Einthoven Triangle Research Articles

Comparison of two methods for electrocardiographic analysis in Gallega sheep

The basal electrocardiographic parameters in 37 adult Gallega breed ewes were studied by comparing two electrode placing systems; the classical system (applying the Einthoven's triangle in the frontal plane) and the experimental system in which the electrodes are placed on the back of the neck (red electrode), in the sacrum area (yellow electrode), in the area beneath the breastbone (green electrode) and on the skin fold of the knee joint of the rear right leg (black electrode). The second derivation (DII with both systems was chosen in order to measure and study the amplitude and duration of P and T waves, QRS complex, P-R, Q-T, and R-R intervals and S-T segment as well as the frequency, axis (using Derivations I and III) and the heart rhythms. With regard to duration in seconds of the waves, complexes, segments and intervals we found no significant differences between the two methods. Significant differences in P-wave amplitude, which was bigger in the experimental method, were seen. There was a greater variability in the morphology of the QRS complex in the classical method than in the experimental method. The heart rhythms found in Gallega ewes in the classical and experimental methods were as follows: sinus rhythm was the most common followed by phasic sinus arrhythmia, and finally sinus tachycardia. The average value obtained for the cardiac frequency using the classical method was 119.7 beats per min and 116.2 beats per min using the experimental method. As for the heart axis, the average values were −165 ° and −137 ° with the classic and the experimental layout, respectively. Despite the subcutaneous fixing of the electrodes in the experimental system, their application points are appropriately related to the position of the heart. This, together with there being points subject to fewer variations related to position, to layout regularity and to the amplitude needed for the correct measurement of all parameters as well as the fulfilment of the Einthoven law, makes the experimental method ideal for electrocardiograms in sheep.

The use of atrial electrograms in the diagnosis of supraventricular dysrhythmias.

Temporary epicardial pacing wires are frequently used to perform atrial electrograms in patients after cardiac surgery. This article reviews Einthoven's triangle and describes a method of obtaining and evaluating atrial electrograms. Examples of specific dysrhythmias and nursing diagnoses relating to atrial wires are also described.

Vector analysis of auditory evoked potential in the brain stem

The planar vectocardiographic method was applied to auditory evoked potential in the brain stem (BAEP). It was assumed that the derivations Cz, A1 and A2 form an Einthoven triangle. BAEP were averaged simultaneously on three channels. It was assumed that if Cz were linked to A1 = lead I, Cz to A2 = II and A1 to A2 = III, then I + III = II and I + III - II = 0 according to the Einthoven rule. Calculations performed in the averager memory confirmed this hypothesis. The planar vectocardiography method was then applied to BAEP with success. Its advantages are high reliability and amenability to computer analysis.

A study of the normal QRS-T angle in the frontal plane

The normal limits of A0 QRS and A0 T in the frontal plane and their relationship to each other have been defined. It has been shown that the QRS-T angle in the frontal plane is not only a function of magnitude but depends on the absolute A0QRS direction itself. As A0QRS shifts left, A0T lags behind so that when A0QRS is less than 0°C, the normal A0T is always to the right of A0QRS. A converse relationship has been demonstrated in vertical hearts. These findings should be of practical value to the interpretor of 12-lead electrocardiograms in which the Einthoven triangle defines the frontal plane. However, we are aware of the limitation of our results which are obtained from a sample of hospitalized patients with a normal cardiovascular system.

The complete heart-lead relationship in the Einthoven triangle.

The relationship between the source strength and the “manifest vector” in the Einthoven Triangle is derived for a line and a point dipole source and confirmed experimentally. The result permits the interpretation of the standard ECG leads in absolute terms and corrected for body size. The manifest vector is shown to be approximately\(\sqrt 3 \) times what it would be in an otherwise similar circular slab which circumscribes the triangle.

Left atrial rhythm: Diagnostic criteria and differentiation from nodal arrhythmias

Left atrial rhythm is characterized by a left-to-right spread of atrial depolarization. The most frequent electrocardiographic pattern of this rhythm consists of upright or isoelectric P waves in lead I and inverted P waves in lead V 6. Two additional patterns, formed by negative P waves in leads I and V 6, with or without “dome and dart” P waves in lead V 1, are less common. A negative P wave in lead V 6 is the most sensitive and, in the absence of atrial inversion, the most specific sign of left atrial rhythm. The occurrence in left atrial rhythm of upright or isoelectric P waves in lead I is explained by the limitations inherent in Einthoven's triangle. Since the effective axis of lead I in Burger's triangle is inclined from the horizontal, a vector directed from left to right frequently gives rise to an upright or isoelectric deflection in lead I. The frequent appearance of inverted P waves in leads II, III and aVF in left atrial rhythm necessitates the establishment of criteria for differential diagnosis from nodal arrhythmias. Vectorial analysis of P waves in the horizontal plane as derived from the precordial leads provides the key for differentiation. In nodal and coronary sinus rhythms the horizontal P vector is directed to the left and slightly posteriorly, giving rise to negative or isodiphasic P waves in lead V 1 and to upright P waves over the left precordial leads. In left atrial rhythm the horizontal P vector points to the right and usually anteriorly, resulting in upright P waves in the right precordial leads and in negative P waves over the left precordial leads, particularly V 6.

DIPOLE MOMENTS OF DOG, MONKEY, AND LAMB HEARTS.

The magnitude and direction of the spatial dipole moments of hearts of a dog, monkey and lamb were obtained in vivo from, multiple potentials on the body surface. A comparison between peak dipole moment and body weight in mammals showed a definite relationship. A comparison with spatial vectors calculated from the equilateral tetrahedron system showed significant differences. Graphs of instantaneous potential distributions around the chest showed that bidipolar conditions existed at certain times and locations, but the distributions were mostly unidipolar. Frontal plane angles calculated from the Einthoven triangle were about 30° too high, on the average.

An orthogonal lead system for clinical electrocardiography

E inthoven, in his early investigations of the electrocardiogram, was concerned with the influence of the orientation of the heart on the form of the complexes. His interest in this relationship led to the introduction of the concepts of the manifest vector and the Einthoven triangle. These concepts are two dimensional in character, and apply to the frontal plane. Despite this limitation, they have proved to be so useful that they are routinely employed in electrocardiography today. The value of Einthoven’s approach has been so evident that the possibility of extending it to include all three components of the manifest vector has been under consideration for many years. There are several reasons why the early research with this objective has not culminated in clinical application. The Einthoven triangle itself had, for many years, no clearly demonstrable scientific basis. This basis has since been provided by the concept of the lead vector introduced by Burger and van Milaan. Another problem has been that of obtaining the sagittal component of the heart vector from potentials induced in electrodes on the chest, close to the heart. The recently developed “lead field” concept has shown that the proximity effects can be suppressed through the use of several electrodes whose potentials are averaged. Still another obstacle has been the difficulty of determining the electrical axis in three dimensions without burdening the clinician with calculations of inordinate mathematical complexity. An answer to this problem is the use of “resolvers,” electronic instruments introduced by Schmitt’ and studied by several other investigators.2-5 It has been shown9 that the approximate mean electrical axis of the “QRS” and “T” complexes can easily be determined with these devices. These instruments can be built as compact and reliable units well adapted to the clinic.6 Because of these relatively recent developments, it is now possible to determine the electrical axis of the heart in the clinic in three rather than two dimensions. All that is required is a lead system which provides the three components of the heart vector. A great number of such orthogonal lead systems have been proposed, each with merits and deficiencies of its own. It is beyond the scope of this article to review each of them. In our opinion, even the best systems, such as Schmitt’s’ and Frank’s8 do not strike the optimum balance between accuracy and simplicity. In this report an orthogonal system is described which is intended to satisfy clinical requirements. It is designed specifi-

A geometric study of the relationship between limb leads and cardiac vector in the frontal plane

The relationship between bipolar limb leads and cardiac vector in the RLF plane was considered in five sections. 1. 1. Various Burger triangular shapes were correlated with the Einthoven triangle. Results indicated that the Einthoven triangle is inaccurate for subjects possessing Burger triangles of either scalene or isosceles shapes. As a rule, the more the Burger triangle departs from the equilateral, the more the vectorial direction, calculated in the Einthoven triangle, deviates from the true one. 2. 2. Using the criteria given in the above section, a study was made of the influence of heart vector eccentricity and length in the inaccuracy of the Einthoven triangle by means of an electrolytic model. It was observed that the inaccuracy of the Einthoven triangle was affected more by the eccentricity than by the length of the “heart vector.” Although the heart vector length also exercised an influence in this regard, the longer the vector (dipole length) the more inaccurate is the Einthoven triangle. Furthermore, the degree of inaccuracy of the Einthoven triangle, if other factors remain equal, depends not solely on the distance between the eccentric position and the geometric center, but on the position itself in the electrolytic model. 3. 3. Burger triangles were constructed directly from living toad hearts in situ, using the graphic method described by Wilson and associates. Burger triangles from toads were similar under similar conditions to those that Wilson obtained from a current dipole located on the anterior aspect of the living human thorax. Depolarization and repolarization Burger triangles from the same toads were almost identical. This suggested that the hypothesis that QRS and T vectors from the same subjects differ in length and occupy different heart regions could not be confirmed by biologic experiments, at least not on toads. 4. 4. In the fourth section a modified technique to construct a Burger triangle with coordinate scales was described. Such a triangle has some interesting features; namely, it obeys the Einthoven law, synthesizes the data of limb leads 1, 2, and 3 into a heart vector arrow within the triangle, or conversely, projects the heart vector arrow on the three sides of the triangle to yield bipolar limb lead data. 5. 5. Described in detail in the final section were two diagrams (A and B) that yielded simultaneous results for the Einthoven triangle and the “average” Burger triangle. Diagrams may also be used to convert Einthoven data into Burger data. From diagram B it is easily seen that, other factors being equal, the inaccuracy of the Einthoven triangle depends upon vectorial direction itself. In other words, the directions obtained in the Einthoven triangle are more inaccurate when referred curves are more distant from each other, less inaccurate when they approach each other, and incidently accurate when they intersect.

Clinical value of Burger's concept as applied in Frank's lead system

1. 1. In each of 156 cases, including 30 normal adults and 126 cardiac patients, vectorcardiograms were taken by three methods, i.e., Frank's, Burch's, and Grishman's methods, and standard 12-lead electrocardiograms were recorded. Burch's and Grishman's vector loops were projected into the conventional lead axes and Frank's vector loops into the lead vectors, and the patterns of ventricular complex thus obtained were compared with actual corresponding electrocardiograms. 2. 2. It was found that the patterns derived from Frank's vector loops showed a much better conformity to the actual electrocardiograms than did those from the vector loops by the other two methods. 3. 3. This good conformity of Frank's vector loops in a number of cases shows that, even though Frank's image surface was obtained from a few individuals, it is applicable to the majority, both healthy persons and cardiac patients. It suggests also the clinical usefulness of Burger's concept. 4. 4. Moreover, such conformity of Frank's vector loops increased the clinical value of his lead system of vectorcardiography. 5. 5. It was pointed out that frontal vector loops by Burch's method should theoretically conform completely with limb lead electrocardiograms regardless of whether Einthoven's triangle does or does not apply to the actual human body. The excellent conformity was also actually verified. This fact gives a strong point, in a sense, to Burch's lead system of vectorcardiography, in so far as its frontal plane is concerned.

Multipole representations of current generators in a volume conductor

As far as the potential distribution outside the current generators is concerned, any current source distribution may be replaced by a suitable collection of multipoles. If these current generators lie close to the geometrical center of the volume conductor, a central dipole is a good approximation for potentials at surface points which are at considerable distances from the center. For better accuracy and for points close to the center, additional singularities such as a central quadrupole, a central octopole, etc., should be included. Potential expressions due to such multipoles in a spherical conductor can be obtained in closed forms by means of the “interior sphere theorem”. This paper presents a method for determining successively better multipole representations of the current generators in a homogeneous conducting sphere by measuring surface potentials at a successively increasing number of points. It is shown that Einthoven's triangle and Wilson's tetrahedron in the theory of electrocardiography are first and second approximations of this method. This concept also applies to conductors of other shapes.

A study of cardiac vectors in the frontal plane

1. 1. The Einthoven triangle has been set forth in the circular form. The circular form correlates easily the polarities written in the six limb leads and the corresponding heart-vector direction in the RLF plane. 2. 2. The average QRS vector was directed toward +45 degrees in normal electrocardiograms, toward +120 degrees in right ventricular hypertrophy, and toward +15 degrees in left ventricular hypertrophy. The average QRS′ vector was directed toward +30 degrees in both complete right bundle branch block and left bundle branch block. The average QRS″ vector was directed toward −165 degrees in complete right bundle branch block, and toward −30 degrees in complete left bundle branch block. 3. 3. In normal electrocardiograms the angle formed by the QRS vector and T vector did not exceed 45 degrees. In right ventricular hypertrophy and left ventricular hypertrophy this angle could range between 0 degree and 180 degrees. In complete right bundle branch block the angle formed by the QRS′ vector and QRS″ vector usually exceeded 90 degrees; the average angle was 150 degrees. In complete left bundle branch block the angle formed by the QRS′ vector and QRS″ vector usually did not exceed 90 degrees; the average angle was 45 degrees. 4. 4. The incidence of complete right bundle branch block was 2 per cent, of which 95 per cent were of the Wilson type. The incidence of complete left bundle branch block was 1 per cent. 5. 5. The T vector could not be determined in 4 per cent of right ventricular hypertrophy and in 11 per cent of left ventricular hypertrophy. 6. 6. In the RLF plane the general direction of activation of a single normal ventricle, either right or left, was nearly the same as that of the normal QRS vector. The route of activation of a blocked ventricle, either right or left, was abnormally altered: toward the right in complete right bundle branch block, and toward the left in complete left bundle branch block. 7. 7. The circular form was found to be advantageous in clinical routine electrocardiographic analysis.

Ventricular Gradientの臨床的意義

From the theoretical point of view, the concept of the ventricular gradient (VG) is thought to be interesting in the interpretation of the clinical electrocardiogram, but there has been few studies on the relationships between the ventricular gradient and the histologic findings of the ventricular myocardium.The author determined the frontal plane VG from the Einthoven's triangle with Leads 1 and 2 and the horizontal plane VG with Leads V1 and V6 in routine electrocardiograms of clinical and autopsied cases.Normal limits of the angle of the VG in fifty healthy young adults were determined. On the basis of these values, there were few abnormalities of the angle of VG in cases of complete right bundle branch block, transitional form to left ventricular strain pattern and so-called myocardial damage, but many abnormal cases were found in right or left ventricular hypertrophy and strain patterns. There were more abnormalities in frontal than in horizontal plane. In cases of right bundle branch block there was no abnormality in the cases which showed no clinical findings of organic heart disease. In right ventricular hypertrophy and strain patterns the author found more abnormalities of the angle of VG in the cases with severe congestive heart failure than without it, but there was no constant relationship between the grade of congestive heart failure and the magnitude of the VG. Furthermore there was no clear difference between the incidence of abnormal VG in congenital malformations of the heart and that in acquired mitral valvular diseases.The magnitude of the VG in both planes showed a tendency similar to the angle of VG, when the lower limit of its magnitude is regarded as 30 microvolt seconds.The manifest magnitude and angle of the VG in both planes obtained from 47 older patients (mean age, 68.5 years) were compared with the autopsied findings. In forty of these patients the magnitude and angle of the VG were compared with the histologic findings of the myocardium.Although no abnormality of the angle of the VG was seen in the autopsied cases with normal electrocardiogram, ther were many abnormalities in the directions of the VG in the cases which showed myocardial infarction or left ventricular hypertrophy and strain patterns.In 74% of the cases which showed abnormalities in the angle of the VG, moderate to severe myocardial fibrosis was seen, irrespective of the patterns of electrocardiogram. But, on the contrary, there was none or slight to mild fibrosis in 85% of the cases with normal VG and no cases of moderate or severe myocardial fibrosis were observed.The relationship between myocardial fibrosis and the magnitude of the VG was the same as that in the angle of VG and myocardial fibrosis.It is suggested that the determination of the VG, especially of its angle, is of clinical significance to decide whether the ST-T changes of the clinical electrocardiogram are based on myocardial damage or not, because the importance of the VG was confirmed by comparison with histologic findings of the heart.

The Burger triangle in curve from

The average Burger triangle gives more accurate results than the Einthoven triangle. This paper described the average Burger triangle in curve form. It is easier to use than the triangle itself. It was pointed out that the curves may be used together with the curves derived from the Einthoven triangle to obtain simultaneous results from both triangles. The physician may check each time at a glance the inaccuracy of the Einthoven triangle in individual electrocardiograms.

A radial device for the RLF plane

A radial device was given on the basis of the Einthoven triangle. Using the quotient e 1 e 3 the corresponding cardiac vectorial direction in the RLF plane can be obtained. It was discussed that a similar device could be constructed on the basis of a Burger triangle. The same quotient could give almost the accurate direction.

An experimental study of Burger triangles constructed from toad hearts in situ.

The present paper presents a method of constructing Burger triangles directly from living toad hearts in situ. Depolarization and repolarization Burger triangles from same toads were almost identical. It was shown, that the Burger triangle is more accurate than the Einthoven triangle. The two expedients of Brody, which simplify the use of the Burger triangle, are illustrated. Burger triangular shapes from toads approximate those of Wilson, constructed from human subjects with a current dipole on thorax.

Burger Triangle as a Method for Correcting Inaccuracies of Einthoven Triangle

Burger Triangle as a Method for Correcting Inaccuracies of Einthoven Triangle

Photochemical activity of chloroplasts isolated from sugar beet infected with virus yellows.

Photochemical activity of chloroplasts isolated from sugar beet infected with virus yellows.

Burger triangle as a method for correcting inaccuracies of Einthoven triangle.

Burger triangle as a method for correcting inaccuracies of Einthoven triangle.

General Theory of Heart-Vector Projection

A mathematical and physical basis for heart-vector projection concepts is presented and its significance for current practices in frontal-plane and spatial electrocardiography is discussed. Assumptions underlying the theory are stated and utilized to derive a general relationship between the heart dipole and the potentials it produces in the body. Specific equations are given for unipolar and bipolar leads and the Wilson central-terminal voltage. Coefficients determined experimentally for human torso models differ markedly from those that stem from Einthoven's hypothesis. Einthoven's equilateral triangle represents a special case of the general theory. Geometric interpretations are applied to a quantitative frontal-plane example, to the Wilson central-terminal voltage and extended to the concept of an image surface corresponding to the human body surface.