movable electrodes & feature- based decoding s. cao, z. nenadic, d. meeker, r. andersen e....

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


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


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


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


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


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


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


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

Shiyan

Talk about the 41 neuron data set first....how they are handpickedMention the 41 neuron is not representative of the neural prosthetic because when you stick a probe in there, you cannot pick the MFR tuned neurons as you like...therefore, the other case is more realistic...and we need to get as much information out of our data as poissible.

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

Shiyan

Mention there are many ways of denoising, here we choose wavelet thresholding...Also, need to stress simulation.

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

Shiyan

Relate the change of firing rate to actual firing rate change with respect to stimulus. Again, stress simulationMention the non-center is an indicator of inhomo Poisson

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

Shiyan

Again stress simulation

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

Shiyan

Lead into it with how other methods won't workStress how COV would fail. Also describe the scale information: when deltaT becomes big, the wavelet at a large scale is able to detect the repetition of structure. That's why the coefficiens jumps at a large scale, not at small scales.

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

Shiyan

Just mention we have a non-renewal process, and our method reveals information that agrees with the original observaion.

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

movable electrodes & feature- based decoding s. cao, z. nenadic, d. meeker, r. andersen e....

Documents

fixed tf spikes

theory slide

soma slide

command slide

isolation curve slide

peak amplitude slide

chronic recording slide

hardware software slide