Inferring Hand Motion from Multi-Cell Recordings in Motor Cortex using a Kalman Filter Wei Wu*, Michael Black †, Yun Gao*, Elie Bienenstock* §, Mijail Serruya §, Ammar Shaikhouni §, Carlos Vargas §†, John Donoghue § *Applied Mathematics † Computer Science § Neuroscience Brown University

Outline Introduction Kalman Filter Model and its Algorithm Experimental Result Analysis Optimal Time Lag Comparison with Linear Filter Conclusion

off-line data processing Goals neural signals neural reconstruction mathematical algorithm hand position Kalman Filter Firing rates observations inference/decoding

on-line direct neural control Goals neural reconstruction visual feedback Kalman Filter Firing rates observations inference/decoding

Related Work Georgopoulos et al. (1986) Taylor et al. (2002) Warland et al. (1997) Linear filter, ANN Wessberg et al.(2000) Linear filter, ANN Brown et al. (1998)Kalman filter Serruya et al.(2002)Linear filter Gao et al. (2002)Particle filter Population Vector

spike wave form Multi-electrode Array Implant for Spike Timing Recordings 1 ms 80µV Utah Array (4x4 mm) 100 electrodes, 400  m separation

Target Tracking Task Motions: fast, unconstrained Data (training 3.5 min, testing 1 min) : Position (Velocity, Acceleration) Firing rate (42 cells, non- overlapping 70ms bins)

has a sound probabilistic framework makes explicit assumptions about the data and noise indicates the uncertainty of the estimate requires a small amount of “training” data provides on-line estimation of hand position with short delay(within 200ms) has more accurate estimation than the standard linear filter does Mathematical Model

42 X 42 matrix 42 X 6 matrix system state vector firing rate vector 6 X 6 matrix Kalman Filter Model Measurement Equation: 6 X 6 matrix System Equation:

System Encoding by Training Data Centralize the training data, such that

Time Update Measurement Update Welch and Bishop 2002 Kalman Filter Algorithm Prior estimate Error covariance Posterior estimate Kalman gain Error covariance

Reconstruction on Test Data

Uniform: lag j time steps (1 time step = 70ms) Optimal Lag Non-uniform: lag time steps Changing it in two ways: Measurement Equation

Methods CC MSE ( x, y ) Kalman(0ms lag) (0.77, 0.91) 6.96 Kalman(70ms lag) (0.79, 0.93) 6.67 Kalman(140ms lag) (0.81, 0.93) 6.09 Kalman(210ms lag) (0.81, 0.89) 6.98 Kalman(280ms lag) (0.76, 0.82) 8.91 Kalman(non-uniform) (0.82, 0.93) 5.24 Optimal Lag on Test Data

Linear Filter hand position vector of firing rates for 42 cells over 20 bins (1.4sec) learned “filter” Simple regression model, fast decoding, reasonable reconstruction No explicitly probabilistic model, No uncertainty estimation, slow encoding constant offset

Linear Reconstruction Methods CC MSE ( x, y ) Kalman(140ms lag) (0.81, 0.93) 6.09 Linear filter (0.76, 0.92) 8.30

Conclusion Kalman Filter: has sound probabilistic framework, explicit assumptions, and uncertainty in estimation is more accurate than linear filter in estimation provides efficient filtering algorithm shows better reconstruction with time lag analysis

Future Work Exploring Poisson model for spiking activity instead of Gaussian Exploring the non-linear system model Further comparison with population vector methods (Taylor et al, 2002) and particle filtering techniques (Gao et al, 2002) on-line experiment of direct neural control using the Kalman filter

Thanks David Mumford Applied Mathematics Juliana Dushanova Neuroscience Lauren Lennox Neuroscience Matthew Fellows Neuroscience Liam Paninski NYU Neuroscience and Mathematics Nicholas Hatsopoulos U. Chicago Comp. Neuroscience Support: National Science Foundation Keck Foundation National Institutes of Health

Firing rate gives better estimation

Linear filters built on-line Mijail Serruya targetNeural control

(off-line) reconstruct monkey’s hand trajectory from its neural activity (on-line) control cursor movement from monkey’s neural activity (ultimate) provide control of prosthetic devices for severely disabled humans Goals