4. For each unit one lag, one polynomial, and one axis were selected based on the quality of fit of the posterior. Thus, the firing rate of each unit is modeled as depending on only 4-7 parameters: - axis - time lag - polynomial order The process was modeled using an autoregressive filter via the matlab package arfit. Only the two independent state variables – x and y – were modeled. PREDICTING ARM DYNAMICS FROM CORTICAL ENSEMBLE ACTIVITY IN PRIMATES VIA PARTICLE FILTER Tim Hanson 1, Jose M. Carmena 1,2,4,5 and Miguel A.L. Nicolelis 1,2,3 Department of Neurobiology 1, Center for Neuroengineering 2, Department of Biomedical Engineering 3, Duke University, Durham, NC, USA Department of Electrical Engineering and Computer Sciences 4, Helen Wills Neuroscience Institute 5, University of California, Berkeley, CA, USA INTRODUCTION Work on brain-machine interfaces (BMIs) has focused on the extraction of kinematic parameters, such as hand position and velocity, using optimal linear filters that correlate neuronal response to behavior. While a linear filter can independently predict each kinematic or dynamic variable from ensemble neuronal response, it cannot predict them consistently – that is, the prediction of velocity does not integrate to the prediction of position, acceleration is inconsistent with force, etc. Since it has been demonstrated that neurons are modulated to a great many behaviorally relevant parameters, a BMI should attempt to integrate all of the information in predicting arm or prosthetic motion. A BMI should also attempt to predict each variable in a consistent manner. A Kalman filter can do both, but it has limited applicability when the state update and measurement equations are nonlinear. A simple and general solution to the problem in these conditions is to use a particle filter to predict state variables. Here we demonstrate the use of a resampling particle filter which is extended to project current particle position into spaces in which recorded neurons exhibit tunings. In this way, we create a decoding method that is both consistent with the breadth of documented tunings in the motor cortex and is consistent with the physical limitations of the arm or prosthetic which the cortex controls. Methods 1. A total of 24,672 center-out trials were recorded from 3 rhesus macaques over a period 108 sessions. The monkeys were implanted as follows: Monkey z: 32 fixed in PMd, 64 fixed in M1, 32 fixed in S1, 39 sessions. Monkey n: 32 movable in PMd, 32 moveable in PMv, 32 moveable in M1, 32 fixed in S1, 48 sessions. Monkey p: 32 movable in PMd, 32 movable in PP, 32 movable in M1, 32 fixed in S1, 21 sessions. (a) (a) Experimental setup. (b) Typical performance of the monkey. units: meters. (c) Waveforms in 128 channels recorded in a typical session. Thickness of colors = 2 standard deviation. ; alpha value ~ sqrt(number of events). B. Fitting the particle filter A. Experiment 1.From the recoded joint angles, a larger set of behaviorally relevant parameters were derived: cartesian position cartesian velocity four-link joint torques cartesian forces Since the kinarm puts an additional load on the monkey's arm, we use newtonian dynamics to determine the joint torques associated with the recorded behavior. It is much easier to formulate the four-link problem in terms of these joints. In order to calculate the torques exerted to cause observed motion, we first transformed to make the angles of the electric motors the two independent variables. Torques were computed for these angles, and converted to elbow and shoulder torques. (1) For online performance, it must be possible to obtain a reasonable estimate of each dependent state variable via a function of the present state and a short history of past states. 2. The spike-dependent marginalized posterior was determined from the compiled set of spike times, t u,I, indexed by neuron u, instance i. This was computed via binning with edges placed equally along the vertical axis of the cdf. This results in the same number of counts per bin when the marginal prior is binned with these unequal-width edges, and has the effect of dividing by the prior, as per Bayes' rule. pdf cdf 2. At the start of each session we manually sorted units. During performance of the task, elbow and shoulder joint angles and derivatives were recorded by the kinarm. In the task the monkey had to reach to one of twelve 2cm targets placed in an 24cm x 15cm ellipse around the center target. Location of the implants in the 3 monkeys. (2) histc(x(t u,i ), binedges) red: posterior / black: polynomial fit / file: nino020305a 22u1 shoulder angle (b) (a) (b) 3. Each posterior – one for every lag, unit, and state variable – was fit using a polynomial: C. Simulating the particle filter The algorithm is essentially a resampling particle filter with state independent measurement, A particle filter is a recursive procedure, in which particles are weighted and moved once per time update. The general steps are outlined below. The innovative aspect of our algorithm is highlighted in teal. x y t Each particle includes a short time history expand the space cdf -1 for each of J particles this probability is the particle weight eval polynomial take product over all units normalize w estimate state resample run one step in AR model use poisson model to estimate p(ns|x) Results 1.The particle filter is generally better than a one dimensional linear filter for cartesian x and y, which follows from the fact that these variables are the state variables. 2. Performance of the particle filter on non-state variables was always less than the linear filter. This makes sense as the particle filter only implicitly generates the dependent variables, and they are not subject to optimization. This was especially true for the second- derivative measures, like force and torque. binedges Correlation coefficients for particle filter and 1D linear filter 1. It is possible to predict a large number of kinematic and dynamic variables in a physically consistent manner using a modified particle filter. 2. Using constant-count bin edges improved the quality of posterior polynomial fits by distributing the effect of each data point equally – outliers had less of an effect. 3.This method, like previous work with particle filters, is suitable for online BMIs if modern parallelization techniques are employed. CONCLUSION Sponsored by Christopher Reeve Paralysis Foundation (JMC), DARPA grant N C-8022, NSF and James S. McDonnell Foundation (MALN). 1 cm PP PMv PMd S1 M1 Array of 32 movable microwires, 1mm spacing AA (c)