Regularization Techniques for BMI Models - Brain-Machine Interface Engineering - page 114

the testing trajectory; specifically, reaching movements shown in the testing plots of Figure 4.5 .
Notice that movements are similar except that movement 3 does not have a decrease in the y coor-
dinate. To visualize trends in how the input affects the output, we plot the neuronal activity (input)
along with the computed sensitivity (averaged over 104 neurons and 20 delays) in Figure 4.5b-c .
We take first a macroscopic view of both the neuronal activity and sensitivity by summing over
104 neurons at each time bin. Comparing Figure 4.5a with Figure 4.5b , we see that it is difficult
to visually extract features that relate neuronal firing counts to hand movement. Despite this fact,
a few trends arise:

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Neuronal activity consists of a time-varying firing rate around some mean firing rate.
Movements 1 and 3 seem to show increased neuronal activity at the beginning and end of
a movement, whereas 2 does not.
All three movements contain a decrease in neuronal activity during the peak of the movement.

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With these three trends in mind, we now include the sensitivity plot estimated for the RMLP
in Figure 4.5c . We can observe the following:

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In general, the network becomes more sensitive during all three movements.
Sensitivity is large when velocity is high.
The sensitivity shows large, sharp values at the beginning and end of the movement, and a
plateau during the peak of the movement.

From sensitivity peaks during the movements in Figure 4.5c , we ascertain that the sensitivity
analysis is a requirement for relating neuronal activity to behavior. Without the model-based sensi-
tivity, finding relationships in the raw data is difficult. Now that we have a mesoscopic view of how
the ensemble of sampled neuronal activity affects the output of the network, we change our focus,
and use the model-based sensitivity to “zoom in” on the important individual neurons. We are inter-
ested in learning why the individual neurons in a given cortical region are necessary for constructing
the network output movement. Using the sensitivity analysis, we can select neurons that are most
closely associated with the reaching movements (i.e., neurons that elicit large perturbations in the
output with small perturbations in firing).
Neurons for a particular movement are selected for the RMLP by choosing the maximum of
a sorted list of neuronal sensitivities computed by averaging the time-varying sensitivity in ( 4.35 )
over the interval of a movement and all three coordinate directions. For comparison, the neurons
from the FIR filter are sorted directly using ( 4.30 ). The sorted ensemble neuronal sensitivities for