Field-Based Parameterisation of Cardiac Muscle Structure from Diffusion Tensors

  • Bianca Freytag
  • Vicky Y. WangEmail author
  • G. Richard Christie
  • Alexander J. Wilson
  • Gregory B. Sands
  • Ian J. LeGrice
  • Alistair A. Young
  • Martyn P. Nash
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9126)


This paper presents a robust method to directly construct parametric representations of myocardial structure using a left ventricular (LV) finite element model customised to diffusion tensors derived from cardiac diffusion tensor magnetic resonance images (DTMRI). This method avoids the need to solve the eigenvector problem, and therefore avoids issues due to ambiguous eigenvector directions, and the non-uniqueness of eigenvectors in regions of isotropic diffusion. Finite element parameters describing the fibre orientations of a geometric model of the LV are directly fitted to diffusion tensors using non-linear least squares optimisation. The method was tested using ex vivo DTMRI data from a Wistar-Kyoto rat and compared against the conventional eigenvector analysis. Close agreement was found in most regions, except at some boundary locations, and in regions with low fractional anisotropy.


Model-based parameterisation Myocardial fibre orientation Diffusion tensor magnetic resonance imaging 


  1. 1.
    Sermesant, M., Chabiniok, R., Chinchapatnam, P., Mansi, T., Billet, F., Moireau, P., Peyrat, J.M., Wong, K., Relan, J., Rhode, K., et al.: Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation. Med. Image Anal. 16(1), 201–215 (2012)CrossRefGoogle Scholar
  2. 2.
    Sermesant, M., Delingette, H., Ayache, N.: An electromechanical model of the heart for image analysis and simulation. IEEE Trans. Med. Imaging 25(5), 612–625 (2006)CrossRefGoogle Scholar
  3. 3.
    Vadakkumpadan, F., Gurev, V., Constantino, J., Arevalo, H., Trayanova, N.: Modeling of whole-heart electrophysiology and mechanics: toward patient-specific simulations. In: Kerckhoffs, R.C. (ed.) Patient-Specific Modeling of the Cardiovascular System, pp. 145–165. Springer, New York (2010)CrossRefGoogle Scholar
  4. 4.
    Krishnamurthy, A., Villongco, C.T., Chuang, J., Frank, L.R., Nigam, V., Belezzuoli, E., Stark, P., Krummen, D.E., Narayan, S., Omens, J.H., et al.: Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244, 4–21 (2013)CrossRefGoogle Scholar
  5. 5.
    Walker, J.C., Ratcliffe, M.B., Zhang, P., Wallace, A.W., Hsu, E.W., Saloner, D.A., Guccione, J.M.: Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J. Thorac. Cardiovasc. Surg. 135(5), 1094–1102 (2008)CrossRefGoogle Scholar
  6. 6.
    Wang, V.Y., Lam, H., Ennis, D.B., Cowan, B.R., Young, A.A., Nash, M.P.: Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Med. Image Anal. 13(5), 773–784 (2009)CrossRefGoogle Scholar
  7. 7.
    Xi, J., Lamata, P., Niederer, S., Land, S., Shi, W., Zhuang, X., Ourselin, S., Duckett, S.G., Shetty, A.K., Rinaldi, C.A., et al.: The estimation of patient-specific cardiac diastolic functions from clinical measurements. Med. Image Anal. 17(2), 133–146 (2013)CrossRefGoogle Scholar
  8. 8.
    Niederer, S.A., Smith, N.P.: The role of the frank-starling law in the transduction of cellular work to whole organ pump function: a computational modeling analysis. PLoS Comput. Biol. 5(4), e1000371 (2009)CrossRefGoogle Scholar
  9. 9.
    Wang, V.Y., Ennis, D.B., Cowan, B.R., Young, A.A., Nash, M.P.: Myocardial contractility and regional work throughout the cardiac cycle using FEM and MRI. In: Camara, O., Konukoglu, E., Pop, M., Rhode, K., Sermesant, M., Young, A. (eds.) STACOM 2011. LNCS, vol. 7085, pp. 149–159. Springer, Heidelberg (2012) Google Scholar
  10. 10.
    Basser, P.J., Mattiello, J., LeBihan, D.: Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. Ser. B 103(3), 247–254 (1994)CrossRefGoogle Scholar
  11. 11.
    Hsu, E., Muzikant, A., Matulevicius, S., Penland, R., Henriquez, C.: Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am. J. Physiol. Heart Circ. Physiol. 274(5), H1627–H1634 (1998)Google Scholar
  12. 12.
    Scollan, D.F., Holmes, A., Winslow, R., Forder, J.: Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am. J. Physiol. Heart Circ. Physiol. 275(6), H2308–H2318 (1998)Google Scholar
  13. 13.
    Lekadir, K., Hoogendoorn, C., Pereanez, M., Albà, X., Pashaei, A., Frangi, A.F.: Statistical personalization of ventricular fiber orientation using shape predictors. IEEE Trans. Med. Imaging 33(4), 882–890 (2014)CrossRefGoogle Scholar
  14. 14.
    Toussaint, N., Stoeck, C.T., Schaeffter, T., Kozerke, S., Sermesant, M., Batchelor, P.G.: In vivo human cardiac fibre architecture estimation using shape-based diffusion tensor processing. Med. Image Anal. 17(8), 1243–1255 (2013)CrossRefGoogle Scholar
  15. 15.
    Jones, D.K., Pierpaoli, C.: Confidence mapping in diffusion tensor magnetic resonance imaging tractography using a bootstrap approach. Magn. Reson. Med. 53(5), 1143–1149 (2005)CrossRefGoogle Scholar
  16. 16.
    Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., Benali, H.: Accurate anisotropic fast marching for diffusion-based geodesic tractography. J. Biomed. Imaging 2008, 2 (2008)Google Scholar
  17. 17.
    Bayer, J., Blake, R., Plank, G., Trayanova, N.: A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann. Biomed. Eng. 40(10), 2243–2254 (2012)CrossRefGoogle Scholar
  18. 18.
    Streeter, D.D., Spotnitz, H.M., Patel, D.P., Ross, J., Sonnenblick, E.H.: Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24(3), 339–347 (1969)CrossRefGoogle Scholar
  19. 19.
    Vadakkumpadan, F., Arevalo, H., Prassl, A.J., Chen, J., Kickinger, F., Kohl, P., Plank, G., Trayanova, N.: Image-based models of cardiac structure in health and disease. Wiley Interdisc. Rev. Syst. Biol. Med. 2(4), 489–506 (2010)CrossRefGoogle Scholar
  20. 20.
    Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. 111, 209–219 (1996)CrossRefGoogle Scholar
  21. 21.
    Farrell, J.A., Landman, B.A., Jones, C.K., Smith, S.A., Prince, J.L., van Zijl, P., Mori, S.: Effects of signal-to-noise ratio on the accuracy and reproducibility of diffusion tensor imaging-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5 t. J. Magn. Reson. Imaging 26(3), 756–767 (2007)CrossRefGoogle Scholar
  22. 22.
    Fomovsky, G.M., Rouillard, A.D., Holmes, J.W.: Regional mechanics determine collagen fiber structure in healing myocardial infarcts. J. Mol. Cell. Cardiol. 52(5), 1083–1090 (2012)CrossRefGoogle Scholar
  23. 23.
    LeGrice, I.J., Hunter, P.J., Smaill, B.: Laminar structure of the heart: a mathematical model. Am. J. Physiol. Heart Circ. Physiol. 272, H2466–H2476 (1997)Google Scholar
  24. 24.
    Christie, G., Bullivant, D., Blackett, S., Hunter, P.J.: Modelling and visualising the heart. Comput. Vis. Sci. 4(4), 227–235 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    Bradley, C., Bowery, A., Britten, R., Budelmann, V., Camara, O., Christie, R., Cookson, A., Frangi, A., Gamage, T., Heidlauf, T., Krittian, S., Ladd, D., Little, C., Mithraratne, K., Nash, M., Nickerson, D., Nielsen, P., Nordbø, T., Omholt, S., Pashaei, A., Paterson, D., Rajagopal, V., Reeve, A., Röhrle, O., Safaei, S., Sebastián, R., Steghfer, M., Wu, T., Yu, T., Zhang, H., Hunter, P.: OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project. Prog. Biophys. Mol. Biol. 107(1), 32–47 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Bianca Freytag
    • 1
  • Vicky Y. Wang
    • 1
    Email author
  • G. Richard Christie
    • 1
  • Alexander J. Wilson
    • 1
    • 2
  • Gregory B. Sands
    • 1
    • 2
  • Ian J. LeGrice
    • 1
    • 2
  • Alistair A. Young
    • 1
    • 3
  • Martyn P. Nash
    • 1
    • 4
  1. 1.Auckland Bioengineering InstituteUniversity of AucklandAucklandNew Zealand
  2. 2.Department of PhysiologyUniversity of AucklandAucklandNew Zealand
  3. 3.Department of Anatomy with RadiologyUniversity of AucklandAucklandNew Zealand
  4. 4.Department of Engineering ScienceUniversity of AucklandAucklandNew Zealand

Personalised recommendations