Zoran Nenadic

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Optimization of Extracellular Recordings Control
Algorithm and Unsupervised Signal Processing
Zoran Nenadic Division of Engineering and Applied
Science California Institute of Technology
Department of Biomedical Engineering University
of California Irvine May 3, 2004
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Why is it important to interface neurons and
electrodes?
1) Neural-Prosthetic Systems
Communication link for ALS patients
Tremor suppression for Parkinsons patients
Functional electrical stimulation for paralyzed
patients
Medtronic, Activa System
(Kennedy Bakay, NeuroReport, 1998)
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Neuroprosthetics studies at Caltech
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2) Electrophysiological Recordings
The technology prompted by the discovery of the
microelectrode (Hubel, Science, 1957 Green,
Nature, 1958)
It enables us to observe the activity of a
single neuron (population of neurons) in response
to external stimuli and cognitive tasks.
Acute
(electrodes in the brain for several hours)
Electrophysiological Recordings
Chronic
(arrays of electrodes implanted surgically)
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Acute Recordings
Basic Tool microelectrode
Key Challenge isolate the activity of a single
cell on a single electrode
Single electrode
Multi-electrode
Limitations time consuming, depends on the
experience of the operator
unmanageable in multi-electrode environment
What can be done?
Automate the process of cell isolation and
tracking.
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Chronic Recordings
Key Challenge record high quality signals from
many neurons (for months/years).
Limitations 1) Fixed geometry of implant A)
signal quality depends upon the luck of surgical
placement B) electrodes drift in the brain
2) Reactive gliosis
(encapsulation of electrode by scar tissue)
Utah array Bionic Technologies LLC
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of active channels decreases over time for
fixed geometry implants
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Movable Probe Concept
Autonomously movable electrodes can find and
maintain high quality of recorded signals.
Applications 1) Acute recordings
2) Chronic recordings

• help experimentalists do better brain science
• by helping them manage large number of
  electodes

• help experimentalists do better brain science
• improve brain-machine interfaces
• (better yield, quality and signal longevity)

Other applications 1) Deep brain stimulation
(Parkinsons disease)
2) Muscle stimulation
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Autonomously movable electrode algorithm -
schematic
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Computational Model
Layer 5 adult cat pyramidal cell
Control algorithm developed in simulated
environment. We can test the features of our
algorithm in a repeatable way. Confirms
biophysical basis of our methodology.
apical dendrite
soma
basal dendrite
Detailed computational model (3720 compartments)
available in NEURON. Cell activated by synaptic
inputs scattered uniformly throughout dendrites.

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Laplace equation Boundary conditions
This system is hard to solve! ? Line source
approximation (Holt Koch, J. Comp. Neurosci.,
1999). For a segment of finite length
can be computed analytically
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Spatio-temporal variations of extracellular
potential
plane passing through the soma
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Virtual Experiment
sulcus
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Signal quality curve basis of our control
methodology

• - The choice of signal quality metric non-unique
• - Our algorithm will work for any reasonable
  signal quality metric
• Multiple noisy observations of signal quality
  function are available
• Objective function defined as a regression
  function of some signal dependent quantity given
  electrodes position

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Signal quality curve in monkey cortex
Q How to find the maximum of the regression
function from noisy observations? A Stochastic
optimization.
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Stochastic Optimization (Kiefer Wolfowitz,
Annals of Math. Stat, 1952)
The sequence can be found so that
with probability 1. Problems unbounded
variance near peak
implies excessive dithering-like movements.
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Stochastic Optimization basis function approach
Key idea estimate objective function adaptively
Key challenge choose n to avoid over-fitting.
Bayesian probability theory used. Two steps 1)
Model Selection (choose the order n)
given a family of models M1, M2, , MN , find
the optimal model order.
For polynomial Yj posterior can be found
analytically (Nenadic Burdick, IEEE Trans.
Biomed. Eng., submitted). Optimal
model maximizes the posterior
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Parameter Estimation linear least squares
estimate on the model Mn .
noisy observations
electrode position
(Newtons method)
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Noisy observations of objective function ? signal
recorded by electrode
simulated data
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Robust Unsupervised Detection of Action
Potentials Using the Continuous Wavelet Transform
data from monkey cortex
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Biophysical variations pose challenges for spike
detection
Moving electrodes will experience displacements
of hundreds of microns. Shape of spikes will
vary significantly over electrodes movement
range. Amplitude of spikes (and therefore SNR)
will vary significantly over electrodes movement
range.
Such a wide dynamic range requires an
unsupervised spike detection method with robust
performance over a range of parameters. We
developed one such method (Nenadic Burdick,
IEEE Trans. Biomed. Eng., 2004, in press).
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Why wavelets?
4 wavelet families
5 spike templates
There exist wavelet basis functions that provide
a sparse representation of neural signals.
Wavelet functions are parameterized by scales
and translations.
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Detection Theory
Statistical detection theory is based on
hypothesis testing
The rejection/acceptance of H0 is based on
signal dependent quantity T(x) called sufficient
statistic.
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Five steps of wavelet detection
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Monte Carlo Simulations
Receiver operating characteristics (ROC)

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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Spike Classification
Purpose identify the sources of individual
spikes in data containing multi-unit activity.
Three steps of spike classification

• Spike Alignment
• Feature Extraction
• Model-based Clustering

data preprocessing
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Model-based Clustering with Gaussian Mixtures

• Traditional clustering based on heuristic
  criteria, e.g.
• hierarchical clustering (Ward, J. Amer. Stat.
  Assoc., 1963),
• k-means (Hartigan, Clustering Algorithms, 1975)
• Deficiencies cant determine of classes in the
  data, cant handle outliers

Probabilistic framework ? features are sampled
from unknown distribution. The corresponding
density is modeled as a linear combination of an
unknown number G 1 of component densities pj .
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Uniform component p0 ? fi declared an
outlier. Gaussian components p1, , pG ?
fi belongs to clusters 1, , G.
Once the functional forms of pj are known, the
parameters P and Q that maximize LMIX
can be found. This is achieved with the help of
the Expectation-Maximization (EM) Algorithm
Once P and Q are known, the class membership
is decided via
Still, the number of clusters G is unknown, and
has to be found.
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Model Selection
Purpose estimates the number of clusters in the
data. Given a family of candidate models
M1,M2, ,MN , find the order of the model that
fits data optimally ? find the number of
clusters in the data . From Bayesian probability
theory
Calculation of p(F MG,I) not feasible ? resort
to approximation
of spikes in data
Bayesian information criterion
known from EM
of parameters
Optimal model is the one with the largest value
of BIC
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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Signal quality estimation

• choose signal quality metric, e.g.
• peak-to-peak amplitude or SNR.

• if SNR chosen ? SNRi / di .

• evaluate signal quality over clusters
• S1, S2, , and select the dominant
• cluster, i.e. the cluster that provides
• the maximal average signal quality.

• spikes within the dominant cluster
• provide multiple observations of
• the objective function.

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• Background
• Control algorithm
• Signal quality metric
• Stochastic optimization
• Unsupervised Signal Processing
• Detection
• Classification
• Signal quality estimation
• Experimental Results

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Experimental Results
Custom-made motorized microdrive
(Cham, Branchaud, Nenadic, Greger, Andersen
Burdick, J. Neurophysiol., submitted)
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• - custom-made piezoelectric actuators
• (Klocke Nanotechnik, Germany)
• range of motion 5 mm in 1 micron
• steps
• - force output 0.03 N
• - direct linear motion ? no backlash
• - electrically driven
• - high speed (up to 2mm/s)
• - magnetic field position sensor

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Assembled Prototype
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Algorithmic State Machine
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Single unit isolation using motorized microdrive
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Single unit isolation using motorized microdrive
constrained case
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Single unit tracking using motorized microdrive
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Where do we go from here?
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Conclusion and Future Work

• Accomplishments
• Introduced the idea of autonomously movable
  electrodes.
• Developed a novel control algorithm and signal
  processing tools.
• Successful implementation of algorithm in
  simulations and practice
• (rats and monkeys).

• Importance
• Improve the productivity of neuroscientists.
• Miniaturized version crucial for successful
  brain-machine interfaces.

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• Short-term Goals
• Exploit the modular structure of the current
  algorithm to resolve
• outstanding issues (the choice of right signal
  quality metric, optimal
• features for low-dimensional representation, fine
  tune the algorithmic
• state machine).
• Long-term Goals
• Integrate the control algorithm with
  neuro-prosthetic implants and
• other BMI applications (electrodes for
  stimulation)
• Decoding algorithms for BMI
• Future implants (even beyond BMI) will have more
  control features
• and will require adequate signal processing
  and control tools.

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Division of Engineering Applied Science Caltech
Division of Biology Caltech