Experimental and computational studies of strain-conduction velocity relationships in cardiac tissue.

Velocity of electrical conduction in cardiac tissue is a function of mechanical strain. Although strain-modulated velocity is a well established finding in experimental cardiology, its underlying mechanisms are not well understood. In this work, we summarized potential factors contributing to strain-velocity relationships and reviewed related experimental and computational studies. We presented results from our experimental studies on rabbit papillary muscle, which supported a biphasic relationship of strain and velocity under uni-axial straining conditions. In the low strain range, the strain-velocity relationship was positive. Conduction velocity peaked with 0.59 m/s at 100% strain corresponding to maximal force development. In the high strain range, the relationship was negative. Conduction was reversibly blocked at 118+/-1.8% strain. Reversible block occurred also in the presence of streptomycin. Furthermore, our studies revealed a moderate hysteresis of conduction velocity, which was reduced by streptomycin. We reconstructed several features of the strain-velocity relationship in a computational study with a myocyte strand. The modeling included strain-modulation of intracellular conductivity and stretch-activated cation non-selective ion channels. The computational study supported our hypotheses, that the positive strain-velocity relationship at low strain is caused by strain-modulation of intracellular conductivity and the negative relationship at high strain results from activity of stretch-activated channels. Conduction block was not reconstructed in our computational studies. We concluded this work by sketching a hypothesis for strain-modulation of conduction and conduction block in papillary muscle. We suggest that this hypothesis can also explain uni-axially measured strain-conduction velocity relationships in other types of cardiac tissue, but apparently necessitates adjustments to reconstruct pressure or volume related changes of velocity in atria and ventricles.

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations.

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study.

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.

A noninvasive imaging modality for cardiac arrhythmias.

BACKGROUND: The last decade witnessed an explosion of information regarding the genetic, molecular, and mechanistic basis of heart disease. Translating this information into clinical practice requires the development of novel functional imaging modalities for diagnosis, localization, and guided intervention. A noninvasive modality for imaging cardiac arrhythmias is not yet available. Present electrocardiographic methods cannot precisely localize a ventricular tachycardia (VT) or its key reentrant circuit components. Recently, we developed a noninvasive electrocardiographic imaging modality (ECGI) that can reconstruct epicardial electrophysiological information from body surface potentials. Here, we extend its application to image reentrant arrhythmias. METHODS AND RESULTS: Epicardial potentials were recorded during VT with a 490 electrode sock during an open chest procedure in 2 dogs with 4-day-old myocardial infarctions. Body surface potentials were generated from these epicardial potentials in a human torso model. Realistic geometry errors and measurement noise were added to the torso data, which were then used to noninvasively reconstruct epicardial isochrones, electrograms, and potentials with excellent accuracy. ECGI reconstructed the reentry pathway and its key components, including (1) the central common pathway, (2) the VT exit site, (3) lines of block, and (4) regions of slow and fast conduction. This allowed for detailed characterization of the reentrant circuit morphology. CONCLUSIONS: ECGI can noninvasively image arrhythmic activation on the epicardium during VT to identify and localize key components of the arrhythmogenic pathway that can be effective targets for antiarrhythmic intervention.

Noninvasive ECG imaging of electrophysiologically abnormal substrates in infarcted hearts : A model study.

BACKGROUND: Myocardial infarction and subsequent remodeling create substrates with altered electrophysiological (EP) properties that are highly arrhythmogenic. Existing ECG methods cannot always detect the existence of such substrates nor provide any detailed information about their EP characteristics. A noninvasive method with such capabilities is greatly needed for identifying patients at risk of arrhythmias and for guidance and evaluation of therapy. Recently, we developed a noninvasive ECG imaging modality that can reconstruct epicardial EP information from body surface potentials. We extended its application to hearts with structural disease and examined its ability to detect and characterize abnormal EP substrates. METHODS AND RESULTS: Epicardial potentials were recorded with a 490-electrode sock from an open-chest dog. Recordings were obtained from a normal heart and from the same heart 2 hours after left anterior descending coronary artery occlusion and ethanol injection to create an infarct. Body surface potentials were generated from these epicardial potentials in a human torso model. Realistic geometry errors and measurement noise were added to the torso data, which were then used to noninvasively reconstruct epicardial potentials and electrograms (EGMs), with excellent accuracy. EP characteristics associated with the infarct substrate were reconstructed, including (1) a negative region over the infarct, (2) EGMs with large predominant negative deflections (eg, Q-wave EGMs), (3) Q-wave EGMs with superimposed RS deflections reflecting local activation of surviving myocardium within the infarct border zone, (4) reduced magnitudes of EGM negative derivatives, and (5) negative QRS integrals of EGMs over the infarct. CONCLUSIONS: ECG imaging can noninvasively detect and map abnormal EP substrates associated with infarction and structural heart disease.

Estimates of repolarization dispersion from electrocardiographic measurements.

BACKGROUND: Repolarization dispersion (Rd) is frequently mentioned as a predictor of cardiac abnormalities. We present a new measure of Rd based on the root-mean-square (RMS) curve of an ECG lead set and compare its performance with that of the commonly used QT dispersion (QTd) measure with the use of recovery times measured from directly recorded canine electrograms. METHODS AND RESULTS: Using isolated, perfused canine hearts suspended in a torso-shaped electrolytic tank, we simultaneously recorded electrograms from 64 epicardial sites and ECGs from 192 "body surface" sites. RMS curves were derived from 4 lead sets: epicardial, body surface, precordial, and a 6-lead optimal set. Repolarization was altered by changing cycle length, temperature, and activation sequence. Rd, calculated directly from recovery times of the 64 epicardial potentials, was then compared with the width of the T wave of the RMS curve and with QTd for each of these 4 lead sets. The correlation between T-wave width and Rd for each lead set, respectively, was epicardium, 0.91; body surface, 0.84; precordial, 0.72; and optimal leads, 0.81. The correlation between QTd and Rd for each lead set was epicardium, 0.46; body surface, 0.47; precordial, 0.17; and optimal leads, 0.11. CONCLUSIONS: RMS curve analysis provides an accurate method of estimating Rd from the body surface. In contrast, QTd analysis provides a poor estimate of Rd.

Noninvasive electrocardiogram imaging of substrate and intramural ventricular tachycardia in infarcted hearts.

OBJECTIVES: The goal of this study was to experimentally evaluate a novel noninvasive electrocardiographic imaging modality during intramural reentrant ventricular tachycardia (VT). BACKGROUND: Myocardial infarction and subsequent remodeling produce abnormal electrophysiologic substrates capable of initiating and maintaining reentrant arrhythmias. Existing noninvasive electrocardiographic methods cannot characterize abnormal electrophysiologic substrates in the heart or the details of associated arrhythmias. A noninvasive method with such capabilities is needed to identify patients at risk of arrhythmias and to guide and evaluate therapy. METHODS: A dog heart with a four-day-old infarction was suspended in a human shaped torso-tank. Measured body surface potentials were used to noninvasively compute epicardial potentials, electrograms and isochrones. Accuracy of reconstruction was evaluated by direct comparison to measured data. Reconstructions were performed during right atrial pacing and nine cycles of VT. RESULTS: Noninvasively reconstructed potential maps, electrograms and isochrones identified: 1) the location of electrophysiologically abnormal infarct substrate; 2) the epicardial activation sequences during the VTs; 3) the locations of epicardial breakthrough sites; and 4) electrophysiologic evidence for activation of the Purkinje system and septum during the reentrant beats. CONCLUSIONS: Electrocardiographic imaging can noninvasively reconstruct electrophysiologic information on the epicardium during VT with intramural reentry, provide information about the location of the intramural components of reentry and image abnormal electrophysiologic substrates associated with infarction.

Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models.

Parallel numerical simulations of excitation and recovery in three-dimensional myocardial domains are presented. The simulations are based on the anisotropic Bidomain and Monodomain models, including intramural fiber rotation and orthotropic or axisymmetric anisotropy of the intra- and extra-cellular conductivity tensors. The Bidomain model consist of a system of two reaction-diffusion equations, while the Monodomain model consists of one reaction-diffusion equation. Both models are coupled with the phase I Luo-Rudy membrane model describing the ionic currents. Simulations of excitation and repolarization sequences on myocardial slabs of different sizes show how the distribution of the action potential durations (APD) is influenced by both the anisotropic electrical conduction and the fiber rotation. This influence occurs in spite of the homogeneous intrinsic properties of the cell membrane. The APD dispersion patterns are closely correlated to the anisotropic curvature of the excitation wavefront.

Diagnostic body surface potential map patterns in left ventricular hypertrophy during PQRST.

Body surface potential maps were recorded from 117 thoracic sites and 3 limb electrodes in 173 normal subjects older than 30 years of age and 122 patients with clinically "pure" left ventricular (LV) hypertrophy. Typical LV hypertrophy map patterns were identified at successive instants during the PQRST waveform by removing from sequential LV hypertrophy maps the corresponding normal variability range at each electrode site. The presence in individual patients of 1 or more patterns typical in time and location of LV hypertrophy allowed retrospective assignment to the LV hypertrophy group. The most consistent discriminant patterns were excessive negative voltages in the anterior torso with reciprocal excess of positive voltages in the upper right chest during the second half of the P wave, excessive negative voltages in the lower right anterior torso at mid-QRS and excessive negative voltages in the left precordium with reciprocal excess of positive voltages in the upper right chest throughout ST-T. Best classification results were achieved with ST-T features, followed by features from the P wave, the QRS waveform and the PR segment. Cumulative use of ST-T and P features yielded a specificity of 94% with a sensitivity of 88%. Little improvement was obtained by the addition of QRS and PR information. The discriminant map criteria were applied to body surface potential maps from 169 new subjects (77 normal subjects ages 20 to 30 years and 92 patients with complicated LV hypertrophy). Little modification in specificity (93%) and sensitivity (90%) was observed. The performance of commonly used standard lead criteria was also tested.(ABSTRACT TRUNCATED AT 250 WORDS)

Qualitative and quantitative analysis of characteristic body surface potential map features in anterior and inferior myocardial infarction.

Body surface potential maps were recorded from 120 electrode sites in 236 normal subjects and 258 patients with initial evidence of either anterior myocardial infarction (MI) or inferior MI to identify characteristic map patterns in both groups. After time normalization, averaged map distributions were displayed at 18 equal time intervals during both QRS and ST-T waveforms from the normal, anterior MI and inferior MI groups. At each time instant, the 120-point averaged normal map was subtracted in turn from the corresponding anterior and inferior MI maps; the resulting differences at each electrode site were divided by the pooled standard deviation and the obtained values (discriminant indexes), plotted as contour lines with 1 standard deviation increments, producing discriminant maps for each bi-group comparison. The most consistent discriminant patterns in 114 patients with anterior MI were observed in early QRS in the upper left anterior chest where abnormal negative voltages reflected loss of electric potentials while reciprocal changes were noticed in the lower back; by mid-QRS, both distributions had moved jointly and vertically, the former in the lower torso on the midsternal line, the latter in the upper back. In 144 patients with inferior MI, abnormal positive distributions were observed in early QRS in the upper back, followed later by excessive negative voltages in the inferior right anterior chest; at mid-QRS, both distributions had migrated horizontally, the former proceeding toward the upper anterior torso, the latter to the lower left dorsal area.(ABSTRACT TRUNCATED AT 250 WORDS)

Body surface potential mapping in ischemic patients with normal resting ECG.

Patients with ischemic heart disease frequently have a normal 12-lead electrocardiogram. We recorded body surface maps from 14 ischemic patients with normal (group A) and 5 with abnormal (group B) resting electrocardiograms. ST-T map data were compared with those of 36 normal subjects. In ischemic patients the following abnormalities were found: an anomalous location and/or trajectory of the potential minimum (lowest potential) on the chest in some; in others the instantaneous values of the time functions: Mxi (highest potential on the chest), delta Vi (highest potential difference) and integral of s/Vi/dS (integral of the absolute value of the potential function extended to the entire chest surface) were lower. In some ischemic patients, both abnormalities were observed. All changes were detectable during the first 200 msec of ST-T. The anomalous potential patterns were similar in group A and B patients, suggesting an ischemic origin of group A abnormalities. By submitting 10 properly selected variables, obtained from body surface maps, to Fisher's discriminant analysis, we succeeded in correctly classifying more than 90% of the cases. The efficacy of the method was validated by using one third of the cases as a test set, with correct allocation in 80.9% of the cases. We conclude that body surface maps at rest can reveal an altered cardiac electrogenesis induced by myocardial ischemia, not apparent in the 12-lead electrocardiogram.

Spread of excitation in 3-D models of the anisotropic cardiac tissue. III. Effects of ventricular geometry and fiber structure on the potential distribution.

In a previous paper we studied the spread of excitation in a simplified model of the left ventricle, affected by fiber structure and obliqueness, curvature of the wall and Purkinje network. In the present paper we investigate the extracellular potential distribution u in the same ventricular model. Given the transmembrane potential v, associated with the spreading excitation, the extracellular potential u is obtained as solution of a linear elliptic equation with the source term related to v. The potential distributions were computed for point stimulations at different intramural depths. The results of the simulations enabled us to identify a number of common features which appears in all the potential patterns irrespective of pacing site. In addition, by splitting the sources into an axial and conormal component, we were able to evaluate the contribution of the classical uniform dipole layer to the total potential field and the role of the superimposed axial component.

Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry.

We investigate a three-dimensional macroscopic model of wave-front propagation related to the excitation process in the left ventricular wall represented by an anisotropic bidomain. The whole left ventricle is modeled, whereas, in a previous paper, only a flat slab of myocardial tissue was considered. The direction of cardiac fibers, which affects the anisotropic conductivity of the myocardium, rotates from the epi- to the endocardium. If the ventricular wall is conceived as a set of packed surfaces, the fibers may be tangent to them or more generally may cross them obliquely; the latter case is described by an "imbrication angle." The effect of a simplified Purkinje network also is investigated. The cardiac excitation process, more particularly the depolarization phase, is modeled by a nonlinear elliptic equation, called an eikonal equation, in the activation time. The numerical solution of this equation is obtained by means of the finite element method, which includes an upwind treatment of the Hamiltonian part of the equation. By means of numerical simulations in an idealized model of the left ventricle, we try to establish whether the eikonal approach contains the essential basic elements for predicting the features of the activation patterns experimentally observed. We discuss and compare these results with those obtained in our previous papers for a flat part of myocardium. The general rules governing the spread of excitation after local stimulations, previously delineated for the flat geometry, are extended to the present, more realistic monoventricular model.

Anatomical architecture and electrical activity of the heart.

In most early studies of cardiac electrophysiology, the correlation between propagation of excitation and the architecture of cardiac fibers was not addressed. More recently, it has become apparent that the spread of excitation, the sequence of recovery, the associated time-varying potential distributions and the intra- and extracardiac electrocardiograms are strongly affected by the complex orientation of myocardial fibers. This article is a review of older and very recent, partly unpublished, mathematical simulations and experimental findings that document the relationships between cardiac electrophysiology and fiber structure. Important anatomical factors that affect propagation and recovery are: the elongated shape of myocardial fibers which is the basis for electrical anisotropy; the epi-endocardial rotation of fiber direction in the ventricular walls; the epi-endocardial obliqueness of the fibers ("imbrication angle"), and the conduction system. Due to the complex architecture of the fibers, many different pathways are available to an excitation wavefront as it spreads from a pacing site: the straight line; the multiple, bent pathways resulting from the epi-endocardial rotation of fiber direction; the coiling intramural pathways associated with the "imbrication" angles (Streeter) and the pathways involving the Purkinje network. Only in a few cases is the straight line the fastest pathway. The shape of an excitation wavefront at a given time instant results from the competition between all possible pathways. To compute the potential distributions and ECG waveforms generated by a spreading excitation wave we must know the successive shapes and positions of the wavefront, the architecture of the fibers through which it propagates and the spatial distribution of their anisotropic electrical properties.

[Multiplexed peroperative mapping in unstable rhythm disorders]. / La cartographie per-opératoire multiplexée dans les troubles du rythme instables.

Since the introduction and development of mapping methods in clinical practice, some arrhythmias can now be treated surgically. We studied an automatized method of epicardial mapping necessitating only a single ventricular complex for the definition of epicardial activation; the signal was acquired from 35 monopolar electrodes spread out over the whole of the ventricular epicardium or concentrated in the zone of epicardial break through to localise its site more accurately. The acquisition, elaboration and tracing of these maps were performed with a computer; the activation can be presented as isochrones or isopotentials. The main value of this method of automatic mapping is the possibility of studying irregular arrhythmias whose potentials are difficult to obtain beat manually. This method has already been applied to 21 patients with ventricular tachycardia unresponsive to medical treatment and referred for surgery.

Anatomical and microstructural factors affecting the electrical activity of the heart. Experimental findings and mathematical simulations.

We developed an experimental preparation in which we record 1500 intramural electrograms from the ventricular walls of an isolated dog heart. The heart is plunged into an electrolytic tank shaped as a human thorax. The tank carries 1300 electrodes uniformly distributed in the conducting volume and on its surface. We obtain 2800 electric signals which enable us to define the spread of excitation and the sequence of repolarization in the heart, and to map the spatial distribution of potentials and currents in the heart, in the chest and on the body surface during a heart beat. Experimental results and mathematical simulations show that excitation, repolarization, the spatial distribution of heart potentials and the shape of the electrocardiograms are dominated by a small number of anatomical factors, namely: the geometry of the ventricles, the epi-endocardial rotation of myocardial fibers orientation in the ventricular walls, the obliqueness of the fibers relative to the epicardial surface and structure of the conduction system.

An approach to inverse calculation of epicardial potentials from body surface maps.

The inverse problem of evaluating epicardial potentials from a knowledge of heart and torso geometry as well as body surface potentials is here formulated as a problem in control theory. As is well known, such an inverse problem is ill-posed and a regularization technique has been devised to overrun this difficulty. The resulting regularized problem is well-posed and requires the minimization of a cost function including, besides the square distance of any predicted surface potential distribution from the experimental one, a regularization term involving the second derivatives of the identified epicardial potentials. The results here presented were obtained on a model problem for a plane geometry. Surface potentials generated by multipoles and perturbated with a noise level reflecting both instrumentation and electrode placement uncertainties were fitted by the proposed method and 'epicardial potentials' were determined with a maximum sum square relative error of 15%. The results suggest that by introducing suited regularity constraints, the a priori difficulties inherent to the problem of computing epicardial potentials from torso potentials, can be overcome.