Performance of ILU preconditioning techniques in simulating anisotropic diffusion in the human brain

Future Generation Computer Systems

Volumn 20, Issue 4, 2004, Pages 687-698

  Kang, Ning ^a   Zhang, Jun ^a   Carlson, Eric S ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b University of Alabama   (United States)

Author keywords

Anisotropic diffusion; DT MRI; FCC grid; Preconditioning

Indexed keywords

ANISOTROPY; BRAIN; COMPUTER SIMULATION; DIFFUSION; FEATURE EXTRACTION; ITERATIVE METHODS; MORPHOLOGY; TENSORS;

ANISOTROPIC DIFFUSION; DIFFUSION TENSOR MAGNETIC RESONANCE IMAGING (DT-MRI); FCC GRIDS; PRECONDITIONING;

MAGNETIC RESONANCE IMAGING;

EID: 1842536459     PISSN: 0167739X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.future.2003.07.014     Document Type: Conference Paper

References (20)

1. http://acts.nersc.gov/.
2. A.B.M. Bjornemo, White matter fiber tracking using diffusion tensor MRI, Master's Thesis, Linkoping University, Sweden, 2002.
3. P.G. Batchelor, D.L.G. Hill, F. Calamante, D. Atkinson, Study of connectivity in the brain using the full diffusion tensor from MRI, in: Proceedings of the 17th International Conference on Information Processing in Medical Imaging, IPMI'01, June 2001, University of California at Davis, USA, Lecture Notes in Computer Science 2082, Springer, Berlin, pp. 121-133.
4. Boghosian B.M., Lattice gases and cellular automata. Future Gen. Comput. Syst. 16:1999;171-185.
5. K.E. Brenan, S.L. Campbell, L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, PA, 1996.
6. D. Gembris, H. Schumacher, D. Suter, Solving the diffusion equation for fiber tracking in the living human brain, in: Proceedings of the International Society for Magnetic Resonance Medicine (ISMRM), vol. 9, Glasgow, Scotland, April 2001, p. 1529.
7. Brown P.N., Hindmarsh A.C., Petzold L.R., Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15:1994;1467-1488.
8. A.C. Hindmarsh A.G. Taylor, User Documentation for IDA: A Differential-Algebraic Equation Solver for Sequential and Parallel Computers, LLNL Report UCRL-MA-136910, Center for Applied Scientific Computing, LLNL, Livermore, CA, 1999.
9. http://acts.nersc.gov/sundials/main.html.
10. L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis, Interscience, New York, 1958.
11. Le Bihan D., Mangin J.F., Poupon C., Clark C.A., Pappata S., Molko N., Chabriat H., Diffusion tensor imaging: concepts and application. J. Magn. Reson. Imag. 13:2001;534-546.
12. Nicholson C., Diffusion and related transport mechanism in brain tissue. Rep. Progr. Phys. 64:2001;815-884.
13. Nicholson C., Syková E., Extracellular space structure revealed by diffusion analysis. Trends Neurosci. 21(5):1998;207-215.
14. Poupon C., Mangin J.F., Clark C.A., Frouin V., Reǵis J., Le Bihan D., Bloch I., Towards inference of human brain connectivity from MR diffusion tensor data. Med. Image Anal. 5:2001;1-15.
15. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, MA, 1996.
16. Saad Y., Schultz M.H., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7:1986;856-869.
17. H. Sun, N. Kang, J. Zhang, E.S. Carlson, A fourth order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation, Technical Report No. 341-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.
18. Vorisek I., Sykova E., Evolution of anisotropic diffusion in the developing rat corpus callosum. J. Neurophysiol. 78:1997;912-919.
19. C.F. Westin, S.E. Maier, B. Khidir, P. Everett, F.A. Jolesz, R. Kikinis, Image processing for diffusion tensor magnetic resonance imaging, in: Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Interventions (MICCAI), Cambridge, UK, July 1999, pp. 441-452.
20. J. Xu, Multidimensional finite differencing (MDFD) with hypersphere-close-pack grids for numerical solution of PDE defined on irregular domains, Ph.D. Thesis, University of Alabama, Tuscaloosa, AL, 2001.