Transcript NCSPoct2010m

Brain Research Leads to
Advances in Signal Processing
and Vice Versa
Nathan Intrator
School of Computer Science
Tel Aviv University
& Brown University
Brief Outline
• Learning and Memory Formation
– Theory
– Experiment and Experimental
Simulations
• Brain and Signal Processing
• Brain Imaging
Simple Model of a Neuron
Output
c
Synaptic
weights
m1
m3
m2
Inputs
d1
d2
d3
Neuron Activation
Output
Synaptic
weights
c
m1
m3
 n

c     mi  d i 
 i 1

  m  d 
 m d
m2
 m  d 
Inputs d1
d2
d3
m d
Hebbian Learning
“When an axon in cell A is near enough to excite cell B
and repeatedly and persistently takes part in firing it,
some growth process or metabolic change takes place
in one or both cells such that A’s efficiency in firing B
is increased.” - Hebb, 1949
“Those that fire together wire together”
•Mathematically:
dmi
 cd i
dt
Synaptic Modification
Output
signal
Output
increase
c  md
Synaptic
weight
Input
signal
d
c
c
m
m
d
Output
decrease
Weight
increase
m
d
Weight
decrease
Hebbian Learning and
Principal Components
•Matrix equivalent of Hebbian Learning
dmi
  Cij m j
dt
j
dm
 Cm
dt
•Eigenvectors of C, the principal components: Cv   v
•Expand in terms of eigenvectors, v : m   a v
dmi
da

v
dt
dt

  a Cv   a  v
da
 a 
dt


a (t )  a (0)e  t
•Component with largest eigenvalue wins

Synaptic Stabilization
Mathematical method implies
Biological mechanism
•Saturation limits mmin  mi  mmax
Synaptic
weights
•Normalization
m1
m3
m2
2
m
 i  constant
i
(Linsker 1986;Miller 1994)
•Decay terms
dmi
 cd i  c 2 mi
dt
(Oja 1982, Blais et. al. 1998)
•Moving threshold
(BCM 1982, IC 1992; Blais et. al. 1999)
Combining Hebbian and
Anti-Hebbian Learning
•A more general Hebbian-like rule
dmi
  (c ) d i
dt
•Includes a decrease of weights in
 (c)
 Hebb
 (c)
 Selective
M
c
•For c   M response increases
•For c   M response decreases
•Yields selectivity…
•… but not stable
BCM Theory
(Bienenstock, Cooper, Munro 1982;
Intrator, Cooper 1992)
•Selectivity learning rule with moving threshold
dmi
dt

M

 (c,  M ) d i
 (c)
M
 
Ec
 BCM
2
  cc   M 
c
•Time average of the square of the neuron activity
M
lim M
 0
 
 E c 2
 c2
Two examples
with N= 5
Note: The stable FP
is such that for one
pattern ci=mdi=θm
while for the others
C(i≠j)=0.
BCM Theory
Stability
•One dimension
•Quadratic form
•Instantaneous limit
c  md
dm
 cc   M d
dt
 M  c2
dm
dt
0

 (c)

 c c  c2 d
c
 c 2 (1  c)d
1
c
BCM Theory: Selectivity
dm
 ck ck   M d k
•Learning Equation
dt
•Four possible fixed points
(unselective) c1  0 , c2
(Selective) c1   M , c2
(Selective) c1  0 , c2
(unselective) c1   M , c2




2
2
2


p
c

p
c

p
c
•Threshold M
1 1
2 2
1 1
 1 / p1
0
0
M
M
m1
d1
d2
m2
Experimental vs. Theoretical
Evidence
Right
Left
Left
Tuning curves
0
90
180
270
360
Right
Receptive field Plasticity
Ocular Dominance
Plasticity (Mioche and Singer, 89)
Left Eye
Right Eye
Synaptic plasticity in Visual
Cortex (Kirkwood and Bear, 94 )
R ecord
S tim ulate
150
125
100
75
1 Hz
50
-3 0
-15
0
15
30
45
Tim e from onset of LFS (m in)
200
150
100
HFS
50
-1 5
0
15
30
Visual Pathway
Visual Cortex
Receptive fields are:
•Binocular
•Orientation
Selective
Area
17
LGN
Receptive fields are:
•Monocular
•Radially
Symmetric
Retina
light
electrical signals
Model Architecture
Image plane
Left
Retina
Right
Retina
LGN
LGN
Left
Synapses
Cortex
(single cell)
Right
Synapses
Inputs
[d iLd iR ]  d i
Synaptic
weights
[miL miR ]  mi
Output


c     mi d i 
 i

Orientation Selectivity
Normal
Binocular
Deprivation
Adult
Adult
Eye-opening angle
angle
Eye-opening
Monocular
Deprivation
Normal
Left
Right
Right
% of cells
angle
Left
angle
20
30
15
10
1 2
3 4
5
group
6
7
Rittenhouse et. al.
1 2
3 4
5
group
6
7
Natural Images, Noise,
and Learning
image
retinal
activity
•present patches
•update weights
•Patches from retinal activity image
•Patches from noise
Hebbian Learning and
Orientation Selectivity
•Orientation selectivity
– responds to bars of light
at a particular orientation
– elongated regions of
strong synapses
experiment
simulation
BCM Learning and
Orientation Selectivity
•Orientation selectivity
– responds to bars of light
at a particular orientation
– elongated regions of
strong synapses
experiment
simulation
Binocularity
Left
Eye
Left
Synapses
Right
Eye
Right
Synapses
Hebbian
Learning
Left
Right
BCM
Learning
Left
Right
BCM neurons can develop both orientation
selectivity and varying degrees of Ocular Dominance
100
50
Right Eye
0
100
Left Eye
Left
Synapses
Right
Synapses
No. of Cells
50
0
40
20
0
100
50
0
12345
Bin
Shouval et. al., Neural Computation, 1996
•BCM Theory
strong activity
160
160
120 N=238
120 N=273
80
80
40
40
0
0
Right Both Left
Right Both
Left
Right
Both
Left
Right
Both
Left
Both
Left
Right
Both
Left
Number of cells
•Synaptic competition
weak activity
Number of cells
•Rittenhouse et. al. 1999
•TTX in retina
•consistent with BCM
Number of cells
Experiment and Theory
Right
Monocular Deprivation
Homosynaptic model (BCM)
Low noise
High noise
Networks of BCM Neurons
BCM Synaptic Plasticity.
Binocular natural image
inputs.
strength
Radially symmetric lateral
connectivity.
distance
Shouval et. al., Vision Research, 1997
Conclusions
• Models of Synaptic Modification
– differ by methods of synaptic stabilization
– synaptic competition
– BCM theory: moving threshold
• Reproduce deprivation experiments
• Dynamics of monocular deprivation
– experiment to distinguish learning rules
– Rittenhouse et. al. 1999 consistent with BCM
Different levels of description
• Molecular
150
•Synaptic
125
100
75
1 Hz
50
-3 0
-15
0
15
30
45
Theoretical
Tim e from onset of LFS (m in)
•Cellular
•System/Maps
Framework
February 2007
Edition of the
Journal Neuron
"Mechanism for
a Sliding
Synaptic
Modification
Threshold“
25 Years
Anniversary
The Amazing Signal
Processing
Capabilities of
Mammalian Brains
Sonar Echo Localization
Sonar Principle
The Uncertainty Principle
 A signal cannot be localized
arbitrarily well both in
time/position and in
frequency/momentum.
 There exists a lower bound to
the Heisenberg’s product:
t f  1/(4)
Improving on this bound would result in sonar with
better temporal resolution at a given frequency range
f = 10kHz, t = 50 sec ~ 10cm
Ultrasound is based on Sonar
Heisenberg’s Uncertainty Principle
f = BCRMS
f > 0
f = 0
t f  1/(4)
Woodward’s: SNR breakpoint
•
•
•
Smallest fc
(solid line)
Intermediate fc (dotted
line)
Largest fc (dashed
line)
A – High SNR: Delay error function of center peak width (Coherent)
B – Low SNR: Ambiguity in peak choice (Semicoherent)
Mosaics and Hi resolution of DIDSON
Sonar Animals
Sea:
Dolphins
Multiple Pings
Air:
Bats
Multiple Pings
Ground: Mole Rats
Multiple Pings
Big Brown Bat
Actual hunt
Target detection can be measured more clearly by training the bat to make an
unambiguous response in an experiment.
A two-choice test requires the bat to move to the left or right to follow the
movement of the target and receive a reward.
We use a two-choice echo jitter discrimination procedure to evaluate the content of the bat’s
images along the dimension of perceived delay.
Underground Exploration
Blind Mole Rat
Lives underground
Has no functional eyes
Builds tunnels system
KIMCHI, ET. AL. 2005
The mole-rate bangs its head on the side of the tunnel
few times per second and explores the 3D environment
using the infrasound that is returned from these
banging.
Underground Exploration
Blind Mole Rat
Lives underground
Has no functional eyes
Builds tunnels system
KIMCHI, ET. AL. 2005
The mole-rate bangs its head on the side of the tunnel
few times per second and explores the 3D environment
using the infrasound that is returned from these
banging.
SNR-DEPENDENT FILTERING FOR TIME OF ARRIVAL ESTIMATION IN HIGH NOISE
Alexander Apartsin1, Leon N. Cooper2, Nathan Intrator1,2
2
1Blavatnik School, Of Computer Science, Tel-Aviv University,
Institute for Brain and Neural Systems and Physics Department, Brown University
Time of Arrival Estimation
Threshold Effect
Phase-Shifted Unmatched Filters
The cornerstone of remote sensing applications(radar, sonar): “…one of the most interesting features of radar theory”,
Time of Arrival Estimation(ToA)
Woodward 1953
Send out a pulse reflected from a target and picked up by a Rapid deterioration in the accuracy as SNR falls below
receiver at time t 0
certain threshold (Figure 2)
Received signal: u  t   c* s  t  t   n(t )
White Gaussian Noise (AWGN) o
where n ( t ) is Additive Coherent receiver operates with SNR above this threshold,
noncoherent receiver operates substantially below the
threshold
Estimated two-way travel time (lag) is used to calculate distance to
the target
Focus of this work: Semi-coherent receiver which balances
Standard Method: Matched Filter Maximum Likelihood (MFML)
Estimator
between coherent and noncoherent states
Matched Filter
Figure 4: Unmatched filters are obtained by phase shifting
the source pulse waveform in opposite directions (top). Note
that the cross-correlation with the pulse waveform has
asymmetric side lobes (bottom)
Matched Filter(MF) maximize peak Signal-To-Noise Ratio (SNR)
Position of the maximum in filter output is Maximum Likelihood
estimator of ToA
Output of MF is pulse Autocorrelation function(Figure 1, bottom)
plus filtered noise
Figure 2:Accuracy vs., SNR (from Woodward,1953)
Threshold Effect Explained
A side lobe of autocorrelation function mistakenly taken as
its global maximum is a major reason behind Threshold
effect
The posteriori distribution of the possible lag locations
becomes multimodal
Figure 5: Unmatched Filter Maximum Likelihood
(UFML)Estimators obtained by taking the position of
maximum in each filter output UFML are biased toward
higher side lobe of cross-correlation function (right) but not
completely correlated (left)
Learning Optimum Phase Shift Value
Figure 1:Gaussian modulated sinusoidal pulse (top) and its Figure 3:The probability density function for MFML estimator Figure 6: RMSE improvement using different values of
autocorrelation function (bottom)
error. There are significant local maxima under low SNR
phase shift. The black line shows improvement obtained by
SNR-dependent phase selection learned from data
Robust Interpretation
of Brain States
• Basic Research on
Brain Imaging
Enhancement
• Epilepsy Prediction
• Brain State
Interpretation
Combined EEG/fMRI Recordings at TAU/Souraski
fMRI:
 High spatial resolution
 Low temporal resolution
 Indirect measure of neuronal
activity
EEG:
 Low spatial resolution
 High temporal resolution
 Direct measure of neuronal
activity
HMM for fMRI
Modeling 4D voxels activity
using HMM
Presentation by Elad Tsur, TAU, May 2010
Nathan Intrator NCSP Lab
Fyodor Dostoyevsky - Aura
(1821-1881)
• Most known epileptic novelist
• Gave vivid accounts of apparent
temporal lobe seizures in his
novel
“The Idiot”
• Describes an aura (sensory
hallucinations) he used to get
before the onset of a seizure
DeToledo, J. C. (2001). Arch. Neurol. 58: 1305-1306.
Need for early seizure prediction
• ~30% of epileptics left untreated and victim of violent seizures
• Injuries resulting from epilepsy are often caused by convulsive
seizures
• Medications (severe side effects) could be taken on demand (can
not rely on patient to decide)
• Deep Brain Stimulation and Vagus Nerve Stimulation require
triggering
Non-Invasive Recordings
MRI and f-MRI
Scalp EEG
MEG
EEG
Post synaptic potentials (50-200ms) are believed to be the
primary generators of EEG activity.
Typical voltage amplitudes of EEG signals are measured in μV.
Outputs brainwaves with associated rhythms and frequencies
30 seconds recording
Normal
Abnormal
Prediction Of Mental Or Physiologic State From EEG
Applications To fMRI And Epilepsy
Podlipsky Ilana1,4, Talma Hendler1,2, Nathan Intrator3
1- Functional Brain Imaging Unit, Wohl Institute for Advanced Imaging, Tel Aviv Sourasky Medical Center, Israel; 2- Sackler Faculty of Medicine, Tel-Aviv University, Israel; 3-School of Computer Science, Tel-Aviv University, Tel-Aviv,
Israel; 4- Bio-Medical Engineering Department, Tel-Aviv University
Introduction
Introduction
Results
EEG signal is a signal recorded from the scalp. It reflects the brain's electrical
activity. This signal changes according to subjects’ physiological and mental
state.
When Ridge regression was applied to all frequencies of the EEG signal the
resulting prediction power was high for most subjects. Frequency weights of
this prediction had the highest values in the alpha frequency range (812Hz), implying that this frequency range explains most of the variance of
the EEG during the experiment as expected from the Berger effect.
This study aims to develop a machine learning technique for prediction of
one’s state using his EEG signal, by distinguishing between various EEG
frequencies and pinpointing the one’s most important for detection of this
state.
Prediction error for all subjects
Significant Ridge coeffs for every frequency of the EEG, p<0.00098039
7
5
Weight
0.35
3
Methods
0.3
In
si
gn
ifi
ca
nt
4
Methods
0.4
Prediction Error [%]
This technique can be used for selection of most important EEG frequencies
for combined EEG-fMRI analysis.
0.45
0.0
5
corr
Si ect
gn ed
ifi
ca
nt
6
0.25
Invasive EEG (iEEG) recording from an epileptic patient
was used. Seizure onsets and focal electrodes were
identified by a specialist.
0.2
2
0.15
1
EEG-fMRI is a multimodal neuroimaging technique where
EEG and fMRI data are recorded synchronously for the
study of brain activity.
0.1
0
-1
Scalp EEG has high resolution in time but low spatial
resolution. fMRI is an imaging technique capable of
detecting haemodynamic changes in the brain through the
BOLD (Blood Oxygen Level Dependent) effect.
It has high spatial resolution but low resolution in time.
EEG-fMRI therefore enables the direct correlation of these
two complementary measures of brain activity.
0.05
0
10
20
30
40
50
Frequency [Hz]
60
70
0
CFSE_02
80
GIET_02
ITGR_09
ITGR_10
ITGR_11
JOHA_03
Subject Name
ROSO_03
YAKU_02
GIEZ_08
ILBE_02
When Ridge regression was applied to frequencies below 30Hz resulting
prediction power was similar to the previous one, where frequency weights
in the alpha range were also highest. This implies that this frequency range
is more important in explaining the signal variance related to subjects’ state
than other frequencies.
Significant Ridge coeffs for every frequency of the EEG, p<0.003125
4
3.5
2.5
Weight
1
“Reading between signals” – using Ridge regression to reveal subject’s
state:
Clustering of spectrograms within a time frame of 10 minutes before a seizure and
2 minutes after it shows clear separation between time windows of seizure and
non-seizure states. Where focal electrodes exhibit the same pattern at the same
time.
0.2
0.15
0.1
0
-1
EEG signal
0.05
0
5
10
15
Frequency [Hz]
20
25
EEG signal
0
CFSE_02GIET_02ITGR_09ITGR_10ITGR_11JOHA_03
ROSO_03
YAKU_02GIEZ_08ILBE_02
Subject Name
When Ridge regression was applied to frequencies above 30Hz resulting
prediction power was very poor, and none of the frequency weights were
significant. This implies that this frequency range contains little information
attributed to subjects’ state.
Significant Ridge coeffs for every frequency of the EEG
Prediction error for all subjects
6
0.7
5
Si
gn
ifi
ca
nt
4
2
0.5
Prediction Error [%]
Weight
0.6
In
si
gn
ifi
ca
nt
3
Existing EEG data sets of 10 subjects performing a simple eyes opening and
closing task designed to trigger appearance of Alpha waves in the EEG (Berger
effect) were used .
Application of classifier to Spectrogram of EEG
0.25
0.5
-0.5
Given d signals (for example originating
from Time-frequency decomposition of
the EEG signal ) we want to find d
weights w1, w2, ..., wd such that the
weighted sum of signals reveals subject's
state (for example opened or closed
eyes).
The classifier was trained to predict the state of the subject (opened or closed
eyes) and its accuracy was tested by means of cross validation (splitting the data
set into testing and training sets).
Time frequency decomposition of seizure and non-seizure time windows show
clearly different patterns.
0.3
In
si
gn
ifi
ca
nt
2
1.5
Results
Prediction error for all subjects
0.35
Prediction Error [%]
EEG signal can be correlated with fMRI activity revealing
areas of the brain functioning during segments of interest
in the EEG.
The iEEG containing a seizure and a pre-seizure period
was taken from 10 electrodes close to the seizure foci.
The signal was segmented into 10 seconds long
intervals and subjected to time frequency decomposition.
The resulting spectrums ware classified into 5 classes
using hierarchical clustering.
0.4
0.0
5
corr
ect
ed
Si
gn
ifi
ca
nt
3
• Epilepsy affects more than 50 million individuals worldwide. In about 25% of
individuals with epilepsy, seizures cannot be controlled by any available therapy.
• Seizure prediction is one of the most important future directions for epilepsy
research. The ability to predict epileptic seizures well before clinical onset
promises new diagnostic applications and novel approaches to seizure control.
• This study aims to establish an algorithm for epileptic seizure prediction from
invasive EEG recordings of epileptic patients, using the approach of machine
learning and classification.
1
0
Clustering of Epileptic EEG time windows
0.4
29
0.3
5
28
Non
seiz
ure
27
0.2
-1
26
0.1
t1
tn
f
1
t2
140
...
120
-3
30
40
50
60
70
80
90
Frequency [Hz]
100
110
120
130
0
CFSE_02GIET_02ITGR_09ITGR_10ITGR_11JOHA_03
ROSO_03
YAKU_02GIEZ_08ILBE_02
Subject Name
Electrode #
-2
Stockwell smoothed
4.5
S
e
i
z
u
r
e
25
4
3.5
3
24
2.5
23
100
2
80
f
60
2
40
.
20
.
20
100
.
0
0
20
40
60
80
100
120
140
160
180
f
d
X  y   
In Ridge Regression
Minimize:
Ve
cto
r
of
we
Ve
cto
r
of
su
Regulari
zation
paramet
er
Conclusions
The preliminary results described here imply that prediction of some one’s state
from his EEG can be done. Further more, the results show that frequencies of the
EEG which contribute the most to this state can be identified.
The set of frequencies which contributed most to the prediction is the one mostly
related to the changes in state caused by the paradigm of the experiment. There
fore they can be used to explore change in fMRI correlated with this activity and
this way reveal areas in the brain functioning under the influence of the
experiment.
Acknowledgments: This study was done with the support of the Adams Super Center for Brain Studies and The Levi-Edersheim-Gitter Institute for
Neuroimaging, Tel Aviv University.
Correspondence: Prof. Nathan Intrator [email protected], Ilana Podlipsky [email protected]
22
1.5
21
20
100
200
300
400
500
Time [sec]
600
700
800
1
Conclusions
This result demonstrates that seizure and non seizure iEEG have clearly separable
patterns allowing detection and prediction of seizures to be done.
Future study will use this classification process to extract important features of the
iEEG data that distinguish between seizure and non-seizure states. These features
will be used in a machine learning algorithm for early prediction of epileptic
seizures.
LVF
LVF vs. RVF
V1 fMRI Activity
fMRI activation
2
% Signal Chnge
Neuro Feedback Training
Self Regulation of Affective State
3
4
R
L
0
V1
4
RVF
1
0
-1
-2
-3
0
Mental Target
fMRI time course
Experimental condition
-4
0
P < 0.05
50
100
150
200
250
TRs
Classification Error at time points
Best time points: 156ms, 232ms
EEG Latency Classifier
ACTA
best tp = 156 msc
EEG Neuro-Feedback
0.28
EEG classifier
0.26
0.25
Error rate
D
Error rate
0.27
0.24
0.23
150msec
ACTA
ACTA
0.22
232msec
ACTA
ACTA
tp=232
tp=232msc
msc
tp=156
tp=156msc
msc
0.01
0.01
0.21
Fp1
Fp1
F7F7
0.2
F3F3
FzFz
0.015
0.015
Fp2
Fp2
F4F4
0.01
0.01
F8F8
T7T7 50 C3
C3
TP9
TP9
CzCz
C4
C4100T8T8
CP1 CP2
CP2 CP6
CP5
CP5 CP1
CP6
P7
P7
P3
P3
PzPz
P4
P4
O1
O1 Oz
O2
Oz O2
P8
P8
F7F7
0.005
0.005
FC5
FC5 FC1
FC6
FC1 FC2
FC2 FC6
0
Fp1
Fp1
TP10
TP10
FzFz
F4F4
0.005
0.005
F8F8
FC5
FC5 FC1
FC6
FC1 FC2
FC2 FC6
0 0 150
-0.005
-0.005
F3F3
Fp2
Fp2
T7T7
200
Time points
C3
C3
250
P7
P7
-0.01
-0.01
CzCz
C4
C4
T8T8
300
CP1 CP2
CP2 CP6
CP5
CP5 CP1
CP6
TP9
TP9
P3
P3
PzPz
P4
P4
00
TP10
TP10
P8
P8
-0.005
-0.005
O1
O1 Oz
O2
Oz O2
-0.015
-0.015
-0.01
-0.01
Alpha Marker
Average Prediction Strength
Alpha Classifier
Channel locations
1
0.95
Fp1
Fp2
0.9
F7
FC5
T7
0.85
F8
F3
FC1
C3
Cz
TP9
C4
CP2
Pz
P3
0.7
CP6
TP10
P8
Oz
0.75
T8
P4
P7
O1
0.8
FC6
FC2
CP1
CP5
F4
Fz
O2
0.65
0.6
0.55
EEG index derived from
fMRI local activation
30 of 32 electrode locations shown
Click on electrodes to toggle name/number
Frequency
(in collaboration with Prof Hendler, School of Medicine, TAU)
350
400
A
Subjects #
C
39
B
60
99
120
141
162
183
204
225
246
267
288
309
330
30
# Voxel connection
in amygdala
25
20
15
Series1
10
5
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Time (Sec)
A. The relationship between the periods of individual’s high fear reports
(colored lines) and the times when the degree of one voxel in the
amygdala was highest (green diamond). B. Changes of the number of
one voxel connections in the HCF Amygdala cluster during the film
viewing. C. The scene of highest fear according to subject #11 self report
and the corresponding amygdala’s inter-voxel highest correlation.
“I’m Scared” Brain Network
Increased
activation brain
network
B1
Decreased
activation brain network
C1
A
C2
B2
B3
C3
The individual fear reaction signal time course (p< 0.01) averaged from the HCF amygdala cluster,
A Right dorsal amygdala.B. Positive correlation with the Dorsal Amygdala.(B1) Bilateral
amygdala (B2) amygdala, ventral hypocampus, perirhinal cortex, putamen, Cerebelum (B3)
mdPFC, DRN, PAG, dorsal and ventral anterior cingulate cortex, precunios, cerebelum,
C.Negative correlation with the Dorsal Amygdala (C1) Subgeniual cingulate cortex(C2) Bi lateral
Caudate Head (Nucleus Accumbens) (C3) insula