Strategies for Direct Volume Rendering of Diffusion Tensor Fields

Diffusion-weighted magnetic resonance imaging is a relatively new modality capable of elucidating the fibrous structure of certain types of tissue, such as the white matter within the brain. One tool for interpreting this data is volume rendering because it permits the visualization of three dimensional structure without a prior segmentation process. In order to use volume rendering, however, we must develop methods for assigning opacity and color to the data, and create a method to shade the data to improve the legibility of the rendering. Previous work introduced three such methods: barycentric opacity maps, hue-balls (for color), and lit-tensors (for shading). The paper expands on and generalizes these methods, describing and demonstrating further means of generating opacity, color, and shading from the tensor information. We also propose anisotropic reaction-diffusion volume textures as an additional tool for visualizing the structure of diffusion data. The patterns generated by this process can be visualized on their own or they can be used to supplement the volume rendering strategies described in the rest of the paper. Finally, because interpolation between data points is a fundamental issue in volume rendering, we conclude with a discussion and evaluation of three distinct interpolation methods suitable for diffusion tensor MRI data.

[1]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[2]  Gregory M. Nielson,et al.  Visualizing functions over a sphere , 1990, IEEE Computer Graphics and Applications.

[3]  H.-C. Hege,et al.  Interactive visualization of 3D-vector fields using illuminated stream lines , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[4]  James F. Blinn,et al.  Models of light reflection for computer synthesized pictures , 1977, SIGGRAPH.

[5]  M. Carter Computer graphics: Principles and practice , 1997 .

[6]  Sinisa Pajevic,et al.  Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: Application to white matter fiber tract mapping in the human brain , 1999, Magnetic resonance in medicine.

[7]  N. Zabusky,et al.  Ellipsoidal quantification of evolving phenomena , 1991 .

[8]  P. V. van Zijl,et al.  Orientation‐independent diffusion imaging without tensor diagonalization: Anisotropy definitions based on physical attributes of the diffusion ellipsoid , 1999, Journal of magnetic resonance imaging : JMRI.

[9]  G. David Kerlick,et al.  Moving iconic objects in scientific visualization , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[10]  T. L. Davis,et al.  Morphometry of in vivo human white matter association pathways with diffusion‐weighted magnetic resonance imaging , 1997, Annals of neurology.

[11]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[12]  R Luypaert,et al.  A method for myelin fiber orientation mapping using diffusion-weighted MR images. , 1994, Magnetic resonance imaging.

[13]  Kwan-Liu Ma,et al.  Visualizing vector fields using line integral convolution and dye advection , 1996, Proceedings of 1996 Symposium on Volume Visualization.

[14]  Darwyn R. Peachey,et al.  Solid texturing of complex surfaces , 1985, SIGGRAPH.

[15]  Alex Pang,et al.  Interactive deformations from tensor fields , 1998 .

[16]  W. J. Freeman,et al.  Alan Turing: The Chemical Basis of Morphogenesis , 1986 .

[17]  M. Raichle,et al.  Tracking neuronal fiber pathways in the living human brain. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[18]  P. Basser,et al.  Estimation of the effective self-diffusion tensor from the NMR spin echo. , 1994, Journal of magnetic resonance. Series B.

[19]  Samuel P. Uselton,et al.  Volume Rendering for Computational Fluid Dynamics: Initial Results , 1991 .

[20]  Greg Turk,et al.  Generating textures on arbitrary surfaces using reaction-diffusion , 1991, SIGGRAPH.

[21]  David N. Kennedy,et al.  Fusion of MRI data for Visualization of White Matter Bundles , 2001 .

[22]  Richard S. Gallagher Computer Visualization: Graphics Techniques for Scientific and Engineering Analysis , 1994 .

[23]  P. Barker,et al.  Diffusion magnetic resonance imaging: Its principle and applications , 1999, The Anatomical record.

[24]  Gordon L. Kindlmann,et al.  Hue-balls and lit-tensors for direct volume rendering of diffusion tensor fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[25]  David Banks,et al.  Image-guided streamline placement , 1996, SIGGRAPH.

[26]  Lambertus Hesselink,et al.  Visualization of second order tensor fields and matrix data , 1992, Proceedings Visualization '92.

[27]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[28]  Robert R. Dickinson A Unified Approach To The Design Of Visualization Software For The Analysis Of Field Problems , 1989, Photonics West - Lasers and Applications in Science and Engineering.

[29]  Victoria Interrante,et al.  Strategies for effectively visualizing 3D flow with volume LIC , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[30]  J. van Wijk,et al.  Spot noise texture synthesis for data visualization , 1991, SIGGRAPH.

[31]  P. Basser,et al.  A simplified method to measure the diffusion tensor from seven MR images , 1998, Magnetic resonance in medicine.

[32]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[33]  Brian Cabral,et al.  Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[34]  David C. Banks,et al.  Illumination in diverse codimensions , 1994, SIGGRAPH.

[35]  Andrew Witkin,et al.  Reaction-diffusion textures , 1991, SIGGRAPH.

[36]  David H. Laidlaw,et al.  Visualizing diffusion tensor images of the mouse spinal cord , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[37]  P. Basser,et al.  Toward a quantitative assessment of diffusion anisotropy , 1996, Magnetic resonance in medicine.

[38]  Victoria Interrante,et al.  Strategies for effectively visualizing 3D flow with volume LIC , 1997 .

[39]  David H. Laidlaw,et al.  Visualizing diffusion tensor images of the mouse spinal cord , 1998 .