A Finite Element Formulation for Atrial Tissue Monolayer

 

 Buy Article Permissions and Reprints

Summary

Objectives: Using computer models for the study of complex atrial arrhythmias such as atrial fibrillation is computationally demanding as long observation periods in the order of tens of seconds are required. A well established approach for reducing computational workload is to approximate the thin atrial walls by curved monolayers. On the other hand, the finite element method (FEM) is a well established approach to solve the underlying partial differential equations.

Methods: A generalized 2D finite element method (FEM) is presented which computes the corresponding stiffness and coupling matrix for arbitrarily shaped monolayers (ML). Compared to standard 2D FEM, only one additional coordinate transformation is required. This allows the use of existing FEM software with minor modifications. The algorithm was tested to simulate wave propagation in benchmark geometries and in a model of atrial anatomy.

Results: The ML model was able to simulate electric activation in curved tissue with anisotropic conductivity. Simulations in branching tissue yielded slightly different patterns when compared to a volumetric model with finite thickness. In the model of atrial anatomy the computed activation times for five different pacing protocols displayed a correlation of 0.88 compared to clinical data.

Conclusions: The presented method provides a useful and easily implemented approach to model wave propagation in MLs with a few restrictions to volumetric models.

• References

• 1 Nattel S. New ideas about atrial fibrillation 50 years on. Nature 2002; 415: 219-226.
  CrossrefPubMedGoogle Scholar
• 2 Schilling RJ. Which Patient Should Be Referred to an Electrophysiologist: Supraventricular Tachycardia. Heart 2002; 87: 299-304.
  CrossrefPubMedGoogle Scholar
• 3 Wijffels MC, Kirchhof CJ, Dorland R, Allessie MA. Atrial Fibrillation Begets Atrial Fibrillation: A Study in Awake Chronically Instrumented Goats. Circulation 1995; 92: 1954-1968.
  CrossrefPubMedGoogle Scholar
• 4 Allessie M, Ausma J, Schotten U. Electrical, contractile and structural remodeling during atrial fibrillation. Cardiovasc Res 2002; 54: 230-246.
  CrossrefPubMedGoogle Scholar
• 5 Wieser L, Fischer G, Hintringer F, Ho SY, Tilg B. Reentry Anchoring at a Pair of Pulmonary Vein Ostia. LNCS 2005; 3504: 183-194.
  PubMedGoogle Scholar
• 6 Vigmond EJ, Ruckdeschel R, Trayanova N. Reentry in a Morphologically Realistic Atrial Model. J Cardiovasc Electrophysiol 2001; 12: 1046-1054.
  CrossrefPubMedGoogle Scholar
• 7 Virag N, Jacquemet V, Henriquez CS, Zozor S, Blanc O, Vesin JM. et al. Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria. Chaos 2002; 12: 754-763.
  CrossrefPubMedGoogle Scholar
• 8 Siregar P, Julen N, Sinteff JP. Computational Integrative Physiology: At the Convergence of the Life and Computational Sciences. Methods Inf Med 2003; 42: 177-184.
  Article in Thieme ConnectPubMedGoogle Scholar
• 9 Harrild DM, Henriquez CS. A Computer Model of Normal Conduction in the Human Atria. Circ Res 2000; 87: e25-e36.
  CrossrefPubMedGoogle Scholar
• 10 Vigmond EJ, Aguel F, Trayanova NA. Computational Techniques for Solving the Bidomain Equations in Three Dimensions. IEEE Trans Biomed Eng 2002; 49: 1260-1269.
  CrossrefPubMedGoogle Scholar
• 11 Zozor S, Blanc O, Jacquemet V, Virag N, Vesin JM, Pruvot E. et al. A Numerical Scheme for Modeling Wavefront Propagation on a Monolayer of Arbitrary Geometry. IEEE Trans Biomed Eng 2003; 50: 412-420.
  CrossrefPubMedGoogle Scholar
• 12 Potse M, Dubé B, Richer J, Vinet A, Gulrajani RM. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans Biomed Eng 2006; 53: 2425-2435.
  CrossrefPubMedGoogle Scholar
• 13 Blanc O, Virag N, Vesin JM, Kappenberger L. A Computer Model of Human Atria with Reasonable Computation Load and Realistic Anatomical Properties. IEEE Trans Biomed Eng 2001; 48: 1229-1237.
  CrossrefPubMedGoogle Scholar
• 14 Seger M, Fischer G, Modre R, Messnarz B, Hanser F, Tilg B. Lead field computation for the electrocardiographic inverse problem – finite elements versus boundary elements. Comput Methods Programs Biomed 2005; 77: 241-252.
  CrossrefPubMedGoogle Scholar
• 15 Ramirez RJ, Nattel S, Courtemanche M. Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling. Am J Physiol 2000; 279: H1767-H1785.
  PubMedGoogle Scholar
• 16 Spach MS, Miller WTI, Barr RC, Geselowitz DB. Electrophysiology of the internodal pathways?. In: Little R. editor. Physiology of Atrial Pacemakers and Conductive Tissue. Armonk, NY: Futura Publishing Co; 1980. pp 367-380.
  Google Scholar
• 17 Ho SY, Sanchez-Quintana D, Anderson RH. Can anatomy define electric pathways?. In: International Workshop on Computer Simulation and Experimental Assessment of Electrical Cardiac Function. 1998. pp 77-86.
  Google Scholar
• 18 Kucera JP, Kléber AG, Rohr S. Slow Conduction in Cardiac Tissue, II – Effects of Branching Tissue Geometry. Circ Res 1998; 83: 795-805.
  CrossrefPubMedGoogle Scholar
• 19 Tilg B, Fischer G, Modre R, Hanser F, Messnarz B, Schocke M. et al. Model-Based Imaging of Cardiac Electrical Excitation in Humans. IEEE Trans Med Imaging 2002; 21: 1031-1039.
  CrossrefPubMedGoogle Scholar
• 20 Pfeifer B, Hanser F, Seger M, Hintermüller C, Modre-Osprian R, Fischer G. et al. Modeling using Active Appearance Models and Morphological Operators. Proc SPIE, Medical Imaging 2005: Visualization, Image-Guided Procedures, and Display; 2005 pp 5744-5732.
  PubMedGoogle Scholar
• 21 Ho SY, Sanchez-Quintana D, Cabrera JA, Anderson RH. Anatomy of the Left Atrium: Implications for Radiofrequency Ablation of Atrial Fibrillation. J Cardiovasc Electrophysiol 1999; 10: 1525-1533.
  CrossrefPubMedGoogle Scholar
• 22 Roithinger FX, Cheng J, SippensGroenewegen A, Lee RJ, Saxon LA, Scheinman MM. et al. Use of Electroanatomic Mapping to Delineate Transseptal Atrial Conduction in Humans. Circulation 1999; 100: 1791-1797.
  CrossrefPubMedGoogle Scholar
• 23 Seemann G, Höper C, Sachse FB, Dössel O, Holden AV, Zhang H. Heterogeneous threedimensional anatomical and electrophysiological model of human atria. Phil Trans R Soc 2006; 364: 1464-1481.
  PubMedGoogle Scholar
• 24 Gozolits S, Fischer G, Berger T, Hanser F, Abou-Harb M, Tilg B. et al. Global P Wave Duration on the 65-Lead ECG: Single-Site and Dual-Site Pacing in the Structurally Normal Human Atrium. J Cardiovasc Electrophysiol 2002; 13: 1240-1245.
  CrossrefPubMedGoogle Scholar
• 25 Plank G, Leon LJ, Kimber S, Vigmond EJ. Defibrillation Depends on Conductivity Fluctuations and the Degree of Disorganization in Reentry Patterns. J Cardiovasc Electrophysiol 2005; 16: 205-216.
  CrossrefPubMedGoogle Scholar
• 26 Fischer G, Pfeifer B, Seger M, Hintermüller C, Hanser F, Modre R. et al. Computationally effcient noninvasive cardiac activation time imaging. Methods Inf Med 2005; 44: 674-686.
  Article in Thieme ConnectPubMedGoogle Scholar
• 27 Jacquemet V, Henriquez CS. Finite volume stiffness matrix for solving anisotropic cardiac propagation in 2-D and 3-D unstructured meshes. IEEE Trans Biomed Eng 2005; 52: 1490-1492.
  CrossrefPubMedGoogle Scholar
• 28 Fast VG, Kléber AG. Cardiac tissue geometry as a determinant of unidirectional conduction block: assessment of microscopic excitation spread by optical mapping in patterned cell cultures and in a computer model. Cardiovasc Res 1995; 29: 697-707.
  CrossrefPubMedGoogle Scholar
• 29 Jalife J, Berenfeld O, Mansour M. Mother rotors and fibrillatory conduction: a mechanism of atrial fibrillation. Cardiovasc Res 2002; 54: 204-216.
  CrossrefPubMedGoogle Scholar
• 30 Wieser L, Fischer G, Nowak CN, Tilg B. Fibrillatory Conduction in Branching Atrial Tissue – Insight from Volumetric and Monolayer Computer Models. Comput Methods Programs Biomed. Comput Methods Programs Biomed 2007; 86: 103-111.
  CrossrefPubMedGoogle Scholar
• 31 Chauvin M, Shah DC, Haïssaguerre M, Marcellin L, Brechenmacher C. The Anatomic Basis of Connections Between the Coronary Sinus Musculature and the Left Atrium in Humans. Circulation 2000; 101: 647-652.
  CrossrefPubMedGoogle Scholar
• 32 de Ponti R, Ho SY, Salerno-Uriarte JA, Tritto M, Spadacini G. Electroanatomic Analysis of Sinus Impulse Propagation in Normal Human Atria. J Cardiovasc Electrophysiol 2002; 13: 1-10.
  CrossrefPubMedGoogle Scholar
• 33 Rantner LJ, Wieser L, Stühlinger MC, Hintringer F, Tilg B, Fischer G. Detection of Phase Singularities in Triangular Meshes. Methods Inf Med 2007; 46: 646-654.
  Article in Thieme ConnectPubMedGoogle Scholar