The Mechanical Cost of Decreasing Conduction Velocity: A Mathematical Model of Pacing-Induced Lower Strain
Ibrahim Marai12, David Carasso3, Shaqed Carasso4, Shemy Carasso12
1Cardiovascular division, B PadehPoriyaMedical Center, Poriya, Israel.2The Azrieli Faculty of Medicine, Bar Ilan University, Zefat, Israel.3Faculty of Electrical Engineering, the Technion, Israel Institute of Technology, Haifa, Israel.4Department of Cell Biology and Cancer Science, The Rappaport Faculty of Medicine, Technion, Israel Institute of Technology,Technion Integrated Cancer Center, Haifa, Israel.
To simulate the effect of decreasing conduction velocity (Cvel) on average segmental myocardial strain using mathematical modeling.
The simulation was run using MatLab version 7.4 (The MathWorks, Inc. Natick, Massachusetts). A normal strain-time curve pattern was sampled from a normal human echo study using the 2D strain imaging software (GE Healthcare, Milwaukee, Wisconsin). Contraction was simulated from simultaneous segmental activation (Cvel=∞) through normal activation (Cvel=400cm/sec) to pacing Cvel (100 to 10cm/sec). The simulation generated average segmental strain-time waveforms for each velocity and peak strain as a function of Cvel and time to peak strain as a function of Cvel curves.
With decreasing Cvel, average peak segmental strain was found to be decreased and delayed. The following correlation equation represents the correlation betweenpeak strain and Cvel : strain= -20.12+27.65 x e (-0.29 x Cvel). At the highest pacing Cvel (100cm/sec) average peak segmental strain dropped by 10%, at 50cm/sec by 30% and at the lowest pacing Cvel (10cm/sec) peak strain dropped by >90%. Time to peak segmental strain was minimally longer with decreasing Cvel down to 70cm/sec (pacing velocity range). Further decreased velocity dramatically increased time to peak strain of the simulated segment.
The simulation yielded a predictive correlation between slower conduction velocities and decreased and delayed segmental strain.
Key Words : Strain, Pacing, Conduction Velocity.
Ibrahim Marai MD, Cardiovascular division, B PadehPoriyaMedical Center, Poriya, Israel
Cardiac resynchronization therapy (CRT) has proven helpful in patients with heart failure (HF) and ventricular dyssynchronization 1-4. The major concept being an attempt to resynchronize early and delayed opposing wall contraction. It is easily understandable how dyssynchronized wall contraction results in lower average function . Right ventricular pacing has been shown to adversely affect left ventricular systolic and diastolic function 5,6. However, biventricular pacing has not been universally successful and even detrimental in some patients7,8. Conduction velocity (Cvel )in the Purkinje system is 2 to 4 M/sec, while the Cvelin muscle is 0.5 to 1 9. As the Cvel during pacing is reduced by 4-10 fold, the electrical impulse propagates sequentially via myocardium causing intrasegmental delay. By applying similar reasoning that correlates reduced left ventricular function due to delayed wall contraction, sequential myocardial cell activation and contraction may result in less average shortening compared to the normal simultaneously activated segmental shortening. We used mathematical modeling to simulate average segmental strain to Cvel correlation.
The simulation was run using MatLab version 7.4 (The Math Works, Inc. Natick, Massachusetts). A normal strain time curve pattern was sampled from a normal human echo study using the Echo PAC PC 2D strain imaging software (GE Healthcare, Milwaukee, Wisconsin). It was generated from 10 healthy volunteers in sinus rhythm at a heart rate of 60-70 beats per minutes. Long axis echocardiographic views were analyzed using Siemens Velocity Vector Imaging (Mountain view, CA, USA) and generated 18 segments strain curves per subject. All 180 segmental curves were normalized to cycle length to generate an average strain curve for the model.This pattern was set as the single sarcomere (oscillator) shortening waveform. The following parameters were entered for segmental representation in the simulation : segmental length of 5cm, myocardial cell length 120µm, 50% longitudinal overlap between cells, and 60 oscillators per cell]10. All oscillators within a single cell were activated simultaneously. Contraction was simulated from simultaneous segmental activation (Cvel=∞) through normal activation (Cvel=400cm/sec) to pacing conduction velocities (100 to 10cm/sec). The simulation generated sequential strain-time waveforms within a segment and average segmental strain-time waveform for each velocity [Figure 1]. This simulation also generated average peak segmental strain as a function of Cvel and time to average peak segmental strain as a function of Cvelcurves.
Strain-time waveforms within a segment in different conduction velocities (Cvel) are showed. With low Cvel of the pacing range (less than 100 cm/sec), the waveforms (dashed lines) within a segment were sequentially generated, while with increasing Cvel (≧200 cm/sec), the waveforms became more and more overlapped until being simultaneously generated when the velocity is within or above the range of normal Cvel ( ≧400 cm/sec). The bold curve generated from the summation of the strain-time waveforms within a segment represents the average strain-time waveform of the segment in each Cvel.
Strain and time-to-peak strain relationship to Cvel was assessed using curve-fitting quadratic regression analysis.
The strain-time waveforms within a segment are showed in [Figure 1]. With low Cvel of the pacing range (less than 100 cm/sec), the waveformswithin a segment were sequentially generated, while with increasing Cvel (≧200 cm/sec), the waveforms became more and more overlapped until being simultaneously generated when the velocity is within the range of normal Cvel( ≧400 cm/sec).
With decreasing Cvel the average peaksegmental strain decreased and was increasingly delayed [Figure 1],[Figure 2]. The decrease in average peaksegmental strain followed the following correlation equation [Figure 3]: strain= -20.12+27.65 x e(-0.29 xCvel). The first part of the formula (-20.12) represents normal peak strain and the second part (27.65 x e (-0.29 xCvel) ) represents a negative exponential function. Maximal average peak strain plateaued atCvel conduction of 400 cm/sec. Increasing the velocity above 400 cm/sec did not further increase strain. However, decreasing Cvelcausedan exponential reduction in strain. At the highest pacing Cvel(100cm/sec) the average peak segmental strain dropped by 10%, at 50cm/sec it dropped by 30% and at the lowest Cvel(10cm/sec) strain dropped by more than 90%.
Average longitudinal segmental strain-time curve patterns at various conduction velocities from simultaneous segmental activation (conduction velocity =∞) through normal activation (400cm/sec) to pacing conduction velocities (<100cm/sec). With decreasing conduction velocity, the average peak longitudinal segmental strain decreased and delayed.
Average peak longitudinal segmental strain (max systolic strain) to conduction velocity correlation. The decrease in average peak strain with decreasing conduction velocity followed the following correlation equation : strain (%)= -20.12+27.65 x e [-0.29 x conduction velocity (cm/sec)].
Simulation and experimental results
The simulation yielded a predictive correlation between slower conduction velocities and decreasing peak segmental strain and increasing delay in its timing, resulting from intra-segmental, or microscopic dyssynchrony. This is very similar to wall (macro) dyssynchrony found in some of the dilated cardiomyopathy patients. It is easily understandable how misaligned wall peak contractions cause a decrease in global strain, forming the basis for resynchronization therapy. Our simulation demonstrates that the same phenomenon may happen microscopically within a single segment, adversely affecting its potential maximal strain in a predictable way related to Cvel. Pacing reduces Cvelto levels that would reduce peak segmental strain in the range of 10% to 90%. As the simulation is not linear an average pacing velocity of 50cm/sec would be expected to decrease strain by 30%.
Time to average peak longitudinal segmental strain (TTP) to conduction velocity correlation. The correlation followed the equation: TTP (msec)= 360+ 406 x e[-0.04 x conduction velocity (cm/sec)].
Represents time-to-average peaksegmental strain correlation with Cvel, following the equation: time-to-peak strain = 360+ 406 x e(-0.04 x Cvel). Time to peak strain was minimally longer with decreasing Cvel down to 70cm/sec (within the pacing velocity range). Further decreased velocity dramatically elongated time-to-peak strain of the simulated segment.
Reduced Cvel and dyssynchrony may cause molecular changes including ion channels and electrical alterations that are similar is some aspects to those inHFand reduced ejection fraction. Chronic left ventricular dyssynchrony due to regionally delayed electrical activation can induce regional and global molecular signalling that alters excitation –contraction coupling, energetics, arrhythmia susceptibility, and myocardial survival 11. Moreover electrical conduction delay and mechanical dyssynchrony can trigger complex biomolecular changes beyond the known changes in HF 11.Spragg et al 12found in animal model that left ventricular dyssynchrony in failing hearts generates myocardial protein dysregulation concentrated in the late-activated, high-stress lateral endocardium. Such molecular polarization within the left ventricle creates transmural and transchamber expression gradients of calcium handling and gap junction proteins that may worsen chamber function and arrhythmia susceptibility.In another study 13, it was demonstrated that left ventricular dyssynchrony induces regional differences in potassium and calcium currents, which increased action potential duration in the lateral wall. Early after depolarizations were increased in the dyssynchronous failing heart.
Significance of the results
The understanding that pacing has a contractility cost may be very important to decision making related to pacemaker implantation in various indications, weighing mechanical cost vs. benefit of pacing. Moreover, as our simulation does not simulate pacing per-se, but rather the effect of decreasing Cvel, it can be generalized to the effect of native conduction defects. Thus, bundle branch blocks would be assumed to decrease contractility at segmental level above and beyond the creation of overall left ventricular dyssynchrony. Importantly, average Cvel at pacing sites adjacent to the conduction system (the conduction system could be early invaded by the electrical impulse generated by the pacing site and thus activates directly part of the myocardium) could be higher than at sites far from the conduction system. This may explainthe differences that could be in contraction in different pacing sites and different forms of fascicular blocks and intraventricular conduction delays.
Specifically in patients candidates for biventricular pacing, higher baseline lateral strain would seem important to identify as pacing may decrease it beyond the power gain from realigning dyssynchronized walls. Moreover, the Cvelat the pacing segment can be measured during implantation to try to predict the mechanical cost of pacing. Finally this predictable loss of contractility could be used in situations where it me be desirable as in obstructive cardiomyopathy.
Beyond the understanding that pacing may reduce myocardial function and work efficiency, the results of this model support contemporary trends of engaging the conduction system in pacing. This may be especially important in patients with reduced ejection fraction before pacing to avoid further functional impairment. This could be assessed during lead positioning by echocardiographic strain imaging to assure best activation patterns with the least impact on contraction. However, the clinical benefit of this strategy should obviously be validated in a clinical trials.Recently, conduction system pacing (His bundle pacing or left bundle branch pacing) has been suggested to restore and retain normal electrical activation of the ventricles or toachieve electrical synchrony of the left ventricle 14,15.His bundle pacing and left bundle branch area pacing have emerged as alternative method for CRT in patients with HF and left bundle branch block16,17. Our simulation suggests yet another advantage for that procedure maximizing contraction and timing of the paced segments. It may help selecting patients for this new procedure.
Theoretically, this model can be applied to atrial myocardium. Pacing at different sites in the atria may cause to different strains as the Cvel is not similar on all parts of atria. For example, Cvelalong Crista Terminalis and Bachmann’s bundleis relatively higher compared to other sites, and Cvelmay be lower at fibrotic sites compared to normal sites. The clinical significance of pacing from different sites is not clear. Indeed, small studies have previously indicated that atrial pacing may precipitate atrial fibrillation 18,19. Two large randomized studies have shown that low inter atrial septal pacing is superior to right atrial appendage pacing in preventing persistent or permanent atrial fibrillation in patients with sinus node dysfunction and intra-atrial conduction delay 20,21.In the other hand, no association between the percentage of atrial pacing and the development of atrial fibrillation was found in patients with sick sinus syndrome in other study 22.
The simulation does not incorporate cellular pre-stretching by earlier activated cells. This is hard to account for, as it is dependent on tissue compliance that may vary according to left ventricular dysfunction etiology. Pre-stretching would adversely affect strain even more, thus the simulation may underestimate the effect of conduction velocity on strain.
The simulation yielded a predictive correlation between slower conduction velocities with a decreasing segmental segmental strain and with increasing delay in its timing, resulting from intra-segmental, or microscopic dyssynchrony. Clinical studies are needed to confirm the clinical significance of this model.