Psychometric functions for efficient and effective psychophysical testing of sensory function

Abstract

An efficient test for sensory function has been reported using random order pairs of real and sham stimuli. The constant magnitude of the real stimulus is chosen such that the first error in a patient’s forced-choice report on the order of real and sham stimulation, immediately indicates abnormal sensory function. This magnitude just exceeds a critical large percentile of the psychometric function (i.e. the relationship between percentage of detection and stimulus magnitude in healthy subjects). The aim was to determine psychometric functions for one tongue site and six facial sites for adjusting three variants of the real/sham stimulus method (i.e. for light touch, cold sensation and for two-point discrimination). All 150 healthy subjects participated in testing for light touch sensation, 100 subjects additionally participated in testing two-point discrimination and 50 subjects participated additionally in testing cold sensation. The stimulus magnitude was varied using a staircase-limits procedure. Following curve fitting with a Boltzmann function, 90th, 95th or 99th percentiles of the psychometric functions were determined. A set of at least two real/sham tests, one testing the function of large nerve fibres and one for small fibres, allows quick assessment of a patient’s disturbed sensory function including its fibre pathology.

Psychophysical and neurophysiological tests have been developed for examining trigeminal nerve sensory function . A psychophysical test uses the relationship between physical stimuli and their perception, whilst a neurophysiological test records an event in bioelectrical activity following stimulation. A disadvantage of psychophysical tests based on sensory thresholds and neurophysiological tests is that they are time-consuming.

Time-management might be involved when choosing an optimal psychophysical test for a patient as different tests measure different aspects, even modalities, of sensory function . Time-management might be important when tests are applied at several sites in one examination. Apart from quantitative but time-consuming tests, there is a need for an efficient but effective method of sensory testing.

In a study on long-term lingual nerve damage, two variants of an efficient and effective test have been applied to determine whether relatively thick or thin nerve fibres are involved in sensory loss . Pairs of real and sham stimuli were presented in random order, on two occasions announced by the examiner whilst the subject kept their eyes closed. After each pair, the patient was asked to report the order of real stimulation, also when the patient was guessing (forced-choice procedure). The constant magnitude of the real stimulus was chosen using information from the psychometric function of the modality tested.

A psychometric function usually resembles a sigmoid function with the percentage of stimulus detection displayed on the y -axis and the magnitude of the physical stimulus on the x -axis. If the magnitude of the stimulus is sufficiently large, a subject will always be able to detect the stimulus (100% detection). If the magnitude is sufficiently small, the subject never perceives the stimulus and therefore the percentage of detection will be zero. In between, there is a transition range of stimulus magnitudes where the percentage of detection will gradually vary between 0 and 100%. The stimulus magnitude at which the function reaches 50% detection is usually taken as the sensory threshold. This magnitude is also a measure of the location of the psychometric function within the range of stimulus magnitudes on the x -axis. Rather than for an individual subject, a psychometric function can also be determined for a subject sample.

The constant magnitude of the real stimulus in a real/sham stimulus test was chosen as the value at which healthy subjects could just detect this stimulus with nearly zero errors. To that end, the magnitude of the real stimulus just exceeded the 95th percentile of the psychometric function of the modality tested from a sample of healthy subjects. When seven successive correct responses occur in the order of real stimulation, the chance of attaining this score by guessing is less than 0.01 (0.5 7 = 0.0078). The first error of a patient in choosing this order immediately indicates that a patient is, at least in part, guessing because of abnormal sensory function. Thus the outcome of the real/sham stimulus test is dichotomously characterized as ‘normal’ (no errors in 7 consecutive trials) or ‘abnormal’ (following the first error).

Regarding psychometric functions, only a few data on 95th percentiles have been reported that are preliminary in terms of sample size, number of test sites and sensory modalities. The first aim of the present study was to determine psychometric functions in a large group of healthy subjects, for a tongue site and six facial sites, and for three variants of the real/sham stimulus method. These variants are related to light touch, cold sensation and to two-point discrimination as a novel variant. The 90th, 95th and 99th percentile were determined to serve as a guideline for adjusting the magnitude of the real stimulus in a real/sham stimulus test. A determination of the 90th percentile enables a less conservative adjustment of the test than those carried out previously.

The second aim was to provide additional information on the real/sham stimulus method that is important for an appropriate application. This information includes a simple way of maintaining the temperature of metal rods at 22 °C that are successively used in test measurements on cold sensation. Recommendations will be given for adjusting the magnitude of the test stimulus when a real/sham stimulus method is applied for the first time in a patient.

The present study involves facial areas, but has potential for other areas (e.g. the hand) where sensory function is frequently examined.

Materials and methods

150 healthy Caucasian volunteers (85 females, 65 males; mean age 28.0 years, SD 8.18, range 15–55 years) who gave written informed consent, participated in the study that was approved by the University Ethics Committee. All 150 subjects participated in the determination of psychometric functions of light touch sensation. Testing of light touch sensation was always carried out first because it has the least complicated instructions. 100 of them (59 females, 41 males; mean age 26.0 years, SD 6.99, range 15–45 years) contributed, apart from light touch sensation, to psychometric functions of two-point discrimination. The remaining 50 out of 150 subjects (25 females, 25 males; mean age: 31.9 years, SD 9.02, range 18–55 years) contributed, apart from light touch sensation, to psychometric functions of cold sensation.

Devices for real/sham stimulation for testing

The first error that occurs in choosing the order of real/sham stimulation indicates major nerve injury of thick afferents when testing light touch sensation. A major reduction in density of afferent fibres that are predominantly involved in touch sensation might be involved when testing two-point discrimination, and major nerve injury of thin myelinated afferent fibres when testing cold sensation.

The real/sham stimulus test of light touch includes the use of a single Semmes-Weinstein monofilament ® of which the index number (stimulus magnitude) is chosen from the psychometric function for light touch in healthy subjects , starting at the 90th percentile ( cf . Discussion). The real stimulus is a touch that bends the test filament ( Fig. 1 A ). The filament is gently moved perpendicular to and from a test site in about 5 s. The contact time is about 1.5 s (the examiner counts silently ‘21, 22’ at the right pace). The sham stimulus is achieved by approaching the subject with the device whilst the filament is turned away ( Fig. 1 B).

Fig. 1
Three types of devices used for studying trigeminal sensory function in the present study. (A) Semmes-Weinstein monofilament for testing light touch sensation. The filament bends when peak force is reached which is related to filament diameter. This diameter varied in a staircase-limits procedure (according to index number) to determine the psychometric function of light touch. Based on this function, a particular filament diameter is chosen in the real/sham stimulus method. (B) Semmes-Weinstein monofilament whilst the filament is turned away from the face illustrating the presentation of a sham stimulus in the real/sham stimulus method. (C) MacKinnon-Dellon Disk-Criminator for testing two-point discrimination. A disk contains a series of metal prongs with rounded tips. Tips are spaced at varying millimetre intervals. Prong distance varied whilst determining the psychometric function for two-point discrimination, and a particular distance is chosen for the real/sham stimulus method. (D) Aluminium rod for testing cold sensation. The tip diameter of the rod varied with steps of 0.25 mm whilst determining the psychometric function for cold sensation, whereas a particular tip diameter is used in the real/sham stimulus method.

The real/sham stimulus test of two-point discrimination includes the use of a single inter-prong distance of a MacKinnon-Dellon Disk-Criminator ® that is based on the psychometric function of two-point discrimination. The real stimulus is a touch with the two prongs just to the point of tissue blanching ( Fig. 1 C; contact time approximately 1.5 s). A sham stimulus is the touch with such a small inter-prong distance that it will at most yield a sensation of an elongated stimulated area, without separation of two points.

The real/sham stimulus test of cold sensation includes the use of a heat-conducting aluminium rod . This rod has a shaft of 35 mm length and a diameter of 7.0 mm that is connected to a non-heat-conducting PVC handgrip ( Fig. 1 D). The aluminium shaft has a small tip of 5 mm length and a diameter that is based on the psychometric function of cold sensation. The real stimulus is provided by a touch (contact time approximately 1.5 s) with the aluminium rod (having a room temperature of 22 °C; touch as well as cold sensation). The sham stimulus is produced by the touch with a non-heat-conducting Perspex ® rod of the same dimensions (only touch sensation of neutral temperature).

For a real/sham stimulus test on cold sensation that possibly includes seven trials, it is important to have a stock of seven aluminium rods at 22 °C. The aluminium rods were vertically placed, and replaced after testing, in cylindrical holes in an aluminium block (170 mm ( l ) × 27 mm ( w ) × 75 mm ( h ); Fig. 2 ) that serves as a temperature reservoir. The aluminium block could also be placed in a water bath of 22 °C when testing was carried out in a room in which the temperature deviates from 22 °C. In order to avoid any sound clue between a real stimulus and a sham one, it is important to take away an aluminium rod from the block just before a trial with a pair of real/sham stimuli will be started.

Fig. 2
A stock of 7 aluminium rods placed in cylindrical holes in an aluminium block that serves as a temperature reservoir. The rods are ready for successive use in a real/sham stimulus test of cold sensation.

Determination of psychometric function

Psychometric functions were determined for seven sites. Apart from a site on the tongue (20 mm from the tip at the dorsoventral junction on the lateral side), six of these seven sites included facial areas. These six facial sites ( Fig. 3 ) were: (1) the anterior cheek, (2) the hair bearing skin of the upper lip, (3) this skin of the lower lip, (3) at the transition of the vermilion border and the mucosa of the upper lip, (4) at this transition of the lower lip, and (6) the mental region. Psychometric functions of touch sensation and of two-point discrimination were determined bilaterally for the facial sites nos. (1), (2), (3) and (6). Otherwise, psychometric functions were determined unilaterally in such a way that the side ipsilateral to the dominant hand was chosen in half of the subjects and the contralateral side in the other half. The subjects were examined with their eyes closed. The points of stimulation were selected in random order. The sensory devices were hand-operated whilst the observer’s elbow was supported on a table.

Fig. 3
Left: Location of test sites (dots) on cheek, on hair-bearing skin of upper and lower lip, and on mental region. Pvl, pupillary vertical line; ml, midline; cvl, commissural vertical line; lior, level of infra-orbital rim; lnb, level of nasal base; lc, level of commissure; lmf, level of mental fold. Cheek site is located on the pvl 1.5 cm below lior. Upper lip site is located in the centre of a rectangle confined by lnb and lc, cvl and ml, and the lower lip site in the centre of a rectangle confined by lc and lmf, cvl and ml. Mental region site is located on the cvl midway between lmf and the mandibular rim. Right: Location of test sites (dots) on the transition of vermilion border and mucosa of the upper and lower lip, midway between cvl and the midline. The indicated locations on the red tissue of the upper lip were sometimes only nearly accessible with the devices used. The site was approached as much as possible in these cases and was then located on the vermillion border.

In order to determine a psychometric function, the stimulus magnitudes were varied according to a staircase-limits method . For each stimulus magnitude, the subject reported either a present or absent sensation (positive or negative response). The first stimulus magnitude of the first series with descending magnitudes was chosen to be so large that the subject clearly reported a positive response. The series was terminated when a positive response was followed by two negative responses to two subsequently smaller stimulus magnitudes. Stimulus magnitudes that were smaller than the endpoint of the descending series were recorded as having a negative response. A second series with an initial negative response was then applied using successively larger stimulus magnitudes. The second series was terminated when a negative response was followed by two positive responses to two successive larger stimulus magnitudes. After two positive responses the other larger stimulus magnitudes were recorded as having positive responses. A third series was then applied with descending stimulus magnitudes and, finally a fourth series with ascending magnitudes.

The sum score of positive responses over four series was determined for each stimulus magnitude. For each stimulus magnitude, the sum score was next cumulated over all subjects from a group. This total number of positive responses was expressed as a fraction of the total number of both positive and negative responses (number of test series × number of subjects). The fraction of positive responses as a function of stimulus magnitude (the psychometric function), is related to the probability of positive responses (hence of stimulus detection) from healthy subjects as a function of stimulus magnitude.

For light touch sensation, stimulus magnitude corresponded with the index number of the filaments (the logarithm of 10 times the force in milligrammes), and a stimulus step corresponded to the transition between two successive index numbers. The first part of the psychometric function was lacking for most of the examined sites because many subjects felt the thinnest filament (no. 1.65). The upper part of the curve was available to assess the 90th, 95th or 99th percentiles in the psychometric function of light touch sensation (see below).

A stimulus magnitude for two-point discrimination corresponded with an inter-prong distance in millimetre (mm) and steps of 1 mm were applied. A full psychometric function could be obtained for all sites examined.

For temperature sensation, a stimulus magnitude, expressed as tip area in mm 2 , corresponded with a tip diameter of the metal rod in mm and steps of 0.25 mm were applied. With this device, touch sensation as well as cold sensation occurred. In order to avoid confusion between these sensations, two rods were used for paired stimulation, a metal rod and a Perspex ® rod were applied in random order and the subject was asked when the cold sensation occurred. The tip diameter of the rod with the real cold stimulus varied equally to the rod with the sham stimulus, both decreased or increased in the procedure. Consequently, a contrast was created between the combination of touch and cold perception and touch perception alone. The subjects also rated the degree of certainty of cold perception after each stimulation pair according to: (1) and (2) being certain or fairly uncertain, respectively about perception of cold, or (3) and (4) no perception of cold, but being fairly uncertain or certain. The response was considered to be positive when the order of cold stimulus was identified correctly and the subject was at least fairly certain of the perception of cold. Many subjects associated the smallest tip diameter with cold sensation. The application of rods with tip diameters less than 0.5 mm was not appropriate because of the risk of needle sensation. The upper part of the curve was available to assess the 90th, 95th or 99th percentiles in the psychometric function of cold sensation.

Data analysis

The relationships between the fraction of positive responses at a group level and stimulus magnitude could be fitted well with a sigmoid curve (Boltzmann model; details in Fig. 4 ) using non-linear regression analysis. Curve fitting reduced the information to two parameters, the stimulus magnitude at which the fraction of positive responses is 0.50 (50%; denoted as SM-0.50), and broadness ( b ). Parameter b is related to the broadness of the range of stimulus magnitudes across which the fraction of positive responses varied from 0 to 1.0. Thereafter, the stimulus magnitudes at which the fraction of positive responses are 0.90, 0.95 and 0.99 (denoted as SM-0.90, SM-0.95 and SM-0.99, thus the 90th, 95th and 99th percentiles) were calculated, using the Boltzmann-equation and the SM-0.50 values and b values for the respective devices and sites. The discrete stimulus value of a device that exceeded most closely the value of SM-0.90, SM-0.95 and SM-0.99, respectively, was chosen as the practical value of these percentiles (denoted as SM-0.90 p , SM-0.95 p and SM-0.99 p , respectively).

Fig. 4
Representative examples of psychometric functions of light touch sensation for mental region (A), of two-point discrimination for hair-bearing lower lip and cheek site (B), and of temperature sensation for the tongue (C). The symbols (●) and (▴) depict the experimental data. The experimental data on the relation between fraction of positive responses (FPR) and stimulus magnitude (SM) have been fitted using the Boltzmann-equation: FPR = (MIN + ((MAX − MIN)/(1 + exp ((SM-0.5 − SM)/b)))). MIN, minimum value of FPR; MAX, maximum value of FPR; SM-50, stimulus magnitude at which fraction of positive responses is 0.5; b , broadness factor related to the slope. A larger value of b corresponds to a less steep slope of the relationship between FPR and SM. As MIN = 0 and MAX = 1.0 for FPR, the Bolzmann-equation is simplified to: FPR = 1/(1 + exp ((SM-0.50 − SM)/b))).

Statistical testing of the differences in SM-0.50 (a measure of the location of psychometric functions on the x -axis of stimulus magnitude) has not been applied because (i) many subjects scored 100% positive responses for the lowest stimulus magnitude available for light touch or cold, (ii) only four test series with descending or ascending stimulus magnitudes were applied, thus the percentage of positive response varied with large steps of 25% in individuals, and (iii) the aim of the study is to determine SM-0.90, SM-0.95 and SM-0.99 in mean psychometric functions as a guideline for real stimulation in a real/sham stimulation method.

The range of stimulus magnitudes at which the fraction of positive responces varies between 0 and 1.0 at a group level (dynamic range of stimulus magnitudes) also provides information on the location of the mean psychometric function. Within-device differences of dynamic range between sites, side, or sex were tested using the Kolmogorov–Smirnov two-sample test. The level of statistical significance was set at p < 0.05. All analysis were conducted using SPSS ® 15.0 (SPSS Inc., Chicago, IL, USA).

Results

Figure 4 shows examples of psychometric functions for light touch ( Fig. 4 A), two-point discrimination ( Fig. 4 B), and temperature sensation ( Fig. 4 C). The psychometric functions for two-point discrimination were always complete and some curves by site were shifted parallel to each other along the axis of stimulus magnitude and these functions had a similar broadness ( Fig. 4 B).

There was no significant effect of side or sex on the dynamic range of stimulus magnitudes of the psychometric functions, regardless of the test of sensory function used (Kolmogorov–Smirnov test). The dynamic range only differed significantly ( p < 0.05) for two-point discrimination, between the cheek and hair-bearing upper lip and between cheek and lower lip (cheek related to larger values of stimulus magnitude, Fig. 4 B).

The estimated SM-0.50 and b values according to curve fitting are shown in Table 1 . Table 2 shows the calculated values of SM-0.90, SM-0.95, SM-0.99 (the 90th, 95th and 99th percentiles of the psychometric functions) and their practical values for devices with discrete steps.

Table 1
Parameter values of the Bolzmann-equation following curve fitting of psychometric functions by device and site.
Device Units of stimulus magnitude Site SM-0.5 b
SWm Calibrated filament number Cheek 1.89 0.29
Upper lip skin 1.99 0.32
Upper lip vermilion 1.94 0.21
Lower lip vermilion 2.30 0.24
Lower lip skin 1.98 0.31
Mental region 2.14 0.32
Tongue 2.18 0.36
Disk-Cr. Inter-prong distance in mm Cheek 13.10 1.16
Upper lip skin 6.21 0.90
Upper lip vermilion
Lower lip vermilion
Lower lip skin 5.73 0.87
Mental region 8.43 1.22
Tongue
Al-rod Tip-area in mm 2 Cheek
Upper lip skin −0.57 * 0.80 *
Upper lip vermilion −0.99 * 0.65 *
Lower lip vermilion −0.43 * 0.54 *
Lower lip skin −0.67 * 1.02 *
Mental region
Tongue −0.77 * 0.83 *
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Feb 5, 2018 | Posted by in Oral and Maxillofacial Surgery | Comments Off on Psychometric functions for efficient and effective psychophysical testing of sensory function
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