Physiology-based modeling and quantification of auditory evoked

potentials

Cliff Kerr Complex Systems Group

School of Physics, University of Sydney

Introduction

• Aim: to develop a physiology-based method of evoked potential (EP) analysis, in order to:– Provide a means to quantify EPs– Relate EP data to brain physiology

• Implementation: biophysical modeling and deconvolution of EEG data

Outline• What are evoked potentials?• Fitting:

– Methods: theory, data, implementation

– Results: group average waveforms – Application: arousal

• Deconvolution:– Motivation– Theory– Results: synthetic and experimental

data

• Discussion and summary• Challenges and future directions

What are EPs?

V(V)

t(s)

EEG:

EP:

V(V)

t(s)

Time-locked averaging

stimulus:

Traditional analysis: scoring

Feature Amplitude

Latency Feature Amplitude

Latency

P50 1.2 mV 56 ms

N1 8.0 mV 120 ms

P2 -8.0 mV 264 ms

N1 6.5 mV 112 ms

N2 3.4 mV 224 ms

P3 -19.6 mV 320 ms

Standard Target

e

i

r

s

n

Cortex

Thalamus

Brainstem

Theory

• Physiology-based continuum modeling: uses 11 vs. 1,000,000,000,000,000 connections

• Five populations of neurons: – Sensory (excitatory; labeled n)

– Cortical (excitatory & inhibitory; e & i )

– Thalamic relay (excitatory; s)

– Thalamic reticular (inhibitory; r)

• Five neuronal loops: – cortical (Gee , Gei )

– thalamic (Gsrs )

– thalamocortical (Gese , Gesre)

e

i

r

s

n

Theory

Theory

• Model has 14 parameters: – 5 for neuronal coupling strength (Gee , Gei , Gese , Gesre ,

Gsrs )

– 4 for neuronal network properties (, , , t0)

– 5 for stimulus properties (tos , ts , ros , rs)

• Most important parameters are the gains Gab

(coupling strength between neuron populations)

• Model describes conversion process (auditory stimulus → neuronal activity → scalp electrical field) using an analytic transfer function e/n:

n

einout SS

Theory

• Direct impulse:

• Cortical modulation:

• Corticothalamic modulation:

• Transfer function:

srs

esnti

GL

GLeI

2

22/

1

0

eeeiec LGLGDM )1(

srs

esreeseti

t GL

GLGLeM

2

32

1

)(0

tcn

e

MM

IT

),(

),(),(

k

kk

Theory

• Impulse:

• Time-domain impulse response:

kkkr k 23

dd),(),()2(

1),(

tiri

n eeTtR

2

||

2

122

2),(

s

r

s

t

tt

n r

e

t

et

s

os

s

os

rr

r

Data• Sampled from 1527 normal

subjects:– Aged 6-80 years

– Equal numbers male & female

– No neurological diseases, chemical dependencies, etc.

• Stimulus: 1 tone/second for 6 minutes (280 standard tones, 80 target tones)

• Used to produce group average standard and target EPs (generated using >100,000 single trials!)

2

P1

P2

.

Fitting1) Initial parameters are chosen

2

P1

P2

.

Fitting2) Gradient descent algorithm reduces 2

of fit

2

P1

P2

Fitting3) Process is repeated using different

initialisations

• Excellent fits to standards (up to 400 ms)

Results

• Excellent fits to targets (up to 300 ms)

Results

Results• Possible changes in neuronal network

properties:

Results• Probable changes in neuronal coupling

strengths:

Results• Definite changes in stability parameters:

Application: arousal

task du

ratio

n (m

in)

0.1 s

-5 μV

0

6

4

2

• Same task (auditory oddball)

• 43 subjects

• Averaged over ten time intervals of 40 seconds each

Application: arousal• Increased cortical activity → decreased

acetylcholine?

Deconvolution: motivation• In model,

thalamocortical loop → N2 feature of targets

• Could target response = standard response + delayed standard response?

Deconvolution: motivation

Theory• Assumption: responses are product of

task-dynamic and task-invariant properties:

• Fourier transform:

• Take the ratio of the two:

• Inverse Fourier transform to get the result:

)]()([)( 1 IDtR SSF )]()([)( 1 IDtR TT

F

)()()]([ IDtR SS F )()()]([ IDtR TT F

)()(

)(

)()(

)()(

CS

T

S

T DD

D

ID

ID

)()]([1 tDD CC F

Theory• Direct deconvolution is uselessly noisy:

• Hence, use Wiener deconvolution:

NSRR

R

R

RD

S

S

S

TC 2

2

|)(|

|)(|

)(

)()(

Synthetic data

Group average data

Single-subject data

Discussion and summary

• Physiology-based EP fitting can be achieved

• Offers significant advantages over traditional methods

• Results tentatively suggest physiology underlying stimulus perception:– Increase in stability: required for a transient

response

– Arousal determined by thalamocortical activity: standards show increased inhibition, targets show increased excitation

– Standards generated by ≈1 thalamocortical impulse, targets by ≈2

Challenges• Fitting challenges

– Degeneracy– Constraints– Testability

• Deconvolution challenges– Noise and artifact– What are we looking for?

• Physiological challenges– Only 1D information– What’s signal?

Future directions• How does the brain change with age?

Standard Target

Future directions• Can our model account for depression?

Future directions• Modeling the ERP “zoo”

– modality

– arousal

– disease

– drugs

Visual: Somatosensory:

Bipolar: Radiculopathy:

Carbonyl sulfide:

Ecstasy:

Quiet sleep:Oddball:

Acknowledgements

Chris J. Rennie

Peter A. Robinson

Jonathon M. Clearwater

Andrew H. Kemp

Brain Resource Ltd.