group-wise analysis on myelination profiles of cerebral cortex using the second eigenvector of...

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


• Method: Parametrization using the second Laplace-Beltrami eigenvector

O V E R V I E W


• 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

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

(cc) Quasar Jarosz

Beck (1928) G M

W M


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



(cc) Quasar Jarosz

Vogt (1903)C Y T O - M Y E L O -

Beck (1928) G M

W M



(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

I N T E R S U B J E C T C O R R E S P O N D E N C E

C S F G M W M

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 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

M Y E L I N AT I O N P R O F I L E E S T I M AT I O N

P R E P R O C E S S I N G

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

T1w at 1mm isovoxel

T1w at 1mm isovoxel

qT1 at 0.7 mm isovoxel

T1w at 1mm isovoxel

qT1 at 0.7 mm isovoxel

Regenerated surfaces

M A N U A L D E L I N E AT I O N O F H G

• Duplication/sulcus (10) • Single HG (LH:1, RH:1)

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 ]

[1] Waehnert et al. (2013) NeuroImage

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

http://www.cbs.mpg.de/institute/software/cbs-hrt

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 · · ·




D f := div(grad f )M 2 R2 ⇢ R3

Dy j = l jy j


y0,y1,y2 · · ·




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


y0,y1,y2 · · ·




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

L E V E L S E T S B A S E D O N L B 2

PA R A M E T E R I Z E D M Y E L I N P R O F I L E S

C S F

G M

W M

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



= I1st

� I2nd

dIorder

= b0

+ edIhemi = b0 + e

• Paired t-test (left vs. right; 1st vs. 2nd)




= I1st

� I2nd

dIorder

= b0

+ edIhemi = b0 + e



• Paired t-test covarying the other variables & interaction

dIhemi = b0

+b1

⇥order+ e dIorder

= b0 +b1 ⇥hemi+ e



= I1st

� I2nd

dIorder

= b0

+ edIhemi = b0 + e



• 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


• Lateralization of HG?

• Structural difference of HG between hemispheres and specialized sensitivity to temporal/spectral information [1]


R E S U LT


• 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


F U R T H E R A P P L I C AT I O N S

• Other regions: primary somatosensory/motor areas

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

T h i s w o r k i s f u n d e d b y t h e I n t e r n a t i o n a l M a x P l a n c k R e s e a r c h S c h o o l o n N e u r o s c i e n c e o f C o m m u n i c a t i o n ( I M P R S - N e u r o c o m )

T H A N K Y O U F O R AT T E N T I O N !

© Hans-Joachim Krumnow

group-wise analysis on myelination profiles of cerebral cortex using the second eigenvector of...

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