Quantitative Susceptibility Mapping and Susceptibility Tensor Imaging. Magnetization and Susceptibility

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1 Quantitative Susceptibility Mapping and Susceptibility Tensor Imaging 1, Chunlei Liu, Ph.D. 1 Brain Imaging and Analysis Center Department of Radiology Duke University, Durham, NC, USA 1 Magnetization and Susceptibility B =μ H magnetization m susceptibility = χh m δb B= B + δb B is perturbed by local magnetization induced by susceptibility

2 Superposition of Field Perturbation δb Paramagnetic: χ > m B Diamagnetic: χ < 3 Voxel Effect of Field Inhomogeneity δ f γ = δ B π R = π FWHM = γ ΔB Full Width at Half Maximum FWHM (Hz) or ΔB (Tesla) Frequency 4

3 Multi-Echo Gradient Echo Images RF α Echo 1 Echo Echo n α 5 Magnitude: T* Decay St () Se tt tt = e = Se tt * * = + OR R T T T = R + R * 6

4 R* Mapping and Contrast T* 5 ms R* 4 Hz White matter Blood vessels Globus pallidus Red nucleus Substatia nigra 7 What Is in the Phase? Sources of phase Phase wraps Receiver coil Objects outside the FOV Objects inside the FOV background background tissue 8

5 Sphere mean value property = Harmonic function θ b θ = θ + θ tissue b Mean phase over a sphere S = S θ = θ b b Phase at the center θ S θ = θ S θ = ( δ S) θ tissue tissue tissue Summary of Phase Processing Raw Phase Unwrapped Phase Filtered Phase 1

6 Mapping Apparent Magnetic Susceptibility Convolution θ () r = π δ f () r TE 1 k { ()} ( z γ FT δ f r = ) χ( k) B 3 k π 11 Difficulty: Magic Angle Effect kz = k z 1 γ FT { δ f () r } = ( ) χ( k) B 3 k π ky kx Deconvolution 1

7 Quantitative Susceptibility Mapping (QSM) Filter Background Phase Solve Inverse Problem Raw Phase Unwrapped Phase Tissue Phase Susceptibility (ppm) Phase of one voxel is affected by all surrounding voxels Susceptibility is an intrinsic property of a voxel Sources of Susceptibility in Tissue Endogenous (ppm cm 3 mol -1 ; cgs) H O O Fe Ca Ca + - Na Na ,449 Ferro +4 < +16 < Exogenous (ppm cm 3 mol -1 ; cgs) Gd Gd-DTPA FeO Mn MnCl +185, +7,93 +7, ,35 14

8 Myelin Dominates Gray/White Contrast CTRL FA Susceptibility Shiverer (no myelin) FA Susceptibility C. Liu, et al, NeuroImage 11; 56: Magnetic Susceptibility is Anisotropic Susceptibility at Orientation # B Magnetic susceptibility is orientation dependent C. Liu, MRM 1; 63:

9 Relate Susceptibility Tensor to MR Signal Magnetic flux density seen by a spin B = μ (1 σ + A χ)( H + h) H Susceptibility inclusion B h Susceptibility tensor 3x3 Applied field vector Demagnetizing field vector Find the Demagnetizing Field B = μ (1 + χ)( H + h) H B = H ( χ) + h= h? { } T 1 k FT χ H k h= FT k

10 Off-Resonance Field and Phase Image In the laboratory frame of reference { } 1 FT μft T k χ H A FT {} ΔB = χ H k k {} ˆ 1 ˆ {} ˆ ˆ FT θ μ FT T A FT T k χ H = H χ H H k γht k Susceptibility tensor is symmetric 6 unknowns Susceptibility Tensor Imaging χ =

11 Color-Coded Principal Susceptibility cc hc cc ac cg ac ac ac y z x C. Liu, et al, NeuroImage 1; 59: Magnetic Susceptibility Anisotropy in the Human Brain W. Li, et al, NeuroImage 11; 55:

12 Quantifying Iron Deposition GP CI Pu SCC GP SS IC Th ppm.1. Iron Content (μg Fe/gww) Reference (AAS) Reference (ICP) Reference (Colorimetry) RN PU SN GP Susceptibility (.1 ppm) B. Wu, et al, MRM 1; 67: Susceptibility Tensor Imaging and Tractography Anterior Commissure Hipocampal Commissure DTI STI C. Liu, et al, NeuroImage 1; 59: STI in vivo W. Li, et al, NeuroImage 1; 59:

13 Summary Artifacts Contrast Oxygen: Iron: Myelin: BOLD fmri Cortical gray matter and nucleus White matter 5