A critical experimental study of the classical tactile threshold theory
© Perez et al; licensee BioMed Central Ltd. 2010
Received: 29 December 2009
Accepted: 18 June 2010
Published: 18 June 2010
The tactile sense is being used in a variety of applications involving tactile human-machine interfaces. In a significant number of publications the classical threshold concept plays a central role in modelling and explaining psychophysical experimental results such as in stochastic resonance (SR) phenomena. In SR, noise enhances detection of sub-threshold stimuli and the phenomenon is explained stating that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. We designed an experiment to test the validity of the classical vibrotactile threshold. Using a second choice experiment, we show that individuals can order sensorial events below the level known as the classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level contradicting the definition of the classical tactile threshold.
We performed a three alternative forced choice detection experiment on 6 subjects asking them first and second choices. In each trial, only one of the intervals contained a stimulus and the others contained only noise. According to the classical threshold assumptions, a correct second choice response corresponds to a guess attempt with a statistical frequency of 50%. Results show an average of 67.35% (STD = 1.41%) for the second choice response that is not explained by the classical threshold definition. Additionally, for low stimulus amplitudes, second choice correct detection is above chance level for any detectability level.
Using a second choice experiment, we show that individuals can order sensorial events below the level known as a classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level. Therefore, if detection exists below the classical threshold level, then the model to explain the SR phenomenon or any other tactile perception phenomena based on the psychophysical classical threshold is not valid. We conclude that a more suitable model of the tactile sensory system is needed.
The tactile sense is being used in a variety of applications such as human-machine interfaces, telesurgery, virtual reality, robotics and in rehabilitation for the deaf and visually handicapped [1–4]. Different tactile threshold tests are routinely performed with the objective of assessing normal function or diagnose sensory loss in workers exposed to vibration, or in the case of aged or in those patients with disease-related sensory loss such as diabetes, stroke, etc. [5–11]. Vibrotactile excitation is the most widely used form of stimulating the tactile system in human-machine interfaces. In tactile research the threshold concept is widely used and therefore its interpretation is important [1, 11–16]. The threshold is defined in classical terms as the minimal quantity of the stimulus that a subject is able to detect . Under classical assumptions, an S-shaped curve called 'psychometric function' (PF) is interpreted as a manifestation of the stochastic nature of the threshold. Therefore, the mean value of the threshold can be obtained from the PF and corresponds to the stimulus level that evokes a 50% of 'yes' responses [11, 18, 19]. According to the classical threshold concept, in any given trial, sensory events below threshold cannot be detected and are indistinguishable from one another.
Signal detection theory (SDT) emerged as an alternative framework to solve the shortcomings associated with classical threshold theory [19–23]. In the context of a psychophysical experiment, the observer sets a particular value of activation as a criterion upon which to make her/his decision. During a given trial, if the level of activation is above the criterion, the observer chooses 'signal present' and if it is below the criterion the observer chooses 'signal absent' [19, 21]. The SDT criterion is just a boundary used to make a decision and it does not impose a sensory limit . Moreover, it can be altered by motivation and bias [18, 19, 21].
Even though several studies mainly in vision and audition science have supported SDT in opposition to the classical threshold concept [20–23, 25, 26], there are only a few studies on the validity of SDT applied to the tactile sense [12, 27, 28]. In particular, the threshold concept, as in the classical or in the SDT interpretation, has not been well discussed in vibrotactile research. In  and , it was shown that there is no such a threshold as conceived by classical theory and for this limit to be consistent with the data it must be much lower than predicted by classical methods as the middle of the psychometric curve. In  it was shown that SDT is a more suitable framework for the study of sensorial processes in tactile perception.
In the present paper we present results of three experiments to show evidence of classical threshold theory failure in the tactile sense from a psychophysical point of view. First we estimated the threshold with a classical psychophysical method. Then we performed a second-choice experiment [22, 26] used previously in vision an audition, in which the subject must provide his/her first choice out of three or more alternatives followed by a second choice where he/she thinks the stimulus was presented. Finally we performed a second-choice experiment with low stimulus amplitude.
Results experiment 1
Results of experiment 1
Results experiment 2
Results experiment 3
Summary of results of experiment 3
Classical threshold hypothesis states that the observer is not able to order sensorial events below threshold. Consider experiment 2 in which the observer must pay attention to 3 intervals and let I N and I S be intervals containing noise alone (in the context of SDT) and signal plus noise, respectively. Observers have only 3 possible ways of ordering the intervals according to the responses in the 1st and 2nd choice sequence: I S I N , I N I S and I N I N . The last two of them correspond to wrong first choices. Since only one of the 3 intervals contains the stimulus, there are 2 ways of answering I N I S . For example, if the stimulus fell on interval 2, an I N I S answer could be 1-2 or 3-2. Analogously, there are 2 ways to achieve the response I N I N . In our example, the possible intervals are 1-3, 3-1. Therefore, there are 4 possible ways of answering an incorrect first choice, i.e., I N I S and I N I N cases. Classical threshold hypothesis does not consider the possibility that I N produces a sensorial event higher than the one produced by I S . Therefore, all 4 possibilities described above have equal probability so that I N I S cases should be 2/4 (i.e., 50%) of the total cases in which the first choice was wrong. On the other hand, SDT does allow observers to order any sensorial event compared to any other even if these are generated under the classical threshold level as in the case of incorrect first choice. According to SDT, when the observer fails in the first choice in the 3AFC, a sensorial event coming from the signal plus noise interval it is more likely to be greater than the other two sensorial events coming from an interval containing only noise. SDT does not provide an exact prediction of a second choice proportion without additional assumptions, but it predicts a second choice to be greater than chance level.
The SDT model does not reject the existence of an abrupt or hard threshold viewed as a limitation of the tactile system to sense extremely weak stimuli. Indeed, it has been shown that several very weak vibrotactile signals of 60 Hz produce detection probabilities which are virtually equivalent when the signals do not exceed 1 micrometer in amplitude . However, it must be emphasized that this limit is much lower than thresholds estimated by classical methods, which are also dependent on observer's criterion. Thus, if the probability of appearance of the stimulus P(S) is set at 0.3, the stimulus value that is detectable 50% of the time equals 1.3 micrometers, while it equals 2.3 micrometers for P(S) of 0.7 . This emphasizes the usual misconception of the threshold concept. Moreover, other threshold models could be hypothesized and could embrace our results and those described above. Indeed, a modification of SDT that includes a low-threshold below which the observer cannot perceive stimuli could be in agreement with the second-choice experiment . Nevertheless, a classical high abrupt threshold is incompatible with our results.
The rejection of the classical high abrupt threshold implies that this concept is not suitable to explain the SR effects observed in psychophysical experiments involving the tactile system. In a recent paper , we proposed that in SR this phenomenon could be due to reduction of uncertainty given that noise points to the temporal window where the stimulus is present. In , we showed experimental results that agree with the uncertainty hypothesis. However, SR in the tactile system at a physiological level  or using EEG recordings  is not explained through the classical psychophysical threshold.
Our findings are in strong contradiction with the classical threshold conception used in psychophysics, just as in . Using a second choice experiment we have shown that individuals can order sensorial events below the level known as a classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. To the contrary, we have shown that a second choice in a 3AFC experiment is better than chance. Our findings are consistent with what was previously shown in the case of visual detection. Importantly, a more suitable model of the tactile sensory system is needed to explain phenomena such as psychophysical SR, design research methods, to interpret experimental results, and for developing prosthetic strategies.
Experiment 1: single psychometric function point estimation
Relation between voltage amplitudes and displacement of the loaded transducer
The experiments were approved by the Bioethics Committee, INTA, Universidad de Chile (resolution No.11, June 14, 2006), and the informed consent was obtained from all subjects.
Experiment 2: first and second choice in the 3AFC method
The objective of this experiment was to analyze the observer's first and second choices under a 3AFC procedure using a constant stimulus level, X80, obtained from experiment 1. A 3AFC method was performed over the same group of subjects. Only one interval, randomly chosen from the sequence of 3, had a stimulus. Timing characteristics were as described in experiment 1. The task of the observer was to order sensorial events by choosing two intervals out of the 3 presented in order of preference considered to be most likely to have contained the stimulus. Two hundred trials were performed for experiment 2 on each of the 5 subjects. Also the actual stimulus level was recorded. Experiment 2 lasted between 30-40 min for each subject.
Experiment 3: first and second choice in the 3AFC method at low-energy stimuli
The objective of this experiment was to analyze the observer's first and second choices under a 3AFC procedure using a low energy stimulus chosen to be just detectable to the individual. Experiment 3 was the same as experiment 2 but using stimulus amplitudes lower than X80. The timing characteristics were also identical to those of experiment 2. Two hundred trials were performed in experiment 3 on six subjects, that is to say, the same group of subjects plus a new one who performed this experiment twice.
The experiments were performed by stimulating the distal part of the index finger using a plastic circular contactor of 1.5 mm diameter mounted on a bimorph rectangular piezo-electric transducer from Morgan Matroc, with dimensions 23 mm length, 3 mm width and 0.5 mm thickness used previously [13, 14] as shown in Figure 5(a). The piezoelectric was mounted in a cantilever manner on a plastic base free to oscillate. This arrangement was mounted on a steel balanced structure to maintain a constant force on the index finger of 0.022 N. The fingers rested on an acrylic cover with a circular perforation of 5 mm diameter to allow the contactor to touch the skin. The index finger was selected for these experiments because it has been used in assistive devices  and is the principal area used for tactile exploration because of its high spatial resolution [13, 38–40].
The waveform and amplitudes were preprogrammed on a computer using 8 bits per sample. Each sample was sent through the parallel port of the computer to an external D/A converter (DAC0808) and operational amplifier LF353 at 200,000 samples/sec. The waveform was then filtered and amplified by an LM343 power operational amplifier polarized between ± 40 V. The average signal to noise ratio at the transducer was 40.8 dB and there was no artificial noise introduced in excitatory waveform. The time involved in changing from one stimulus amplitude to another was not significant since the waveform was preprogrammed. The waveform and the parameters have been used in previous studies to determine stochastic resonance on the tactile system , power consumption [13, 41] and two-point spatial resolution . One day prior to the test, all individuals were familiarized with the vibrotactile measurement method, in two 20 min sessions.
This research was supported by Grant No. 1040693 from FONDECYT, Chile and by the Department of Electrical Engineering, U. de Chile. We want to acknowledge the valuable contributions of Prof. Theodore Cohn from U.C., Berkeley in the design of the experimental methods. Prof. Theodore Cohn sadly passed away on May 2006. Also, we want to thank Dr. Nancy Lacourly for her recommendation on the statistical tests.
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