Computational Methods in NeuroImage Analysis!

Transcription

1 Computational Methods in NeuroImage Analysis! Instructor: Moo K. Chung" Lecture 8" Geometric computation" October 29, 2010"

2 NOTICE! Final Exam: December 3 9:00-12:00am (35%)" Topics: Covers everything discussed in lectures" (lecture notes + required reading)" Open book exam: you can bring laptops, calculators, books or even your puppy." Previous exam in the directory /exam/"

3 NOTICE! Oral presentation (15%)" December 10 9:00-12:00am. " Each student will present 20min." Final report submission (40%)" Deadline: December 17 9:00am." 10% penalty/day after 9:00am. " Sample final reports in the directory /projects"

4 3D images to! surface models"

5 Computed Tomograpy (CT) scanner " 3D image"

6 Binary segmentation" 3D image" 70 subject models "

7 Topological defects" Automatic topological correction" using the Euler characteristic method "

8 Holes and handles in teeth regions need to be fixed for subsequent image processing and analysis."

9 Additional morphological closing operation was done to patch up the space that was occupied by teeth. Without this morphological operation, the final statistical result will be highly biased in teeth regions."

10 Limbic system associated with longterm memory and spatial navigation"

11 3D image" 3.0 Tesla GE Scanner"

12 Manual hippocampus segmentation on MRI template"

13 Each subject has different brain shape. So how do we compare across subjects?" Group comparison?" Group 1" Group 2"

14 Voxel by voxel comparison causes anatomical mismatching. "

15 Deformable template framework".... " Subject 1" Subject 2" Subject 3" Subject 122" Subject 123" Subject 124" deformation field" template" MRIs will be warped into a template and anatomical differences can be compared at a common reference frame."

16 Image registration" Deformation from the template to a subject." sample size = 124 subjects"

17 Left hippocampus surface template " Deformation field" of warping the template" to a subject"

18 MATLAB demonstration"

19 Basis functions! on surface"

20 How to compute basis in an arbitrary domain" Steady-state oscillations in wave equation" Helmholtz equation" Basis functions in the" L-shaped membrane"

21 Orthonormal basis" f = λf

22 Finite Element Method"

23 Finite Element Method (FEM) " A C f = λf Cψ = λaψ

24 Amygdala spectrum" Generalized eigenvalue problem" discretization" PhD thesis (2001), ISBI (2004) Qiu et al. (2005, IEEE TMI)"

25 Amygdala" Weyl s formula" Eigenvalues can t discriminate similarly shaped objects." Eigenvalue vs. degree of basis" Red: autism" Gray: control"

26 Finite Element Method (FEM) " Let s see chapter 4.6 "

27 Limitation: Computational bottleneck" Challenge: Solve the above matrix equation for extremely large matrices." Implicitly Restarted Arnoldi method "

28 First 10 orthonormal basis on left hippocampus" Basis functions will be used to construct a smoothing kernel."

29 Limitation: No common coordinate system" There is no common extrinsic coordinate system for every manifolds." D Arcy Thompson " Need an extrinsic approach for local shape comparison:" deformable modeling"

30 How to match surfaces intrinsically" Landmarks: Identify min and maximum of eigenfunctions" Develop thin-plate spline with landmarks. "

31 MATLAB demonstration"

32 Data smoothing! on surface models"

33 Persistence homology based signal detection" Euler characteristic, Betti numbers, Morse functions, Worsley s random field theory.! cortical thickness" Topological classification 96% " Previous method 90%" cortical flattening" Persistence diagram"

34 Heat kernel smoothing on surface" Heat kernel:" K t (p, q) = K t f = i=0 M e λ it ψ i (p)ψ i (q) K t (p, q)f(q) dq X-coordinate on " mandible surface" smoothed with bandwidth 10" and 1269 eigenfunctions"

35 Heat kernel smoothing of hippocampus"

36 Heat kernel smoothing on mandible shape" Heat kernel smoothing (Seo et al., 2010 MICCAI)" Iternated kernel smoothing (Chung et al., 2005 NeuroImage)"

37 MATLAB demonstration"

38 Statistical Analysis"

39 2 nd eigenfunction of elongated objects" Hot spot conjecture:" Min and max always occur at the extreme end points"

40 Center of isocontour circles"

41 70 subjects"

42 MATLAB demonstration"

43 Elongation of mandible (length increase)" mm" age"

44 Elongation of mandible (angle decrease)" angle" age"

45 Growth projectory" children" We are becoming more as we gets older." Need more data to differentiate gender specific growth difference." adults"

46 Left hippocampus surface template " Total number of subjects 124! High income family 86 = 24 males + 62 females" Average age = 140 +/- 45 months = 12+/- 4 years old! Low income family 38 = 13 males + 25 females" Average Age= 137 +/- 45 months = 12 +/- 4 years old! Balanced study design except there is no info on handness.! Each subject has multiple MRI scans (1-2 scans).!

47 ()*+,#-)% 0)12/*#32$%12/*%-4)%-)*+,#-)%-2%!"#$'%56%758)$%9:%.#/+&%;%.#/+'<%

48 B5A)?%)M)"-%*2?),%#""2>$3$7%-/)#3$7%*>,3+,)% 6"#$6%.5-45$%#%6>9N)"-%#6%5$?)+?)$)$-%?56+,#")*)$-%C%#7)%;%7)$?)/%;%7/2>+%;%#7)O7/2>+% *#A%B%C%'D<E% "2//)"-)?%+8#,>)%F%G<GG&% 5-%5$H#-)6%6-#363"#,%657$5I"#$")% 056+,#")*)$-% K**L%!"#$%&'"(()*+,(-.& J7)%K*2$-46L%

49 =5$)#/%*5A)?%)M)"-%*2?),%#""2>$3$7%12/%5$-)/P "2//),#32$%21%*>,3+,)%6"#$6%.5-45$%#%6>9N)"-%?56+,#")*)$-%C%#7)%;%7)$?)/%;%7/2>+%;%#7)O7/2>+% *5$%-%C%PQ<QQRST%% "2//)"-)?%+8#,>)%C%G<G'D%

50 U574-%45++2"#*+>6% *#A%-%C%Q<GDQ&% "2//)"-)?%+8#,>)%C%G<GD%

51 =5$)#/%*5A)?%)M)"-%*2?),%2$%,)W%45++2"#*+>6%?56+,#")*)$-%C%#7)%;%7)$?)/%;%7/2>+%;%#7)O7/2>+% *5$%-%C%%P&<RDSRT%% "2//)"-)?%+8#,>)%V%G<E% /01&'"(()*+,(-.&

52 !>**#/:% B#*5,:%5$"2*)%,)8),%56%4574,:%"2//),#-)?%.5-4% 45++2"#*+>6%7/2.-4<% J?8)/6)%)$85/2$*)$-T%6-/)66% %!%45++2"#*+>6%!%*)*2/:%,266%

53 =)"->/)%R% X/#5$%Y)-.2/Z%[2?),5$7%

54 MATLAB demonstration"