Figure 1.
Experimental setup of the dynamic neural interface.
We placed two 16-channel microwire arrays (recording and stimulating arrays) in the vibrissa motor (M1) and sensory areas (S1) of a rat brain cortex. (A) In this example 4 electrical stimulation patterns are set by specifying the pair of electrodes in the 16-channel microwire stimulating array placed in area S1. (B) The activity of a small population of single neurons (11 in this illustration) of area M1 is recorded in response to each electrical stimulation pattern. The activity of each neuron is plotted on a row over a rectangular frame, whose color indicates the correspondence with a stimulation pattern. (C) The motor interface generates a force vector from the first two principal components of the response of the M1 neurons. (D) The obtained force vector is applied to a simulated point-mass moving in a viscous medium. The interaction with such dynamical system aims to emulate a reaching movement creating a convergent force field similar to the force fields observed during microstimulation of the spinal gray matter. (E) The sensory interface maps each point in the field into the corresponding stimulation pattern.
Figure 2.
The purpose of the calibration procedure is to set the parameters of the neural interface. The calibration consists of 4 steps. (A) Recording a training set. The calibration procedure is performed upon a training set (r1…rn) built by recording the neural activities evoked over multiple presentations (usually 100) of each of the n stimulation patterns (s1…sn with n = 4 in this example). (B) Motor Map. The training set is also used to set the motor map. The spike trains from multiple neurons are reduced by PCA to two coordinates of a force vector. In this example the result of this operation is a set of 4 template vectors, each corresponding to a stimulation pattern. (C) Desired force field map. The chosen desired force field to be approximated (e.g. a continuous radial force field converging towards a central equilibrium point) establishes a relationship between the n template vectors and the n positions in the two-dimensional space. (D) Sensory Map. The n positions are used to partition the external device space by using a space partition algorithm (e.g. in this case a nearest neighbor map) and, as a consequence, n sensory regions (A1…An) are defined. A look-up table connects each sensory region to a corresponding stimulation pattern. As a result, the sensory map converts each position of the space into a stimulation pattern.
Figure 3.
An example of motor and sensory interfaces and on-line closed-loop trajectories generated by evoked activity of a population of neurons.
(A) The output of the motor interface during the test phase is represented as the force vectors (black arrows) generated during 100 “test set” repetitions of each stimulation pattern. The spread of the distribution of the single trial vectors represents neural variability at fixed stimulus. The small discrepancies between the angles of the template vectors computed during calibration (blue arrows) and the trial-averaged vector observed for each stimulus during the test phase (red arrows) originates from differences between training and test dataset due to neural variability and limited sampling. (B) A graphical representation of 4 sensory regions generated by the sensory interface. Each position of the point-mass is mapped onto a stimulation pattern and is color coded. (C) Spike rasters and Post Stimulus Time Histograms (PSTH) of a single neuron evoked by 4 different stimulation patterns, using the same color code as in panel B to distinguish responses to different stimuli. (D) Trajectories of the point-mass (dotted black line) generated on-line starting from 4 different initial points (yellow circles). For each trajectory, the force vector applied step by step by the motor interface to the simulated point-mass is indicated with a color code representing the stimulation pattern chosen by the sensory interface. In this example the forces were applied with an interval of 1 s and the point mass reached the target respectively in 6, 16, 25 and 29 s.
Figure 4.
Off-line analysis of dependence of the dNI performances on the temporal parameters defining the neural response.
(A) A closed-loop trajectory recorded on-line (green line) compared to 100 trajectories generated off-line (blue dotted line indicates the mean trajectory and shaded areas represent the p = 0.05 confidence region of trajectory). (B) We compared 70 converging on-line trajectories selected from 13 rats with 70 corresponding off-line trajectories using different parameters such as the root mean square error (RMSE) from the ideal trajectory, the mean integrated distance to target (MIDT) and the number of steps to convergence. Setting the time interval of 1 s between two consecutive steps, these values (mean±SEM: online = 18.2±1.6 and offline = 19.9±1.8) indicate also how long it took for this particular point mass to reach the target. Off-line and on-line behaviors were not significantly different (p>0.1; paired t-test), indicating that off-line simulated trajectories are representative of on-line behavior. (C) Mean convergence rate (CR) subtracted by the mean convergence rate obtained from a random choice of the stimulation patterns, calculated using different sizes for Δt. (D) Mean CR of the dNI calculated using Δt = 5 ms. The CR of the off-line trajectories is used to evaluate the performances of the interface, which is found to be maximal for small temporal resolutions (Δt≈5–10 ms). In particular, by using a bin size of 5 ms the mean CR is 6 times higher than the CR randomly built. The Mutual Information between the expected force vector and the actual force vector is highly correlated both to the CR (E) and to the inverse of the mean number of steps to convergence (F) calculated for all the simulated off-line trajectories.
Figure 5.
Role of recording parameters on Mutual Information measures of the performance of the dNI and dependence of performances on number of recorded single units.
(A) Dependence of the Mutual Information between the expected force vector and the actual force vector upon the temporal bin size Δt. Results were calculated using data computed in the response window with zero offset and 600 ms duration and are reported as average±SEM over all experimental sessions. Information was maximal for small bin sizes, such as Δt = 5–10 ms, meaning that the best performance of the dNI is obtained when recording neural activity with fine temporal precision. (B) Dependence of the Mutual Information
, calculated with temporal resolution of Δt = 5 ms, upon duration (T·Δt) and offset defining the response window. Results are reported as average over all experimental sessions. (C) Convergence rate vs. population size. We compared the convergence rates when using all the neurons of each datasets with those using only half or one quarter of the units (subtracted by the mean convergence rate of trajectories randomly generated). Data are represented as box plots: red lines are the medians, lower and higher borders of the boxes indicate respectively the 25th and 75th percentiles, while the whiskers indicate the minimum and maximum value of each group. ANOVA test revealed that only the quarter case is statistically different from the other two (p = 3.3552e-006).
Figure 6.
Recorded neural activities in M1 evoked by electrical stimulation in S1.
At the beginning of each experimental session a series of electrical stimulation patterns is delivered and a sorting procedure is performed on the raw neural signal to identify both the stimulation artifacts and the single unit activities. Panels (A) and (B) show a portion of a raw signal close to a stimulation event. The sorting procedure is able of identifying the stimulus artifacts (red lines) and the spike occurrences (green lines). Panel (C) shows the unit templates used by the sorting algorithm (left) and a representation of the sorted data onto the first two principal components plane (right). (D) Post Stimulus Time Histograms (PSTH) of neural evoked responses of a subset of three neurons selected from three experiments. The color code represents different stimulation patterns. (E) Scatter plot of variance vs. mean of spike counts (computed in sliding 20 ms long post-stimulus windows) of all pooled data points across units and sessions. This measure is a relatively standard measure of cortical response variability. The best-fit power law curve ( with α = 0.7 and β = 0.93) is plotted with the best fit parameters. These data are at the most reliable end of the range of response variability reported in the cortical literature. (F) CO stained section (AP = −3.3 mm from bregma) of the rat brain with microelectrode track. The black dotted line indicates the boundary of the barrel. The perpendicular length from the tip of the electrodes (the center of the hole) to the cortical surface measured 730 µm.