Fast grim angular structure development based streamline tractography

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1 Volume 9 No. 08, ISSN: (on-line version) url: ijpam.eu Fast grim angular structure development based streamline tractography Chintalapati Sai Sita Sri, Ramya Laksmi V.S, M.Malini Deepika, A. Srinivasan, N.R.Raajan *,k.hariharan 3 School of Electrical and Electronics Engineering, SASTRA Deemed University, Tamil Nadu, India Head Radiology, Thanjavur Medical College (TMC), Tamil Nadu, India 3 School of Computing, SASTRA Deemed University, Tamil Nadu, India chsaisita8@gmail.com, ramyasrinivasan8@gmail.com,malinideepika@gmail.com, srinimdr@gmail.com, nrraajan@gmail.com ABSTRACT: Diffusion Tensor Imaging is a technique to portray minute structural changes or aberrations with treatment and neuropathology. Diffusion Tensor Imaging is best defined as a neuro-imaging method based on MRI to trace the orientation, position and the anisotropy of tracts encompassed in the brain's white matter. This technique estimates molecular diffusion using a Gaussian model which also accounts for the anisotropy arising. This model allows quick estimation of diffusivity in all directions. The Brownian motion is characterized by a model known as random walk best depicted by differential equations that are stochastic and not linear. This random walk model 649

2 allows us to efficiently connect the source region to the sink region. We show that the most likely trajectories are of least energy. INTRODUCTION: In our body, water molecules are under translational motion known as Brownian motion. The translational motion makes the MR images sensitive when special gradients are applied to encoding diffusion The extent of diffusion is manipulated using value of 'b'. If the 'b' is zero, then they are not diffusion-weighted images. If 'b' is greater than zero then they are diffusion-weighted images. When there is free diffusion, then spins procure phases that are random and it leads to a signal loss. This is seen as the black appearance of ventricles on the images that are diffusion-weighted. When hindered diffusion subsists, the signal is better and there is a gray appearance on the diffusion-weighted images. White matter of the brain is a fibrous tissue and we perceive anisotropic diffusion. The water molecules tend to traverse along a track that is parallel to the axis of the fiber tract that is dominant. Gaussian model is used to estimate the diffusion. Random walk is known as a stochastic process which traces a path. The path traced comprises of random steps in a sequence. METHODOLOGY: 3D STOCHASTIC COMPLETION FIELDS: The state of a particle is best portrayed by its position and orientation. 3 R S is amended using a set of non-linear differential equation: a sin.cos;. b sin.sin ; c cos.. ; N 0, ; N 0,...() To endorse the shortest tracts a segment of particles is permitted to decay. Fraction : e The particle moves at a speed that is constant. It travels in a direction which changes continually. These distortions can be best portrayed by two successive aberrations. The primary deviation is proportional to in the XY -plane. This correlates to the rotation in the osculating plane. The local Frenet frame contains both tangential and normal vectors, which lies within the osculating plane. The secondary deviation is proportional to and orthogonal to the XY- plane in which lies the current tangential vector. This measures up to the rotation occurring in the binormal plane. The local Frenet Frame has both tangential and normal vectors that are 640

3 incorporated in the bi-normal plane.a particle from a particular source state( a0, b0, c0, 0, 0 ) prior to its decay supposedly reaches an arbitrary state( abc),,,, in a time t. 3D RANDOM WALK: The random walk generated paths can be obtained. Let us consider p as a source voxel. q is assumed to be a sink voxel. A particular particle traverses the track depicted by random walk originating at p.each path will consist of many steps that are of unit length. There is a change in direction at each and every step. Change in θ is given by k, k... k n. Change in is given by,... n. k i n f ( p) e e e i...() k i n g( pq) e e e f d i q p p...(3) Minimizing the energy, k t dt t dt dt...(4) where log log DIFFERENTIAL EQUATION FOR RANDOM WALK: n N i, i, i i i i P D A t P D A t P t A A...(5) n n n ' M A, t A i A i i P A i t t At i A i Ai dai 3D RANDOM WALK BASED DIFFERENTIAL EQUATIONS: 64

4 Exploiting Fokker Planck equation and using the Markov property, P a, b, c,, ; t Pa, b, c,,, t Pa, b, c,, ;0 dt t...(6) P sin cos P sin sin P cos P P P P t x y z...(7) BAYESIAN STOCHASTIC COMPLETION FIELD TRACTOGRAPHY Here, and t P( a, b, c,, ) P ( a, b, c,, ) dt 0 t t,,,,,,,,, P a b c t P a b c 0...(8)...(9) EXPERIMENTAL RESULT: 3 3,,,,,,,, cos 0,,,,,,,, cos { t t t t Pa b c Pa b c if a b c a b c t t P 3 3 a, b, c,, Pa, b, c,, if cos 0 P P t 6 t Pa,,,,,,,, sin cos 0,,,,,,,, sin cos { t b c Pa t b c if a b c a b c t t Pa, b, c,, Pa, b, c,, if sincos0 P P 64

5 Fig. Diffusion tensor for direction x, y,z Fig. Fractional Anistropy and vector fields 643

6 Fig 3. Three dimensional view of brain with single tractography Fig 4. Sectional view of tract with white matters 644

7 Fig 5. Trac data without white matters CONCLUSION: The algorithm characterizes Brownian motion by a random walk model. The proposed algorithm is used to produce diffusion tensor images of brain data. The diffusion parameters are incorporated to obtain efficient solutions. The variations in the source and sink voxels effects the generated pathways. Further more efforts have to be made to assess the stochastic completion field tractography. Computationally it is proved that connectivity exists amid the stochastic completion fields and tensor imaging. Tracing the more subtle connectivity pathways in the cortical and sub-cortical regions is a subject for ongoing work. Another important subject is to formulate the measure of generated fiber tracts. ACKNOWLEDGEMENT: This work would not have been possible without the guidance support by Dr. A.Srinivasan, Head, Department of Radiology and Radiological Sciences, Thanjavur Medical College, Tamil nadu. I am especially indebted to Ethical committee members, Dean, TMC, and Other technical support faculty, Chief of the Section of Radiology, who have been supportive of my career goals and who worked actively to provide me with the protected academic time to pursue those goals. REFERENCES: [] Takayuki Sakaia,b, Kunio Doic,d, Masami Yoneyamae, Atsuya Watanabef,g, Tosiaki Miyatib."Distortion-free diffusion tensor imaging for evaluation of lumbar nerveroots: Utility of direct coronal single-shot turbo spin-echo diffusion sequence Magnetic Resonance Imaging- Accepted 7 January 08 [].Parya Momayyez and Kaleem Siddiqi- Centre for Intelligent Machines- 3D- Stochastic Completion Fields for Fiber Tractography-McGill University, Montr eal, QC, Canada, IEEE

8 [3] D. Le Bihan, Looking into the functional architecture of the brain with diffusion MRI, Nat. Rev. Neurosci.4, 003, pp [4]. E.H.Badran, E.G. Mahmoud, and N. Hamdy, An Algorithm for Detecting Brain Tumors in MRI,IEEE 00 [5] J. Berman, S. Chung, P. Mukherjee, C. Hess, E. Han, and R. Henrya. Probabilistic streamline q-ball tractography using the residual bootstrap. NeuroImage, 39:5, 008. [6] P. Savadjiev, J. Campbell, and B. P. K. Siddiqi. 3d curve inference for diffusion MRI regularization and fibre tractography. Med. Image Anal., 0:799 83, Aug [7] J. Tournier, F. Calamante, D. Gadian, and A. Connelly. Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage, 3:76 85, Sept [8] Khalil C, Budzik JF, Kermarrec E, Balbi V, Le Thuc V, Cotten A. Tractography of peripheral nerves and skeletal muscles. Eur J Radiol 00;76:39 7. [9] Andreisek G, White LM, Kassner A, Sussman MS. Evaluation of diffusion tensor imaging and fiber tractography of the median nerve: preliminary results on intrasubject variability and precision of measurements. Am J Roentgenol 00;94:W65 7. [0] Manoliu A, Ho M, Nanz D, et al. Diffusion tensor imaging of lumbar nerve roots:comparison between fast readout-segmented and selective-excitation acquisitions. Investig Radiol 06 Aug;5(8): [] B.J. Jellisona, A.S. Fielda, J. Medowb, M. Lazarc, M.S.Salamatd, and A.L. Alexander, Diffusion Tensor Imaging of Cerebral White Matter: A Pictorial Review of Physics, Fiber Tract Anatomy, and Tumor Imaging Patterns, AJNR. Am. J.Neuroradiology 5, 004, pp [] S. Mori, B. Crain, V.P. Chacko, and P.C. M. van Zijl, Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging, Ann. Neurol. 45, 999, pp [3] S. Napel, D.H. Lee, R. Frayne, and B.K. Rutt, Visualizing three dimensional flow with simulated streamlines and threedimensional phase-contrast MR imaging, J. Magn. Reson.Imaging, 99, pp [4] S. Wakana, H.Y. Jiang, L.M. Nagae-Poetscher, P.C.M. van Zijl, and S. Mori, Fiber Tract based Atlas of Human White Matter Anatomy, Radiology 30, 004, pp [5] Mori S., S. Wakana, and L.M. Nagae-Poetscher, PeterC.M.van Zijl, MRI Atlas of Human White Matter, ELSEVIER,

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