Chapter 11. Dipolar Electrocardiotopography Imaging

Vectorcardiography

The vector principle is the basic principle of electrocardiography for the interpretation of the standard 12-lead electrocardiogram (ECG) as well as for teaching.1 However, its application in the interpretation of the standard 12-lead ECG is demanding for a mental three-dimensional imagination, and the "mental image" requires linking the orientation and magnitude of the vector to the anatomy of the heart, its position in the chest, and the sequence of activation (Fig. 11–1).

Vectorcardiography partially reduces these problems. It presents the distributed electric field at every instant of time by a dipole—the equivalent dipole. This dipole is represented by a vector, defined by its magnitude and orientation, theoretically corresponding to the extent of the activation front and its location. The origin of the dipole is fixed in the center of an orthogonal coordinate system, and the trajectory of the end point of the vector during the atrial/ventricular depolarization and repolarization depicts the spatial vectorcardiographic loop. The classical graphical presentation of vectorcardiography is the planar vectorcardiogram—the planar projection of the spatial vectorcardiographic loop onto three perpendicular planes: the frontal, sagittal, and horizontal (transverse) planes.

Compared with the standard 12-lead ECG, the orthogonal ECG does not contain redundant information. The coordinate system of the orthogonal ECG/vectorcardiogram may be aligned with the geometry of the heart and to our knowledge about the sequence of atrial and ventricular activation. These characteristics make the vectorcardiogram instrumental for teaching the principles of ECG diagnosis, as well as for comparative studies with other imaging methods. However, the interpretation of vectorcardiograms is demanding for three-dimensional imagination and for good orientation in the anatomic structures and their relationships to the processes in the heart. In addition, these graphical presentations—scalar tracings of orthogonal ECG and planar vectorcardiogram—are not directly comparable with images of the heart developed from another imaging method.

In this chapter, we describe a method for graphical presentation of the orthogonal ECG/vectorcardiogram that allows the visualization of the vectors representing the cardiac electrical field comparably to other imaging methods used in cardiology. This graphical presentation of ECG is suitable for side-to-side comparisons as well as for superimposition or fusion of information from multiple imaging modalities.

Dipolar Electrocardiotopography

In dipolar electrocardiotopography (DECARTO), the orthogonal ECG is transformed to areas projected on a spherical image surface. The original DECARTO model2,3 was developed for the presentation of the QRS complex (ie, for the process of ventricular depolarization).

The mathematical model of the DECARTO transformation is based on modeling of the cardiac electrical field. A detailed description of the electric field of the excitable myocardium would require a highly complex electrodynamics model that could link the heart as electrical generator with its electrical field. In general, outputs from electrodynamics models of the heart are ill posed in relation to the structure of the cardiac generator. It means that the given distribution of the electric field around the cardiac generator can be attributed to different generators' shapes and/or spatial structure. This fact provides an opportunity to substitute a real source of the cardiac electrical field with a functionally equivalent generator with known compositions.4

The electrical generator of the cardiac electric field can be effectively approximated by double layers of current sources with an approximately constant density of electrical dipoles that are bounded by closed contours on the inner and outer surfaces of the ventricles. The electrostatic potential in the proximity of a double-layered object may be, in principle, calculated with any accuracy by the method of expansion in a convergent electrical multipole series describing distributions of dipoles over the double layers. The final potential is then determined by the sum of this multipole expansion.5 The number of used multipole components in the expansion depends on the required accuracy of the potential field description. The DECARTO model is based on the double-layer representation of the field generator and uses dipole representation with minimal number of multipole components. Another simplification of the DECARTO model is the assumption that the inner and outer surfaces of the heart ventricles have a spherical form, so the double layer has a spherical shape and represents so-called image surface.

The basic principle of DECARTO transformation is based on the consideration that the electrical field of the generator is formed exclusively by the electrical dipoles of the double layer and delimited to its area. This activated area is projected onto the surface of a sphere called the imaged surface. The point of intersection of the vector with the image surface is considered to be the center of the activated area. Around this point, a circle with a radius proportional to the spatial magnitude of the instantaneous vector is drawn encompassing all activated elements. In particular, the radius r of the activated area is computed for a given instantaneous spatial vectorcardiogram (VCG) vector according the following formula:

where D represents the length of the instantaneous spatial VCG vector, Dmax is the maximal spatial vector during the QRS duration, and Rs is the radius of the image sphere (Rs can be set arbitrarily; the DECARTO model uses the value of 1) (Fig. 11–2).

The activated area or activated points representing this area on the image sphere are graphically presented as maps—so-called decartograms. Visualization of ventricular activation can be performed by a series of decartograms calculated and displayed individually for discrete time points or by using summary maps where activations at given time points are superimposed onto one decartogram.

The image sphere is a hypothetical surface that represents the cardiac generator, and the activated areas on this image surface (decartograms) can be visualized by projecting them on a variety of shapes in two or three dimensions (Fig. 11–3). The selection of geometrical shapes aims to optimize the topographic relations of the abstract representations of the cardiac electric field to the activation process in the myocardium. Determination of the spatial localization of instantaneous vector end points enables the bridging between characteristics of myocardial activation propagation in this conceptual model and abstract representation of the cardiac electric field.

The spherical image surface can be easily transformed to any suitable analytical spatial or planar surfaces to visualize decartograms, such as polar (azimuthal) planar projection, rectangle projection, spherical projection, and parabolic projection, as well as to real heart surfaces rendered from other imaging methods.

Normal Values for Decartograms

The DECARTO method of graphical presentation extends the possibilities for presentation of the normal values of ECG and for its quantitative analysis. Areas of occurrence of the activated points in the normal population for decartograms were reported for the McFee-Parungao and the Frank lead systems.6 They were constructed by indicating the areas of activation at given points of QRS duration, and the probability of being activated at the given point of time for every point of the matrix was computed. In this way, reference probability matrices of normal activation were constructed (Fig. 11–4).

Ruttkay-Nedecky7 used these probability matrices of normal activation for application of fuzzy mathematics to quantify the normality of the QRS complex. In this method, the subset of elements in the spherical surface is regarded as a fuzzy subset with membership characteristic functions derived from objective probabilities computed for the reference sample of normal subjects. In an individual case, the difference between the sum of membership function values and the mean of the reference sample at any instant of the QRS duration, or during the whole QRS, divided by the standard deviation quantifies the deviation from the reference mean value.

A similar approach was used for graphical presentation of the location and extent of the myocardium at risk in patients with acute myocardial infarction.8 This method is based on the processing of ST-segment deviations of standard 12-lead ECG following the lines set by the DECARTO method. In this ST-DECARTO method, the center of the location of the area at risk is given by the spatial orientation of the resultant spatial ST vector, and the extent of the area at risk is derived from the Aldrich score.10 The areas at risk are projected on a spherical image surface. On this image surface, a texture of the anatomic quadrants of the ventricular surface and the coronary artery supply are projected. The initial testing showed that the method allows a graphical presentation of estimated area at risk using clinically defined diagnostic rules. The area at risk can be displayed in images that are familiar for clinicians and can be compared with or superimposed on results of other imaging methods used in cardiology.

As mentioned earlier, the vector principle is the basic principle in the interpretation of ECGs. It follows that, in principle, the DECARTO method is applicable in any cardiac pathology. However, the most illustrative is the application in pathologies characterized by changes of the instantaneous spatial vector orientation. Here, we present examples of the application of DECARTO in visualizing the QRS changes in myocardial infarction and of the modified ST-DECARTO method for visualizing the area at risk based on ST-segment deviations.

Myocardial Infarction

Acute myocardial infarction (MI) and resulting fibrosis (scars) create regions of altered conduction. The typical signs of MI in the standard 12-lead ECG are pathologic Q waves observed in leads related to the MI location. In the VCG, the signs are manifested as changes of the instantaneous QRS vector orientation and magnitude. In decartograms, the changes in orientation and magnitude of instantaneous QRS are visible as dislocations of activated areas when compared with the normal sequence of depolarization. Figure 11–5 shows examples of instantaneous decartograms in anterior and inferior MIs and their visual comparison with the sequence of depolarization in a healthy subject.

The quantitative evaluation of decartograms using the fuzzy set mathematics was presented in 1994 by Ruttkay-Nedecky and Riecansky9 in patients with coronary heart disease. They recognized the following five classes of ventricular activation taking into account the locations of the activated points with respect to the normal areas: abnormal; abnormal with normal component; normal with abnormal component; marginally normal; and normal. Thus, they demonstrated the possibility to quantify not only the abnormal decartograms, but also borderline location of the activated areas.

Location and Extent of the Area at Risk in MI

ST-segment deviations in patients with acute MI (AMI) are associated with the location and extent of myocardium at risk, with severity of acute transmural ischemia, and with clinical outcomes.10-14 Additionally, early resolution of ST-segment elevation correlates with myocardial salvage and better prognosis in patients with AMI treated with reperfusion therapy.15-19

In practical ECG diagnostics, the location of the area of myocardium at risk is estimated from the presence of ST-segment elevation and/or depression in particular leads of the 12-lead ECG.20 For the quantification of the estimated extent of the area at risk, several formulas have been reported10,21,22 that are, in principle, derived from the number of leads involved and/or the ST-segment deviation amplitude. Both the location and the extent of the area at risk estimated from the ST-segment deviations are therefore easily displayable in decartograms.

However, the relationship between the areas at risk estimated from the ST-segment deviations is moderate or poor,22-27 and the performance of the ST changes–based algorithms needs to be further validated. Because the DECARTO graphical presentation allows visualization of the location and extent of the involved area using corresponding algorithms, it enables visualization of the differences between different scores. Also, its graphical presentation is suitable for side-to-side comparison or superimposition to analyze both the agreements and disagreements with other imaging methods (Fig. 11–6).

Ventricular Hypertrophy

The possibility of the DECARTO method to visualize and quantify the redistribution of activation duration over the myocardium was also demonstrated for left and right ventricular hypertrophy.28,29 Comparing decartograms from hypertensive patients with left ventricular hypertrophy and with those from healthy subjects, differences in the redistribution of activation duration over the myocardium were seen.

The orthogonal coordinate system and the spherical image surface used in the DECARTO model for the QRS presentation and the DECARTO-like graphical presentation of the ST segment are convenient for further data processing and sufficiently flexible in adapting the decartograms to suitable graphical forms for combination with other imaging modalities. The possibilities for the combination are demonstrated by the example of the DECARTO-like presentation of ST-segment deviations compared with other graphical presentation of ST-segment deviations that can be used for the estimation of the area and extent of myocardium at risk in patients with AMI, and with other non-ECG imaging methods that can serve as reference or complementary methods.

Side‐by-Side Comparison of DECARTO-Like Presentation of ST-Segment Deviations with Other ECG-Based Graphical Methods

Several methods for the graphical presentation of the location and extent of the area of myocardium at risk have been recently reported.8,30-33 The methods use different approaches for the estimation of the location and extent of the area at risk, but because these graphical methods are using basically identical or similar graphical presentation, their results can be easily visually compared side by side.

The method described by Andersen et al,33 the ST Compass, is based on the standard 12-lead configuration of the traditional coordination system. It calculates the planar ST vectors for the frontal and horizontal planes from the ST-segment deviations of the 12-lead ECG, and the resultant planar vectors are drawn on the two perpendicular planes with hexaxial lead coordinates of the standard 12-lead ECG. These planes are displayed as circles with additional spatial and/or anatomic description. This method recommends calculating the spatial vector magnitude as a surrogate for the extent of the myocardium at risk because despite the limitation of this estimation, the ST-vector spatial magnitude corresponds better with the spatial character of the injured myocardium. Thus, this method represents a useful bridging from the evaluation of the individual ST-segment deviations of the 12-lead ECG to the vector analysis and visualization of the spatial ST-segment deviations. However, mentally visualizing the relationship of the planar vectors with the anatomic structures of the heart and the coronary artery distribution still requires a great deal of a three-dimensional mental imaging.

Strauss et al31 developed a graphical method that synthesizes a VCG from the 12-lead ECG. The ST-segment vector direction is projected on two image surfaces of the heart—the Mercator surface with a schematic average coronary artery distribution and the polar plot. This approach provides the location of the center of the area at risk with respect to the coronary artery distribution and/or to the anatomic segments of the left ventricle. This method also gives the value of the spatial ST-vector magnitude as an estimate of the extent of the area at risk; however, similarly to the previous method, the extent is not graphically displayed.

The polar image surface suitable for side-by-side comparison with single photon emission computed tomography (SPECT) images was used also by Galeotti et al,32 and the location and extent of the myocardium at risk are estimated from the similarities of the ST-segment deviation of a real patient's ECG with a database of simulated ECGs with known location and extent of ischemia.

A different approach was used by Ubachs et al.30 They estimated the location and extent of the area at risk using the 12-segment model used previously for ECG infarct quantification (QRS score). For the final graphical presentation, both Mercator and polar presentations were used and thus are comparable with polar SPECT or adapted magnetic resonance imaging (MRI) images. Figure 11–6 shows a visual side-by-side comparison of two graphical methods for displaying the ST-segment deviation—the DECARTO-like method and a method described by Ubachs et al30 showing the areas at risk in the two patients.

The methods of ST-segment visualization described here approach the estimation of the location and extent of the area at risk from different perspectives (Table 11–1). Knowing the principles and studying differences and agreement in the results of these ECG methods can contribute to understanding the roles of individual factors that influence the final ST-segment deviation in AMI. A challenge will be to move from descriptive visual comparison to analytical quantitative evaluation of agreements and disagreements between methods.

Side‐by-Side Comparison with Non-ECG Methods

The non-ECG imaging methods used in cardiology include a variety of two- and three-dimensional images; however, the side-by-side comparison naturally requires the use of identical/comparable images. As was demonstrated earlier, the methods for graphical presentation of area at risk based on the ST-segment deviations tend to use polar or Mercator projections.

The polar projection is frequently used as one of the possibilities of displaying results for visual comparison with non-ECG imaging methods.8,30-32 The advantage of using the polar projection is the direct visual comparability among different imaging methods and potential possibility for superimposition of the findings. Thus, the ECG-based images can be compared with, for example, SPECT images of perfusion (Fig. 11–7), wall motion, and wall thickening; MRI wall thickening; and echocardiographic images of dyskinesis. However, this projection suffers from a considerable deformation of the basal and apical regions, which must be taken into account in the interpretation of the results.

The Mercator projection with the texture of the coronary artery distribution reduces the deformation of the polar projection and illustrates well the anatomic segments of the heart and corresponding coronary artery distribution. This projection is not generally used for displaying results of the non-ECG imaging techniques, but it can be potentially used as the image surface of choice.

The common advantage of planar projections is the ability to display the whole surface, which balances the main disadvantage, which is the deformation of the shape and size of the imaged structures.

Superimposition of the DECARTO Images onto Three-Dimensional Images

The planar image surfaces are not able to display accurately a three-dimensional structure or to capture the individual anatomy. DECARTO allows projection of the decartograms/activation areas onto the "realistic" individual surfaces rendered from other image methods used in cardiology. Such surfaces may be acquired from a variety of clinically available imaging techniques such as SPECT, echocardiography, and MRI. In relation to ECG, these cardiac imaging techniques are used mainly as reference methods for comparative studies. However, they bear basically different and potentially complementary information, including information on the structural characteristics of the cardiac source, which can but does not necessarily influence its function, or on the functional characteristics other than electrical properties.38

The transformation of ECG data into the decartograms creates a two-dimensional, image-like representation of ECG signal that is more suitable for direct comparison with imaging data. The comparison of decartograms and imaging data is done by an approximate merging of a separate coordinate system of imaging data and image sphere used in the DECARTO model, followed by the projection of decartograms onto functional and structural surfaces that were identified in imaging data. This process is called superimposition and allows effective visualization of information about the structural and functional state of the heart and its electrical characteristics derived from the VCG signal. The identification of the surfaces in imaging data is done using standard segmentation and quantification algorithms that are based on the forming of surface according to specific iso-values in data.39 The identified surfaces do not necessarily need to be attributed only to real structures of the heart (as in MRI or echocardiography); they can also describe a functional status of the heart muscle (eg, SPECT imaging).

The main output of data merging is a projection of the information about the spatial localization of a VCG vector end point defined by DECARTO onto the area of defined localization and size of the myocardium, and this can be used to study the relationship between electrogenesis and the myocardial structures and metabolism. However, due to several simplifications of the DECARTO model (eg, assumption about dipole content of the electrical field), the information presented by DECARTO does not need to correspond exactly to the real sequence of activation front in the myocardium. However, the visualization of ECG signal in the same context as cardiac imaging techniques offers an investigative and instructional modality for comparative studies of functional and structural changes of the heart.

The superposition of imaging data and DECARTO data provides the opportunity to study both the diagnostic and prognostic importance of agreements and disagreements of findings of both methods. In the interpretation of the superposition of DECARTO and imaging data, the same parameters embedded in the provided information inherent to both methods are considered. The first group of parameters, which influences the quality of the fusion process, has to do with the solution of merging spatial coordinates of ECG and the imaging data system. These parameters are related to the proper merging of the orthogonal ECG/VCG coordinate center with the center of the anatomic structure or the center of the geometric surface from the heart imaging data.

The second group of parameters is directly related to the diagnostic evaluation of data obtained from the fusion process. Clinically used diagnostic methods have a set of individual decision-making procedures that can differentiate between normal and pathologic findings. Fusion of two diagnostic methods thus increases the number of possible parameters suitable for diagnostic evaluation. In the case of a dynamic system such as the heart, the presence of time dimension in monitoring may lead to a dramatic increase of accessible data describing the functionality of the system. The heterogeneous parameters inherent to these diverse types of diagnostic techniques can be evaluated using multivariate statistics in order to identify new characteristics that could be useful, especially in treatment of normal and borderline pathologic findings.

The superimposition of the decartogram on the rendered three-dimensional surface positions the activated area on the anatomic structure given by the used imaging method (eg, MRI, SPECT, or coronarography). The superimposition of the QRS decartograms or ST-segment deviation decartograms can visualize, for example, the relationship between the flow in particular coronary arteries and estimated location of MI or area at risk, by superimposing the activated areas/decartograms on a three-dimensional image of the coronary artery distribution.

In the interpretation of the final superimposed images, the following key principles must be considered:

• The principles of the imaging methods (ie, what information is provided by the particular method)
• How to treat the three-dimensional images that are rendered in the case of a fuzzy border (eg, in the case of low signal as demonstrated in a case of a perfusion defect in SPECT; Fig. 11–8)
• What anatomic structure is visualized (eg, the left ventricle or the whole heart)
• How to visualize a structure located intramurally with respect to the surface (eg, a case of a scar in an MRI image that is located intramurally while the DECARTO image is projected on the surface of the heart)

The side-by-side comparison of different imaging methods and the superimposition of methods providing different primary information on the structure and function of the heart can thus complement the view of the pathologic process/disease. Imaging ECG signals will contribute to the process of moving from using the ECG as a surrogate to understand better the processes behind particular ECG changes/patterns and their clinical or prognostic relevance.

The superimposition of the decartogram on the SPECT three-dimensional image is an example of a graphical presentation of two methods that provide two complementary sets of information on the function of the heart. The decartogram visualizes depolarization as a sequence of activated points on the image surface, showing the dipolar content of the cardiac electric field. SPECT is a routinely used clinical imaging method that provides information on the function and structure of myocardium based on the retention of radioactive substances depending on cellular viability and integrity of cell membranes. By superimposing the decartogram onto the graphical imaging of viability, the relationships between the viability and electrical activity can be analyzed.

In the interpretation of the superimposition of DECARTO and SPECT, the following factors and limitations of both methods need to be considered:

• Proper definition and position of the coordinate system center of the orthogonal ECG that is used for construction of decartograms need to be ensured, with the center of the real heart surface constructed from SPECT. The image surface constructed from SPECT data can differ from the real surface, especially in cases with severe pathology.
• Differences exist between the anatomic axis/description of the heart and the electrical coordinate system. This requires approximating anatomic structures of the heart (eg, apex, interventricular septum) based on conventionally used views/terms (eg, anterior, posterior, lateral).
• In the clinical evaluation of both SPECT and DECARTO, it is assumed that they provide information mainly about the left ventricle, because it dominates in the image. In reality, DECARTO contains an undefined proportion of information from the right ventricle.
• If the image surface is constructed based on perfusion SPECT data, the surface represents "healthy" myocardium in terms of perfusion. In cases of pronounced pathology (eg, in cases of considerable perfusion defects), the constructed surface can differ considerably from the real anatomic left ventricular surface. Moreover, the shape of the surface depends on the threshold that was used for rendering.
• The information presented by decartogram is based on the representation of the cardiac electrical field as a resultant single dipole and its projection on the selected image surface. This projection, however, does not necessarily correspond to the real sequence of depolarization. For example, the initial part of the depolarization can be projected onto the posterior wall, or the activation areas are projected during depolarization repetitively on the same place.
• DECARTO is constructed primarily from one heartbeat (ie, it visualizes the sequence of activated areas during one depolarization). In contrast, SPECT presents average information from several heartbeats.

These factors/limitations define a framework for the potential use of the superimposition of decartograms and SPECT images. Within this framework, the superimposition of these two methods creates a strong potential for their utilization as illustrative and innovative tools for comparative studies focused on the relationship between functional and structural/anatomic characteristics of the heart. This method of superimposition, including awareness of its limitations, is applicable to other methods as well, such as CT, MRI, and PET, that provide information on the source of the cardiac field from additional aspects.

Limitations of the DECARTO Method

The DECARTO method involves several simplifications related to the basic principles of the method. First, the cardiac electrical field is represented by a single dipole, and DECARTO and the decartograms are primarily defined as circles on the spherical image surface. Second, if the spatial vector is approximated from the standard 12-lead ECG, the result depends on the used formula. Third, the primary image surface is spherical; therefore, deformations due to the projection of this three-dimensional spherical surface onto two-dimensional surfaces (eg, Mercator, polar) can be considerable and will require further optimization of the method. Finally, the relations of the VCG orthogonal coordinate system, the 12-lead hexaxial coordinate system, and the anatomic axis of the heart are considered to be constant and do not consider interindividual variability of patients.

Despite the listed simplifications and limitations, the DECARTO method has its advantages. It allows the visualization of the sequence of depolarization and the areas at risk using clinically accepted concepts and defined formulas. As was demonstrated in the case of the DECARTO-like method for the estimation of the area at risk in patients with AMI, the method is flexible, allowing the following modifications:

• Use of any defined formula for the estimation of area at risk; thus, the performance of different score formulas can be graphically compared
• The optimization/individualization of the spatial angle between the anatomic axis of the heart and the ECG coordinate system
• Use of any three-dimensional surface or three-dimensional image for the projection of the area at risk
• Superimposition of any texture on the image surface, including results of other imaging methods used in cardiology

The DECARTO method and its modification can be used to visualize the direction and size of the electric forces of the heart approximated by a single dipole. It contributes to understanding the electrical forces responsible for the changes in the shape of ECG tracings and associates them with pathophysiologic/disease processes.

Supported in part by grants VEGA: 1/0530/09, Slovak Republic, and by the Slovak Research and Development Agency under the contract APVV-20-05610. The data for the ST-DECARTO images were kindly provided by the Lund Cardiac MR Group, Lund, Sweden.