ABSTRACT
Absolute threshold is understood as the minimum level of energy required for a stimulus to
be perceived. The concept leads to the interpretation that there might be a certain value
after which stimulus is always perceived by the subject. Psychophysics experiments show
that such a specific value leading to 100% certainty that a stimulus will be perceived does
not exist but rather show that the process of stimulus perception occurs gradually. In this
report psychophysics and MEG analysis are reported in the attempt to demonstrate how the
stimulus perception occurs gradually rather than following absolute trends.
INTRODUCTION
In neuroscience, absolute threshold is the minimal energy required for a stimulus to be
perceived. There are three different methods to measure the threshold: adjustment
method, adaptive method and constant stimulus method.
Contrary to what could be expected, the threshold is not a clear line above which all
stimulus is perceived. In fact, the process that goes from 0% probability of stimulus
recognition to 100% probability of recognition is gradual and tends to present a sigmoid
shape when plotted against stimulus intensity, as shown in figure 1. Usually the threshold is
set at 50% probability of stimulus recognition.
Figure 1. (from power-point presentation)
The brain is constantly active, noisy, and so the response to stimulus measurement is based
on the sensitivity to distinguish noise vs noise + stimulus conditions, where different
participants might have different sensitivity. The higher the difference between noise and
noise+stimulus, the lower the threshold value.
Another factor that influences the threshold value is the criteria the participants use to
assess how confident they must be to assert if a stimulus is recognisable or not. Depending
on the criteria used, participants can be classified into liberal, conservative or neutral.
Liberals, who respond affirmatively more often, will tend to have more hits, but also more
false alarms (low threshold values) whereas conservatives, who do not respond as often,
will tend to have less false alarms, but will also miss the stimulus more often (high threshold
values).
Taking in consideration these influential factors, a useful tool to estimate how reliable a
certain threshold is, is the receiver operating characteristic (ROC) curve. The ROC curve plots
the hit rates against the false alarm rates for every criterion point in the noise vs noise +
stimulus plot and uses the area below the obtained function as a reliability measure. As
figure 2 shows, the higher the area found, the more reliable is the threshold. In broad terms,
ROC is a technique that provides the language and the graphic notation to analyse decision
making in the presence of uncertainty (Heeger, 2003).
Figure 2.
In terms of variability of neuronal responses, ROC can be used as a tool to determine
whether a certain signal is noise or stimulus (Lemon & Smith, 2006). The use of ROC in
determining the difference between noise and noise + stimulus is used instead of the
normal d’ calculation because the ROC analysis does not involve the assumption that the
distributions are Gaussian and have equal variance (Lemon & Smith, 2006).
In the experiments that follow, an attempt to demonstrate the absolute threshold was
made through the use of psychophysics and MEG techniques.
METHODS
Psychophysics
The experiment was performed in one single participant. Visual stimuli consisting of an X
and a back-ground with varying levels of intensities were presented in a computer screen.
The participant was asked to press ‘x’ or the spacebar on the keyboard according to
whether the X in the stimulus was noticeable (x) or not (spacebar). The stimulus was
presented for 0.05 seconds and the strength of the stimulus was manipulated by altering
the number of squares in the background (the more squares, the higher the noise level).
Two different experiments were performed based on these parameters. The first to be
performed was an adaptive method experiment following the Levitt and Wetherill
guidelines. It was set that 4 different responses would be necessary to step up to a harder
(noisier) stimulus and 1 single error would be necessary to step down to an easier (less
noisy) stimulus. Because the probability of a correct response (Pc) in the Levitt and Wetherill
method relates to the number of correct responses (Nc) necessary to step up in such a way
that 𝑃𝑐 = 0.5 '( (Zwislocki & Relkin, 2001), the percent of correct responses in this
experiment should be equal to 0.84%. The experiment was set to start from a hard level
(noisy) and then step down to easier levels.
Once the data had been collected, the threshold was calculated by finding the arithmetic
mean of the last 14 reversal points, where the direction of the stimulus change is reversed.
The second experiment followed the constant stimulus method. For this experiment, 5
different conditions were used. One condition with the same level obtained in the threshold
in the adaptive method and the others were this same level multiplied by 2, 1.5, 0.75 and
0.5 respectively. The conditions were set to these levels so that they could represent near
perfect performance, chance level performance and in-between performance. 50 trials per
condition were performed and every trial included a present and a non-present X in the
stimulus. Because of this, there was a total of 500 trials (𝑇𝑜𝑡𝑎𝑙 𝑡𝑟𝑖𝑎𝑙 = 50 𝑡𝑟𝑖𝑎𝑙 Å~
5 𝑐𝑜𝑛𝑑𝑖𝑜𝑡𝑛𝑠 Å~ 2 𝑠𝑢𝑏𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠).
The constant stimulus experiment was performed 3 times under different instructions. The
first to be performed carried no specific instruction: all the participant had to do was to
indicate when the X was recognised and, when a miss or a false alarm occurred, no warning
would show up. The second experiment to be performed had the instruction of pressing x
whenever the participant was unsure of whether the X had being perceived or not. A
warning every time an X was missed would show up. The third experiment had the
instruction of pressing spacebar whenever the participant was unsure about seeing an X. A
warning would show up every time an ‘x’ was pressed in the absence of an X stimulus on the
screen. These different instructions were created to simulate neutral, liberal and
conservative responses, respectively. Liberal responses were expected to lead to a lower
threshold and conservative responses to a higher threshold; neutral were expected to be inbetween.
With the data gathered, the threshold for the constant stimulus experiment was
determined by fitting a Weibul function to the plotted graphs. The function was of the form
y=mx + c where c and m where the free parameter values. The c value equalled the stimulus
intensity threshold and the m value equalled the slope (rate of improvement from condition
to condition).
To calculate the difference between noise and noise + stimulus (D’), the data gathered from
the constant stimulus experiment with liberal instructions was used. D’ was calculated by
subtracting the hit rate z-score value from the false alarm z-score value. The criterion was
calculated by diving the D’ value by two.
MEG
The data for this experiment was obtained from the experiment published under the name
‘Parametric variation of gamma frequency and power with luminance contrast: A
comparative study of human MEG and monkey LFP and spike responses’ by Hadjipapas et al.
Here, the participant was asked to look at a screen that presented different stimuli of
varying contrast (20%, 36%, 48%, 66% and 96%) while inside a MEG scan. Each condition
was presented 100 times forming a total of 500 trials. In every trial the orientation (0° to
90°) and the phase (8 phases) of the granting was changed. After each block of 50 trials
there was a 10s break. To ensure the participant had the gaze fixed, the target would
occasionally change colour, which the participant had to indicate by pressing a button. The
stimuli were presented in the lower right visual quadrant and so the response was expected
to be found in the left hemisphere. In total, there were 278 channels and the sampling
frequency used to measure the data was 1200Hz.
The Fieldtrip Matlab toolbox was used to analyse the data. As the sampling rate was quite
high, the Fieldtrip function ft_resampledata was used to down sample the data to 600Hz.
The data was aligned to the onset of the stimulus and the channel of interest was selected
based on how clearly the ‘dip’ of neuronal activity could be seen.
RESULTS
Psychophysics
Staircase measurements
As a result of the adaptive method or staircase method, the following plot on figure 3 was
obtained. As can be seen, stimulus intensity is plotted against number of trials and the
correct and false responses are plotted in such a way that every time that a false response is
given, the stimulus intensity is increased and every 4 correct responses, the stimulus
intensity is decreases. The round circles stand for reversal, when the direction of the
intensity change is swapped. After 20 reversals, the threshold was calculated based on the
last 14 reversals and was found to be 0.25.
Figure 3.
Constant stimuli measurements
The constant stimuli measurement gave the following plot on figure 4. The plot shows the
experimental result plotted with the expected result calculated based on the staircase
experiment. The threshold in this experiment was set at 0.33.
Figure 4.
The plot on figure 5 shows the comparison between the 3 different conditions that
underwent the constant stimuli experiment. Against what was expected, the liberal
condition showed the lowest correct response rate whereas the non-bias showed the
highest. The reason for this might be that, when asked to change the behaviour, the
participant could not maintain the same pattern of response, leading to lower hit rate.
Figure 5.
Signal Detection Theory analysis
The table 1 bellows shows how the D’ value and the criterion value were calculated. The
values on the table were obtained from the liberal condition.
Stimulus + Stimulus - Mean D’ = Z(Hit
rate)- Z(FA
rate)
Criterion =
Z(Hit rate)+
Z(FA
rate))/2
YES 0.62 (hit) 0.1 (False
Alarm)
0.315 1.587 0.794
NO 0.38 (miss) 0.9 (correct
rejection)
0.64
1 1
Table 1.
Figure 6 shows how the different aspects of the functions change according to the condition
used. The hit rate plot shows how the liberal condition indeed leads to higher hit rates and
the conservative leads to lower hit rates; the correct rejection plot, as expected, show the
opposite of that. The D’ plot shows how the non-biased condition made the difference
between noise and noise + stimulus higher. The criterion value shows that the liberal
condition had the highest criteria, which is also expected, as the liberal condition takes the
largest area of the noise and noise + stimulus functions.
Figure 6.
MEG
Time domain analysis
Figure 7 shows the time locked responses to the different contrast conditions. It can be
noted from the graphs that as the contrast increases (contrast increases from condition 1 to
5), the neural response also increases (blue to yellow). This increase is explained by the
increasing ‘dip’ (in between dotted lines) that becomes more prominent as the contrast
increases.
Figure 7
Figure 8 shows how the chosen channel reacts differently to the different contrast
conditions. It shows how the intensity of the neural reaction is directly proportional to the
intensity of the stimulus.
Figure 8.
Frequency domain analysis
The following plot on figure 9 shows the time-frequency responses to different contrasts. It
shows how the intensity at different frequencies vary according to time. As can be noted, as
the contrast level increases, the intensity of the frequencies on the 30Hz to 60Hz range also
increases.
Figure 9.
The graph below, figure 10, shows the intensity against frequency of the different contrast
conditions. As can be noted, the highest contrast has the highest activity intensity, whereas
the lowest contrast has near no change in intensity.
Figure 10.
Signal Detection Theory and ROC analysis
Below, on figure 11, sensitivity was calculated under different distributions of neuronal
responses. For the ‘stimulus absent’ condition, data carrying a lot of noise was used. This is
seen on plot 1, where the intensity of the stimulus is randomly distributed along time and
frequency. This random distribution is then observed on the noise vs noise+stimulus plot,
where the peaks seem to almost overlap, leading to a ROC curve where the AUC is just on
the 50% line (meaning hits and FAs happens half the time each).
For the ‘stimulus present’ condition, the plot with the clearest intensity pattern (plot 5) was
chosen. This plot lead to a noise and noise+stimulus plot with a D’ value of 2.7, leading to an
almost perfect ROC curve, with an AUC of 0.98.
The hit and FA rates were calculated by finding the area to the right of the criteria line (blue
line in the noise vs noise+stimulus plot. The hit rate is the area under the red plot
(noise+stimulus) and the FA is the area under the black plot (noise).
Figure 11.
A plot displaying the ROC curve of the 5 different conditions above is displayed below on the
right (figure 11). In this plot, it is clear how the AUC is greatly improved for the condition 5,
whereas condition 1 lies just under the 50% line. On the left, the ROC sensitivity is plotted
against the different contrast conditions. As can be seen, the plot shows that the lowest
contrast level at which the observer has an above chance level of recognition is at contrast
36%.
Figure 11.
DISCUSSION
The analysis of the data gathered showed that the idea of an absolute threshold, after
which all stimuli is perceived, is not a reality. Indeed, the perception of stimuli happens
gradually and, as is shown in the psychophysics and MEG results, the stimulus strength has a
non-linear effect on the perception.
Neurons in the brain are always active, no matter if in presence or absence of stimuli, and
so the differentiation between stimuli and no stimuli perception through neural signalling is
hampered by the uncertainty of whether a certain signal represent stimulus or just noise.
ROC analysis can be useful in the differentiation of this two states, but the results should
always be taken carefully.
Not all stimuli that comes from the outside world will provoke a significant response in the
brain leading to perception. Our senses are not as reliable as one would expect and the
perception of stimuli is influenced by more than the stimulus itself.
This study dealt with a single participant and so the results cannot be easily generalised to a
whole population. Variables such as stress, tiredness, or attention were not taken in
consideration and might have affected the results of the experiment. To make the
experiment more accurate, more participants could be included and variables such as those
mentioned should be taken into consideration.
REFERENCES
Heeger, D. (2003). Signal Detection Theory. Retrieved from
http://www.cns.nyu.edu/~david/handouts/sdt/sdt.html
Lemon, C. H., & Smith, D. V. (2006). Influence of response variability on the coding
performance of central gustatory neurons. J Neurosci, 26(28), 7433-7443.
doi:10.1523/JNEUROSCI.0106-06.2006
Zwislocki, J. J., & Relkin, E. M. (2001). On a psychophysical transformed-rule up and down
method converging on a 75% level of correct responses. Proc Natl Acad Sci U S A,
98(8), 4811-4814. doi:10.1073/pnas.081082598