## Statistical encoding model for a primary motor
cortical brain-machine interface

IEEE Transactions on Biomedical Engineering 52: 1312-1322.

A number of studies of the motor system suggest that the majority of
primary motor cortical neurons represent simple movement-related
kinematic and dynamic quantities in their time-varying activity
patterns. An example of such an encoding relationship is the cosine
tuning of firing rate with respect to the direction of hand motion
[1]. We present a systematic development of statistical encoding
models for movementrelated motor neurons using multielectrode array
recordings during a dynamical two-dimensional target-tracking
experiment. Our approach avoids massive averaging of responses by
utilizing two dimensional normalized occupancy plots, cascaded Linear-
Nonlinear (LN) system models and a method for describing variability
in discrete random systems. We found that the expected firing rate of
most movement-related motor neurons is related to the kinematic values
by a linear transformation, with a significant nonlinear distortion in
about 1/3 of the neurons. The measured variability of the neural
responses is markedly non-Poisson in many neurons and is well captured
by a "Normalized-Gaussian" statistical model that is defined and
introduced here. The statistical model is seamlessly integrated into a
nearly-optimal recursive method for decoding movement from neural
responses based on a Sequential Monte-Carlo filter.

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