Annals of Biomedical Engineering

, Volume 40, Issue 10, pp 2243–2254 | Cite as

A Novel Rule-Based Algorithm for Assigning Myocardial Fiber Orientation to Computational Heart Models

  • J. D. BayerEmail author
  • R. C. Blake
  • G. Plank
  • N. A. Trayanova


Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace–Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.


Diffusion tensor Magnetic resonance Imaging Finite element Mesh Laplace–Dirichlet 



The authors would like to thank Dr. Edward Vigmond at the University of Bordeaux for his software Meshalyzer. This work was supported by grants AHA 10PRE3650037 to Jason Bayer, NIH R01 HL082729 and HL103428, and NSF CBET-0933029 to Natalia Trayanova, and FWF F3210-N18 and NIH R01 HL10119601 to Gernot Plank.

Supplementary material

10439_2012_593_MOESM1_ESM.pdf (25.5 mb)
Supplementary material 1 (PDF 26,121 kb)


  1. 1.
    Alexander, A. L., K. M. Hasan, M. Lazar, J. S. Tsuruda, and D. L. Parker. Analysis of partial volume effects in diffusion-tensor MRI. Magn. Reson. Med. 45(5):770–780, 2001.PubMedCrossRefGoogle Scholar
  2. 2.
    Ashikaga, H., J. C. Criscione, J. H. Omens, J. W. Covell, and N. B. Ingels. Transmural left ventricular mechanics underlying torsional recoil during relaxation. Am. J. Physiol. Heart Circ. Physiol. 286(2):H640–H647, 2004.PubMedCrossRefGoogle Scholar
  3. 3.
    Bayer, J. D., J. Beaumont, and A. Krol. Laplace–Dirichlet energy field specification for deformable models. An FEM approach to active contour fitting. Ann. Biomed. Eng. 33(9):1175–1186, 2005.PubMedCrossRefGoogle Scholar
  4. 4.
    Beyar, R., and S. Sideman. A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity. Circ. Res. 55(3):358–375, 1984.PubMedCrossRefGoogle Scholar
  5. 5.
    Bishop, M. J., P. M. Boyle, G. Plank, D. G. Welsh, and E. J. Vigmond. Modeling the role of the coronary vasculature during external field stimulation. IEEE Trans. Biomed. Eng. 57(10):2335–2345, 2010.PubMedCrossRefGoogle Scholar
  6. 6.
    Bishop, M. J., G. Plank, R. A. Burton, J. E. Schneider, D. J. Gavaghan, V. Grau, and P. Kohl. 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.PubMedCrossRefGoogle Scholar
  7. 7.
    Bovendeerd, P. H., T. Arts, J. M. Huyghe, D. H. van Campen, amd R. S. Reneman. Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study. J. Biomech. 25(10):1129–1140, 1992.PubMedCrossRefGoogle Scholar
  8. 8.
    Caldwell, B. J., M. L. Trew, G. B. Sands, D. A. Hooks, I. J. LeGrice, and B. H. Smaill. Three distinct directions of intramural activation reveal nonuniform side-to-side electrical coupling of ventricular myocytes. Circ. Arrhythm. Electrophysiol. 2(4):433–440, 2009.PubMedCrossRefGoogle Scholar
  9. 9.
    Cherry, E. M., H. S. Greenside, and C. S. Henriquez. Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method. Choas 13(3):853–865, 2003.CrossRefGoogle Scholar
  10. 10.
    Costa, K. D., Y. Takayama, A. D. McCulloch, and J. W. Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol. 276(2 Pt 2):H595–H607, 1999.PubMedGoogle Scholar
  11. 11.
    Fernandez-Teran, M. A., and J. M. Hurle. Myocardial fiber architecture of the human heart ventricles. Anat. Rec. 204(2):137–147, 1982.PubMedCrossRefGoogle Scholar
  12. 12.
    Greenstein, J. L., and R. L. Winslow. An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. Biophys. J. 83(6):2918–2945, 2002.PubMedCrossRefGoogle Scholar
  13. 13.
    Han, C., S. M. Pogwizd, C. R. Killingsworth, and B. He. Noninvasive reconstruction of the three-dimensional ventricular activation sequence during pacing and ventricular tachycardia in the canine heart. Am. J. Physiol. Heart Circ. Physiol. 302(1):H244–H252, 2012.PubMedCrossRefGoogle Scholar
  14. 14.
    Harrington, K. B., F. Rodriguez, A. Cheng, F. Langer, H. Ashikaga, G. T. Daughters, J. C. Criscione, N. B. Ingels, and D. C. Miller. Direct measurement of transmural laminar architecture in the anterolateral wall of the ovine left ventricle: new implications for wall thickening mechanics. Am. J. Physiol. Heart Circ. Physiol. 288(3):H1324–H1330, 2005.PubMedCrossRefGoogle Scholar
  15. 15.
    Helm, P., M. F. Beg, M. I. Miller, and R. L. Winslow. Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Ann. N. Y. Acad. Sci. 1047:296–307, 2005.PubMedCrossRefGoogle Scholar
  16. 16.
    Helm, P. A., L. Younes, M. F. Beg, D. B. Ennis, C. Leclercq, O. P. Faris, E. McVeigh, D. Kass, M. I. Miller, and R. L. Winslow. Evidence of structural remodeling in the dyssynchronous failing heart. Circ. Res. 98(1):125–132, 2006.PubMedCrossRefGoogle Scholar
  17. 17.
    Hristov, N., O. J. Liakopoulos, G. D. Buckberg, and G. Trummer. Septal structure and function relationships parallel the left ventricular free wall ascending and descending segments of the helical heart. Eur. J. Cardiothorac. Surg. 29S:S115–S125, 2006.CrossRefGoogle Scholar
  18. 18.
    Hooks, D. A., M. L. Trew, B. J. Caldwell, G. B. Sands, I. J. LeGrice, and B. H. Smaill. Laminar arrangement of ventricular myocytes influences electrical behavior of the heart. Circ. Res. 101(10):e103–e112, 2007.PubMedCrossRefGoogle Scholar
  19. 19.
    Hsu, E. W., A. L. Muzikant, S. A. Matulevicius, R. C. Penland, and C. S. Henriquez. Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am. J. Physiol. 274(5 Pt 2):H1627–H1634, 1998.PubMedGoogle Scholar
  20. 20.
    Keller, D. U. J., D. L. Weiss, O. Dossel, and G. Seemann. Influence of I Ks heterogeneities on the genesis of the T-wave: a computational evaluation. IEEE Trans. Biomed. Eng. 59(2):311–322, 2012.PubMedCrossRefGoogle Scholar
  21. 21.
    Kim, Y. H., F. Xie, M. Yashima, T. J. Wu, M. Valderrbano, M. H. Lee, T. Ohara, O. Voroshilovsky, R. N. Doshi, M. C. Fishbein, Z. Qu, A. Garfinkel, J. N. Weiss, H. S. Karagueuzian, and P. S. Chen. Role of papillary muscle in the generation and maintenance of reentry during ventricular tachycardia and fibrillation in isolated swine right ventricle. Circulation 100(13):1450–1459, 1999.PubMedCrossRefGoogle Scholar
  22. 22.
    LeGrice, I. J., B. H. Smaill, L. Z. Chai, S. G. Edgar, J. B. Gavin, and P. J. Hunter. Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. 269(2 Pt 2):H571–H582, 1995.PubMedGoogle Scholar
  23. 23.
    Lombaert, H., J.-M. Peyrat, P. Croisille, S. Rapacchi, L. Fanton, P. Clarysse, H. Delingette, and N. Ayache. Statistical analysis of the human cardiac fiber architecture from DT-MRI. In Proceedings of the 6th International Conference on Functional Imaging and Modeling of the Heart (FIMH’11), pp. 171–179, 2011.Google Scholar
  24. 24.
    Pierpaoli, C., and P. J. Basser. Toward a quantitative assessment of diffusion anisotropy. Magn. Reson. Med. 36(6):893–906, 1996.PubMedCrossRefGoogle Scholar
  25. 25.
    Potse, M., B. Dub, J. Richer, A. Vinet, and R. M. Gulrajani. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 53(12 Pt 1):2425–2435, 2006.PubMedCrossRefGoogle Scholar
  26. 26.
    Reddy, J. N. An Introduction to the Finite Element Method, 3rd ed. New York: McGraw-Hill, 766 pp., 2006.Google Scholar
  27. 27.
    Rijcken, J., P. H. Bovendeerd, A. J. Schoofs, D. H. van Campen, and T. Arts. Optimization of cardiac fiber orientation for homogeneous fiber strain during ejection. Ann. Biomed. Eng. 27(3):289–297, 1999.PubMedCrossRefGoogle Scholar
  28. 28.
    Roberts, D. E., L. T. Hersh, and A. M. Scher. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ. Res. 44(5):701–712, 1979.PubMedCrossRefGoogle Scholar
  29. 29.
    Rohmer, D., A. Sitek, and G. T. Gullberg. Reconstruction and visualization of fiber and laminar structure in the normal human heart from ex vivo diffusion tensor magnetic resonance imaging (DTMRI) data. Invest. Radiol. 42(11):777–789, 2007.PubMedCrossRefGoogle Scholar
  30. 30.
    Scollan, D. F., A. Holmes, R. Winslow, and J. Forder. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am. J. Physiol. 275(6 Pt 2):H2308–H2318, 1998.PubMedGoogle Scholar
  31. 31.
    Scollan, D. F., A. Holmes, J. Zhang, and R. L. Winslow. Reconstruction of cardiac ventricular geometry and fiber orientation using magnetic resonance imaging. Ann. Biomed. Eng. 28(8):934–944, 2000.PubMedCrossRefGoogle Scholar
  32. 32.
    Streeter, D. D., H. M. Spotnitz, D. P. Patel, J. Ross, and E. H. Sonnenblick. Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24(3):339–347, 1969.PubMedCrossRefGoogle Scholar
  33. 33.
    Trayanova, N. A. Whole-heart modeling: applications to cardiac electrophysiology and electromechanics. Circ. Res. 108(1):113–128, 2011.PubMedCrossRefGoogle Scholar
  34. 34.
    Vadakkumpadan, F., H. Arevalo, A. J. Prassl, J. Chen, F. Kickinger, P. Kohl, G. Plank, and N. Trayanova. Image-based models of cardiac structure in health and disease. Wiley Interdiscip. Rev. Syst. Biol. Med. 2(4):489–506, 2010.PubMedCrossRefGoogle Scholar
  35. 35.
    Vendelin, M., P. H. Bovendeerd, J. Engelbrecht, and T. Arts. Optimizing ventricular fibers: uniform strain or stress, but not ATP consumption, leads to high efficiency. Am. J. Physiol. Heart Circ. Physiol. 283(3):H1072–H1081, 2002.PubMedGoogle Scholar
  36. 36.
    Vetter, F. J., S. B. Simons, S. Mironov, C. J. Hyatt, and A. M. Pertsov. Epicardial fiber organization in swine right ventricle and its impact on propagation. Circ. Res. 96(2):244–251, 2005.PubMedCrossRefGoogle Scholar
  37. 37.
    Vigmond, E. J., R. Weber dos Santos, A. J. Prassl, M. Deo, and G. Plank. Solvers for the cardiac bidomain equations. Prog. Biophys. Mol. Biol. 96(1–3):3–18, 2008.PubMedCrossRefGoogle Scholar
  38. 38.
    Weiss, D. L., G. Seemann, D. U. J. Keller, D. Farina, F. B. Sachse, and O. Dossel. Modeling of heterogeneous electrophysiology in the human heart with respect to ECG genesis. In Proceedings of Computers in Cardiology, pp. 49–52, 2007.Google Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • J. D. Bayer
    • 1
    Email author
  • R. C. Blake
    • 1
  • G. Plank
    • 2
  • N. A. Trayanova
    • 1
  1. 1.Department of Biomedical Engineering and Institute for Computational MedicineThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Institute of Biophysics and Center for Physiological MedicineMedical University of GrazGrazAustria

Personalised recommendations