Abstract
Water diffusion is anisotropic in organized tissues such as white matter and muscle. Diffusion tensor imaging (DTI), a non-invasive MR technique, measures water self-diffusion rates and thus gives an indication of the underlying tissue microstructure. The diffusion rate is often expressed by a second-order tensor. Insightful DTI visualization is challenging because of the multivariate nature and the complex spatial relationships in a diffusion tensor field. This chapter surveys the different visualization techniques that have been developed for DTI and compares their main characteristics and drawbacks. We also discuss some of the many biomedical applications in which DTI helps extend our understanding or improve clinical procedures. We conclude with an overview of open problems and research directions.
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References
C. Pierpaoli, A.S. Barnett, S. Pajevic, A. Virta, and P.J. Basser. Validation of DT-MRI tractography in the descending motor pathways of human subjects. In ISMRM, Conf. Proc., p. 501, 2001.
D.S. Tuch, R.M. Weisskoff, J.W. Belliveau, and V.J. Wedeen. High angular resolution diffusion imaging of the human brain. In ISMRM, Conf. Proc., p. 321, 1999.
L.R. Frank. Anisotropy in high angular resolution diffusion-weighted MRI. MR in Medicine, 45(6):935–939, 2001.
A. Einstein. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 17:549–560, 1905.
E.M. Purcell, H.C. Torrey, and R.V. Pound. Resonance absorption by nuclear magnetic moments in a solid. Physical Review, 69:37–43, 1946.
F. Bloc. Nuclear induction. Physical Review, 70:460–474, 1946.
E.L. Hahn. Spin echoes. Physical Review, 80:580–594, 1950.
P.C. Lauterbur. Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature, 242:190–191, 1973.
G.J. Stanisz and R.M. Henkelman. Tissue compartments, exchange and diffusion. In Workshop on Diffusion MRI: Biophysical Issues, pp. 34–37, 2002.
P.T. Callaghan. Principles of Nuclear Magnetic Resonance Microscopy. Oxford, 1993.
P.J. Basser, J. Mattiello, and D. LeBihan. Estimation of the effective self-diffusion tensor from the NMR spin echo. MR Journal, 103(3):247–54, 1994.
D. LeBihan. Molecular diffusion nuclear magnetic resonance imaging. Magn. Reson. Quant., 17:1–30, 1991.
D.F. Scollan, A. Holmes, R. Winslow, and J. Forder. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am J Physiol, 275:2308–2318, 1998.
E.W. Hsu, 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, 274:1627–1634, 1998.
J.K. Jones. Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. MR in Medicine, 49:7–12, 2003.
Y. Assaf, A. Mayk, and Y. Cohen. Displacement imaging of spinal cord using q-space diffusion-weighted MRI. MR in Medicine, 44:713–722, 2000.
D.S. Tuch, T.G. Reese, M.R. Wiegell, N. Makris, J.W. Belliveau, and V.J. Wedeen. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. MR in Medicine, 48(4):577–582, 2002.
L.R. Frank. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. MR in Medicine, 47:1083–1099, 2002.
C. Pierpaoli and P.J. Basser. Toward a quantitative assessment of diffusion anisotropy. MR in Medicine, 36(6):893–906, 1996.
P.J. Basser and C. Pierpaoli. Microstructural features measured using diffusion tensor imaging. MR Journal, pp. 209–219, 1996.
C.F. Westin, S. Peled, H. Gubjartsson, R. Kikinis, and F.A. Jolesz. Geometrical diffusion measures for MRI from tensor basis analysis. In ISMRM, Conf. Proc., p. 1742, April 1997.
P. van Gelderen, M.H. de Vleeschouwer, D. Despres, J. Pekar, P.C. van Zijl, and C.T. Moonen. Water diffusion and acute stroke. MR in Medicine, 31:154–63, 1994.
P. Douek, R. Turner, J. Pekar, N. Patronas, and D. LeBihan. MR color mapping of myelin fiber orientation. J. Comput. Assist. Tomogr, 15:923–929, 1991.
G. Kindlmann, D. Weinstein, and D.A. Hart. Strategies for direct volume rendering of diffusion tensor fields. IEEE Trans. on Visualization and Computer Graphics, 6(2):124–138, 2000.
R.A. Drebin, L. Carpenter, and P. Hanrahan. Volume rendering. Computer Graphics, SIGGRAPH Proc., 22(4):65–74, 1988.
M. Levoy. Display of surfaces from volume data. IEEE Computer Graphics & Applications, 8(5):29–37, 1988.
W.E. Lorensen and H.E. Cline. Marching cubes: a high resolution 3D surface reconstruction algorithm. Computer Graphics, SIGGRAPH Proc., 21(4):163–169, 1987.
A. Wenger, D. Keefe, S. Zhang, and D.H. Laidlaw. Interactive volume rendering of thin thread structures within multivalued scientific datasets. IEEE Trans. on Visualization and Computer Graphics, 2004. In press.
B. Cabral, N. Cam, and J. Foran. Accelerated volume rendering and tomographic reconstruction using texture mapping hardware. In Symposium on Volume Visualization, Conf. Proc., pp. 91–98, 1994.
J. Kniss, G. Kindlmann, and C. Hansen. Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets. In IEEE Visualization, Conf. Proc., pp. 255–262, October 2001.
R. Fernando, editor. GPU Gems: Programming Techniques, Tips, and Tricks for Real-Time Graphics. Addison-Wesley, 2004.
D.H. Laidlaw, E.T. Ahrens, D. Kremers, M.J. Avalos, C. Readhead, and R.E. Jacobs. Visualizing diffusion tensor images of the mouse spinal cord. In IEEE Visualization, Conf. Proc., pp. 127–134, October 1998.
G. Kindlmann. Superquadric tensor glyphs. In Proceedings IEEE TVCG/EG Symposium on Visualization 2004, pp. 147–154, May 2004.
F. Post, B. Vrolijk, H. Hauser, R.S. Laramee, and H. Doleisch. Feature extraction and visualization of flow fields. In State-of-the-Art EG, Conf. Proc., pp. 69–100, 2002.
J.J. van Wijk. Image based flow visualization. Computer Graphics, SIGGRAPH Proc., 21(3):745–754, 2002.
S. Mori and P.C.M. van Zijl. Fiber tracking: principles and strategies — a technical review. NMR in Biomedicine, 15(7–8):468–480, 2002.
P.J. Basser, S. Pajevic, C. Pierpaoli, J. Duda, and A. Aldroubi. In vivo fiber tractography using DT-MRI data. MR in Medicine, 44:625–632, 2000.
A. Vilanova, G. Berenschot, and C. van Pul. DTI visualization with stream-surfaces and evenly-spaced volume seeding. In VisSym’ 04 Joint EG — IEEE TCVG Symposium on Visualization, Conf. Proc., pp. 173–182, 2004.
T. Delmarcelle and L Hesselink. Visualizing second order-tensor fields with hyperstreamlines. IEEE Computer Graphics & Applications, 13(4):25–33, 1993.
S. Zhang, C. Demiralp, and D.H. Laidlaw. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. IEEE Trans. on Visualization and Computer Graphics, 9(4):454–462, 2003.
D. Weinstein, G. Kindlmann, and E.C. Lundberg. Tensorlines: advection-diffusion based propagation through diffusion tensor fields. In IEEE Visualization, Conf. Proc., pp. 249–253, 1999.
L. Zhukov and A.H. Barr. Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI. In IEEE Visualization, Conf. Proc., pp. 387–394, 2002.
B. Jobard and W. Lefer. Creating evenly-spaced streamlines of arbitrary density. In Visualization in Scientific Computing. Proc. of the EG Workshop, pp. 43–56. Springer Verlag, 1997.
Z. Ding, J.C. Gore, and A.A. Anderson. Classification and quantification of neuronal fiber pathways using diffusion tensor MRI. MR in Medicine, 49(4):716–721, 2003.
A. Brun, H-J. Park, H. Knutsson, and C.-F. Westin. Coloring of DT-MRI fiber traces using Laplacian eigenmaps. In EUROCAST, Conf. Proc., volume 2809 of LNCS, February 2003.
S. Zhang and D.H. Laidlaw. Hierarchical clustering of streamtubes. Technical Report CS-02-18, Brown University Computer Science Dep., August 2002.
I. Corouge, G. Gerig, and S. Gouttard. Towards a shape model of white matter fiber bundles using diffusion tensor MRI. In IEEE International Symposium on Biomedical Imaging, Conf. Proc., pp. 344–347, 2004.
G.J.M. Parker, C.A. Wheeker-Kingshott, and G.J. Barker. Distributed anatomical connectivity derived from diffusion tensor imaging. IPMI, LNCS, 2082:106–120, 2001.
A. Brun, M. Björnemo, R. Kikinis, and C.-F. Westin. White matter tractography using sequential importance sampling. In ISMRM, Conf. Proc., May 2002.
P.G. Batchelor, D.L.G. Hill, F. Calamante, and D. Atkinson. Study of connectivity in the brain using the full diffusion tensor from MRI. In IPMI, Conf. Proc., pp. 121–133, 2001.
L. O’Donnell, S. Haker, and C.F. Westing. New approaches to estimation of white matter connectivity in diffusion tensor MRI: elliptic PDE’s and geodesics in tensor-warped space. In MICCAI, Conf. Proc., pp. 459–466, 2002.
X. Zheng and A. Pang. Volume deformation for tensor visualization. In IEEE Visualization, Conf. Proc., pp. 379–386, 2002.
A. Sigfridsson, T. Ebbers, E. Heiberg, and L. Wigström. Tensor field visualisation using adaptive filtering of noise fields combined with glyph rendering. In IEEE Visualization, Conf. Proc., pp. 371–378, 2002.
X. Zheng and A. Pang. Hyperlic. In IEEE Visualization, Conf. Proc., pp. 249–256, 2003.
A. Bhalerao and C.-F. Westin. Tensor splats: Visualising tensor fields by texture mapped volume rendering. In MICCAI, Conf. Proc., pp. 294–901, 2003.
L. Hesselink, Y. Levy, and Y. Lavin. The topology of symmetric, second-order 3D tensor fields:. IEEE Trans. on Visualization and Computer Graphics, 3(1):1–11, 1997.
D. Akers, A. Sherbondy, R. Mackenzie, R. Dougherty, and B. Wandell. Exploration of the brain’s white matter pathways with dynamic queries. In IEEE Visualization, Conf. Proc., October 2004.
Ç. Demiralp, D.H. Laidlaw, C. Jackson, D. Keefe, and S. Zhang. Subjective usefulness of CAVE and fishtank VR display systems for a scientific visualization application. In IEEE Visualization Poster Compendium, 2003.
S. Zhang, Ç. Demiralp, D. Keefe, M. DaSilva, B.D. Greenberg, P.J. Basser, C. Pierpaoli, E.A. Chiocca, T.S. Deisboeck, and D.H. Laidlaw. An immersive virtual environment for DT-MRI volume visualization applications: a case study. In IEEE Visualization, Conf. Proc., pp. 437–440, October 2001.
R. Westerhausen, C. Walter, F. Kreuder, R.A. Wittling, E. Schweiger, and W. Wittling. The influence of handedness and gender on the microstructure of the human corpus callosum: a diffusion-tensor magnetic resonance imaging study. Neuroscience Letters, 351:99–102, 2003.
A. Pfefferbaum, E.V. Sullivan, M. Hedehus, K.O. Lim, E. Adalsteinsson, and M. Moseley. Age-related decline in brain white matter anisotropy measured with spatially corrected echo-planar diffusion tensor imaging. MR in Medicine, 44(2):259–268, 2000.
M. O’Sullivan, D.K. Jones, P.E. Summers, R.G. Morris, S.C.R. Williams, and H.S. Markus. Evidence for cortical disconnection as a mechanism of age-related cognitive decline. Neurology, 57:632–638, 2001.
M. Catani, D.K. Jones, R. Donato, and D.H. Ffytche. Occipito-temporal connections in the human brain. Brain, 126:2093–2107, 2003.
S. Wakana, H. Jiang, L.M. Nagae-Poetscher, P.C.M. van Zijl, and S. Mori. Fiber tract based atlas of human white matter anatomy. Radiology, 230:77–87, 2004.
D.-S. Kim, M. Kima, I. Ronena, E. Formisano, K.-H. Kima, K. Ugurbila, S. Moric, and R. Goebel. In vivo mapping of functional domains and axonal connectivity in cat visual cortex using magnetic resonance imaging. MRI Journal, 21(10):1131–1140, 2003.
J.J. Volpe. Neurology of the Newborn. W.B. Saunders Company, 1995.
K.O. Lim and J.A. Helpern. Neuropsychiatric applications of DTI — a review. NMR in Biomedicine, 15(7–8):587–593, 2002.
M.A. Horsfield and D.K. Jones. Applications of diffusion-weighted and diffusion tensor MRI to white matter diseases — a review. NMR in Biomedicine, 15(7–8):570–577, 2002.
M. Kubicki, C.-F. Westin, S.E. Maier, H. Mamata, M. Frumin, H. Ersner-Hershfield, R. Kikinis, F.A. Jolesz, R. McCarley, and M.E. Shenton. Diffusion tensor imaging and its application to neuropsychiatric disorders. Harvard Rev. of Psychiatry, 10:234–336, 2002.
P.C. Sundgren, Q. Dong, D. Gomez-Hassan, S.K. Mukherji, P. Maly, and R. Welsh. Diffusion tensor imaging of the brain: review of clinical applications. Neuroradiology, 46(5):339–350, 2004.
N.I. Bohnen, K. Radharkrishnan, B.P. O’Neil, and L.T. Kurland. Descriptive and Analytic Epidemiology of Brain Tumours. Cancer of the Nervous System. Blackwell Publishing, 2001.
U.C. Wieshmann, M.R. Symms, G.J. Parker, C.A. Clark, L. Lemieux, G.J. Barker, and S.D. Shorvon. Diffusion tensor imaging demonstrates deviation of fibres in normal appearing white matter adjacent to a brain tumour. J. Neurol. Neurosurg. Psychiatry, 68(4):501–3, 2000.
S. Mori, K. Frederiksen, P.C. van Zijl, B. Stieltjes, M.A. Kraut, M. Solaiyappa, and M.G. Pomper. Brain white matter anatomy of tumor patients evaluated with diffusion tensor imaging. Ann. Neurol., 51(3):337–8, 2002.
C. Gossl, L. Fahrmeir, B. Putz, L.M. Auer, and D.P. Auer. Fiber tracking from DTI using linear state space models: detectability of the pyramidal tract. Neuroimage, 16(2):378–88, 2002.
B.P. Witwer, R. Moftakhar, K.M. Hasan, P. Deshmukh, V. Haughton, A. Field, K. Arfanakis, J. Noyes, C.H. Moritz, M.E. Meyerand, H.A. Rowley, A.L. Alexander, and B. Badie. Diffusion-tensor imaging of white matter tracts in patients with cerebral neoplasm. J. Neurosurg., 97(3):568–75, 2002.
S. Zhang, M.E. Bastin, D.H. Laidlaw, S. Sinha, P.A. Armitage, and T.S. Deisboeck. Visualization and analysis of white matter structural asymmetry in diffusion tensor MR imaging data. MR in Medicine, 51(1):140–147, 2004.
D.J. Werring, C.A. Clark, G.J. Barker, A.J. Thompson, and D.H. Miller. Diffusion tensor imaging of lesions and normal-appearing white matter in multiple sclerosis. Neurology, 52:1626–1632, 1999.
R.H. Paul, R. Cohen, and R. Stern. Neurocognitive manifestations of HIV. CNS Spectrums, 7(12):860–866, 2003.
R.H. Paul, R. Cohen, B. Navia, and K. Tashima. Relationships between cognition and structural neuroimaging findings in adults with human immunodeficiency virus type-1. Neurosci. Biobehav. Rev., 26(3):353–9, 2002.
N. Pomara, D.T. Crandall, S.J. Choi, G. Johnson, and K.O. Lim. White matter abnormalities in HIV-1 infection: a diffusion tensor imaging study. Psychiatry Res., 106(1):15–24, 2001.
C.G. Filippi, A.M. Ulug, E. Ryan, S.J. Ferrando, and W. van Gorp. Diffusion tensor imaging of patients with HIV and normal-appearing white matter on MR images of the brain. American Journal of Neuroradiology, 22:277–283, 2001.
A. B. Ragin, P. Storey, B. A. Cohen, L. G. Epstein, and R. R. Edelman. Whole brain diffusion tensor imaging in HIV-associated cognitive impairment. American Journal of Neuroradiology, 25(2):195–200, 2004.
F.B. Sachse. Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. LNCS Vol. 2966. Springer Verlag, 2004.
D.B. Ennis, G. Kindlmann, P.A. Helm, I. Rodriguez, H. Wen, and E.R. McVeigh. Visualization of high-resolution myocardial strain and diffusion tensors using superquadric glyphs. In ISMRM, Conf. Proc., May 2004.
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Vilanova, A., Zhang, S., Kindlmann, G., Laidlaw, D. (2006). An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications. In: Weickert, J., Hagen, H. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31272-2_7
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DOI: https://doi.org/10.1007/3-540-31272-2_7
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