Zoran Nenadic Division of Engineering and Applied Science California Institute of Technology

1. 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

2. Why is it important to interface neurons and electrodes? 1) Neural-Prosthetic Systems Communication link for ALS patients Tremor suppression for Parkinson’s patients Functional electrical stimulation for paralyzed patients Medtronic, Activa System (Kennedy & Bakay, NeuroReport, 1998)

3. For successful neural prosthesis it is critically important to record signals with high quality, signal yield and longevity. Neuroprosthetics studies at Caltech

4. 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)

5. 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.

6. Make the probes autonomously track neurons, find new neurons, break through encapsulation etc. Chronic Recordings Key Challenge: record high quality signals from many neurons (for months/years). • Limitations: • 1)Fixed geometryof 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

7. # of active channels decreases over time for fixed geometry implants

8. 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 (Parkinson’s disease) 2) Muscle stimulation

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

10. Autonomously movable electrode algorithm - schematic

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

12. (Mainen & Sejnowski, Nature, 1996). 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.

13. conductivity membrane current normal to the membrane 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

14. Spatio-temporal variations of extracellular potential plane passing through the soma

15. neural noise added Virtual Experiment sulcus

16. Goal: find a maximum (or vicinity of a maximum) of the objective function 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 electrode’s position:

17. peak-to-peak amplitude Goal: find this region Signal quality curve in monkey cortex Q: How to find the maximum of the regression function from noisy observations? A: Stochastic optimization.

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

19. Find: optimal electrode position noisy observations of objective (stochastic gradient ascent) step size future position stochastic gradient current position 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.

20. posterior likelihood prior data evidence prior information 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 polynomialYjposterior can be found analytically (Nenadic & Burdick, IEEE Trans. Biomed. Eng., submitted). Optimal model maximizes the posterior:

21. Parameter Estimation: linear least squares estimate on the model Mn* . noisy observations electrode position (Newton’s method)

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

24. Looking ahead - unsupervised spike detection and classification Noisy observations of objective function  signal recorded by electrode simulated data

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

26. The presence of spikes (events) must be detected in this sampled data. The spike arrival times need to be estimated and a segment of data centered at the arrival time needs to be extracted. This is achieved through spike detection. Robust Unsupervised Detection of Action Potentials Using the Continuous Wavelet Transform data from monkey cortex

27. Biophysical variations pose challenges for spike detection Moving electrodes will experience displacements of hundreds of microns. Shape of spikes will vary significantly over electrode’s movement range. Amplitude of spikes (and therefore SNR) will vary significantly over electrode’s 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).

28. Vast majority of action potentials in primate cortex are highly localized in time (0.5 – 1.0 ms) This determines the relevant scales. Time-frequency analogy. 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.

29. cannot be applied in an unsupervised fashion Detection Theory Statistical detection theory is based on hypothesis testing: The rejection/acceptance of H0is based on signal dependent quantity T(x) called sufficient statistic.

30. perform multi-scale decomposition of the signal over the set of relevant scales separate the signal and noise at each scale using non-linear filtering techniques (Donoho & Johnstone, Biometrika, 1994) perform Bayesian hypothesis testing combine decisions across scales estimate spike arrival times Five steps of wavelet detection:

31. Monte Carlo Simulations Receiver operating characteristics (ROC) +

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

33. feature matrix transformation matrix spike matrix 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

34. feature component the density at fi : overall mixture likelihood: 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: can’t determine # of classes in the data, can’t 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 .

35. Uniform component: p0 fideclared an outlier. Gaussian components: { p1, …, pG }  fibelongs 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.

36. Assuming models have uniform priors : 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

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

38. feature(2) S2 d2 S1 d1 feature(1) N objective position 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.

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

40. Experimental Results Custom-made motorized microdrive: (Cham, Branchaud, Nenadic, Greger, Andersen & Burdick, J. Neurophysiol., submitted)

41. - 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

42. 10mm Assembled Prototype

43. Algorithmic State Machine

44. Single unit isolation using motorized microdrive

45. Single unit isolation using motorized microdrive – constrained case

46. Single unit tracking using motorized microdrive

47. Where do we go from here?

49. 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.

50. 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.