Efficient cardiac diffusion tensor MRI by three-dimensional reconstruction of solenoidal tensor fields

Magnetic Resonance Imaging

Volumn 19, Issue 2, 2001, Pages 233-256

  Gullberg, Grant T ^a,b   Defrise, Michel ^a   Panin, Vladimir Y ^b   Zeng, Gengsheng L ^b  

^a UNIVERSITY HOSPITAL BRUSSELS   (Belgium)

^b UNIVERSITY OF UTAH SCHOOL OF MEDICINE   (United States)

Author keywords

Computed tomography; Diffusion; Tensor

Indexed keywords

ARTICLE; HEART SCINTISCANNING; IMAGE ANALYSIS; IMAGE QUALITY; MATHEMATICAL MODEL; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; THEORY; THREE DIMENSIONAL IMAGING;

COMPUTER SIMULATION; DIFFUSION; FOURIER ANALYSIS; HUMANS; IMAGE ENHANCEMENT; IMAGE PROCESSING, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MAGNETIC RESONANCE IMAGING; MYOCARDIAL CONTRACTION; MYOCARDIUM; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 0034996633     PISSN: 0730725X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0730-725X(01)00232-6     Document Type: Article

References (87)

1. Pierpaoli C, Jezzard P, Barnett PJ, et al. Diffusion tensor MR imaging of the human brain. Radiol 1999;201:637-48.
2. Edelman RR, Gaa J, Wedeen VJ, Loh E, Hare JM, Prasad P, Li W. In vivo measurement of water diffusion in the human heart. Magn Reson Med 1994;32:423-8.
3. Reese TG, Weisskoff RM, Smith RN, Rosen BR, Dinsmore RE, Wedeen VJ. Imaging myocardial fiber architecture in vivo with magnetic resonance. Magn Reson Med 1995;34:786-91.
4. Reese TG, Wedeen VJ, Weisskoff RM. Measuring diffusion in the presence of material strain. J Magn Reson B 1996;112:253-8.
5. Tseng WY, Reese TG, Weisskoff RM, Wedeen VJ. Cardiac diffusion tensor MRI in vivo without strain correction. Magn Reson Med 1999;42:393-403.
6. Wedeen VJ. Magnetic resonance imaging of myocardial kinematics. Technique to detect, localize, and quantify the strain rates of the active human myocardium. J Magn Reson Imag 1992;2:575-82.
7. Wedeen VJ, Weisskoff RM, Reese TG, Beache GM, Poncelet BP, Rosen BR, Dinsmore RE. Motionless movies of myocardial strain rates using stimulated echoes. Magn Reson Med 1995;33:401-8.
8. Robson MD, Constable RT. Three-dimensional strain-rate imaging. Magn Reson Med 1996;36:537-46.
9. Guccione JM, McCulloch AD, Waldman LK. Passive material properties of intact ventricular myocardium determined from a cylindrical model. Trans of the ASME 1991;113:42-55.
10. Guccione JM, McCulloch AD. Mechanics of active contraction in cardiac muscle: Part I - Constitutive relations for fiber stress that describe deactivation. Trans of the ASME 1993;115:72-81.
11. Guccione JM, Waldman LK, McCulloch AD. Mechanics of active contraction in cardiac muscle: Part II-Cylindrical models of the systolic left ventricle. Trans of the ASME 1993;115:82-90.
12. Costa KD, Hunter PJ, Rogers JM, Guccione JM, Waldman LK, McCulloch AD. A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I - Cylindrical and spherical polar coordinates. Trans of the ASME 1996;118:452-63.
13. Costa KD, Hunter PJ, Rogers JM, Guccione JM, Waldman LK, McCulloch AD. A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II-Prolate spheroidal coordinates. Trans of the ASME 1996;118:464-72.
14. Gullberg GT, Sitek A, Di Bella EVR, Feng B, Christian PE, Adams WD. Mechanical modeling of the myocardium using gated SPECT. J Nucl Cardiol 1999;6:S116.
15. Tuch DS, Wedeen VJ, Dale AM, Belliveau JW. Electrical conductivity tensor map of the human brain using NMR diffusion imaging: An effective medium approach. Proceedings of the International Society for Magnetic Resonance in Medicine-Sixth Scientific Meeting and Exhibition, Berkeley, CA. ISMRM 1998;1:527.
16. Gmitro AF, Alexander AL. Use of a projection reconstruction method to decrease motion sensitivity in diffusion-weighted MRI. Magn Reson Med 1993;9:835-8.
17. Mattiello J, Basser PJ, LeBihan D. Analytical expressions for the b matrix in NMR diffusion tensor imaging and spectroscopy. J Magn Reson A 1994;108:131-41.
18. Mattiello J, Basser PJ, LeBihan D. The b matrix in diffusion tensor echo-planar imaging. Magn Reson Med 1997;37(2):292-300.
19. Gullberg GT, Ghosh Roy D, Zeng GL, Alexander AL, Parker DL. Tensor tomography. IEEE Trans on Nucl Sci 1999;46:991-1000.
20. Prince JL. Convolution backprojection formulas for 3-D vector tomography with application to MRI. IEEE Trans on Image Processing 1996;5:1462-72.
21. Johnson SA, Greenleaf JE, Tanaka M, Flandro G. Reconstructing three-dimensional fluid velocity vector fields from acoustic transmission measurements. In: Kesler L, editor. Acoustical Holography, Vol. 7. New York: Plenum, 1977. p. 307-26.
22. Arfken G. Mathematical methods for physicists. San Diego: Academic Press, Inc., 1985.
23. Takuso S, et al. Introduction of mass conservation law to improve the tomographic estimation of flow velocity distribution from differential time-of-flight data. J Acoust Soc Amer 1985;77:2104-6.
24. Munk W, Wunsch C. Ocean acoustic tomography: A scheme for large-scale monitoring. Deep Sea Research 1979;26A:123-61.
25. Howe BM, Worchester PF, Munk W. Ocean acoustic tomography: Mesoscale velocity. J Geophys Res 1987;92:3785-805.
26. Norton SJ. Tomographic reconstruction of 2-D vector fields: Application to flow imaging. Geophys J 1988;97:161-8.
27. Norton SJ. Unique tomographic reconstruction of vector fields using boundary data. IEEE Trans on Image Processing 1992;1:406-12.
28. Kramer DM, Lauterbur PC. On the problem of reconstructing images of nonscalar parameters from projections: Application to vector fields. IEEE Trans on Nucl Sci 1979;NS-26:2674-7.
29. Winters KB, Rouseff D. A filtered backprojection method for the tomographic reconstruction of fluid vorticity. Inverse Problems 1990;6:L33-8.
30. Winters KB, Rouseff D. Tomographic reconstruction of stratified fluid flow. IEEE Trans on Ultrasonics Ferroelectrics and Frequency Control 1993;40:26-33.
31. Rouseff D, Winters KB, Ewart TE. Reconstruction of oceanic microstructure by tomography: A numerical feasibility study. J Geophys Res 1991;96:8823-33.
32. Braun H, Hauck A. Tomographic reconstruction of vector fields. IEEE Trans on Signal Process 1991;39:464-71.
33. Osman NF, Prince JL. 3D vector tomography on bounded domains. Inv Prob 1998;14:185-96.
34. Faris GW, Byer RL. Three-dimensional beam-deflection optical tomography of a supersonic jet. Appl Opt 1988;27:5202-12.
35. Zahn M. Transform relationship between Kerr-effect optical phase shift and non-uniform electrical field distributions. Trans on Diel Elect Insul 1994;1:235-46.
36. Andrienko YA, Duboikov MS, Gladun AD. Optical tensor field tomography: The Kerr effect and axisymmetric integrated photoelasticity. J Opt Soc Am A 1992;9:1765-8.
37. Sharafutdinov VA. Tomographic method in optics. In: Proceedings of SPIE: Tomographic Methods in Optics, 1991.
38. Aben H. Integrated photoelasticity. New York: McGraw-Hill, Inc., 1979.
39. Aben H, Puro A. Photoelastic tomography for three-dimensional flow birefringence studies. Inv Prob 1995;13:215-21.
40. Schwarz A. Three-dimensional reconstruction of temperature and velocity fields in a furnace. In: Proceeding of ECAPT, The European Concerted Action on Process Tomography, 1994:227-33.
41. Efremov N, Pamentov N, Kharachenko V. Tomography of ion and atom velocities in plasmas. J Quant Spectrosc Radiat Trans 1995;6:723-8.
42. Juhlin P. Doppler tomography. In: Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1993.
43. Juhlin P. Principles of Doppler Tomography. Lund, Sweden: Technical Report, Department of Mathematics, Lund Institute of Technology, 1992.
44. Strahlen K. Some integral transforms of vector fields. Lund, Sweden: Licentiate Thesis, Department of Mathematics, Lund Institute of Technology, 1996.
45. Sparr G, Strahlen K, Lindstrom K, Persson HW. Doppler tomography for vector fields. Inv Prob 1995;11:1051-61.
46. Denisov AM, Popov AA, Sterlyadkin VV. Doppler tomography problem for a two-dimensional vector field. Moscow University Computational Mathematics and Cybernetics 1995;1:17-20.
47. Desbat L, Wernsdorfer A. Direct algebraic reconstruction and optimal sampling in vector field tomography. IEEE Trans on Signal Processing 1995;43:1798-808.
48. Desbat L. Efficient parallel sampling in vector field tomography. Inv Prob 1995;11:995-1003.
49. Sparr G, Vertgeim L, Strahlen K. Vector field tomography, an overview. Dept of Mathematics Report, Lund University, ISRN LUTFD2/TFMA-97/7007-SE. To appear in Inverse Problems.
50. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: National Academy Press, 1996.
51. Sharafutdinov VA. Integral geometry of tensor fields. Utrecht: VSP, 1994.
52. Kay DC. Tensor calculus - Schaum's outline series in mathematics. New York: McGraw-Hill Book Company, 1988.
53. Spain B. Tensor calculus. Oliver and Boyd, Edinburgh and London, New York: Interscience Publishers, Inc. 1956.
54. McConnell AJ. Applications of tensor analysis. New York: Dover Publications, Inc., 1957.
55. Tyldesley JR. An introduction to tensor analysis for engineers and applied scientists. London: Longman Group Limited, 1975.
56. Panin VY, Zeng GL, Gullberg GT. Iterative approach in tensor tomography. In: 2000 IEEE Nuclear Science Symposium and Medical Imaging Conference Record, (in press).
57. Chiu M-Y, Barrett HH, Simpson RG. Three-dimensional reconstruction from planar projections. J Opt Soc Am 1980;70:755-62.
58. Streeter DD, Bassett DL. An engineering analysis of myocardial fiber orientation in a pig's left ventricle in systole. Anat Rec 1966;155:503-11.
59. Streeter DD, Spotnitz HM, Patel P, Ross J, Sonnenblick EH. Fiber orientation in the canine left ventricle during systole and diastole. Circ Res 1969;24:339-47.
60. Streeter DD, Hanna WT. Engineering mechanics for successive states in canine left ventricular myocardium. I. Cavity and wall geometry. Circ Res 1973;33:639-55.
61. Streeter DD. Gross morphology and fiber geometry of the heart. In: Berne RM, editor. Handbook of Physiology. Besthesda, MD: American Physiological Society, 1979, p. 61-112.
62. McCulloch AD, Smaill BH, Hunter PJ. Regional left ventricular epicardial deformation in the passive dog heart. Circ Res 1989;64:721-33.
63. Villarreal FJ, Waldman LK, Lew WYW. A technique for measuring regional two-dimensional finite strains in the canine left ventricle. Cir Res 1988;62:711-21.
64. Waldman LK, Nosan D, Villarreal FJ, Covell JW. Relation between transmural deformation and local myofiber direction in canine left ventricle. Circ Res 1988;63:550-62.
65. Scollan DF, Holmes A, Winslow R, Forder J. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am J Physiol 1998;275:H2308-18.
66. Hsu E, Muzikant A, Matulevicius S, Penland R, Henriquez C. Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am J Physiol 1998;274:H1627-34.
67. Weiss JA, Maker BN, Govindjee S. Finite element implementation of incompressible, transversely Isotropic hyperelasticity. Comp Meths In Appl Mechs and Eng 1996;135:107-28.
68. Martins JAC, Pires EB, Salvado R, Dinis PB. A numerical model of passive and active behavior of skeletal muscles. Comput Methods Appl Mech Engrg 1998;151:419-33.
69. Wackers FJ, Maniawski P, Sinusas AJ. Evaluation of left ventricular regional wall function by ECG-gated technetium-99m-sestamibi imaging. In: Zaret BL, Beller GA, editors. Nuclear Cardiology - State of the Art and Future Directions. St. Louis, MO: Mosby-Year Book, Inc., 1993. p. 201-8.
70. Gallagher KP, Matsuzaki, Osakada G, Kemper WS, Ross J. Effect of exercise on the relationship between myocardial blood flow and systolic wall thickening in dogs with acute coronary stenosis. Circ Res 1983;52:716-29.
71. Stroink G, Moshage W, Achenbach S, Cardiomagnetism. In: Andra W, Nowak H, editors. Magnetism in Medicine: A Handbook. New York: Wiley-VC, 1998. p. 136-89.
72. Baker LL, et al. Recent advances in MR imaging/spectroscopy of cerebral ischemia. AJR Am J Roentgenol 1991;156:1133-43.
73. Warach S, et al. Fast magnetic resonance diffusion-weighted imaging of acute human stroke [published erratum appears in Neurology 1992;42:1717-23].
74. Neurology 1992;42:1717-23.
75. Chien D, et al. MR diffusion imaging of cerebral infarction in humans. Am J Neuroradiol 1992;13:1097-102.
76. Discussion 1992;13:1103-5.
77. Le Bihan D, et al. Diffusion MR imaging: Clinical applications. Am J Roentgenol 1992;159:591-9.
78. Peled S. Magnetic resonance imaging shows orientation and asymmetry of white matter fiber tracts. Brain Res 1998;780:27-33.
79. Makris N, et al. Morphometry of in vivo human white matter association pathways with diffusion-weighted magnetic resonance imaging. Ann Neurol 1997;42:951-62.
80. Conturo TE, et al. Tracking neuronal fiber pathways in the living human brain. Proc Natl Acad Sci US 1999;96:10422-7.
81. Werring DJ, et al. A direct demonstration of both structure and function in the visual system: Combining diffusion tensor imaging with functional magnetic resonance imaging. Neuroimag 1999;9:352-61.
82. Florence SL, Taub HB, Kaas JH. Large-scale sprouting of cortical connections after peripheral injury in adult macaque monkeys. Science 1998;282:1117-21.
83. Zerhouni EA, Parish DM, Rogers WJ, Yang A, Shapiro EP. Human heart: Tagging with MR imaging - a method for noninvasive assessment of myocardial motion. Radiol 1988;169:59-63.
84. Axel L, Dougherty L. MR imaging of motion with spatial modulation of magnetization. Radiol 1989;171:841-5.
85. Pelc NJ, Herfkens RJ, Shimakawa A, Enzmann DR. Phase contrast cine magnetic resonance imaging [review]. Magn Reson Q 1991;7:229-54.
86. McVeigh ER, Zerhouni EA. Non-invasive measurement of transmural gradients in myocardial strain with magnetic resonance imaging. Radiol 1991;180:677-83.
87. McVeigh ER. MRI of myocardial function: Motion tracking technique. Magn Reson Imag 1996;14:137-50.