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**Optimal acquisition schemes for high angular resolution diffusion imaging**

Master thesis by H.C Achterberg Supervised by V. Prčkovska and A. Vilanova In collaboration with A.F. Roebroeck and W.L.P.M. Pullens

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**Introduction Fibers elongated cells or threadlike structures**

Important information of tissues Cannot be imaged directly Image indirect via diffusion - Can be imaged directly, but not non-invasive / BioMedical Image Analysis

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**Diffusion Result of random thermal motion**

Described by probability density function Full PDF: P(r,t) Gaussian PDF Partial PDF: P(R0,u) Measure diffusion Use a specific MRI method Describe different PDF’s briefly / BioMedical Image Analysis

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**Diffusion Weighted MRI**

RF Gslice Gphase Gdiff Gread Signal 90° 180° δ Δ two diffusion encoding gradients b is a combination of new parameters Signal is complex Measures diffusion in one direction Only magnitude is used q Mention delta’s Effective diffusion time - b-value / BioMedical Image Analysis

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**Gradient Sampling Gradient only in one direction Amount of gradients**

Multiple acquisitions Amount of gradients Clinically feasible Evenly spaced Static repulsion Zero gradients Gradients Zero gradients 25 3 37 4 49 5 61 6 73 7 97 9 121 11 / BioMedical Image Analysis

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**Diffusion reconstruction methods**

Diffusion Spectrum Imaging High Angular Resolution Diffusion Imaging Diffusion Tensor Imaging Full PDF Multiple fibers per voxel 200+ directions 15-60 min b: up to 8000 Partial PDF or ODF Multiple fibers per voxel 25-121directions 5-20 min b: between 1000 and 4000 Gaussian PDF Only 1 fiber per voxel 6+ directions 3-6 minutes b: between 1000 and 1500 / BioMedical Image Analysis

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Goal Determine which parameters are optimal for a high angular resolution diffusion imaging acquisition / BioMedical Image Analysis

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**Simulation: Multi-tensor**

Overview Acquisition Reconstruction Maxima detection Validation DW-MRI scan Phantom In-vivo Q-ball (ODF) Numerical Angular Error DOT (PDF) Analytical Simulation: Multi-tensor Söderman DOT ODF DOT mODF b-value gradients SH order regularization Tessellation order Parameters / BioMedical Image Analysis

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**Simulation data Multi-tensor model Södermans Model**

Models signal as rank-2 tensor Models signal Quick to compute Parameters fixed λ1,λ2,λ3, varying: b, gradients, angle Models restricted diffusion Models physical process Slow to compute Parameters fixed D0, ρ, L varying: b, gradients, angle / BioMedical Image Analysis

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**Rician Noise DW-MRI uses magnitude of complex signal**

Gaussian noise on real and complex part Results in Rician noise Rician noise is not additive noise Signal dependant / BioMedical Image Analysis

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**Simulation: Multi-tensor**

Overview Acquisition Reconstruction Maxima detection Validation DW-MRI scan Phantom In-vivo Q-ball (ODF) Numerical Angular Error DOT (PDF) Analytical Simulation: Multi-tensor Söderman DOT ODF DOT mODF b-value gradients SH order regularization Tessellation order Parameters / BioMedical Image Analysis

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**How to represent the data?**

Show the values on a sphere Deforms the sphere Shows orientation better Not iso-surfaces / BioMedical Image Analysis

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**How to represent the data?**

Show the values on a sphere Deforms the sphere Shows orientation better Not iso-surfaces / BioMedical Image Analysis

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**About the PDF and ODF Probability Density Function (PDF)**

Orientation Distribution Function (ODF) Probability in 3D space Micro-scale properties of tissue Probability on a sphere Radial integral of PDF Only orientational properties of tissue / BioMedical Image Analysis

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**Spherical Harmonics Function on sphere Ortho-normal basis**

Comparable to Fourier series on a sphere SH have an order Order dictates detail / BioMedical Image Analysis

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**Q-ball and DOT Q-ball Imaging Diffusion Orientation Transform**

No signal decay assumption Maps signal to ODF No extra parameters Uses real SH basis Find SH coefficients via Least Squares Fit Assumes mono-exponential decay Maps apparent diffusion coefficients to probability PDF at radius R0 Uses complex SH basis Finds SH coefficients via integral / BioMedical Image Analysis

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**DOT derived methods DOT ODF DOT marginal ODF Implemented numerical**

Inspired by Q-ball DOT marginal ODF Inspired by Diffusion Spectrum Imaging Implemented numerical Compute number of shells and average Still need number of R0’s DOT ODF and Q-ball can be compared in a fairer way, since they are both ODF’s / BioMedical Image Analysis

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**DOT ODF analytical Solved radial integral analytical Similar to Q-ball**

Factors for SH coefficients Eliminate R0 completely / BioMedical Image Analysis

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**Validation and speed comparison**

Validated that DOT ODF approximates true ODF Artificial signal Compare with ground truth ODF Speed comparison Test computation time per method The validation uses an Euclidian error The speed test is in seconds and done on a 128x128 slice / BioMedical Image Analysis

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**Simulation: Multi-tensor**

Overview Acquisition Reconstruction Maxima detection Validation DW-MRI scan Phantom In-vivo Q-ball (ODF) Numerical Angular Error DOT (PDF) Analytical Simulation: Multi-tensor Söderman DOT ODF DOT mODF b-value gradients SH order regularization Tessellation order Parameters / BioMedical Image Analysis

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**Maxima detection Reconstruct ODF/PDF Set threshold**

Define isolated regions Find local maxima in region Analytical Alternatives / BioMedical Image Analysis

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**Simulation: Multi-tensor**

Overview Acquisition Reconstruction Maxima detection Validation DW-MRI scan Phantom In-vivo Q-ball (ODF) Numerical Angular Error DOT (PDF) Analytical Simulation: Multi-tensor Söderman DOT ODF DOT mODF b-value gradients SH order regularization Tessellation order Parameters / BioMedical Image Analysis

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**Angular Error and Tolerance**

Discrete sampling Small errors Depending on orientation Use tolerance to compensate / BioMedical Image Analysis

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**Noiseless results: simulation models**

The multi-tensor model has fatter glyphs, except for DOT\ This might be due to the fact that DOT and MT both assume a mono-exponential signal / BioMedical Image Analysis

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**Noiseless results: gradient directions**

If gradients increase Mean error indifferent Standard deviation decreases / BioMedical Image Analysis

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**Noiseless results: b-value**

Response differs per method DOT ODF and Q-ball dependant on angle DOT slightly dependant on angle DOT marginal ODF independent of angle / BioMedical Image Analysis

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**Noise added results: SH order**

Crossing angle 90 degrees Crossing angle 45 degrees / BioMedical Image Analysis

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**Noise added results: gradient directions**

/ BioMedical Image Analysis

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**Noise added results: b-values**

Optimal b-value depends on SNR SNR depends on imaging equipment Create lookup table Mention what is x-bar, s and p / BioMedical Image Analysis

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**Phantom Created by Pim Pullens Clinically feasible phantom**

Three angles: 30, 50 and 65 / BioMedical Image Analysis

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**Phantom results Averaged over 4 voxels Needs manual registration**

/ BioMedical Image Analysis

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**Human data Centrum semioval Challenging region Crossing region**

/ BioMedical Image Analysis

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Human data results The rest of the human data was used in a similar qualitative way / BioMedical Image Analysis

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Conclusion Optimal acquisition and reconstruction parameters depend on measured structures The smaller the crossing, the higher SH order required 90 degrees needs 4th order, 60 degrees needs 6th order and 45 degrees needs 8th order Number of gradients mostly influences robustness The improvement are minimal after 97 gradient directions Optimal b-value dependant on scanning equipment We create tables to help determine the optimal b-value / BioMedical Image Analysis

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**Discussion Phantom need for verification**

Only simulation data was quantitative Maxima detection can be improved No single optimal set of parameters Show how to create an optimal scheme / BioMedical Image Analysis

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