Effect of cardiac ventricular mechanical contraction on the characteristics of the ECG : A simulation study

Introduction: The 12-lead electrocardiogram (ECG) is the most widely-used tool for the detection and diagnosis of cardiac conditions including myocardial infarction and ischemia. It has therefore been a focus of cardiac modeling. However, the most contemporary in silico ECG investigations of the intact heart have assumed a static heart and ignored the mechanical contraction that is an essential component of cardiac function. The aim of this study was to utilize electromechanically coupled human ventricle models to explore the consequences of ventricular mechanical contraction on the ECG profiles. Methods and Results: Biophysically detailed human ventricular cell models incorporating contractile activity and a stretchactivated current (Isac) were incorporated into a 3D human ventricular model within a human torso, from which 12-lead ECGs were computed at a stimulation rate of 1 Hz. Compared to the static model, ventricular contraction without Isac had little effect on the QRS complex, but shifted the T-wave peak leftwards and reduced its peak amplitude. With Isac, ventricular mechanical contraction increased the QRS duration by 23% and QT interval by 5%. Conclusion: Mechanical contraction of the heart has a significant effect on the morphology and characteristics of the ECG particularly on the T-wave. The alteration of the cell membrane kinetics by stretch via Isac further exacerbates these effects. Our simulation data suggest that mechanical contraction should be considered in the interpretation of ECGs in pathological conditions, especially those in which mechanical contraction of the heart is impaired.


INTRODUCTION
The 12-lead electrocardiogram (ECG) is used to understand a person's cardiac electrical activity by measuring the electrical potential on the body surface in order to obtain diagnostic information on the status of the heart.Common ECG monitoring' uses include the detection of complex arrhythmias, shortened or prolonged QT intervals, ST-segment elevation and ischemia monitoring [1][2][3].The 12-lead ECG system consists of six frontal plane leads (Lead I, Lead II, Lead III, aVR, aVL and aVF) and six chest leads (V 1 -V 6 ) [1][2][3].Though being the most widely-used cardiac diagnostic tool, the ECG has some shortcomings, e.g., low sensitivity for detecting acute inferior myocardial infarction (its sensitivity is only approximately 60%) [4].Complex ECG patterns associated with left bundle branch block (LBBB), ventricular-paced rhythm (VPR) and left ventricular hypertrophy (LVH) reduce the ability of the ECG to detect acute coronary ischemic change and acute myocardial infarction [5].
Biophysically detailed computer models of the heart that relate cardiac cellular mechanisms to a clinical measurement of ECG may establish a correlation atlas between ECG characteristics and various pathological conditions.This may be beneficial for mitigating the shortcomings of the use of clinical ECGs for diagnosing cardiac diseases.However, the majority of cardiac modelling studies have focused mainly on the electrical activity of the heart, with an assumption that the heart is stationary in the thorax [6][7][8][9][10].This assumption ignores the fact that the heart is a mechanical pump, which undergoes rhythmic mechanical contractions in response to cardiac electrical excitation waves.The mechanical contraction alters the geometry of the heart as well as the cardiac electrical excitation via the mechanism of mechanoelectric feedback (MEF) [11][12][13][14].
It can be anticipated that the motion of the heart during the cardiac cycle alters the relative position of the ECG leads on the body surface to the electrical signal sources in the heart, as well as the anisotropic conductivity of the electrical propagation within the torso; all of which may have influences on the ECG, therefore, producing differences to the ECG characteristics is compared to a stationary heart, particularly during the T-wave when the heart is subjected to maximum systolic pressure [2,15].In addition, in response to changes in volume load or contractile state (changing geometry), the heart regulates its electrical activity via MEF [11,16,17], which activates stretch-activated channels (SACs) [18,19] that regulate cardiac cell action potentials (APs), such as prolongation or shortening [13,20,21] of AP duration (APD), changes of AP morphology and AP refractory properties (such as the diastolic depolarisation and premature excitation) [11,[22][23][24].However, it is incompletely understood how these changes of cardiac geometry and electrophysiology influence the body surface ECG.Therefore, the aim of this study was to investigate the consequences of ventricular wall motion on the 12-lead ECG in the absence and presence of a stretch-activated current (I sac ) during the cardiac cycle.

Single Cell Electromechanical Model
For simulating electrophysiology (EP), we utilized the O'Hara-Rudy (ORd) human ventricular single cell model [25], which was developed from undiseased human ventricle data and recapitulates human ventricular cell electrical and membrane channel properties, as well as the transmural heterogeneity of ventricular action potential (AP) across the ventricular wall [25].The ORd model also reproduces Ca 2+ versus voltage-dependent inactivation of L-type Ca 2+ current and Ca 2+ /calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca 2+ cycling [25].For simulating cellular mechanical properties, we used the Rice et al. myofilament (MM) model [26].This model was chosen as it is based on the cross-bridge cycling model of cardiac muscle contraction and is able to replicate a wide range of experimental data including steady-state force-sarcomere length (F-SL), force-calcium and sarcomere length-calcium relationships [26].
The intracellular calcium concentration where Cai  is the buffer factor for i  , I pCa is the sarcolemmal Ca 2+ pump current, I Cab is the Ca 2+ background current, I NaCa,i is the myoplasmic component of Na + /Ca 2+ exchange current, A cap is capacitive area, F is the Faraday constant, v myo is the volume of the myoplasmic compartment, v nsr is the volume of the network sarcoplasmic reticulum compartment, v ss is the volume of the subspace compartment, J up is the total Ca 2+ uptake flux, via SERCA pump from myoplasm to the network sarcoplasmic reticulum and J diff,Ca is the flux of the diffusion of Ca 2+ from the subspace to the myoplasm.
where [CMDN] and [TRPN] are the calmodulin and troponin Ca 2+ buffers in the myoplasm respectively, and K m,CMDN and K m,TRPN are the half-saturation concentrations of calmodulin and troponin respectively.
In the original ORd model, Eq.2 considers Ca 2+ binding to both calmodulin and troponin.However, as the MM model implements actual regulatory sites for the apparent Ca 2+ binding to troponin, Eq.2 was modified to: Now, the EP model only handles Ca 2+ binding to calmodulin with the MM model handling Ca 2+ binding to troponin.The flux of the binding of Ca 2+ to troponin via the MM model was incorporated into the EP model via Eq.1 as follows:   where J Trop is the flux of Ca 2+ binding to troponin.The combination of all state variables from the EP model with the MM model and the substitution of Eq.3 and Eq.4 for Eqs.1 and 2 yielded a human ventricular myocyte electromechanical cell model.

Stretch-Activated Current
In accord with previous studies [19,[27][28][29][30][31], we incorporated a stretch-activated current (I sac ) into the electromechanics model using the following formulation: where G sac and E sac are the maximum channel conductance and reversal potential of the SAC respectively.In the electromechanics model, E sac was typically set to −6.3 mV and describes the experimentally observed depolarising effect of the channel [32,33].V m is the membrane potential and P m is the channel's open probability modelled as: where  and  1/2 are the strain (with an explicit dependence on the sarcomere length) and half-activation strain respectively, k e = 0.02 [19,29,34] is the activation slope.
The SAC is assumed to be permeable to Na + , K + and Ca 2+ [19,30,35] in the ratio 1:1:1 with I sac therefore defined as: where I sac,Na , I sac,K and I sac,Ca are the contributions of Na + , K + and Ca 2+ to I sac .

Tissue Mechanics Model
We modelled cardiac tissue mechanics within the theoretical framework of nonlinear elasticity [36,37] as an inhomogeneous, anisotropic, nearly incompressible nonlinear material similar to previous studies [27,[38][39][40][41][42].We used a two-field variational principle with the deformation u and the hydrostatic pressure p as the two fields [37,43,44].p is utilised as the Lagrange multiplier to enforce the near incompressibility constraint.Thus, the total potential energy functional  for the mechanics problem is formulated as: where is the internal potential energy or total strain energy of the body and is the external potential energy or potential energy of the external loading of the body.As in previous studies [38,41,42,45], in the absence of body forces, and assuming that the body is always in instantaneous equilibrium and no inertia effects, the coordinates of the deformed body satisfies the steady-state equilibrium equation with near incompressibility enforced.
According to standard variational principles, equilibrium is derived by searching for critical points of (Eq.8) in suitable admissible displacement and pressure spaces and Û P .The corresponding Euler-Lagrange equations resulting from (Eq.8) lead to solving the problem [44,[46][47][48][49]: Find (u,p) in ˆÛ P  such that: where and U P are the admissible variation spaces for the displacements and the pressures, respectively.
is the material stored energy function and corresponds to the density of elastic energy locally stored in the body during the deformation.

Ŵ
With the axes of the geometry aligned to the underlying tissue microstructure [50,51], the second Piola-Kirchhoff stress tensor S, obtained from the directional derivative of (Eq.8) in the direction of an arbitrary virtual displacement and which relates a stress to a strain measure [37,43] and a manipulation of Eq.9 is defined as: where W is a strain energy function that defines the constitutive behaviour of the material, E is the Green-Lagrange strain tensor that quantifies the length changes in a material fibre and angles between fibre pairs in a deformed solid, C is the Right-Cauchy green strain tensor, p is a Lagrange multiplier (referred to as the hydrostatic pressure in the literature) used to enforce incompressibility of the cardiac tissue, S Active Tension is a stress tensor incorporating active tension from the electromechanics cell model and enables the reproduction of the three physiological movements of the ventricular wall: longitudinal shortening, wall thickening and rotational twisting [52][53][54][55][56][57][58].
For the strain energy function W, we used the Guccione constitutive law [59] given by: where Following previous work [27,60], ,

Tissue Electrophysiology Model
The monodomain representation [61][62][63] of cardiac tissue was used for the electrophysiology model with a modification (the incorporation of the Right Cauchy Green deformation tensor C), which allows the monodomain equation to take into account the effect of the deforming tissue, similar to previous studies [38,42,64]: where C m is the cell capacitance per unit surface area, V is the membrane potential, I ion is the sum of all transmembrane ionic currents from the electromechanics single cell model, I stim is an externally applied stimulus and D is the diffusion tensor.In simulations, intracellular conductivities in the fibre, cross-fibre and sheet directions were set to 3.0, 0.1 and 0.31525 ms•mm -1 respectively.These gave a conduction velocity of 65 cm•s -1 in the fibre direction along multiple cells, which is close to the value 70 cm•s -1 observed in the fibre direction in human myocardium [65].

Torso Model
The electrical potential in the torso (Figure 1(B)) is obtained via the Poisson equation: where D T is the torso conductivity and V T is the electrical potential in the torso.The torso is modelled as a passive conductor surrounded by air.Consequently, the normal component of its outer surface is zero leading to the first boundary condition: (16) where n is the outward unit normal on the torso surface, T is the outer surface of the torso.The torso is a conductor surrounding the ventricles.Therefore, from the conservation of charge and current, on the boundary between the ventricles and the torso, the normal component of the current in the ventricles must equal the normal component of the current in the surrounding torso.Since there cannot be a discontinuity in the potentials on the boundary of two directly connected volume conductors, i.e., the ventricles and the torso, this condition implies the following boundary condition: where V VENTRICLES is the electrical potential on the sur-face between the ventricles and the torso.The torso conductivity was set to 0.3 ms•mm -1 .

Computing the 12-Lead ECGs
We computed the ECGs according to the standard definitions [3,66] (Figure 1(B)).The limb leads were calculated as follows: where LA, LL and RA refer to the left arm, left leg and right arm respectively and  X is the potential of the appropriate lead.The augmented limb leads were calculated as: The precordial leads, V 1 -V 6 are located over the left chest as shown in Figure 1(B).Their potentials are measured directly from their locations.

Geometry and Meshes
The 3D simulations were carried out on a DT-MRI reconstructed anatomical human ventricle geometry (Figure 1(A)), incorporating anisotropic fibre orientation (Figure 1(A)), from a healthy 34-year old male.This had a spatial resolution of 0.2 mm and approximately 24.2 million nodes in total and was segmented into distinct ENDO (60%), MCELL (30%) and EPI (10%) regions (Figure 1(A)).The chosen cell proportion in each region reflects experimental data for cells spanning the left ventricular wall of the human heart [67].The conditional activation sites were determined empirically across the ventricle wall and were validated by reproducing the activation sequence and QRS complex in the measured 64-channel ECG [68] of that person (Figure 1(A)).

Solving the Electromechanics Problem
The electromechanics problem consists of two subproblems: the electrophysiology problem and the mechanics problem.The electrophysiology problem Eq.10 was solved with a Strang splitting method [69] ensuring that the solution is second-order accurate.It was discretised in time using the Crank-Nicholson method [70], which is also second-order accurate and discretised in space with Finite Elements [48,49,70,71].I ion in Eq.10 epresents the single cell electromechanics model from r which the active tension input to the tissue mechanics model for contraction is obtained.The system of ordinary differential equations (ODE) composing I ion was solved with a combination of the Rush-Larsen scheme [72] and the CVODE solver [73,74].a) Solve the electrophysiology problem for t mechanics = 1 ms with C as input and active tension T a as output (t electrophysiology = 0.01 ms).
b) Project T a from the electrophysiology mesh onto the mechanics mesh.The mechanics problem Eq.8 was also solved using the Finite Element Method using the automated scientific computing library, FEniCS [75].The resulting nonlinear system of equations was solved iteratively using the Newton method to determine the equilibrium configuration of the system.The value of the Right Cauchy Green Tensor C was then used to update the diffusion coefficient tensor in (Eq.14).Over a typical finite element domain, P 2 elements [48,49,71] were used to discretize the displacement variable u, while the pressure variable p was discretised with P 1 elements [48,49,71].This P 2 -P 1 mixed finite element has been proven to ensure stability [75][76][77] and an optimal convergence rate [71,76,78].c) Solve the mechanics problem with T a as input and C as output.

Simulations without Incorporation of I sac
We first investigated at the cellular level, how mechanical contraction (via the MEF mechanism) affected cardiac electrical activity.Without consideration of I sac , the simulated electrical and mechanical behaviors at a stimulation frequency of 1 Hz are shown in Figure 2 for the ENDO, MCELL and EPI cell types (Figure 2).The correlation between the action potential and the i  agrees with experimental data [15,19,20,  22,23,25,26,79].Of note is the fact that the  amplitude is smallest for the ENDO cell (Figure 2(B)) despite it having a greater APD 90 than the EPI cell (Figure 2(A)).This was because the model considered a greater amount of i  buffered by Ca 2+ /calmodu- lin-dependent kinase II (CaMK) in the ENDO cell type as compared to the EPI cell type [25] as observed in undiseased non-failing human ventricles.This observation was also consistent with the observation from the ORd electrophysiology model [25].Consequently, the amplitudes of the SL shortening (Figure 2 We further investigated the force-frequency relationship (FFR) of the electromechanics model.The FFR was obtained by stimulating the single cell at different frequencies for 1000 beats until steady state was reached.The maximum force developed at each stimulation frequency was recorded and plotted against the stimulation frequency.Results from the EPI cell model are shown in Figure 3 (results from the other two cell types were similar).In the considered frequency range, 0.5 -3 Hz, the simulated FFR showed the Bowditch staircase or Treppe effect [80][81][82], which matched experimental data [81].
As the normal heart rate is near 1Hz, all subsequent simulations in this study were carried out at 1 Hz (Figure 3; dashed vertical blue line).

Simulations with Incorporation of I sac
We then investigated how I sac affected the cardiac electrical and mechanical activity at the single cell level.Figure 4 shows the results from the three cell models, with consideration of I sac that are permeable to Na + , K + and Ca 2+ with a permeability ratio Na + :K + :Ca 2+ = 1:1:1.Compared to the case in which I sac was absent, I sac produced an elevation in the resting potential for the EPI,  ).This is also consistent with previous experimental studies which showed a stretch-related APD shortening [12,13,21,22,84] and control data from a previous modelling study from our laboratories on electromechanical consequences of the Short QT Syndrome [27].In the model, the most significant consequences of inclusion of I sac were upon increase in the activation of the reverse-mode of the Na + -Ca 2+ exchanger leading to greater contractility as has been demonstrated in several studies [19,27,[86][87][88][89][90].For extensive coverage of further SAC and mechano-electric feedback mechanisms, see the study by Youm et al. [19].

12-Lead ECG
At the intact tissue level, we used the 3D heart-torso model to investigate the functional impact of the mechanical contraction of the heart on the body surface potential, and therefore upon the characteristics of the 12-lead ECG.In simulations, the 12-lead ECG was obtained by incorporating the single cell electromechanics model into 3D anatomical ventricular geometry within the torso (see Figure 1).Three settings were considered: 1) static ventricles, 2) contracting ventricles with no I sac and 3) contracting ventricles with I sac .The results obtained from settings 2 and 3 were compared with those from setting 1.
and the contractile activity.I sac increased the Ca   i  amplitude by 60% in the EPI; 23% in the MCELL and 72% in the ENDO cell model (Figures 4(Aii)-(Cii)), which consequently led to greater SL shortening (Figures 4(Aiii)-(Ciii)) and greater contractile force by 42% in the EPI, 3.5% in the MCELL and 119% in the ENDO cells (Figures 4(Aiv)-(Civ)).The increase of the i  amplitude can be attributed to the permeability of the SACs to Na + , K + and Ca 2+ , the activation of which brought more Na + and Ca 2+ into the cell that increased i  and i  .These results are similar to those observed previously with a different human ventricular cell model [27].During stretch, the Figure 5 shows the time course of simulated 12-lead ECGs.Compared to the static heart, contraction without I sac had minimal effect on the QRS complex in all the leads-its duration was decreased by 1.95%; and the S-wave component was elevated by 1.86% (Figure 5).Detailed analysis of the active force generated by a left ventricular (LV) cell during contraction showed nonnotable developed active force during the QRS complex as indicated by the dashed line in Figure 6.This is in agreement with clinical observations as during the QRS complex period of the cardiac cycle, the heart is undergoing isovolumic contraction [2,91,92] with little active force developed particularly during the QR component.

OPEN ACCESS
There was a leftward shift in the peak of the T-wave and a reduction in its peak amplitude (T peak ) by 18% (Figure 5); but the QT interval was unchanged.Clinically, the T-wave is the period of ventricular repolarisation, during which maximum systolic pressure occurs in a single cardiac cycle [2,93,94].Inclusion of I sac had more marked effects on the characteristics of the ECGs, such as the width and amplitude of the QRS and the QT interval.In simulations, inclusion of I sac in the contraction heart model reduced the amplitude of the R-wave by 17% as compared to the static heart model.It also produced a more negative S-wave (by 59%), a wider QRS duration (by 18%), an elevated ST segment, a prolonged QT interval (by 5%) and an increased T peak (by 45%).Table 1 summarizes the ECG properties for all three scenarios investigated.to an altered electrical field in and around the heart that varies with time during the cardiac cycle [2,15,92].Such a changed electrical field surrounding the heart is reflected by changes in the ECG characteristics.Another important characteristic of the heart is the muscle contraction and relaxation, which also varies with time during the cardiac cycle [2,15,92].In addition, in response to mechanical events such as stretch and volume load, the heart regulates its own electrical activity via MEF [2,18,19]; which includes the activation of SACs [18,19,95].So far, how cardiac mechanical contraction influences ECG characteristics is less well-understood.In the present study, we have incorporated biophysically detailed coupled electromechanical ventricular cell models into a 3D-anatomical human ventricle situated within a human thorax to investigate the effects of mechanical contraction with and without I sac on the 12-lead ECG.
Our simulations suggest that: 1) contraction without consideration of I sac has no significant effect on the QRS complex, no effect on the QT interval, but shifts the T-wave leftwards and reduces T peak (Figure 5); 2) contraction with consideration of I sac reduces the R-wave amplitude, widens the QRS complex duration, increases T peak significantly, shifts the T-wave rightwards and increases the QT interval (Figure 5).These findings are dependent on the degree of stretch and are influenced by the magnitude of I sac .Several aspects of our findings merit more detailed discussion.

Mechanistic Insights
With mechanically contracting ventricles without consideration of I sac , the QRS complex was not affected significantly, either in duration (1.95% decrease) or morphology (Figure 5).Contraction during the QRS complex is isovolumic [2,91,92], thus explaining the insignificant effect of contraction on the ECG during this period.Contraction of each myocyte in the intact tissue is not necessarily isometric, however, as each undergoes different length changes with time.Some myocytes contract isotonically, some isometrically whilst others contract eccentrically [2,91,92,94].Therefore, even though the ventricular volume does not change substantially, the ventricle chamber geometry changes considerably [2,94,[96][97][98].Consequently, compared to a static heart, the position of the cardiac electrical sources, the distance of the ventricles from the body surface and the varying anisotropic conductivity due to MEF are altered in a mechanically contracting heart; hence, there was a 1.95% decrease in QRS duration without I sac .With consideration of I sac , these differential changes in myocyte lengths and hence ventricular geometry are exacerbated; hence, there was a greater and more significant effect of contraction with I sac on the QRS complex (Figure 5).By the Frank-Starling law, with the increased stretch of the myocardial fibers during diastole by I sac , contractility would increase [2,94,99].During the T-wave, ventricular contraction attains a maximum, after which ventricular pressure declines with ventricular repolarisation causing a decline in the active force of the myocytes [2,94,[96][97][98].The ventricular pressure during this period is ~30% greater than during the QRS complex [2,94,[96][97][98].Therefore, during contraction, the aforementioned changes in ventricular geometry, the distance of the ventricles from the body surface and the varying anisotropic conductivity due to MEF are altered markedly compared to a static heart.This results in a marked effect on the T-wave; without I sac , it is shifted leftwards and the T peak is reduced in amplitude by 18%.With I sac , the myocardial fibers are stretched during diastole leading to increased contractility, which in turn increases systolic pressure [2,94,99] leading to a greater effect on the T-wave (Figure 5); T peak is increased in amplitude significantly by ~45% and QT interval is increased by ~5%.

Relevance to Previous Studies
Our simulations suggest that ventricular contraction alters 12-lead ECG morphology.This is consistent with previous studies [100][101][102][103].In their study, Wei et al. [100] used MRI time sequences of the motion of a human ventricular geometry to compute 12-lead ECGs by mounting the geometry in a model of the human body.They found that ventricular motion reduced T peak with minimal change to the QRS complex.However, they did not consider the incorporation of I sac .Xia et al. [101] also obtained similar results with a human whole heart geometry mounted in a human torso but their simulations lacked the use of biophysically detailed electromechanical single cell models and the incorporation of I sac .Therefore, the present work is the first study to investigate the effects of I sac on the characteristics of simulated body surface 12-lead ECGs using anatomically detailed and mechanically contracting ventricles.The findings from the present study improve our understanding of the effects of electrical-mechanical coupling on the characteristics of ECG.This was achieved by 1) using biophysically detailed human ventricular myocyte models [25] coupled with the Rice et al. myofilament model [26]; employed with and without I sac and 2) by demonstrating the importance of ventricular motion on the morphology, properties and subsequently interpretation of the 12 lead ECG.

Limitations
In addition to acknowledged limitations of both the ORd electrophysiology model [25] and the Rice et al. [26] myofilament model, I sac density was based on prior studies [19,[28][29][30][31], due to lack of experimental data on the I sac from human ventricular myocytes.Additionally, the simulations here were performed at a single, physiologically relevant frequency (1 Hz), but rate-dependent differences in MEF have not been pursued in this initial study Experimentally observed effects of cycle length (restitution curve) [104] have also not been studied.These rate-dependent phenomena would constitute a valuable future line of investigation.It should also be acknowledged that I sac .may not be the only mechanism responsible for MEF (e.g.[105]) and that due to an absence of functional data in human myocytes, the electromechanical model lacks stretch sensitive K + channels (e.g.TREK).The model also lacks interactions between myocytes and fibroblasts, which have been proposed to contribute to ventricular MEF [106,107].Whilst it would be useful for such components to be incorporated into future models, the advantage of the approach adopted here is that it has been possible to isolate and attribute with confidence electrical changes to the incorporation of I sac .Finally, the use of a ventricular computational fluid dynamics model to determine pressure boundary conditions would allow a more realistic pressure profile.Although it is important that these potential limitations are stated, they do not fundamentally influence the principal conclusions of this study.

CONCLUSION
With the use of a biophysically detailed electromechanical human ventricular single cell model incorporated into a thorax-mounted human ventricular geometry, we have shown that the morphology and properties of the ECG are dependent on ventricular contraction.We have also shown that cellular stretch incorporated at the single cell level as an SAC has a significant influence on the ECG in a mechanically contracting ventricle.

10 C
 .ij are the components of the Green-Lagrange strain tensor.

Figure 1 .
Figure 1.Schematic diagram of the 3D electromechanical ventricular system.(A) Left and right ventricular single cell electromechanical models incorporated into a 3D human ventricular geometry with fibre orientations and segmented into distinct right and left ventricular endocardial, mid-myocardial and epicardial regions resulting in the electrical activation sequence of mechanically contracting 3D human ventricles.(B) Thorax model constructed from CT images with embedded ventricles (top) and electrode placements for 12-lead ECG computation (bottom).
Fig- ure 2(A) shows the simulated action potentials (APs) for the three cell types.The computed action potential duration at 90% repolarization (APD 90 ) was 228 ms for the EPI cell, 339 ms for the MCELL and 269 ms for the ENDO cell.

Figure 2 Figure 2 .
Figure 2. Simulation of ventricular electromechanical characteristics (without I sac ).(A) Action potentials in the EPI (blue), MCELL (green) and ENDO (red) cell models.(B) Ca 2+ transients in the EPI (blue), MCELL (green) and ENDO (red) cell models.(C) Sarcomere length in the EPI (blue), MCELL (green) and ENDO (red) cell models.(D) Active force in the EPI (blue), MCELL (green) and ENDO (red) cell models.Values are normalised to MCELL maximum active force for each cell type. 2 Ca    (C)) and active force (Figure 2(D)) in the ENDO cell type are the smallest among the three cell types.The simulated larger (and hence greater contractility) in the MCELL compared to the EPI and ENDO cells was also consistent with experimental data [79].

Figure 3 .
Figure 3. Plot of steady state normalised active force vs. heart rate using the EPI cell model.Red continuous line represents the WT electromechanics model while symbols represent experimental data from non-failing control preparations of human myocardium.Experimental data from Mulieri et al. [81].The blue, vertical dashed line indicates the FFR at 1 Hz.

Figure 4 .
Figure 4. Single cell effects of I sac on the electromechanics model.(Ai-Ci) Action potentials without stretch (black) and with stretch (red) in the EPI, MCELL and ENDO cell models.(Aii-Cii) Ca 2+ transients without stretch (black) and with stretch (red) in the EPI, MCELL and ENDO cell models.(Aiii-Ciii) Sarcomere length without stretch (black) and with stretch (red) in the EPI, MCELL and ENDO cell models.(Aiv-Civ) Active force without stretch (black) and with stretch (red) in the EPI, MCELL and ENDO cell models.Values are normalised to maximum active force for each cell type with stretch.MCELL and ENDO cells (the resting potential changed from −87.5 mV to −85.9 mV) (Figures4(Ai)-(Ci)).This is consistent with experimental observations[13,35,83,84]. I sac also shortened the AP duration (EPI APD 90 changed from 228 ms to 223 ms (Figure4(Ai)), MCELL APD 90 from 339 ms to 333 ms (Figure4(Bi)) and ENDO APD 90 from 269 ms to 257 ms) (Figure4(Ci)).This is also consistent with previous experimental studies which showed a stretch-related APD shortening[12,13,21,22,84] and control data from a previous modelling study from our laboratories on electromechanical consequences of the Short QT Syndrome[27].In the model, the most significant consequences of inclusion of I sac were upon

Figure 5 .
Figure 5. 12-lead ECG recordings from static ventricles without stretch (green), contracting ventricles without stretch (black) and from contracting ventricles with stretch (red).
dynamic output from the EP model during the time course of the AP served as input to the MM model from which the amount of Ca 2+ bound to troponin was calculated.The formulation of the myoplasmic Ca 2+ concentration in the EP model is: i  produced as

Table 1 .
Effects of contraction with and without I sac on the ECG.