Humans Use a Temporally Local Code for Vibrotactile Perception

Stimulus space, iso-feature-lines, and terminology

The first variable characterizing a change between reference and comparison stimulus, pulse rate, determines the number of pulses per time interval (Fig. 2A, blue), and can only be decoded by integrating across pulses. It, therefore, requires “temporally global” decoding, either summing signal (intensity) or frequency contributions (spectrum). The second variable was the shape of the individual pulses, which came in two variants, namely changes in pulse amplitude and/or width (Fig. 2A, magenta). It is noteworthy that a seemingly local manipulation, in principle detectable instantaneously by observing pulse kinematics, also affects the global variable, the intensity (i.e., the signal summed across pulses; Fig. 1B). Individual pulses always had the sinusoidal shape (single-period sine-wave starting from one minimum and ending at the next), starting from the resting position (at 1 mm skin indentation), and protruding further toward larger depths. For pulse shape, two parameters were manipulated independently, pulse width and amplitude, by changing the frequency and/or amplitude of the sinusoid that was used for constructing the pulse (pulsewidth=1/frequency ). To disambiguate our terms, we use “pulse rate” to refer to the number of pulses per time unit exclusively, and we reserve the terms “pulse shape” (i.e., “amplitude” and “width”) as a proxy for the amplitude and frequency of the sinusoid used to generate the individual pulses. Whenever we use the term “frequency,” we refer to long sinusoidal stimulation used in classical studies or to the frequency of the sinusoid used to construct our pulses. Our approach implies that pulse rate and pulse shape are independent experimental variables as long as pulse rate is less than the frequency of the sinusoids used to construct the pulses; this approach is different from traditional frequency discrimination experiments using long sinusoids, where changing the pulse rate inadvertently changes the pulse shape.

Pulse amplitudes and widths were chosen from a two-dimensional stimulus space shown in Figure 2B (pulse rate: 90Hz ; pulse width: w∈[4.167,5.882]ms ; pulse amplitude a∈[20,40]μm ). The reference stimulus was composed of the widest and highest pulses (w=5.882ms;a=40μm ), located at the upper left corner of the stimulus space (large circle), whereas the comparison stimuli were composed of pulses that were reduced in width ( w) and/or amplitude ( a). In preliminary experiments (using lab members as participants; data not shown), we found that our stimulus space roughly divides into a region with relatively poor and graded responses (orange), and another with extremely good performance (gray). Whereas the gray zones predicted ceiling performances in participants and would be uninformative experimentally, the responses within the orange field, which is sensitive to shape parameters, promised to unearth evidence toward principles of pulse shape coding. The performance on stimuli bordering the gray high-performance fields was still very good and it decayed toward a line of “worst” performance in the center of the orange field (Fig. 2B).

The orange stimulus space covers a wide range of pulse width and amplitude combinations, from the upper left corner (our reference stimulus) where the pulses are wider and higher compared with the ones down in the lower right corner where the pulses are lower and narrower (i.e., steeply rising pulses). That is, the orange stimulus space is characterized by stimuli that trade decreasing amplitude with increasing steepness. In fact, starting from the reference stimulus in the upper left corner, it is possible to trace out lines through the orange stimulus space, on which important coding variables (“features”) remain unchanged, we tag them as “iso-feature-lines.” In this study, we considered seven such iso-feature-lines (labeled a–g in Fig. 2B). Amongst them are six iso-feature-lines (a to f) that hold variants of global intensity variables constant, defined as “mean velocity” (line a), “mean squared velocity” (line b), “mean cubic velocity” (line c), “mean acceleration” (line d), “mean squared acceleration” (line e), and “mean cubic acceleration” (line f). Note that to increase clarity, we omitted the attribute “absolute” (i.e., directions and signs of velocity and acceleration are not considered – all variables are positive valued). Moreover, the seven iso-feature-lines also comprise three lines that hold local variables constant describing the “maximal position” (i.e., maximal displacement), “maximal velocity,” and “maximal acceleration” of a pulse (iso-feature-lines a, d, and g, respectively). The first two respective local iso-feature-lines are in fact congruent with the global iso-feature-lines mean velocity and mean acceleration (lines a and d), whereas “maximal acceleration,” the third local variable, is characterized by the bottom-most iso-feature-line (g) in Figure 2B. Note that throughout this article we use the letters a–g to label iso-feature-lines, but also to refer to the intensities and kinematic variables held constant on them.

Having identified the relevant stimulus range we decided to pick comparison stimuli located on the seven iso-feature-lines. We reasoned that if one of these encoding variables a critical for performing the change detection task, the performance on the corresponding iso-feature-line should be poor compared with the other ones. To quantify this, we designed our testing sessions under the presumption that decreasing pulse width (from the pulse width of the reference stimuli) will increase the participants’ probability of detecting a change and the pulse width at which the probability to detect the change is 50% will be the threshold. In other words, in all the iso-feature-line sessions we reduced the pulse width of the comparison stimuli (while adjusting for the pulse amplitude as guided by the iso-feature-line definition) to finally identify the iso-feature-line session that yielded the highest threshold. We tested each participant through seven sessions corresponding to each iso-feature-line; the sessions were randomized such that each participant was tested on a unique sequence of sessions probing the seven iso-feature-lines (Table 1).

Comparison between isolated changes in pulse rate and shape

In anticipation of results that we will report in detail further below, we found that among the sessions on the seven iso-feature-lines, stimuli on line d gave rise to the highest threshold, i.e., worst performance. To start comparing the effect of local and global cues on performance, we selected stimuli on line d, with the worst performance among the stimulus sets containing local cues (Fig. 1A, orange; compare Table 1 under “shape change condition”), and pitted them against stimuli that are devoid of local cues, i.e., reference and comparison stimuli containing pulses of identical shape but different rate (Fig. 1A, blue; compare Table 1 under “rate change condition”). In the blue stimulus set the pulse rates changed from 90 Hz (reference) to 135 Hz in 10 stimulus steps (i.e., 90, 95, …, 130, 135 Hz). We present data obtained from eight of nine people tested, as the ninth participant did not give us any logistic fit that crossed the probability of 0.5 of detected change. On average, participants required a pulse rate change of 35% (SD 13%) to reliably detect it 50% of the time. The orange stimulus set included 15 pulse shapes, whose width varied from 5.882 to 4.167 ms (the interpulse intervals of reference and the comparison stimuli were identical), and amplitudes were defined by line d (Fig. 2A, right, and panel B). For detection of changes in the pulse shape task, we obtained valid psychometric curves (threshold higher than detection probability of 0.5) from all 10 participants.

Although one set of experiments dealt with changes in pulse rate and the other with pulse shapes, the performance on the two types of stimulus changes can be plotted in one graph according to their intensity content. Figure 2C presents the mean performance of the population of participants in the two experiments plotted across intensity formulated as mean velocity. The success of 8 out of 9 participants to detect pulse rate changes first of all demonstrated that humans in principle are able to use global variables as a basis for their decision. However, the comparison of the two behavioral datasets based on change of intensity in Figure 2C suggested that pulse shape changes (magenta) were detected in a different way (i.e., had a lower intensity threshold) than the ones based on pulse rate (blue).

However, the premises for the comparison made in Figure 2C are, first, that intensity is actually a coding variable, and second, that its formulation as mean velocity is correct. The first premise is firmly supported by a host of studies starting from early times of tactile research (LaMotte and Mountcastle, 1975). The second premise is definitely weaker, but has been supported by work comparing some of the possible formulations (Arabzadeh et al., 2003; Hipp et al., 2006; Gerdjikov et al., 2010). Nevertheless, in many studies on the tactile system the formulation of intensity was chosen for reasons of parsimony or tradition. In order to strengthen our argument, we took the opportunity that was provided by the outline of our relevant stimulus range and the set of iso-feature-lines running through it (Fig. 2B), and performed a more systematic analysis: we reasoned that the true intensity formulation for indentation stimuli (if it exists) must be associated within this stimulus range, where relevant intensity formulations do not vary considerably and performance accordingly is relatively poor. We therefore repeated the plot of Figure 2C with combinations of data from all seven iso-feature-lines (colored curves in Fig. 2D), and scaling them to the six intensity formulations a–f, whose iso-feature-lines span the whole stimulus range (the six graphs in Fig. 2D). We did not find any intensity formulation that would group psychometric curves consistently close to the one from pulse rate changes. They are either concentrated at sites indicating far better performance than rate changes (e.g., mean velocity and mean acceleration, labeled a and d), or they are dispersed across a large intensity range (e.g., “mean squared” or “cubic acceleration,” intensities e and f). We argue that a consistent grouping of curves around the one found with rate changes would be required to conclude that the respective intensity formulation was perceptually dominant. The absence of such a grouping suggests that none of the intensity variables singularly determined the performance on the present tasks. The most conspicuous mismatch was the one found when scaling to intensity d (mean acceleration; Fig. 2D, lower left). Actually, the poor performance on line d, mentioned before, had made mean acceleration a major candidate for intensity-based coding. However, the huge difference in performance between rate and shape change stimuli, when scaling with this variable, casted serious doubts on its relevance. From these initial results we, thus, suggest that the observed performance differences are likely based on differences in local pulse shapes rather than intensity.

Comparison of changes when presenting simultaneous changes in pulse rate and shape

So far, we tested shape and rate changes in different sessions, leaving room for the possibility that the participants (or their tactile systems, respectively), were able to adapt to these different tasks. We therefore aimed to support the finding in a more direct way, trading pulse rate against shape within the same comparison stimulus (Fig. 3A). As a starting point for this experiment, we chose again iso-feature-line d (Fig. 3B). The poor performance on this line would predict that the variables kept constant on it (i.e., global mean acceleration or local “maximal velocity”) are likely relevant for coding. Further, the poor performance would provide added pulses a good chance to result in measurable improvements in performance (conversely, basing the experiment on iso-feature-lines with stronger performance would run the risk that performance there is already saturated preventing the assessment of improvement by adding pulses). Adding pulses of identical shape to comparison stimuli on line d generated line d’ (Fig. 3, gray; also see Table 1, pulse rate-and-shape change experiment), which keeps being a local iso-feature-line identical to line d (because of identical pulses), but introduces differences in global intensity (via the increased pulse rate). We selected an increase of pulse rate of 15 Hz (i.e., comparison stimuli on line d’ have a pulse rate of 105 Hz as opposed to 90 Hz for line d), which is subthreshold based on participants performance in the pulse rate change experiment (compare Fig. 2C, the stimulus is indicated by the leftmost blue hexagon). Expectedly then, increasing pulse rate did not significantly improve the performance in iso-feature-line d’ over what was seen in iso-feature-line d [change of threshold from 1.272 ms (SD 0.27 ms) to 1.101 ms (SD 0.19 ms); t test: t = −2.084, n = 8, p = 0.08; effect size: discriminability = 0.74]. In other words, the participants largely failed to use the increased global intensity variable in the comparison stimuli and continued informing their perceptual decisions using local cues. Therefore, our next manipulation aimed at deciding whether the same intensity change, this time realized by reducing pulse shapes further (thereby, strengthening local cues), would have a better effect on performance. To test this, we compensated intensity (that was previously increased via rate change in line d’) by reducing the pulse shape. This resulted in line d’’ (Fig. 3, red; also see Table 1). Performance on line d’’ significantly improved in comparison to line d’ [gray to red; change of threshold from 1.101 ms (SD 0.194 ms) to 0.764 ms (SD = 0.368 ms); t test: t = 2.868, n = 8, p = 0.024; effect size: discriminability = 0.98]. That is, relative to the reference (d, magenta), increasing the pulse rate had no effect on performance (d’, gray) whereas changing the pulse shape enhanced it (d’’, red). In other words, there is no significant difference in performance between d’ and d, likely because there is no difference in the local cue. In contrast, there is a significant difference in performance between d’ and d’’ likely because here local cues vary, while intensities are kept the same, and rate change alone has been shown before to be perceptually ineffective.

The tactile system does not prefer a specific kinematic variable

Translating the width of our sinusoidal pulses into frequency, i.e., the variable classically considered when testing the tactile system with long sinusoidal stimuli, it becomes evident that so far we only probed a small portion of the wide tactile range accessible to the human tactile perceptual system (Bolanowski et al., 1988; for a justification of the comparison of stimulus ranges composed of sinusoids in the classical studies and our sinusoidal pulses, see Discussion). The subrange investigated thus far (Range I in Fig. 4A; pulse widths were between 5.882 and 4.167 ms) corresponds to sinusoidal frequencies between 170 and 240 Hz, which is well within the range of frequencies classically called “the Pacinian range”; a range that is dominated by responses of rapidly adapting primary afferents type 2, which innervate the PCs. We therefore aimed, firstly, to quantify performance on all iso-feature-lines of Range I, and secondly, compare it to a second range, the so-called “flutter range”, located at much lower frequencies, known to predominantly activate rapidly adapting primary afferents type 1 (Range II in Fig. 4A; amplitudes 100–30 μm and widths 28.571−15.385ms⇔35−65Hz ; see also Table 1). To provide an intuition about pulse shapes used in Ranges I and II, we plot the largest and the smallest pulses, defined by the top left (i.e., a reference stimulus pulse) and bottom right corners of the two ranges (Fig. 4A, bottom).

The performances of exemplary participants on the stimulus Ranges I and II (Fig. 4B,E), already hint that the preference does not generalize across the entire stimulus space. As mentioned before, iso-feature-line d (maximum velocity) yielded the worst performance in Range I (Fig. 4B), while in Range II the worst performance was seen with iso-feature-line g (maximum acceleration; Fig. 4E). Population data, thresholds as well as psychometric curves, confirm this impression (Fig. 4C,D,F,G). For statistical appraisal we computed the discriminability (ranging from 0 to 1; see Materials and Methods), as well as the p values obtained from a t test (two-tailed, paired samples), comparing thresholds from iso-feature-line d to all others for the Range I (discriminability = [0.96, 0.64, 0.06, ∼, 0.66, 0.82, 0.80]; order: line [a, b, c, d, e, f, g], note the fourth position is marked with “∼” as it is the comparison of line d with itself). The corresponding p values were p = [0.015, 0.044, 0.624, ∼, 0.357, 0.049, 0.055]; and number of tested participants were n = [10, 9, 9, ∼, 9, 10, 10]. Similarly for Range II, we computed discriminability comparing the iso-feature-line g (maximum acceleration) to all the other iso-feature-lines, and ordered the results as above: discriminability = [0.88, 0.78, 0.68, 0.64, 0.38, 0.14, ∼]; the corresponding p value in the t tests were p = [0.027, 0.086, 0.134, 0.166, 0.413, 0.989, ∼], and the number of participants were n = [10, 10, 10, 10, 10, 10, ∼]. The best fit logistic functions corrected for false alarm rates to the pooled data from 10 participants for the experiments on isolines (a, d, g) are shown in Figure 4D,G. The different sequence in performance can be readily observed from them (a→g→d in Fig. 4D vs a→d→g Fig. 4G). We note that both tasks were challenging for the participants. This fact was reflected by a consistently high false alarm rate of [0.12, 0.18, 0.16, 0.14, 0.09, 0.04, 0.07] in stimulus Range I, and [0.03, 0.03, 0.04, 0.04, 0.02, 0.04, 0.05] in Range II (same order as before). In summary, for human vibrotactile perception, the relative performance across iso-feature-lines was distinct in the two studied stimulus ranges, a result that does not argue in favor of a single consistent weighing of kinematic parameters for encoding; instead, participants seemed to switch between encoded variables to perform the task in the different stimulus subspaces.

How is change detection related to primary afferent activity?

The schematic in Figure 5A plots again our stimulus subspaces within the larger perceptual range, but now adds the threshold curve of PC primary afferents (Freeman and Johnson, 1982). As our stimulus spaces are quite small, relative to the curvature of the threshold curve, it is possible to approximate the curve with straight line segments, and thus, we arrive at “iso-response-lines” (Fig. 5A, green and blue lines). The primary afferent response to a pair of discriminanda located on an iso-feature-line is then governed by the angle with which an iso-feature-line runs relative to the afferent’s iso-response orientation. For example, a pair of stimuli located on an iso-feature-line would engage a class of afferents similarly if the iso-feature-line is parallel to the iso-response orientation, whereas the stimuli would engage the afferents most differently, if the iso-feature-line and iso-response orientation are orthogonal. The schematic comparison of the cited classical work to our data in Figure 5A demonstrates how the orientation of the PC threshold line can be transferred to our stimulus ranges and respective iso-feature-lines. It turns out that, to a first approximation, the angle between iso-response-lines and iso-feature-lines is different in the two stimulus subspaces (Fig. 5A, blue vs green lines). From here it is straight forward to hypothesize that minute changes in the angle of iso-response-lines and iso-feature-lines are responsible for the observed difference in preferred coding variables in Subspaces I and II (Fig. 4).

We put this hypothesis to the test by taking advantage of an established model of primary afferent responses based on quasi-static and dynamic skin mechanics linked to an integrate-and-fire neuronal model (Saal et al., 2017). The model very precisely recreates the classical threshold and entrainment curves of the three most important classes of primary afferents in primates (Saal et al., 2017; see their Fig. 7), and its output therefore, as argued above, can be compared with our human behavioral data. Importantly, the model accepts any waveform of indentation stimuli, it is sensitive to stimulation location, and it realistically simulates multiple end organs distributed across the glabrous skin. We only quantified the discriminability carried by spikes of the PC class of primary afferents (also called rapidly adapting type 2), as they qualitatively reproduced the main aspects of our behavioral results (Fig. 5), while the other two (SA1 and RA1) did not. (The spike responses of all modelled primary afferent classes are presented in the Extended Data Fig. 5-1.) We modelled the spike output of 192 PC afferents to our pulsatile stimuli, distributed in spatially realistic fashion across the index finger as shown in Figure 5B. We ran the model presenting the reference stimuli and all stimuli on the seven iso-feature-lines, covering both stimulus ranges presented to the human participants in this study. We plot the discriminability of population PC spike counts calculated from the number of spikes evoked by the reference stimulus versus that obtained with the comparison stimuli for three isolines in each stimulus range. We performed this analysis by summing across responses to all pulses contained in one stimulus (reference vs all comparison stimuli), to be consistent with the psychophysical experiments. However, because of the known lack of spike rate adaptation in primary afferents (for details, see Discussion), captured by the model, we did not find relevant differences when presenting single sinusoidal pulses or 500-ms-long pulsatile sequences to the model (the differences were smaller than the line thickness of the plots in Fig. 5C,D). So, for discrimination analysis, the quantification of primary afferent activity based on responses to single and repetitive pulses can be used interchangeably. Couching these long-known facts in the terminology introduced in this study, we can call primary afferents as “temporally local encoders.” The neurometric curves of the modelled PC population recreated the discriminability of comparison stimuli picked from different iso-feature-lines in the same sequence as observed with human psychometric curves. In the stimulus Range I the sequence was a→g→d and in Range II it was a→d→g (Fig. 5C,D; compare Fig. 4D,G). This relationship is predicted by the co-linearity of iso-feature-lines and iso-response line of PCs approximated in Figure 5A. In summary, the modeling exercise suggested that human performance on iso-feature-lines, as studied here, may be largely determined by PC population spiking activity.

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Figure 7.

Reinterpretation of the classic sinusoidal frequency threshold curve for PCs, adapted from Bolanowski et al. (1988; see their Fig. 8), in terms of local coding variables (i.e., maximum position, maximum velocity, and maximum acceleration). A, The threshold curve (black line) plotted across the original coordinates, sinusoidal frequency (abscissa) and amplitude (ordinate). The colored background in the three graphs codes for maximum position, velocity, and acceleration of the sinusoids. The stimulus Ranges I and II investigated in the present study (using sinusoidal pulses) are marked for reference (compare Fig. 4). Note that the color-coded iso-kinematic contours (i.e., the iso-feature-lines introduced in this study) appear as straight lines on the log-log scale. The ovals mark regions in stimulus space where kinematic variables vary little along the threshold curve (i.e., the slope of the PC-threshold curve and the slope of the iso-kinematic contour match). B, Replotting the PC threshold curve in terms of the local kinematic variables. The abscissa is converted to pulse width (i.e., 1/f of the sinusoid) and the ordinate now holds the difference between the slope of the PC-based behavioral threshold and the slope of iso-kinematic contours. The best fit dashed lines and ovals indicate where the two slopes get very similar. These sites indicate stimulus sets that code optimally for the given kinematic variable, because the gradient (of the contours) orthogonal to the threshold curve is steepest. Conversely, stimuli located on or parallel to the kinematic contour (i.e., on the iso-feature-line) at these sites are difficult to discriminate, because PC activity and its concomitant perceptual effects do not vary. The behavioral data presented in Figure 4 and the modelled PC spike data in Figure 5 are compatible with this expectation that velocity coding is dominant at middle frequencies/pulse widths (close to 100 Hz/10 ms; Fig. 4B–D), while acceleration coding is optimal at low frequencies/narrow widths (>200 Hz/<5 ms; Fig. 4E–G).

Next, we aimed at recreating our experimental findings with mixed changes of pulse rate and shape as well using the model PC spiking. Again, by feeding the respective stimuli to the same model as before, we successfully recreated major characteristics of the psychophysical finding (Fig. 6). In this approach, we only modeled local coding (i.e., measuring spike responses to single pulses, typically consisting in 0 or 1 spike per pulse) because integrating the response across pulses rendered PC-based discriminability error-free (i.e., invariably reaching a discriminability value of 1), a phenomenon consistent with our notion (and with the results of numerous previous studies) that afferents are indeed temporally local encoders (Gerdjikov et al., 2010; Stüttgen and Schwarz, 2010; Birznieks et al., 2019). A trivial consequence of measuring responses to single pulses, from neurons devoid of spike adaptation, is that increasing pulse frequency does not affect discriminability. This is expressed by the coincident magenta and gray curves [Fig. 6, right; note, this is a discrepancy to the experimental data because human tactile system does integrate to a certain degree (compare Fig. 2C), very likely using neurons upstream of primary afferents]. The interesting part was thus modeling the second step of our experiment, compensating intensity increment (caused by additional pulses) by reduction of pulse amplitudes (red curve). Compared with the reference stimulus (magenta), reducing pulse amplitudes indeed increased discriminability by ∼0.2 (red), a fact that qualitatively matches human performance (compare Fig. 3C), and is compatible with the hypothesis that locally encoded information in primary afferent spikes is used as such, without relevant further integration, by the human tactile system up to the perceptual level.