motion correction on high resolution pet brain imaging
TRANSCRIPT
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4'7878)
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0 50 100 150 200 250 3000
50
100
150
200
250
300
3D RMS=1.13mm
x /mm
Alignment of run no. 4
Position of the 45 Markers in the Image Frame
y
/mm
trans P positions
TR positions
!"#$% &'() !"#$% &' %(! )$*+,-!,% &' .#, /0 !1 1&%"2 3&"*%*&," &' %(!
*1!,%*4!1 -).5!." &, %(! 6 78 *-)+!"0 9$):5 1&%"2 7.),"'&.-!1 3&"*%*&,"
*,%& %(! *-)+! '.)-! &' %(! 3&"*%*&, &;%)*,!1 '.&- %(!
-
!"#$%& ' !"#$%'()* +)$( ,,- !"#$%"%&'(')*& *+ ',% -*')*& .*//%0')*&
!" #$%&'()$*+ *, )-. /'$0+%.+)
( )*+$% "&,* -./0,"$.*+ *1 $!% $&"+-1*&/"$.*+ /"$&.23 ApolarisHRRT 3 4"- /"5%
$* 6",.5"$% "+5 %6%+$0",,7 *#$./.8% $!% ",.9+/%+$ /%$!*5: ;!% /"$&.23 Aest: ;!% %&&*& 4"- $!%+ 1*0+5 0-.+9 " +%4 -%$ *1 9%+%&"$%5 #*.+$- @A.9:
':BC:
D+ $!% E&-$ -$%#3 Atrue 4"- 9%+%&"$%5 *1 $!&%% &"+5*/ $&"+-,"$.*+- F%$4%%+ GBH// "+5 $!&%% &"+5*/ &*$"$.*+- F%$4%%+ : D+ $!% -%*,"&.-: ;!% -#&%"5 *1 $!% #*.+$- .+ $!%x "+5 y 5.&%!
n, y!
n, z!
nC 4!%&% N 4"- $!% +0/F%&*1 -./0,"$%5Aest3 4!.
!" #$%&'()"* #")&+,
B]
-
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!"#$% &'() !"#$ %& !'" ()*+,-",! $*-.)(!*%,/ !"# 01 2","3(!*%, %& ( !3."
4 -(!3*5/ !"# 61 2","3(!*%, %& #%*,!$ *, !'" 7%%38*,(!" $9$!"- %& :%)(3*$
.$*,+ !'" +"%-"!39 %& !'" #(!*",! !%%)/ !"# ;1
-
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()*+%& ,- &%#%$.$.,(/ ,- "00 $!% /%1%( /$%#/ "(2 r = 1...R3
3D RMSaccuracy =
1
NP
NP
n=1
(xn x n)2 + (yn y n)
2 + (zn z n)2, 4'35367
3D RMSrep =
1
NPR
R
r=1
NP
n=1
(xnr x nr)2 + (ynr y nr)
2 + (znr z nr)2. 4'35357
8!% 9:; &%#%"$"+.0.$< ,- $!% 2.=%&%($ 2.&%>$.,(/ ?%&% 2%$%&*.(%2 "/@
RMSx =
Rr=1
NPn=1(xnr x
nr)2
NPR, RMSy =
Rr=1
NPn=1(ynr y
nr)2
NPR,
4'353A7
"(2 RMSz =
Rr=1
NPn=1(znr z
nr)2
NPR.
2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
Found 3D RMS
Number of Paired Measurements, M
RM
S r
ep
ea
tab
ilit
y /
mm
Repeatability of Apolaris HRRT
3D RMS
RMSx
RMSy
RMSz
!"#$% &'() !"#$ %&'(! )*+,(*!" !- #.$ 3D RMS '$/$&0*(*#1 $''!'!- ApolarisHRRT &) & -,"2#*!" !- "!3 !- /&*'$4 +$&),'$+$"#)3 N = 1505P = 10005 R = 305 TXerror = 0.5 ++ &"4 zmarker = 6 ++3
B.C3 '3D /!,?/ $!% 3D RMS &%#%"$"+.0.$< %&&,& ,- $!% $&"(/-,&*"$.,( "/ " -)(>$.,( ,-$!% ()*+%& ,- #".&%2 8E .*"C%/ "(2 F,0"&./ $&">G.(C/3 H$ ./ $!% &%/)0$ ,- " /.*)0"$.,(
,- 6IJ Aest .( %">! ,- AJ &%#%$.$.,(/3 8!% +0">G >)&1% ./ $!% 3D RMS %&&,& ?!.0% $!%$!&%% >,0,&%2 >)&1%/ "&% $!% %&&,&/ .( %">! 2.&%>$.,(/3 8!% 3D RMS %&&,& &%#&%/%($/
D6
-
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#*! +$,-./#!0 /""-1/"$!+2 .$,$#/#$%& %3 #*! +41!/0 %3 #*! 4%$+ $& 5678 -&"!1#/$
%3 #*! $0!$:"/#$%& %3 #*! ,/1;!1+ %& #*! ! /&0 -&"!1#/$ %3 #*! ?%./1$+
#1/";$&>( &,!+ H/+ 3%-&0 #% F(F ,, $& #*! 41!@$%-+ +!"#$%&( ( '(J /&0 #*$+ !11%1 $+ /"*$!@! /3#!1 K 4/$1!0 ,!/+-1!,!+(
%$&> 31%, TXerror N L(K,, #% TXerror N F ,, $&"1!/+!+ #*! 3D RMS !11%1 31%, F(L ,, #% )(L ,,( 5$>('(' +*%H+ #*! 1!+-.#+ %3 @/19$&> #*! +41!/0 %3 #*! 4%$+ $& #*! z 0$1!"#$%&( &$:"/.9 *$>*!1 #*/& x /&0 y 3%1 zmarker Q )KL ,,8 H*$"* $+ #*!+41!/0 %3 #*! 4%$+ $& x /&0 y( &,! %3 1-& )RM
1!+-.#!0 $& ./ 01 !11%1+ /+ !E4!"#!0( 1!!0
J)
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()$! $!% %&&*& +*,-. )- $!% */$")-%. "0)1-2%-$3 *+ &,- 4567 (!)8! (%&% 2".% *+ 67
9 "-. 9 #")&%. 2%"3,&%2%-$3 &%3#%8$):%0;< =!)3 3,##*&$3 $!"$ $!% 3)2,0"$)*- &%#&*5
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8"- /% )2#&*:%. /; >?@ (!%- )-8&%"3)-1 $!% -,2/%& *+ #")&%. 2%"3,&%2%-$3 $* A
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$!% $**0 ("3 #0"8%. )- #%&)#!%&; #*3)$)*-3 *+ $!% CDE "-. $!% -,2/%& *+ #")&%.
2%"3,&%2%-$3 (%&% )-8&%"3%. $* A +*& &,- -,2/%& 'L &)1).
$&"-3+*&2"$)*- "##0;)-1 KM< N>
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5 10 15 20 25 30 350
0.5
1
1.5
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No. of TX scan
FL
E (
mm
2)
Error of the identification of the markers on the TX images
FLE
=0.47mm2
run 2
run 3
run 4
run 5
run 6
run 7
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No. of aligment run
3D
RM
S e
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0 50 100 150 200 250
350
300
250
200
150
x /mm
z /m
m
Coordinate System of PolarisCentral Points
0 100 200 3000
50
100
150
200
250
x /mm
z /m
m Image FrameCentral Points
3DRMS
=0.82mm
3DRMS
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0 50 100 150 200 250
350
300
250
200
150
x /mm
z /m
m
Outlying Points
0 100 200 3000
50
100
150
200
250
x /mm
z /m
m
Outlying Points
3DRMS
=1.8mm
3DRMS
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2
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Frame
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Error Relative to the Movement
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PS 1zoom
PS 2
PS 2zoom
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2 4 6 8 10 120
10
20
30
40
50
60
70
80
90
100
Frame
Perc
en
tag
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verl
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(%
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Overlap of Corrected/Original Frames
corrected frames
original frames
B
C
D
E
H
I
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0.5 1 1.5 2 2.5 3
x 104
0
20
40
60
80
100
r = 1.9 mm Th 2
r = 2.4 mm Th 3
r = 0.75 mm Th 1
Overlap as a Function of Number of Voxels Above Threshold
No of voxels above threshold
overl
ap
%
A
B
C
D
E
H
I
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0 20 40 60 80 1000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Mean of the overlap at a given rotation (%)
Bia
s o
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%)
Bias of the Overlap for the Original Frames
R = 0.96 Fr. 11,
10o rotation
Fr. 2,
2o rotation
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Atrack# = Atrack#,frame1 A1track#,frame11 .
0 100 200 3000
50
100
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250
300
x /mm
y /m
m
Simulated PointsCentral Points
0 100 200 3000
50
100
150
200
250
300
x /mm
y /m
m Transformed Points
Central Points
3DRMS
=0.67mm
3DRMS
=0.52mm
0 100 200 3000
50
100
150
200
250
300
x /mm
y /m
m
Outlying Points
0 100 200 3000
50
100
150
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300
x /mm
y /m
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Outlying Points
3DRMS
=0.88mm
3DRMS
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0 10 20 30 40 50 60 705
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Time (min)
Tra
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x, y a
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z
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Fr. 12 Fr. 3 Fr. 46
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x (mm)
z (
mm
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100 150 200
50
100
150
2000.25
0.2
0.15
0.1
0.05
0
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0.1
0.15
0.2
0.25
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x (mm)
z (
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100 150 200
50
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0.2
0.15
0.1
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0
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0.2
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x (mm)
z (
mm
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100 150 200
50
100
150
2000
0.2
0.4
0.6
0.8
1
3" 6*''2(&23
x (mm)
z (
mm
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100 150 200
50
100
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0.2
0.4
0.6
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1
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0 0.5 10
0.2
0.4
0.6
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1
r2 = 0.65
Scatter Plot Before Correction
Pixel value of original Fr. 1
Pix
el
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Fr.
4
0 0.5 10
0.2
0.4
0.6
0.8
1 Scatter Plot After Correction
Pixel value of original Fr. 1
Pix
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r. 4
r2 = 0.79
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