Table of Contents Author Guidelines Submit a Manuscript
International Journal of Biomedical Imaging
Volume 2006, Article ID 45957, 15 pages
http://dx.doi.org/10.1155/IJBI/2006/45957

Anisotropic Elastography for Local Passive Properties and Active Contractility of Myocardium from Dynamic Heart Imaging Sequence

Yi Liu,1,2 Ge Wang,1 and L. Z. Sun3

1Center for X-Ray and Optical Tomography, Department of Radiology, The University of Iowa Hospitals and Clinics, Iowa City, IA 52242, USA
2Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46204, USA
3Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697, USA

Received 26 June 2006; Accepted 19 September 2006

Academic Editor: Seung Wook Lee

Copyright © 2006 Yi Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. American Heart Association, “2004, Heart disease and Stroke Stastistics-2004 update,” Dallas, Texas.
  2. S. Sasayama, H. Nonogi, S. Miyazaki et al., “Changes in diastolic properties of the regional myocardium during pacing-induced ischemia in human subjects,” Journal of the American College of Cardiology, vol. 5, no. 3, pp. 599–606, 1985. View at Google Scholar
  3. M. S. Visner, C. E. Arentzen, D. G. Parrish et al., “Effects of global ischemia on the diastolic properties of the left ventricle in the conscious dog,” Circulation, vol. 71, no. 3, pp. 610–619, 1985. View at Google Scholar
  4. D. D. McPherson, D. J. Skorton, S. Kodiyalam et al., “Finite element analysis of myocardial diastolic function using three-dimensional echocardiographic reconstructions: application of a new method for study of acute ischemia in dogs,” Circulation Research, vol. 60, no. 5, pp. 674–682, 1987. View at Google Scholar
  5. D. K. Bogen, A. Needleman, and T. A. McMahon, “An analysis of myocardial infarction. The effect of regional changes in contractility,” Circulation Research, vol. 55, no. 6, pp. 805–815, 1984. View at Google Scholar
  6. R. A. Leyton, “Cardiac ultrastructure and function in the normal and failing heart,” in Cardiac Mechanics: Physiological, Clinical, and Mathematical Considerations, I. Mirsky, D. N. Ghista, and H. Sandler, Eds., pp. 11–65, John Wiley & Sons, New York, NY, USA, 1974. View at Google Scholar
  7. L. K. Waldman, Y. C. Fung, and J. W. Covell, “Transmural myocardial deformation in the canine left ventricle: normal in vivo three-dimensional finite strains,” Circulation Research, vol. 57, no. 1, pp. 152–163, 1985. View at Google Scholar
  8. J. M. Guccione, K. D. Costa, and A. D. McCulloch, “Finite element stress analysis of left ventricular mechanics in the beating dog heart,” Journal of Biomechanics, vol. 28, no. 10, pp. 1167–1177, 1995. View at Publisher · View at Google Scholar
  9. M. Nash, Mechanics and material properties of the heart using an anatomically accurate mathematical model, M.S. thesis, University of Auckland, Auckland, New Zealand, 1998.
  10. J. D. Humphrey, “Continuum biomechanics of soft biological tissues,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 459, no. 2029, pp. 3–46, 2003. View at Publisher · View at Google Scholar
  11. P. J. Hunter, A. D. McCulloch, and H. E. D. J. ter Keurs, “Modelling the mechanical properties of cardiac muscle,” Progress in Biophysics and Molecular Biology, vol. 69, no. 2-3, pp. 289–331, 1998. View at Publisher · View at Google Scholar
  12. T. P. Usyk, R. Mazhari, and A. D. McCulloch, “Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle,” Journal of Elasticity, vol. 61, no. 1–3, pp. 143–164, 2000. View at Publisher · View at Google Scholar
  13. K. D. Costa, J. W. Holmes, and A. D. McCulloch, “Modelling cardiac mechanical properties in three dimensions,” Philosophical Transactions of the Royal Society of London A, vol. 359, no. 1783, pp. 1233–1250, 2001. View at Publisher · View at Google Scholar
  14. J. C. Criscione, A. D. McCulloch, and W. C. Hunter, “Constitutive framework optimized for myocardium and other high-strain, laminar materials with one fiber family,” Journal of the Mechanics and Physics of Solids, vol. 50, no. 8, pp. 1681–1702, 2002. View at Publisher · View at Google Scholar
  15. S. J. Sarnoff, E. Braunwald, G. H. Welch Jr., R. B. Case, W. N. Stainsby, and R. Macruz, “Hemodynamic determinants of oxygen consumption of the heart with special reference to the tension-time index,” The American Journal of Physiology, vol. 192, no. 1, pp. 148–156, 1958. View at Google Scholar
  16. K.-M. Jan, “Distribution of myocardial stress and its influence on coronary blood flow,” Journal of Biomechanics, vol. 18, no. 11, pp. 815–820, 1985. View at Publisher · View at Google Scholar
  17. Y. C. Fung, Biomechanics: Motion, Flow, Stress and Growth, Springer, New York, NY, USA, 1990.
  18. A. D. McCulloch, L. K. Waldman, J. Rogers, and J. M. Guccione, “Large-scale finite element analysis of the beating heart,” Critical Reviews in Biomedical Engineering, vol. 20, no. 5-6, pp. 427–449, 1992. View at Google Scholar
  19. Y. Lanir, “A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues,” Journal of Biomechanics, vol. 12, no. 6, pp. 423–436, 1979. View at Publisher · View at Google Scholar
  20. L. L. Demer and F. C. P. Yin, “Passive biaxial mechanical properties of isolated canine myocardium,” The Journal of Physiology, vol. 339, no. 1, pp. 615–630, 1983. View at Google Scholar
  21. J. D. Humphrey and F. C. P. Yin, “On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy function,” Journal of Biomechanical Engineering, vol. 109, no. 4, pp. 298–304, 1987. View at Google Scholar
  22. A. J. Shacklock, Biaxial testing of cardiac tissues, M.S. thesis, University of Auckland, Auckland, New Zealand, 1987.
  23. F. C. P. Yin, R. K. Strumpf, P. H. Chew, and S. L. Zeger, “Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading,” Journal of Biomechanics, vol. 20, no. 6, pp. 577–589, 1987. View at Publisher · View at Google Scholar
  24. P. M. F. Nielsen, P. J. Hunter, and B. H. Smaill, “Biaxial testing of membrane biomaterials: testing equipment and procedures,” Journal of Biomechanical Engineering, vol. 113, no. 3, pp. 295–300, 1991. View at Google Scholar
  25. V. P. Novak, F. C. P. Yin, and J. D. Humphrey, “Regional mechanical properties of passive myocardium,” Journal of Biomechanics, vol. 27, no. 4, pp. 403–412, 1994. View at Publisher · View at Google Scholar
  26. C. A. Phillips and J. S. Petrofsky, “Myocardial material mechanics: characteristic variation of the circumferential and longitudinal systolic moduli in left ventricular dysfunction,” Journal of Biomechanics, vol. 17, no. 8, pp. 561–568, 1984. View at Publisher · View at Google Scholar
  27. J. H. Omens, D. A. Mackenna, and A. D. McCulloch, “Measurement of strain and analysis of stress in resting rat left ventricular myocardium,” Journal of Biomechanics, vol. 26, no. 6, pp. 665–676, 1993. View at Publisher · View at Google Scholar
  28. G. J. Han, K. B. Chandran, N. L. Gotteiner et al., “Application of finite-element analysis with optimisation to assess the in vivo non-linear myocardial material properties using echocardiographic imaging,” Medical and Biological Engineering and Computing, vol. 31, no. 5, pp. 459–467, 1993. View at Publisher · View at Google Scholar
  29. L. L. Creswell, M. J. Moulton, S. G. Wyers et al., “An experimental method for evaluating constitutive models of myocardium in in vivo hearts,” American Journal of Physiology, Heart and Circulatory Physiology, vol. 267, no. 2, part 2, pp. H853–H863, 1994. View at Google Scholar
  30. M. J. Moulton, L. L. Creswell, R. L. Actis et al., “An inverse approach to determining myocardial material properties,” Journal of Biomechanics, vol. 28, no. 8, pp. 935–948, 1995. View at Publisher · View at Google Scholar
  31. N. L. Gotteiner, G. Han, K. B. Chandran et al., “In vivo assessment of nonlinear myocardial deformation using finite element analysis and three-dimensional echocardiographic reconstruction,” American Journal of Cardiac Imaging, vol. 9, no. 3, pp. 185–194, 1995. View at Google Scholar
  32. E. L. Dove, K. P. Phillip, D. D. McPherson, and K. B. Chandran, “Quantitative shape description of left-ventricular cine-CT image,” IEEE Transactions on Biomedical Engineering, vol. 38, no. 12, pp. 1256–1261, 1991. View at Publisher · View at Google Scholar
  33. J. Duncan, P. Shi, T. Constable, and A. Sinusas, “Physical and geometrical modeling for image-based recovery of left ventricular deformation,” Progress in Biophysics and Molecular Biology, vol. 69, no. 2-3, pp. 333–351, 1998. View at Publisher · View at Google Scholar
  34. W.-t. Lin and R. A. Robb, “Visualization of cardiac dynamics using physics-based deformable model,” in Medical Imaging 2000: Image Display and Visualization, vol. 3976 of Proceedings of SPIE, pp. 210–217, San Diego, Calif, USA, February 2000. View at Publisher · View at Google Scholar
  35. C. D. Eusemann, E. L. Ritman, M. E. Bellemann, and R. A. Robb, “Parametric display of myocardial function,” Computerized Medical Imaging and Graphics, vol. 25, no. 6, pp. 483–493, 2001. View at Publisher · View at Google Scholar
  36. I. J. LeGrice, P. J. Hunter, and B. H. Smaill, “Laminar structure of the heart: a mathematical model,” American Journal of Physiology, Heart and Circulatory Physiology, vol. 272, no. 5, pp. H2466–H2476, 1997. View at Google Scholar
  37. E. A. Zamir, S. Sheth, J. M. Guccione, K. D. Costa, and L. A. Taber, “A remodeling algorithm for development of transmural cardiac fiber angle distribution,” in Proceedings of ASME Summer Bioengineering Conference, Big Sky, Mont, USA, June 1999.
  38. D. F. Scollan, A. Holmes, J. Zhang, and R. L. Winslow, “Reconstruction of cardiac ventricular geometry and fiber orientation using magnetic resonance imaging,” Annals of Biomedical Engineering, vol. 28, no. 8, pp. 934–944, 2000. View at Publisher · View at Google Scholar
  39. H. Kanai, S.-I. Katsumata, H. Honda, and Y. Koiwa, “Measurement and analysis of vibration in the myocardium telescopic motion for novel echo-graphic diagnosis,” Acoustical Science and Technology, vol. 24, no. 1, pp. 17–22, 2003. View at Publisher · View at Google Scholar
  40. J. B. Weaver, E. E. W. Van Houten, M. I. Miga, F. E. Kennedy, and K. D. Paulsen, “Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion,” Medical Physics, vol. 28, no. 8, pp. 1620–1628, 2001. View at Publisher · View at Google Scholar
  41. G. I. N. Rozvany, M. P. Bendsøe, and U. Kirsh, “Layout optimization of structures,” Applied Mechanics Reviews, vol. 48, pp. 41–119, 1995. View at Google Scholar
  42. N. Tardieu and A. Constantinescu, “On the determination of elastic coefficients from indentation experiments,” Inverse Problems, vol. 16, no. 3, pp. 577–588, 2000. View at Publisher · View at Google Scholar
  43. A. A. Oberai, N. H. Gokhale, and G. R. Feijóo, “Solution of inverse problems in elasticity imaging using the adjoint method,” Inverse Problems, vol. 19, no. 2, pp. 297–313, 2003. View at Publisher · View at Google Scholar
  44. Y. Liu, L. Z. Sun, and G. Wang, “Tomography-based 3-D anisotropic elastography using boundary measurements,” IEEE Transactions on Medical Imaging, vol. 24, no. 10, pp. 1323–1333, 2005. View at Publisher · View at Google Scholar
  45. A. A. Oberai, N. H. Gokhale, M. M. Doyley, and J. C. Bamber, “Evaluation of the adjoint equation based algorithm for elasticity imaging,” Physics in Medicine and Biology, vol. 49, no. 13, pp. 2955–2974, 2004. View at Publisher · View at Google Scholar
  46. D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming, vol. 45, no. 1–3, pp. 503–528, 1989. View at Publisher · View at Google Scholar
  47. M. G. Khan, Encyclopedia of Heart Diseases, Academic Press, New York, NY, USA, 2005.
  48. K. D. Costa, Y. Takayama, A. D. McCulloch, and J. W. Covell, “Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium,” American Journal of Physiology, Heart and Circulatory Physiology, vol. 276, no. 2, part 2, pp. H595–H607, 1999. View at Google Scholar
  49. J. M. Guccione and A. D. McCulloch, “Mechanics of active contraction in cardiac muscle: part I—constitutive relations for fiber stress that describe deactivation,” Journal of Biomechanical Engineering, vol. 115, no. 1, pp. 72–81, 1993. View at Google Scholar
  50. J. M. Guccione, L. K. Waldman, and A. D. McCulloch, “Mechanics of active contraction in cardiac muscle: part II—cylindrical models of the systolic left ventricle,” Journal of Biomechanical Engineering, vol. 115, no. 1, pp. 82–90, 1993. View at Google Scholar
  51. G. I. Zahalak, “Non-axial muscle stress and stiffness,” Journal of Theoretical Biology, vol. 182, no. 1, pp. 59–84, 1996. View at Publisher · View at Google Scholar
  52. G. I. Zahalak, V. De Laborderie, and J. M. Guccione, “The effects of cross-fiber deformation on axial fiber stress in myocardium,” Journal of Biomechanical Engineering, vol. 121, no. 4, pp. 376–385, 1999. View at Google Scholar
  53. A. Rachev and K. Hayashi, “Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries,” Annals of Biomedical Engineering, vol. 27, no. 4, pp. 459–468, 1999. View at Publisher · View at Google Scholar
  54. I. Mirsky, D. N. Ghista, and H. Sandler, Cardiac Mechanics: Physiological, Clinical, and Mathematical Considerations, John Wiley & Sons, New York, NY, USA, 1974.
  55. R. Mazhari and A. D. McCulloch, “Integrative models for understanding the structural basis of regional mechanical dysfunction in ischemic myocardium,” Annals of Biomedical Engineering, vol. 28, no. 8, pp. 979–990, 2000. View at Publisher · View at Google Scholar
  56. J. M. Tyszka, D. H. Laidlaw, J. W. Asa, and J. M. Silverman, “Three-dimensional, time-resolved (4D) relative pressure mapping using magnetic resonance imaging,” Journal of Magnetic Resonance Imaging, vol. 12, no. 2, pp. 321–329, 2000. View at Publisher · View at Google Scholar
  57. O. P. Faris, F. J. Evans, D. B. Ennis et al., “A novel technique for cardiac electromechanical mapping with magnetic resonance imaging tagging and an epicardial electrode sock,” Annals of Biomedical Engineering, vol. 31, no. 4, pp. 430–440, 2003. View at Publisher · View at Google Scholar
  58. D. B. Ennis, F. H. Epstein, P. Kellman, L. Fananapazir, E. R. McVeigh, and A. E. Arai, “Assessment of regional systolic and diastolic dysfunction in familial hypertrophic cardiomyopathy using MR tagging,” Magnetic Resonance in Medicine, vol. 50, no. 3, pp. 638–642, 2003. View at Publisher · View at Google Scholar
  59. D. D. Streeter Jr. and W. T. Hanna, “Engineering mechanics for successive states in canine left ventricular myocardium. I. Cavity and wall geometry,” Circulation Research, vol. 33, no. 6, pp. 639–655, 1973. View at Google Scholar
  60. D. D. Streeter Jr. and W. T. Hanna, “Engineering mechanics for successive states in canine left ventricular myocardium. II. Fiber angles and sarcomere length,” Circulation Research, vol. 33, no. 6, pp. 656–664, 1973. View at Google Scholar
  61. P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, and P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” American Journal of Physiology, Heart and Circulatory Physiology, vol. 260, no. 4, part 2, pp. H1365–H1378, 1991. View at Google Scholar