Efficient Computational Modeling of Human Ventricular Activation and Its Electrocardiographic Representation: A Sensitivity Study
Patient-specific models of the ventricular myocardium, combined with the computational power to run rapid simulations, are approaching the level where they could be used for personalized cardiovascular medicine. A major remaining challenge is determining model parameters from available patient data, especially for models of the Purkinje-myocardial junctions (PMJs): the sites of initial ventricular electrical activation. There are no non-invasive methods for localizing PMJs in patients, and the relationship between the standard clinical ECG and PMJ model parameters is underexplored. Thus, this study aimed to determine the sensitivity of the QRS complex of the ECG to the anatomical location and regional number of PMJs. The QRS complex was simulated using an image-based human torso and biventricular model, and cardiac electrophysiology was simulated using Cardioid. The PMJs were modeled as discrete current injection stimuli, and the location and number of stimuli were varied within initial activation regions based on published experiments. Results indicate that the QRS complex features were most sensitive to the presence or absence of four “seed” stimuli, and adjusting locations of nearby “regional” stimuli provided finer tuning. Decreasing number of regional stimuli by an order of magnitude resulted in virtually no change in the QRS complex. Thus, a minimal 12-stimuli configuration was identified that resulted in physiological excitation, defined by QRS complex feature metrics and ventricular excitation pattern. Overall, the sensitivity results suggest that parameterizing PMJ location, rather than number, be given significantly higher priority in future studies creating personalized ventricular models from patient-derived ECGs.
KeywordsHuman ventricular excitation Sensitivity analysis Electrocardiogram Patient-specific modeling Computational electrophysiology Bundle branch block
As modeling and computational methodologies evolve, the ability to use these techniques to provide more effective, customized medical care for patients is fast approaching, generally termed “patient-specific modeling”.1,28,32 Even now, the potential applications of patient-specific modeling has drawn attention from NIH in the form of numerous funding announcements.15 Patient-specific modeling facilitates the ability to move away from using population-based metrics to prescribe treatment for an individual, a practice that does not result in optimal care for many patients.30 It has the potential to reduce dependence on “trial and error” techniques to determine a patient’s response to a particular treatment, and to move towards lower risk, more effective, truly personalized therapy.30
Despite the promise and excitement of the clinical implications of patient-specific modeling, it has not yet advanced to the point where it can be used as a standard of clinical care. One of the ongoing challenges is determining model parameters from available patient data in a minimally invasive fashion.10 In many cases, parameters of larger scale geometries may be obtained, yet parameters related to detailed structures are more difficult to obtain. This challenge is particularly evident in modeling initial electrical activation of the ventricles. Initial ventricular activation is crucial for coordinated ventricular contraction, and activation disorders include bundle branch block (BBB), higher-degree heart block, and symptomatic profound sinus bradycardia. Yet, the Purkinje network that carries the electrical signal to the ventricular muscle is too fine to be captured by current clinical imaging technologies, and the Purkinje-myocardial junctions (PMJs) that activate the muscle are even more elusive.17,31
Previous studies that have modeled initial ventricular activation have offered valuable insights into obtaining appropriate model parameters; yet, there are still challenges in implementing them in the context of patient-specific modeling. Some approaches yield very detailed and specific information, but require extracting the heart and imaging intact or dissected ventricles,5,6,11,23,24,27 which is not viable for designing customized treatment of patients in the clinic. Other approaches use a fractal tree rule-based approach for growing the Purkinje network and defining the PMJs along the subendocardium, which enables parameter exploration and sensitivity analyses of model parameters.3,8,17,31 Some of these rule-based approaches use activation times from patient endocardial mappings to customize the network and junctions to a particular patient17,31; yet, this requires an invasive procedure that still does not guarantee exact architecture of the patient’s Purkinje network. Furthermore, while full representation of the Purkinje network and PMJs may be required for certain disorders of initial activation, customizing this full network drastically increases the parameter space that must be explored in parameter fitting. Finally, a limited number of studies are emerging that explore the relationship between PMJ model parameters and the QRS complex of the standard, noninvasive ECG.7,19 These studies offer initial insight into using patient-derived ECGs to determine PMJ model parameters, yet only a subset of the possible parameters and their interactions have been fully explored.
Our work begins by recognizing the potential benefit of determining PMJ model parameters from the patient-derived, noninvasive QRS complex of the ECG that is commonly measured in the clinic. We posit that an important step in advancing this approach is to further determine the sensitivity of the QRS complex to properties of the PMJs, and in turn, which PMJ properties are most important in model parameter fitting. To perform this analysis, we build upon previous work by our team, having already successfully demonstrated a simulation of several heart beats and the resulting QRS complexes in an image-based biventricular and torso model.12,20 Specifically, we use our existing codes and tools to explore the sensitivity of the simulated QRS complex to ventricular model input parameters related to regional number and anatomical location of PMJs, modeling the PMJs as discrete current-injection activation stimuli. Number and location of PMJs are important parameters that have been explored previously,3,14 but their interplay and relative importance have not been fully explored in the context of the QRS complex.7,19 As an extension to our sensitivity analysis in healthy ventricles, we also simulate the QRS complex features seen in LBBB and RBBB. Finally, as a control and to provide greater connection to other models in the community that calculate the QRS complex in different ways, we repeat the sensitivity analysis using an alternate model for calculation of the QRS complex.
Materials and Methods
Biventricular and Torso Models Used in Sensitivity Analysis
Equation (1) is solved on the domain comprised of geometry from images of human ventricles obtained from the Visible Human Project® (VHP) of The National Library of Medicine.29 To obtain this ventricular domain, the full torso from VHP was segmented and meshed as follows: two-dimensional full-body cryosection images were stacked together to form a three-dimensional image. The 3D image was segmented using a combination of thresholding, level set, and manual techniques using the software package Seg3D.21 Next, a linear tetrahedral finite element mesh was generated from the segmented image. The resulting mesh contained 11 different tissues in the torso and was conformal along interfaces, including multiple-material interfaces. The ventricular mesh was extracted from the full torso mesh, and used to generate a 3D Cartesian grid (0.1 mm resolution), which is the domain in which Eq. (1) is solved using finite volumes for the divergence operator and finite differences for the gradient operator. Muscle fiber orientations were generated using a rule-based approach similar to that of Bayer et al.2 A forward Euler scheme is used for time integration. For additional detailed information, see prior Cardioid publications.12,20
Ventricular Stimuli Parameters in the Sensitivity Analysis
Prior to performing sensitivity analysis simulations, four initial activation regions (IARs) in the ventricles were defined based on experiments by Durrer et al.9 Durrer et al.9 performed seminal studies nearly half a century ago, which still represent the “gold standard” dataset and remain in wide use.4,8,11,22 In their work, activation timings (ATs) were recorded from seven healthy human hearts, each investigated using the Langendorff preparation with 870 intramural plunge electrode recordings. Across all seven hearts, four IARs were found (Figs. 1b and 1c): 1) the left side of the midseptum (S), 2) the left anterior superior wall near the base (LASW), 3) the left posterior inferior wall (LPIW) in the paraseptal region approximately one-third the distance between the apex and base, and 4) the right anterior inferior wall (RAIW) near the insertion of the anterior papillary muscle. The sensitivity analysis was built upon different configurations of stimuli in these IARs. Stimuli were placed subendocardially, where the PMJs reside, to excite the ventricles. Each stimulus was defined as an 8 mm3 volume (rectangular parallelepiped) of tissue with an injected stimulus current (Istim in Eq. (1)). All stimuli had the following square wave pulse parameters: magnitude = 72 µA/µF, duration = 1.0 ms, period = 1000 ms. All stimuli were initiated at the beginning of the period, except that stimuli in the right ventricular wall were delayed by 5 ms, based on experimental observations of Durrer et al.9
Sensitivity of QRS Complex Features to Number of Seed Stimuli
Overall, the QRS complex feature metrics are sensitive to the number of seed stimuli, with the most sensitive metrics being QRS duration, and the R and S wave amplitudes. The trends in the metrics as the number of stimuli increase are different for each metric, and some are non-monotonic. In reality, representing activation in each IAR by one stimulus per region is an oversimplification. Thus, in the next section, the consequences of adding “regional” activation stimuli around the seed stimuli are analyzed, in terms of the effects on the QRS complex feature metrics.
Sensitivity of QRS Complex Features to Number of Regional Stimuli Around the Four Seed Stimuli
Sensitivity of QRS Complex Features to Number Versus Topographical Extent of Stimuli
Bundle Branch Block (BBB) Simulations
Sensitivity of QRS Complex Features to Heterogeneous Versus Homogeneous Material Torso Models
QRS complex sensitivity simulations were performed using a biventricular and torso model by varying the number and location of current injection stimuli (i.e., PMJs) in the biventricular model. Locations of stimuli were constrained to the approximate volume of tissue corresponding to the IARs identified in Durrer et al.9 Simulations revealed relative sensitivity differences between altering number vs. location of stimuli. Overall, results suggest that patient-specific modeling of PMJs should focus parameter fitting on the location of just a few stimuli in each IAR, rather than parameterizing the number of stimuli. This trend is observed in several of the results. First, the DF (Figs. 7 and 17) quantifies the decrease in sensitivity observed in the QRS complex feature metrics (Figs. 6 and 16) to increasing number of stimuli at the regional scale. The DF values indicate that all QRS complex features are at least two-fold more sensitive to adding up to only 4 seed stimuli than to adding up to 380 regional stimuli, regardless of torso composition. In fact, for modeling healthy hearts, the QRS complex features attain physiological values when one stimulus per IAR is used. Thus, having at least one seed stimulus in each IAR may be thought of as a prerequisite for any further parameter fitting of stimuli that may follow. Second, it is evident that location plays a greater role in simulating BBB diseased states: RBBB simulated using only 3 seed stimuli (Fig. 4) produced similar QRS complex features as using 7 stimuli (Fig. 15a). Third, to the degree that the QRS complex features are sensitive to regional stimuli, it is the topographical extent of the stimuli rather than number of stimuli that make the difference (Figs. 12 and 13). In fact, for a given topographical extent of stimuli, the QRS complex shows virtually no sensitivity to the number of stimuli situated between the peripheral stimuli even when total number of stimuli is decreased by more than an order of magnitude (384 to 36 stimuli in Fig. 13g). Thus, for reproducing QRS complexes, it appears sufficient to vary regional topographical extent using no more than 36 stimuli distributed evenly amongst the four IARs (Figs. 11, 12, and 13). Understanding the maximum number of stimuli needed is important in patient-specific modeling, as reducing number of stimuli decreases the parameter space that must be explored, which increases efficiency.
As mentioned above, the QRS complex features are less sensitive to regional stimuli than to seed stimuli, and within the context of patient-specific modeling, regional stimuli may be viewed as a “fine tuning” step in parameter fitting. This fine tuning may prove more effective for features with lower DF values, namely, QRS duration and S wave amplitude. Stated slightly differently, changing the topographical extent of regional stimuli may have a greater effect when trying to model QRS duration (especially smaller durations, Figs. 6 and 16) and S wave amplitude (e.g., RBBB, Fig. 6d) accurately. Given that the QRS duration is affected by many diseases, the locations of regional stimuli may be an important consideration in model fitting. Certainly, the importance of altering locations of regional stimuli was observed in simulating RBBB and LBBB, where the septal stimulus close to the base needed to be translated by small amounts to produce appropriate BBB QRS complex features (Figs. 14 and 15). In contrast, there may be less added value in altering locations of regional stimuli when the focus of fitting is on Q wave amplitude (e.g., myocardial infarction) and R wave amplitude (e.g., hypertrophy), given their high DF values (Figs. 7 and 17). Also, torso material composition appears to be another factor that determines how much the topographical extent of regional stimuli affects QRS complex feature metrics (Fig. 16). The S wave amplitude appears to be exceptionally sensitive to torso material composition, as it is absent for many stimuli configurations in the homogeneous torso material model. Thus, for certain applications where S wave amplitude fitting is critical, it may be worthwhile to incorporate heterogeneous materials in the torso model. The DF for the Q wave amplitude is even higher for the homogeneous torso material, which means adding regional stimuli is likely to have even less effect on the Q wave amplitude than for the heterogeneous torso material model. Ideally, fitting parameters to patient-derived QRS complexes will involve matching all QRS complex features, but understanding the sensitivity of individual features may be beneficial when the focus is on a diseased state that manifests as a particular feature.
Using regional stimuli for fine tuning may also be viewed from a precision argument: how much precision does one need to reproduce faithfully patient-derived QRS complex features? While the precision needed and focus on particular features will vary by application in patient-specific modeling, results indicate that it is sufficient to use 12 stimuli (i.e., 28 stimuli dense configuration in Fig. 10) aligned in the apico-basal direction with regional inter-stimulus distance of no more than 0.7 cm (1.6 cm in septum). Using more than 12 stimuli, and increasing the topographical extent in directions other than apico-basal, produce only a per-stimulus change in QRS duration of less than 0.08 ms, and in wave amplitude of 0.01 mV or less (Fig. 10). Obtaining these kinds of precisions is likely not needed in terms of disease diagnosis, and exceed standard ECG precision. It is also worth noting that QRS complex features appear more sensitive to regional stimuli being shifted in the apico-basal direction than in other directions, which may provide guidance in constraining location of stimuli in parameter fitting procedures. Overall, altering the location of 12 stimuli (4 seed, 8 regional) arranged in the apico-basal direction appears to be a reasonable compromise between ability to manipulate QRS complex features, and having drastically more stimuli than needed for fitting precision.
Our results both contrast and corroborate results from previous modeling studies that examine the sensitivity of the QRS complex to PMJ parameters. The findings of Simelius et al.22 did emphasize the importance of location of stimulus sites; yet, these authors attributed their importance primarily to producing physiological AT maps on the heart rather than the QRS complex. They found that the QRS complex is primarily affected by carefully balancing stimuli firing times in the left and right ventricles. While our work does not explore sensitivity to stimuli firing times, it does show that the location of stimuli (topographical extent) affects the QRS complex, in addition to the AT maps. In fact, even in absence of the more sophisticated stimuli firing timings used in other studies, we were able to reproduce some of the same general phenomena in these studies. Specifically, we simulated signature BBB QRS complex features by removing specific stimuli (Fig. 15), altered magnitudes of QRS complex features via torso material manipulation (Fig. 16), and altered the S wave via changes in apico-basal location of stimuli (Fig. 12d).7 Regarding the S wave, studies by Potse et al.19 found it difficult to match simulated-to-measured S wave amplitudes. Our results combined with those of Cardone-Noott et al.7 suggest employing apico-basal location changes of stimuli (Fig. 12d), as well as alteration of torso composition (Fig. 16d), for control of S wave amplitude. Overall, despite these trends, the relationships between number, location, and activation timing of stimuli deserves further investigation in future studies.
Other studies that model the full Purkinje network tend to focus on obtaining high density of the network and the PMJs.3,8 Costabal et al.8 used special techniques to achieve smaller maximum distance between branches in generating the network over irregular geometric domains, which are ubiquitous in the heart. In contrast, our work suggests that emphasis on density and number of PMJs in the network may be less important for reproducing QRS complex features than strategic, physiologic placement of a limited number of PMJs.
Still, the added sophistication of a dense, anatomically accurate Purkinje network representation may be required for some modeling applications, even if not for all. For example, it is clearly advantageous to model a full Purkinje network if network topology or Purkinje cell function is the focus of investigation. Furthermore, studies such as those by Behradfar et al. have found that the number of junctions in a Purkinje network model plays a role in simulating reentry during arrhythmia.3 Their work was performed using a rabbit heart model, but when geometry is scaled to human size, they varied the number of PMJs between 1000 and 5000. Thus, while in our study relatively little added value is found beyond using 12 stimuli (the 28 stimuli dense configuration in Fig. 10) to simulate a healthy heart, there may be value in having more stimuli to simulate diseased hearts. Nayak et al. also found that increasing number of PMJs resulted in little-to-no spiral-wave breakup activity.14 Thus, future directions should include a sensitivity analysis of a wide range of ventricular disorders. To do so, our model may need to be altered in significant ways, given the Purkinje network fibers can act as a current sink during arrhythmias.4,13,34 This effect is not currently captured in the model and is beyond the scope of the current study, but would be an important addition in future studies.
Another outcome of the sensitivity analysis is a simple 12-stimuli configuration for modeling ventricular activation without the full Purkinje network. Such a simple protocol may be useful for studies in the community where it is desirable to model activation, but with a primary focus on diseases and phenomena downstream of initial activation, such as defects in ionic channel activities of myocytes and their impact on whole-organ ventricular dynamics. Still, even at the stage of initial activation, the 12-stimuli configuration has some relevance in modeling disorders, as shown for simulating QRS complex features of RBBB and LBBB (Figs. 14 and 15).
In the next phase of this work, the analysis will be expanded to include a more comprehensive examination of sensitivity in other disease states, and additional parameters of activation beyond number and location of stimuli will be examined. Furthermore, given that these results were derived from a single biventricular/torso model, the analysis will be performed in a variety of image-based heart and torso sets to test the repeatability and universality of the sensitivity results across users and geometries. Factors such as heart position and orientation will be evaluated in terms of how they affect sensitivity of the QRS complex features to stimuli parameters. Such studies could be compared to the work of Nguyên et al.16 Their research varied heart position and orientation, and examined effects on the QRS complex, but they did not alter initial ventricular activation parameters.
In summary, this sensitivity analysis models PMJs as current injection stimuli in one biventricular/torso model, and investigates the sensitivity of simulated QRS complex features to number and location of these stimuli. We found that the QRS complex features are most sensitive to the locations of a few well-placed stimuli rather than to the sheer number of stimuli. The presence or absence of just one seed stimulus per IAR has significant effects on the QRS complex features, and to the extent that the regional stimuli affect QRS complex features, the topographical extent of relatively few stimuli (between 12 and 36) dominates QRS complex features. The QRS complex features are more sensitive to seed stimuli, but regional stimuli changes may offer “fine tuning” of these features to match patient-derived data. The stimulus configuration with 12 total stimuli oriented in an apico-basal direction and regional inter-stimuli distance of 0.7 cm (1.6 cm in septum) produced QRS complex features of a healthy heart with reasonable precision. This 12-stimuli configuration also served as a good basis for simulating BBB, yet it is undeniable that there are certain disease states and application spaces where a dense, full Purkinje network is useful. Ultimately, this work establishes a new approach in describing the sensitivity of QRS complex features for patient-specific modeling of activation. The QRS complex of the ECG is a noninvasive, standardized measurement of electrical activity in the ventricles, and thus is an attractive tool for model parameter fitting. Our results should be viewed within the context of our model limitations (current-injection stimuli model of PMJs), as well as viewed as a catalyst for future explorations of QRS complex sensitivities to numerous other PMJ parameters. Still, the results provided herein should aid in effectively decreasing the sheer number of parameters to be considered in fitting studies, and illuminate which parameters should be given the greatest weight, i.e., location over number. By providing knowledge that may increase the efficiency of fitting model parameters to clinically derived QRS complexes, this work represents another step towards the realization of patient-specific medicine. As the horizon of patient-specific medicine approaches, it brings with it the promise of lower risk and more effective treatment.
We thank the Lawrence Livermore National Laboratory (LLNL) Computing Grand Challenge Program for the computational resources that enabled this work. We thank William D. Krauss at LLNL for his technical consultations on visualization and Erik W. Draeger at LLNL for contributing post-processing scripts for ECG generation. Seg3D software used in this study is supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number P41 GM103545-18. We thank the Blender Foundation (https://www.blender.org/foundation/) for creating superb technical software that we used for visualization of our ventricular activation timing maps. We thank the Laboratory Directed Research and Development (LDRD) program at Lawrence Livermore National Laboratory under the National Nuclear Security Administration (NNSA) for their support of this work, project numbers 15-SI-002 and 13-ERD-035. Financial support to O.M.H. from Department of Energy Computational Science Graduate Fellowship (CSGF) grant DE-FG02-97ER25308 is gratefully acknowledged, as well as to C.T.V. from National Institutes of Health, National Heart, Lung, and Blood Institute (NHLBI) Ruth L. Kirschstein National Research Service Award under Institutional T32 Research Training grant 5 T32 HL 7444-32. Support was provided to J.L. from National Institute of Health grants HL61795, HG007690, and GM107618. Support was provided to A.D.M. by National Institutes of Health grants including the National Biomedical Computation Resource (P41 GM103426), U01 grants HL122199 and HL126273, R01 grants HL105242 and HL111197, and a subaward of U54 HL119893. Support to D.E.K. was provided by the University of California San Diego Clinical Translational Research Institute (CTRI) Galvanizing Engineering in Medicine (GEM) grant. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This is LLNL report LLNL-JRNL-723037.
CONFLICT OF INTEREST
C.T.V. is an equity holder and consultant for Vektor Medical, Inc., unrelated to the present work. R.C.B. is a minority owner in Cardiosolv LLC. A.D.M. is a co-founder of, has an equity interest in, and serves as a scientific advisory board member of Vektor Medical and Insilicomed, Inc., licensees of UCSD intellectual property that was not used in this research. Some research grants to A.D.M., including those acknowledged here, have been identified for conflict of interest management based on the overall scope of the project and its potential benefit to Insilicomed, Inc. They are required to disclose this relationship in publications acknowledging the grant support, however the research subject and findings reported here did not involve the company in any way. The terms of this arrangement have been reviewed and approved by the University of California San Diego in accordance with its conflict of interest policies. D.E.K. is a consultant to Abbott Laboratories, and an equity holder and consultant for Vektor Medical, both unrelated to the present work. No other conflicts of interest, financial or otherwise, are declared by the authors.
RESEARCH INVOLVING HUMAN AND ANIMAL STUDIES
No human studies were carried out by the authors for this article. No animal studies were carried out by the authors for this article.
- 5.Bishop, M. J., G. Plank, R. A. B. Burton, J. E. Schneider, D. J. Gavaghan, V. Grau, et al. Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function. Am. J. Physiol. Heart Circ. Physiol. 298(2):H699–H718, 2010. https://doi.org/10.1152/ajpheart.00606.2009.CrossRefGoogle Scholar
- 6.Bordas, R., K. Gillow, Q. Lou, I. R. Efimov, D. Gavaghan, P. Kohl, et al. Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system. Prog. Biophys. Mol. Biol. 107(1):90–100, 2011. https://doi.org/10.1016/j.pbiomolbio.2011.05.002.CrossRefGoogle Scholar
- 7.Cardone-Noott, L., A. Bueno-Orovio, A. Minchole, N. Zemzemi, and B. Rodriguez. Human ventricular activation sequence and the simulation of the electrocardiographic QRS complex and its variability in healthy and intraventricular block conditions. Europace. 18:4–15, 2016. https://doi.org/10.1093/europace/euw346.CrossRefGoogle Scholar
- 12.Mirin, A. A., D. F. Richards, J. N. Glosli, E. W. Draeger, B. Chan, J. L. Fattebert, et al. Toward real-time modeling of human heart ventricles at cellular resolution: simulation of drug-induced arrhythmias. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis. Washington, DC: IEEE Computer Society Press, 2012.Google Scholar
- 13.Monserrat, M., and J. Saiz. Reentry based on the development of early after depolarizations in a Purkinje-ventricular muscle ring model. Comput. Cardiol. 26:491–494, 1999.Google Scholar
- 16.Nguyên, U. C., M. Potse, F. Regoli, M. L. Caputo, G. Conte, R. Murzilli, et al. An in-silico analysis of the effect of heart position and orientation on the ECG morphology and vectorcardiogram parameters in patients with heart failure and intraventricular conduction defects. J. Electrocardiol. 48(4):617–625, 2015. https://doi.org/10.1016/j.jelectrocard.2015.05.004.CrossRefGoogle Scholar
- 20.Richards, D. F., J. N. Glosli, E. W. Draeger, A. A. Mirin, B. Chan, J. L. Fattebert, et al. Towards real-time simulation of cardiac electrophysiology in a human heart at high resolution. Comput. Methods Biomech. 16(7):802–805, 2013. https://doi.org/10.1080/10255842.2013.795556.CrossRefGoogle Scholar
- 21.Scientific Computing and Imaging Institute. “Seg3D” Volumetric Image Segmentation and Visualization. Scientific Computing and Imaging Institute (SCI), 2015. http://www.seg3d.org/.
- 22.Simelius, K., J. Nenonen, and M. Horáček. Modeling cardiac ventricular activation. Int. J. Bioelectromagn. 3(2):51–58, 2001.Google Scholar
- 24.Stephenson, R. S., M. R. Boyett, G. Hart, T. Nikolaidou, X. Cai, A. F. Corno, et al. Contrast enhanced micro-computed tomography resolves the 3-dimensional morphology of the cardiac conduction system in mammalian hearts. PLoS ONE 7(4):e35299, 2012. https://doi.org/10.1371/journal.pone.0035299.CrossRefGoogle Scholar
- 25.Surawicz, B., and T. K. Knilans. Chou’s Electrocardiography in Clinical Practice (5th ed.). Philadelphia, PA: W.B. Saunders Company, 2001.Google Scholar
- 29.U. S. National Library of Medicine. Visible Human Project®. National Institutes of Health, U.S. Department of Health & Human Services, 2015. https://www.nlm.nih.gov/research/visible/visible_human.html. Accessed 1 Feb 2017.
- 30.Vadakkumpadan, F., V. Gurev, J. Constantino, H. Arevalo, and N. Trayanova. Modeling of whole-heart electrophysiology and mechanics: toward patient-specific simulations. In: Patient-Specific Modeling of the Cardiovascular System: Technology-Driven Personalized Medicine, edited by R. C. P. Kerckhoffs. New York: Springer, 2010, pp. 145–165.CrossRefGoogle Scholar
- 31.Vergara, C., S. Palamara, D. Catanzariti, F. Nobile, E. Faggiano, C. Pangrazzi, et al. Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation. Med. Biol. Eng. Comput. 52(10):813–826, 2014. https://doi.org/10.1007/s11517-014-1183-5.CrossRefGoogle Scholar
- 33.Wagner, G. S. Marriott’s Practical Electrocardiography (10th ed.). Philadelphia, PA: Lippincott Williams and Wilkins, 2001.Google Scholar
- 34.Walter, P. F., and S. Pollak. Rapid ventricular-tachycardia due to his-Purkinje reentry. PACE 7(4):728–734, 1984. https://doi.org/10.1111/j.1540-8159.1984.tb05603.x.CrossRefGoogle Scholar
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