Heart failure is a major and costly problem in public health, which, in certain cases, may lead to death. The failing heart undergo a series of electrical and structural changes that provide the underlying basis for disturbances like arrhythmias. Computer models of coupled electrical and mechanical activities of the heart can be used to advance our understanding of the complex feedback mechanisms involved. In this context, there is a lack of studies that consider heart failure remodeling using strongly coupled electromechanics. We present a strongly coupled electromechanical model to study the effects of deformation on a human left ventricle wedge considering normal and hypertrophic heart failure conditions. We demonstrate through a series of simulations that when a strongly coupled electromechanical model is used, deformation results in the thickening of the ventricular wall that in turn increases transmural dispersion of repolarization. These effects were analyzed in both normal and failing heart conditions. We also present transmural electrograms obtained from these simulations. Our results suggest that the waveform of electrograms, particularly the T-wave, is influenced by cardiac contraction on both normal and pathological conditions.
The failing heart undergoes a series of changes, from electrophysiological alterations in ion channels, exchangers, and pumps to structural modifications of tissue properties, that provide the underlying basis for arrhythmias. Some notable characteristics of the failing heart include the prolonged action potential and alterations in the intracellular calcium handling, which alter the contractile function of myocytes [
Electrophysiology in nonfailing (NF) and heart failure (HF) conditions is well described (see [
In [
In this work, we extended the strongly coupled electromechanical model used in [
To understand the effects of deformation on the transmural dispersion of repolarization in a normal and in a failing tissue we used a previously developed computer model of the human left ventricle wedge preparation [
Cardiac biomechanics was computed by solving the quasistatic equilibrium equations
The fiber direction in the undeformed configuration is denoted here by
We used the active stress approach that splits the second Piola-Kirchhoff stress in passive and active stress parts. The passive part is given by the Holzapfel-Ogden model, described by (
The electrophysiology of cardiac tissue, considering the effects of deformation, can be described by the bidomain model, which in this case is given by
Note that, in (
Dynamics of human ventricular myocyte was described using a cell model that couples the electrophysiology model proposed by ten Tusscher et al. [
The main variables of the TNNP + Rice cell model are the transmembrane potential, the intracellular calcium concentration
Coupled electromechanical TNNP + Rice cell model: (a) normalized transmembrane potential and active force and (b) intracellular calcium concentration.
Cardiac myocytes from failing hearts experience a series of changes; among them the most prominent changes are action potential prolongation and alterations in the intracellular calcium and sodium. Here we limit ourselves to describe the changes that were applied to our specific coupled electromechanical cell model; for more details about HF remodeling see [
In this work, we modified the cell model by (i) adding the late sodium current, (ii) modifying some ion currents in a homogeneous way (same change for all cell types), and (iii) heterogeneous changes to ion currents and exchangers, that is, different changes for endocardial (endo), M, and epicardial (epi) cells.
The
Then, (
In [
Homogeneous heart failure remodeling in cardiac myocytes.
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Table
Heterogeneous heart failure remodeling in cardiac myocytes.
Parameter | Epi (%) | M (%) | Endo (%) | Reference | |
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NCX |
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During HF the cardiac tissue undergoes several changes in its properties; among them the changes in electrical conductivity and stiffness of the material are the most prominent. Experimental studies have shown alterations in Cx43 gap junctions, as well as a reduction in the conduction velocity of the electrical wave propagation in the cardiac tissue [
To take into account the mechanical alterations in the failing heart, the constants of the HO constitutive model were modified as proposed in [
The electrophysiology models were spatially discretized using the finite element method (FEM) using trilinear hexahedral elements, whereas the time discretization was performed using the Crank-Nicolson method. For the bidomain system, we used the
The numerical solution of cardiac biomechanics is more complex and requires a robust numerical treatment for incompressibility in order to avoid locking phenomena. In this work we used a mixed three-field variational formulation proposed by Simo et al. [
The coupled electromechanical problem is solved sequentially using the same finite element mesh for both problems. Although the spatial scales of the electrical and mechanical problems are quite different, we adopted this approach due to its simplicity. First, we solve the bidomain model using an operator splitting approach: first, we advance the system of ODEs (TNNP + Rice model) at each node in time using the Rush-Larsen method [
In this work, we considered simulations of the electromechanical activity of a left ventricle wedge under normal and heart failure conditions. The coupled electromechanical cell model TNNP + Rice was embedded in tissue simulations using bidomain and nonlinear elasticity equations. In both cases, we carried simulations without coupling the mechanics and with coupled mechanics to assess the effects of tissue deformation on electrophysiological metrics.
Under normal conditions, we considered a cubic domain of
To simplify the simulations and the mechanical response, the behavior of the constitutive model and the conductivity tensor were assumed to be transversely isotropic. The fiber direction was assumed to be parallel to the
An electrical stimulus was applied on the endocardial face of the mesh to initiate the electrical activity, which was simulated for
For each simulation, the activation time (ACT), repolarization time (REP), and action potential duration (APD) were computed for the nodes. Dispersion of ACT, REP, and APD were measured as the difference between the maximum and minimum values, that is,
In Table
Parameters used in the numerical experiments.
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The results of incorporating the heart failure electrical remodeling changes, described in Tables
After the modifications for heart failure for each cell type (endo, M, and epi), a simulation was carried out applying an electrical stimulus with a frequency of
HF changes: (a) steady state calcium transient; (b) transmembrane potential for endo, M, and epi myocytes.
Figure
The results of the HF changes in the TNNP + Rice model in terms of transmembrane potential, intracellular calcium concentration, and active force are shown in Figure
Action potential, calcium transient, and active force for cell types under normal (solid line) and failing heart (dashed line) conditions.
The intracellular calcium concentration in normal and HF conditions is shown in the middle of Figure
In the coupled electromechanical TNNP + Rice cell model, the intracellular calcium concentration is used as input for generation of the active force, which is described by the Rice et al. model. Since, in the HF conditions, the intracellular calcium concentration changes, the resulting active force will change accordingly. The modified active forces for all the cell types are shown in the bottom of Figure
Before we discuss how deformation affects transmural dispersion of repolarization in HF conditions, we analyze first the interplay of mechanics and electrophysiology under normal or control condition. Thus, simulations of the cubic domain considering the transmural distribution of the cell types, with and without deformation, were carried out.
Figure
Spatial distribution of the transmembrane potential
The measures of ACT, REP, and APD are reported in Table
Minimum (min), maximum (max), and dispersion (disp) of ACT, REP, and APD computed from the simulations with and without considering deformation.
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ACT (ms) | 2.5 | 31.6 | 29.1 | 2.6 | 33.4 | 30.8 |
REP (ms) | 309.3 | 322.8 | 13.5 | 303.5 | 327.7 | 24.2 |
APD (ms) | 281.1 | 309.1 | 28.0 | 277.9 | 311.9 | 34.0 |
Figure
Comparisons of simulations with and without deformation (pure electrophysiology). (a) Repolarization time and (b) action potential duration in a transmural line of the domain. The dashed red line in (b) represents the single cell APD. (c) Simulated electrogram obtained with the extracellular potential
The electrograms obtained from the extracellular potential
An increase in the T-wave amplitude was observed in the coupled electromechanics simulation with respect to the simulation without deformation. The deformation causes the LV wall to stretch in the transmural direction, which reduces the electrotonic effect and therefore increases the transmural dispersion of repolarization, that results in an increase in the amplitude of the T-wave. This effect was studied previously in [
The coupled electromechanical model with heart failure is now studied using the same simulation setup already described but now considering the heart failure remodeling of the cell model and also the changes in tissue properties.
In the complete HF model, due to the reduced conductivity and increased size of the slab, we observed that the entire block of tissue is electrically activated after
We observed that, in comparison with the normal case without heart failure, the LV wall thickening was reduced due to increased stiffness of the material and also due to the reduced active stress. In the simulations of the normal case, a maximum of 39% was obtained for the wall thickening, whereas in the hypertrophic heart failure case a maximum of 18% was achieved.
Figure
Transmural electrograms computed from simulations with and without (w/o) deformation for the HF case considering a hypertrophic LV wedge. On the right panel, the graph shows a zoom on the T-wave region.
As before, an increase in the T-wave amplitude (but now towards a more negative value) was observed in the simulations with deformation; see Figure
It was shown in [
Our HF wedge model that includes a strong couple between mechanics and electrophysiology was able to reproduce many known features of this particular pathology. Important changes in myocyte electromechanics were observed. Electrophysiological remodeling resulted in a prolongation of APD, in agreement with clinical and experimental observations [
In comparison with the normal case, the HF model was able to reproduce another important characteristic which is the increase in the diastolic calcium. It is important to note that the calcium concentration profile obtained in the simulation is similar to experimental [
In the complete HF wedge model, LV wall thickening was reduced from 39% (control) to 18% (HF). Finally, from the computed transmural electrogram a negative T-wave was observed. This occurred because, in the HF model, the APD of the endocardial cells is smaller than that of the epicardial cells and, therefore, they repolarize before the epicardial and M-cells. This negative T-wave for the HF is in agreement with experimental, clinical, and computational works [
In the single cell simulations we have observed that both intracellular calcium and active force peaks were reduced in average by 50% (see Figure
To highlight how each of these changes influences cardiac contraction, we also simulated a second case of HF wedge (case 2) where tissue stiffness was unaltered; that is, the parameters that model it were set to the control ones. For this case, the LV wall stretched more than in the previous case, achieving 33% of wall thickening. Therefore, by only considering changes at the myocyte level, LV wall thickening decreased from 39% (control) to 33% (HF); that is, cardiac contraction was impaired but not as significantly as in the case that considers an increase of tissue stiffness. For completeness, Figure
Comparison of the electrograms for the simulations considering HF conditions. Control denotes the HF simulation without deformation; HF-case 1 is the full HF remodeling with changes on both single cell and tissue properties; HF-case 2 is the HF remodeling case without changing the properties of the HO constitutive model.
It is clear from Figures
Under the pathological condition of HF (see Figure
Finally, under the pathological condition of HF without changes on tissue stiffness (case 2, see Figure
Therefore, our results suggest that half of the information carried by the T-wave is somehow related to cardiac contraction. Both LV wall thickening and T-wave amplitude are metrics that can be clinically obtained in a noninvasive way by cardiac imaging techniques and electrocardiography, respectively. However, the relation between these two metrics is nonlinear and as the numbers above suggest, one can not make a straight forward relation between LV wall thickening and T-wave amplitude. T-wave peak can be more easily associated with APD or repolarization dispersion. But dispersion of repolarization is affected by myocyte electrophysiology, myocyte phenotype distributions, tissue properties, and contraction in a very nonlinear and complex fashion.
In this work the transmural heterogeneity of action potential duration of endocardial, M, and epicardial ventricular myocytes was considered. However, the apex-to-base gradient of action potential duration was neglected. Further studies should consider the apex-base gradient, which is an important electrophysiological characteristic of the left ventricle as demonstrated in [
Another strong limitation of this work consists in the fact that only a transmural slab of the LV was used in the simulations. Simulations of the entire left ventricle geometry, including both transmural and apex-base action potential duration gradient, are the next steps of this work.
The contraction of the LV is composed of three different mechanisms: circumferential shortening, longitudinal shortening, and wall thickening [
Our current, simplified, wedge model achieved 39% of wall thickening in the NF case, which is very close to the physiological values which ranges between 40% and 50%, as reported in the literature [
A wedge model with a physiological fiber distribution (transmural rotation of the fibers from endo- to epicardial surface) might also be able to reach the physiological range values of wall thickening of the LV. However, since WT is the combined result of a circumferential shortening and endo- and epicardial fiber contraction, it would probably provide smaller values for wall thickening.
It is important to remark that our focus was on the relationship between wall thickening and electrophysiological properties. Therefore, with this in mind, we decided to use a simplified fiber distribution for the wedge model which resulted in the moderate but physiological wall thickening of 39%, as mentioned before.
In general, each of the constitutive properties of the electrophysiological model (monodomain or bidomain) may depend on the state of deformation. For the monodomain model, this results in
In this work, we have neglected the capacitive, the ionic, and also the surface-to-volume ratio dependencies on deformation, as presented in [
Our current implementation is limited and would not support an entire human left ventricle. To consider such geometry, we need to parallelize our code using a distributed memory approach with MPI. Another possibility, which has been shown to improve significantly the performance [
In this work, we presented a strongly coupled electromechanical model of a human left ventricle wedge preparation suitable for analyzing the effects of cardiac tissue deformation on electrophysiological metrics. We adapted our cell model to reproduce heart failure conditions and embedded this model in tissue simulations. Within this framework, we observed that also in HF conditions the deformation of the tissue reduces the electrotonic effect and consequently increases TDR and APD dispersion. The computed transmural electrograms presented a negative T-wave due to HF remodeling. Nevertheless, even in HF conditions with a negative T-wave, the wall thickening of the LV resulted in an increase of the T-wave amplitude.
Therefore, our results suggest that in both normal and HF conditions half of the information carried by the T-wave is related to cardiac contraction. Both LV wall thickening and T-wave amplitude are metrics that can be clinically obtained in a noninvasive way by cardiac imaging techniques and electrocardiography, respectively. However, we have shown that the relation between these two metrics is complex and nonlinear, which prevents a direct correlation of these two important clinical metrics. Only using a sophisticated and strongly coupled electromechanical model, we were able to correlate cardiac contraction and T-wave. This work highlights how important it is to further improve cardiac models so that they can be used as another important complementary tool in clinical cardiology.
The authors declare that there is no conflict of interests regarding the publication of this paper.