We describe accurate algorithms for simulating propagated electric activation in three-dimensional anisotropic cardiac muscle, based on bidomain theory under subthreshold conditions and governed by a cellular automaton when an action potential is elicited. In a bidomain formulation, we represent the anisotropic electric properties of cardiac muscle by conductivity tensors Gi and Ge in intracellular and extracellular domains, separated by a cell membrane with capacitance cm per unit area. For an equal anisotropy ratio (Gi kGe), propagated activation is described by a parabolic reaction-diffusion equation for the transmembrane potential. For general anisotropies (Gi kGe), the transmembrane and extracellular potentials need to be solved from a coupled system of parabolic and elliptic partial differential equations. We show how this full system can be decoupled into one parabolic system of reactiondiffusion type by introducing the harmonic means of conductivities in the intracellular and extracellular domains. We also describe an algorithm that accounts for a size of model cells which are larger than the thickness of the wave front and thus permit the accurate simulation on a macroscopic scale. We found that the decoupling via the harmonic-mean approximation of bidomain conductivities allows physiologically accurate simulations of cardiac electric propagation phenomena in a manner that is computationally tractable.

In this study self-organizing maps (SOM) were utilized for spatiotemporal analysis and classification of body surface potential mapping (BSPM) data. Altogether 86 cardiac depolarization (QRS) sequences paced by a catheter in 18 patients were included. Spatial BSPM distributions at every 5 ms over the QRS complex were first presented to an untrained SOM. The learning process of the SOM units organized the maps in such a way that similar BSPMs are represented in particular areas of the SOM network. Thereafter, time trajectories and distance maps were created on the trained SOM from sequential maps in a selected paced QRS. The trajectories and distance maps can be applied as such for the localization of abnormal ventricular activation, as well as quantitative input for statistical classification. The results indicate that the method has potential for locating endocardial sites of abnormal ventricular activation, despite the patient material being too limited to provide a reliable statistical evaluation of the source localization accuracy.

Determination of an accurate electrocardiographic (ECG) baseline is generally needed for localization of ventricular arrhythmias with body surface potential mapping (BSPM). We suggest a novel signal processing method for ECG baseline reconstruction during monomorphic ventricular tachycardias (VT). The method is based on an assumption that VT consists of similar ventricular extrasystolic beats with overlapping depolarization and repolarization. The sequential reconstruction algorithm utilizes information of small variations in the heart rate and yields a non-overlapping QRST-signal, provided that the measurement set-up has a high enough temporal resolution to avoid distortions due to sampling differences and misalignment of individual beats. The reconstructed QRST-signal is utilized to subtract overlapping T-waves from the QRS complexes during VT. The use of the method is demonstrated with clinically measured BSPM data.

BACKGROUND:Delayed electrical activity necessary for re-entrant ventricular tachycardia (VT) is detectable noninvasively with high resolution techniques. We compared high resolution signal-averaged analysis of magnetocardiography (MCG), body surface potential mapping (BSPM), and orthogonal three-lead ECG (SA-ECG) in the identification of patients prone to VT after myocardial infarction (MI).METHODS:Patients with remote myocardial infarction and cardiac dysfunction were studied, 22 with (VT group) and 22 without VT (control group). MCG with seven channels and BSPM with 63 and SA-ECG with three orthogonal leads were registered. After signal-averaging and highpass filtering, three time domain analysis (TDA) parameters describing late electrical activity were computed: QRS duration (QRSd), root mean square amplitude (RMS) of the last 40 ms of QRS, and the duration of the low-amplitude QRS end (LAS).RESULTS:All parameters by each method were significantly different between the patients' groups. For example, LAS parameter in MCG was 59 (SD 22) ms in the VT group vs. 37 (SD 13) ms in controls (P < 0.001), 77 (SD 22) ms vs. 56 (SD 19) ms in BSPM (P = 0.002), and 60 (SD 24) ms vs. 39 (SD 22) ms in SA-ECG (P = 0.005). The combination of LAS parameter in MCG and SA-ECG resulted in improved performance in comparison to any single parameter with 95% sensitivity and 68% specificity.CONCLUSIONS:All three high resolution methods identified VT propensity among post-MI patients with cardiac dysfunction and between-method differences were small. Information in MCG and SA-ECG may be complementary and their combination could be of value in postinfarction arrhythmia risk assessment.

Conventional determination of the ventricular effective refractory period (VERP) is unsuitable for detection of rapid fluctuations in the effective refractory period (ERP). A programmed stimulation system was developed that adapts continuous atrioventricular sequential pacing, incremental extrastimulus interval (S1S2) scanning, and automatic detection of extrastimulus capture which is followed by shortening of S1S2 to execute repeated scanning. The accuracy of ERP determination was tested using variable incremental (2 and 4 ms) and decremental (4-16 ms) steps of the S1S2 interval. Based on a mean of 82 determinations in eight patients, the average VERP values stayed at 249.8-251.0 ms except during the highest capture frequency. Standard deviation of ERP values ranged from 1.1 to 2.5 ms on average at the tested incremental and decremental steps. One determination was accomplished within 7.8-15.6 seconds on average. The ability to track changes in ERP was tested by changing the drive cycle length. Time constants for the adaptation rate of VERP and ventricular monophasic action potential duration at a 90% level of repolarization were determined from each test, and were similar, 51 +/- 8 seconds (mean +/- SEM) for ERP and 51 +/- 6 seconds for the action potential duration. Thus, the developed method provides accurate ERP measurements during rapid variation in ventricular refractoriness. It allows studying the recovery of excitability and the action potential duration simultaneously, and would be valuable particularly in pathological conditions and pharmacologic interventions where these electrophysiological variables become dissociated.

Introduction This study aimed to identify the optimal locations in multichannel magnetocardiography (MCG) and body surface potential mapping (BSPM) to detect exercise-induced myocardial ischemia. Methods We studied 17 healthy controls and 24 coronary artery disease (CAD) patients with stenosis in one of the main coronary artery branches: left anterior descending (LAD) in 11 patients, right (RCA) in 7 patients, and left circumflex (LCX) in 6 patients. MCG and BSPM signals were recorded during a supine bicycle stress test. The capability of a recording location to separate the groups was quantified by subtracting the mean signal amplitude of the normal group from that of the patient group during the ST segment and at the T-wave apex, and dividing the resulting amplitude difference by the corresponding standard deviation within all subjects. Results In MCG the optimal location for ST depression was at the right inferior grid for the RCA, at the mid-inferior grid for the LCX, and in the middle of these locations for the LAD subgroup (mean ST amplitudes: CAD −80 ± 360fT, controls 610 ± 660fT; p < 0.001). In BSPM it was on the left upper anterior thorax for the LAD, left lower anterior thorax for the RCA, and on the lower back for the LCX subgroup (mean ST amplitudes: CAD −39 ± 61 μV and controls 38 ± 38 μV; p < 0.001). In MCG the optimal site for T-wave amplitude decrease was the same as the one for the ST depression. In BSPM it was on the middle front for the LAD, on the back for the LCX and on the left abdominal area for the RCA group. In accordance with electromagnetic theory, the largest ST segment and T-wave amplitude changes took place in MCG in locations orthogonal to those in BSPM. Conclusion This study identified magnetocardiographic and BSPM recording locations which are sensitive for detecting transient myocardial ischemia by evaluation of the ST segment as well as the T-wave. These locations strongly depend on ischemic regions and are outside the conventional 12-lead ECG recording sites.

1 Introduction First idealized models describing the normal activation sequence in the human heart were reported over two decades ago [1, 2]. Mainly due to computational limitations, the models did not include myocardial anisotropy nor physiological propagation. On the basis of anisotropic bidomain theory [3] and cellular automata theory [4], development of more realistic whole-heart models have become feasible [5]. A ventricular model that produces a correct normal activation sequence is a prerequisite for simulating pathological conditions, such as ischemia, infarction or ventricular arrhythmias. A comprehensive model should feature an anatomically accurate geometry, intramural fibrous structure, and a conduction system. Implementation of the ventricular conduction system is a challenge, since it should be flexible enough to allow " rewiring " of the conduction system for each individual case where endocardial mapping data are available. Advances in computer technology have only recently made this approach possible. Detailed studies on the anatomy of the human conduction system are scarce, and often report a high degree of interindividual variability. Therefore, we followed the criterion that the conduction system should rather accurately reproduce correct the pattern of ventricular activation sequence than to follow any predetermined anatomical design. The conduction system model was validated, first by comparing the simulated activation isochrones to those reported in the literature, and second by comparing the resulting body surface potential maps and magnetocardiographic distributions to our recordings obtained in normal subjects. 2 Methods 2.1 Anisotropic propagation model Our hybrid model of the anisotropic myocardium describes the subthreshold behaviour of the elements according to the bidomain theory [3], while in the suprathreshold region the elements behave as cellular automata [4]. Each element is assigned a specific type and a vector of local fiber direction [5, 6]. Each element can be in one of four macrostates, corresponding to different phases of an action potential: resting, excitatory, absolute refractory, or relative refractory. During simulation, elements undergo a series of macrostate transitions, which have been described in detail in Ref. [7]. The subthreshold transmembrane potential, v m is calculated from the generalized cable equation, derived from the anisotropic bidomain theory [3]: c m ∂v m / ∂t = k / (k+1) ∇ • D i ∇v m-i ion + i app (1) Here we assume that the assumption of equal anisotropy ratios is valid [5, 7]. In Eq. 1, c m is the specific membrane capacitance, D i is the intracellular conductivity tensor, …

Body surface potential mapping (BSPM) is superior to 12-lead electrocardiography for detection of acute and old myocardial infarctions (MIs). We used BSPM to examine electrocardiographic criteria for acute reversible myocardial ischemia. BSPM with 123 channels was performed in 45 patients with coronary artery disease (CAD) and 25 healthy controls during supine bicycle exercise testing. Of the 45 patients, 18 patients had anterior, 14 had posterior, and 13 had inferior ischemia documented by coronary angiography and thallium scintigraphy. The ST amplitude was measured 60 ms after the J-point and the ST slope calculated by fitting a regression line from the J-point to 60 ms after it. The optimal locations for detecting ST depression and ST-slope decrease were identified. In the pooled CAD patient group, the optimal location for ST depression was 5 cm below standard lead V5 (CAD group: −70 ± 70 μV; controls: 70 ± 80 μV, p <0.001). Using a cut-off value of −10 μV, the ST depression separated the patients with CAD from controls with a sensitivity of 84% and a specificity of 96%. The ST slope became more horizontal in the patient group than in the control group. The optimal location for ST-slope decrease was over the left side (CAD group: 20 ± 20 μV/s; controls: 720 ± 320 μV/s, p <0.001). Using a cut-off value of 320 μV/s, the ST slope separated patients with CAD from controls with a sensitivity of 93% at a specificity level of 88%. The area under the receiver operating characteristic curve of ST slope tended to be higher than the one of ST depression (97% vs 93%; p = 0.097). In conclusion, regions sensitive for ST depression and for ST-slope decrease could be identified in BSPM, despite variation in the location of ischemia and the presence or absence of a history of MI. ST slope is a sensitive and specific marker of transient myocardial ischemia, and might perform even better than ST depression.

In 12-lead electrocardiography (ECG), detection of myocardial ischemia is based on ST-segment changes in exercise testing. Magnetocardiography (MCG) is a complementary method to the ECG for a noninvasive study of the electric activity of the heart. In the MCG, ST-segment changes due to stress have also been found in healthy subjects. To further study the normal response to exercise, we performed MCG mappings in 12 healthy volunteers during supine bicycle ergometry. We also recorded body surface potential mappings (BSPM) with 123 channels using the same protocol. In this paper we compare, for the first time, multichannel MCG recorded in bicycle exercise testing with BSPM over the whole thorax in middle-aged healthy subjects. We quantified changes induced by the exercise in the MCG and BSPM with parameters based on signal amplitude, and correlation between signal distributions at rest and after exercise. At the ST-segment and T-wave apex, the exercise induced a magnetic field component outward the precordium and the minimum value of the MCG signal over the mapped area was found to be amplified. The response to exercise was smaller in the BSPM than in the MCG. A negative component in the MCG signal at the repolarization period of the cardiac cycle should be considered as a normal response to exercise. Therefore, maximum ST-segment depression over the mapped area in the MCG may not be an eligible parameter when evaluating the presence of ischemia. © 2001 Biomedical Engineering Society. PAC01: 8719Nn, 8719Hh, 8780Tq

Using a three-dimensional computer model of the human ventricular myocardium, we studied the role of ventricular architecture and conduction system in generating intramural activation patterns and the extracardiac electric field. The model represents the myocardium as an anisotropic bidomain; it incorporates detailed anatomical features, including intramural fiber rotation, the differences in the fiber arrangement of the trabeculae and papillary muscles, and a conduction system. Ectopic activation was elicited at various depths, and “normal” activation was initiated via the conduction system. Extracardiac potentials were calculated throughout each activation sequence. The simulated epicardial potential maps resembled those measured in canine hearts, featuring a central minimum accompanied by two maxima in the early stages of ectopic activation, with the axis joining these extrema approximately parallel to the fibers near the pacing site. The simulated isochrones for the “normal” activation had characteristics very similar to those observed in isolated perfused human hearts.

We have applied various methods to extract parameters from high-resolution magnetocardiographic (MCG) and electrocardiographic (ECG) recordings for characterizing the risk of life-threatening arrhythmias. The methods include detection of late fields and late potentials at the end of the QRS, abnormalities in spectral variability and signal fragmentation during the QRS, and variability in the heart rate. In addition, we have developed methods to convert MCG signals measured with any sensor configurations to a common presentation form. The signal processing methods have been implemented on a user-friendly interface which allows fast and easy use in a clinical environment.

The BioMag Laboratory was established in 1994–1995 in the Helsinki University Central Hospital (HUCH) to provide a facility for versatile biomagnetic studies in a clinical environment. A three-layer magnetically shielded room (MSR) [7] together with a 68-channel cardiomagnetometer and a 122-channel neuromagnetometer [2, 3] form the core of the laboratory, owned together by HUCH, Helsinki University of Technology (HUT) and the University of Helsinki. In this paper, we focus on magnetocardiographic (MCG) functional imaging, started in May 1995 in the BioMag Laboratory.

Body surface potential mapping (BSPM) data obtained during endocardial stimulation at multiple ventricular pacing sites show a broad spectrum of potential distributions. In this study, BSPM sequences are analysed using a neural network approach based on self-organisation that provides a noninvasive estimation of the site of origin of stimulated ventricular activation. The Self-Organizing Map (SOM) network used in this study is arranged as a two-dimensional lattice of neurons, each of them representing a particular distribution of body surface potentials. For the training of the SOM network, 123-channel BSPM recordings were obtained from 86 endocardial pacing locations in 19 patients with a previous myocardial infarction. Ventricular activation patterns from different pacing sites are visualized as time traces on the trained SOM. Classification of the activation patterns with respect to the endocardial pacing location is performed by Learning Vector quantization. The localisation results are visualized on a realistic model of the endocardial surfaces of the right and left ventricles.

We implemented a method for interactive creation and manipulation of a conduction system in our computer model of the ventricular myocardium. The conduction system was defined interactively in terms of nodes and a connectivity matrix with a computer program utilizing the OpenGL capabilities of the SGI Visual PC. To validate the conduction system, simulations were run where the activation propagated from the His bundle to Purkinje myocardial junction (PMJ) sites and through the ventricular myocardium. The simulated activation sequence agreed with isochrones obtained from an isolated human heart. The calculated body surface potential maps during the initial QRS complex correlated well with our clinical recordings on normal subjects