anal´yza funkcion´aln´ıch dat z´aznam˚u vyvolan´ych...
TRANSCRIPT
Analyza funkcionalnıch dat zaznamuvyvolanych potencialu ve sluchove draze
Ondrej Pokora, Jan [email protected], [email protected]
Ustav matematiky a statistiky, Prırodovedecka fakulta, Masarykova univerzita, Brno
ROBUST, Rybnık 21.–26. ledna 2018
Spoluautori, motivace, data
▸ Tzai-Wen Chiu (Dept. of Biological Science and Technology,National Chiao Tung University, Hsinchu, Taiwan)▸ Paul W. F. Poon▸ Puvodnı motivace: model tinnitu (selestu v usıch) u krys. Tinnitus
umele vyvolan aplikacı salicylatu.▸ Nahravajı se vyvolane potencialy (Auditory Evoked Potentials)
v auditornım kortexu.
Ð→
1/28
Data – typicke AEP
2/28
Data
▸ Sıla vyvolanych potencialu je charakterizovana ve smyslu integraluAEP pres definovane casove okno jako tzv. Evoked PotentialIntegral, y i k , v jednotkach µV ms.▸ Schema exprimentu: 6 dnı kontrolnı merenı, nasledovne podavana
davka salicylatu a merenı provadena 8 dnı. 79 pruchodu kazdy den.▸ zvuky: tony 10, 16 kHz (10 ms) a sirokospektralnı signal (klik,
klepnutı 0,01 ms)▸ postupne se menıcı intenzita zvuku, tk , od −15 do 75 dB SPL.
3/28
Data – typicke AEP
400
-400
0
400
-400
0
400
0400
0
Am
plit
ud
e (
a.u
.)
Peri-stimulus Time (sec)-0.05 0 0.05 0.10 0.15 0.02 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
0
20
40
100
120
Stimulus level (dB SPL)
EP
I (a
.u.)
60
80
B
Am
plit
ud
e (
a.u
.)
400
200
-200
-400
0
-0.05 0 0.05 0.10 0.15 0.02-0.05 0 0.05 0.10 0.15 0.02
ACon SS
C
4/28
Data – typicke AEP
5/28
Data (detail)
10k, SS−1, 79 trials
0
30
60
90
0 30 60sound intensity [dB SPL]
EP
inte
gral
[µV
ms]
6/28
Vyhlazovacı splajny
Baze: B-splajny B j(t)
Reprezentace EPI:
x i(t) =N∑j=1
c i jB j(t), i = 1, . . . , n
Penalizovana chyba:n∑i=1
K∑k=1
[y i k − x i(tk)]2 + λ ∫ tK
t0[ d2
dt2x i(t)]
2
dt Ð→ minc i j
GCV:n∑i=1
K∑k=1
[y i k − x i(tk , λ, − k)]2 Ð→ minλ
Analogicky, reprezentace derivace EPI:
x′i(t) =N∑j=1
c′i jB j(t), i = 1, . . . , n.
7/28
Baze
0.00
0.25
0.50
0.75
1.00
−15 0 15 30 45 60 75sound intensity [dB SPL]
8/28
Vyhlazena data (detail)
10k, SS−1, 79 trials
0
30
60
90
0 30 60sound intensity [dB SPL]
EP
inte
gral
[µV
ms]
9/28
Vyhlazena data – EPI
con 1 con 2 con 3 con 4 con 5 con 6 SS 1 SS 2 SS 3 SS 4 SS 5 SS 7 SS 8
10k16k
click
0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60
0
50
100
0
50
100
0
50
100
sound intensity [dB SPL]
EP
inte
gral
[µV
ms]
10/28
Vyhlazena data – derivace EPI
con 1 con 2 con 3 con 4 con 5 con 6 SS 1 SS 2 SS 3 SS 4 SS 5 SS 7 SS 8
10k16k
click
0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60 0 30 60
−1
0
1
2
−1
0
1
2
−1
0
1
2
sound intensity [dB SPL]
first
der
ivat
ive
of E
P in
tegr
al
11/28
Vzdalenosti v FDA
▸ Vzdalenost mezi dvema splajny x1, x2:
d0(x1, x2) =√
∫ tK
t0[x1(t) − x2(t)]
2dt
d1(x1, x2) =√
∫ tK
t0[x′1(t) − x′2(t)]
2dt
▸ Median {x1, . . . , xm} je takovy splajn, minimalizujıcı soucet∑m
j=1 d∗(xk , x j), k = 1, . . . ,m, pro zvolenou vzdalenost d∗ = d0, d1.
12/28
Vzdalenosti d0, d1 mezi mediany (relativnı skala)
d0 d1
10k
16k
clic
k
con
2
con
3
con
4
con
5
con
6
SS
1
SS
2
SS
3
SS
4
SS
5
SS
7
SS
8
con
2
con
3
con
4
con
5
con
6
SS
1
SS
2
SS
3
SS
4
SS
5
SS
7
SS
8
SS 7
SS 5
SS 4
SS 3
SS 2
SS 1
con 6
con 5
con 4
con 3
con 2
con 1
SS 7
SS 5
SS 4
SS 3
SS 2
SS 1
con 6
con 5
con 4
con 3
con 2
con 1
SS 7
SS 5
SS 4
SS 3
SS 2
SS 1
con 6
con 5
con 4
con 3
con 2
con 1
13/28
Rozdelenı vzdalenostı d0, d1 od kontrolnıch (> 20 dB SPL)
SS 7 SS 7
SS 4 SS 4
SS 5 SS 5
SS 1 SS 1
SS 8 SS 8
SS 3 SS 3
0 100 200 300 0.0 2.5 5.0 7.5 10.0 12.5
0 100 200 300 0.0 2.5 5.0 7.5 10.0 12.5
100 200 300 0.0 2.5 5.0 7.5 10.0 12.5
100 200 300 0 4 8 12
0 100 200 300 0 4 8 12
100 200 300 0.0 2.5 5.0 7.5 10.0 12.5
distances
dens
ity
A B
●
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1
3
457
8
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3
4
578
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1
2
358
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1
3
45
7
8
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2
3
4
5
7
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1
2
3
58
d0 d110k
16kclick
100 150 200 1 2 3 4 5
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
mean
skew
ness
14/28
Vyhlazena data derivace EPI (detail)
A 10k, con, n = 474
−1
0
1
2
0 25 50 75sound intensity [dB SPL]
first
der
ivat
ive
of E
P in
tegr
al
B 10k, SS7, n = 79
−1
0
1
2
0 25 50 75sound intensity [dB SPL]
first
der
ivat
ive
of E
P in
tegr
al
C 10k, SS3, n = 79
−1
0
1
2
0 25 50 75sound intensity [dB SPL]
first
der
ivat
ive
of E
P in
tegr
al
15/28
Funkcionalnı PCA (fPCA)
x i(t) = x(t) +N∑j=1
s i jξ j(t)
x′i(t) = x′(t) +N∑j=1
s′i jη j(t),
Strednı funkce: x(t) = 1n
n∑i=1
x i(t), resp. x′(t) = 1n
n∑i=1
x′i(t)
Hlavnı komponenty: ξ j(t), resp. η j(t)
Skory: s i j, resp. s′i j
16/28
fPCA – podıl vysvetleneho rozptylu
●
●●
● ●
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5number of PCs
cum
ulat
ive
prop
ortio
n of
var
ianc
e
17/28
Funkcionalnı PCA (fPCA)
x i(t) ≈ x(t) + s i1ξ1(t) + s i2ξ2(t)
x′i(t) ≈ x′(t) + s′i1η1(t) + s′i2η2(t)
18/28
fPCA – strednı krivky (A) a hlavnı komponenty (B)
A
EP
IE
PI derivative
0 30 60
30
50
0.3
0.6
sound intensity [dB SPL]
B
EP
IE
PI derivative
0 30 60
−0.1
0.0
0.1
0.2
−0.1
0.0
0.1
0.2
sound intensity [dB SPL]
19/28
fPCA
Jadrove odhady hustoty rozdelenı pravdepodobnosti skoru (S1, S2), resp.(S′1, S′2): f(S1 ,S2)(u1,u2), resp. f(S′1 ,S′2)(u1,u2)
(s1, s2) = argmax(u1 , u2)
f(S1 ,S2)(u1,u2)
(s′1, s′2) = argmax(u1 , u2)
f(S′1 ,S′2)(u1,u2)
Reprezentanti:xML(t) = x(t) + s1ξ1(t) + s2ξ2(t)
x′ML(t) = x′(t) + s′1η1(t) + s′2η2(t)
20/28
fPCA – reprezentanti
10k 16k click
EP
IE
PI derivative
0 30 60 0 30 60 0 30 60
30
60
90
0
1
2
sound intensity [dB SPL]
10k:con10k:SS16k:con16k:SSclick:conclick:SS
21/28
Skore EPI – con vs. SS
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MR = 0.0042
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MR = 0.043
con SS
0 250 0 250−150
−100
−50
0
50
100
score 1
scor
e 2 ●
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10k:con10k:SS16k:con16k:SSclick:conclick:SS
22/28
Skore EPI – ton vs. klik
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MR = 0.055
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MR = 0.033
tone click
0 250 0 250−150
−100
−50
0
50
100
score 1
scor
e 2 ●
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10k:con10k:SS16k:con16k:SSclick:conclick:SS
23/28
Skore derivace EPI – con vs. SS
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con SS
0 5 10 0 5 10
−10
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10
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e 2 ●
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24/28
Skore derivace EPI – ton vs. klik
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MR = 0.016
tone click
0 5 10 0 5 10
−10
−5
0
5
10
score 1
scor
e 2 ●
●
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●
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10k:con10k:SS16k:con16k:SSclick:conclick:SS
25/28
Skore
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EPI derivative
tone
EPI derivative
click
EPI
tone
EPI
click
−4 −2 0 2 4 0 5 10
−200 −100 0 100 200 0 200 400−150
−100
−50
0
50
100
−10
−5
0
5
10
−50
0
50
100
−5
0
5
10
sc1
sc2
●
●
●
10k:con10k:SS16k:con16k:SSclick:conclick:SS
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Oblasti dle hloubky
10k 16k click
EP
IE
PI derivative
0 30 60 0 30 60 0 30 60
0
50
100
−1
0
1
2
3
sound intensity [dB SPL]
10k:con10k:SS16k:con16k:SSclick:conclick:SS
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Odkazy
▸ Pokora O., Kolacek J., Chiu T.-W., Qiu W. (2017) Functional dataanalysis of single-trial auditory evoked potentials recorded in theawake rat. Biosystems 161, 67–75.▸ Wan I., Pokora O., Chiu T.-W., Lansky P., Poon P. W. (2015)
Altered intensity coding in the salicylate-overdose animal model oftinnitus. BioSystems 136, 113–119.▸ Ferraty, F. and Vieu, P. (2006) Nonparametric functional data
analysis: theory and practice. Springer.▸ Norena, A. J. (2011) An integrative model of tinnitus based on a
central gain controlling neural sensitivity. Neurosci Biobehav Rev.35: 1089–1109.▸ Wang, J.-L., Chiou, J.-M. and Muller, H. G. (2016) Functional Data
Analysis. Annual Review of Statistics and Its Application 3 (1):257–295.
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