Post on 21-Jul-2015
G R O U P - W I S E A N A LY S I S O N M Y E L I N AT I O N P R O F I L E S O F C E R E B R A L C O R T E X U S I N G T H E S E C O N D E I G E N V E C T O R O F L A P L A C E - B E LT R A M I O P E R AT O R
S E U N G - G O O K I M , J O H A N N E S S T E L Z E R , P I E R R E - L O U I S B A Z I N
A D R I A N V I E H W E G E R , T H O M A S K N Ö S C H E
ISBI 2014, 1st of May, Beijing, China
O V E R V I E W
• Aim: Intersubject correspondence for group-wise analysis on myelination profiles from the high-field MRI
O V E R V I E W
• Aim: Intersubject correspondence for group-wise analysis on myelination profiles from the high-field MRI
• Method: Parametrization using the second Laplace-Beltrami eigenvector
O V E R V I E W
• Aim: Intersubject correspondence for group-wise analysis on myelination profiles from the high-field MRI
• Method: Parametrization using the second Laplace-Beltrami eigenvector
• Application: Statistical inference using random field theory on Heschl’s gyrus in auditory cortex
M Y E L I N AT I O N P R O F I L E A N D I N - V I V O I M A G I N G
I N T R O D U C T I O N & M O T I VA T I O N
Beck (1928) G M
W M
M Y E L O A R C H I T E C T U R E O F C O R T E X
Nieuwenhuys (2013) Ed. Geyer & Turner
(cc) Quasar Jarosz
Vogt (1903)C Y T O - M Y E L O -
Beck (1928) G M
W M
M Y E L O A R C H I T E C T U R E O F C O R T E X
Nieuwenhuys (2013) Ed. Geyer & Turner
(cc) Quasar Jarosz
Vogt (1903)C Y T O - M Y E L O -
Beck (1928) G M
W M
M Y E L O A R C H I T E C T U R E O F C O R T E X
Nieuwenhuys (2013) Ed. Geyer & Turner
(cc) Quasar Jarosz
Hopf (1954)
Vogt (1903)C Y T O - M Y E L O -
Beck (1928) G M
W M
M Y E L O A R C H I T E C T U R E O F C O R T E X
Nieuwenhuys (2013) Ed. Geyer & Turner
(cc) Quasar Jarosz
Hopf (1954)
I N - V I V O I M A G I N G O F I N T R A C O R T I C A L M Y E L O A R C H I T E C T U R E U S I N G 7 T M R I
• Quantitative T1 mapping (qT1)
• T1 inversely correlates with myelination
• Myelin is the main contribution to the T1 contrast [1]
Geyer et al. (2011) Front Hum Neurosci
ex-vivo
in-vivo
[1] Eickhoff et al. (2005) Hum Brain Mapp
W H O L E B R A I N R E G I S T R AT I O N ?
• Not yet fully developed for high-field MRIs
• Signal loss in ventral regions
• Different image contrast (quantitative T1 mapping)
• Dimensionality from sub-mm resolution
M O T I VAT I O N : C O R R E S P O N D E N C E
• To construct correspondence between myelination profiles in order to infer group-wise differences
• Circumventing whole-brain registration issues
• More precise than averaging within a ROI
M O T I VAT I O N : C O R R E S P O N D E N C E
• To construct correspondence between myelination profiles in order to infer group-wise differences
• Circumventing whole-brain registration issues
• More precise than averaging within a ROI
• Parametrization using the second Laplace-Beltrami eigenvector
Lévy (2006) SMI
T H E S E C O N D L A P L A C E - B E LT R A M I E I G E N V E C T O R• Monotonous increase along the longest
geodesic distance
T H E S E C O N D L A P L A C E - B E LT R A M I E I G E N V E C T O R• Monotonous increase along the longest
geodesic distance
• Used to construct medial axes & Reeb graph for arbitrarily shaped structures
Seo et al. (2011) SPIE
Shi et al. (2008) MICCAIShi et al. (2008) IEEE CVPR
Reuter et al. (2009) CAD
A P P L I C AT I O N : H E S C H L’ S G Y R U S ( H G )A I L P
Wallace et al. (2002) Exp Brain Res
A I
L PS TA
S U B J E C T S & I N - V I V O I M A G I N G
• Six healthy participants: all male, age=25 ± 2 y.o.
• MP2RAGE (magnetization-prepared rapid gradient echo with two inversion times) at 0.7 mm isovoxel using a 7 T scanner (Siemens)
Marques et al. (2010) NeuroImage
qT1T1w
R E A L I S T I C C O R T I C A L L AY E R I N G [ 1 ]
http://www.cbs.mpg.de/institute/software/cbs-hrt [1] Waehnert et al. (2013) NeuroImage
T H E S E C O N D L A P L A C E -B E LT R A M I E I G E N V E C T O R
PA R A M E T E R I Z A T I O N & I N F E R E N C E
• Laplace-Beltrami (LB) operator 𝚫 of function 𝒇 defined on an
arbitrary manifold is given by:
L A P L A C E - B E LT R A M I E I G E N V E C T O R S
D f := div(grad f )M 2 R2 ⇢ R3
• To find eigenvector Ѱj and eigenvalue 𝝀j of LB, solve: 0 = l0 < l1 l2 · · ·
y0,y1,y2 · · ·
• Laplace-Beltrami (LB) operator 𝚫 of function 𝒇 defined on an
arbitrary manifold is given by:
L A P L A C E - B E LT R A M I E I G E N V E C T O R S
D f := div(grad f )M 2 R2 ⇢ R3
Dy j = l jy j
• To find eigenvector Ѱj and eigenvalue 𝝀j of LB, solve: 0 = l0 < l1 l2 · · ·
y0,y1,y2 · · ·
• Laplace-Beltrami (LB) operator 𝚫 of function 𝒇 defined on an
arbitrary manifold is given by:
L A P L A C E - B E LT R A M I E I G E N V E C T O R S
D f := div(grad f )
[1] Qui et al., (2006) TMI; [2] Aubry et al. (2011) ICCV
CY = lAY C Cotagent matrixA Mass matrix
• Discretization of LB using FEM, then the eigenvectors can be computed from generalized eigenvalue problem [1,2]:
M 2 R2 ⇢ R3
Dy j = l jy j
• To find eigenvector Ѱj and eigenvalue 𝝀j of LB, solve: 0 = l0 < l1 l2 · · ·
y0,y1,y2 · · ·
• Laplace-Beltrami (LB) operator 𝚫 of function 𝒇 defined on an
arbitrary manifold is given by:
L A P L A C E - B E LT R A M I E I G E N V E C T O R S
D f := div(grad f )
[1] Qui et al., (2006) TMI; [2] Aubry et al. (2011) ICCV
CY = lAY C Cotagent matrixA Mass matrix
• Discretization of LB using FEM, then the eigenvectors can be computed from generalized eigenvalue problem [1,2]:
http://www.di.ens.fr/~aubry/wks.html
*smoothed for visualization
M 2 R2 ⇢ R3
Dy j = l jy j
AV E R A G E D M Y E L I N I M A G E SLeft Right
1st
2nd
2315
2827
Cor
tical
dep
th
AL PM
0
0.5
1 2435
2773
Cor
tical
dep
th
AL PM
0
0.5
1
2493
2762
Cor
tical
dep
th
AL PM
0
0.5
1
2543
2833C
ortic
al d
epth
AL PM
0
0.5
1
T1 (ms)
AV E R A G E D M Y E L I N I M A G E SLeft Right
1st
2nd
2315
2827
Cor
tical
dep
th
AL PM
0
0.5
1 2435
2773
Cor
tical
dep
th
AL PM
0
0.5
1
2493
2762
Cor
tical
dep
th
AL PM
0
0.5
1
2543
2833C
ortic
al d
epth
AL PM
0
0.5
1
T1 (ms)
S TAT I S T I C A L I N F E R E N C E
dIhemi = Ileft � Iright dIorder
= I1st
� I2nd
• Paired differences matching order or hemisphere
S TAT I S T I C A L I N F E R E N C E
dIhemi = Ileft � Iright dIorder
= I1st
� I2nd
dIorder
= b0
+ edIhemi = b0 + e
• Paired t-test (left vs. right; 1st vs. 2nd)
• Paired differences matching order or hemisphere
S TAT I S T I C A L I N F E R E N C E
dIhemi = Ileft � Iright dIorder
= I1st
� I2nd
dIorder
= b0
+ edIhemi = b0 + e
• Paired t-test (left vs. right; 1st vs. 2nd)
• Paired differences matching order or hemisphere
• Paired t-test covarying the other variables & interaction
dIhemi = b0
+b1
⇥order+ e dIorder
= b0 +b1 ⇥hemi+ e
S TAT I S T I C A L I N F E R E N C E
dIhemi = Ileft � Iright dIorder
= I1st
� I2nd
dIorder
= b0
+ edIhemi = b0 + e
• Paired t-test (left vs. right; 1st vs. 2nd)
• Paired differences matching order or hemisphere
• Paired t-test covarying the other variables & interaction
dIhemi = b0
+b1
⇥order+ e dIorder
= b0 +b1 ⇥hemi+ e
http://www.math.mcgill.ca/keith/surfstat/Worsely et al. (2009) NeuroImage
• RFT for multiple comparisons correction; FWHM= 2 pixels
Left - RightL-R controlling
orderEffect of order
in L-R diff
1st - 2nd1st-2nd covarying
hemisphere Effect of hemi in 1st-2nd diff
R E S U LT
• Greater T1 in the left HG (Higher myelin in the right HG)
[1] Warrier et al., 2009, J Neurosci
R E S U LT
• Greater T1 in the left HG (Higher myelin in the right HG)
• Lateralization of HG?
• Structural difference of HG between hemispheres and specialized sensitivity to temporal/spectral information [1]
[1] Warrier et al., 2009, J Neurosci
R E S U LT
• Greater T1 in the left HG (Higher myelin in the right HG)
• Lateralization of HG?
• Structural difference of HG between hemispheres and specialized sensitivity to temporal/spectral information [1]
• The application is for demonstration of inter-structure comparison of myelination profiles
[1] Warrier et al., 2009, J Neurosci
F U R T H E R A P P L I C AT I O N S
5 10 15 200
20
40
60
` in
x−c
oord
inat
e
Order of eigenvector
5 10 15 200
2
4
6
8
` in
y−c
oord
inat
e
Order of eigenvector5 10 15 20
0
5
10
15
` in
z−c
oord
inat
e
Order of eigenvector
data1data2data3data4data5data6
Y (p) = q(p)+ e(p),
q(p) =k
Âi=0
b jy jb̂ = (y 0y)�1y 0Y
[1] Kim et al. (2012) MMBIA
• Other regions: primary somatosensory/motor areas
• Shape descriptor for group differentiation (e.g. musicians): Fourier coefficients [1] or the eigenvalues of LB operator