The effect of electrical conductivity of myocardium on cardiac pumping efficacy: a computational study
© The Author(s) 2017
Received: 8 July 2016
Accepted: 8 December 2016
Published: 10 January 2017
Background and aims
The existence of non-excitable cells in the myocardium leads to the increasing conduction non-uniformity and decreasing myocardial electrical conductivity. Slowed myocardial conduction velocity (MCV) believed to enhance the probability of cardiac arryhthmia and alter the cardiac mechanical pumping efficacy, even in sinus rhythm. Though several studies on the correlation between MCV and cardiac electrical instabilities exist, there has been no study concerning correlation or causality between MCV and cardiac mechanical pumping efficacy, due to the limitation in clinical methods to document and evaluate cardiac mechanical responses directly. The goal of this study was to examine quantitatively the cardiac pumping efficacy under various MCV conditions using three-dimensional (3D) electromechanical model of canine’s failing ventricle.
The electromechanical model used in this study composed of the electrical model coupled with the mechanical contraction model along with a lumped model of the circulatory system. The electrical model consisted of 241,725 nodes and 1,298,751 elements of tetrahedral mesh, whereas the mechanical model consisted of 356 nodes and 172 elements of hexahedral mesh with Hermite basis. First, we performed the electrical simulation for five different MCV conditions, from 30 to 70 cm/s with 10 cm/s interval during sinus pacing. Then, we compared the cardiac electrical and mechanical responses of each MCV condition, such as the electrical activation time (EAT), pressure, volume, and energy consumption of the myocardium. The energy consumption of the myocardium was calculated by integrating ATP consumption rate of each node in myofilament model.
The result showed that under higher MCV conditions, the EAT, energy consumption, end diastolic and systolic volume are gradually decreased. Meanwhile, the systolic pressure, stroke volume, stroke work, and stroke work to ATP are increased as the MCV values increased. The cardiac functions and performances are more efficient under higher MCV conditions by consuming smaller energy (ATP) while carrying more works.
In conclusion, this study reveals that MCV has strong correlation with the cardiac pumping efficacy. The obtained results provide useful information to estimate the effect of MCV on the electro-physiology and hemodynamic responses of the ventricle and can be used for further study about arrhythmogeneis and heart failure.
KeywordsConduction velocity Electromechanical model Cardiac pumping efficacy
Action potential (AP) propagates from one myocyte to the next myocyte through gap junctions. However, there are not only myocytes exist in the myocardium but also non-excitable cells such as collagenous strands, blood vessels, and fibroblasts. Those non-excitable cells affect electrical properties by increasing conduction non-uniformity and decreasing myocardial electrical conductivity. Myocardial conduction velocity (MCV) varies from 30 to 70 cm/s depending on the level of non-uniformity. Slowed MCV is associated with an increased risk of re-entrant excitation, predisposing to cardiac arrhythmia  and will also change cardiac mechanical pumping efficacy, even in sinus rhythm.
Quantitative analysis of the effect of MCV on cardiac electrophysiology and mechanical pumping function is highly important for further research of cardiac arrhythmia and heart failure. Though several studies on the correlation between MCV and cardiac electrical instabilities exist [2–5], there has been no study concerning correlation or causality between MCV and cardiac mechanical pumping efficacy. This is because experimental methods to document and evaluate cardiac mechanical responses directly, such as cardiac output, myocardial tension and strain generation throughout the ventricular volume, and cardiac electromechanical interaction, are hampered by low spatiotemporal resolution. Computational modeling is an alternative approach that overcomes this limitation.
We have previously developed a three-dimensional (3D) electromechanical model of failing canine ventricles along with a lumped model of the circulatory system [6–8]. The goal of this study is to use the computational model of the heart to examine the cardiac mechanical responses under various MCV conditions, and determine any causality between MCV and cardiac pumping efficacy.
Computational model of the heart
To construct the computational model for this study, we employed the existing 3D electromechanical model, combined with a lumped model of cardiovascular system [6–8]. The electromechanical model consists of finite element electrical and mechanical model, which describe the behavior and interaction between electrical activation and mechanical contraction of the ventricle. Both of electrical and mechanical model was reconstructed from high resolution magnetic resonance (MR) and diffusion tensor (DT) MR imaging of the failing canine ventricle. The methodology to reconstruct the model from image has been described elsewhere . The whole schematic for this model can be seen in Fig. 1.
Description of electrical model
Description of EC coupling model
The cardiac muscle contracts via excitation–contraction (EC) coupling. EC coupling can be described as the process of converting an electrical excitation into a force generation, resulting in the occurrence of contraction of the heart. EC coupling occurs, as the AP depolarized through the heart, activating the release of calcium (Ca2+) from the sarcoplasmic reticulum (SR), which causes the Ca2+ concentration in the cytoplasm to increase. The Ca2+ then binds to troponin C, inducing a deformation of troponin and subsequently moves the tropomyosin away from the actin-binding sites. This removal of tropomyosin allows the myosin head to pull the actin filament toward the center of sarcomere, forming the cross-bridge cycles and triggering contraction.
Description of a lumped model of circulatory system
To simulate the ventricular hemodynamics, we coupled the finite element electromechanical model with a lumped model of the systemic and pulmonic circulations based on Kerckhoffs et al. . Both of the circulation systems were modeled as two lumped Windkessel compartments in series, one compartment for arterial and capillary blood, and one for venous blood. Each compartment was indicated by a resistance and compliance parameter. Resistance (i.e resistor) expresses flow resistance inside blood vessels due to viscosity, and compliance (i.e capacitor) determines the pressure–volume (PV) relationship for each segment through the fluid analog of the law of capacitance. All segments were modeled with linear PV relationships. Using conservation of mass law (for incompressible blood leading to conservation of volume), the volume change of a Windkessel segment was determined by inflow minus outflow. The circuit diagram of this circulatory system can be seen in Fig. 1, along with the finite element of mechanical model. Next, to implement the failing ventricle, we decreased 10% compliances of vascular system  in order to mimic the atherosclerosis and hypertensive condition.
Therefore, stroke volume (SV) and ejection fraction (EF) were the greatest (i.e., 34.2 mL and 38.3%, respectively) under the 70 cm/s MCV condition, were lowest (32 mL and 35.7%, respectively) under 30 cm/s MCV condition (see Fig. 4c). These results indicate that cardiac output is greater under higher MCV conditions. Accordingly, stroke work (SW), the area within the PV curves, was greater under the higher MCV conditions (Fig. 4d). However, ventricular ATP consumption rate was lower under higher MCV condition (Fig. 4e). Under 30 cm/s MCV, the ATP consumption was approximately 98.6 s−1, followed by the 40 cm/s MCV with 96 s−1, 50 cm/s MCV with 94 s−1, 60 cm/s MCV with 93 s−1, and 70 cm/s MCV with 92 s−1, respectively. The ATP consumption decreased by approximately 6% between these cases. Finally, SW over ventricular ATP consumption, which indicates energetic pumping efficiency of the ventricle, was smaller under higher MCV conditions (Fig. 4f), which indicates that the ventricle consumes less energy and does more work under higher MCV conditions. The index SW/ATP was greatest under the 70 cm/s MCV condition, with approximately 47 mmHg mL/ATP, followed by 46 mmHg mL/ATP under the 60 cm/s MCV condition, 45 mmHg mL/ATP under the 50 cm/s MCV condition, 42 mmHg mL/ATP under the 40 cm/s MCV condition, and 39 mmHg mL/ATP under the 30 cm/s MCV condition.
EAT is shorter under higher MCV conditions.
Ventricles under higher MCV conditions produces greater mechanical functions including better generation of intra-ventricular pressure, cardiac output, and stroke work.
ATP consumption rate is decreased under higher MCV conditions.
The ventricle depolarization timing is shorter with the higher MCV. According to equation (6) in the method section, MCV is inversely proportional with the time. This is why increasing the MCV will decrease the activation time, and conversely, reducing MCV will increase activation time, when considering the same distance (d). This phenomenon described by Fig. 3a that the EAT duration is gradually decreased with the increasing MCV value.
The cardiac systole occurs in response to the spontaneous electrical conduction of the whole ventricles. Rapid and organized conduction is necessary to generate efficient pressure during systole to pump blood out of ventricles. Our results showed that the pressure of left ventricle (LV) during systole is higher under faster MCV (see Fig. 4a). It describes that LV has more forces to pump blood out through circulation with faster MCV. However, the systolic and diastolic pressure resulted in this study is more than 120 and 80 mmHg, respectively, for all MCV cases, because we simulated using failing ventricle model with hypertensive condition. As we mentioned before in the Methods section, that we modeled the failing ventricle condition by decreasing 10% compliances of vascular system, so that the arterial blood pressure increased from normal condition. To best to our knowledge, the normal systolic pressure is less than 120 mmHg, and normal diastolic pressure is less than 80 mmHg (American Heart Association).
SV is calculated by subtracting the end systolic volume (ESV) from end diastolic volume (EDV) in the PV curves. Both ESV and EDV of the LV are reduced under higher MCV. The ESV reduced by approximately 1.5%, whereas the EDV reduced by approximately 0.5%. The reduction in the ESV is higher than in the EDV, thereby forming a horizontally extended PV curves, generating larger SV values. Subsequently, EF is calculated by dividing the SV by the EDV of the LV in one cycle contraction. EF also increased under higher MCV conditions. Increasing in SV and EF (Fig. 4c) indicates that the LV ejects more blood with higher MCV. Consequently, SW, which means the amount of work done by ventricle during one cycle, is increased under higher MCV (see Fig. 4d). In contrast, the ventricular ATP consumption rate is decreased in response to the increasing in the MCV value (Fig. 4e). This indicates that the ventricle consumes less energy to pump out the blood with higher MCV. Higher MCV values allow the regions of ventricle to contract more synchronously than the lower MCV values, due to the larger wavelengths. Synchronous contraction helps the ventricle to pump out more blood. This synchronization explains why the ATP consumed by a ventricle with higher MCV values is smaller than that of a lower MCV. These results explicate that the ventricular pumping activity is more efficient under higher MCV by consuming smaller energy (ATP) while carrying out more works (Fig. 4f).
In conclusion, this study reveals that MCV has strong correlation with the cardiac pumping efficacy. The alteration of MCV affects to the electrical and mechanical behavior of the heart. The obtained results provide useful information to estimate the effect of MCV on the electro-physiology and hemodynamic responses of the ventricle and can be used for further study about arrhythmogeneis and heart failure.
There are several limitations of the present study. First, we did not conduct experimental or clinical data in the study. Instead, we used the validated cell model and methodologies from previous studies [6–8, 12, 13]. For cardiac electrophysiology, we implemented human ventricular cell model from ten Tusscher et al.  which has been already validated with experimentally measured data . For cardiac mechanics model, we applied the myofilament dynamics model from Rice et al. . Next, we used the computational model of a failing canine ventricle, which have different mechanical characteristic than that of a failing human ventricles. We also only implemented one way EC Coupling model in this study, so that the cardiac mechanical activity can not affect to the electrophysiological behavior of the heart. Although in fact, such phenomena could occur physiologically. Next, the lumped model of the circulatory system was used to reduce the complexity of the model. Additionally, engaging electromechanical delay in further study might improve the understanding about the effect of MCV to the cardiac mechanical behavior. However, these potential limitations are not expected to influence our conclusion significantly.
Over the past 3 decades, the clinical, experimental, and theoretical studies have validated that slow conduction, plays important role in the pathogenesis of cardiac arrhythmias. Slowed myocardial conduction can increase the probability of the occurrence of cardiac arrhythmia through the formation of slow conducting re-entry circuits . However, Not only arrhythmia, the reduction of myocardium conduction velocity also had been widely linked to the pathogenesis of heart failure such as fibrosis and hypertrophy. Several studies have validated that fibrosis induced the reduction of myocardium conduction velocity, which further cause the impaired cardiac function. Therefore, knowing how far the reduction in conduction velocity affect to the pumping efficacy would be valuable to study the pathogenesis of the fibrosis and hypertrophy.
Based on these findings, we conclude that the cardiac pumping efficacy is better under higher MCV conditions due to an increasing in the force generation during systole and cardiac output while consuming less energy.
action potential duration
electrical activation time
end diastolic volume
end systolic volume
myocardial conduction velocity
This work is the product of the intellectual environment of the entire team. ARY and KML designed the study. ARY performed simulation, data analysis, interpretation of results, and drafting of the manuscript. and statistical analysis. KML wrote simulation source code, and participated in simulation design, data analysis, interpretation of results, and revised the manuscript. All authors read and approved the final manuscript.
This research was partially supported by the MSIP, Korea, under the CITRC support program (IITP-2015-H8601-15-1011) supervised by the IITP and NRF (2016R1D1A1B0101440 and 2016M3C1A6936607).
The authors declare that they have no competing interests.
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Authors can confirm that all relevant data are included in the article.
This research was supported by Korean Ministry of Science, ICT and Future Planning (IITP-2015-H8601-15-1011) and National Research Foundation (2016R1D1A1B0101440 and 2016M3C1A6936607).
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