Figure 1.
Measurement of skin vibrations.
A. Experimental set-up. Vibrations are delivered to the fingertip through a probe while movements of the skin are measured with a laser Doppler vibrometer at various distances from the locus of stimulation (see top left inset). B. Traces from the LDV for a 50-Hz stimulus recorded at 4 distances away from the locus of stimulation. C. Amplitude of the vibrations, measured at distance d from the locus of stimulation as a function of the amplitude of the vibrations delivered (f = 200 Hz), computed from sample data from one participant (numbers to the right denote the slope of the corresponding function). D. Ratio of the measured amplitude to the delivered amplitude as a function of distance, averaged across participants (error bars denote the SEM). As expected, surfaces waves decay as they travel away from the stimulator, and the relationship can be approximated using Equation 1. However, the rate of decay depends on the vibratory frequency.
Figure 2.
Decay exponent as a function of frequency across participants (error bars denote SEM).
The decay exponent is lowest (and so decay is slowest) at around 200–250 Hz, at which Pacinian afferents are most sensitive.
Figure 3.
Estimated PC population firing rate or number of active PC fibers (normalized by their respective maxima) as a function of amplitude for a 200-Hz stimulus, using an γ of 1.3 (blue) and 1.1 (red).
As can be seen, the firing rate and active population is almost twice as large for the latter than it is for the former for large amplitudes. Note that, given that the stimulus frequency remains constant, the number of active fibers and the overall firing rate of the population are linearly related.
Figure 4.
Propagation speed as a function of frequency for band-pass noise stimuli, filtered using narrow-band filters, averaged across participants.
The values on the x-axis represent the center frequency of the filters (each 100 Hz wide). Error bars denote the SEM. Surprisingly, low-frequency components (<200 Hz) seem to travel faster than high frequency components.
Figure 5.
Response of a population of simulated PC afferents to a 100-Hz (left) and a 400-Hz (right) sinusoid applied to the skin.
The PC population exhibits a highly temporally patterned response to the 100-Hz but not the 400-Hz stimulus as reflected in the vector strengths of 0.87 and 0.44, respectively. The lack of temporal patterning at 400 Hz is due in part to the delay in the response for fibers whose receptive fields are progressively further from the locus of stimulation.
Figure 6.
Entrainment (measured using vector strength) of a population of PC afferents in response to stimuli as a function of the frequency of the stimulus and of the propagation speed of the surface waves.
Low frequencies are less susceptible to temporal blur and higher speeds tend to cause less blur.
Figure 7.
Waveform distortion as a function of distance from the locus of stimulation.
A. Traces of traveling waves produced by a noise stimulus (low- and high- frequency cut-offs of 300 and 600 Hz, respectively) measured 1, 8 and 16 mm away from the locus of stimulation. B. Correlation between the stimulus applied to the skin (measured using the accelerometer on the vibration exciter) and the stimulus measured at various distances from the locus of stimulation, averaged across participants (error bars denote SEM). Stimuli consisted of band-pass noise with various low- and high-frequency cut offs. We find that the waveform is, on average, well preserved as it travels along the finger.
Figure 8.
Results from finite element analysis.
A. Decay of the traveling waves as a function of distance from the locus of stimulation (at d = 0) (Dots are measured points, traces are fitted functions). The results are qualitatively similar to those obtained using the vibrometry data, but the predicted decay is lower at intermediate frequencies (200–300 Hz) than the observed decay (Figure 1). Note that the propagating waves become severely distorted as they travel away from the locus of stimulation, so the measured amplitudes are not a smooth function of distance as they are in the vibrometry recordings. B. Decay exponent, γ, as a function of frequency. The decay exponent is lowest (and so decay is slowest) at around 200–300 Hz, but the modulation as a function of frequency is overestimated by the FEA. C. Traces of simulated traveling waves measured at four locations away from the locus of stimulation. As the wave travels away from the locus of stimulation, the waveform gets rapidly distorted. D. Correlation between the actual waveform delivered by the (virtual) motor and the waveform as it travels down the figure. The rate at which the waveform gets distorted based on the FEA prediction is much more rapid than that observed in the finger (Figure 7).