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 FeatureAmplitudeLatency FeatureAmplitudeLatency P mV56 ms N1 8.0 mV120 ms P mV264 ms N1 6.5 mV112 ms N2 3.4 mV224 ms P mV320 ms Standard Target

e i r s n Cortex Thalamus Brain stem 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 (G ee, G ei ) –thalamic (G srs ) –thalamocortical (G ese, G esre ) e i r s n Theory

Model has 14 parameters: –5 for neuronal coupling strength (G ee, G ei, G ese, G esre, G srs ) –4 for neuronal network properties ( , , , t 0 ) –5 for stimulus properties (t os, t s, r os, r s ) Most important parameters are the gains G ab (coupling strength between neuron populations) Model describes conversion process (auditory stimulus → neuronal activity → scalp electrical field) using an analytic transfer function  e /  n :

Theory Direct impulse: Cortical modulation: Corticothalamic modulation: Transfer function:

Theory Impulse: Time-domain impulse response:

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2 P1P1 P2P2. Fitting 1) Initial parameters are chosen

22 P1P1 P2P2. Fitting 2) Gradient descent algorithm reduces  2 of fit

22 P1P1 P2P2 Fitting 3) Process is repeated using different initialisations

Excellent fits to standards (up to 400 ms) Results

Excellent fits to targets (up to 300 ms) Results

Possible changes in neuronal network properties:

Results Probable changes in neuronal coupling strengths:

Results Definite changes in stability parameters:

Application: arousal task duration (min) 0.1 s -5 μV 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:

Theory Direct deconvolution is uselessly noisy: Hence, use Wiener deconvolution:

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.