movable electrodes & feature-based decoding
DESCRIPTION
Movable Electrodes & Feature-Based Decoding. S. Cao , Z. Nenadic, D. Meeker, R. Andersen E. Branchaud, J. Cham, J. Burdick Engineering & Applied Science Biology. Reach. Feature Based Spike Decoding. Prosthetic Control Signal. - PowerPoint PPT PresentationTRANSCRIPT
Movable Electrodes & Feature-Based Decoding
S. Cao , Z. Nenadic, D. Meeker, R. Andersen E. Branchaud, J. Cham, J. Burdick Engineering & Applied Science Biology
• Get the max yield of high quality signals
• Extract max info from (non-optimal?) neurons
Electrical
Signal
Feature Based Spike Decoding
Feature Based LFP Decoding
Reach
State
Reach
State
Prosthetic Control Signal
Goals:
(hardware)
(software)
Limitations of Neuro-Probes for Chronic Recording
Key Challenge: record high quality signals from many neurons for months/years
Fixed positioning of implant• Non-optimal (or wrong!) receptive fields.
• Non-optimal cell type
• Electrode not near cell body:
Array moves in brain matrix
Inflammation, Gliosis, encapsulation, …
Movable electrodes could: • track movement due to migration
• improve SNR
• overcome implant errors
• find “better” neurons
• break through encapsulation
Make the electrodes movable!(autonomously controlled)
Limitations of Neuro-Probes for Chronic Recording
Current Research Program Outline
Theory – develop probe control algorithms using computational model
• Model extra-cellular neuron potentials
• Control algorithm development guided by computational model
Hardware– meso-scale test-beds• Validate concept, evaluate algorithms
• Determine spec.s for MEMS devices
• Test biomechanics of movable electrodes
Experiments– verify theory
Single Cell Extracellular Potential Simulation (adapted from Holt & Koch ’98)
3720 compartment NEURON pyramidal cell model (adapted from Mainen & Sejnowski ‘96)
Synaptic inputs scattered uniformlythroughout dendrites.
Laplace equation:
Boundary condition:
Since solution nearly impossible, useline source approximation (Holt & Koch ‘99) soma
Spatio-temporal variations of extracellular potential
Virtual experiment
Add neural noise
Keep electrode in this region!
Quality Metric Isolation curve
How to find the maximum point of the average isolation curve when all we have are noisy observations?
Peak-to-Peak Amplitude
Solution offered by variant ofStochastic optimization.
Basis function approach
Iterative Algorithm
Experimental Setup
Microdrive in the brain
Filters / Preamps
X
Computer with:
• Data Acquisition
• Electrode Control algorithm
Move Command
Experimental Results(monkey Parietal Reach Region)
Electrode Position
Pea
k-t
o-P
eak
Am
plit
ud
eA
vera
ged
W
avef
orm
Cell Isolation Curve
Electrode Path
Algorithmic State Machine
Initial State
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
No Spikes Detected
1 2 3 4 5 6 7 8 9 10-5
0
5x 10
-5
Algorithmic State Machine
Initial State
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
No Spikes Detected
1 2 3 4 5 6 7 8 9 10-5
0
5x 10
-5
Algorithmic State Machine
No Spikes Detected
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
1 2 3 4 5 6 7 8 9 10-5
0
5x 10
-5
Algorithmic State Machine
No Spikes Detected
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
1 2 3 4 5 6 7 8 9 10-5
0
5x 10
-5
Algorithmic State Machine
No Spikes Detected
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6-3
-2
-1
0
1
2
3x 10
-5
Algorithmic State Machine
No Spikes Detected
Spikes Detected?
Move Fixed
Move Fixed
T F
Spikes Detected
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6-3
-2
-1
0
1
2
3x 10
-5
Algorithmic State Machine
Spikes Detected
Isolation Curve to maximize?
Move Fixed
Move Gradien
t
T F
Maximize Isolation Curve
1 1.5 2 2.5-5
0
5x 10
-5
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
Algorithmic State Machine
Spikes Detected
Isolation Curve to maximize?
Move Fixed
Move Gradien
t
T F
Maximize Isolation Curve
1 1.5 2 2.5-5
0
5x 10
-5
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
Algorithmic State Machine
Spikes Detected
Isolation Curve to maximize?
Move Fixed
Move Gradien
t
T F
Maximize Isolation Curve
1 1.5 2 2.5-5
0
5x 10
-5
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
Algorithmic State Machine
Spikes Detected
Isolation Curve to maximize?
Move Fixed
Move Gradien
t
T F
Maximize Isolation Curve
1 1.5 2 2.5-5
0
5x 10
-5
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
Algorithmic State Machine
Maximize Isolation Curve
Is Cell Isolated?
Move Gradien
t
Do Not Move
T F
Maintain Isolation
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
1 1.5 2 2.5-6
-4
-2
0
2
4
6x 10
-5
Algorithmic State Machine
Maximize Isolation Curve
Is Cell Isolated?
Move Gradien
t
Do Not Move
T F
Maintain Isolation
4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
1 1.5 2 2.5-6
-4
-2
0
2
4
6x 10
-5
Algorithmic State Machine
Maintain Isolation
Is Cell Isolated?
Move small Fixed
Do Not Move
T F
Regain Isolation
0 5 10 15 20 25-4
-3
-2
-1
0
1
2
3x 10
-5
minutes
Algorithmic State Machine
Regain Isolation
Is Cell Isolated?
Move small fixed
Do Not Move
T F
Maintain Isolation4920 4930 4940 4950 4960 4970 4980 4990 5000 5010 5020
6
7
8
9
10
11
12x 10
-5
• Re-isolate when signal falls below threshold
Movable Multi-Electrode Testbed
• sub-micron steps, 1cm range
• fits in standard chamber
• many adjustments
• can insert micro-capillary
• Test Multi-electrode issues
• Test electrode/fluid combos
• gather data for MEMS spec.s
“Nanomotors”
Chamber
AcrylicSkull
Dura
BrainTissue
MEMS Electrolysis Actuator Concept(with Y.C. Tai)
Large Force Generation Low Temperature Low Power Lockable
4
23
1Pa
yEh
Electrode
Bellows
Z-Movement Actuator
Electrolysis Electrodes
Feature Based Bayesian Decoding
5 deg
Neuron 3
Neuron 2
Neuron 1
5 deg
Time
Characterize receptive Fields
Predict movement plan
x=argmax[P(x|v)]
In real time, record cell activities
)(
)|()()|(
vP
vPPvP
xxx )|( xvP
What features to use?
Decoding the Planned Reach Direction
)(
)|()()|(
vP
xvPPvP
xx
Bayesian ClassifierFiring Rate
5 deg
Neuron 3
Neuron 2
Neuron 1
5 deg
T im e
P RR recep tive fie lds span w orkspace. For any g iven reach ... Calcu late probab ility of a ll reaches:
Com plete set o f reaches: P (n|x) ... m easure spike tra ins: n P (x |n ) P (n ) = P (n |x ) P (x)
S elect m ost p robable: m ax (P (x |n ))
)}|{Pr(maxarg~
xxx
Feature Extraction
x-Reach Direction
v-Feature
Wavelet Packet Overview
(0,0)
(1,0) (1,1)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7)
(4,0) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10)(4,11)(4,12)(4,13)(4,14)(4,15)
Wavelet Packet Tree
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 10
0.5
1
1.5
0 0.5 1-2
0
2
0 0.5 1-2
0
2Haar Wavelet Packet--indexed at 19
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
0 0.5 1-2
0
2
Wavelet Packet Tree Haar Wavelet Packet up to Level 14
)(),(}{ ttxv mnmn
n
iijij
n
j
tvtx1
)()( 0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
0 50 100 150 200 250 300 350 400 450 500-2
-1
0
1
2
0 50 100 150 200 250 300 350 400 450 500-2
-1
0
1
2
Number of spiking in a window (firing rate)
Local change of firing rate (slope in PSTH)
Local oscillation in spiking train (bursting)
L H
L H
Feature Selection
Goal: select the most informative wavelet bases (features)
v XX
ij
ijijij XpXvp
XvpXpXvpvXI
)()|(
)|(log)()|();(
• X is reach class
• p(v|X) is conditional probability of feature v given class X
Solution: choose cost function to quantify the decodability of each feature ) Mutual Information
n
iijij
n
j
tvts1
)()(
0 50 100 150 200 250 300 350 400 450 5000
1
2
3
0 50 100 150 200 250 300 350 400 450 500-2
-1
0
1
2
0 50 100 150 200 250 300 350 400 450 500-2
-1
0
1
2
Spike train
Basis Functions
Wavelet Packet Tree Pruning
Prune the wavelet packet tree in searching for the most informative features.
• Features with large mutual information
• Features that are orthogonal to each other
(0,0)
(1,0) (1,1)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7)
(4,0) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10)(4,11)(4,12)(4,13)(4,14)(4,15)
Wavelet Packet Tree
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(0,0)
(1,0) (1,1)
(2,0) (2,1) (2,2) (2,3)
(3,0) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7)
(4,0) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10)(4,11)(4,12)(4,13)(4,14)(4,15)
Wavelet Packet Tree
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Feature Template
t
0 50 100 150 200 250 300 350 400 450 500
-1
0
1
0 50 100 150 200 250 300 350 400 450 500
-1
0
1
0 50 100 150 200 250 300 350 400 450 500
-1
0
1
Time
Simple Sanity Check
Poisson Spike Trains with repeatable spikes at specific times
Identified Features
Decode Performance
• MFR = 25%
• Feature: 91%
-4 -2 0 2 4 6 8 100
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Projection Coefficient Value
Pro
babi
lity
-5 0 5 10 15 20 250
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Mean Firing Rate Value
Pro
babi
lity
Single neuron decoding comparison(PRR Neuron, left-right reach task)
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
Time ms
Tria
ls o
f Spi
ke T
rain
s
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
30
35
40
Time ms
Tria
ls o
f Spi
ke T
rain
s
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
TimeV
alue
Mean Firing Rate Optimal Feature
Coef value
Probability
Decoding Performance 52.5% 68.0%
Feature Probability
Optimal Feature
Multiple Neuron Performance Comparison
8-direction decoding using up to PRR 41 neurons(from single electrode acute recordings)
10%
20%
30%
40%
50%
30
210
60
240
90
270
120
300
150
330
180 0
4 neurons with no obvious MFR tuning All 41 available neurons
20
40
60
80
100
30
210
60
240
90
270
120
300
150
330
180 0
-red MI
-blue MFR
Step 1. Estimate the firing rate function from the spike train ensemble
• Wavelet thresholding method [Donoho 1994]
0 50 100 150 200 250 300 350 400 450 5000
10
20
30
A
lemda(t) = 10sin(4pit/512)+15
0 50 100 150 200 250 300 350 400 450 5000
10
20
30
B
0 50 100 150 200 250 300 350 400 450 5000
10
20
30
C
Firing rate function estimation using wavelet thresholding
otherwise
ifsign jkjkjkjk
0
)(*'
jk
dbjkjk t)(*
1
0
)(T
l
dbjk
nsljk l
Projecting Noising Estimation
Thresholding
Denoising
Step 2: Computing the Theoretical Wavelet Packet Coefficient Distribution
If the spike train process is a homogeneous Poisson …
TN
N
N
eN
T
nN
NnvP
)!2(2/
2
2
1)(
2
0
2
TN
N
N
eN
TnN
NnvP
)!2(2
12
2
1)(
2
0
2
even
odd-10 -8 -6 -4 -2 0 2 4 6 8 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5Prob of Projection Coef of Homogeneous Poisson of diff rate
10 Hz20 Hz30 Hz40 Hz
Pro
ba
bility
Coefficient Value
If the spike train process is an inhomogeneous Poisson …
Computational method that computes the probabilities exists
Example Distribution of Inhomogeneous Poisson Process
-15 -10 -5 0 5 10 15 200
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2lemda = 10*step(t)+10*step(t-256), Wavelet Packet coeffcient at level 9
Wavelet packet coefficient values
Pro
babi
lity
WP coef 1 (firing rate)WP coef2 (firing rate diff)All other WP coefs
(t)=10step(t)+10step(t-256)
time
freq
ue
ncy
NOTE: The error on the probability P*(v) caused by the estimation error of the rate function decays exponentially with the number of spike trains in the ensemble
Step 3. Estimate the empirical distribution of the wavelet packet coefficients
• Each wavelet packet coefficient is integer valued
• Histogram rule estimation
N
vvvvP jk
jk
)'(#)'(
-15 -10 -5 0 5 10 15 20 250
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.210Step(t)+10Step(t-256) WP Coef Dist at j=9
V91 TheoreticV91 EmpiricalV92 EmpiricalV92 TheoreticRemain EmpiricalRemain Theoretic
Coefficient ValueP
rob
ab
ility
Step 4: Goodness-of-fit Test between the Theoretical and Empirical Distributions
Use 2 test to assess the difference between the two distributions
Mv
vv jk
jkjkjk vP
vvPvvP
1)(
)]()([*
2*2 DOF is the cardinality of the coefficient vjk
If p-value > 0.95, the coefficient’s distribution deviates significantly from its Poisson counterpart
If p-value < 0.95, both distributions conform
-20 -10 0 10 20 30
0
0.05
0.1
0.15
ResultsResult 1: Cyclic Poisson Process
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
30
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
30
Δt
Δt
T
vvaluepvkjkj
j
}95.0)(|{# **
*
1 2 3 4 5 6 7 8 90
10
20
30
40
50
60
70
80
90
100
Scale
j
t = 32
t = 64
Δt
Δt
Results (II)Result 2: Brandman-Nelson Non-renewal Model [Brandman 2002]
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
0 50 100 150 200 250 300 350 400 450 500-4
-2
0
2
4
1 2 3 4 5 6 7 8 90
10
20
30
40
50
60
70
80
90
100
T
vvaluepvkjkj
j
}95.0)(|{# **
*
Scale
j
b = 0.5
b = 0.25
As slope b decreases, the scale of renewal increases; equivalently, the process becomes more Poisson like.
Spike Train
Generating Process
Poisson Scale-Gram
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
50 100 150 200 250 300 350 400 450 500
1
2
3
4
5
6
7
8
90
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
50 100 150 200 250 300 350 400 450 500
1
2
3
4
5
6
7
8
9
Characterize Poisson-ness at different scales (i.e., is rate coding appropriate?)
Short time-scale non-Poisson-ness
Longer time-scale non-Poisson-ness
Relatively Poisson
Populations of PRR neurons during virtual reach experiments (D. Meeker)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
50 100 150 200 250 300 350 400 450 500
1
2
3
4
5
6
7
8
9
Tim
e sc
ale
Coefficient index
First Experimental Results(monkey Parietal Reach Region)
Cell Isolation Curve
Electrode Path