Population-response model for vibrotactile spatial summation

A computational model based on previous physiological and psychophysical data is presented for the human Pacinian (P) psychophysical channel. The model can predict the probability of detection in simple psychophysical tasks, and hence psychometric functions and thresholds. The model simulates stimulating variable and fixed glabrous skin sites with different-sized contactors and includes spatial variation of monkey P-fiber sensitivities. Therefore, it is especially suitable for studying spatial summation, i.e. the improvement of threshold with increasing contactor area. Selective contributions of neural integration (n.i.) and probability summation (p.s.) are also incorporated into the model. Model predictions are compared to psychophysical results of Gescheider et al. (2005). The performance of the model regarding the effects of contactor size is very good. In addition to predicting approximately 3 dB improvement of thresholds when the contactor area is doubled, the model also reveals nonlinear contributions of p.s. and n.i. Furthermore, the model asserts that thresholds are largely governed by neural integration when small contactors are used. These and other findings discussed in the article show that the presented model is a helpful tool for formulating testable hypotheses. Although the model can also simulate some temporal summation effects, simulation results do not conform well to previous data on temporal response properties. Thus, the model needs to be refined in that respect.     

Spatial summation in the tactile sensory system: probability summation and neural integration

Psychophysical thresholds for the detection of a 300-Hz burst of vibration applied to the thenar eminence were measured for stimuli applied to the skin through 1.5 cm2 and through 0.05 cm2 contactors. Thresholds were approximately 13 dB lower when the area of the contactor was 1.5 cm2 than when it was 0.05 cm2. The difference between the thresholds measured with the large and small contactors was significantly reduced when only the lowest thresholds obtained in the testing sessions were considered. This result supports the hypothesis that one component of spatial summation in the P channel is probability summation. In addition, threshold measurements within a session were less variable when measured with the 1.5 cm2 contactor. We conclude that spatial summation in the P channel is a joint function of two processes that occur as the areal extent of the stimulus increases: probability summation in which the probability of exceeding the psychophysical detection threshold increases as the number of receptors of varying sensitivities increases, and neural integration in which neural activity originating from separate receptors is combined within the central nervous system rendering the channel more sensitive to the stimulus.     

Spatial summation in the tactile sensory system: Probability summation and neural integration

Psychophysical thresholds for the detection of a 300-Hz burst of vibration applied to the thenar eminence were measured for stimuli applied to the skin through 1.5?cm² and through 0.05?cm² contactors. Thresholds were approximately 13?dB lower when the area of the contactor was 1.5?cm² than when it was 0.05?cm². The difference between the thresholds measured with the large and small contactors was significantly reduced when only the lowest thresholds obtained in the testing sessions were considered. This result supports the hypothesis that one component of spatial summation in the P channel is probability summation. In addition, threshold measurements within a session were less variable when measured with the 1.5?cm² contactor. We conclude that spatial summation in the P channel is a joint function of two processes that occur as the areal extent of the stimulus increases: probability summation in which the probability of exceeding the psychophysical detection threshold increases as the number of receptors of varying sensitivities increases, and neural integration in which neural activity originating from separate receptors is combined within the central nervous system rendering the channel more sensitive to the stimulus.     

Mechanisms for spatial integration in visual detection: a model based on lateral interactions

Recent studies of visual detection show a configuration dependent weak improvement of thresholds with the number of targets, which corresponds to a fourth-root power law. We find this result to be inconsistent with probability summation models, and account for it by a model of 'physiological' integration that is based on excitatory lateral interactions in the visual cortex. The model explains several phenomena which are confirmed by the experimental data, such as the absence of spatial and temporal uncertainty effects, temporal summation curves, and facilitation by a pedestal in 2AFC tasks. The summation exponents are dependent on the strength of the lateral interactions, and on the distance and orientation relationship between the elements.     

Effect of contact location on vibrotactile thresholds at the fingertip

Vibrotactile thresholds depend on the characteristics of the vibration, the location of contact with the skin, and the geometry of the contact with the skin. This experimental study investigated vibrotactile thresholds (from 8 to 250 Hz) at five locations on the distal phalanx of the finger with two contactors: (i) a 1-mm diameter circular probe (0.78-mm(2) area) with a 1-mm gap to a fixed circular surround (i.e., 7.1-mm(2) excitation area), and (ii) a 6-mm diameter circular probe (28-mm(2) area) with a 2-mm gap to a fixed circular surround (i.e., 79-mm(2) excitation area). With both contactors, especially the smaller contactor at low frequencies (i.e., 8, 16, and 31.5 Hz), thresholds decreased towards the tip of the finger, although there was little variation around the whorl. With low frequencies of vibration, and at all five locations on the finger, similar thresholds were obtained with both contactors, consistent with the NPI channel not changing in sensitivity with a change in the area of stimulation. At high frequencies (i.e., 63, 125, and 250 Hz), thresholds were lower with the larger area of stimulation at all locations, except at the extreme tip of the finger, consistent with spatial summation in the Pacinian channel. It is concluded that with a 6-mm diameter contactor, moderate variations in location around the whorl have little influence on the measured thresholds. With the 1-mm diameter contactor there were greater variations in thresholds and extreme locations, near the nail and the distal interphalangeal joint, may be unsuitable for investigating sensorineural disorders.     

A four-channel analysis of the tactile sensitivity of the fingertip: frequency selectivity,spatial summation,and temporal summation

Thresholds were measured for the detection of vibratory stimuli of variable frequency and duration applied to the index fingertip and thenar eminence through contactors of different sizes. The effects of stimulus frequency could be accounted for by the frequency characteristics of the Pacinian (P), non-Pacinian (NP) I, and NP III channels previously determined for the thenar eminence (Bolanowski et al., J Acoust Soc Am 84: 1680-1694, 1988; Gescheider et al., Somatosens Mot Res 18: 191-201, 2001). The effect of changing stimulus duration was also essentially identical for both sites, demonstrating the same amount of temporal summation in the P channel. Although the effect of changing stimulus frequency and changing stimulus duration did not differ for the two sites, the effect of varying the size of the stimulus was significantly greater for the thenar eminence than for the fingertip. The attenuated amount of spatial summation on the fingertip was interpreted as an indication that the mechanism of spatial summation consists of the operations of both neural integration and probability summation.     

Effect of contact location on vibrotactile thresholds at the fingertip

Vibrotactile thresholds depend on the characteristics of the vibration, the location of contact with the skin, and the geometry of the contact with the skin. This experimental study investigated vibrotactile thresholds (from 8 to 250?Hz) at five locations on the distal phalanx of the finger with two contactors: (i) a 1-mm diameter circular probe (0.78-mm² area) with a 1-mm gap to a fixed circular surround (i.e., 7.1-mm² excitation area), and (ii) a 6-mm diameter circular probe (28-mm² area) with a 2-mm gap to a fixed circular surround (i.e., 79-mm² excitation area). With both contactors, especially the smaller contactor at low frequencies (i.e., 8, 16, and 31.5?Hz), thresholds decreased towards the tip of the finger, although there was little variation around the whorl. With low frequencies of vibration, and at all five locations on the finger, similar thresholds were obtained with both contactors, consistent with the NPI channel not changing in sensitivity with a change in the area of stimulation. At high frequencies (i.e., 63, 125, and 250?Hz), thresholds were lower with the larger area of stimulation at all locations, except at the extreme tip of the finger, consistent with spatial summation in the Pacinian channel. It is concluded that with a 6-mm diameter contactor, moderate variations in location around the whorl have little influence on the measured thresholds. With the 1-mm diameter contactor there were greater variations in thresholds and extreme locations, near the nail and the distal interphalangeal joint, may be unsuitable for investigating sensorineural disorders.     

Vibrotactile thresholds at the fingertip, volar forearm, large toe, and heel

Thresholds for the perception of vibration vary with location on the body due to the organization of tactile channels in hairy and non-hairy skin, and variations in receptor density. This study determined vibration thresholds at four locations on the body with two different contactors so as to assist the identification of the tactile channel determining the threshold at each location. Vibrotactile thresholds at six frequencies from 8 to 250 Hz were measured on the distal phalanx of the index finger, the volar forearm, the large toe, and the heel with two contactors: (i) a 1-mm diameter circular probe with a 1-mm gap to a fixed circular surround (i.e., 7.1-mm(2) excitation area), and (ii) a 6-mm diameter circular probe with a 2-mm gap to a fixed circular surround (i.e., 79-mm(2) excitation area). At all frequencies and with both contactors, thresholds on the fingertip were lower than thresholds on the volar forearm, the large toe, and the heel, consistent with a greater density of mechanoreceptors at the fingertip. Thresholds with the larger contactor were lower than thresholds with the smaller contactor on the fingertip at high frequencies (63, 125, and 250 Hz), on the large toe (except at 250 Hz), on the heel (at all frequencies), and on the volar forearm at 250 Hz. It is concluded that at least two tactile channels (Pacinian from 63 to 250 Hz, and non-Pacinian from 8 to 31.5 Hz) determined vibrotactile thresholds at the fingertip, whereas non-Pacinian channels had a dominant influence on vibrotactile thresholds at the volar forearm. The role of Pacinian and non-Pacinian channels could not be confirmed at the large toe or the heel despite some evidence of spatial summation.     

A four-channel analysis of the tactile sensitivity of the fingertip: frequency selectivity,spatial summation,and temporal summation

Thresholds were measured for the detection of vibratory stimuli of variable frequency and duration applied to the index fingertip and thenar eminence through contactors of different sizes. The effects of stimulus frequency could be accounted for by the frequency characteristics of the Pacinian (P), non-Pacinian (NP) I, and NP III channels previously determined for the thenar eminence (Bolanowski et al., J Acoust Soc Am 84 : 1680-1694, 1988; Gescheider et al., Somatosens Mot Res 18: 191- 201, 2001). The effect of changing stimulus duration was also essentially identical for both sites, demonstrating the same amount of temporal summation in the P channel. Although the effect of changing stimulus frequency and changing stimulus duration did not differ for the two sites, the effect of varying the size of the stimulus was significantly greater for the thenar eminence than for the fingertip. The attenuated amount of spatial summation on the fingertip was interpreted as an indication that the mechanism of spatial summation consists of the operations of both neural integration and probability summation.     

Spatial variation in sensitivity as a factor in measurements of spatial summation of warmth and cold

Perception of cutaneous heating and cooling depends strongly on stimulus size. Although this dependence has been attributed solely to spatial summation, topographical variations in temperature sensitivity may also play a role. These variations, which differentially affect perception of small stimuli, may have led to overestimation of spatial summation. This possibility was investigated by measuring detection thresholds and perceived intensity for heating and cooling on the volar surface of the forearm using a multiple-thermode stimulus array. By keeping the array in place throughout each testing session we were able to measure threshold sensitivity and suprathreshold responsiveness at eight individual sites and for combinations of these sites having total stimulus areas of 0.64-5.12 cm2. When spatial summation was calculated in the traditional way by averaging the data for all stimuli of each size, the results agreed closely with previous estimates of summation for warmth and cold. When calculations were based instead on the most sensitive test site for each stimulus size, estimates of summation were reduced by about two-thirds. This outcome indicates that the spatial heterogeneity of thermal sensitivity likely contributed to estimates of spatial summation reported in earlier psychophysical studies. A schematic model of cutaneous thermoreception is presented that shows how neural summation and the density of innervation may combine to produce the psychophysical effects of increasing stimulus size (spatial enhancement).     

Neural correlates of contrast detection at threshold

Human psychophysical studies have demonstrated that, for stimuli near the threshold of visibility, detection of motion in one direction is unaffected by the superimposition of motion in the opposite direction. To investigate the neural basis for this perceptual phenomenon, we recorded from directionally selective neurons in macaque visual area MT (middle temporal visual area). Contrast thresholds obtained for single gratings moving in a neuron's preferred direction were compared with those obtained for motion presented simultaneously in the neuron's preferred and antipreferred directions. A simple model based on probability summation between neurons tuned to opposite directions could sufficiently account for contrast thresholds revealed psychophysically, suggesting that area MT is likely to provide the neural basis for contrast detection of stimuli modulated in time.     

Attenuation of vibrotactile spatial summation.

Masked and quiet thresholds at several frequencies of vibratory stimuli were measured as a function of contactor area. The test site was the left index finger; the masking site was the left little finger. The quiet threshold data were consistent with previous investigations: Low-frequency stimuli showed no spatial summation, whereas high-frequency stimuli did. In the presence of a masker, spatial summation was reduced or eliminated for high-frequency stimuli, i.e., the masked threshold was, under some conditions, independent of contactor area. Low-frequency stimuli continued to show no spatial summation in the presence of a masker. The attenuation of spatial summation appears to be a direct function of the intensity of the masking stimulus. Additional measurements with the left thenar eminence as the test site showed that spatial summation could be attenuated by a masker placed on a contralateral body site. The implications of the results for quantifying the effectiveness of a masking stimulus, for the duplex mechanoreceptor hypothesis, and for the nature of spatial summation on the skin are discussed.     

Relationship between vibrotactile detection threshold in the Pacinian channel and complex mechanical modulus of the human glabrous skin

The goal of this study was to investigate the relationship between the psychophysical vibrotactile thresholds of the Pacinian (P) channel and the mechanical properties of the skin at the fingertip. Seven healthy adult subjects (age: 23–30) participated in the study. The mechanical stimuli were 250-Hz sinusoidal bursts and applied with cylindrical contactor probes of radii 1, 2, and 3.5?mm on three locations at the fingertip. The duration of each burst was 0.5?s (rise and fall time: 50?ms). The subjects performed a two-interval forced-choice task while the stimulus levels changed for tracking the threshold at 75% probability of detection. There were significant main effects of contactor radius and location (two-way ANOVA, values of p?<?0.001). The thresholds decreased as the contactor radius increased (i.e., spatial summation effect) at all locations. The thresholds were lowest near the whorl at the fingertip. Additionally, we measured the mechanical impedance (specifically, the storage and loss moduli) at the contact locations. The storage moduli did not change with the contactor location, but the loss moduli were lowest near the whorl. While the loss moduli decreased, the storage moduli increased (e.g., more springiness) as the contactor radius increased. There was moderate and barely significant correlation between the absolute thresholds and the storage moduli (r?=?0.650, p?=?0.058). However, the correlation between the absolute thresholds and the loss moduli was high and very significant (r?=?0.951, p?<?0.001). The results suggest that skin mechanics may be important for locally shaping psychophysical detection thresholds, which would otherwise be expected to be constant due to uniform Pacinian innervention density at the fingertip.     

Vibrotactile difference thresholds: Effects of vibration frequency,vibration magnitude,contact area,and body location

It has not been established whether the smallest perceptible change in the intensity of vibrotactile stimuli depends on the somatosensory channel mediating the sensation. This study investigated intensity difference thresholds for vibration using contact conditions (different frequencies, magnitudes, contact areas, body locations) selected so that perception would be mediated by more than one psychophysical channel. It was hypothesized that difference thresholds mediated by the non-Pacinian I (NPI) channel and the Pacinian (P) channel would differ. Using two different contactors (1-mm diameter contactor with 1-mm gap to a fixed surround; 10-mm diameter contactor with 2-mm gap to the surround) vibration was applied to the thenar eminence and the volar forearm at two frequencies (10 and 125?Hz). The up-down-transformed-response method with a three-down-one-up rule provided absolute thresholds and also difference thresholds at various levels above the absolute thresholds of 12 subjects (i.e., sensation levels, SLs) selected to activate preferentially either single channels or multiple channels. Median difference thresholds varied from 0.20 (thenar eminence with 125-Hz vibration at 10?dB SL) to 0.58 (thenar eminence with 10-Hz vibration at 20?dB SL). Median difference thresholds tended to be lower for the P channel than the NPI channel. The NPII channel may have reduced difference thresholds with the smaller contactor at 125?Hz. It is concluded that there are large and systematic variations in difference thresholds associated with the frequency, the magnitude, the area of contact, and the location of contact with vibrotactile stimuli that cannot be explained without increased understanding of the perception of supra-threshold vibrotactile stimuli.     

Spatial variation in sensitivity as a factor in measurements of spatial summation of warmth and cold

Perception of cutaneous heating and cooling depends strongly on stimulus size. Although this dependence has been attributed solely to spatial summation, topographical variations in temperature sensitivity may also play a role. These variations, which differentially affect perception of small stimuli, may have led to overestimation of spatial summation. This possibility was investigated by measuring detection thresholds and perceived intensity for heating and cooling on the volar surface of the forearm using a multiple-thermode stimulus array. By keeping the array in place throughout each testing session we were able to measure threshold sensitivity and suprathreshold responsiveness at eight individual sites and for combinations of these sites having total stimulus areas of 0.64-5.12 cm². When spatial summation was calculated in the traditional way by averaging the data for all stimuli of each size, the results agreed closely with previous estimates of summation for warmth and cold. When calculations were based instead on the most sensitive test site for each stimulus size, estimates of summation were reduced by about two-thirds. This outcome indicates that the spatial heterogeneity of thermal sensitivity likely contributed to estimates of spatial summation reported in earlier psychophysical studies. A schematic model of cutaneous thermoreception is presented that shows how neural summation and the density of innervation may combine to produce the psychophysical effects of increasing stimulus size (spatial enhancement).     

Factors affecting tactile spatial acuity

Tactile spatial acuity on the fingerpad was measured using a grating orientation task. In this task, subjects are required to identify the orientation of square-wave gratings placed on the skin. Previous studies have shown that performance varies as a function of the width of the grooves in the gratings. In the present study, both groove width and the overall size and configuration of the contactors were varied. Sensitivity improved with wider grooves and with larger contactors. Additional measurements showed that the improved sensitivity is not the result of the increase in total area contacted, but rather is due to two other factors associated with larger contactors. One is the greater linear extent of the larger contactors. The other appears to be due to the reduction in the interference produced by the outer edge of the contactor. Specifically, as the contactor increases in size, the distance between the outer edge and the center portion of the grooves also increases. It was also shown that subjects are more sensitive to a single, continuous groove as compared with two grooves of the same total length but spatially discontinuous. Similarly, subjects are more sensitive to a contactor with a continuous groove than to a contactor in which just the end points of the groove are presented. The results are generally consistent with the results of peripheral, neurophysiological recordings. The results are discussed in terms of the way in which both spatial and intensive factors may affect sensitivity to grating orientation.     

Visual detection of spatial contrast; Influence of location in the visual field,target extent and illuminance level

A model is proposed that permits the prediction of contrast detection thresholds for arbitrary spatial patterns. The influence of the inhomogeneous structure of the visual field and a form of spatial integration are incorporated in the model. A hypothetical density function for the spatial sampling units, which specifies the distribution of these units with respect to both size and location, is described. The density function is compared with anatomical and electrophysiological knowledge of the density of retinal and cortical receptive fields. This density function permits a particularly lucid interpretation in terms of pattern processing. It can be considered as a system that permits simultaneous global and focal views of the surroundings. The density function, together with a schematized adaptation behaviour of single units, and an incoherent summation rule permit us to calculate a measure of the mass response, and consequently the threshold function. Predictions of the model are compared with recently obtained psychophysical data. In particular an explanation is offered for certain invariance properties of spatial contrast detection that seems to possess promising generality.     

Learning a grating discrimination task broadens human spatial frequency tuning

 The effect of spatial frequency discrimination learning on spatial frequency detection tuning curves, obtained by a summation to threshold paradigm, has been investigated. Three human observers were exposed to a grating discrimination task for longer than two weeks, and their detection thresholds for compound Gabor gratings were measured before and after this time interval. Discrimination thresholds decreased continuously and substantially during the course of learning, while the spatial frequency detection tuning curves show significant broadening in the posttest. Calculating the discrimination resolution of an ensemble of sensory coding units shows that larger bandwidths lead to better spatial frequency discrimination performance if pattern discrimination rests on multidimensional comparison or one-dimensional scaling of the spatial frequency parameter. Further, it is shown that a multiple-mechanism nonlinear pooling model is capable of explaining the results if plasticity of coding unit bandwidth or adaptive weights of the coding unit responses at the stage of response integration is assumed. The alternative sources of plasticity and the consequences of the findings for psychophysical modeling are discussed. Received: 8 September 1999 / Accepted in revised form: 16 October 2000     

Independent responses of Pacinian and Non-Pacinian systems with hand-transmitted vibration detected from masked thresholds

This study was designed to identify psychophysical channels responsible for the detection of hand-transmitted vibration. Perception thresholds for vibration (16, 31.5, 63 and 125?Hz sinusoidal for 600?ms) at the distal phalanx of the middle finger and the whole hand were determined with and without simultaneous masking stimuli (1/3 octave bandwidth Gaussian random vibration centered on either 16?Hz or 125?Hz for 3000?ms, varying in magnitude 0 to 30?dB above threshold). At all frequencies from 16 to 125?Hz, absolute thresholds for the hand were significantly lower than those for the finger. Changes in threshold as a function of masker level were used to estimate the thresholds of three psychophysical channels (i.e. P, NP I, and NP II channels). Increased vibrotactile sensitivity of the hand compared to the finger seems to be not entirely due to increased spatial summation via the Pacinian system (P channel); non-Pacinian system (NP I and NP II channels) also contributed to perception. Differing transmission of vibration between the hand and the finger may have also influenced the thresholds.     

Independent responses of Pacinian and Non-Pacinian systems with hand-transmitted vibration detected from masked thresholds

This study was designed to identify psychophysical channels responsible for the detection of hand-transmitted vibration. Perception thresholds for vibration (16, 31.5, 63 and 125 Hz sinusoidal for 600 ms) at the distal phalanx of the middle finger and the whole hand were determined with and without simultaneous masking stimuli (1/3 octave bandwidth Gaussian random vibration centered on either 16 Hz or 125 Hz for 3000 ms, varying in magnitude 0 to 30 dB above threshold). At all frequencies from 16 to 125 Hz, absolute thresholds for the hand were significantly lower than those for the finger. Changes in threshold as a function of masker level were used to estimate the thresholds of three psychophysical channels (i.e. P, NP I, and NP II channels). Increased vibrotactile sensitivity of the hand compared to the finger seems to be not entirely due to increased spatial summation via the Pacinian system (P channel); non-Pacinian system (NP I and NP II channels) also contributed to perception. Differing transmission of vibration between the hand and the finger may have also influenced the thresholds.