Modeling and visualization of the activation wavefront propagation to improve understanding the QRS complex changes indicating left ventricular hypertrophy

    Modeling and visualization of the activation wavefront propagation to improve understanding the QRS complex changes indicating left ventricular hypertrophy Jana Svehlikova PhD, Jan Zelinka, Ljuba Bacharova MD, DSc, MBA, Milan Tysler PhD PII: DOI: Reference:

S0022-0736(16)30032-2 doi: 10.1016/j.jelectrocard.2016.05.007 YJELC 52238

To appear in:

Journal of Electrocardiology

Please cite this article as: Svehlikova Jana, Zelinka Jan, Bacharova Ljuba, Tysler Milan, Modeling and visualization of the activation wavefront propagation to improve understanding the QRS complex changes indicating left ventricular hypertrophy, Journal of Electrocardiology (2016), doi: 10.1016/j.jelectrocard.2016.05.007

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ACCEPTED MANUSCRIPT Modeling and visualization of the activation wavefront propagation to improve

Jana Svehlikova

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Institute of Measurement Science SAS, Bratislava, Slovakia

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understanding the QRS complex changes indicating left ventricular hypertrophy

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Jan Zelinka

Institute of Measurement Science SAS, Bratislava, Slovakia

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Ljuba Bacharova International Laser Center, Bratislava, Slovakia

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Institute of Pathophysiology, Medical Faculty, Comenius University, Bratislava, Slovakia Milan Tysler

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Institute of Measurement Science SAS, Bratislava, Slovakia

Corresponding author:

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Jana Svehlikova, Institute of Measurement Science, Slovak Academy of Sciences Dubravska cesta 9, 841 04 Bratislava, Slovakia Phone: +421 2 5910 4556 E-mail: [email protected]

ACCEPTED MANUSCRIPT Abstract Activation wavefront propagation was computed and visualized in a geometrical heart model for

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pathological cases of reduced velocity of propagation, left ventricular hypertrophy and their combination. Selected parameters of a multiple dipole equivalent heart generator were computed

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and compared for three heart geometries and several degrees and extents of reduction of

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propagation velocity.

First, the influence of geometrical changes modeling the left ventricular hypertrophy at reference

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propagation velocity was compared with reduction of the propagation velocity in the reference heart geometry. Reduced propagation velocity yielded similar or greater changes of the

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magnitude of the (electrical) heart vector representing the activation wavefront than the geometrical changes. Observations of the wavefront propagation with reduced velocity revealed

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longer presence of a large extent of the wavefront during depolarization which resulted in

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increased magnitude of the heart vector. The duration of depolarization was significantly prolonged only when the propagation velocity was decreased to 25% of its normal value.

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Changes of the direction of the maximal heart vector were dependent on the position of the region where the propagation velocity was reduced. Then the combination of the left ventricular hypertrophy and reduced propagation velocity was studied. Such combination enhanced the enlargement of the electrical heart vector and significantly prolonged the duration of depolarization. The influence of reduced activation velocity on the observed parameters was greater than the effect of the enlargement of the left ventricular mass.

ACCEPTED MANUSCRIPT The presented study showed that intramyocardial conduction disturbances might cause increase of the actual surface area of propagation wavefront leading to changes of the amplitudes of ECG

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signals comparable with the changes resulting from the left ventricular hypertrophy.

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Intramyocardial conduction disturbances, as well as the modeled 50% increase of the thickness of the left ventricular wall, did not cause prolongation of the QRS complex out of normal range.

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Considerable prolongation of the QRS complex duration was observed only for transmural

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slowing of the propagation velocity to 25% of its reference value in large ventricular areas or for

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combination of such slowing with the left ventricular hypertrophy. Keywords

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heart model, depolarization simulation, intra-myocardial conduction disturbances, wavefront

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propagation visualization, ECG amplitudes enlargement

ACCEPTED MANUSCRIPT Introduction Electrocardiography presents a basic tool in cardiac diagnostics. In the last decades this

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noninvasive method was extended by imaging modalities such as ultrasound methods or CT and MR tomography. Combinations of these methods offer better insight into the processes within the

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heart and increase precision of the diagnostics. However, combined results from various imaging techniques sometimes are beside the common diagnostic practices. One of such situations occurs

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when the increased amplitudes in ECG signals do not correspond to the increase of the left

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ventricular mass estimated by imaging techniques [1].

New imaging techniques also allow observation of the impaired myocardial tissue [2].

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A simulation study by Bacharova et al. [3] has shown that slowing of the action potential (AP) propagation can result in increased magnitudes of the heart vector and therefore also in increased

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ECG signals. However, slowing of the activation propagation (“Nonspecific or Unspecific

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Intraventricular Conduction Disturbance”) is in general associated particularly with prolongation

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of the QRS duration and not with the increase of ECG signals [4]. The aim of the study was to simulate the slowing of activation propagation in various regions of the left ventricle using a multiple dipole heart model [5] and to calculate and observe the resulting magnitudes of the heart vectors and depolarization time periods. The obtained results were then compared with those obtained by simulations of the normal activation propagation for two models of the left ventricular hypertrophy (LVH). Finally, combinations of LVH and conduction velocity reduction were also studied. Visualization of the activation wavefront movement allowed the authors to investigate the changes of dispersion of activation times in simulated cases. Such changes can be used as a possible physical explanation of the clinical

ACCEPTED MANUSCRIPT findings where increased ECG signals do not correspond to increased volume of left ventricular mass.

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Materials and Methods

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Heart model

A simplified geometrical model of the ventricles created from parts of ellipsoids proposed in [6]

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was used in the study. The modeled volume can be discretized to regular rectangular grid with a chosen grid resolution. In this study grid elements of 1 mm3 were used and desired properties of

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myocardial cells were assigned to each grid element.

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To model various physiological properties within the myocardium, the wall of each ventricle was divided into five layers. For each layer the action potential amplitude and duration as well as the

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propagation velocity was defined. Additionally, the model provided an option to create arbitrary

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areas as subvolumes of the modelled myocardial volume and properties of myocytes (AP

areas.

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duration and amplitude) together with propagation velocity were changed separately for such

As shown in Fig.1, realistic action potential shapes and durations were predefined through the myocardial wall according to the experiments on canine wedge preparations [7], [8]. To mimic Purkinje fibers properties, the endocardial layer (L1) with the lowest possible thickness equal to the basic grid resolution of 1 mm was used. The associated propagation velocity in the endocardial layer (i.e. along the endocardium) was defined as three times higher than the velocity in the other tissue, which was assumed 0.4 mm/ms [9].

ACCEPTED MANUSCRIPT The action potential propagation using the cellular automaton principle was started in selected starting points on the endocardial surface according to Durrer’s findings [10] and progressed in

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spherical or ellipsoidal wavefronts. Tissue anisotropy characterized by different propagation

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velocities along and across the fiber direction was not included in the simulation.

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An updated algorithm for simulation of activation propagation was used. While the original algorithm used only discrete velocity values and computed the activation in integer time steps [6],

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the new algorithm allows any chosen real values of propagation velocity and works with any

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chosen time steps. Maximal time step which can be used in the simulation depends on the defined model grid resolution and on the maximal propagation velocity assumed in the simulation: (1)

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max_time_step = grid_resolution / max_propagation_velocity

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In each grid point an elementary electrical dipole moment is computed from the differences between action potentials in the given point and the adjacent points and from their mutual

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distance [5]. Thus the resulting equivalent electrical heart generator is computed in the form of a

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multiple-dipole. The density of elementary dipoles can be optionally reduced by merging together the basic grid elements (regardless to their affiliation to the layers) to larger cubic volumes and summing up their elementary dipoles to one resulting dipole. The model also provides a facility for the visual inspection of the time development of the 3D activation wavefront during the simulated depolarization. In the presented study each resulting dipole represented cubic volume of 3x3x3 mm and the equivalent electrical heart generator consisted of 7100 dipoles. The basic grid resolution of 1 mm3 as well as the size of resulting cubic volumes for multiple dipole heart generator was the

ACCEPTED MANUSCRIPT same also when a hypertrophic heart was modeled, i.e. the number of grid points and resulting dipoles was increased in such model.

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In each time step of the simulation the electrical heart vector (HV) representing the activation wavefront was computed as the sum of the elementary dipoles. Results of simulation were

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displayed in the form of HV loops depicted analogically to vectorcardiographic loops (frontal, sagittal and horizontal view). In order to enable standard visualization of the HV loops the whole

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heart model was rotated to the position corresponding to the realistic location of the heart within

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a torso. Simulations

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First, as a reference, the normal heart activation was simulated. Then two different pathological

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conditions were modeled: reduced activation propagation velocity and left ventricular

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hypertrophy.

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Reduced propagation velocity

Three levels of reduced propagation velocity (75%, 50% and 25% of the reference velocity) were simulated in the following four locations: in the whole left ventricle (LV); and in three selected regions of the LV (anteroseptal, lateral and posterior) (Tab 1). Changes in the whole LV represented a global LV impairment/failure or scattered small regions with changed properties of myocytes (diffuse fibrosis). The chosen regional changes were located around the three main coronary vessels and imitated a fibrosis or a tissue impaired after myocardial infarction. The reduced propagation velocity was modeled either in the whole region (in layers L2-L5) or only in the two midwall layers (L3, L4) of the region, while the properties of the subendocardial

ACCEPTED MANUSCRIPT layer L1 (modeling the Purkinje fibers) remained unchanged during all simulations. Altogether,

Part of the LV

Layers Size of involved region

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whole LV

L2 – L5

LV_mw

midwall layers L3, L4

40 %

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anteroseptal region

39 %

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midwall layers L3, L4 of AS

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lateral region

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midwall layers L3, L4 of LAT

24 %

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posteroseptal region

39 %

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midwall layers L3, L4 of PS

38 %

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L2 – L5

26 %

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L2 – L5

63 %

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L2 – L5

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Case

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eight cases were simulated (Table 1) with the three levels of reduced propagation velocity.

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25 %

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Table 1: Cases used for simulation of a reduced propagation velocity in different regions of the LV. The size of region is expressed as a percentage of the whole modeled volume of ventricular

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myocardium.

Left ventricular hypertrophy Two cases of the LVH were modeled. First, a concentric hypertrophy (ConcHyp) was modeled by increasing the thickness of the left ventricular wall and the septum by 50% without changing the outer size of the ventricular volume (i.e. the volume of the left ventricular cavity was reduced). In this case, the left ventricular mass was increased by 24%. Second, an eccentric hypertrophy (EccHyp) was modeled by increasing the left ventricular wall thickness by 50% without changing the left cavity volume. As a result, the left ventricular mass was increased by 80%. Then, analogically to the normal/non-hypertrophied heart model, the propagation velocity

ACCEPTED MANUSCRIPT was reduced to 25%, 50% and 75% of the reference velocity in the whole left ventricle and in the three subregions of the left ventricle. The velocities were changed in the whole ventricular wall

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(except the endocardial layer) as well as only in the midwall myocardial cells. Computed parameters

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For all simulations the corresponding HV for the depolarization time interval was computed and

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the following parameters of the HV were evaluated and compared with the reference (normal heart) simulation:

maxHV - the maximal amplitude of the HV during the depolarization period,

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time_HVmax - the time instant when the HV reached the maxHV,

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QRSdur - duration of the depolarization period computed from the beginning of

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simulation to the first minimal amplitude of the HV which follows time_HVmax.

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For all simulated cases the activation wavefront was visualized and changes of its shape and

Results

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extent represented by the above parameters were compared with the reference simulation.

Reduced propagation velocity The relative values of the maxHV for all simulated cases depending on the percentage of the change of activation propagation velocity are shown in Fig. 3. The time of occurrence of the maximal HV amplitude and the duration of the depolarization period for all simulated cases depending on the percentage of the change of activation propagation velocity are in Fig. 4 and Fig. 5, respectively.

ACCEPTED MANUSCRIPT The time loops of the HV during depolarization and the direction of the maxHV for all simulated changes of the activation propagation velocity, for the cases where changes were present only in

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the midwall layers, are depicted in Fig. 6 in frontal and horizontal plane similarly to

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vectorcardiographic loops. The HV loops for the referenceheart geometry and for two modeled

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cases of LVH without changes of propagation velocity are in Fig. 7.

The extents of the activation propagation wavefront for the reference simulation in 41, 45, 50 and

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55 ms are depicted in Fig. 8. The time 41ms corresponds to the time_HVmax for the reference

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simulation.

The extent of the activation wavefront for the same time instants as in the reference simulation

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but for propagation velocity reduced to 50% of the reference velocity in midwall layers in three

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regions of the left ventricle is shown in Fig. 9.

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Left ventricular hypertrophy

The relative values of the maxHV and the duration of the depolarization period for combinations

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of LVH (concentric or eccentric) and reduced conduction velocity in dependence on the percentage of the change of activation propagation velocity are shown in Fig. 10 and Fig. 11, respectively. In the Fig. 12 and Fig. 13 the time loops of the HV during depolarization and the direction of the maxHV for the concentric and eccentric hypertrophy in combination with reduced activation velocity in midwall layers are displayed in frontal and horizontal plane similarly to vectorcardiographic loops. Discussion

ACCEPTED MANUSCRIPT The aim of the study was to compare the resulting HV from simulations for the modeled heart with reduced activation propagation velocity and the heart with modeled LVH. The maximal

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amplitude of the HV increased in all simulated cases when the activation propagation velocity

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was reduced. The HVmax amplitude was strongly dependent on the degree of the activation velocity reduction - the greater was the reduction the higher was the HV amplitude. On the other

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hand, the amplitude of the HVmax was not significantly dependent on the size and position of the

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affected region with reduced activation propagation velocity. For the same degree of slowing, HVmax increased similarly in all regions, regardless whether only midwall layers or the whole

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myocardial region were affected. The HVmax amplitudes computed in simulations of the LVH were in most cases comparable with the HVmax obtained by slowing the activation propagation.

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It means that in clinical practice the enlargement of left ventricular mass might not be the only

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possible explanation of increased amplitudes in ECG signals.

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In most of the cases with reduced propagation velocity the time_ HVmax was increased by 10% to 40% in comparison with the reference time_HVmax. Those values were similar or higher than

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the values of time_HVmax for the simulations of the LVH. The increase of time_HVmax by more than 100% occurred in two cases when a significant reduction of activation propagation velocity to 25% of the reference value was modeled in large regions of the LV. The depolarization period QRSdur remained within the range of normal inter-individual variability (74-114 ms) [4] in simulated hypertrophies as well as in most cases with simulated reduction of activation propagation velocity. Significantly longer depolarization periods were obtained only when the propagation velocity was slowed down to 25% of the reference value in the whole affected regions.

ACCEPTED MANUSCRIPT The changes of maxHV direction strongly depended on the position of the region where the activation propagation velocity was slowed down. The effect on the maxHV direction was

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apparent even if only midwall layers of modeled myocardial volume were affected. The largest

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angle between the maxHV for the reference simulation and the other simulated cases was

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obtained for the changes in posteroseptal region.

The simulations showed that reduction of the activation propagation velocity and volumetric

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changes modeling the left ventricular hypertrophy resulted in similar changes of the parameters

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of equivalent heart generator. Possible explanation for this phenomenon was obtained from the visualization of the activation wavefront in various time instants of the depolarization period. In

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the reference simulation the time instant 41 ms represented the value of the time_HVmax. After this time instant (at 45, 50 and 55 ms) the extent of the activation wavefront decreased or was

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compensated in such a way that it yielded reduction of the HV amplitude. The time_HVmax in

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the reference simulation appeared earlier than in the other (pathological) simulated cases. Comparing the wavefronts shown for the three midwall regions with propagation slowed down to

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50% of the reference value it is apparent that in the time instant when the reference simulation achieved maxHV, the activation wavefront in pathological cases was of similar extent. However, when in pathological cases the time_HVmax was reached, the reference wavefront was more or less decreasing, thus producing smaller HV. Exploration of different degrees of conduction velocity reduction in combination with LVH confirmed the expectations that the influence of the phenomena with similar effect will enhance the results obtained for the reference geometry. The maximal amplitude of the HV was greater for the eccentric hypertrophy than for the concentric one. This can be explained by the larger increase of the left ventricular mass in case of eccentric hypertrophy. The prolongation of QRS

ACCEPTED MANUSCRIPT duration was again dependent on the degree of the activation velocity reduction and on the extent of the affected area. Comparison of the directions of maximal heart vectors showed that the

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changes were similar to the results for the reference geometry. HVmax direction was more

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affected by the position of the area with reduced activation velocity than by the changes of the LV mass volume. While pure LVH moved the maximal vector down (in the frontal view) and

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backwards (in the horizontal view), in combination with the activation velocity reduction the

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latter was dominant for the resulting direction of the maximal HV.

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The main limitation of the used ventricular model lies in the simplification of the geometry as well as in simulation of the wavefront propagation. In spite of this, the model can provide a

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valuable insight into the processes in the ventricles and their reflection in the resulting HV, which is in clinical practice manifested in observed surface ECG. In comparison with the uniform

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double layer model [11] the model also has the additional possibility to define the tissue

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parameters within the ventricular wall, e.g. different AP durations of the myocytes depending on their position relative to endocardium and epicardium. It is also possible to simulate and visualize

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the activation wavefront inside the ventricular wall in specific time instants of the depolarization. The anisotropic electrical conduction related to the muscle fibers and their rotation [12] was not accounted for in our model. Different activation propagation velocities in different directions (along and across the muscle fibers) can change the activation wavefront shape and extent. However, it should not change the principal observation of this study that the reduced activation propagation velocity implies the longer existence of a largely extended activation wavefront, also yielding an increase of the amplitude of the resulting electrical HV.

ACCEPTED MANUSCRIPT In the presented ventricular model the parameters of activation propagation – the propagation velocity and AP amplitude - can be defined independently. In more advanced models based e.g.

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on reaction-diffussion equations [13] these parameters are coupled together and their proportion

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results from parameters defining the physiology of myocardial cells. Changing a single parameter (activation propagation velocity) without assuming some coupling with other parameters presents

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another substantial simplification in our study. The influence of a combination of changes of

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more than one parameter on the resulting HV might be investigated in future studies.

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Conclusion

The simplified heart model was used for simulation of activation propagation for the reference

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heart geometry and two modeled cases of LVH. The influence of different degrees of activation velocity reduction was observed by evaluation of three parameters of the electrical HV

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representing an equivalent heart generator: the maximal amplitude of the HV, the time instant

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when the maximal amplitude of the HV was achieved and the duration of the depolarization time interval. Direction of the maximal HV was also analyzed. For the reference heart geometry and

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the reduced activation propagation velocity the observed parameters were comparable or greater than the values obtained in cases of LVH without changes of propagation velocity. Combinations of LVH and reduction of propagation velocity demonstrated a dominant influence of the propagation velocity changes on the amplitudes and directions of HV as well as on the duration of depolarization. Visualization of the activation propagation wavefront movement showed that the reduction of the activation propagation velocity produced longer presence of the activation wavefront within the ventricular wall what yielded the enlargement of the resulting HV. These results can substantiate

ACCEPTED MANUSCRIPT new interpretation of clinical findings with increased QRS amplitudes which previously used to be attributed to LVH.

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Acknowledgements

This work was supported by the research grant 2/0071/16 from the VEGA Grant Agency in

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Slovakia and by the grant APVV-14-0875 from the Slovak Research and Development Agency.

Bacharova L, Chen H, Estes EH, Mateasik A, Bluemke D a., Lima J a. C, et al.

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[1]

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ACCEPTED MANUSCRIPT Figure captions

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Fig. 1 Action potential shapes and durations defined for modeled left and right ventricles

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Fig. 2 Geometrical model of the heart with examples of regions of LV where the reduced velocity of the action potential propagation was modeled (red): a - midwall layers of the LV, b – the

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whole anteroseptal region, c – the whole lateral region, d – the whole posteroseptal region.

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Fig. 3 Relative values of the maxHV and their values for different propagation velocity reductions. For 100% of propagation velocity the value for the reference simulation and values

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for concentric hypertrophy (ConcHyp) and eccentric hypertrophy (EccHyp) are depicted. The values for decreased propagation velocities are marked by circles if the reduced propagation

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velocity was simulated in the whole selected region or by triangles if the reduced propagation

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velocity was simulated only in midwall layers.

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Fig. 4 Time of occurrence of the maximal HV amplitude as it depends on the decreasing propagation velocity. For 100% of propagation velocity the time_HVmax value for the reference

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simulation and values for concentric hypertrophy (ConcHyp) and eccentric hypertrophy (EccHyp) are depicted. The values for decreased propagation velocities are marked by circles if the reduced propagation velocity was simulated in the whole selected region or by triangles if the reduced propagation velocity was simulated only in midwall layers. Fig. 5 Duration of the depolarization period for all simulated cases depending on the decreasing propagation velocity. For 100% of propagation velocity the QRSdur value for the reference simulation and values for concentric hypertrophy (ConcHyp) and eccentric hypertrophy (EccHyp) are depicted. The values for decreased propagation velocities are marked by circles if

ACCEPTED MANUSCRIPT the decreased propagation velocity was simulated in the whole selected region or by triangles if the decreased propagation velocity was simulated only in midwall layers.

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Fig. 6 Frontal and horizontal views of the HV loops during depolarization with marked maxHV for the reference simulation (solid line) and for reduced propagation velocities in midwall layers

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of the selected region (LV – the whole left ventricle, AS – anteroseptal, LAT – lateral, PS –

reference propagation velocity, respectively.

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posteroseptal region) to 75% (dotted line), 50% (dashed line) and 25% (dashdot line) of the

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Fig. 7 Frontal and horizontal view of HV loops during depolarization with marked maxHV for the reference activation velocity and three modeled heart geometries: reference (solid line),

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concentric (dotted line) and eccentric (dashed line) hypertrophy.

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Fig. 8 Visualization of the activation propagation wavefront of the reference simulation in four

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time instants: 41, 45, 50 and 55 ms.

Fig 9 Propagation wavefront in 41, 45, 50 and 55 ms for simulated slowing of the activation

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propagation to 50 % of the reference value in midwall layers of the anteroseptal, lateral and posteroseptal region.

Fig. 10 Relative values of the maxHV for different propagation velocitiescombined with two types of LV hypertrophy. For 100% of propagation velocity the values obtained for the reference heart geometry as well as for concentric (ConcHyp) and eccentric hypertrophy (EccHyp) are depicted. The values for decreased propagation velocities are marked by filled markers if the reduced propagation velocity was simulated in the whole selected region or by crosses if the reduced propagation velocity was simulated only in midwall layers. Note that for better resolution in the graph the vertical axis does not start at zero level.

ACCEPTED MANUSCRIPT Fig. 11 Duration of the depolarization period for all simulated cases depending on the decreasing propagation velocity. For 100% of propagation velocity the QRSdur value obtained for the

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reference heart geometry as well as for concentric (ConcHyp) and eccentric hypertrophy

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(EccHyp) are depicted. The values for decreased propagation velocities are marked by filled markers if the reduced propagation velocity was simulated in the whole selected region or by

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crosses if the reduced propagation velocity was simulated only in midwall layers. Note that for

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better resolution in the graph the vertical axis does not start at zero level.

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Fig. 12 Frontal and horizontal views of the HV loops during depolarization with marked maxHV for the modeled concentric hypertrophy and the reference velocity (solid line) as well as for

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reduced propagation velocities in midwall layers of the selected region (LV – the whole left ventricle, AS – anteroseptal, LAT – lateral, PS – posteroseptal region) to 75% (dotted line), 50%

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(dashed line) and 25% (dashdot line) of the reference propagation velocity, respectively.

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Fig. 13 Frontal and horizontal views of the HV loops during depolarization with marked maxHV for the modeled eccentric hypertrophy and the reference velocity (solid line) as well as for

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reduced propagation velocities in midwall layers of the selected region (LV – the whole left ventricle, AS – anteroseptal, LAT – lateral, PS – posteroseptal region) to 75% (dotted line), 50% (dashed line) and 25% (dashdot line) of the reference propagation velocity, respectively.

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ACCEPTED MANUSCRIPT Highlights Action potential propagation slowing to 25, 50 and 75% of reference was simulated.

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Wavefront propagation in ventricular wall was visualized.

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Slowing causes long-lasting presence of the large extent of the wavefront.

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Propagation slowing resulted in increased amplitudes of a heart vector.

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Studied parameters for slowing and hypertrophy in the left ventricle were similar.

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