The Animal Policy and Welfare Committee of the University of Alberta approved all procedures under the guidelines of the Canadian Council of Animal Care. Seven adult cats were anaesthetized with sodium pentobarbitone (40 mg kg−1i.p.). A tracheal cannula was inserted to maintain respiration and a jugular catheter was used to administer fluids and the same anaesthetic, as required to maintain a surgical level of anaesthesia. The back was shaved and a skin incision was made along the mid-line of the back. Paraspinal muscles overlying the transverse processes of L5–S1 were removed and a laminectomy was performed to expose the spinal cord and dorsal roots. Two 5 × 10 arrays of penetrating microelectrodes (Cyberkinetics Inc., Foxborough, MA, USA) were implanted through the dura into the L6 and L7 dorsal root ganglia (DRGs) on one side with a high-velocity inserter (Rousche & Normann, 1992). Reference wires were placed in the fluid surrounding the DRGs and the skin flap was closed over the back. After surgery the animals were suspended in a spinal frame and radiant heat was used to maintain the body temperature near 37°C. At the end of the experiment the animal was killed using an overdose of the anaesthesia and the cessation of cardiac activity was monitored for several minutes.
Multichannel neural recording technique
The electrodes used in these experiments were arranged in a rectangular configuration with 5 rows of 10 electrodes, 1.5 mm in length and spaced 400 μm apart. In addition to providing many sites for recording action potentials, this dense arrangement of electrodes serves to anchor the implanted array among the densely packed cell bodies within the ganglion. The electrode arrays were connected to a 100- channel amplifier. The gain of the amplifiers was 5000 (bandwidth 250–7500 Hz) and signals from each electrode were sampled at 30 kHz. A Pentium class computer recorded and saved the signals in conjunction with a Neural Signal Acquisition System (NSAS; Cyberkinetics Inc.). This system required thresholds to be set on each channel and only saved brief (1 ms) segments of the signal around the time that the threshold was crossed (Guillory & Normann, 1999).
Single units were discriminated offline from the set of recorded waveforms on each electrode using a Matlab-based algorithm (Shoham et al. 2003). The waveforms were first projected onto their principle components (PC), and an expectation-maximization clustering algorithm then identified the number of clusters and their parameters (see Fig. 1).
Figure 1. Methods for analyzing waveforms on a single electrode Various waveforms recorded on one electrode were sorted (A) into three distinct units (red, blue and green) and unclassified waveforms (black) using cluster analysis in a space (B) representing the first two principal components (PC1, PC2) of the waveforms. The ellipses were computed using an automatic spike classifier (Shoham et al. 2003). The pattern of activity and joint angles are shown below (C).
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Following the cluster estimation procedure, additional automated procedures for ‘spike train editing’ were applied (Stein & Weber, 2004). For example, an algorithm applied statistical tests to eliminate spikes that produced instantaneous firing rates more than double the smoothed firing rate and added spikes to long intervals that produced an instantaneous rate about half of the smoothed firing rate. These deviations occurred when an erroneous waveform was accepted or a correct waveform was missed; see Stein & Weber (2004) for a detailed justification. The spike-editing techniques facilitated analysis of units for which the threshold was not set ideally or the signal-to-noise ratio was marginal. For control purposes, we repeated the analysis using traditional analysis techniques. The results were virtually identical, but the variability was slightly greater with the unedited spike trains, as expected.
Sensory afferents were activated by palpation and manipulation of the hindlimb. The response properties were used to categorize each unit (Aoyagi et al. 2003). Briefly, the hip, knee, ankle and toes were moved manually to identify muscle and joint receptors. A hand-held vibrator (∼140 Hz) was generally applied over the tendon or muscle belly to identify primary spindle afferents. Golgi tendon organs may have been missed, because the animals were deeply anaesthetized and the muscles were completely flaccid. Cutaneous receptors were identified by palpation (touch, pressure, pinch and vibration). Gentle blowing or focal touch was used to identify hair receptors. During each manipulation, 10 s recordings were made to document the waveform and response for each unit.
After the units on each electrode were categorized, various movements were applied to the foot manually or with a robotic manipulator. The manipulator had two DC servomotors (BE233DJ; Parker Hannifin, Rohnert Park, CA, USA) and was programmed to deliver repeatable movements. For example, to generate random movements, the manipulator moved through a series of positions selected at random from a rectangular grid of points in the sagittal plane and the velocity of each movement was also chosen at random over a range of speeds. The movements continued until all points in the grid had been reached so there was a uniform coverage of the workspace. In several experiments, the identification and application of movements were repeated several hours later. For example, in one experiment in which 60 units were initially recorded 22 of them were still present in a second series of movements applied more than 4 h later. Thus, over a third of the units could be recorded for at least 4 h.
Kinematic recording technique
Walking-like, centre-out movements (from a central point to eight points in the periphery) and random movements were studied, all of which were largely confined to the sagittal plane. For example, the random movements (Fig. 2) covered most of the physiological range of the cat's hindlimb in the anterior–posterior plane (30 cm) and in the vertical direction (20 cm), but only 1–2 cm in the medio-lateral plane. A U- shaped holder made of dental acrylic was fitted around the cat's paw, proximal to the metatarsophalangeal (MTP) joint. The top of the U was tied so that the paw was held securely. Any pressure on the skin was distributed widely and direct contact with the skin by the experimenters or the manipulator was minimized.
Figure 2. Methods for applying and recording movements Position sensors (ϒ) were attached at the hip, near the knee and the ankle and on the paw near the metatarsophalangeal joint. From the positions of the sensors a stick figure of the cat's hindlimb in the sagittal plane was calculated. A, pseudorandom movement of the paw manually over its passive range of motion is shown as a dotted line. The position of the paw can be represented in terms of the forward (x) and vertical (y) position with respect to the hip (Cartesian coordinates). It can also be represented in polar coordinates as the distance (r) and the orientation angle (φ) of the paw with respect to the hip or in terms of the joint angles. Note that the orientation and hip (h) angles are measured with respect to the horizontal and increase as the hip and leg are extended. The knee and ankle angles (not shown) are defined according to the usual convention and increase with extension of the joint. B, random movements over a more restricted range (approximately 20 × 15 cm) using a robotic manipulator (see details in Methods).
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During manual movements of the limb, electromagnetic, motion-tracking sensors (6D- Research, Skill Technologies Inc., Phoenix, AZ, USA) measured the limb kinematics. Four magnetic sensors were placed on: (1) the skin near the hip joint; (2) the lateral epicondyle of the femur near the knee; (3) the lateral malleolus of the tibia near the ankle; and (4) the lateral surface of the foot holder near the metatarsophalangeal joint. For simplicity we will refer to this as the ‘toe sensor’ and use it as a measure of the toe position in space. To avoid skin slippage or displacement during movement, magnetic sensors (2) and (3) were rigidly fixed to the femur and tibia by surgical sutures through holes drilled in the respective bones. The distance of each sensor from its neighbouring joints was measured to allow calculation of the position of the joint centre. Intersegmental (joint) angles were calculated, together with the position of the toe sensor in rectangular and polar coordinates, using the hip sensor as the origin. The medio-lateral movements of the limb were also recorded, but were small (<2 cm) and are not shown. Results computed from the 3D angles, obtained with the electromagnetic motion-tracking system, were compared with those computed from 2D projections onto the sagittal plane and no significant differences in the fits were found. Therefore, 2D angles are analysed here.
The sampling rate of the 6D- Research system was 30 Hz and was well above the highest frequency components applied to the cat's paw (5–10 Hz). For the magnetic recordings we ensured that all instruments near the sensors, including sections of the spinal frame, contained no metal to avoid distorting the signals from the electromagnetic sensors. A synchronization pulse was used to align the neural and motion data offline.
A high-speed digital video camera (120 fields s−1, GRDV9800R, JVC Corp.) recorded the limb movements produced by the robotic manipulator. A light-emitting diode (LED) was used to synchronize the video with the neural data. White markers were glued to the skin over the iliac crest, and the joint centres of the hip, knee, ankle and MTP joints. The centroid of the marker was automatically located in each image of the video using custom Matlab (Mathworks, Inc.) software. The camera plane was parallel to the sagittal plane of the leg. Calibration markers were spaced 10 cm apart in the horizontal and vertical planes and used to calibrate the camera view. Parallax errors were compensated by scaling the segment vectors by the measured separation distance between the ankle and MTP markers (i.e. foot length, which is constant).
Hip, knee and ankle joint angles were computed from the digitized marker positions, extension corresponding to a positive angular displacement. The knee marker was not used, because the skin overlying the knee tends to slide over the joint. Instead, the knee-joint angle was calculated using eqn (1), which follows from the law of cosines.
The three distances used in this calculation are: (1) Lfemur, femur length; (2) Lshank, shank length; and (3) d, distance between the hip and ankle markers. The MTP was regarded as the end-point (toe position) for the limb measured in a polar coordinate system relative to the hip (r, radial distance; φ, orientation).
A multivariate linear regression was used to model the firing rate of each neurone as a function of kinematic variables of the hindlimb (neural encoding). The full procedure included three processing steps.
(1) The neural and kinematic data were aligned at the LED onset time. Neural firing rates were calculated using the filter in eqn (2).
The firing rate (fi) is computed at each time index i, ti is the current time, tj is the time of spike j in the interval [ti−Δt, ti+Δt], and Δt is the sampling interval. Essentially, a contribution to the rate is added for the two nearest sample times for the kinematic variables in a way that all spikes are equally weighted and the mean time of the weights is the actual time of the spike. This method is similar to the partial binning methods previously described (Richmond et al. 1987; Schwartz, 1992; Stein et al. 2004).
(2) The rate function was filtered with a critically damped, second-order, low-pass filter (Stein et al. 2004). The impulse response of this filter is an EPSP-like waveform (Jack et al. 1975). Rate constants between 15 and 30 rad s−1 were used, corresponding to time constants of 67–33 ms. Different filters and other time constants for the EPSP-like filter were also applied using the Matlab function ‘filt’. In general, longer time constants (more filtering) gave better fits, as expected. However, if the time constant was extended beyond the values cited, very little improvement was seen. The same filtering was also applied to the kinematic variables to avoid introducing relative time delays. Filtering was done after step (1) above to ensure that all spikes were given equal weight.
(3) The filtered firing rates were fitted to a weighted sum of position and velocity variables in each of three coordinate systems: Cartesian (x, y) and polar (r, φ) coordinates for the toe sensor, and joint angles (hip, knee and ankle) for the limb. This allowed a comparison of the predictions in Cartesian, polar and joint angular coordinates. For example, the predicted firing rate (gi) for the ith neurone can be written in Cartesian coordinates:
The five coefficients were chosen so as to minimize the difference between the predicted firing rates and the filtered firing rates for that neurone. If there are n neurones, the process was repeated for each neurone (1 ≤i ≤ n). Corresponding forms of eqn (3) were used to accommodate kinematics expressed in polar and joint angular coordinates. In joint coordinates, intersegmental angles (extension was taken as positive) were used to describe the limb position in the sagittal plane. In polar coordinates, the toe position and velocity were also expressed with respect to an origin at the hip, which was fixed in space. The variance accounted for (VAF) expressed as a percentage was used to evaluate the goodness of fit for each coordinate. Prediction of position in the sagittal plane requires combining coordinates and the root mean square (r.m.s.) error for the predictions was calculated. The coefficients of the linear encoding model (eqn (3)) describe the sensitivity of the neural response to each kinematic variable and linear correlation coefficients were also calculated for the relation between each kinematic variable and the firing rates.
A linear filter model was used to reconstruct the hindlimb trajectories from the ensemble of neural firing rates f. Equation (4) shows the form of the model for decoding the horizontal (x) position of the toe in Cartesian coordinates:
where is the predicted value of x at the time point j. This is the prediction from the filtered firing rates of n neurones, based on the present (j) and one previous (j–1) time point. In general, for L previous time points and n neurones, the decoding model takes the form:
Similar, independent predictions were made for other variables, such as y, dx/dt and dy/dt in Cartesian coordinates and for variables in polar and joint angular coordinates. Values of L between 1 and 3 were used in the figures shown here. The b coefficients were chosen so as to minimize the mean square error between the predicted and measured values for each variable.