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ECG waveforms and cardiac electric sources
Journal of Electrocardiology Vol. 29 Supplement
ECG W a v e f o r m s a n d Cardiac Electric S o u r c e s
Bruno Taccardi, MD, PhD, Robert L. Lux, PhD, Robert S. MacLeod, PhD, Philip R. Ershler, PhD, Theodore J. Dustman, Marshall Scott, Yonild Vyhmeister, and Nicole Ingebrigtsen
Experimental studies (1-3) and numerical simulations (4-7) showed that ventricular pacing produces an elongated excitation wavefront that spreads with higher velocity along fibers rather than across fibers. The higher longitudinal velocity results from the intracellular and extracellular electrical conductances being higher along fibers rather than across fibers (8). As a res'ult, those portions of the wavefront that propagate along fibers generate more current per unit area than is produced by the portions that spread across fibers. The extracellular currents generated by the spreading excitatory process flow through the entire heart and body tissues, and their distribution is affected by the anisotropic resistivity of the heart muscle through which they flow, as is the associated potential distribution. Previous studies (1-3,8) showed that epicardial or intramural pacing produces extracellular potential fields with two maxima in the two regions toward which excitation spreads along fibers. Unipolar electrograms recorded from these regions exhibit an initial R wave. Conversely, electrocardiograms (ECGs) recorded from regions toward which excitation propagates across fibers show art initial Q wave. A large n u m b e r of experimental observations show that the simple rules described above invariably apply in the vicinity of a pacing site both at the epicardium and intramurally (9). However, recent unpublished data revealed that at distances greater than 4-5 cm from an epicardial pacing site, the same rules no longer apply. In these areas, initial tall positive R waves were recorded from both along fibers and across fibers epicardial areas, the unipolar electrograms showed both a positive (R) and a negative (S) wave, and the R/S amplitude ratio increased with increasing distance from the stimulus site. Finally, in the epicardial regions that activated during the last 10 ms of ventricular excitation, the QRS complexes were entirely positive.
The ECG waveforms just described were observed in exposed canine hearts and also in isolated hearts immersed in an electrolytic tank shaped as a h u m a n torso, irrespective of whether the recorded unipolar signals were referenced to the Wilson central terminal, the left hindleg, or to the average of 242 or 490 epicardial potentials. The presence of positive potentials, potential maxima, and ECG R waves in the regions toward which excitation spreads along fibers can be explained in light of the oblique dipole layer, a mathematical model of the excitation wavefront developed by Colli Franzone et al. in 1982 (10) and recently updated ( l l ) . The 1982 model represents the electrical generators associated with an excitation wavefront as the superposition of an axial and a normal dipole layer. Both layers cover the entire wavefront. The axial dipole layer is constituted by dipoles that are parallel to the local fiber direction at all points of the wavefront. The normal dipole layer is made up of dipoles that are oriented normal to the wavefront and is identical to the classic model of the excitation wave (uniform dipole layer). The updated version takes into consideration the structure of the heart muscle as an anisotropic bidomain and the finite thickness of the wavefront. The extracellular currents generated by the axial dipole layer flow from portions of the wavefront that propagate along fibers and, initially, point toward the resting tissue. These currents then follow a series of curved pathways and point toward those portions of the wavefront that spread across fibers, where the axial dipole m o m e n t density is almost zero. Thereafter, the currents cross the wavefront, enter the excited area, and flow toward two potential minima located near the narrow ends of the elongated wavefront (3). The potential field associated with these currents exhibits two potential maxima in those regions toward which the wavefront spreads along fibers. Accordingly, unipolar ECGs recorded from these regions show initial R waves, as described earlier. The electrical effects of the axial dipole layer and the rotational anisotropy of the ventricular myocardium can also explain part of the positive potentials and R waves observed in the regions toward which excitation propagates across fibers. W h e n an excitation wave elicited by
From the Nora Eccles Harrison Cardiovascular Training and Research fnstitute, The University of Utah, Salt Lake City, Utah.
Supported by NII-I grant ROI EIL43276-07 and by awards from the Nora Eccles Treadwell Foundation. Reprint requests: Bruno Taccardi, MD, PED, CVRTI,The University o~ Utah, Building 500, Salt Lake City, UT 84112.
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ECG Waveforms and Cardiac Sources epicardial pacing propagates through the thickness of the ventricular wall, it encounters deep layers of myocardial fibers whose direction rotates counterclockwise (CCW) by approximately 120 °, from epicardium to endocardium (12). Thus, the direction of fast propagation rotates CCW from epicardium to endocardium and the intramural wavefront acquires a helical shape. The axial dipoles attached to the deep portions of the wavefront produce potential maxima in those deep regions toward which they propagate along fibers. Epicardial far-field reflections of these deep potential maxima result in a C-shaped crest or ridge of positive potentials flanking those portions of the epicardial wavefront that spread across fibers. In these areas, positive R waves result from the epicardial reflection of the deep, rotating potential maxima. The normal component of the oblique dipole layer can also explain part of the potential maxima and R waves observed in the cross-fiber areas. W h e n the excitation wavefront is a closed surface, or its rim is epicardial and exposed to air, the normal dipole layer does not generate any potential field outside or inside the wavefront. Its only electrical manifestation is a uniform potential jump of approximately 40 mV across the entire wavefront surface. This property of the normal dipole layer explains the absence of potential maxima facing the portions of the wavefront that spread across fibers in exposed heart preparations in the early stages of propagation (10-20 ms) after epicardial pacing (3). However, when the heart is in the chest, or is immersed in an electrolytic tank, the normal dipole layer elicited by epicardial pacing has a rim that is in contact with a conducting medium. In these conditions, the normal dipole layer generates electric currents that spread through the heart and the extracardiac conducting media. These currents flow from the entire leading surface of the wavefront toward the resting tissues and then back toward the trailing surface of the wavefront. In the cross-fiber areas, the currents that flow from the wavefront toward the resting tissue are partially or totally counterbalanced by the currents coming from the axial dipole layer that flow in the opposite direction, toward and into the advancing wavefront, as explained earlier. If the density of the normal currents in the cross-fiber regions is higher than that of the axial currents, potential maxima and R waves will appear in these same areas. In addition, as soon as an excitation wave elicited by epicardial pacing reaches the endocardium, the wavefront acquires a second rim, which is in contact with cavitary blood, a highly conducting medium. The size of the endocardial rim will increase rapidly because of Purkinje involvement. At this stage, more currents will flow from the wavefront toward the resting tissues, both along and across fibers, and the likelihood of potential maxima and R waves appearing in those regions will increase. While the mechanisms just described can explain part of the positive potentials and R waves in the cross-fiber areas, they cannot account for the totally positive unipolar ECGs that are invariably observed in the relatively extensive regions that are excited at the end of the QRS interval. Model simulations representing a spherical norrnal dipole layer spreading through a spherical heart
•
Taccardi et al.
99
show that totally positive ECGs with entirely positive intrinsic deflections cannot be produced by a uniform dipole layer moving past a unipolar recording electrode, nor can an axial dipole layer generate such totally positive waveforms (1). Because neither the axial nor the normal current sources associated with an excitation wavefront can explain the observed ECG waveforms, we made the hypothesis that a third factor, namely the reference potential, may have affected the measured potential values and the shape of the unipolar ECGs in our experiments. The hypothesis was suggested by the behavior of the zero line in epicardial and intramural potential maps during the spread of excitation. The zero line is the locus of the points whose potential is equal to that of the remote or indifferent reference electrode, generally the Wilson central terminal. In epicardial potential maps recorded after epicardial stimulation, the zero line does not occupy a stable position within the array of densely packed equipotential lines that reveal the underlying wavefront. In the early stages of propagation (10-20 ms), in the cross-fiber areas, the zero line leaves the entire potential drop associated with a wavefront on the negative side of the distribution. Accordingly, the spatial potential profile across the wavefront ranges from -30 or -40 mV in the excited area to zero in the resting area, and the densely packed equipotential lines that outline the wavefront are all negative. At 40-50 ms after the stimulus, the zero line is in the middle of the potential drop and the potential profile ranges from -15 to +15 mV. Here, 50% of the equipotential lines are negative and 50% are positive. Finally, during the last 10 ms of the QRS, the zero line leaves the entire wavefront on the positive side of the distribution, the potential profile goes from approximately +30 or +40 mV to zero, and all of the equipotential lines that outline the wavefront are positive. This behavior of the zero line shows that during the QRS interval, the reference potential moves from one extreme of the potential drop associated with the wavefront to the other extreme. An opposite shift occurs during repolarization. In another series of observations, we analyzed the position of the reference potential within the range of potential values measured over the entire heart surface at a series of time instants during the QRS interval. In the early stages of ventricular excitation, the reference potential was near the positive extremum of the potential range, in the middle of the QRS it was approximately equidistant from the two extrema, and at the end of the QRS it was close to the negative extremum. Our present tentative explanation of the mechanism that produces the drift of the zero line during the QRS can be summarized as follows: 1. Recent experimental observations from our laboratory performed with an isolated canine heart in a torso-shaped electrolytic tank showed that at any given time instant during the cardiac cycle, the potential of the Wilson central terminal is close to (within I-2 mV) the average potential measured on the ventricular surface. This result was anticipated by Brody and Evans (13) who
100
Journal of Electrocardiology Vol. 29 Supplement
considered the case of a remote indifferent reference electrode in a large electrolytic tank. 2. Taking the average heart surface potential as the reference potential, produces a zero line that divides the surface of the heart into two portions, such that the integral of the potential over one portion has equal magnitude and opposite polarity compared to the integral over the other portion. This is a general property of the average. In the initial stages of propagation after an epicardial stimulus, the most negative epicardial potentials ( - 2 0 - - 4 0 mV relative to the highest epicardial potential) are concentrated in a very small excited area. To achieve equality of the integrals in the positive and negative areas, the zero line must leave the entire excited area and the entire wavefront in the negative portion of the epicardial surface. W h e n 50% of the surface is excited, the zero line will leave 50% of the potential drop associated with the wavefront on the positive side and 50% on the negative side. At the end of ventricular excitation, w h e n the resting area is small, the zero line will leave the entire resting area and the wavefront itself in the positive portion of the epicardial surface. This interpretation of the shift of the zero line during propagation and repolarization is currently being tested by means of numerical simulations that will be reported elsewhere. The same interpretation enabled us to predict the behavior of the unipolar ECGs in a n u m b e r of experimental conditions, namely, local conduction delays and local accelerations. Local delays produced b y local cooling or by intracoronary injection of procainamide increased the R/S amplitude ratio in the delayed areas, as predicted by the theory, whereas local warming decreased the ratio. The negative drift of the reference potential introduces a positive trend into the unipolar ECGs that progressively develops during the QRS interval and can be clearly revealed by superimposing a series of timealigned epicardial ECGs recorded at increasing distances from a pacing site. An opposite drift occurs during repolarization. This previously unrecognized component of the ECG may have clinical relevance because it affects the slope, polarity, and area of the ECG waveforms and therefore influences a n u m b e r of measurements based on the slope or area of ECG waves, namely, excitation times, recovery times, activation-recovery intervals, and QRS, ST-T, and QRST integrals. We have not yet quantified these effects in normal and abnormal beats, but preliminary observations suggest that the drift of the reference potential affects the QRST area in part of the cases in which the recovery sequence is different from the activation sequence.
References 1. Corbin LV, Scher AM: The canine heart as an electrocardiographic generator. Circ Res 41:58, 1977 2. Spach MS, Miller III WT, Miller-Jones E et ah Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle. Circ Res 45:188, 1979 3. Taccardi B, Macchi E, Lux RL et ah Effect of myocardial fiber direction on epicardial potentials. Circulation 90:3076, 1994 4. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part I. Rectangular and cubic arrays of excitable elements. J Electrocardiol 24:1, 1991 5. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part II. Excitation in the simplified left ventricle. J Electrocardiol 24:17, 1991 6. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part IIL Arrhythmogenic conditions in the simplified 1eft ventricle. J Electrocardiol 24:33, 1991 7. Colli Franzone P, Guerri L, Taccardi B: Spread of excitation in a myocardial volume: simulation studies in a model of ventricular muscle activated by point stimulation. J Cardiovasc Electrophysiol 4:144, 1993 8. Roberts DE, Scher AM: Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ Res 50:342, 1982 9. Taccardi B, Lux RL, Ershler PR et al: Effect of myocardial fiber direction on 3-D shape of wavefronts and associated potential distributions in ventricular walls. (abstract) Circulation 86(suppl I):I-752, 1992 10. Colli Franzone P, Guerri L, Viganotti C et aI: Potential fields generated by oblique dipole layer modeling excitation wavefronts in the anisotropic myocardium: comparison with potential fields elicited by paced dog hearts in a volume conductor. Circ Res 51:330, 1982 11. Cole Franzone E Guerri L, Taccardi B: Potential distributions generated by point stimulation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle. J Cardiovasc Electrophysiol 4:438, 1993 12. Streeter D: Gross morphology and fiber geometry of the heart, p. 61. In Berne RM (ed): Handbook of physiology. Vol. 1: The heart. Sect. 2: The cardiovascular system. Williams and Wilkins, Baltimore, 1979 13. Brody DA, Evans JW: Some reflections on zero potential in electrocardiography. Am Heart J 60:661, 1960
ECG W a v e f o r m s a n d Cardiac Electric S o u r c e s
Bruno Taccardi, MD, PhD, Robert L. Lux, PhD, Robert S. MacLeod, PhD, Philip R. Ershler, PhD, Theodore J. Dustman, Marshall Scott, Yonild Vyhmeister, and Nicole Ingebrigtsen
Experimental studies (1-3) and numerical simulations (4-7) showed that ventricular pacing produces an elongated excitation wavefront that spreads with higher velocity along fibers rather than across fibers. The higher longitudinal velocity results from the intracellular and extracellular electrical conductances being higher along fibers rather than across fibers (8). As a res'ult, those portions of the wavefront that propagate along fibers generate more current per unit area than is produced by the portions that spread across fibers. The extracellular currents generated by the spreading excitatory process flow through the entire heart and body tissues, and their distribution is affected by the anisotropic resistivity of the heart muscle through which they flow, as is the associated potential distribution. Previous studies (1-3,8) showed that epicardial or intramural pacing produces extracellular potential fields with two maxima in the two regions toward which excitation spreads along fibers. Unipolar electrograms recorded from these regions exhibit an initial R wave. Conversely, electrocardiograms (ECGs) recorded from regions toward which excitation propagates across fibers show art initial Q wave. A large n u m b e r of experimental observations show that the simple rules described above invariably apply in the vicinity of a pacing site both at the epicardium and intramurally (9). However, recent unpublished data revealed that at distances greater than 4-5 cm from an epicardial pacing site, the same rules no longer apply. In these areas, initial tall positive R waves were recorded from both along fibers and across fibers epicardial areas, the unipolar electrograms showed both a positive (R) and a negative (S) wave, and the R/S amplitude ratio increased with increasing distance from the stimulus site. Finally, in the epicardial regions that activated during the last 10 ms of ventricular excitation, the QRS complexes were entirely positive.
The ECG waveforms just described were observed in exposed canine hearts and also in isolated hearts immersed in an electrolytic tank shaped as a h u m a n torso, irrespective of whether the recorded unipolar signals were referenced to the Wilson central terminal, the left hindleg, or to the average of 242 or 490 epicardial potentials. The presence of positive potentials, potential maxima, and ECG R waves in the regions toward which excitation spreads along fibers can be explained in light of the oblique dipole layer, a mathematical model of the excitation wavefront developed by Colli Franzone et al. in 1982 (10) and recently updated ( l l ) . The 1982 model represents the electrical generators associated with an excitation wavefront as the superposition of an axial and a normal dipole layer. Both layers cover the entire wavefront. The axial dipole layer is constituted by dipoles that are parallel to the local fiber direction at all points of the wavefront. The normal dipole layer is made up of dipoles that are oriented normal to the wavefront and is identical to the classic model of the excitation wave (uniform dipole layer). The updated version takes into consideration the structure of the heart muscle as an anisotropic bidomain and the finite thickness of the wavefront. The extracellular currents generated by the axial dipole layer flow from portions of the wavefront that propagate along fibers and, initially, point toward the resting tissue. These currents then follow a series of curved pathways and point toward those portions of the wavefront that spread across fibers, where the axial dipole m o m e n t density is almost zero. Thereafter, the currents cross the wavefront, enter the excited area, and flow toward two potential minima located near the narrow ends of the elongated wavefront (3). The potential field associated with these currents exhibits two potential maxima in those regions toward which the wavefront spreads along fibers. Accordingly, unipolar ECGs recorded from these regions show initial R waves, as described earlier. The electrical effects of the axial dipole layer and the rotational anisotropy of the ventricular myocardium can also explain part of the positive potentials and R waves observed in the regions toward which excitation propagates across fibers. W h e n an excitation wave elicited by
From the Nora Eccles Harrison Cardiovascular Training and Research fnstitute, The University of Utah, Salt Lake City, Utah.
Supported by NII-I grant ROI EIL43276-07 and by awards from the Nora Eccles Treadwell Foundation. Reprint requests: Bruno Taccardi, MD, PED, CVRTI,The University o~ Utah, Building 500, Salt Lake City, UT 84112.
98
ECG Waveforms and Cardiac Sources epicardial pacing propagates through the thickness of the ventricular wall, it encounters deep layers of myocardial fibers whose direction rotates counterclockwise (CCW) by approximately 120 °, from epicardium to endocardium (12). Thus, the direction of fast propagation rotates CCW from epicardium to endocardium and the intramural wavefront acquires a helical shape. The axial dipoles attached to the deep portions of the wavefront produce potential maxima in those deep regions toward which they propagate along fibers. Epicardial far-field reflections of these deep potential maxima result in a C-shaped crest or ridge of positive potentials flanking those portions of the epicardial wavefront that spread across fibers. In these areas, positive R waves result from the epicardial reflection of the deep, rotating potential maxima. The normal component of the oblique dipole layer can also explain part of the potential maxima and R waves observed in the cross-fiber areas. W h e n the excitation wavefront is a closed surface, or its rim is epicardial and exposed to air, the normal dipole layer does not generate any potential field outside or inside the wavefront. Its only electrical manifestation is a uniform potential jump of approximately 40 mV across the entire wavefront surface. This property of the normal dipole layer explains the absence of potential maxima facing the portions of the wavefront that spread across fibers in exposed heart preparations in the early stages of propagation (10-20 ms) after epicardial pacing (3). However, when the heart is in the chest, or is immersed in an electrolytic tank, the normal dipole layer elicited by epicardial pacing has a rim that is in contact with a conducting medium. In these conditions, the normal dipole layer generates electric currents that spread through the heart and the extracardiac conducting media. These currents flow from the entire leading surface of the wavefront toward the resting tissues and then back toward the trailing surface of the wavefront. In the cross-fiber areas, the currents that flow from the wavefront toward the resting tissue are partially or totally counterbalanced by the currents coming from the axial dipole layer that flow in the opposite direction, toward and into the advancing wavefront, as explained earlier. If the density of the normal currents in the cross-fiber regions is higher than that of the axial currents, potential maxima and R waves will appear in these same areas. In addition, as soon as an excitation wave elicited by epicardial pacing reaches the endocardium, the wavefront acquires a second rim, which is in contact with cavitary blood, a highly conducting medium. The size of the endocardial rim will increase rapidly because of Purkinje involvement. At this stage, more currents will flow from the wavefront toward the resting tissues, both along and across fibers, and the likelihood of potential maxima and R waves appearing in those regions will increase. While the mechanisms just described can explain part of the positive potentials and R waves in the cross-fiber areas, they cannot account for the totally positive unipolar ECGs that are invariably observed in the relatively extensive regions that are excited at the end of the QRS interval. Model simulations representing a spherical norrnal dipole layer spreading through a spherical heart
•
Taccardi et al.
99
show that totally positive ECGs with entirely positive intrinsic deflections cannot be produced by a uniform dipole layer moving past a unipolar recording electrode, nor can an axial dipole layer generate such totally positive waveforms (1). Because neither the axial nor the normal current sources associated with an excitation wavefront can explain the observed ECG waveforms, we made the hypothesis that a third factor, namely the reference potential, may have affected the measured potential values and the shape of the unipolar ECGs in our experiments. The hypothesis was suggested by the behavior of the zero line in epicardial and intramural potential maps during the spread of excitation. The zero line is the locus of the points whose potential is equal to that of the remote or indifferent reference electrode, generally the Wilson central terminal. In epicardial potential maps recorded after epicardial stimulation, the zero line does not occupy a stable position within the array of densely packed equipotential lines that reveal the underlying wavefront. In the early stages of propagation (10-20 ms), in the cross-fiber areas, the zero line leaves the entire potential drop associated with a wavefront on the negative side of the distribution. Accordingly, the spatial potential profile across the wavefront ranges from -30 or -40 mV in the excited area to zero in the resting area, and the densely packed equipotential lines that outline the wavefront are all negative. At 40-50 ms after the stimulus, the zero line is in the middle of the potential drop and the potential profile ranges from -15 to +15 mV. Here, 50% of the equipotential lines are negative and 50% are positive. Finally, during the last 10 ms of the QRS, the zero line leaves the entire wavefront on the positive side of the distribution, the potential profile goes from approximately +30 or +40 mV to zero, and all of the equipotential lines that outline the wavefront are positive. This behavior of the zero line shows that during the QRS interval, the reference potential moves from one extreme of the potential drop associated with the wavefront to the other extreme. An opposite shift occurs during repolarization. In another series of observations, we analyzed the position of the reference potential within the range of potential values measured over the entire heart surface at a series of time instants during the QRS interval. In the early stages of ventricular excitation, the reference potential was near the positive extremum of the potential range, in the middle of the QRS it was approximately equidistant from the two extrema, and at the end of the QRS it was close to the negative extremum. Our present tentative explanation of the mechanism that produces the drift of the zero line during the QRS can be summarized as follows: 1. Recent experimental observations from our laboratory performed with an isolated canine heart in a torso-shaped electrolytic tank showed that at any given time instant during the cardiac cycle, the potential of the Wilson central terminal is close to (within I-2 mV) the average potential measured on the ventricular surface. This result was anticipated by Brody and Evans (13) who
100
Journal of Electrocardiology Vol. 29 Supplement
considered the case of a remote indifferent reference electrode in a large electrolytic tank. 2. Taking the average heart surface potential as the reference potential, produces a zero line that divides the surface of the heart into two portions, such that the integral of the potential over one portion has equal magnitude and opposite polarity compared to the integral over the other portion. This is a general property of the average. In the initial stages of propagation after an epicardial stimulus, the most negative epicardial potentials ( - 2 0 - - 4 0 mV relative to the highest epicardial potential) are concentrated in a very small excited area. To achieve equality of the integrals in the positive and negative areas, the zero line must leave the entire excited area and the entire wavefront in the negative portion of the epicardial surface. W h e n 50% of the surface is excited, the zero line will leave 50% of the potential drop associated with the wavefront on the positive side and 50% on the negative side. At the end of ventricular excitation, w h e n the resting area is small, the zero line will leave the entire resting area and the wavefront itself in the positive portion of the epicardial surface. This interpretation of the shift of the zero line during propagation and repolarization is currently being tested by means of numerical simulations that will be reported elsewhere. The same interpretation enabled us to predict the behavior of the unipolar ECGs in a n u m b e r of experimental conditions, namely, local conduction delays and local accelerations. Local delays produced b y local cooling or by intracoronary injection of procainamide increased the R/S amplitude ratio in the delayed areas, as predicted by the theory, whereas local warming decreased the ratio. The negative drift of the reference potential introduces a positive trend into the unipolar ECGs that progressively develops during the QRS interval and can be clearly revealed by superimposing a series of timealigned epicardial ECGs recorded at increasing distances from a pacing site. An opposite drift occurs during repolarization. This previously unrecognized component of the ECG may have clinical relevance because it affects the slope, polarity, and area of the ECG waveforms and therefore influences a n u m b e r of measurements based on the slope or area of ECG waves, namely, excitation times, recovery times, activation-recovery intervals, and QRS, ST-T, and QRST integrals. We have not yet quantified these effects in normal and abnormal beats, but preliminary observations suggest that the drift of the reference potential affects the QRST area in part of the cases in which the recovery sequence is different from the activation sequence.
References 1. Corbin LV, Scher AM: The canine heart as an electrocardiographic generator. Circ Res 41:58, 1977 2. Spach MS, Miller III WT, Miller-Jones E et ah Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle. Circ Res 45:188, 1979 3. Taccardi B, Macchi E, Lux RL et ah Effect of myocardial fiber direction on epicardial potentials. Circulation 90:3076, 1994 4. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part I. Rectangular and cubic arrays of excitable elements. J Electrocardiol 24:1, 1991 5. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part II. Excitation in the simplified left ventricle. J Electrocardiol 24:17, 1991 6. Leon LJ, Horacek BM: Computer model of excitation and recovery in the anisotropic myocardium. Part IIL Arrhythmogenic conditions in the simplified 1eft ventricle. J Electrocardiol 24:33, 1991 7. Colli Franzone P, Guerri L, Taccardi B: Spread of excitation in a myocardial volume: simulation studies in a model of ventricular muscle activated by point stimulation. J Cardiovasc Electrophysiol 4:144, 1993 8. Roberts DE, Scher AM: Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ Res 50:342, 1982 9. Taccardi B, Lux RL, Ershler PR et al: Effect of myocardial fiber direction on 3-D shape of wavefronts and associated potential distributions in ventricular walls. (abstract) Circulation 86(suppl I):I-752, 1992 10. Colli Franzone P, Guerri L, Viganotti C et aI: Potential fields generated by oblique dipole layer modeling excitation wavefronts in the anisotropic myocardium: comparison with potential fields elicited by paced dog hearts in a volume conductor. Circ Res 51:330, 1982 11. Cole Franzone E Guerri L, Taccardi B: Potential distributions generated by point stimulation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle. J Cardiovasc Electrophysiol 4:438, 1993 12. Streeter D: Gross morphology and fiber geometry of the heart, p. 61. In Berne RM (ed): Handbook of physiology. Vol. 1: The heart. Sect. 2: The cardiovascular system. Williams and Wilkins, Baltimore, 1979 13. Brody DA, Evans JW: Some reflections on zero potential in electrocardiography. Am Heart J 60:661, 1960