# Selected references on diffusion-weighted and diffusion tensor MRI

These references were selected from outside the standard visualization literature, in order to assist those interested in visualization in learning more about this research area.

## Background

* PT Callaghan. Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press, Inc., New York, New York, 1991.

* J Crank. The Mathematics of Diffusion. Oxford University Press, Oxford, England, 1975.

* DA Danielson. Vectors and Tensors in Engineering and Physics. Westview Press, Boulder, Colorado, 2nd edition, 2003.

* A Einstein. Investigations on the Theory of Brownian Motion. Dover Publications, New York, 1956. R F ̈urthe, editor. AD Cowper, translator.

* Z-P Liang and PC Lauterbur. Principles of Magnetic Resonance Imaging: A Signal Processing Perspective. Wiley-IEEE Press, 1999.

* D Pickens. Magnetic resonance imaging. In J Beutel, HL Kundel, and RL van Metter, editors, Handbook of Medical Imaging, pages 373–461. Society of Photo-Optical Instrumentation Engineers (SPIE), Bellingham, Washington, 2000. Volume 1: Physics and Psychophysics.

* HH Schild. MRI Made Easy. Berlex Laboratories, Wayne, New Jersey, 1994.

## On DWI and DTI acquisition

* PJ Basser and DK Jones. Diffusion-tensor MRI: Theory, experimental design and data analysis - A technical review. Nuclear Magnetic Resonance in Biomedicine, 15:456–467, 2002.

* PJ Basser, J Mattiello, and D Le Bihan. Estimation of the effective self-diffusion tensor from the NMR spin-echo. Journal of Magnetic Resonance, B, 103(3):247– 254, 1994.

* PJ Basser, J Mattiello, and D Le Bihan. MR diffusion tensor spectroscopy and imaging. Biophysics Journal, 66(1):259–267, 1994.

* PJ Basser and C Pierpaoli. A simplified method to measure the diffusion tensor from seven MR images. Magnetic Resonance in Medicine, 39:928–923, 1998.

* TE Conturo, RC McKinstry, E Akbudak, and BH Robinson. Encoding of anisotropic diffusion with tetrahedral gradients: A general mathematical diffusion formalism and experimental results. Magnetic Resonance in Medicine, 35(3):399– 412, 1996.

* DK Jones. The effect of gradient sampling schemes on measures derived from diffusion tensor MRI: A monte carlo study. Magnetic Resonance in Medicine, 51:807–815, 2004.

* E Stejskal and J Tanner. Spin diffusion measurements: Spin echos in the presence of time-dependent field gradient. Journal of Chemical Physics, 42:288–292, 1965.

## The origins and measurement of anisotropy

* C Beaulieu. The basis of anisotropic water diffusion in the nervous system - A technical review. Nuclear Magnetic Resonance in Biomedicine, 15:435–455, 2002.

* D Le Bihan. Molecular diffusion, tissue microdynamics and microstructure. Nuclear Magnetic Resonance in Biomedicine, 8:375–386, 1995.

* D Le Bihan, R Tuner, and P Douek. Is water diffusion restricted in human brain white matter? An echo-planar NMR imaging study. Neuroreport, 4:887–890, 1993.

* AL Alexander, K Hasan, G Kindlmann, DL Parker, and JS Tsurada. A geometric analysis of diffusion tensor measurements of the human brain. Magnetic Resonance in Medicine, 44:283–291, 2000.

* PJ Basser. New histological and physiological stains derived from diffusion-tensor MR images. Annals of the New York Academy of Sciences, 820:123–138, 1997.

* LR Frank. Anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine, 45:935–939, 2001.

* LR Frank. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine, 47:1083–1099, 2002.

* C Pierpaoli and PJ Basser. Toward a quantitative assessment of diffusion anisotropy. Magnetic Resonance in Medicine, 33:893–906, 1996.

* AM Ulŭg and PCM van Zijl. Orientation-independent diffusion imaging without tensor diagonalization: Anisotropy definitions based on physical attributes of the diffusion ellipsoid. Journal of Magnetic Resonance Imaging, 9:804–813, 1999.

* C-F Westin, S Peled, H Gub jartsson, R Kikinis, and FA Jolesz. Geometrical diffusion measures for MRI from tensor basis analysis. In Proceedings of the 5th Annual Meeting of ISMRM, 1997.

## Applications of diffusion MRI

* DS Tuch, TG Reese, MR Wiegell, N Makris, JW Belliveau, and VJ Wedeen. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine, 48:577–582, 2002.

* DS Tuch, RM Weisskoff, JW Belliveau, and VJ Wedeen. High angular resolution diffusion imaging of the human brain. In Proceedings of the 7th Annual Meeting of ISMRM, page 321, 1999.

* MA Horsfield and DK Jones. Applications of diffusion-weighted and diffusion tensor MRI to white matter diseases - a review. NMR in Biomedecine, 15:570–577, 2002.

* J Dou, W-YI Tseng, TG Reese, and VJ Wedeen. Combined diffusion and strain MRI reveals structure and function of human myocardial laminar sheets in vivo. Magnetic Resonance in Medicine, 50:107–113, 2003.

* EW Hsu, AL Muzikant, SA Matulevicius, RC Penland, and CS Henriquez. Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. American Journal of Physiology, 274:1627–1634, 1998.

* DF Scollan, A Holmes, R Winslow, and J Forder. Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. American Journal of Physiology, 275:2308–2318, 1998.

* C Pierpaoli, P Jezzard, PJ Basser, A Barnett, and G DiChiro. Diffusion tensor MR imaging of the human brain. Radiology, 201(3):637–648, 1996.

* Y Seo, H Shinar, Y Morita, and G Navon. Anisotropic and restricted diffusion of water in the sciatic nerve: A (2)H double-quantum-filtered NMR study. Magnetic Resonance in Medicine, 42:461–466, 1999.

* CH Sotak. The role of diffusion tensor imagging in the evaluation of ischemic brain injury - a review. NMR in Biomedicine, 15:561–569, 2002.

* VJ Wedeen, TG Reese, VJ Napadow, and RJ Gilbert. Demonstration of primary and secondary muscle fiber architecture of the bovine tongue by diffusion tensor magnetic resonance imaging. Biophysical Journal, 80:1024–1028, Feb 2001.

* MR Wiegell, HBW Larsson, and VJ Wedeen. Fiber crossing in human brain depicted with diffusion tensor MR imaging. Radiology, 217(3):897–903, Dec 2000.

## Processing and analysis of DTI

* AL Alexander, KM Hasan, M Lazar, JS Tsuruda, and DL Parker. Analysis of partial volume effects in diffusion-tensor MRI. Magnetic Resonance in Medicine, 45:770–780, 2001.

* DC Alexander, GJ Barker, and SR Arridge. Detection and modeling of non-gaussian apparent diffusion coefficients profiles in human brain data. Magnetic Resonance in Medicine, 48:331–340, 2002.

* MM Bahn. Invariant and orthonormal scalar measures derived from magnetic resonance diffusion tensor imaging. Journal of Magnetic Resonance, 141:68–77, 1999.

* PJ Basser and C Pierpaoli. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111:209–219, 1996.

* JC Criscione, JD Humphrey, AS Douglas, and WC Hunter. An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. Journal of Mechanics and Physics of Solids, 48:2445–2465, 2000.

* KM Hasan, PJ Basser, DL Parker, and AL Alexander. Analytical computation of the eigenvalues and eigenvectors in DT-MRI. Journal of Magnetic Resonance, 152:41–47, 2001.

* S Pajevic, A Aldroubi, and PJ Basser. A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue. Journal of Magnetic Resonance, 154:85–100, 2002.

* S Pajevic and PJ Basser. Parametric and non-parametric statistical analysis of DT-MRI data. Journal of Magnetic Resonance, 161:1–14, 2003.

* C-F Westin, SE Maier, B Khidhir, P Everett, FA Jolesz, and R Kikinis. Image processing for diffusion tensor magnetic resonance imaging. In Proceedings of the 2nd Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), pages 441–452, September 1999.

* C-F Westin, SE Maier, H Mamata, A Nabavi, FA Jolesz, and R Kikinis. Processing and visualization for diffusion tensor MRI. Medical Image Analysis, 6:93–108, 2003.

* S Pajevic and C Pierpaoli. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: Application to white matter fiber tract mapping in the human brain. Magnetic Resonance in Medicine, 42(3):526–540, 1999.

* C Pierpaoli. Oh no! One more method for color mapping of fiber tract direction using diffusion MR imaging data. In Proceedings of the 5th Annual Meeting of ISMRM, page 1741, 1997.

## Fiber tractography

* PJ Basser. Fiber-tractography via diffusion tensor MRI (DT-MRI). In Proceedings of the 6th Annual Meeting of ISMRM, page 1226, 1998.

* PJ Basser, S Pajevic, C Pierpaoli, J Duda, and A Aldroubi. In vivo fiber tractograpy using DT-MRI data. Magnetic Resonance in Medicine, 44:625–632, 2000.

* T Conturo, N Lori, T Cull, E Akbudak, A Snyder, J Shimony, R McKinstry, H Burton, and M Raichle. Tracking neuronal fiber pathways in the living human brain. Proceedings of the National Academy of Sciences, 96:10422–10427, 1999.

* P Hagmann, J-P Thiran, L Jonasson, P Vandergheynst, S Clarke, P Maeder, and R Meuli. DTI mapping of human brain connectivity: Statistical fibre tracking and virtual dissection. NeuroImage, 19:545–554, 2003.

* M Lazar, D Weinstein, K Hasan, and AL Alexander. Axon tractography with tensorlines. In Proceedings of the 8th Annual Meeting of ISMRM, page 481, 2000.

* M Lazar, DM Weinstein, JS Tsuruda, KM Hasan, K Arfanakis, E Meyer, B Badie, HA Rowley, V Haughton, A Field, and AL Alexander. White matter tractography using diffusion tensor deflection. Human Brain Mapping, 18:306–321, 2003.

* N Makris, AJ Worth, G Sorensen, GM Papadimitriou, O Wu, TK Reese, VJ Wedeen, TL Davis, JW Stakes, VS Caviness, E Kaplan, BR Rosen, DN Pandya, and DN Kennedy. Morphometry of in vivo human white matter association pathways with diffusion weighted MRI. Annals of Neurology, 42(6):951–962, 1997.

* S Mori, BJ Crain, VP Chacko, and PCM van Zijl. Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals Neurology, 45:265–269, 1999.

* S Mori and PC Van Zijl. Fiber tracking: Principles and strategies - A technical review. Nuclear Magnetic Resonance in Biomedicine, 15:468–480, 2002.