Modeling of realistic heart electrical excitation based on DTI scans and modified reaction diffusion equation

Modeling of realistic heart electrical excitation based on DTI scans and modified reaction diffusion equation

A new method is proposed for modeling realistic heart activation using diffusion tensor imaging (DTI) scans based on biological properties of its tissues in addition to the working methodology of the DTI scanner. Modeling of the excitation propagation inside the heart is initiated by applying activation at only one pacing site at the root of the conduction network. The excitation propagation has been accomplished based on a proposed conduction system that is extracted from DTI heart scans and a modified version of monodomain reaction diffusion equation (RDE) that considers the heart inhomogeneous–anisotropic material. The Aliev–Panfilov method was used to model the reaction part of the equation and inhomogeneous–anisotropic diffusion to model the diffusion part in the equation. Variation in conduction speeds between the myocardium and the conduction system has been also taken into consideration. Employing the proposed conduction system and the modified RDE on the heart model shows (somewhat) realistic heart activation where the produced ventricular excitation propagation isochrones are similar to real measurements.

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  • Guyton AC. Human Physiology and Mechanisms of Diseases. 5th ed. Philadelphia, PA, USA: Saunders, 1992.
  • Weidmann S. The electrical constants of Purkinje fibers. J Physiol 1952; 118: 348-360.
  • Roberts DE, Hersh LT, Scher AM. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ Res 1979; 44; 701-712.
  • Osman Gania M, Ogawa T. Stability of periodic traveling waves in the Aliev–Panfilov reaction–diffusion system. Commun Nonlinear Sci 2016; 33: 30-42.
  • Aliev RR, Panfilov AV. A simple two-variable model of cardiac excitation. Chaos Soliton Fract 1996; 7: 293-301.
  • Winfree AT. Varieties of spiral wave behavior: an experimentalist’s approach to the theory of excitable media. Chaos 1991; 1: 303-334.
  • Panfilov AV, Hogeweg P. Spiral breakup in a modified FitzHugh–Nagumo model. Phys Lett A 1993; 176: 295-299.
  • Franovic I, Perc M, Todorovic K, Kostic S, Buric N. Activation process in excitable systems with multiple noise sources: large number of units. Phys Rev 2015; E92: 062912.
  • Franovic I, Todorovic K, Perc M, Vasovic N, Buric N. Activation process in excitable systems with multiple noise sources: One and two interacting units. Phys Rev 2015; E92: 062911.
  • FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1961; 1: 445-466
  • [39] Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res 1991; 68: 1501-1526.
  • Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibers. J Physiol 1977; 268:177-210.
  • Noble D. A modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pacemaker potentials. J Physiol 1962; 160: 317-352.
  • [36] Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 1952; 117: 500-544.
  • Seger M, Modre R, Pfeifer B, Hintermuller C, Tilg B. Non-invasive imaging of atrial flutter. Comput Cardiol 2006; 33: 601-604.
  • Sermesant M, Coudiere Y, Delingette H, Ayache N, Sainte-Marie J, Chapelle D, Clement F, Sorine M. Progress towards model-based estimation of the cardiac electromechanical activity from ECG signals and 4D images. ESAIM Proc 2002; 12: 153-162.
  • Wang LW, Zhang HY, Shi PC. Simultaneous recovery of three-dimensional myocardial conductivity and electrophysiological dynamics: a nonlinear system approach. Comput Cardiol 2006; 33: 45-48.
  • Potse M, Dube B, Vinet A, Cardinal R. A comparison of monodomain and bidomain propagation models for the human heart. IEEE T Bio-Med Eng 2006; 53: 2425-2435.
  • Malmivuo J, Plonsey R. Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields.1st ed. Oxford, UK: Oxford University Press, 1995.
  • Geselowitz DB. On bioelectric potentials in an inhomogeneous volume conductor. Biophys J 1967; 7: 1-11.
  • Elaff I, El-Kemany A, Kholif M. Universal and stable medical image generation for tissue segmentation (The unistable method). Turk J Electr Eng & Comp Sci 2017; 25: 1070-1081.
  • Bushong SC. Magnetic Resonance Imaging: Physical and Biological Principles. 3rd ed. Maryland Heights, MO, USA: Mosby, 2003
  • Lufkin RB. The MRI Manual. 2nd ed. Maryland Heights, MO, USA: C.V. Mosby, 1998.
  • Stark DD, Bradley WG. Magnetic Resonance Imaging. 3rd ed. Maryland Heights, MO, USA: C.V. Mosby, 1999.
  • Margulis AR. Open Field Magnetic Resonance Imaging: Equipment, Diagnosis and Interventional Procedures. 1st ed. New York, NY, USA: Springer-Verlag Telos, 2000.
  • Eliska O. Purkinje fibers of the heart conduction system: The history and present relevance of the Purkinje discoveries. Casopis Lekaru Ceskych 2006; 145: 329-335.
  • Hurst JW, Logue RB, Schlant RC, Wenger NK. The Heart. 3rd ed. New York, NY, USA: McGraw-Hill, 1974.
  • Sommer JR, Johnson EA. Cardiac muscle: A comparative study of Purkinje fibres and ventricular fibres. J Cell Biol 1968; 36: 497-526.
  • El-Aff I. Extraction of human heart conduction network from diffusion tensor MRI. In: IASTED BioMed 2010;17–19 February 2010; Innsbruck, Austria: pp. 680-051.
  • Berger T, Fischer G, Pfeifer B, Modre R, Hanser F, Trieb T, Roithinger FX, Stuehlinger M, Pachinger O, Tilg B et al. Single-beat noninvasive imaging of cardiac electrophysiology of ventricular pre-excitation. J Am Coll Cardiol 2006; 48: 2045-2052.
  • Knisley SB, Trayanova N, Aguel F. Roles of electric field and fibre structure in cardiac electric stimulation. Biophys J 1999; 77: 1404-1417.
  • Smaill BH, LeGrice IJ, Hooks DA, Pullan AJ, Caldwell BJ, Hunter PJ. Cardiac structure and electrical activation: Models and measurement. Proc Aust Physiol Pharmacol Soc 2004; 34: 141-149.
  • Lorange M, Gulrajani RM. A computer heart model incorporating anisotropic propagation. J Electrocardiol 1993;26: 245-261.
  • Simeliusa K, Nenonena J, Horacekb M. Modeling cardiac ventricular activation. International Journal of Bioelectromagnetism 2001; 3: 51-58.
  • Berenfeld O, Jalife J. Purkinje-muscle reentry as a mechanism of polymorphic ventricular, arrhythmias in a 3-dimensional model of the ventricles. Circ Res 1998; 82: 1063-1077.
  • Farina DS, Skipa O, Kaltwasser C, Dossel O, Bauer WR. Personalized model of cardiac electrophysiology of a patient. International Journal of Bioelectromagnetism 2005; 7: 303-306.
  • Ohyu S, Okamoto Y, Kuriki S. Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties. IEEE T Bio-Med Eng 2002; 49: 509-518.
  • Pollard AE, Barr RC. The construction of an anatomically based model of the human ventricular conduction system. IEEE T Bio-Med Eng 1990; 37: 1173-1185.
  • Sermesant M, Delingette H, Ayache N. An electromechanical model of the heart for image analysis and simulation. IEEE T Med Imaging 2006; 25: 612-625.
  • Ohyu S, Okamoto Y, Kuriki S. Use of the ventricular propagated excitation model in the magnetocardiographic inverse problem for reconstruction of electrophysiological properties. IEEE T Bio-Med Eng 2002; 49: 509-518.
  • Durrer D, Van Dam RTH, Freud GE, Janse MJ, Meijler FL, Arzbaecher RC. Total excitation of the isolated human heart. Circulation 1970; 41: 899-912.
  • Massing GK, James TN. Anatomical configuration of the His bundle and bundle branches in the human heart. Circulation 1976; 53: 609-621.
  • Tawara S. The Conduction System of the Mammalian Heart. English ed. London, UK: Imperial College Press, 2000.
  • Widmaier EP, Raff H, Strang KT. Vander’s Human Physiology: The Mechanisms of Body Function. 10th ed. Boston, MA, USA: McGraw-Hill, 2006.
  • Kessel RG. Basic Medical Histology: The Biology of Cells, Tissues, and Organs. Oxford, UK: Oxford University Press, Inc., 1998.
  • Brooker C. Human Structure and Function. 2nd ed. London, UK: Mosby Int. Ltd., 1998.
  • Standring S. Gray’s Anatomy. 39th ed. New York, NY, USA: Elsevier Churchill Livingstone, 2005.
  • Tortora GJ, Derrickson B. Principles of Anatomy and Physiology. 11th ed. Oxford, UK: John Wiley & Sons, Inc., 2006.
  • Jordan PN, Christini DJ. Therapies for ventricular cardiac arrhythmias. Crit Rev Biomed Eng 2005; 33: 557-604.