Diffusion Imaging Models 1: from DTI to HARDI models

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uk @flavioua Diffusion Tensor Imaging (DTI) z λ 1 λ 2

by the Compact Description x λ 3 y three eigenvalues

1 Diffusion Imaging Models 1: from DTI to HARDI models Flavio Dell Acqua, PhD. Diffusion Tensor Imaging (DTI) z λ 1 λ 2 The profile of the Diffusion Ellipsoid is defined only by the Compact Description x λ 3 y three eigenvalues (λ1, λ2, λ3) Oversimplified Description for different eigenvalues λ1 >> λ2 λ3 λ 1 λ2 >> λ3 λ1 λ2 λ3 Axial Anisotropy Planar Anisotropy Isotropy 1

2 Diffusion Tensor Imaging (DTI) Single Fibre Crossing Fibres Real Diffusion DTI Diffusion Tensor Imaging (DTI) Tractography Maps FA False Negative False Positive (Catani, Brain 2007) 2

3 Do we need advanced models? "Not that many crossings in the brain..." anonymous, OHBM 2006 Do we need advanced models? Crossing fibres can be detected in 70% - 90% of WM voxel Behrens et al. Neuroimage 2007 Jeurissen et al. HBM 2013 Dell'Acqua et al. HBM 2013 Number of Fibre Orientations (NuFO) maps Dell'Acqua et al. HBM

4 Crossing is not the only problem... Real Fibres with Diffusion MRI (not only DTI) Kissing??? Crossing Adapted from C. Pierpaoli Beyond DTI... 4

complex signal profiles can be described S = f i Si Crossing fibers

5 High Angular Resolution Diffusion Imaging - HARDI (L.R. Frank 2001) The DW signal is sampled along an uniformly distributed set of directions on a sphere. Fibre Orientation Physical Model MRI Signal Profile HARDI S bd = S 0 e More complex signal profiles can be described S = f i Si Crossing fibers Multi-tensor approach DTI Multi-tensor Multiple fibre orientations can be resolved Tuch et al but Model selection issues Problems for more than 2 fibres Additional constraints required Parke r and Ale xande r 2003 Tuch et al. 2002, Parker and Alexander 2003, Behrens et al 2003, Chen et al

Ball and Stick(s) model 1 Fibre 2 Fibres Medial SLF Fibre Diffusivity 1

diffusion-odf DSI, qball, DOT, GQI, etc. (Tuch et al.

..) fibre-odf Spherical Deconvolution (Tournieret al.

6 Ball and Stick(s) model 1 Fibre 2 Fibres Medial SLF Fibre Diffusivity 1 Fibre 2 Fibres Behrens et al 2003 Hosey et al Behrens et al Kaden et al diffusion-odf & fibre-odf Orientation Distribution Function (ODF) diffusion-odf DSI, qball, DOT, GQI, etc. (Tuch et al. 2004, Wedeen et al 2005; Ozarslan et al. 2006, Descoteaux et al. 2009, etc...) fibre-odf Spherical Deconvolution (Tournieret al. 2004,2007, Alexander 2005, Anderson 2005, Dell'Acqua et al 2007,2010, Kadenet al Jian B. and Vemuri B. 2007, Sakaie 2007, etc... ) Diffusion Propagator model independent model based 6

diffusion ODF vs fibre ODF Diffusion Orientation Distribution

displacement of water molecules (DSI, QBI, DOT, etc.

are sharper because they directly recover underlying fibre

2000, 2005] 3D diffusion propagator P(r,θ,φ) Diffusion ODF

7 diffusion ODF vs fibre ODF Diffusion Orientation Distribution Function (dodf) dodf profiles are directly related to the displacement of water molecules (DSI, QBI, DOT, etc.) Fibre Orientation Distribution Function (fodf) fodf profiles are sharper because they directly recover underlying fibre orientations (Spherical Deconvolution methods) Alexander D (ISMRM 2008) fodf (Courtesy of M. Descoteaux) DSI - Diffusion Spectrum Imaging [Wedeen et al. 2000, 2005] 3D diffusion propagator P(r,θ,φ) Diffusion ODF Ψ(θ,φ) r [Descoteaux et al. 2007, Aganj et al. 2009, Tristan-Vega et al. 2009] Diffusion Signal Fourier Transform Diffusion Propagator Time consuming scan protocols Requires high b-values to get enough angular resolution (b ~ 8000 s/mm 2 ) 7

8 Q-Ball Imaging Q-ball imaging with Funk-Radon Transform (D.S. Tuch2004) u DSI qball Analytical Q-ball Imaging (Hess 2006, Descoteaux 2007) Sharpening - Q-ball (Descoteaux 2009) Spherical Harmonics Funk-Radon Transform dodf R fodf Spherical Deconvolution 8

Regularized and Constrained Spherical Deconvolution Spherical Deconvolution Spherical Harmonics Deconvolution (Tournier et al.

2005/2007) Non Negative Least Square (Jian B. and Vemuri B. 2007) Regularized Spherical deconvolution (Sakaie et al.

9 Spherical Deconvolution Hypothesis : Different fibres can be described by the same signal profile fibre response (H) S S1 S2 H fodf The Fibre Orientation Distribution Function (fodf) can be obtained by deconvolving the HARDI signal with a known Fibre Response. Regularized and Constrained Spherical Deconvolution Spherical Deconvolution Spherical Harmonics Deconvolution (Tournier et al. 2004) FORECAST Deconvolution (Anderson 2005) Maximum Entropy Approach (Alexander 2005) Richardson-Lucy Algorithm (Dell Acqua et al. 2005/2007) Non Negative Least Square (Jian B. and Vemuri B. 2007) Regularized Spherical deconvolution (Sakaie et al. 2007) Parametric Spherical deconvolution (Kaden et al. 2007) Constrained Spherical deconvolution (Tournieret al.2007) Spurious Orientations Negative peaks Noise Variability First methods Later methods Angular Resolution 9

Constrained Spherical Deconvolution - CSD (Tournier et al.

Robust to Noise Unknown Fiber response Robust to PSF/Fiber Response

10 20 50 400 800 iterations 100 Modified Richardson-Lucy Algorithm

Truncation Effect as with Spherical harmonics Global Convergence to

10 Constrained Spherical Deconvolution - CSD (Tournier et al. 2007) 60 dir - b-value = 3000 s/mm 2 The Richardson-Lucy Algorithm (Dell Acqua et al. 2005/2007/2010) Our Problem Richardson-Lucy DW data are noisy Robust to Noise Unknown Fiber response Robust to PSF/Fiber Response errors Fiber Orientations are > 0 Non-negative constraint S f(0) iterations 100 Modified Richardson-Lucy Algorithm [H s] T fi (k +1) = fi (k) [H T Hf i (k ) ] 200 iterations No Truncation Effect as with Spherical harmonics Global Convergence to the NNLS solution Semi-convergence Property (M. Bertero, Astron. Astrophys, 2000) (A.R. De Pierro, IEEE TMI 1987 and IEEE TMI 1993) i 10

11 damped-richardson Lucy SD drl Robust to partial volume contamination from other compartments (Dell Acqua et al. NeuroImage2010) damped-richardson Lucy SD drl Robust to partial volume contamination from other compartments RL drl (Dell Acqua et al. NeuroImage2010) 11

Effects of Model Errors CSD drl CSD drl SNR=30 l = 8 SNR=10

generations of spurious fibers orientations.

12 Effects of Model Errors CSD drl CSD drl SNR=30 l = 8 SNR=10 SNR=20 l = 6 l = 4 - CSD more sensitive to model errors and generations of spurious fibers orientations. - drl robust to model error but can lose angular resolution in low anisotropy voxels Parker et al. Neuroimage 2013 BAD & WRONG Tractography. More fibre orientations to follow More chances to get it wrong! 12

13 Going multi-shell (Jeurissen et al. Neuroimage 2014) Spherical Deconvolution Tractography 60 DW dir, Cardiac Gated, b

Spherical Deconvolution Tractography DTI

14 Spherical Deconvolution Tractography DTI Tractography Spherical Deconvolution Tractography 60 DW dir, Cardiac Gated, b1500 diffusion ODF & fibre ODF Hundreds of options spread across the dodf/fodf spectrum... dodf Deconvolution - Sharpening More Regularisation fodf

15 Different Methods......Different Anatomies Wedeen et al. Science 2012 Krieg 1954, pg Catani, Bodi, Dell'Acqua. Science 2012 Krieg 1954, pg 115 Different Methods......Different Anatomies 15

16 Beyond Crossing Fibres... From Voxel to Tract-Specific Measures: SD as a quantitative index Fibre 2 DTI Fibre 1 The amplitude of each fodf lobe can provide useful tract-specific information about the microstructural diffusion properties of distinct fibre orientations: Hindrance Modulated Orientational Anisotropy - HMOA [Dell Acqua et al. Neuroimage 2010, HBM 2013] Apparent Fibre Density - AFD [Raffelt et al. Neuroimage 2012] Angular Fibre Density AFD, Fibre Spread FS [Riffert et al. Neuroimage 2014] 16

17 SD as a quantitative index Sagittal View - Arcuate Fascicle Dell Acqua et al. HBM 2013 SD as a quantitative index FROM VOXEL TO TRACT-SPECIFIC QUANTITATIVE MEASURES FA HMOA Arcuate Fasciculus and Corticospinal Tract Dell Acqua et al. HBM

Although similar, dodf and fodf have different meanings and fodfs seem to be better for

18 take home messages Complex white matter organizations are not the exception in the brain NuFO We can now resolve crossing well but this is not the only problem for tractography / / Although similar, dodf and fodf have different meanings and fodfs seem to be better for tractography take home messages DSI SD Fibre orientations need to be accurate and reflect the real anatomy. 18

take home messages It s not only about the

and HMOA tract specific measurements are

19 take home messages It s not only about the diffusion model other factors to consider: - SNR - Resolution - Scan Time - Tractography Algorithm Spatial Resolution remains an important limitation of diffusion imaging (1.5 x 1.5 x 1.5 or 2 x 2 x 2 mm vs um... ) Acknowledgments Thank you! Department of Neuroimaging drl-sd, NuFO and HMOA tract specific measurements are all available inside StarTrack matlab toolbox. If interested please contact: 19

20 Suggested Reading Alexander, D. C. (2005). Multiple-fiber reconstruction algorithms for diffusion MRI. Annals of the New York Academy of Sciences, 1064(1), Jones, D. K. (2008). Studying connections in the living human brain with diffusion MRI. Cortex, 44(8), Tournier, J.-D., Mori, S., & Leemans, A. (2011). Diffusion tensor imaging and beyond. Magnetic Resonance in Medicine, 65(6), Dell Acqua F. and Catani M. (2012). Structural human brain networks: hot topics in diffusion tractography. Current Opinion in Neurology, 25(4), Jones, D. K., Kn ösch e, T. R., & T urner, R. (2013). White matter integrity, fiber count, and other fallacies: The do s and don ts of diffusion MRI. NeuroImage, 73(C), Dell'Acqua, F., Simmons, A., Williams, S. C. R., & Catani, M. (2013). Can spherical deconvolution provide more information than fiber orientations?. Human Brain Mapping, 34(10), Jbabdi, S., Sotiropoulos, S. N., Haber, S. N., Van Essen, D. C., & Behrens, T. E. (2015). Measuring macroscopic brain connections in vivo. Nature Neuroscience, 18(11),

Diffusion MRI. Introduction and Modern Methods. John Plass. Department Of Psychology

Diffusion MRI. Introduction and Modern Methods. John Plass. Department Of Psychology Diffusion MRI Introduction and Modern Methods John Plass Department Of Psychology Diffusion MRI Introduction and Modern Methods John Plass Department Of Psychology Overview I. Why use diffusion MRI? II.