Technical Improvements in Quantitative Susceptibility Mapping

Transcription

1 Technical Improvements in Quantitative Susceptibility Mapping 1-2 Saifeng Liu 1 School of Biomedical Engineering, McMaster University 2 The Magnetic Resonance Imaging Institute for Biomedical Research April 9 th,

2 Outline Background Theories of Quantitative Susceptibility Mapping (QSM) QSM Data Processing Steps Solving the Inverse Problem: iterative SWIM algorithm Background Field Removal: Local Spherical Mean Value filtering (LSMV) for double-echo phase data processing Improved Venography using true Susceptibility Weighted Imaging (tswi) Improved Susceptibility Quantification of Small Objects using Volume Constraints Applications of QSM Conclusions 2

3 Background Magnetic Susceptibility Magnetic susceptibility is the measure of how materials modify the applied magnetic field. Based on the susceptibilities, materials can be classified into paramagnetic, diamagnetic and ferromagnetic materials. For biological tissues, magnetic susceptibility may be related to concentration of deoxyhemoblogin, iron deposition and calcium etc. The susceptibility effects were utilized by combining phase images with magnitude images in SWI. However, phase information is a function of susceptibility distribution, and is geometry-dependent. 3

4 Motivation B 0 Phase image of a normal volunteer showing dipolar phase around the veins (TE = 19.2msec at 4T) Corresponding susceptibility map showing the vessels. Note that the dipolar phase of the veins is almost completely deconvolved (red arrow) and the vein has uniform signal. 4

5 Air on the g string Gradient echo sequence

6 Magnitude Phase TE=7.8ms TE=20.8ms ρ(r, TE) = mag(r, TE)e iφ(r,te) [1] φ(r, TE) = γδb r TE [2] ΔB r = f(δχ(r)) [3]

7 Theories of QSM Forward process: from Δχ r to φ(r, TE) ΔB z r = μ 0 4π V d 3 r * 3M z r z z 2 r r 5 M z r r r 3+ ΔB r = B 0 G r Δχ r [2] G r = 1 4π 3 cos2 θ 1 r 3 [3] [1] G k = FT,G r - = 1 k z 2 3 k 2 [4] φ r = γδb r TE [5] 7

8 Theories of QSM Inverse process: from φ(r, TE) to Δχ r Δχ r = FT 1 *G 1 (k) FT φ r γb 0 TE + G(k) cannot be directly inverted since G(k)=0 along the magic angles. Solving the inverse problem Regularized k-space division Optimization using a priori information, e.g., gradients in magnitude and phase images B 0 Zero plane of G k 8

9 Solving the inverse problem Thresholded k-space division χ r = FT 1 *G 1 (k) G 1 k = 1 k z 3 k 2 sgn 1 3 k z 2 k 2 1 FT φ r γb 0 TE + 2 k 2 z 3 k 2 1, for 1 2 k z 3 k 2 2 t 3, for > t 2 1 k z 3 k 2 t B 0 B 0 9

10 Solving the inverse problem Δχ r φ r Forward process Δχ r g r B 0 Inverse process Streaking artifacts Δχ r φ r g 1 r φ r B 0 10

11 Solving the inverse problem Optimization using a priori information argmin X W GX ΔB λ prior K-space/image domain iterative algorithm (iterative SWIM) Initial image Thresholded image Updated image Image Domain Fourier Domain (k-space) 11

12 iterative SWIM with multi-level thresholding Δχ initial (r) Δχ i (r) Δχ i (k) Thresholding using χ t Merging Δχ i (r) Δχ i (k) Δχ i,new (k) i=i+1 No Converged? Yes Finished? Yes No χ t Δχ final (r) 12

13 Improved iterative SWIM: 3D brain model result 13

14 QSM data processing steps Phase Unwrapped Phase* Local Phase Susceptibility Map Phase Unwrapping * Background Field Removal Inverse Filtering Magnitude Brain Mask Brain Extraction 14

15 Background field removal Original Phase Image Final Phase Image?

16 Multi-channel phase data combination Step1 Original Corrected Linear Gradient and Baseline Correction Signal cancelation and cusp artifacts

17 Background field removal ΔB = Δφ γb 0 TE = ΔB local + ΔB background = ΔB local geo + ΔB cs + ΔB global geo + ΔB main field Low Spatial Frequency High Spatial Frequency Low spatial frequency Spectrum of Background Field Loss of Information Spectrum of Local Field 17

18 Background field removal Spherical mean value filtering (SMV) B background s = B background B s = B background s + B local s B s = B background + B local s B B s = B local B local s ΔB s δ : SMV filtered field map Variable high-pass filtering (VHP) ΔB s δ SMV filtering with different sizes of s. SHARP (Sophisticated Harmonic Artifact Reduction for Phase data) ΔB s δ = ΔB local s δ ΔB local can be obtained from the SMV filtered field map through deconvolution. 18

19 Comparison of different background field removal algorithms Homodyne HP64 high-pass filter Variable VHP high-pass filter SHARP SHARP PDF PDF HP64 a b c d VHP SHARP PDF e f g h 19

20 Susceptibility /ppm Comparison of different background field removal algorithms HP64 VHP SHARP PDF Veins GP PUT CN SN RN THA 20

21 Background field removal Except for homodyne high-pass filtering, all of these algorithms work on unwrapped phase images. Phase unwrapping is sensitive to noise and could be time-consuming. Original phase image Path-following phase unwrapping result 21

22 Background field removal without phase unwrapping TE1=7.38ms TE2-2TE1= 2.84ms TE2=17.6ms Step1 Original Phase Images a b c Step2 Final Phase Images d e f φ r, TE = γδb r TE [1] φ r, ΔTE = arg *exp i φ r, TE 2 2 φ r, TE 1 + [2]

23 Background Field Removal using LSMV LSMV 3D SNRCP +SHARP Difference φ(te 1 ) φ(te 2 ) χ(te 2 ) 23

24 Background Field Removal using LSMV: dealing with cusp artifact Original phase image Phase unwrapped with 3DSRNCP Phase unwrapped with Laplacian Processed phase images LSMV SHARP SHARP 24

25 QSM data processing steps Phase Unwrapped Phase* Local Phase Susceptibility Map Phase Unwrapping * Background Field Removal Inverse Filtering Magnitude Brain Mask Brain Extraction 25

26 Improved venography using tswi* W W = 1 for χ χ 1 1 χ χ 1 for χ χ 2 χ 1 < χ χ for χ > χ 2 tswi = mag W n χ 1 = 0 χ 2 When χ 1 = 0, χ 2 = 0.45, the optimal n=2 which maximize the CNR between veins and surrounding tissue. 1 χ *Liu S, Mok K, Neelavalli J, Cheng YCN, Tang J, Ye Y, Haacke EM. Improved MR Venography Using Quantitative Susceptibility-Weighted Imaging. J. Magn. Reson. Imaging 2013; Article first published online: 31 OCT 2013 DOI: /jmri

27 Improved venography using tswi Comparison between SWI and tswi Proper visualization of veins in different orientations in tswi Phase image Susceptibility map Phase mask Susceptibility mask SWI tswi mip of SWI mip of tswi 27

28 Improved venography using tswi Comparison between SWI and tswi Better delineation of microbleeds in tswi SWI tswi SWI tswi 28

29 Quantifying the susceptibilities of air bubbles and glass beads Susceptibility map created from the phase at the shortest TE Susceptibility map created from the phase at the longest TE 29

30 Improving the susceptibility quantification of small objects using volume constraints* χ true V true = χ a V a χ a and V a are the measured susceptibility and apparent volume, respectively. The effective magnetic moment is constant. Liu S, Neelavalli J, Cheng Y-CN, Tang J, Haacke EM. Quantitative susceptibility mapping of small objects using volume constraints. Magn. Reson. Med. 2013;69:

31 Improving the susceptibility quantification of small objects using volume constraints Susceptibilities quantified using the original phase images Susceptibilities corrected using the volumes estimated from spin echo magnitude images 31

32 Applications of QSM Visualization of veins, iron deposition and calcifications in the brain a (a)maximum intensity projection: Veins and Iron deposition b (b) Minimum intensity projection: Calcifications 32

33 Applications of QSM Quantification of venous oxygen saturation and cerebral iron deposition Δχ=4π 0.27 Hct 1 Y ppm Δχ 0.45ppm, when Y=70%, Hct=

34 Applications of QSM: TBI Visualization and quantification of cerebral microbleeds 34

35 Applications of QSM: TBI Visualization and quantification of venous oxygen saturation and iron deposition in TBI. 35

36 Applications of QSM Quantitative susceptibility mapping of air, bones, and teeth. By Sagar Buch 36

37 Applications of QSM Quantitative susceptibility mapping of air, bones, and teeth. By Sagar Buch 37

38 Conclusions QSM is an ill-posed inverse problem. The accuracy of QSM is dependent on background field removal. Susceptibility maps can be combined with magnitude images to generate tswi images The accuracy in susceptibility quantification can be further improved using the volume constraint. QSM provides quantitative information related to iron content in tissue and micobleeds as well as critical information about oxygen saturation 38

39 The End. 39