Diffusion Tensor Imaging Visualization Techniques and Applications - PDF document

Diffusion Tensor Imaging Visualization Techniques and Applications Tim Peeters (t.peeters@tue,nl) - Anna Vilanova ( a.vilanova@tue.nl ) BioMedical Image Analysis ( bmia.bmt.tue.nl ) Eindhoven University of Technology,The Netherlands Overview Overview • Diffusion Tensor Imaging (DTI) data • DTI visualization techniques • Applications: newborn and ischemic heart • Fiber clustering • DTI segmentation IEEE Visualization 2008 DTI Visualization Techniques and Applications 2/54

Motivation Motivation www.spiralnotebook.org/ mousehunt/ http://www.shands.org/ T.H. Williams et al. IEEE Visualization 2008 DTI Visualization Techniques and Applications 3/54 Motivation Motivation MRI and Diffusion Tensor Imaging MRI and Diffusion Tensor Imaging Fibers – Micrometers (~2-10 μ m) Scanner (MR) – Millimeters (~1-2 mm) voxel 1-2 mm ~ 2-10 μ m IEEE Visualization 2008 DTI Visualization Techniques and Applications 4/54

Water Diffusion Water Diffusion Brownian Motion Brownian Motion IEEE Visualization 2008 DTI Visualization Techniques and Applications 5/54 Fick’ ’s s Law Law Fick ∂ = ⋅∇ 2 ( , ) ( , ) P r t D P r t ∂ t Diffusion time t r 2 Diffusion Coefficient (m /s) D ( , ) Probability that a particle P r t = travels ( , , ) in time r x y z t Solution -3D Gaussian 1 − 1 − 2 1 r D = ( , ) 4 P t e t r ( ) 3/ 2 π 4 Dt IEEE Visualization 2008 DTI Visualization Techniques and Applications 6/54

Anisotropic Diffusion Anisotropic Diffusion 1 − 1 − 2 1 r D = ( , ) 4 t P r t e ( ) 3/ 2 π 4 r Dt i 1 − 1 − 2 1 r D = i i ( , ) 4 t P r t e ( ) i i 3/ 2 π 4 Dt i 2 Indicates the distance r squared of the vector r IEEE Visualization 2008 DTI Visualization Techniques and Applications 7/54 Anisotropic Diffusion – – Anisotropic Diffusion Diffusion Tensor Tensor Diffusion ⎡ ⎤ Diffusion Tensor D D D xx xy xz ⎢ ⎥ = ⎢ D D D D ⎥ yx yy yz ⎢ ⎥ D D D ⎣ ⎦ D zx zy zz D = r Dr yy t i i i = D D 6 different values ij ji D D = r Dr xx t i i i 1 − 1 − 1 t r D r = ( , ) 4 t P r t e ( ) 3/2 π 4 | | D t IEEE Visualization 2008 DTI Visualization Techniques and Applications 8/54

MR measurements MR measurements • Measure Diffusion Weighted signal in a given direction S i • Stejskal-Tanner relationship attenuation signal to S i diffusion coefficient D i − = b D S S e where S not diffusion weighted value i 0 0 i b protocol parameter (diffusion time, ...) is often called ADC i (Apparent Diffusion Coefficient ) – D i diffusion in a given direction IEEE Visualization 2008 DTI Visualization Techniques and Applications 9/54 MRI- -Diffusion Measurement Diffusion Measurement MRI Measure in a lot of ADC i directions (Minimum 6) D i Fit D 2nd Order Tensor Symmetric Positive Definite Axis indicates Assume Gaussian preferred direction within a voxel IEEE Visualization 2008 DTI Visualization Techniques and Applications 10/54

What problems problems does the does the Gaussian Gaussian What model have? model have? No preferred diffusion direction! IEEE Visualization 2008 DTI Visualization Techniques and Applications 11/54 Other models models Other • HARDI - use other models for the probability density function. • We will just talk about the Gaussian model! IEEE Visualization 2008 DTI Visualization Techniques and Applications 12/54

Diffusion Tensor Tensor Imaging Imaging Diffusion Visualization Visualization ⎡ ⎤ D D D ⎢ xx xy xz ⎥ = ⎢ D D D D ⎥ yx yy yz ⎢ ⎥ D D D ⎣ ⎦ zx zy zz IEEE Visualization 2008 DTI Visualization Techniques and Applications 13/54 Diffusion Tensor Tensor Imaging Imaging Diffusion Visualization Visualization D D D xx xy xz D D D yx yy yz ⎡ ⎤ D D D xx xy xz ⎢ ⎥ = D D D D ⎢ ⎥ D D D yx yy yz zy zx zz ⎢ ⎥ D D D ⎣ ⎦ zx zy zz IEEE Visualization 2008 DTI Visualization Techniques and Applications 14/54

Main diffusion diffusion directions directions Main r λ Eigenanalysis 1 e 1 D r r λ − = det( ) 0 I D = λ e e i i i I identity matrix Eigenvalues r r λ ≥ λ ≥ λ ≥ λ 0 λ 2 e 3 e 1 2 3 2 3 Eigenvectors r r r , , e e e 1 2 3 IEEE Visualization 2008 DTI Visualization Techniques and Applications 15/54 DTI Visualization Anisotropy Indices Glyphs Fiber Tracking IEEE Visualization 2008 DTI Visualization Techniques and Applications 16/54

Anisotropy indices Anisotropy indices Index that indicates anisotropy • Fractional Anisotropy λ − λ + λ − λ + λ − λ 2 2 2 ( ) ( ) ( ) 2 = 1 2 2 3 1 3 FA λ + λ + λ 2 2 2 2 1 2 3 FA IEEE Visualization 2008 DTI Visualization Techniques and Applications 17/54 Geometric Diffusion Diffusion Measures Measures Geometric λ ≈ λ ≈ λ Isotropy: 1 2 3 λ 3 = 3 C λ + λ + λ s 1 2 3 Anisotropy: λ >> λ ≈ λ Linear 1 2 3 λ − λ = 1 2 C λ + λ + λ l 1 2 3 λ ≈ λ >> λ Planar 1 2 3 + + = λ − λ 1 C C C 2 ( ) = 2 3 s l p C [Westin et al. 97] λ + λ + λ p 1 2 3 IEEE Visualization 2008 DTI Visualization Techniques and Applications 18/54

Volume Rendering Volume Rendering [Kindlmann et al. 00] Scalar (e.g., Anisotropy index) Image from [Vilanova et al. 04] IEEE Visualization 2008 DTI Visualization Techniques and Applications 19/54 Anisotropy Indices Anisotropy Indices There are much more anisotropy indices: Relative anisotropy (RA), Mean diffusion, etc. Pros and Cons � “Easy” to visualize � Simplification 6D � 1D IEEE Visualization 2008 DTI Visualization Techniques and Applications 20/54

Glyphs/Icons Glyphs/Icons Ellipsoids Cuboids Superquadrics [Kindlmann et al. 04] IEEE Visualization 2008 DTI Visualization Techniques and Applications 21/54 Glyps/Icons /Icons Glyps Pros and Cons � Shows 6D information � Local information � Cluttering extended to 3D image from [Kondratieva et al. 05] wwwcg.in.tum.de IEEE Visualization 2008 DTI Visualization Techniques and Applications 22/54

Color Coding of the Main Diffusion Color Coding of the Main Diffusion Direction Direction r = map to ( , , ) ( , , ) e x y z R G B 1 Pros and Cons � Shows directional information � Simple to implement � Simplification 6D � 3D � Difficult to extract fiber information IEEE Visualization 2008 DTI Visualization Techniques and Applications 23/54 Fiber Tracking Fiber Tracking Streamline tracing Streamline tracing Streamline tracing = ∫ r ( ) ( ( )) ( ) p s e p s ds p s path with parameter s 1 Integration scheme • Euler Forward ( ) p s • Runge Kutta • etc. IEEE Visualization 2008 DTI Visualization Techniques and Applications 24/54

Fiber Tracking Fiber Tracking Streamline Tracing Streamline Tracing Pros and Cons � Analogy with fibers � Shows global information � Simplification 6D � 3D � Problems with Crossing � Seeding – Region of Interest � Cluttering IEEE Visualization 2008 DTI Visualization Techniques and Applications 25/54 Tracing Glyphs Tracing Glyphs Video from [Kondratieva et al. 05] wwwcg.in.tum.de IEEE Visualization 2008 DTI Visualization Techniques and Applications 26/54

Other Fiber Tracking Other Fiber Tracking Techniques Techniques Pros and Cons � Analogy with fibers � Shows global information � Seeding – Initial and end � Computational cost � Cluttering [N.Wotawa et al. 05] [L. O’Donnell et al. 02] IEEE Visualization 2008 DTI Visualization Techniques and Applications 27/54 Applications Applications Understanding • Brain Development • Brain Injuries • Ischemic heart • ... Diagnosis • Epilepsy • Multiple Sclerosis • ... Treatment • Tumor resection • ... [Vilanova et al. 04] IEEE Visualization 2008 DTI Visualization Techniques and Applications 28/54

DTI in the newborn newborn brain brain DTI in the • DTI can reveal detailed anatomy of white matter development. • Characterization of normal axonal growth of the white matter tracts. • Understanding the extensive inhomogeneity of white matter injuries (e.g., hypoxic- ischemic regions) • Reference standards for diagnostic radiology of premature newborns. • Early detection can improve treatment IEEE Visualization 2008 DTI Visualization Techniques and Applications 29/54 Human brain developmentn developmentn Human brain Picture from Prentice Hall - cwx.prenticehall.com Brain myelination starts with 30 weeks of conception and it is not completed until the age 20-30 IEEE Visualization 2008 DTI Visualization Techniques and Applications 30/54