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Comparative Study
. 2010 Sep;104(3):1484-96.
doi: 10.1152/jn.00187.2010. Epub 2010 Jul 7.

Predicting the Timing of Spikes Evoked by Tactile Stimulation of the Hand

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Free PMC article
Comparative Study

Predicting the Timing of Spikes Evoked by Tactile Stimulation of the Hand

Sung Soo Kim et al. J Neurophysiol. .
Free PMC article

Abstract

What does the hand tell the brain? Tactile stimulation of the hand evokes remarkably precise patterns of neural activity, suggesting that the timing of individual spikes may convey information. However, many aspects of the transformation of mechanical deformations of the skin into spike trains remain unknown. Here we describe an integrate-and-fire model that accurately predicts the timing of individual spikes evoked by arbitrary mechanical vibrations in three types of mechanoreceptive afferent fibers that innervate the hand. The model accounts for most known properties of the three fiber types, including rectification, frequency-sensitivity, and patterns of spike entrainment as a function of stimulus frequency. These results not only shed light on the mechanisms of mechanotransduction but can be used to provide realistic tactile feedback in upper-limb neuroprostheses.

Figures

Fig. 1.
Fig. 1.
Model description. A: Summary of the model used to fit the neuronal data. The stimulus, specified as a time-varying indentation, is converted into position (p), velocity (v), acceleration (a) and jerk (j) signals. Each signal is separated into its positive (—) and negative (- - -) components and filtered using a linear filter. This allows for rectification and frequency sensitivity to be accounted for using linear transformations. The temporal filtering is likely the product of the viscous properties of the skin and of the transducer mechanisms. Finally, the transformed inputs are summed and form the current input to a leaky, noisy integrate-and-fire (LNIF) model. In the LNIF model, a spike is produced whenever the input currents cause the membrane potential to depolarize beyond a threshold. After the production of a spike, a postspike inhibitory current is injected to mimic refractoriness. We tested models with the following input combinations: p, v, a, j, pv, va, aj, pva, vaj, pvaj. B: responses of a simulated slowly adapting type 1 (SA1) fiber, sensitive to both stimulus position and velocity, and of an rapidly adapting (RA) fiber, sensitive to velocity alone. Note that the firing rate of the SA1 afferent is higher during the on ramp than it is during the holding phase of the stimulus. Were this fiber sensitive to position alone, its firing rate would be lower during the on ramp. The RA fiber fires only during the on and off ramps of the stimulus. Were this fiber sensitive to positive velocities alone (half-wave rectification), it would fire during the on ramp but not during the off ramp.
Fig. 2.
Fig. 2.
Model predictions for an SA1 afferent. Measured and predicted afferent responses to a subset of training stimuli (A, diharmonic stimuli), triharmonic test stimuli (B), and a noise test stimulus (C). The black traces show the stimulus position as a function of time, red rasters show the responses of the afferent to 5 repeated presentations of the stimulus, and the blue rasters show the responses predicted by the model.
Fig. 3.
Fig. 3.
Model predictions for an RA afferent. Conventions as in Fig. 2.
Fig. 4.
Fig. 4.
Model predictions for a Pacinian (PC) afferent. Conventions as in Fig. 2.
Fig. 5.
Fig. 5.
Discrepancy between model predictions and data. Coarse structure (top) and fine temporal structure (bottom) across the population of neurons: SA1 (A), RA (B), and PC (C). The scatter plot in each panel represents the relationship between the firing rate predicted by the model and the firing rate observed in the data. The bars indicate the jitter in spike times between spike trains elicited by repeated presentations of the stimulus (obs vs. obs) and the jitter in spike times between model predictions and observed spikes (pred vs. obs). Data from the diharmonic training set is shown in blue, from the triharmonic test set in red, and from the noise test set in green.
Fig. 6.
Fig. 6.
Model fit. Mean spike distance (Dspike) per spike for each of the 10 models for each afferent type for the test data, pooled across the population of neurons sampled. A: for SA1 afferents, the best model was one with position and velocity as inputs. This model provided equivalently good fits as the full model (p, v, a, j) as well as one of the two triplet models (p, v, a and v, a, j) but comprised far fewer parameters. B: for RA afferents, a model with only velocity as input was as good as any other model. C: for PC afferents, the position, velocity, and acceleration model was as good as or better than the other models.
Fig. 7.
Fig. 7.
Contribution to the stimulus induced currents. Current contribution of position (blue), velocity (green) and acceleration (red) for SA1 (A) and PC (B) afferents.
Fig. 8.
Fig. 8.
Rate-intensity (top) and phase-intensity (bottom) functions for a typical SA1 (A), RA (B), and PC (C) afferent, stimulated with sinusoids varying over a range of intensities at 10, 30, and 40 Hz, respectively. The predicted rate and impulse phase (—) matched their observed counterparts (●) for all 3 afferent types. At low intensities, the phase of the spikes was bimodal (i.e., spikes alternated between 2 phases within stimulus cycles), and the mean of each mode is shown.
Fig. 9.
Fig. 9.
Threshold frequency functions: SA1 (A), RA (B), and PC (C) afferents threshold frequency functions predicted by the model (dashed). Absolute threshold (red) represents the minimum indentation amplitude required to generate a single spike, and the entrainment threshold (blue) represents the minimum amplitude necessary to generate a spike on every cycle. Observed thresholds (solid) were extracted from previous neurophysiological studies (Freeman and Johnson 1982; Muniak et al. 2007) and were shifted along the vertical axis to compensate for differences in adaptation levels (Bensmaia et al. 2005) and for differences in sensitivity across afferents of a given type (Freeman and Johnson 1982).
Fig. 10.
Fig. 10.
A simulation of neurophysiological experiments conducted by Phillips, Johnson, and Hsiao showing the representation of embossed letters in SA1 (A) and RA (B) afferent responses. Gray-scale images: strain profile; Top row of spike rasters: model prediction; bottom row of spike rasters: Data reproduced from Phillips, Johnson and Hsiao (1988). Each letter (height = 7 mm) is horizontally scanned across the receptive field of the simulated afferent at 50 successive positions, separated by 200 μm. Tissue strain, computed using a continuum mechanics model, along with its 1st time-derivative, is used as input to the model. The strain profiles were computed using the mean parameters for SA1 and RA fibers obtained in a previous study (Sripati et al. 2006) in which we concluded that SA1 and RA fibers respond to different strain components. The structure of the spatial event plot (as they are called) is similar to that observed in the study. The similarity is striking given that the simulations were derived from data obtained from different afferents than those the actual data of which are shown here. Scale bar = 200 ms.
Fig. 11.
Fig. 11.
Mean filters in the frequency domain for SA1 (A), RA (B), and PC (C) neurons. Filters corresponding to position (blue) and velocity (green) and acceleration (red). The width of the shaded bands denote the SE at each frequency. Filters exhibit low- or band-pass characteristics with different frequency cut-offs. Note that although they respond to static indentations, SA1 afferents have high thresholds for these stimuli (Johnson 2001), a fact reflected in the low power of the filter at 0 Hz. For typical filter waveforms in the time domain, see Supplemental Fig. S5.
Fig. 12.
Fig. 12.
Model parameters and properties. A: correlation between indentation and retraction filters for SA1 (blue), RA (red), and PC (green) fibers. The indentation and retraction filters tended to be correlated for all fiber types and all stimulus quantities (position, velocity, acceleration). B: rectification index=1−4πtan1(t|Hi(t)Hr(t)|t|Hi(t)+Hr(t)|) where Hi(f) and Hr(f) are the indentation and retraction filters. A rectification index of −1 indicates no rectification; 0 half-wave rectification; 1 full-wave rectification. Afferents tended to exhibit rectification properties intermediate between half- and full-wave. C: mean postspike inhibitory currents. SA1 and RA currents were similar, whereas PC currents exhibited a considerably faster time course. D: mean membrane time constants, τm, for the three afferent types. SA1 and RA afferents yielded similar membrane time constants, whereas those obtained from PC afferents were considerably faster.

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