S IMULATION OF EXTRASYSTOLE IN BIDOMAIN VENTRICULAR MODEL WITH PATIENT SPECIFIC GEOMETRY

The goal of the study was to simulate electrical activation on the heart ventricles and body surface potentials (BSP) during extrasystole using a realistic homogeneous model of cardiac ventricles and the patient torso. Electrical activation in the ventricular model was started in the known position of the initial ectopic activation confirmed by successful ablation in the left ventricle near the heart base as well as in several other sites near this position. The propagated electrical activation in the ventricular model was modeled using bidomain reaction-diffusion (RD) equations with the ionic transmembrane current density defined by the modified FitzHugh-Nagumo (FHN) equations. The torso was treated as a homogeneous passive volume conductor. The whole simulation was numerically solved in the Comsol Multiphysics environment. Simulated BSP were compared with BSP measured in a real patient during extrasystole. The polarity and shape of selected simulated and measured ECG leads as well as the whole body surface potential distribution during the initial ectopic activation were in the best accordance when the stimulated region was close to the real position of the site of initial ectopic focus.


INTRODUCTION
In healthy heart, electrical activation and muscle contractions occur in regular rhythm.The electrical activation of the ventricles starts from the atrioventricular node and propagates through the fast conduction system to the working ventricular myocardium [1].In the pathologically changed heart, electrical activation may start in inappropriate extraordinary time in an improper ectopic site in ventricles, resulting in an extrasystole with abnormal electrocardiographic (ECG) signals without the P wave and with changed shape of the QRS complex and T wave.Since the velocity of activation propagation in the conduction system is several times higher than that in the working ventricular myocardium, normal activation occurs rapidly during the first about 20 milliseconds at several regions of the healthy ventricular myocardium and spreads along the endocardium and toward the epicardium.During extrasystole, the ectopic electrical activation begins at only one site in the myocardium and spreads mainly through the working myocardium.The activation sequence is changed, and the time needed to activate both ventricles is markedly prolonged.The electrical activity of the heart is manifested on the patient torso as body surface potentials (BSP).The ectopic activation is reflected in changed BSP dynamics and the QRS complex in the ECG signal is prolonged significantly over 120 ms.

TRENDY BMI 2023
In this study, we simulated the ventricular activation and corresponding BSP during extrasystole.The model of ventricular activation was based on bidomain reaction-diffusion (RD) equations with the modified FitzHugh-Nagumo (FHN) equations for the local ionic transmembrane current density.BSP were computed in patient-specific homogeneous model of the heart ventricles and torso.Several initial positions of the ectopic activation were tested in order to obtain the BSP distribution and ECG signals as close as possible to the measured ones.

SUBJECT AND METHODS
The data were recorded from a 50-year-old man (P034), a patient after large myocardial infarction on the anterior wall of the left ventricle and with frequent ventricular extrasystoles.ECG signals from limb leads and BSP maps were recorded from 128 electrodes on the chest.The geometry of torso and heart ventricles and real positions of measuring ECG electrodes were obtained from a CT scan of the torso taken immediately after the BSP measurement with ECG electrodes attached.The patient was indicated to radiofrequency ablation of the ectopic focus in the electrophysiological lab.The ectopic focus was localized in the left ventricle near the heart base and was confirmed by successful ablation.

MODEL OF THE TORSO AND HEART VENTRICLES
The model of the patient torso and heart ventricles as well as the positions of ECG electrodes were obtained from the patient CT scan using the Tomocon and the Comsol Multiphysics software (Fig. 4).The size of the ventricular model was approximately 130 mm in base-to-apex direction (height), 140 mm in the left-to-right and 100 mm in the anterior-to-posterior direction.The thickness of the ventricular wall was about 5-9 mm in the right ventricle and about 8-11 mm in the left ventricle in the middle of the model height.

THE BIDOMAIN REACTION DIFFUSION MODEL
The propagation of electrical activation in the model of ventricles was modeled using bidomain reactiondiffusion (RD) equations with the ionic transmembrane current density defined by the modified FitzHugh-Nagumo (FHN) equations.The torso was treated as a passive volume conductor region.The whole simulation was numerically solved in the Comsol Multiphysics environment.
The bidomain RD model [2], [3] is described by partial differential equations where Ve is the extracellular potential, Vi is the intracellular potential, De and Di is the extracellular and intracellular tissue diffusivity, iion is the local ionic transmembrane current density, and is is the stimulation current density.Current densities were normalized to the membrane capacitance.
The tissue diffusivity D (in this model D = De = Di) is dependent on the tissue conductivity  , on the membrane surface-to-volume ratio  , and on the membrane capacitance per unit area Cm  =  (  ) ⁄ . ( The ionic transmembrane current density iion and the membrane potential ( ) were modeled using the modified FitzHugh-Nagumo (FHN) equations [3], [4]).For homogeneous model of the ventricles, value of the tissue diffusivity in the myocardium was set to D = 0.0008 m 2 /s (corresponding to tissue conductivity σ = 0.8 S/m).Values of the modified FHN model parameters were the same as in [4].For these parameters, the activation propagation velocity of a planar wave front was about 0.7 m/s.Torso conductivity was set to σ = 0.02 S/m.Initial value of the intracellular potential was set to -0.085 V and the other variables were set to 0. Fluxes through all external boundaries of the torso were set to zero and the potential on the internal torso boundary with the ventricles was set to Ve.

EXTRASYSTOLE MODELING
The known position of the initial ectopic activation confirmed by successful ablation in the left ventricle near the heart base is shown in Fig. 2.This position as well as several other were tested as possible ectopic focus region.The ectopic focus was modeled as spherical region with a radius of 4 mm where the stimulation current is injected.The "smoothed rectangular" pulse with a duration of 10 ms and an amplitude of 40 A/F was used for stimulation.

RESULTS
The ventricular activation and BSP were simulated for five positions of the stimulated region: Case 1reported position of the ectopic focus ablation, Case 2 to 5other positions around the focus.The best agreement between measured and simulated BSP was obtained in the Case 2. For other positions of the stimulated region, the simulated ECG potentials changed their shape (Fig. 8), e.g. the second part with negative polarity in limb lead II and III was missing.Spatial distribution of the simulated transmembrane potential Vm in selected time instants for the Case 2 is shown in Fig. 3.

DISCUSSION AND CONCLUSIONS
Obtained BSP distribution from the simulated ectopic position was similar to the measured one namely during the initial time interval.When looking on the QRS complexes in simulated limb leads ECG, the high peak of positive polarity in leads II and III was correctly occurring in all tested positions of the stimulated region but its shape was changed, and the maximum was delayed.The further small negative potentials were seen only in two cases (Case 2 and Case 3).Differences between the measured and simulated ECG and BSPs, namely during the terminal part of the ventricular depolarization can be caused by not considering the anterior myocardial infarction region present in patient P034 and by not taking into account the possible role of the conduction system in the ventricular model.From these results it can be concluded that the simulation of the ventricular ectopic activation can produce BSP close to reality only in the first part of activation propagation.In later parts it is difficult to predict whether activation is spreading only in myocardium, or it enter to the conduction system or how it may pass by the infarction scar.

Fig. 1
Fig. 1 Left anterior view of the torso model with ECG electrode positions (left) and model of the ventricles in the transparent torso model (right).The position of ectopic focus is highlighted in blue.

Fig. 2
Fig. 2 The posterior view (left) and top posterior view (right) of the tested stimulated regions in the ventricular model (ablation area is highlighted in green, other positions in blue).

Fig. 3
Fig. 3 The transmembrane potential Vm [V] in time t = 104 ms, 144 ms and 184 ms for the Case 2.

Fig. 4
Fig. 4 Measured BSP map [mV] in time tECG = 60 ms and the corresponding simulated BSP [mV] in time t = 104 ms for the Case 2.

Fig. 5
Fig. 5 Measured BSP map [mV] in time tECG = 80 ms and the corresponding simulated BSP [mV] in time t = 124 ms for the Case 2.

Fig. 7
Fig. 7 Measured potentials (left) and simulated (right) potentials in limb leads I, II and III during QRS complex and initial part of T wave.Measured signals have time tECG and simulated signals have time t = tECG -44 ms.

Fig. 8
Fig. 8 Simulated potentials in limb leads I, II and III during QRS complex and initial part of T wave for the Case 1, 3, 4 and 5.