Computational Functional Anatomy

Transcription

1 Compuaoal Fucoal Aaomy Aq Qu Dvso of Boegeerg

2 Compuaoal Fucoal Aaomy CFA s he mahemacal sudy of aaomcal cofguraos ad sgals assocaed wh aaomy ad fucos aaomcal coordaes. ulmodal Images MRI DTI fmri 5 Sascal Aalyss shape AD hcess SCZ Poseror STG reoopc mappg Aeror 2 Segmeao 3 LDDMM Shape Aalyss 4 Fucos Aaomy volume surface

3 Large Deformao Dffeomorphc Merc Mappg LDDMM I I Sac LDDMM Qu, A. e. al. NeuroImage, specal ssue

4 Tracg Growh, Arophy, Dyamc Moo Growh Arophy Dyamc Moo ew bor 6 mohs 2 mohs

5 Tme Sequece Large Deformao Dffeomorphc Merc Mappg TS-LDDMM I I 2 I I Dyamc LDDMM Qu, A. e. al. NeuroImage, specal ssue

6 Tme Sequece Large Deformao Dffeomorphc Merc Mappg TS-LDDMM I v I I & v, d J v Equvalely, J m where m V : v arg m v : & v m : &, d arg m, I d,, ermed as momeum, s defed by he erel m V V m, d v v 2 V argm v < d + m V E, I, a lear rasformao of m > 2 d + E I v., I d, Qu, A. e. al. NeuroImage, specal ssue

7 Sulcal or Gyral Curves Surfaces Tme Sequece Large Deformao Dffeomorphc Merc Mappg TS-LDDMM + + > <, : 2, :, ], [ arg m TS - LDDMM : - based Po,, arg m TS - LDDMM :. a me po he vecor of momeum he s where, he sgular form aes, The momeum,. } { } { Defe he raecory. } {, } { d y E d J d y E d m m m J m m y y I I V d V d m m h V V δ & & * * * * * * * * Ladmars * * * Qu, A. e. al. NeuroImage, specal ssue

8 Sulcal or Gyral Curves Surfaces Tme Sequece Large Deformao Dffeomorphc Merc Mappg TS-LDDMM * * * * * * * * Ladmars * * *. ~ ] ~, [ ] ~, [ 2 ], [,, ~ ad Wh. s gve as o he dscree measure The aco of. ], [ wh he orm, dscree measures he form : ad surfaces are represeed as curves, Ulabeled ladmars, 2 2 * * W W W W y y y W W y y y μ μ y E μ μ μ μ μ μ ω ω ω ω ω ω δ ω δ ω δ ω ω ω δ ω + Qu, A. e. al. NeuroImage, 28; Glaues, J., Qu, A. e.al. IJCV, 28; Valla, M. ad Glaues, J., IPMI, 25

9 Euler-Lagrage Equao for Po-Based TS-LDDMM., Flow Equao : ]., [ Euler - Lagrage Equao wh s,, ], [ arg m - based LDDMM : po revew Le's., 2 ], [ Is Euler - Lagrage Equao :., ], [ arg m - based TS - LDDMM : The po, :, : V V V d V V d d d d d y E d J sac y E d d d y E d J V V & & Qu, A. e. al. NeuroImage, specal ssue

10 Sampled TS-LDDMM I I 2 I I The opmal flow coecg he observables y J : & sasfes Euler - Lagrage opmaly codos for he po - based TS - LDDMM gve by d d arg m V, d,, ], wh umps a observao mes defed as [ V [ V,,2, LN, gve by ] d + E, N / 2, ad,,2, LN, + E, y / 2. Qu, A. e. al. NeuroImage, specal ssue E.

11 TS-LDDMM for Curves I I I2 I3 sysole I4 I5 I dasole Qu, A. e. al. NeuroImage, specal ssue

12 TS-LDDMM for Curves Momeum Vecors : I I I 2 I 3 sysole I 4 I 5 I dasole Qu, A. e. al. NeuroImage, specal ssue

13 TS-LDDMM for Surfaces I I I 2 I 3 I 6mm 4mm 2mm mm Qu, A. e. al. NeuroImage, specal ssue

14 Iferece o Growh, Arophy, Dyamc Moo sub sub 2 sub 2

15 Geeral Approach subec subec 2 subec emplae 2

16 Geeral Approach 2 emplae sub sub 2 sub

17 Parallel Traspor Dffeomorphsms emplae ω v sub sub 2 sub v A B v, v 2 2, v,

18 Parallel Traspor Dffeomorphsms Subec emplae v Ep δ v v v v Ep ε δ + v εv +,,,, : V v v v J v v v Ep v v J Feld Jacob + δ δ ε δ ε δ 2 V v

19 Parallel Traspor Dffeomorphsms β Subec z ω X ³ dω V z,z d X O V z,z ³ + X l O V z,z l β ω l +ω β l X V z,z l ω l l X V z,z l β l l X V z,z l ω l β l X V z,z l β l ω l Youes, L. Qu, A., Wslow, R., Mller, M.I., J Mah Imagg Vs, 28..

20 Iegrao of TS-LDDMM ad Parallel Traspor global emplae z dy 4. Eeso : d, whe ω PT y V y,, ω,, y, ω, subec, 3. Traslao : ω PT z,, β, 2. Reraco : β PT,,,,,. Cosruco :, TS - LDDMM, y Qu, A. e. al. NeuroImage, specal ssue

21 Eample of Parallel Traspor basele global emplae global emplae Qu, A. e. al. NeuroImage, specal ssue

22 Tme-Depede Paer of Hppocampal Surface Deformao Dsgushes Healhy Agg ad Alzhemer s Dsease Obecve: dsgush he Tme-Depede Paer of Hppocampal Surface Deformao due o Healhy Agg ad Alzhemer s Dsease Subecs: 26 Healhy Comparso Corols 8 Paes wh very mld AD, scored as CDR.5 9 Coverers Acquso:.5T Mageom SP-4, MPRAGE, TR ms, TE 4 ms, Resoluo: XXmm, acqured a WUSTL Process: hppocampus deleao a WUSTL shape deformao bewee basele ad follow-up wh each subec sascal esg each subfeld of he hppocampus Qu, A., Youes, L., Mller M.I., Cserasy, J.G., NeuroImage, 4:68-76, 28

23 Mea Jacoba Deerma corols subculum CA ohers coverers paes Average Jacoba wh Subfelds subculum CA ohers corol coverer pae Qu, A., Youes, L., Mller M.I., Cserasy, J.G., NeuroImage, 4:68-76, 28

24 Shape Aalyss he Global Templae Radom Feld Model: m F Fψ, M emplae Dfferece bewee corols ad coverers Dfferece bewee corols ad AD paes Qu, A., Youes, L., Mller M.I., Cserasy, J.G., NeuroImage, 4:68-76, 28

25 Iegrao of TS-LDDMM ad Parallel Traspor global emplae z dy 4. Eeso : d, whe ω PT y V y,, ω,, y, ω, subec, 3. Traslao : ω PT z,, β, 2. Reraco : β PT,,,,,. Cosruco :, TS - LDDMM, y

26 Compuaoal Fucoal Aaomy CFA s he mahemacal sudy of aaomcal cofguraos ad sgals assocaed wh aaomy ad fucos aaomcal coordaes. ulmodal Images MRI DTI fmri 5 Sascal Aalyss shape AD hcess SCZ Poseror STG reoopc mappg Aeror 2 Segmeao 3 LDDMM Shape Aalyss 4 Fucos Aaomy volume surface

27 Ersc Aalyss o Fucos Sascal Mehod: Characerze aaomcal ad physologcal sgals F bra coordaes. F 2 2 F 3 F, F2,L 3 F F o Fψ, I emp Qu, A. e. al. NeuroImage, 28; Qu, A., Youes, L., e.al. NeuroImage, 27, 37:

28 Combg Aaomcal Mafold Iformao va LDDMM for Sudyg Corcal Thg of he Cgulae Gyrus Schzophrea WUSTL: Cserasy, Wag Obecve: corcal varao of he cgulae gyrus schzophrea Subecs: 49 schzophrea subecs 64 healhy comparso corols Acquso:.5T Semes, FLASH, TR 2ms, TE 5.4ms, Resoluo XXmm, acqured a WUSTL corol schzophrea 3.5 3mm 3.5mm mm Qu, A., Youes, L., e.al. NeuroImage, 27, 37:82-833

29 LDDMM Ladmar Mappg Subec Templae LDDMM-ladmars 72 ladmars F o F L ψ, I emp Qu, A., Youes, L., e.al. NeuroImage, 27, 37:82-833

30 LDDMM Curve Mappg Subec Templae LDDMM-curves 6 curves F o F C ψ, I emp Qu, A., Youes, L., e.al. NeuroImage, 27, 37:82-833

31 LDDMM Surface Mappg Subec Templae LDDMM-surface F o F S ψ, I emp Qu, A., Youes, L., e.al. NeuroImage, 27, 37:82-833

32 Corcal Thg of he Cgulae Gyrus Schzophrea F o F F Fψ, + ε, ε ~ 2 N, σ, F I emp ~ F L N, σ 2 F, F C, F S.mm mm 2.5 Combg ladmar, curve, surface LDDMM mappgs provded relable sascal resuls ad elmaed ambguous resuls due o surface msmaches. 2 mm.5 Qu, A., Youes, L., e.al. NeuroImage, 27, 37:82-833

33 Compuaoal Fucoal Aaomy CFA s he mahemacal sudy of aaomcal cofguraos ad sgals assocaed wh aaomy ad fucos aaomcal coordaes. ulmodal Images MRI DTI fmri 5 Sascal Aalyss shape AD hcess SCZ Poseror STG reoopc mappg Aeror 2 Segmeao 3 LDDMM Shape Aalyss 4 Fucos Aaomy volume surface

34 Reoopc Mappg Huma Prmary Vsual Core JHU: Yas Age-Relaed Macular Degeerao; Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

35 Vsual Core Reorgazao? Real Scooma due o Age- Relaed Macular Degeerao: Ths mage was ae by Dr. Jae Suess wh a scag laser ophhalmoscope a he Wlmer Eye Isue, Johs Hops Uversy School of Medce. Arrows po o he fovea, ad he ouled area dcaes damaged rea. Real Leso Proeco Zoes Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

36 Reoopc Mappg Reoopc Eccercy Mappg Vsual Feld Vsual Core pareooccpal fssure occpal pole Reoopc Polar Agle Mappg pareooccpal fssure occpal pole Qu, e al., esmag lear corcal magfcao, NeuroImage, 26, 3:25-38.

37 Lear Corcal Magfcao Real Area Corcal Area real space agle degree core space mm Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

38 Epermeal Desg Saoary Coras-Reversg Rgs Polar Wedge Smul: Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

39 Aaomcal MRI Aalyss Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

40 Spaal Smoohg fmri Neocore Laplace- Belram Bases : Δψ u + λψ u M, M ψ u 2 dm, ψu, M Qu, A. e. al. IEEE TMI, 26, 25:

41 Corcal Fuco ad Srucure: Prmary Vsual Core Reoopc Mappg rg smulus fucoal map o he occpal surface lear corcal magfcao esmao reoopc smul reoopc maps he prmary vsual core Qu, e al., esmag lear corcal magfcao, NeuroImage, 26,

42 Pae Eample rg rg 2 rg 3 rg 4 rg 5

43 Pae Eample rg rg 4 rg 5 θ e.577 d

44 Pae Eample θ e.577 d rg 2 d mm rg 3 d33.89mm

45 Pae Eample

46 Compuaoal Fucoal Aaomy CFA s he mahemacal sudy of aaomcal cofguraos ad sgals assocaed wh aaomy ad fucos aaomcal coordaes. ulmodal Images MRI DTI fmri 5 Sascal Aalyss shape AD hcess SCZ Poseror STG reoopc mappg Aeror 2 Segmeao 3 LDDMM Shape Aalyss 4 Fucos Aaomy volume surface

47 Acowledgmes: JHU Mchael I. Mller Laure Youes J. Tla Raaaher Parc Bara Seve Yas e. al.. WUSTL Joh G. Cserasy Le Wag Mchael P. Harms NUS Jda Zhog Ta Ah Tua Way Cherg Che Yg Su

48 Tha you! hp://