1. Encoding/Decoding of Arm Kinematics from Simultaneously Recorded MI Neurons Y. Gao, E. Bienenstock, M. Black, S.Shoham, M.Serruya, J. Donoghue Brown Univ., Univ. of Utah Departments of Applied Mathematics Computer Science, and Neuroscience 63.3

2. Goals, Problems and Approaches Goals –Investigate the nature of encoding in motor cortex –Optimally reconstruct hand trajectory from population activity to smoothly control a prosthetic robot arm Problems –Need models of cells’ conditional firing –Need to deal with noisy, ambiguous, and sparse data –Need to make real time reconstruction (< 200ms delay) and cope with non-linear dynamics of hand motion Approaches –Nonparametric models for encoding –Sound probabilistic framework for inference –Propagation of information over time using particle filtering

3. Experiment A.10*10 matrix of electrodes B. Location of array in the MI arm area C. Illustration of implated array D. Continuous tracking task E. Typical trajectory L. Paninski, M. Fellows, N. Hatsopoulos, and J. Donoghue. Temporal tuning properties for hand position and velocity in motor cortical neurons. Submitted to J. Neurophysiology, 2001

4. Modeling the Activity  0 12 Cell 3 speed r (cm/s) Cell 16Cell 19 Empirical mean rate in non-overlapping 50ms bins, 100ms lag Parametric models: cosine model (Georgopoulos et al ’86), Moran and Schwartz ’99 Our approach: nonparametric model, permitting rigorous setting of parameters and comparison of methods, supporting higher-level analysis angle(radians)

5. Modeling the Activity Likelihood: Gaussian or Poisson Spatial prior: Markov Random Field assumption, Gaussian or Robust prior: likelihood spatial prior :observed mean firing rate,:true mean firing rate For each velocity is a noisy realization of the

6. Cosine Model Moran & Schwartz Model Gaussian & Gaussian Model Poisson& Robust Model

7. Evaluation mean firing rate estimated from various models

8. Evaluation Quantitative comparison using log likelihood ratio (LLR) with cross-validation, Wilcoxon signed rank test for significance test Comparing rate from nonparametric models to parametric models MethodsRaw dataCosineM/SG/GP/R Median of LLR’s-1667.1 189.7 201.4215.2236.8 P-value7.6e-06 Pairs of methodsG/G over cosineG/G over M/SP/R over cosineP/R over M/S Median of LLR’s 24.9 15.850.132.2 P-value7.6e-060.00477.6e-06 Comparing rate from various models to constant rate

9. Temporal Inference Use the learned representation of hand motion to infer the motion of a monkey’s hand from neural activity. Model  r ? Ambiguities. Need temporal integration.

10. prior Temporal dynamics Bayesian Formulation Want to infer state of hand given the activity, C t, of (~25 cells) up to time t. likelihood Poisson with conditional mean firing rate as a function of kinematics learned in encoding stage

11. Method: Particle Filter Isard & Blake ‘96 Posterior Temporal dynamics sample sample Posterior Likelihood normalize non-Gaussian likelihood, non-linear temporal dynamics --- nonparametric approach

12. 1000 “Clone” Cells v x : r 2 = 0.8746, v x : r 2 = 0.7735 v y : r 2 = 0.9033 v y : r 2 = 0.8096 a. particle filtering b. linear regression

13. Conclusions Non-parametric model of neural activity in MI * probabilistic relationship between neural activity and events in the world. * superior to previous methods Introduced particle filtering for the Bayesian inference of hand motion in non-overlapping 50 ms intervals * non-Gaussian likelihood and non-linear dynamics * supports more sophisticated analysis Acknowledgements: This work is supported by Keck Foundation grant #R01 NS25074, the NIH #N01-NS-9-2322, and NSF ITR #0113679.