. Such a configuration is shown in Fig. 3, b, along with a sketch of the quadripole magnetic field. At remote points this field diminishes with the fourth power of the distance to the loops. Consider two extremes of simplified heart-lung models. In the first, all resistivities are considered equal, and in the second the lung is considered to be a perfect insulator. The difference in resistivity between muscle and blood will be ignored. Fig. 4, a and b, illustrate these two cases, and in each is shown an electromotive surface located in the outer part of the heart and perpendicular to the heart’s periphery. For the homogeneous model (Fig. 4, a), the electromotive surface (EMS) causes a dipolar electric current flow throughout the heart and torso. This current distribution is a “smeared” form of the two current loops shown in Fig. 3, b, and the resulting magnetic field will be of the magnetic quadripolar type. For the orientations of Fig. 4, a, magnetic flux will leave the chest on the left side of the heart, and re-enter on the right side. In Fig. 4, b, all current flow is within the heart, since the lung is assumed to be an insulator. There will be no voltage drops
anywhere on the body surface,* i.e., the ECG will be silent. This current flow distribution resembles that of the single current loop of Fig. 3, a, and will give rise to a dipolar magnetic field. Magnetic flux will leave the chest over the heart and re-enter the chest in a circular region around the heart. When the lung resistivity is higher than heart and blood resistivities, but not infinite, the current distribution and magnetic field distributions can be considered, as a first approximation, to be a mixture of the two extreme case distributions. This is illustrated in Fig. 4, c. The electromotive surface in the ventricular walls is seldom purely tangential. It is often oblique, as shown in Fig. 5, a, with a radial component parallel to the epicardial surface, as well as a tangential component from endocardium to epicardium. Such an EMS can be replaced by an equivalent surface consisting of a radial component and a tangential component, as is shown in Fig. 5, b.t The component coincident with the heart-lung boundary will not cause currents to circulate within the heart, and will not give rise to the dipolar form of magnetic field. Note also that an EMS whose entire boundary lies on the epicardium (Fig. 5, c) has no tangential component since it can be replaced by an equivalent surface entirely coincident with the heart-lung boundary. An EMS in the center of the heart, as might arise for example from septal depolarization, will cause a quadripolar rather than a dipolar magnetic field even assuming the lung to be an insulator (Fig. 6, a). As the EMS is moved from the center to the periphery of the heart maintaining an orientation perpendicular to the periphery, the opposing loop pairs of current flow change to unidirectional loops. The magnetic field will change from the quadripolar to the dipolar form. In Fig. 6, b, where the EMS lies to the right of center, the current circulates clockwise, and the magnetic field is directed into the paper. In Fig. 6, C, the EMS lies to the left of center, the current circulates counterclockwise, and the mag*Assuming the muscle layer around the torso is not an insulator. tThe complete equivalency of the two surfaces follows from a theorem by Gauss. A completely closed uniform electromotive surface causes no current flow. This is true even for a nonhomogeneous and nonisotropic volume conductor.
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(b)
(al obliqye
ems
Fig. 5. The decomposition of a typical activation shown in (c) has no tangential component.
front
radial
and tangential
components.
(b)
(a) Fig. 6. Current flow located in the center,
into
wave
front
(cl
in the heart, when the lung conductivity right side, and left side of the heart.
netic field points out of the paper. Thus the EMS to the right of center will give a deflection opposite to that left of center. This is in contrast to a vectorcardiographic lead (ideally sensitive only to strength and orientation of an EMS) which will give the same deflection for the EMS illustrating the three cases. It is possible to build a magnetic pickup system sensitive to. the dipole magnetic field but not to the quadripole field. From the previous considerations, it is seen that such a pickup configuration will be sensitive primarily to the tangential components of the heart’s electromotive surfaces, and that this sensitivity will be in proportion to the distance of the EMS from the center of the heart. Such a magnetocardiograph should provide information that differs substantially from that found with electrocardiography, where the tangential com-
The
is considered
negligible
for elemental
EMF’s
ponents of the EMS are suppressed and the radial components are accentuated due to the intracavitary blood resistivity being lower than the ventricular muscle resistivity (“Brady” effect). We parenthetically note one other difference, The voltage induced in electric leads is strongly influenced by the low resistivity muscle layer around the torso.’ This is not true for magnetic leads. Fig. 7 shows one possible apparatus for picking up the magnetic dipole and rejecting the magnetic quadripole due to current loops lying in the frontal plane. The subject lies between two fairly large high permeability disks. The disks are magnetically connected by the remainder of the high permeability structure. The two pickup coils are wound in the same direction. In Fig. 7, b, a single current loop is used to represent a magnetic dipole source and the
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high permeobility ( iron or ferrite
moteriol
magnetic flux lines
1
single current loop in frontal plan+!
I
two
opposing
current
loops
\
d (b) Fig. 7. An example of a magnetic pickup assembly that will register a dipolar magnetic field and not register a quadripolar magnetic field. For clarity, the coils have been omitted from (b) and (c). The single loop of (a) causes flux through coils causing an output voltage. For two opposing loops there is no flux through the coils.
(a)
(b)
VCG reference
system
(cl
current loop circulating about Y axis ( in horizontal plane )
(e)
z
current loop circulating about Z axis (in frontal plane 1
current loop circulating about X axis (in sagittal plane 1
(f)
-?
(d)
(91
7
Y vector I of loop
Y to plane
components vector V
3
of
components of loop
3
Fig. 8. The magnetic heart vector. Parts (b), (c), and (d) show current loops in three orthogonal planes. Each is represented by a vector directed along the axis of circulation. The vector direction is determined using the “right-hand rule.” The vector strength is proportional to the current strength times its distance from the axis of circulation (analogous to torque in mechanics). Part (e) shows a spatial current loop (taken 45 degrees to each axis) and its vector representation. The components, vector and loop, are shown in (f) and (g).
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Magnetic
(0) r Fig.
9. An
example
illustrating
the use of reciprocity
lines of magnetic flux due to this source as they travel through the magnetic structure are sketched. Flux travels through the cores of the two coils and induces additive voltages. In Fig. 7, c, two loops of current are used to represent a magnetic quadripole source. The lines of magnetic flux are again sketched. No flux passes through the windings and hence there is no output. the magnetic
heart
vector
The heart vector of electrovectorcardiography has three components; one along the x axis (right side to left side), one along the y axis (head to foot), and one along the z axis (front to back). The magnetic heart vector may also be viewed qualitatively as arising from three components: a current circulating in the heart about the x axis and two other currents circulating about the y and z axes, respectively, where each of the circulating currents is established by tangential components of the heart’s EMF’s. This is shown in Fig. 8, b through d. These three circulating currents may each be represented by a vector along the axis of circulation with a magnitude proportional to the strength of the circulation and a polarity determined according to the right-hand rule.* The sum of these three vector components is the total spatial magnetic heart vector. For example, Fig. 8, e, shows a current loop 45 degrees to all *Curl
the fingers of the right hand and extend the thumb. Consider the fingernails to be arrowheads. When the curled fingers point in the direction of current flow. the thumb points in the direction of the loop vector.
heart vector
229
(bl for an electrocardiographic
lead.
axes and its representative vector V. Fig. 8, f, shows the three components of vector V, namely V,, 1/‘,, and Irl. These components represent current flows around the x, y, and z axes, respectively. Since vector V was chosen to have equal lengths on all three axes, the three component current loops are of equal strength as shown in Fig. 8, g. As in vectorcardiography, the vector representing the magnetic dipole current will change in direction and strength throughout the depolarization and repolarization cycle. Any of the display systems of vectorcardiography can be applied to magnetovectorcardiography. Magnetic heart vector lead jields. The interpretation of magnetocardiograms, and the design of appropriate magnetic pickup configurations, is greatly simplified by the use of the reciprocal or “lead field” method.s-10 The extension of the electrocardiographic lead field method to magnetocardiography is given in reference 9. A brief nonmathematical review is given here. To illustrate the lead field concept as used in electrocardiography, consider a y-lead ECG (Fig. 9). Fig. 9, a, shows the electromotive surface of the heart across which there is a uniform potential difference e. Due to this EMS, there is a voltage v across the two wires which go to the recorder input. Because of the complicated boundary conditions the visualization of how voltage v is related to the EMS and the location of the electrodes upon the body is not always easy. Fig. 8, b, illustrates the reciprocal or lead field method. The
230
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across
ems
Heart
February,
magnetic flux due to current I 1 The body is “transparent” to this flux )
1. 1970
current flow induced by magnetic flux I current intercepted by the ems is i
+r -1
v -=e
(a) Fig. would
10. An example be magnetically
i
I
(b 1 illustrating induced
(cl
the use of reciprocity for a magnetic lead. The lead field is the current that in the torso if a fluctuating current I were passed through the pickup windings.
potential e across the electromotive surface is first set to zero. A current I is then injected into the lead that was previously labeled “minus” and a current I removed from the lead that was previously labeled “plus.” The distribution of this current as it flows through the body is the lead field. A certain percentage of the injected current, denoted by i, is intercepted by the electromotive surface. By the reciprocity theorem it can be shown that the ratio of the intercepted current to the injected current is identical to the ratio of the voltage at the recorder input to the voltage across the EMS, that is, v-=- i e I The advantage to this method of attack is that it is easy to visualize the lines of current flow or “lead field” within the body. In magnetocardiography we are interested in the voltage produced across the pickup coil winding as a result of the EMS of the heart. This relation can be obtained by putting a current I into the pickup coil and finding the resultant current i intercepted by the electrotiotive surface under consideration. The magnetic assembly of Fig. 7 is used as an example. To mqke a direct evaluation of the voltage across the coil winding, one must first find the current field in the body
which is produced by the electromotive surface, then find the magnetic field due to this current, taking into account the fact that it will be distorted by the high permeability iron of the pickup assembly. The portion of the magnetic field passing through the winding will induce a voltage in it which is proportional to the rate change of the field. In the reciprocal method we go through a sequence of steps illustrated in Fig. 10. The electromotive potential e of the heart (Fig. 10, a) is first set equal to zero. A fluctuating current I is (conceptually) injected into the pickup winding. This current causes a magnetic flux to emanate from the disk above the chest, to flow through the torso, and enter the disk beneath the back.* This flow of magnetic flux through the torso induces “eddy” currents therein, as shown by the circular flow lines in Fig. 10, c. (The secondary magnetic field caused by the eddy currents is negligible for typical tissue resistivities.) These induced currents are proportional to the rate change of flux through the torso and thus require that the initial injected current I be changing with time, if there is not to be a zero result. Some of this induced current, denoted by i, is in*The
permeability of the body tissues (space. i.e.. the torsa is “transparent”
differs little to magnetic
from flux.
. free
Magnetic
Volume 79 Number 2
. ZiEg
ideal x vcg lead
heart vector
231
cross section
ideol mvcg leod
(b)
ideal y vcg lead (0)
Fig. 11. Ideal magnetovectorcardiographic leadfields.For comparison, (a) showsthe uniform leadfieldsassociated with idealelectrovectorcardiographic leads.The leadfield of an idealmagnetovectorcardiographic lead (b) consistsof circularcurrent flow aroundan axis and confinedto planesperpendicular to that axis.The lead field strength is zero at the axis and increases in proportion to the distancefrom it. The strength doesnot dependon the directionfrom the axis,i.e., it is the samefor A, B, C, andD of (bf.
tercepted by the electromotive surface. By use of the reciprocity theorem the ratio of the intercepted current i to the current I fed into the pickup coil is the same as the ratio of the voltage w measured across the pickup coil due to the potential e across the electromotive surface of the heart. The induced currents then constitute the lead field which is produced magnetically. This lead field is determined by anatomical boundaries between tissues of different resistivities (including the outside torso-air boundary), and by the magnetic pickup configuration. This statement is analogous to the statement that the lead field in electrocardiography is determined by the torso boundaries and the number and location of electrodes placed on the torso. Because of this close analogy, the disks of the pickup units from which magnetic flux leaves or enters might well be called “magnodes”; thus the number and location of the magnodes and the torso geometry determine the lead field. Both arrangements of electrodes and arrangements of magnodes can be characterized completely by the lead field which they produce. There is one major difference between
the lead field which can be produced by magnetic electrodes (magnodes) and those which can be produced by conventional electrodes. For electrodes, the lines of current flow must begin and end on electrodes. In contrast to this, the magnetic lead field consists of currents which swirl around without starting at surface electrodes. ‘LIdeal” lead field for magnetmectorcardiography. Since the electromotive surface representing the activation boundaries lies in the heart, electrocardiographic or magnetocardiographic lead fields need only be known within this region. The ideal electrovectorcardiographic lead is one which is uniform throughout the heart region. Three such leads, orthogonal and of equal strength, are required. Ideal x and y vectorcardiographic leads are illustrated in Fig. 11, a. Due to their uniformity, they are sensitive only to the strength and orientation of an elemental electromotive surface, but not to its position, i.e., there are no “proximity effects.” A magnetovectorcardiographic lead field will be considered ideal if it consists of essentially circular flow lines, zero on an axis through the center of the heart, and
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magnetic field in the heart region. Note that this was the case for the example of Figs. 7 and 10. In the presence of a uniform (time-varying) magnetic field, the heartlung boundary will result in circular lead field flow lines centered in the heart, and lying in planes perpendicular to the magnetic flux. Using Faraday’s law that the line integral of the electric force around a closed loop is equal to the rate change of the enclosed flux f E . de = d/dt f JB * dA, it can be seen that the lead field strength increases in proportion to the distance from the heart center. Since B is constant (Fig. 13), the enclosed flux for a loop of radius a is (?ra2)P,and thus:
2
X
Y v?
12. Three
Fig. heart
x
orthogonal
leads
for
the
magnetic
vector.
UNIFORM MAGNETIC FLUX x x x Y x
(6) x
x x Y
x Y Fig. ideal
x
x
x
x
13. A uniform magnetic magnetovectorcardiographic
x flux
x will induce lead field.
an
increasing linearly in strength towards the periphery (Fig. 11, b). This lead is sensitive only to tangentially oriented elemental electromotive surfaces. There are no proximity effects in the sense that the output due to a tangential EMS will depend only on its distance from the axis, e.g., surfaces A, B, C, and D of Fig. 11, b, will give equal outputs. For a complete magnetovectorcardiogram, three such lead fields are needed, mutually orthogonal and of equal strength. This is illustrated in Fig. 12. To the extent that the heart can be represented by a homogeneous sphere imbedded in a high resistivity lung, there is a simple criterion for generating ideal magnetovectorcardiographic leads. Considered reciprocally, current into the coils of the magnetic pickup should produce a uniform
where p is the resistivity of the “heart.” Note that the exact anatomical location of the heart need not be known for the lead field to center itself. Self-centering will occur so long as the lung conductivity is negligible and the heart may be considered to be spherically homogeneous and to lie within the region of uniformity of the magnetic flux produced by the reciprocally energized coils. This is analogous to the case for ideal vectorcardiographic leads, where lead design can make the location of the heart noncritical by insuring a sufficiently large region of uniform lead field current. Design of a magnetic pickup suitable for magnetovectorcardiography. The magnetic pickup configuration previously discussed (Fig. 7) is suitable for inducing an ideal magnetovectorcardiographic lead field in the frontal plane, and by turning the subject on his side, the sagittal plane. It would be difficult to implement for the horizontal plane. Fig. 14 shows a structure suitable for all 3 planes. It consists of 6 “magnodes,” 3 above the chest and 3 beneath the back. The distal ends of the upper magnetic pickup units are connected by a “magnetic shorting” bar. The same is true for the bottom units. The 4 corner coils, A, B, C, and D are connected in series, and the winding directions are such that when energized magnetic flux will leave magnodes A and C and enter mag-
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bar (a)
IIIn\Lametic
1
(b) Fig. 14. A coil configuration capable of measuring all 3 components of the magnetic heart vector. The subject is lying on a nonmagnetic bed (not shown). From the reciprocal point of view, energizing coils A, B, C, and D in part (a) will result in a uniform magnetic flux in the heart region directed from foot to head and inducing the y magnetovectorcardiographic lead. With an appropriate pivot on the bed, the subject can be rotated 90 degrees so the magnetic flux passes from right to left, inducing an x directed lead. Energizing coils E and F will result in a z directed lead, as shown in (b).
nodes B and D. Magnodes E and F are not energized. The resulting magnetic flux distribution is sketched in Fig. 14, a. At the structure’s center the magnetic field distribution is directed from head to foot and is quite uniform. The induced lead field current flows in planes perpendicular to the magnetic flux, i.e., the subject’s
“horizontal” plane. By rotating the subject 90 degrees, still lying on his back, the lead field current will lie in sagittal planes. A magnetic flux distribution directed from front to back and uniform in the heart region is generated by energizing coils E and F such that flux leaves E and enters F. This induces lead field current in the
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pick-up 0
(b)
Fig. 15. The “single coil lead” of our present magnetocardiograph. (a), The lead field current for a single pickup unit flows in circles centered under the pickup. The lead field strength is zero at the center and increases with radius a so long as a is less than 4 2 d. (b), The present magnetccardiograph has two pickup units 20 cm. apart. In the records of Fig. 16, coil A is placed over the heart region (fifth intercostal space and 2 cm. left of the sternal margin) and coil B is beyond the left boundary of the torso. Here the influence of coil B on the lead field in the heart region is small and the lead field will be approximately that described in (a). This lead is sensitive primarily to tangential EMF’s.
Fig. 16. A test of the influence of coil B. Coil A remains centered over the heart, while B is moved from the left side location to a location over the neck, right side, and abdomen. The magnetocardiogram obtained at each position for a normal subject shows little change. This was true for all persons (5) so tested. In every subject a record taken with coil B over the right side was compared to that obtained with coil B over the left side. There were no large discrepancies. The S-T segment depression is due to the poor (0.3 cycle per second) low frequency response of the magnetocardiogram.
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Fig. 17. Magnetocardiograms obtained with a magnetic lead that emphasizes tangential EMF’s. The first column shows 4 subjects from a series of 20 with the magnetocardiograms ordered from smallest to largest. The second column shows the 4 (out of 20) subjects with heart disease for whom the single coil lead deflections were most abnormal. The ECG’s were obtained with the axial lead system. All records are at 50 mm. per second and the ECG’s are at 10 mm. per millivolt. All magnetocardiograms are taken at the same gain as determined by a calibration coil.
frontal plane. If desired, all 3 leads could be obtained simultaneously by the use of ten coils. The arrangement of these 10 coils is shown schematically in Fig. 14, c. Some preliminary measurements of tangential EMF’s. A pickup unit in our present magnetocardiograph consists of a 1.6 cm. diameter ferrite rod 30 cm. long, capped on each end with a ferrite disk 6 cm, in diameter. A pickup coil of 5,000 turns is wrapped around the ferrite rod. Fig. 1.5,a, shows such a unit over a homogeneous resistive slab with a top boundary (“chest”) and a bottom boundary (“back”), but no side boundaries. It is easily shown” that the induced lead fieId current will flow in circles around an axis perpendicular to the front (and back) boundaries and centered underneath the pickup unit. The circular lead field shape is but little altered
by the boundaries corresponding to the torso sides, top and bottom,12 or consideration of the resistivity differences between heart and lung. This “magnetic lead” thus measures tangential EMF components lying in frontal planes. The present magnetocardiograph,13 designed primarily to duplicate ECG’s, has two such pickup units 20 cm. apart.* The above “single coil lead” is approximated by placing the heart under one of the two coils (labeled A in Fig. 15, b) with the other (labeled B in Fig. 15, b) positioned beyond *There are actually four units. Two of these are used only to cancel interfering fields and are suilidentl~ far from the heart that they can he ignored with regard to the cardiac magnetic field. The need to cancel interference also explains why the “tingle coil lead” ie not realized by removing coil B of Fig. 15. b, entirely. When the heart is centered between the two coils it lies in a roughly uniform lead field and hence the magnetocardiograms should be comparable to ECG’s obtained with vectorcardiographic leads.
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the left side of the torso. Fig. 16 shows a test of the influence of coil B, made by rotating the subject (the specially made bed had a pivot point for this purpose) such that coil A remained fixed over the heart, and coil B assumed positions over the left side, the head, the right side, and the abdomen. If the influence of coil B were completely negligible, the magnetocardiograms for the four positions would be identical. The observed change was on the order of 5 to 15 per cent. Fig. 17 shows magnetocardiograms obtained for the “single coil lead,” i.e., frontal plane tangential EMF’s, along with x, y, and z lead ECG’s (axial system). The first column of four records are from a group of 20 normal subjects. Fifteen normal subjects had entirely upright QRS deflections, with 5 having a small negative terminal deflection (e.g., F. B.). The smallest amplitude normal magnetocardiogram was from subject B. C. and the largest from F. B. From a group of 20 subjects with heart disease, 4 had strikingly abnormal deflections for the single coil lead. These are shown in the second column of Fig. 17. The magnetocardiogram for subject M. Pf. with right ventricular enlargement shows a large negative terminal deflection in addition to a larger than normal upright deflection. Subjects J. F. and R. C. have aortic insufficiency (LVE). Here the magnetic record amplitude has increased much more markedly than the electrocardiographic voltages. For infarct subject C. G., the magnetic deflection was entirely negative. Summary
Records of the magnetic field due to the heart can be obtained in a hospital environment without the use of a magnetically shielded room. It is possible to build a magnetocardiograph sensitive primarily to the tangential components of the heart’s EMF’s. This is in contrast to ECG’s where the radial component is emphasized and usually masks any tangential components. Tangential EMF components lying in frontal planes cause current to circulate around the front-to-back (z) axis, and can be assigned a vector direction along this axis. Similarly, tangential EMF’s in sagittal and horizontal planes can be associated
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with x and y directed vectors. The vector sum of these three components is the spatial “magnetic heart vector.” The magnetic heart vector is conceptually similar to, and can be displayed using the same techniques as, the “heart vector” of electrovectorcardiography but is of radically different interpretation. Ideal magnetocardiographic leads, analogous to ideal electrovectorcardiographic leads, are defined in terms of the lead fields produced. Our present magnetocardiograph, while not specifically designed to implement the ideas of this paper, does give evidence that there are some tangentially oriented EMF components in persons without heart disease, and often much larger tangential EMF’s in persons with heart disease. REFERENCES 1. Baule, G., and McFee, R.: Detection of the magnetic field of the heart, AM. HEART J. 55:95, 1963. 2. Safonov, Y. D., and Provotorov, V. M.: Method of recording the magnetic field of the heart (magnetocardiography), Bull. Exper. Biol. Med. 64:1022, 1967. 3. Cohen, D.: Magnetic fields around the torso: Production by electrical activity of the human heart, Science 156:652, 1967. 4. Rush, S., Abildskov, J. A., and McFee, R.: Resistivity of body tissues at low frequencies, Circulation Res. 12:40, 1963. L. A., and Baker, L. E.: The specific 5. Geddes, resistance of biological material, Med. & Biol. Eng. 5:271, 1967. 6. Brady, D. A.: A theoretic analysis of intercavitary blood mass influence on the electrocardiogram. Circulation Res. 4:731. 1956. 7. McFee, R.,‘and Rush,‘S.: Qualitative effects of thoracic resistivity variations on the interpretation of electrocardiograms: The low resistance surface layer, AM. HEART J. 76:48, 1968. 8. McFee, R., and Johnston, F. D.: Electrocardiographic leads. I. Introduction, Circulation 8:554, 1953. 9. McFee, R., and Johnston, F. D.: Electrocardiographic leads. II. Analysis, Circulation 9:255, 1954. R., and Johnston, F. D.: Electrocardio10. McFee, graphic leads. III. Synthesis, Circulation 9:868, 1954. 11. Baule, G., and McFee, R.: Theory of magnetic detection of the heart’s electrical activity, J. Appl. Phys. 36:2066, 196.5. 12. Rov._ T. K.: Experimental study on the magnetic field of the- human heart, Master’s the& Syracuse University, Department of Electrical Engineering, March, 1969. 13. Baule, G.: Instrumentation for measuring the heart’s magnetic field, Trans. New York Acad. SC. 27:689, 1965.