Title of Thesis
Research on Haptic Angle Discriminability andDevelopment of Angle Magnitude Sorting
System2022 March

Yulong Liu

The Graduate School of Interdisciplinary Science andEngineering in Health Systems(Doctor’s Course)
OKAYAMA UNIVERSITY

Table of Contents
Table of Contents ......................................................................................................... I
Abstract...................................................................................................................... IV
Chapter 1 Introduction ................................................................................................ 1
1.1 Touch ............................................................................................................................... 2
1.2 Haptic perception of shape ............................................................................................ 3
1.3 The purpose of the present dissertation ....................................................................... 4
1.4 The contents of the dissertation .................................................................................... 5

Chapter 2 Haptic Angle Discrimination Evaluation ................................................. 7
2.1 Background .................................................................................................................... 9
2.2 The Characteristics of difference between two independent variables................... 11
2.3 Methods......................................................................................................................... 17
2.3.1 Participants ............................................................................................................................. 17
2.3.2 Stimuli .................................................................................................................................... 17
2.3.3 Experimental (Exp.1) procedure ............................................................................................ 18

2.4 Data Analysis ................................................................................................................ 20
2.5 Results and Discussion................................................................................................. 22
2.5.1 Characteristics of the haptic angle stimulus distinctive feature by experiment data ............. 22
2.5.2 The evaluation performance values of the Discrimination Index .......................................... 25

2.6 Conclusions ................................................................................................................... 27

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination ....... 29
3.1 Background .................................................................................................................. 30
3.2 Angle Sorting ................................................................................................................ 33I

3.2.1 Procedure of Haptic Angle Sorting ........................................................................................ 33
3.2.2 Data Processing and Analysis ................................................................................................ 35

3.3 The Evaluation Experiment (Exp.2) of Sorting Method .......................................... 45
3.3.1 Participant .............................................................................................................................. 45
3.3.2 Stimuli .................................................................................................................................... 46
3.3.3 Procedure ............................................................................................................................... 46
3.3.4 Results and Discussion........................................................................................................... 47

3.5 General discussion ....................................................................................................... 49
3.6 Conclusion .................................................................................................................... 52

Chapter 4 Development of Haptic Angle Sorting Evaluation System ................... 54
4.1 Background .................................................................................................................. 55
4.2 Haptic Angle Sorting System ...................................................................................... 58
4.2.1 Haptic Pattern ......................................................................................................................... 58
4.2.2 Design of the Haptic Angle Sorting Device ........................................................................... 59
4.2.3 System software ..................................................................................................................... 62
4.2.4 System Implementation.......................................................................................................... 64

4.3 System Evaluation (Hardware Test)........................................................................... 65
4.3.1 The identification of stimuli angle ......................................................................................... 65
4.3.2 The operation of system ......................................................................................................... 66

4.5 Conclusions ................................................................................................................... 66

Chapter 5 Application Evaluation for Difference Group People ........................... 68
5.1 Background .................................................................................................................. 69
5.2 Experiment (Exp.3: Young and Old) .......................................................................... 69
5.2.1 Participants ............................................................................................................................. 69II

5.2.2 Prudence ................................................................................................................................. 69
5.2.3 Result and Discussion ............................................................................................................ 70

5.3 Experiment (Exp.4: Normal, MCI and AD) .............................................................. 72
5.3.1 Participants ............................................................................................................................. 72
5.3.2 Prudence ................................................................................................................................. 72
5.3.3 Result and Discussion ............................................................................................................ 73

5.4 General Discussion ....................................................................................................... 74
5.5 Conclusions ................................................................................................................... 77

Chapter 6 General Conclusion and Future Projections ......................................... 78
6.1 General Conclusions .................................................................................................... 79
6.2 Future Projections ....................................................................................................... 82

Appendix ..................................................................................................................... 86
Publications ................................................................................................................ 87
Acknowledgements .................................................................................................... 88
References ................................................................................................................... 89IIIAbstract
In humans, although most of the information received from the outside world isthrough visual pathways, when confirming the real of the information from visual, it ismore through the sense of touch. Especially When we see something amazing,
unexpected, or simply surprising, we sometimes don't feel confused about its "reality",
yes, we will touch it whenever possible[1]. Human fingers, especially the surface of thefingertips, the skin, have high touch sensitivity. It provides us with the means to connect
with the detailed information in the surrounding environment. For example, we
perceive physical information such as the material [2], softness [3], shape [4], and sizeof external objects through finger touch. Although our vision can obtain some
information, touch is the oldest and largest part of our sensory organs [5,6]. The
differences in the ability of fingertips to discrimination the physical characteristics ofobjects, for instance size of angle, not only exist among individuals[7–11], but also
among different groups of people [12,13]. To differentiate two different objects bytouch alone, we need to remember the spatial information of the first object in theirworking memory and then compare the spatial construction of the first object to that of
the second. This procedure activates a widely distributed cerebral network that mainly
includes areas involved with the initial processing of skin indentations (i.e., primaryand secondary somatosensory cortex), the high-class areas for computation andelaborate reconstruction of shapes (i.e., part of the intraparietal sulcus, etc.) [4], and theprefrontal cortex[4,14], which is activated for tactile working memory processing.
Evenly, touch shape discriminability is commonly used clinically to assess tactile
perception and even to estimate higher-level functions such as working memory[15–17]. In our previous studies, tactile angle discrimination was found to be related tohigher cognitive functions, where the impairment of working memory significantlyIVreduced tactile angle discriminability. Therefore, we developed an angle stimuli
presentation device [18] for the evaluation of cognitive impairment by testing tactile
angle discriminability. In that experiment, the two-alternative forced-choice (2AFC)
method was used. We presented 20 pairs of angle stimuli in pseudorandom order andcalculated the angle discrimination threshold [13,19]. However, there are still two
problems in our previous research on angle threshold discrimination. (1) The 2AFC
paradigm needs many pairwise comparisons, which are necessary for an accurate
discrimination threshold, consequently, it takes ap- proximately 2.5 h for eachparticipant to complete the task. In particular, it is difficult for some groups toconcentrate on long-term tests. (2) The device was controlled using an extra computer
to code and required a technician to run the control program, which makes thesecomplex operations difficult for the device to be used clinically, especially by
nonprofessionals.
Firstly, in the 2AFC experiment, to compare the relationship between thediscrimination threshold obtained from the logical curve model fitted according to thecorrect rate and the standard variance obtained from the Gaussian cumulative
distribution fitted with the probability of the answer "big". Although the mathematicalmodel used is different, due to the similarity between the logistic function and theGaussian cumulative function, the final two results (the angle discrimination threshold
and the standard deviation of the Gaussian cumulative distribution) can be converted.
In this way, the standard deviation of the Gaussian cumulative distribution and the angle
discrimination threshold can show individual differences, which can be used to evaluate
the individual's angle discrimination ability.
Secondly, according to the verification that the standard deviation in the Gaussian
cumulative distribution function can be used to evaluate the model, a new evaluationVmethod of angle sorting was proposed. Among them, the maximum likelihood
estimation evaluation method under the normal model is described in detail, from theresults of angle sorting to the standard variance that can be used to evaluate theindividual angle discrimination ability of humans. Using this method, the same subjects
as the 2AFC experiment were measured at the same time. The standard deviation
obtained according to the sorting evaluation method also has personal differences, andthere is a strong correlation with the standard deviation obtained in 2AFC (Among them,
the Pearson correlation coefficient is 𝑟 = 0.7750, 𝑝 = 0.0031 ). The personal
difference and the strong correlation with 2AFC proved that the angle sorting method
can also be used to evaluate the ability of individual angle discrimination. At the sametime, different variance values are obtained by comparing 2AFC and angle sorting
evaluation (the standard variance of 2AFC is greater than that of angle sorting
evaluation). In order to explore the reasons for such results, it is further found by using
the Maximum Likelihood Difference Scale experiment that the size of the reference
angle difference is more conducive to the identification of angles in the angle sorting.
That is, in the sorting, with the increase of the number of placement angle stimuli, morereferences are provided for the presented angles, which is more conducive todetermining the size of angles. So as to improve the discrimination of angle.
Thirdly, to test and evaluate more conveniently by using the angle sorting method,
we designed and developed a haptic angle discrimination evaluation system. In this partof work, the metal is reused as angle stimulation to reduce the previous plastic angle
stimulation which is used for a long time, the stimulation accuracy will be reduced due
to wear; At the same time, several sets of angle stimuli with different angle differenceswere designed to test a wider range of people; to use more conveniently and get theevaluation results faster, the evaluation hardware and software for automatic calculationVIof sorting results are also designed, including hardware design of angle stimulus
identification, data calculation software, data display, storage and transmission andother operation functions.
Lastly, to investigate the application of angle sorting method in practicalevaluation, we tested different populations, for example, between healthy elderly andyoung people, and between people with different cognitive impairment include ofnormal control (NC), mild cognitive impairment (MCI) , and Alzheimer’s disease (AD).
According to the current situation, future research will focus on exploring theactivity process of human brain in the process of angle sorting, so as to reveal themechanism of human brain's tactile multi-information processing and provide animportant basis for us in the field of artificial intelligence.

VIIChapter 1 Introduction

Chapter 1 Introduction

SummaryThis chapter introduces touch perception and the touch of field. The previous
studies related to the objects of three-dimensional and the pattern of two-dimensional
touch have also been summarized here. At last, the purpose and contents of the thesis
are briefly explained.

1

Chapter 1 Introduction
1.1 Touch

As one of the fields of psychological research, touch perception has received far
less attention than vision. In previous studies, however, there is a wealth of literature
available about touch that covers everything from neurophysiology to basic psychiatry
to cognitive problems such as memory and object recognition.
The different sensory systems are divided into the cutaneous system, kinesthetic
system, and haptic system, which are based on neural input to define the modes of touch.
The cutaneous system receives mechanoreceptors - specialized nerve endings that
respond to mechanical stimuli (forces) - sensory inputs embedded in the skin [19]. The
kinesthetic system receives sensory input from mechanoreceptors located in the body's
muscles, tendons, and joints. The haptic system uses a combination of input informationfrom the kinesthetic system. The word “haptic” is usually particularly relevant to“active touch”. And in everyday life, touch is active; The senses are interwoven withthe body structures that produce movement. The basic input of haptic perception can beaugmented by the movement of the body and skin relative to surfaces and objects, thus
helping to reveal a range of properties of the world.
However, in previous studies on the characteristics of tactile sensing systems,
researchers often distinguish active and passive touch modes. Among them, the processof acquiring information by defining only cutaneous system input and muscle nonmovement is considered as passive touch [20,21]. Then, through the combination of thethree classifications of the three sensory systems -- cutaneous, kinesthetic and haptic[19], these combinations are generated as follows: (1) tactile (cutaneous) perception,(2) passive kinesthetic perception (kinesthetic afferents respond in the absence ofvoluntary movement), (3) passive tactile perception (cutaneous and kinesthetic
2

Chapter 1 Introduction
afferents respond in the absence of voluntary movement), (4) active kinesthetic
perception, and (5) active haptic perception. Under modes (4) and (5) is the touchprocess for motion control. The research of this thesis mainly focuses on the haptic
mode, because this mode is a way that human beings often use to explore the outside
world by touch.

1.2 Haptic perception of shapePrevious studies have pointed out that the peripheral nerve unit of the tactile
system puts forward the object surface attribute[22]. After the early coding processingof the receptor, there are quite a lot of high-level processing in the brain before defining
the basic attribute of the object. Although in the advanced processing level, there aredifferences in properties such as geometric properties, material properties, andtemperature. That is to say that geometric properties are the specificities between
different objects, while the material properties and temperature properties are
independent of the objects.
Furthermore, geometric properties are divided into size and shape. The two naturalscales of these properties are distinguished within the touch by the role of cutaneousand kinesthetic receptors. The discriminability of touch shape is usually used clinicallyto evaluate tactile perception, and even to evaluate higher-level functions, such as
working memory[13,15,16]. In our previous studies, it found that the ability of tactile
angle discrimination is related to higher cognitive function, where the impairment ofworking memory significantly reduces the tactile angle discriminability[12,23].
Therefore, we developed an angle stimuli presentation device [11] for the evaluation of
cognitive impairment through testing the tactile angle discriminability. In that3

Chapter 1 Introduction
experiment, the Two-Alternative Forced Choice (2AFC) method used，we presented
20 pairs of angle stimuli in a pseudo-random order and calculated the angle
discrimination threshold[11,12]. However, there are still two problems in our previous
studies on angle threshold discrimination: (1) the paradigm of 2AFC needs many timesof each pairwise comparison which is necessary for an accurate discriminationthreshold，it takes about 30 min for each participant during the task. Especially, it isdifficult for the special crowd to concentrate on the long-time test. (2) the device wascontrolled by using an extra computer to program code and requires a technician to run
the control program, which these complex operations make difficult for the device tobe used clinically, especially by non-professionals.

1.3 The purpose of the present dissertation

In current study, we proposed a new method to evaluate the angle discrimination
ability. A new paradigm, rather than 2AFC, transformed by the 100 Hue test for thecolor vision test [24–26] was used in the present study. After participants sorted a seriesof angle stimuli during tests, we calculated the mean sorting discrimination index (DI)which enable us to evaluate the angle discriminability detection in a reliable and timesaving way. We explained in detail the paradigm process of angle sort and the evaluation
calculation method under this paradigm. In this thesis, we detailed and compared thismethod with previous evaluation methods and analyzed its differences and reliability.
Furthermore, we designed a new device integrated automatic control system that isfriendly to non-professionals. Instead of using the hardware structure of the previous
device to rely on the computer, a microcomputer is directly integrated into the newdevice. And a special analysis software is designed for the system, which can collect4

Chapter 1 Introduction
and analyze data the paradigm of angle sort, and then display and transmit the results.
To verify the reliability of this method, we recruited a group of participants to complete
the haptic angle sorting and the tactile two-angle discrimination task. We also applied
the method and system to different groups of people in practice to test whether it issuitable to describe the human judgment of perception and cognitive differences in any
specific experimental environment.

1.4 The contents of the dissertation

In this thesis, the haptic discrimination test method of angle sorting and thederivation of its evaluation calculation model are proposed, and the angle sorting
automatic evaluation test system is developed according to the test method. Finally, themethod and system are applied to test different people.
Chapter 1 introduces the tactile perception and the higher cognition of touch, aswell as the related previous studies. The aim and content of the paper are also briefly
introduced.
Chapter 2 describes the first 2AFC experiment, which was evaluated using two
different methods. It is revealed that in different evaluation methods, the test can show
the difference in the individual's angle discrimination ability. At the same time, thetransformation relationship between these two different methods is given.
Chapter 3 describes the angle sorting evaluation method and the calculation modelof the method, and the sorting test and evaluation of the same population in the firstexperiment, and finally compares the differences with the 2AFC evaluation model. A
new method of angle sorting and its evaluation calculation is proposed. Through theperformance of the same population under different trials, an evaluation similar to theangle discrimination ability of 2AFC can be obtained.
5

Chapter 1 Introduction
Chapter 4 describes the design and development of the tactile angle sorting system.
According to the experimental paradigm, the experimental process is standardized asmuch as possible to make the test simple, and the test results can be obtained quickly,
and an independent test system has been developed. In the system, there are multiple
sets of different angle stimuli (2°,4° and 6°); the recognition of angle stimuli; theoperation of the system process, the calculation, display, storage, and transmission oftest results, etc.
Chapter 5 describes the fourth and fifth experiments. The experiments were two
behavioral experiments comparing young people and old people, and people withdifferent cognition levels. This method is used to evaluate the ability of different people
to distinguish from different perspectives.
Chapter 6 provides general conclusions for future research advancement based on
the evaluation of the angle sorting method and the application of the system.

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Chapter 2 Haptic Angle Discrimination Evaluation

Chapter 2 Haptic Angle Discrimination Evaluation

Summary
The Two-alternative forced choice (2AFC) method is usually used to evaluate thediscrimination threshold of perception. The stimulus difference at 75% position was
calculated by fitting the logical growth curve according to the accuracy results byselecting the larger or smaller in pairs comparison. For the discrimination of objects
with different physical characteristics such as two points, length, curve, grating andshape, the discrimination threshold was evaluated to evaluate the sensitivity of thesubjects to the stimulus, and the touch penetration performance of the subjects isreflected through such evaluation and further applied research. In the evaluation of theproperties of these objects, the same tests were performed in our previous studies on
the angle stimulus but were based on the Angle discrimination threshold derived fromthe logical growth function. In fact, the curve shape of the logical growth function isvery similar to that of the Gaussian cumulative distribution function, and the numericalvalues are also very close. Gaussian cumulative distribution function is also used as
evaluation model in that same research. And there is a rule between the standard
variance and its value change in the Gaussian cumulative distribution function.
Therefore, the standard variance estimated by the gaussian cumulative distribution canalso be used as a parameter to evaluate the performance of angle haptic discrimination.
There is a linear relationship between the discrimination threshold calculated by logical
growth curve and the standard variance calculated by gaussian cumulative distribution.
This well shows that the standard variance reflects the performance of haptic angle
discrimination - the greater the standard variance, the worse the performance of angle
7Chapter 2 Haptic Angle Discrimination Evaluation
discrimination; The smaller the standard variance, the better the performance.

8Chapter 2 Haptic Angle Discrimination Evaluation
2.1 BackgroundIn daily life, individuals usually use touch to determine the size, shape, material
and roughness of objects in a more detailed way. Some researchers have questioned inprevious whether touch can retrieve useful spatial information from raised-line images.
So, they used “tactile pictures” that could be made from heat-sensitive materials (suchas plastic paper) or pressure-sensitive plastic sheets (such as mylar paper)[27]. Pictures
made in this way were touched by the subjects' fingers. You can simply define theexternal shape or contour of the object by touching. Moreover, shape is an inherent
physical property. Although the direction or translation in space has changed, it always
remains the same one. The raised line drawing of an object can also show thesecharacteristics through a series of pairs of lines in a two-dimensional space. We canthen define the physical characteristics of the object, such as edge length and curvature,etc., by discrimination the features of the raised-line drawing. The tactile pictures in thedesign (including but not limited to raised line drawings) were potentially highly usefulfor the visually impaired, because they could use them to retrieve information about
objects, locations, spaces, and shapes [28]. The design gradually used different types oftactile pictures, such as the raised line drawings of objects such as cars, scissors, plants,
ashtrays, etc. [29–44], and also using these objects as identification task materials is
also effective for blind people and Normal adults' perception of tactile shapes[45–47].
There is a dispute in the recognition theory between the tactile picture that recognizes
two-dimensional non-raised lines and the raised-line drawing. However, twodimensional raised-line drawing can delete the information of real objects and then beprocessed by comparison research. In the past, cognitive psychology has been used to
explore the perceptual processing of two-dimensional raised-line drawing.
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Chapter 2 Haptic Angle Discrimination Evaluation
Early researchers used raised dots, edges, gratings, or letter patterns pressed onto
skin surfaces to study spatial sensitivity and cognitive abilities associated with touch,as well as discrimination in shape [48–52]. There are also studies on the effects oflength[53] and curvature [44,54] on tactile discrimination. Taking the angle between
two edges as another important factor for tactile stimulation, especially in tasks thatinvolve the use of fingers to discriminate simple raised-line triangles or rectangles, andthe ability to discriminate human tactile angles was also studied. Through active touch
to identify large angles to explore the central nervous mechanism[55–58], and foundthat skin feedback and proprioception can promote angle discrimination. Under thecondition of single use of proprioceptive feedback system, the recognition ability isfurther reduced [59]. In subsequent studies, the cutaneous feedback is further separated,
and its ability to discriminate angles will also be inferior to the combined feedback[60].
In the past, the Two-Alternative Forced Choice (2AFC) method was mostly used
to evaluate the angle discrimination ability. By presenting two angle stimuli to the rightindex finger of the subjects one by one, the subjects were asked to identify the size ofthe pair of angles and record the correctness and error of each pair of comparison results.
Then the logical growth curve was fitted by the correct rate of each pair of angle
difference, and the angle difference corresponding to 75% position of the logical curve
was selected as the angle discrimination threshold. And there are also some researchthat used Gaussian Cumulative Distribution fitting data, and the corresponding value
when screening 84% is defined as the angle discrimination threshold.
Although there are subtle differences between these two evaluation calculation
methods, they all use the estimated angle value as the evaluated discriminationthreshold. This value can intuitively reflect the participant’s ability to discriminate theangle, however, this evaluation could also be transformed into the standard error of a
10

Chapter 2 Haptic Angle Discrimination Evaluation
Gaussian Cumulative Distribution as an evaluation parameter. Therefore, we designed
the 2AFC evaluation experiment to calculate the estimated results by above two
methods, then the result of discrimination threshold and discrimination index. At thesame time, we compared the relationship between the two results and further provedthat the discrimination error can be used as an evaluation parameter to reflect theindividual's ability to distinguish angles.
The purpose of this chapter is to explore how the haptic discrimination of thestimulated angle is characterized by different functions in 2AFC. We particularly
verified that the normal distribution function and the cumulative normal distributionfunction were represented in the 2AFC data analysis. Furthermore, through theexperimental results, we elucidate that the cumulative probability function and thenormal distribution function were the fundamental functions that determine themechanism of tactile stimulus angle discriminability.

2.2 The Characteristics of difference between two independent variables

Random errors vary unpredictably and unavoidably in each measurement[61], butcluster around the true value in multiple measurements. The primary causes of random
error are instrument limitations, environmental factors, and subtle variations inprocedures, for example, when weighing on a scale, you get a slightly different weight
each time; when taking a volume reading in a flask, you may read the value from adifferent angle each time; measuring your height can be affected by slight posturalchanges. Since gusts and directional changes can affect values, it is important to obtain
multiple readings and calculate an average. Readings must be estimated when they fall
between marks on the scale or when the thickness of the measurement mark is
considered. Therefore, the characteristics of random error require that after obtaining
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Chapter 2 Haptic Angle Discrimination Evaluation
multiple data points and averaging them, it is very important to understand the variationand estimate the real value. Moreover, it is not difficult to find that the random error
has the following characteristics[61–63]:
1) The positive and negative errors of size occur with equal probability.
2) Small mistakes are more likely to happen than big ones.
3) Errors greater than a certain limit did not actually occur.
These characteristics show that the random error obeys the probability distributionof normal distribution[63].
When we estimate the angle of a stimulus single through haptic, it is inevitablethat random errors will occur. The same as, when considering a measure using the true
value M, the measure includes random errors, resulting in a normal distribution
characterized by a mean of 𝑴 and a standard deviation of 𝝈, as shown in Figure 2.1.
The vertical axis represents the relative frequency of measurements, and the horizontal
axis takes the observations in 𝝈 as the variable unit.

12Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.1 The Normal distribution. M is the Mean of Measurements. The 𝜎means Standard Deviation of Measurements. 68% of the measurements lie in theinterval 𝑀 − 𝜎 < 𝑥 < 𝑀 + 𝜎 ; 95% lie within 𝑀 − 2𝜎 < 𝑥 < 𝑀 + 2𝜎 ; and99.7% lie within 𝑀 − 3𝜎 < 𝑥 < 𝑀 + 3𝜎.

However, the current 2AFC experiment utilizes one reference angle compared toanother stimulus angle, so when we compare the difference between such two quantities,
how does the measured difference cluster around the true value? Here, let X and Y be
normally distributed independent random variables. Probability theory states that theirdifferences between X and Y are also normally distributed,
𝑋~𝑁 (𝑀1 , 𝜎12 ), 𝑌~𝑁 ( 𝑀2, 𝜎22 ).
When 𝑍 = 𝑋 − 𝑌 , the relation between is Z~𝑁 (𝑀1 − 𝑀2 , 𝜎22 + 𝜎22 ). It is notdifficult to find that the difference of two independent normally distributed randomvariables is also normal, with its mean being the difference of the two means, and its
variance being the sum of the two variances (i.e., the square of the standard deviation
13

Chapter 2 Haptic Angle Discrimination Evaluationis the sum of the squares of the standard deviations). When 𝑀2 = 𝑀1 + 1.5 ∙ 𝜎, 𝜎1 =𝜎 and 𝜎1 = 𝜎, the characteristics of the difference are shown in Figure 2.2.
𝑥𝐹(𝑥) = ∫−∞ 𝑓(𝑡)𝑑𝑡(2.1)

Next, we also considered the difference between a reference and two comparisons.
As in the 2AFC experiment, the reference angle was discriminated from different
comparison stimuli, here we discuss such comparison stimuli as two stimuli angles
separated by the same interval from the reference angle. Let the mean of the reference
to be M and those of the comparisons to be 𝑀 − 1.5𝜎 and 𝑀 + 1.5𝜎, respectively.
The characteristics of the difference may be considered in two aspects, using theprobability and the cumulative probability of the difference as shown in Figure 2.3. One
aspect is concerned about the difference in the negative region of measured difference
between the reference and the small comparison, while another aspect is about thedifference in the positive region of measured difference between the reference and thelarge comparison. The critical value in the negative region is 𝑋 = 𝑀 − 1.5𝜎, and in
the positive region is 𝑋 = 𝑀 + 1.5𝜎 . Here, both the cumulative probability of thereference being smaller than the small comparison and of the reference being larger
than the large comparison is 0.144, as show in Figure 2.3. By continuously changing
the comparison from small to large, it is possible to know how the smaller vs larger
judgment ratio of the reference to the comparison varies.

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Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.2 Typical characteristics of difference between two random variables. (a)The figure shows the probability of difference (dashed line) and cumulative
probability (solid line) for one example. where the probability of the difference isrepresented by the normal distribution function (dashed curve) of 𝑆𝐷 = 1.41𝜎
and the mean of 1.5𝜎 (𝑀2 − 𝑀1 = 1.5𝜎). The vertical axis represents relative or
cumulative probability (in Equation 2.1). The horizontal axis represents themeasured difference. (b) Figure shows that cumulative probabilities smaller than X
are represented by narrow gray grid areas, while cumulative probabilities larger
than X are represented by wide white areas. For example, the cumulative
probability that figure (a) is smaller than X=0 corresponds to the value of thecorresponding y-axis at the red dot, which is 0.144 in the figure (a).
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Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.3 Example of the probability (dotted curve) and the cumulative probability(solid curve) of the reference. (a)The probability is expressed by a normal
distribution function with 𝑆𝐷 = 1.4𝜎 , under the condition of comparison. The
vertical axis denotes relative probability or cumulative probability. The horizontal
axis denotes measured difference values from the reference. (b)The probability ofsmaller than 𝑋 = −1.5 (the comparison with 𝑀 − 1.5𝜎) is represented by the
cumulative probability of 0.144, as the red area shown in the panel, while that oflarger than 𝑌 = 1.5 (the comparison with 𝑀 + 1.5𝜎 ) is represented by the
cumulated probability of 0.144 (= 1 − 0.856) as the blue area shown in the panel.
16Chapter 2 Haptic Angle Discrimination Evaluation
The above theoretical consideration concerns the difference between two
independent variables is a basis of exploration of the haptic discriminability in the next
session.

2.3 Methods

2.3.1 Participants

A total of 12 healthy volunteers, include six females, ranging in age from 23 to 33
years, with mean age of 28.1 years, participated in this experiment. The participants
reported normal or corrected-to-normal touch. All participants provided written
informed consent, and the study procedures were approved in advance by the ethics
committee of Okayama University.

2.3.2 Stimuli

We used nine raised-line angles, consisting of a reference angle (26°) and eightcomparison angles (18°, 20°, 22°, 24°, 28°, 30°, 32°, 34°). The angle stimulus changes
in two directions, both of which are formed by two raised-line (angle arms) with a longarm length of 8.0 mm and a width of 1.5 mm. They are located in the centre of a 38.0
mm square base, and the accuracy of the angle is 0.1°, as show in figure 2.4. Because
the length and width of the angle arm are the same, the changing components are theendpoint distance of the arms and vertex angle. There are two important factors in theexistence of all angle stimuli - the first is the vertex angle between the two arms (alpha);
The second is the distance between the two ends - respectively (2 × 8 × sin α/ 2) mm,
where α = 18°, 20°, 22°, 24°, 26°, 28°, 30°, 32°, 34°.
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Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.4 The angle stimulus of the plastic material used in the experiment. (a)Three-dimensional view of an example of raised angle. (b) An example of a raisedangle (𝛼) used in 2afc experiment.

In the experiment, all angles were fixed, and their vertices point to the right, sothat the two arms of the angle symmetrically surround the imaginary bisector. The sizeof the reference angle is 26°; There are 8 Comparison angles with a difference of 2°, 4°,6° and 8° respectively from the reference angle.

2.3.3 Experimental (Exp.1) procedure

In this study, we used active tactile methods to distinguish the angle. All angle
stimuli are fixed on the sliding plate, except that the reference angle is fixed in the
middle, and the other angles are respectively guaranteed to have 4 angles on the left
and right sides of the reference angle. The ordering arrangement of the comparison
angle stimulus ensures that the number of angles on both sides of the reference angle isequal and not arranged in an asymmetrical size. According to the experimental task, we
made a simple manual stimulus presentation device, as shown in Figure 2.5(a). The
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Chapter 2 Haptic Angle Discrimination Evaluation
whole experiment requires the experimenter to manually operate and record theexperimental data. This device was placed horizontally on the table directly in front of
the subject. We asked the subjects to place their arm on the device platform and ensurethat their index finger is positioned to touch the angular stimulus when moving fromside to side. They were also asked to raise their right index finger vertically, keep it
perpendicular to their arm, attach their right hand to a flat plate, and attach their forearm
to a movable device parallel to the bracket. The subjects wore blindfolds during the task
to prevent them from receiving visual feedback. Since all the angle stimuli are fixed tothe movable skateboard, each slide of a specific position can present the angle stimuli
to the subject to touch.
During the experiment, to move the skateboard to place the first angle directly
under the index finger of the subject’s right hand, and then give the participant a touch
signal. The subject puts down the index finger and touches the angle to stimulate it
twice, then lifts the index finger and moves again the skateboard to present a second
angle stimulus, which also gives the subject a touchable signal. The subject puts down
the index finger, and touches the angle stimulus back and forth twice, and then verbally
responds to the larger angle stimulus in each pair (2AFC— —Two-alternative forcedchoice), as show in figure 2.5(b).
Before each set of trials, the subjects practiced more than 10 trials on the standard
angle. During the experiment, one reference angle and eight comparison angles were
presented 40 times in pseudo-random order. The experiment consists of 320 trials, andeach participant rests for 5 minutes after 40 trials. Trial duration, including the time tochange the angle and the subject's response time, varied from 20.0 to 30.0 s. Eachsession lasted a total of 2.5 to 3.5 h.

19

Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.5 The apparatus used in 2AFC experiment and the time chart duringexperiment. (a) stimulus angle presentation apparatus. (b) Time chart of haptic
angle discrimination trial.

2.4 Data Analysis

The Two-Alternative Forced Choice (2AFC) responses collected were converted
into scores for the number of times the test angle was judged to be greater than thereference angle.

20

Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.6 The Gaussian cumulative function fitting diagram of all subjects’ angle
comparison data.

In the Gaussian cumulative model, the rate, 𝑦 , is the proportion which wasselected the response of answering ‘larger’ from each comparison angle and reference
angle calculated for each subject. It is used to fit this function (2.2) [10], as show in
Figure 2.6,1𝛼𝑓(𝛼, 𝜎, 𝜇) = 𝜎 2𝜋 ∫−∝ exp [−√(𝛼 ′ −𝜇)22𝜎2] 𝑑𝛼 ′(2.2)

In this equation, 𝛼 mean the angle stimulus, and 𝜇 mean the point of subjective
equality (PSE). Since all the angular stimuli are asymmetric and perfectly balanced with
the number of differences between the reference angles, we fit the variance 𝜎 of thefunction to assess individual’s angle discriminability, not the mean 𝜇. All subject data
were used in this model to calculate the angle Discrimination Index (𝐷𝐼 = 𝜎) for eachsubject.

21

Chapter 2 Haptic Angle Discrimination Evaluation
2.5 Results and Discussion

2.5.1 Characteristics of the haptic angle stimulus distinctive feature byexperiment data

To verify whether the theoretical in the previous session applies to the propertiesof actual haptic sensation. Among the stimulation angles in the 2AFC experiment, 26°
degrees is the reference angle, and 18°, 20°, 22°, 24°, 28°, 30°, 32°, and 34° arecomparative angles, so its Gaussian function and Gaussian cumulative distributionfunction (for example, 𝜎 = 3) are shown in Figure 2.7.

Figure 2.7 The Gaussian distribution. 26° is the reference stimulus angle.

We fitted the Gaussian cumulative distribution function with the same data results
and could get the standard deviation (𝜎) of the fitted curve, as shown in Figure 2.7. We
called the 𝜎 as the Discrimination Index, which is used as an index parameter toevaluate the angle discrimination performance for subjects-when the value is larger, the22Chapter 2 Haptic Angle Discrimination Evaluation
angle discrimination performance is poor; when the value is small, the discrimination
performance is better. The result data fitted by all subjects are shown in Figure 2.8.
Therefore, according to the fitting curve of each subject, we could get the standard
deviation (𝜎) and mean (𝜇). According to the equation 2.2, we can calculate the angle
discrimination Index of each subject, as show in Table 2.1. At the same time, the fitting
goodness of data on all subjects in the curve fitting quality evaluation is high,
SSE<0.026, R-square>0.975, as shown in Table 2.1.

Table 2.1 The result of Gaussian cumulative distribution function fitting calculation
Fitting Goodness
Subject No.

Discrimination Index (𝝈)SSER-square

1

3.439

0.008

0.994

2

2.631

0.025

0.981

3

4.080

0.023

0.980

4

3.731

0.006

0.995

5

2.936

0.032

0.976

6

2.782

0.007

0.995

7

3.872

0.021

0.982

8

3.976

0.004

0.997

9

3.344

0.010

0.992

10

3.757

0.011

0.991

11

3.783

0.017

0.986

12

3.754

0.023

0.98
23

Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.8 The Gaussian cumulative distribution function fitting diagram of all
subjects’ angle comparison data.

Through theoretical application of the mathematical model of Gaussian function
and Gaussian cumulative distribution function, as well as verification in 2AFC
experimental data, we have well proved that the standard deviation (discriminationindex - 𝜎 ) of the function is an important indicator value for evaluating angle
discriminability. For instance, when two subjects with different discrimination
24

Chapter 2 Haptic Angle Discrimination Evaluation
performance perform data fitting, as shown in Figure 2.9, they will eventually get
different discrimination indices (𝜎). Here, the discrimination performance of a subject
with 𝜎 = 2.63 was better than that of a subject with 𝜎 = 4.08.

Figure 2.9 The Gaussian function and Gaussian cumulative distribution function
fitting diagram of two subjects’ angle comparison data in Experiment 1.

2.5.2 The evaluation performance values of the Discrimination Index

In the evaluation of the results of 2AFC experiment, the correct accuracy rate ofeach pair of stimulus results is 50%, and the maximum is 100%. As the angle differenceis smaller, the accuracy rate gradually decreases; as the angle difference increases, the25Chapter 2 Haptic Angle Discrimination Evaluation
accuracy rate also increases. Such a distribution is called the sigmoid psychometricfunction in psychological measurement which is often fitted with Logistic function orGaussian cumulative distribution function to measure the threshold [55–57,64,69–72].
Therefore, according to those calculation, discrimination indices of all subjects wereobtained.
In comparison with the previous angle threshold, we found that the evaluation of
two angle discrimination is equivalent, because the estimation method of discriminationindex and discrimination threshold could be calculated by mathematical derivation torealize the conversion between the two parameters. This equivalence is not onlyreflected in the consistency of data fitting (Table 2.1), but also in the logistic function
1( 𝑔(𝑥) = 1+𝑒 −1.7𝑥 ) when 𝑑 = 1.7 [73,74] and Gaussian cumulative distributionfunction (𝜓(𝑥) =

1

𝑥

∫ 𝑒
√2𝜋 −∞

𝑡2−2𝑑𝑡 ), 𝜇 = 0 , 𝜎 = 1, the curves are also very similar.

Meanwhile, we made use of the similarity of Euclidian distance evaluation between thetwo functions in the y-axis direction, as shown in Figure 2.10 (b). Even the twofunctions have very small relative changes in the interval [-5, 5], and the maximum
difference is less than 0.01, 𝑑 = |𝑔(𝑥) − 𝜓(𝑥)| < 0.01. In addition, in the normal
cumulative function, through the properties of this function, it can be found that thestandard variance (𝜎) of the change and its cumulative distribution function is a certain
relationship, namely 𝜓(0.675) = 0.7498. In this way, the conversion factor between
the discrimination threshold and discrimination index of each subject is 0.675, then therelation can be obtained:
𝑫𝑻 = 0.675 ∙ 𝑫𝑰

(2.3)

26

Chapter 2 Haptic Angle Discrimination Evaluation

Figure 2.10 The logistic function fitting diagram of all subjects’ angle comparison
data.
Through the above comparison, it can be found that the two evaluation parameters
used to evaluate the individual’s angle discrimination performance are completely
equivalent. The smaller the discrimination index is, the better the discrimination
performance; and vice versa.

2.6 Conclusions

In this research, we used two different evaluation models, logistic function andGaussian cumulative distribution function, and use the calculated discriminationthreshold and discrimination index to evaluate the angle discrimination ability. At thesame time, it also proved that there is an actual linear relationship between the two
evaluation indexes, that is, the two parameters are equivalent to the evaluation. The
next chapter would further improve the improvement and calculation of the evaluation
method of the discrimination index (𝜎 ), so that the test of personal discrimination
27

Chapter 2 Haptic Angle Discrimination Evaluation
performance would be efficient and saved time. In the future, we will further verify themethod's discussion and Research on psychophysical diversified stimuli and different
perceptions through other perception evaluation tests.

28

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Chapter 3 The Sorting Evaluation Method of Haptic Angle
Discrimination

Summary
We proposed an angle sorting method that could be also used to estimate thediscrimination index. Although the 2AFC experiment can be used to test thediscrimination performance, it takes a long time to compare multiple times. The lower
test efficiency is not easy to apply to a wide range of tests and data collection of a large
number of people, especially, who it is difficult to take the test for a long time forpatients with some diseases. In this chapter, our goal is to propose an improved methodthat can also be used to evaluate the angle sorting method of discrimination
performance and has higher test efficiency. Here, the tester only needs to complete one
sorting experiment to get the result. This method also used to measure thediscrimination index, which the previous chapter has verified the equivalence of thediscrimination index and discrimination threshold. The experiment task process of thismethod and the mathematical evaluation model of the result analysis were described indetail. The high correlation of the experimental results also shows very well that thetwo different evaluation methods can have evaluation angle discrimination performance.
We look forward to the effective improvement methods that is able to be well appliedin practice.
.

29

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
3.1 BackgroundThe changes in human perception are affected by many factors, not only aging but
other neurological and brain diseases will also lead to the significant decline of humanperception, such as Parkinson’s disease, Alzheimer’s disease, and other neurologicaldegenerative disease[75–78] . It has been generally confirmed in previous research thatchanges in perception caused by diseases can be quantitatively evaluated and reliable
methods can be further studied for early screening of these diseases by studying theevaluation methods of perception discrimination. Moreover, previous studies havefound that using a single skin feedback can not only further investigate the brain
advanced cognitive processing mechanism of tactile information.
In previous studies, different tactile stimuli have been used to assess the effects ofsome human diseases on tactile discrimination. A grating of alternating ridges andgrooves was used in a quantitative psychophysical survey of tactile perception in
Parkinson's disease (PD) patients and age-matched normal controls. Studies have foundthat among healthy adults, as they age, the tactile spatial acuity decreases slightly but
significantly. In the comparison between healthy and Parkinson's disease, it was foundthat the tactile spatial threshold of PD patients increased twice. This also suggests that
PD disorders can significantly affect the performance of tactile tasks [13,18,79–82].
The sense of touch not only requires tactile perception in distinguishing different
stimuli, but also requires advanced cognitive functions, such as working memory, inangle comparison. In this way, when working memory is damaged, it will significantly
reduce the ability to distinguish the stimulus. Previous related studies used this ability
to distinguish angles to test different groups of people, including normal and cognitively
impaired patients. This assessment method has potential applications in the screening
30

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationof early clinical conditions, such as mild cognitive impairment (MCI) and Alzheimer's(AD) [12,83].
In contrast, the 2AFC angle discrimination evaluation method was usually used in
the past, by presenting two angle stimuli to the subject's right index finger one by one,
asking him/her to discriminate the larger of the pair, and recording the correctness ofeach pair of comparison results. A logical growth curve was then fitted by the correct
rate of each pair of differential angle pairs, and the angle difference corresponding to
the 75% position of the logical curve was then selected as the participant’s final angle
discrimination threshold [11].. Although the result of the assessment is the angle
discrimination threshold obtained by multiple comparisons, the subject needs to store
the spatial information of the first angle stimulus in working memory during eachcomparison of multiple pairs of angle stimuli by haptics, and then compare the spatialconstruction of the first angle stimulus with the second one. During the comparison ofeach pair of angle stimuli, a widely distributed neural network is activated, consisting
mainly of peripheral perceptual nerves (cutaneous mechanosensory neurons) generated
by skin indentation, initial processing areas for tactile perception (primary andsecondary somatosensory cortex of the brain) [84,85], and higher areas for computationand fine reconstruction of higher regions (parietal sulcus) responsible for thecomputation and fine reconstruction of shape [85], and higher regions (parietal sulcus)
responsible for the computation and fine reconstruction of shap), and prefrontal cortex
responsible for tactile working memory [85,86]. Thus, human differences,abnormalities or even impairments at any point in between will respond through theresult of the angle discrimination threshold. When assessed by the 2AFC method inparticipants of the same age group with normal nerves for the same tactile peripheral
perception, it is more the differences in brain cognitive that lead to significant individual
31

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationdifferences in the ability to discriminate tactile angles. The angle discriminability iscommonly used clinically to assess tactile perception and even to estimate higher-level
functions such as working memory[15–17]. In our previous studies, tactile angle
discrimination was found to be related to higher cognitive functions, where theimpairment of working memory significantly reduced tactile angle discriminability[12,13]. Therefore, we developed an angle stimuli presentation device [87] for theevaluation of cognitive impairment by testing tactile angle discriminability. In thatexperiment, the two-alternative forced-choice (2AFC) method was used. We presented
20 pairs of angle stimuli in pseudorandom order and calculated the angle discriminationthreshold [11,12]. In subsequent studies, the highly centralized evaluation automatic
device was developed to further improve the application in practical testing, which
consisted of separate systems that stimulated automatic presentation, automatic
calculation of test results, and display, storage, and export of test results [88]. Despite
the expectation of further improvement in practical applications by improving thetesting equipment, the efficiency of testing in practical applications is still not as good
as expected.
However, there are still two problems in our previous research on angle thresholddiscrimination. (1) The 2AFC paradigm needs many pairwise comparisons, which arenecessary for an accurate discrimination threshold, yet it takes approximately 2.5 hours
for each participant to complete the task. In particular, it is difficult for particular groups
to concentrate on long-term tests. (2) The device was controlled by using an extra
computer to code and required a technician to run the control program, which makesthese complex operations difficult for the device to be used clinically, especially by
nonprofessionals. To solve these two problems, we proposed a new method in which
participants are asked to sort a series of five angle stimuli. To solve these two problems,
32Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
we proposed a new method in which participants are asked to sort a series of five angle
stimuli. By using the obtained angle sorting data, we derived the discrimination indexes(DIs), enabling us to evaluate angle discriminability detection efficiently for subjects.
We explained in detail the paradigm process of angle sorting and the evaluation
calculation method in this paradigm.

3.2 Angle Sorting

3.2.1 Procedure of Haptic Angle Sorting

Sorting is an efficient method that can be used for psychophysical measurements[20], such as the 100-hue test for measuring hue discrimination. Referring to this visual
test paradigm, we propose a new method of angle sorting for haptic shapediscrimination. In the angle sorting paradigm, there are a series of 7 angle stimuli, forinstance, with an angle difference of 2° in the present study, including the smallest andthe largest reference angles, and 5 angles between these two reference angles.
The participants included one of the authors and five healthy students (three males,27.7±3.8 years old). All participants had normal vision or corrected-to-normal visionand provided written informed consent for the procedure, which was previously
approved by the ethics committee of Okayama University and was organized to ensure
conformity to the Declaration of Helsinki.
During the experiment, the participant was wearing an eye mask, and the heightsof the chair and table were adjusted to ensure that the participant's arms were33

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
comfortable. The experimenter placed the angle stimulus at a minimum angle in the 1st

Figure 3.1. The procedure of a haptic angle sorting paradigm. Each target is
randomly selected and submitted to the participant for comparison. After touching
the first target, the participant compared it with the reference angle and placed it ina suitable sorting position according to the angle difference. Then, all angles thatwere placed on the device were used as references to determine the position of the
new target. When all 5 angle stimuli were placed, the participant was required totouch the angle stimuli again from small to large to confirm whether the order wascorrect. When the participant thought that it was incorrect, he could adjust the sortingas many times as desired. When the participant thought that it was correct, he/she
submitted the final result to end the test.

34

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
position of the device and a maximum angle in the 7th position, as shown in Figure 3.1.
Then, the remaining 5 angle stimuli to be sorted were randomly presented to theparticipant one by one. The participant was asked to discriminate and compare eachangle stimulus with the index finger of their right hand and sort it with his/her left hand.
The participant placed the angle stimulus in one of the positions from the 2nd to the 6th
position and ensured that the angle stimulus is placed from the 1st to the 7th position insequence from small to large. All angle stimuli are horizontally placed with the vertex
to the right and two rays to the left. Fixing the minimum and maximum angle stimuli
at the 1st and 7th positions provides a very clear reference for the participant andreduces the difficulty of the angle sorting experiment. In addition, the angle stimuli
placed by the participant in the 2nd to 6th positions can be adjusted an unlimited numberof times, although the direction of the angle stimulus remains the same.
The participant was allowed to touch the angle stimuli of the 1st position and 7th
position in the experiment but could not move their positions. After each adjustment of
the stimulus, the participant was asked to confirm the sort of the haptic angles from left
to right. From the evaluation experiment, it was found that all the participants submitted
results after approximately 3 to 5 sorting confirmations. After angle sorting was
confirmed and sub-mitted, 1 trial was performed. A trial of the angle sorting paradigm
is shown in Figure 3.1. With this paradigm, the participant needs only 1 trial to obtain
the result of an assessment. The angle sort of 1 trial only takes only 3 to 5 minutes.

3.2.2 Data Processing and Analysis

The maximum likelihood probability of each sorting result was statisticallyanalyzed. Here， Channel X is defined as a neural mechanism that responds specificallyto a range of acute angled devices. The angular characteristics of the response can be
35

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
expressed by the probability density function and are maximized with respect to x. The
response intensity for the angle Y is expressed by channel x(y), and this probability
density is consistent with a Gaussian normal distribution. For instance, thecorresponding distribution of the different 𝜎 in each channel CH is shown in Figure
3.2.

Figure 3.2. The relative response intensity relationship of between stimulus angle
and discrimination index (𝜎 ). (a) when 𝜎 is 1, the relative response intensity ofdifferent stimulus angles in each channel. (b) when 𝜎 is 2, the relative response
intensity of different stimulus angles in each channel. (c) when 𝜎 is 3, the relative
response intensity of different stimulus angles in each channel. (d) When 𝜎 isdifferent and the reference angle is 26 deg, the probabilities of larger angle are
selected for each stimulus angle. (e) when 𝜎 was difference, the relative response
intensity of different stimulus angles on channel CH26.
36

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
In the data analysis, we hypothesized that the participant always chooses thesmallest from the unplaced angle every time starting from the 2nd position when sorting,until the last one is placed in the 6th position, and that once each stimulus was selected,
they could not be selected again. The participant’s angle discrimination ability wasconstant, and we supposed that the probability of selecting each stimulus angle at the
2nd position was 𝑃(2,𝑛). Assuming that this probability obeys the normal distribution
𝑃(2,𝑛) ~𝑁(𝜇, 𝜎 2 ), according to the central limit theorem of statistics, the probability ofchoosing the smallest angle at the 2nd position is the largest, that is, the peak value ofthe normal distribution probability curve; the selection probability of adjacent andspaced angles obeys the normal distribution probability density and decreases withincreasing distance. Similarly, at the 3rd, 4th, 5th, and 6th positions, the probability thatthe participant will choose the smallest angle from the rest is still the highest, and theprobability is also the peak of the same normal distribution probability curve. The
selection probability of the adjacent angle and the interval angle obeys the normal
distribution probability density and decreases with increasing distance between themand the minimum angle. It should be noted that this probability is zero if the adjacentangle has been placed before, and the next angle category due to the large difference
between it and the smallest angle will still reduce the probability of being selected.
More importantly, it is appropriate to apply the normal distribution to thepsychophysical calculations of behavior [89–91]. When a normal distribution is used,
the haptic angle sorting discriminability between each participant can be assessed by 𝜎in the normal distribution. If 𝜇 = 𝑎 and 𝑥 = 𝑏 are determined in the normal
distribution; When 𝜎 is smaller, the probability density value, 𝑓(𝑥 = 𝑏; 𝜇 = 𝑎; 𝜎), of
the normal distribution at 𝑥 = 𝑏 is larger, which reflects that participants are more
likely to discriminate the smallest angle, that is, the participant has better discrimination
37

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationof the angle; the larger 𝜎 , the smaller the probability density value, the lower the
probability of choosing the smallest angle, and the worse the participant's haptic angle
discriminability, as shown in Figure 3.3. For instance, the probability of response toeach angle stimulus when a subject is on the channel CH𝛼1 is obeyed with different
probabilities 𝑃1 , 𝑃2 , 𝑃3 , 𝑃4 , 𝑃5 as shown in Figure 3.3(a); while the probability of
response to the same angle (𝛼) stimulus for different subjects on the same channel is
𝑃𝐴 , 𝑃𝐵 , 𝑃𝐶 , as shown in figure 3.3(b). Therefore, according to this meaning of thestandard deviation of the normal distribution 𝜎 in the psychophysical quantity, 𝜎 isthe unique standard deviation of the normal distribution curve, of which themathematical model can be established as follows.

Figure 3.3 The relative response intensity relationship between discriminationindex (𝜎 )and stimulus angle for individual and interindividual. (a) the relative
response intensity of a participant at different stimulus angle on channel CH𝛼1. (b)the relative response intensity of difference participants at stimulus angle (𝛼) on thesame channel.
Since the smallest angle stimulus is always selected at each position during sorting,the normal distribution determines that the probability is related to the smallest angle
38

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
among the remaining angles, the probability is as shown in Figure 3.3(a). For example,
a trial of angle sorting (𝐴𝑆1 ) is 26°, 22°, 24°, 28°, and 30°. Here, we set up 𝜇 =min(𝐴𝑆); if 𝜎 = 3, and min(𝐴𝑆) as the smallest angle value among the remaining
angle categories, then1

𝑃2,𝑛 = 𝑓(𝑥; 𝑢; 𝜎 = 3) = 3√2𝜋 𝑒

1 𝑥−𝜇 2
)
2 3

− (

(3.1)

In equation (3.1), 𝑃2,𝑛 is the probability that the remaining angle category stimulus isselected at the channel CH22, 𝑛 = (22, 24, 26, 28, 30). The smallest angle among theremaining angle categories in the channel CH22 is 22°, 𝜇 = 22, and as the peak valueof the normal distribution is 𝑃2,22 = 𝑓(𝑥 = 22; 𝜇 = 22; 𝜎) = 𝑃1 , the adjacent andother angle probabilities are 𝑃2,24 = 𝑓(𝑥 = 24; 𝜇 = 22; 𝜎) = 𝑃2 , 𝑃2,26 = 𝑓(𝑥 =26; 𝜇 = 22; 𝜎) = 𝑃3 ,𝑃2,28 = 𝑓(𝑥 = 28; 𝜇 = 22; 𝜎) = 𝑃4 , and𝑃2,30 = 𝑓(𝑥 =30; 𝜇 = 22; 𝜎) = 𝑃5 , as shown in Figure3.4(a). So, in the channel 22, all angle stimuli
are the probability as shown in Figure 3.4(b), if the 𝜎 = 3. In the calculated result, thestimulus angle of 26° was placed on channel 22, when 𝜎 = 3, so the final probabilityof CH22 is 0.17.

39Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Figure 3.4. The relative response intensity of difference stimulus angle in second
position. (a) when the channel is CH22, the relative response intensity of 5 stimulus
angles were 𝑃1 , 𝑃2 , 𝑃3 , 𝑃4 , 𝑃5 . (b) when 𝜎 = 3, the probability of CH22 for eachstimulus angle.
In the 3rd position, the probability, 𝑃3,𝑛 , is also the probability of the remaining
angle category stimulus selected at the channel 22, 𝑛 ∈ (22, 24, 28, 30) . The
smallest angle among the remaining angle categories in the 3rd position is still 22°,
𝜇 = 22, and as the peak value of the normal distribution is 𝑃3,22 = 𝑓(𝑥 = 22; 𝑢 =22; 𝜎) = 𝑃1 , the adjacent and other angle probabilities are 𝑃3,24 = 𝑓(𝑥 = 24; 𝑢 =22; 𝜎) = 𝑃2, 𝑃3,26 = 𝑓(𝑥 = 26; 𝑢 = 22; 𝜎) = 𝑃3, since the stimulus angle of 26° has
been placed in the 2nd position and the probability of 𝑃3 is 0; 𝑃3,28 = 𝑓 (𝑥 = 28; 𝑢 =22; 𝜎) = 𝑃4 and 𝑃3,30 = 𝑓(𝑥 = 30; 𝑢 = 22; 𝜎) = 𝑃5 , as shown in Figure 3.5(a). At
the same method, in the channel 22, but all angle stimuli are the probability as shownin Figure 3.5(b), if the 𝜎 = 3. In the calculated result, the stimulus angle of 22° wasplaced on channel 22, when 𝜎 = 3, so the final probability of CH22 is 0.51.

40Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Figure 3.5. The relative response intensity of difference stimulus angle in third
position. (a) when the channel is CH22, the relative response intensity of 4 stimulus
angles were 𝑃1 , 𝑃2 , 𝑃4 , 𝑃5 , since stimulus angle 26° was placed in second
position, 𝑃3 = 0. (b) when 𝜎 = 3, the probability of CH22 for each stimulus angle
in remaining stimulus angles.

In the subsequent position, 4th, 5th, and 6th position, since each stimulus cannot
be selected again once it has been selected, the probability of the angle stimulus selected
before is also 0. In addition, the probability of choosing the smallest angle at eachposition is also always the greatest; that is, the probability of the angle being selected
is the peak in its probability distribution, 𝑓(𝑥 = 𝜇; 𝜇; 𝜎) = 𝑃. According to the same
principle, we can calculate the probability of the remaining stimulus angles in eachposition, as shown in Figure 3.6. The probability density of the remaining angle selected
decreases with increasing distance and obeys the normal distribution. Therefore, we canobtain the probability at the 4th, 5th and 6th positions , respectively, as shown in
Table 3.1.

41

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Figure 3.6. The relative response intensity of difference stimulus angle in fourth,fifth and sixth position. (a) when the channel is CH24, the relative response
intensity of 3 stimulus angles were 𝑃2 , 𝑃4 , 𝑃5 , since stimulus angles 22° and 26°
were placed in second and third position , 𝑃1 = 𝑃3 = 0 . (b) when 𝜎 = 3 , theprobability of CH24 for each stimulus angle in remaining stimulus angles. (c) when
the channel is CH28, the relative response intensity of 3 stimulus angles were
𝑃4 , 𝑃5, since stimulus angles 22°, 24° and 26° were placed in second, third andfourth position, 𝑃1 = 𝑃2 = 𝑃3 = 0. (d) when 𝜎 = 3, the probability of CH28 foreach stimulus angle in remaining stimulus angles. (e) when the channel is CH30,
the relative response intensity of 3 stimulus angles were 𝑃5, since stimulus angles
22°, 24°, 26 and 28° were placed in front of position, 𝑃1 = 𝑃2 = 𝑃3 = 𝑃4 = 0.
(f) when 𝜎 = 3, the probability of CH30 for each stimulus angle in remaining
stimulus angles.
42

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Table 3.1. An example of the method to calculate angle sorting when 𝜎 is 3.
2nd

Angle
Categories

𝑷𝟐,𝒏𝑷𝐋𝟐 (𝟐𝟔°)22°0.133024°

0.106526°

0.054728°

0.0180

30°

3rd
𝑷𝟑,𝒏
0.13300.17

4th

𝑷𝐋𝟑 (𝟐𝟐°)

𝑷𝟒,𝒏

0.51

0

𝑷𝐋𝟒 (𝟐𝟒°)
0.65

5th

𝑷𝟓,𝒏

6th

𝑷𝐋𝟒 (𝟐𝟖°) 𝑷𝟔,𝒏

𝑷𝐋𝟔 (𝟑𝟎°)000.10650.1330

0

0

0

0

0

0

0.01800.05470.13300.00380.00380.01800.10650.316

0.26130.20570.2395

0.56

0
0.
1330

1.00

0.
1330

𝑃(𝜎, 𝐴𝑆1 ) = 𝑃𝐿2 𝑃𝐿3 𝑃𝐿4 𝑃𝐿5 𝑃𝐿6 = 0.0316

In the table, Angle Categories is the angle category sorted by the participant;𝑃2,𝑛 is the probability distributions from all angle categories in the 2nd position;
𝑃3,𝑛 , 𝑃4,𝑛 , 𝑃5,𝑛 and 𝑃6𝑛 are the same as before; 𝑃𝐿2 is the probability ofchoosing the angle (26°) when the probability distribution is 𝑃2,𝑛 ; and 𝑃𝐿3, 𝑃𝐿4,
𝑃𝐿5 and 𝑃𝐿6 are the same.

In Table 3.1, the trial angle sort is 26°, 22°, 24°, 28°, and 30°. When weevaluate the probability of being selected at the second position, the probability of eachangle is different. And our assumption is that participants are always asked to choose
the smallest angle, and the probability of choosing different angles obeys a normal
distribution, so 𝜇 = min(22, 24, 26, 28, 30) = 22 . And the probability of eachcategory of angle being selected is 𝑃2,𝑛 (𝑛 = 22,24,26,28,30), as show in Table 3.1.
The angle of the 2nd position is 26°, and the probability of its occurrence is𝑃𝐿2 =𝑓(𝑥=26;𝜇=22;𝜎=3)0.0547== 0.17.
30∑𝑛=22 𝑃2,𝑛0.133+0.1065+0.0547+0.180+0.0038(3.2)

In equation (3.2), 𝑃𝐿2 is the probability of choosing this angle (26°) among theremaining angle stimuli (26°, 22°, 24°, 28°, 30°) at the 2nd position. At the 3rd position,
the rest angles are 22°, 24°, 28°, and 30°, so 𝜇 = min(22, 24, 28, 30) = 22. The angle
stimulus of 26° has been placed in the 2nd position, and according to the assumptionthat once each stimulus was selected, they could not be selected again, so its probability
43

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationof being selected is 0. Since the rest of angles still obeys the normal distribution, theprobability of each category of angle being selected is also 𝑃3,𝑛 (𝑛 = 22,24,26,28,30),
as show in Table 3.1. the angle of the 3rd position is 22°, and the probability of its
occurrence is𝑃𝐿3 =𝑓(𝑥=22;𝜇=22;𝜎=3)∑30
𝑛=22 𝑃2,𝑛0.133= 0.133+0.1065+0+0.180+0.0038 = 0.51.

(3.3)

In equation (3), 𝑃𝐿3 is the probability of choosing this angle (22°) among theremaining angle stimuli (22°, 24°, 28°, 30°). Similarly, we have 𝑃𝐿4 = 0.65, 𝑃𝐿5 =0.56 , 𝑃𝐿6 = 1 . Therefore, when 𝜎 = 3 and 𝐴𝑆1 = (26°, 22°, 24°, 28°, 30°) , theprobability is 𝑃(𝜎, 𝐴𝑆1 ) = 𝑃𝐿2 𝑃𝐿3 𝑃𝐿4 𝑃𝐿5 𝑃𝐿6 = 0.0316, as shown in Table 3.1.
Here, we know that this result has nothing to do with the mean 𝜇 and 𝑥 range ofthenormaldistribution

and

is

based

on

the

angle

sorting

𝐴𝑆1 =(26°, 22°, 24°, 28°, 30°) and the assumption of 𝜎 = 3 . The result, 𝑃(𝜎, 𝐴𝑆1 ) ,changes with each different value chosen for 𝜎. According to the above data analysis
model, when 𝐴𝑆1 was determined, we can construct the relationship function of𝑃(𝜎, 𝐴𝑆1 ) = 𝑓(𝜎) with 𝜎 as the independent variable. For example, when 𝐴𝑆1 =(26°, 22°, 24°, 28°, 30°), we can obtain the relationship between 𝜎 and 𝑃(𝜎, 𝐴𝑆1 ), as
shown in Figure 3.7(a).
Second, if the angle sorting is 𝐴𝑆3 = (28°, 30°, 26°, 24°, 22°), that is, when theparticipant made a big mistake the larger angle as the smallest angle during sorting, therelationship between 𝑃(𝜎, 𝐴𝑆3 ) and 𝜎 is shown in Figure 3.7(c). As shown in Figure
3.7(c), 𝑃(𝜎, 𝐴𝑆3 ) increases with increasing 𝜎, and the result of 𝜎 is the upper boundthat we set. At this point, we considered that the 𝐴𝑆3 could not be used to evaluate theparticipant's 𝜎. If this happens, the result is invalid. This is because the participant was
unable to identify the angles of this series, even when the difference angle is between
the maximum and minimum angles. If you want to further measure the participant’s
44Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
discrimination index, this series of angle stimuli for the sorting should be replaced bya larger angle difference, larger than 2°; if it still cannot be obtained, 𝜎, which is not
the upper bound value, continues to replace the larger angle difference. Through above
the analysis and calculation method of the sorting results, a discrimination index (𝜎)can be calculated after the participants complete the sorting every time.

Figure 3.7 The relationship between 𝜎 and the probability of the angle sorting
result 𝑃(𝜎, 𝐴𝑆𝑛 ) . (a) When the angle sorting 𝐴𝑆1 is wrong, the relationshipbetween the 𝜎 and the probability of the angle sort result 𝑃(𝜎, 𝐴𝑆1 ) is 𝐴𝑆1 =(26°, 22°, 24°, 28°, 30°); (b) When the angle sort 𝐴𝑆2 is completely correct, therelationship between the 𝜎 and the probability of the angle sort result 𝑃(𝜎, 𝐴𝑆2 )is, 𝐴𝑆2 = (22°, 24°, 26°, 28°, 30°). (c) When the angle sort 𝐴𝑆3 is wrong, treating
the larger angle as the smaller angle, the relationship between 𝜎 and the probabilityof the angle sorting result 𝑃(𝜎, 𝐴𝑆3 ) . The relationship between 𝜎 and theprobability

of

the

angle

sorting

result𝑃(𝜎, 𝐴𝑆3 )

is

𝐴𝑆3 =

(28°, 30°, 26°, 24°, 22°).
3.3 The Evaluation Experiment (Exp.2) of Sorting Method

3.3.1 Participant

The same participants in 2AFC experiment were again recruited. A total of 12
45

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
healthy volunteers, include six females, ranging in age from 23 to 33 years, with mean
age of 28.1 years, participated in this experiment. The participants reported normal orcorrected-to-normal touch. All participants provided written informed consent, and thestudy procedures were approved in advance by the ethics committee of Okayama
University.

3.3.2 Stimuli

The sorting experiment used seven angle stimuli with a 2-degree angulardifference, and the angular stimuli were distributed as 20°, 22°, 24°, 26°, 28°, 30°, and
32. where the smallest angle of 20 degrees and the largest angle of 32 degrees wereused as the reference angles.

3.3.3 Procedure

Before the sorting, the experimenter placed the stimulus angle at the minimum
angle in the 1st position of the device and the maximum angle in the 7th position.
During the sorting experiment, the participant with an eye mask, and the participant's
arms were comfortably placed on the table. Then, the remaining 5 angle stimuli to besorted were randomly presented to the participant one by one. The participant was asked
to discriminate and compare each angle stimulus with the index finger of their righthand and sort it with his/her left hand. The participant placed the stimulus angle in oneof the positions from the 2nd to the 6th position and ensured that the angle stimulus isplaced from the 1st to the 7th position in sequence from small to large. All angle stimuli
are horizontally placed with the vertex to the right and two rays to the left. Fixing theminimum and maximum angle stimuli at the 1st and 7th positions provides a very clear
46

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationreference for the participant and reduces the difficulty of the angle sorting experiment.
In addition, the angle stimuli placed by the participant in the 2nd to 6th positions canbe adjusted an unlimited number of times, although the direction. All steps of theexperiment are described in Section 3.2.1, as shown in Figure 3.1.

3.3.4 Results and Discussion

Discrimination index
The angle discrimination performance of active finger movement was evaluatedin terms of the sorting of 5 equal difference angles (2°). According to the dataprocessing and analysis methods in Section 3.2.2, the discrimination index of eachparticipant was obtained by calculating the results of each sorting. And the mean
discrimination index was also calculated for each participant after completing ten angle
sorting trials. The average discrimination index for all subjects was 1.015, and the SEM
for all participants was 0.05. And all participants’ assessments are within the effective
test range. The results of twelve participants are shown in table 3.2.
Table 3.2 The discriminant index 𝜎 was assessed for each participant sort.
No.

The σ of sortingNo.

The σ of sorting

01

0.923

07

1.229

02

0.720

08

1.061

03

1.190

09

0.986

04

0.813

10

1.042

05

0.879

11

1.302

06

0.932

12

1.107

Mean σ 1.015
47

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination

Correlation with 2AFC
At the same time, to compare the equivalence of the 2AFC evaluation method forthe same participants in the sorting method, the Pearson correlation analysis was
performed between the results. According to Pearson's correlation analysis, thecorrelation coefficient is 𝑟 = 0.7750 (p value is 0.0031), which is a strong correlation.
The significant correlation indicates that the evaluation results obtained by sorting canbe used to evaluate the angle discrimination ability in terms of magnitude, instead of
directly using the angle value that is the discrimination angle threshold calculated by
2AFC evaluation method.

Figure 3.8 The Pearson correlation analysis of 𝜎 obtained between 2AFC andsorting.

48

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
3.5 General discussion

In the present study, we propose a new method to evaluate participants' angle
discrimination ability by sorting. In this method, we introduced the parameter of
discrimination index, which is used to measure the angle discrimination ability, andestablished an evaluation calculation model for this parameter. The discriminationindex is used to measure the haptic angle discrimination performance instead of theprevious discrimination threshold.
The sorting method greatly improve the testing efficiency through the experiments.
In previous threshold test usually used Two-alternative forced choice (2AFC).
Although this method has great range of applied to evaluate the effectiveness of thepsychophysics, this method on the universality of the test or do many people used less.
Because this test needs more number of paired comparison to get results and bring a lotof work, which usually just stay in the lab. Moreover, a large number of paircomparisons will greatly affect the accuracy of the results, that is to say, a stable result
may be obtained by repeated comparisons for many times. For example, in the previous
angle discrimination threshold measurement, Wu et al. 2010 the two experiments
repeated the same angle stimulus presented to each participant for 10 times, totaling
more than 280 times. Yang et al. 2010, presented the same angle stimulus to eachparticipant for 10 times, a total of 80 times; Zhang et al., 2019, presented a total of 30
times of angular stimulus to each participant. Wang et al., 2019. The same angle
stimulus presented to each subject was repeated 10 times, for a total of 100 times. In
the experiment of chapter 2, the same Angle stimulus presented by each participant in
the 2AFC experiment was repeated 40 times, and the same 8 pairs were presented 320
times in total. Although 2AFC method has achieved significant results in the assessment
49Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationof cognitive ability based on the angle discrimination threshold, it is still difficult to be
applied in practical early clinical tests due to the cost of long time for test. Especiallyfor some special populations, such as the elderly, people with mild cognitive
impairment and Alzheimer's disease, long-term testing is not easy. At present, thesorting method solved the problem of test efficiency. The sorting evaluation method
calculates the discrimination index through the analysis of only one sorting. Whensorting multiple times we will calculate the average discrimination index. In addition,in order to prevent the difficulty of determining the multiple angle stimuli and spend
time in the sorting experiment, we also provide the maximum and minimum reference
for the angle stimulus and decompose the experimental steps of each sorting into twoparts, sorting and adjustment, to avoid at this point. Finally, through the evaluation
experiment, it is found that it can effectively avoid the subjects' repeated hesitation,
spending 3 ~ 5 minutes in each sorting.
The proposed discrimination index is better than the discrimination threshold in
evaluation. In the angle discrimination threshold evaluation experiment, it is notdifficult to find that the threshold is not only affected by the number of repetitions, butalso by the change of reference angle. Wu et al. 2010 found that in the acute angle (𝛼 <90°) comparing, the discrimination threshold would increase with the gradual increaseof the reference angle. When the reference angle is obtuse (𝛼 > 90°), the discriminationthreshold no longer changes. This indicates that the 2AFC assessment discriminationthreshold is not a unique result for each participant and will be measured differently
depending on the reference angle you use. This feature also brings some complexity to
the expression of test results. However, the results, discrimination index, obtained bycurrent sorting evaluation methods are unique. Through the calculation of the sorting
results, we find that only the change of the discrimination index in the angle difference50Chapter 3 The Sorting Evaluation Method of Haptic Angle Discrimination
between the sorting series of angle stimuli will cause the change of this value. Moreover,in the first test, the angle stimulus would start with 2° of angle difference. Only when
the subjects could not get the optimal solution, discrimination index, by the evaluation
calculation, we would consider increasing the angle difference to conduct the sorting
test again. This sorting evaluation method is able to measure a unique discriminationindex, but also can expand the scope of the test population. This method is also moreconvenient when evaluating differences between groups and individual differences.
Compared with the 2AFC, the human brain neural network activation andparticipation area may be more extensive during the angle sorting task. The task processof 2AFC is firstly the perception of the angular spatial information by the tactile
peripheral nerves and the storage of the angular stimulus information presented by thebrain for the first time, and then the perception of the second angular spatial information
during the second stimulus perception, and at the same time make precise comparisonand calculation with the stored spatial information of the first angle. More specifically,
this part is more focused on investigating tactile perception and working memory inadvanced cognition. However, in addition to these two parts, the process of sorting tasks
may involve more advanced cognitive. In the current sorting task, it is divided into theorder placement of angle stimuli and the adjustment of its order. In the process ofstimulus prevention, every time an angle stimulus is presented to require the participant
to place, the more spatial information capacity required for the memory angle stimulus
will be. At the same time, the participant is also required to have corresponding
strategies for the comparison of stimuli at each angle. For example, when stimuli witha small difference and difficult to distinguish exist, whether he/she will consider using
a stimulus with a larger/smaller difference as a reference to determine its position. In
addition, in the process of adjusting the sorting, although we need to touch the angles
51

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationthat have been prevented in order from small to large, it is not necessarily required todetermine the smallest angle first. For example, when placing the angle stimulus, theminimum and maximum angles are incorrectly placed together, which is extremely easy
to identify. In such a sorting process, not only the primary tactile perception areas
related to the angular spatial information and the precise calculation and comparison
areas related to the spatial information need to be activated, but also the information
integration coding may be activated. The overall treatment of these areas will inevitably
differ among individuals, especially groups with cognitive decline or impairment.
Therefore, compared with the 2AFC task, the sorting task may also be a deeper
evaluation of the brain's advanced cognitive level.
According to the analysis of the current mathematical model and the test results ofthe participants, there are high expectations, especially for the comparison between
different groups. Of course, the new method of proposed will also have certain
limitations. It is not easy to obtain the optimal solution if the calculation is toocomplicated. And for its actual test, a lot of data verification is needed, especially for
individual cognitive differences, or the definition of the scope of group cognitive
impairment still needs more tests and verifications.

3.6 Conclusion

The angle sorting evaluation method and calculation model which we proposed
are used to efficiently evaluate the haptic angle discrimination ability. Since previous
studies have found that the ability of angle discrimination is related to the cognitive
ability of the human brain. And it can well improve the time-consuming andinconvenient application scenarios in the previous 2AFC method to calculate the angle
discrimination threshold. In the angle sorting, the same size of stimulus angles was used,52

Chapter 3 The Sorting Evaluation Method of Haptic Angle Discriminationand the same angle difference is sorted to evaluate the task. Moreover, thediscrimination index obtained from the analysis of the experimental task established inthis way can also be used to evaluate the participant's angle discrimination ability. Such
new methods provide new ideas for the same sorting of psychophysical testing inpractice.

53

Chapter 4 Development of Haptic Angle Sorting Evaluation System

Chapter 4 Development of Haptic Angle Sorting Evaluation
SystemSummary
We have developed a new system based on the sorting tasks in the previous chapter.
In this system, the hardware design standardizes the test process, and the software
simplifies the operation and calculation of the results. We respectively redesigned theangle stimulation and improved the material to avoid the loss of accuracy due to wear.
According to the experimental process, we also developed a recognition module forangular stimulation, a main control module for calculating results and supporting
operating functions. To further simplify the calculation and facilitate the operation in
the experiment, we designed and developed software to guide the completion of theexperiment. The completed system can not only support all the processes of theexperiment, but also complete other additional functions, such as viewing historical
data, exporting all data results, and so on. After the system was completed, we not only
tested the reliability of the hardware, but also tested different groups of people.

54

Chapter 4 Development of Haptic Angle Sorting Evaluation System
4.1 Background

Among the tools currently used for cognitive assessment, early assessments are all
through scoring tools. The cognitive rating tool is a means of organizing cognitive
assessment and gives the score value of the overall function. The score is affected by
the subject’s previous level of education and intelligence, as well as the familiarity with
culture and language. The upper and lower limit effects mean that patients with severe
cognitive impairment (lower limit) or mild cognitive impairment (upper limit) lose theirability to discriminate. In research, shorter cognitive tools are often used for screening
so that subjects with scores below the cut-off score can be identified for further
evaluation. The commonly used method is the Mini-Mental State Examination(MMSE) [92]. Its main advantage is that it comprehensively covers basic cognitive
functions in about 10 minutes, and it has been widely recognized internationally. It
covers the cognitive domains of orientation, memory, concentration, language, praxis,
and gnosis. In addition, there are other cognitive assessments. The Comprehensive
Clifton Assessment Program for the Elderly (CAPE) [93,94] and the Cambridge
Examination for Mental Disorders in the Elderly (CAMDEX) [95] respectively include
cognitive subscales: the information/orientation subscale and CAMCOG [96–98],
respectively. The information/orientation subscale has 12 questions, is easy toadminister and widely used. CAMCOG is a comprehensive cognitive ability test thatcovers a wide range. The total score is 104. In all these tests, the qualitative information
is usually equal to Scores are equally important. This is of course the case of the clock
pull test [99](Ainslie et al, 1993). The subject is asked to draw a circle, put in thenumbers and set the hands at ten minutes past eleven. It is interesting to note whether
the patient starts by establishing the four poles of 12, 3, 6 and 9 and then fills in the55

Chapter 4 Development of Haptic Angle Sorting Evaluation System
numbers, or starts with 12 and then laboriously goes round to 11. It is surprising how
often those who can tell the time will turn out to have a lot of difficulty in deciding
which of the clock hands should be the longer or shorter
Although these assessment tools have the advantage of being comprehensive andrepeatable, they can only be used as a supplement to the inspection. A thoroughassessment of the patient is needed to provide the best treatment or medication at an
early stage of the disease, avoiding missing the most appropriate treatment period. The
experience is used for help professionals to know which parts of an assessment are
particularly useful to individual patients. However, the evaluation of body function,
especially the evaluation of sensory perception [100–102], is a hot topic in current
research, and many studies have found that the decline, lesions and even damage ofbody function will completely change at an early stage through the changes of sensory
perception, such as vision, touch, hearing and taste. Therefore, changes in theseassessments can be used to assess the state of physical health.
It is used to test haptic function, such as the task of tactile perception through handstimulation, which is very important for early clinical screening or diagnosis ofneurological diseases and disorders, and even cognitive decline and impairment. There
are many tactile evaluation methods, and corresponding evaluation equipment has beendeveloped and designed. Therefore, it is particularly important that the related researchand evaluation methods of tactile can be well realized as a convenient test method.
In the method of using and evaluating through angular stimuli, there is also theinitial manual presentation of stimuli one by one. The method of manually presenting
stimuli has some recognized shortcomings. For example, it is difficult to quantitatively
control the interval between stimuli and the position of stimuli. During the test, thesubject can obtain real or visual cues from the experimenter and make a second guess
56

Chapter 4 Development of Haptic Angle Sorting Evaluation System
to try to improve or worsen his performance. All these factors have a great influence on
the results of the test, which may be different in different courses of treatment, which
limits the authenticity of the data obtained. Due to the specialization of testing andanalysis, professionals are often required to perform experimental operations and data
analysis. This leads to the fact that even if the proposed method is effective, it is often
far from being applied in practice. Therefore, to standardize experimental operations
and reduce data analysis, we consider designing automated equipment to make testing
more suitable for non-specialists. Practical application in testing for a wide range oflarge populations.
We have also increased automated equipment to present stimuli. By stably
controlling the interval between the angles of stimuli, the experiment has also been
improved. However, when there are many repetitions, a large amount of data needs tobe completed on the computer through professional operations during analysis, which
will delay the display of test results. To further improve these problems, a highly
integrated angle discrimination automatic evaluation device was developed in the laterstage. The 3AFC evaluation method requires the subjects to complete the task ofidentifying angles. This design improves the test efficiency and further improves theequipment's friendliness to non-professionals. These technological advancements havealways played a vital role in the progress of tactile research. From manual tasks that
require the participation of experimenters to test tasks that can be completed
automatically only by allowing the program, testing has become simple and convenient.
In this chapter, we aim at the angle sorting evaluation method proposed above, andwe develop an automatic evaluation device for haptic angle sorting. This equipment
was developed to standardize experimental operations and reduce data analysis, whichis convenient and simple for experimenters and testers. Standardize the experimental
57

Chapter 4 Development of Haptic Angle Sorting Evaluation Systemprocess by developing automated equipment that conforms to the experimental process.
At the same time, it also automates the calculation of test results, which is more friendly
to non-professionals.

4.2 Haptic Angle Sorting System

The automated equipment designed and completed in accordance with effective
evaluation methods can be simplified and better applied in actual testing. We attempted
to design a test system that can be used to complete experiments and calculate
experimental results. Among them, the process of completing the experiment is thesame as that described in Chapter 3 section 3.2.1. At the same time, before theexperiment, the experimenter only needs to input the information of the participant, andafter the participant completes the experiment, they can view the specific results, andcan store, transmit and view historical tests and other operations of the experimental
results. Participants only need to complete the sorting process in the experiment andpress the confirm button after confirming the sorting. Such equipment becomes simple
and efficient both for experimenters and subjects and is more conducive to applicationin practice.

4.2.1 Haptic Pattern

In some previous studies, the stimuli of two-dimensional (2-D) raised-line
drawings were used to explore the touch perception process [103–106]. The accuracyof 2-D raised-line drawings is amenable to control when being designed, and thedrawings can remove the information of real objects [107]. Therefore, we designed a
2-D raised-angle stimulus [11,12] for the sorting test, where the angle difference of the58

Chapter 4 Development of Haptic Angle Sorting Evaluation System
2-D raised-angle is 2°, as shown in Figure 4.1. In our previous research, the stimulus
angles were made of plastic material, which is mainly used in the experimental
environment. In the application environment of long-term use and testing with a large
number of people, plastic materials are prone to wear and reduce the accuracy of theangle, resulting in large errors in the test results. To avoid this situation, the angle
stimulus we designed is all made of metal.

Figure 4.1. The design of a haptic pattern.

4.2.2 Design of the Haptic Angle Sorting Device

Figure 4.2 illustrates a schematic diagram of the structure of the haptic angle
sorting system. The system includes four parts: 1) an interaction part, 2) an angle
stimulus detection part, 3) a system control part, and 4) a power supply and data output
part. The interactive part consists of a touch screen, which is used by the experimenterfor experiments and data manipulation, and 5 keycode positions where the participantssort the angle stimulus. The angle stimulus detection part is a keycode conversion
59

Chapter 4 Development of Haptic Angle Sorting Evaluation Systemmodule (STC89C51, STC Microcontroller Inc., China) that can identify 5 different
keycodes of angles of stimuli simultaneously and send the angle stimulus sorting
information to the system software control part. The system control part is a field
programmable gate array (FPGA) main control module (ZYNQ 7010, Xilinx Inc. US)of the microcomputer. And the reason why FPGA is chosen as the main control is thatthe functions of this module can be configured according to requirements, and its many
interfaces also provide the possibility for later function expansion, including runningsystem software and controlling touch screen, in addition the experimental data
calculation, storage, and transmission though multiple interfaces.

Figure 4.2. Schematic diagram of the structure of the haptic angle sorting system.

Figure 4.3(b) shows the appearance and structure model diagram of the designed
haptic angle sorting device, and all operating parts (except the power button), during
the experiment: 1) The 7-inch touch screen is used to input the information of theparticipants and display the results after the test; 2) A square of 7 grooves (40×40 mm)
was placed on the top part of the device; 3) confirmation key; and 4) a box embedded
60

Chapter 4 Development of Haptic Angle Sorting Evaluation Systemin the device is de-signed to store angular stimuli to prevent loss during carrying.

Figure 4.3. The configuration of the haptic angle sorting device: (a) Design of thehaptic pattern (I), which includes the angle stimulus at the front (II) and keycodebase at the back (III); (b) Interface design of the haptic angle device; and (c) Designof the haptic angle stimulus position in a fixed position and a sequence position.
Three microswitches are arranged in a group in each position from the grooves ofthe 2nd to 6th positions to identify each angle stimulus, as shown in Figure 4.3(c). These
three microswitches constitute a code unit which is one of the five code units, as shownin Figure 4.2. In the sorting experiment, the keycodes are triggered by the base of theiron block adsorbed by a magnet, which is combined with an angle stimulus to form astimulus module. The haptic angle sorting test system must identify 5 sets of keys toconfirm the sequence of angle stimuli in the experiment, as shown in Figure 4.3(b).
61Chapter 4 Development of Haptic Angle Sorting Evaluation System
Each microswitch is connected to an I/O port for processing and transmission efficiency.
The haptic angle sorting test system must identify 5 sets of keys to confirm the sequenceof angle stimuli in the angle sort. When each microswitch is connected to an I/O portof the 51 microcontroller unit (MCU) chip, the triggered microswitches can realize highand low levels of the chip at each I/O port so that the MCU can identify the digital
signal of the I/O port as 1 or 0. To transform different angle stimulus information into
digital code, the 3 microswitches in the groove will stimulate the trigger switch
according to different angles, so the three switches closing or opening combination
mode can be converted into three-bit binary the sole digital signals. The recognition
method of angle stimuli is not affected by the environment, and it can quickly andaccurately identify different angle stimuli. There are 5 keycodes (000, 001, 011, 100,110), corresponding to the value of each angle stimulus and the output binary data value.
To obtain those input keycodes, 5 types of stimulus block bases were designed, as
shown in Figure 4.5(a). Among them, the base key codes of the four stimulation blocks(001 and 100, 011 and 110) are symmetrical. Therefore, the same stimulus block basewas rotated 180° for installation, which reduced the processing cost of the equipment.
When placing the angle stimulation module, which is composed of the angle stimulationand iron base block, the stimulus module at each position is attracted by a 12-mmdiameter magnet and triggers the micro-switch in the groove.

4.2.3 System software

The design of the software was based on hardware considerations using MATLAB(The MathWorks, Inc. US) App Designer platform. At the same time, to simplify thedata processing process, we also added the evaluation algorithm of the angle sorting
paradigm in Section 2 into the software. At the end of the experiment, participants were62

Chapter 4 Development of Haptic Angle Sorting Evaluation Systemable to obtain the assessment results from the software immediately. The touch screen
is very convenient and user-friendly. According to the angle sorting paradigm, theflowchart of the software is shown in Figure 4.4. The operation of the software is mainly
designed to operate in three steps according to the experimental process, as shown in
Figure 4.5(c).

Figure 4.4. The flowchart of the software design.

63

Chapter 4 Development of Haptic Angle Sorting Evaluation System

4.2.4 System Implementation

Figure 4.5 is the implementation of the system. The haptic patterns have 7 angle
stimulations, including 20°, 22°, 24°, 26°, 28°, 30°, and 32°. These angle stimulations

Figure 4.5. The implementation of the system: (a) Angular stimulus module: theraised-angle drawing (I) on the front side and different trigger keycodes (II) on thebackside; (b) Interface design of the haptic angle device; (c) Software interface tooperate in the experiment; and (d) Operation of the angle sorting device by theparticipant in the experiment.
64Chapter 4 Development of Haptic Angle Sorting Evaluation Systemprevent wear and reduce accuracy. The device is made of aluminum alloy, and themachining accuracy is ±0.01 mm. The back of the haptic pattern is a keycode block,and the angle stimuli are bolted together. Each haptic pattern that needs to be sorted byparticipants is different, in which the patterns are angle stimuli other than the maximum
and minimum position fixed, as shown in Figure 4.5(a). Figure 4.5(b) is the final device.
Figure 4.5(c) shows the operation interface of the software in the experiment.

4.3 System Evaluation (Hardware Test)

4.3.1 The identification of stimuli angle

The correct recognition of the stimulus at each angle is essential for calculating
the evaluation results. To accurately identify the angle, we uniquely code each angle,
use the mechanical micro-keys to start the digital circuit to read the angle information,and then the angle information is recognized by the system after the code conversion.
Because to ensure that all angles can be identified in each position, we conduct
identification tests on all angles in each position. Each angle was tested 10 times at 5
different positions, and the final test results of a total of 250 tests are shown in Table
Table 4.1 The recognition accuracy of stimuli angle in test
Stimuli

BinaryConversion

Accuracy Of

Angle/Deg

CodingCode

Recognition

22

000

22

100%

24

001

24

100%

26

011

26

100%

28

100

28

100%

30

110

30

100%
65

Chapter 4 Development of Haptic Angle Sorting Evaluation System
4.1.

According to the test results of the above table, it can be found that the key code
design for the angle stimulus can identify different angle stimuli at each position. This
digital code activated by a different mechanical structure is a reliable identification
method.

4.3.2 The operation of system

The operation evaluation of system focused on the convenience of equipment inuse. During the use of the equipment, the experimenter only needs to input theparticipant's information, such as name, age, and angle of the test, and then press tostart the test. These operations are all operated through the 4.3-inch touch screen, as
shown in Figure 4.5(c). Moreover, the use of the software is designed with a concise
and easy to understand UI, and the operation of the software is also extremely
convenient. For the subject test, only need to install the steps of the experiment tocomplete the placement of the angle stimulus and the adjustment of the sequence. Afterconfirming the sequence, press the confirm button to complete the test. Such a design
does not need to undertake too many cumbersome processes for the subjects andexperimenters. Through the records in the follow-up test, it is found that, on average,
each subject is inputting information, completing a sorting, and then getting the test
result, the whole test process is 3 to 4 minutes. This test efficiency also proves the easeof operation of the system.

4.5 Conclusions

66

Chapter 4 Development of Haptic Angle Sorting Evaluation System
In this work, we have presented a new method for haptic angle discrimination andan angle sorting evaluation system developed according to this method. The method
includes an efficient angle sorting paradigm and an effective angle sorting system. The
angle sorting paradigm has high efficiency for testing haptic shape discrimination
ability. The system is easy to use for both the experimenters and participants in theevaluation experiments. The contribution of the system is to unify the experimental
procedure, simplify the operation, and be convenient for analyzing the experimental
data results. In comparing the two-angle discrimination method, the user only needs tooperate the software, and the results are obtained in a few seconds on the angle sorting
system. By testing the hardware, the recognition rate of angular stimulus is verified.

67

Chapter 5 Application Evaluation for Difference Group People

Chapter 5 Application Evaluation for Difference Group
PeopleSummary
Although the improved assessment methods and testing system described above
have been completed and evaluated in healthy young adults. The performance of suchan assessment still needs to be validated in an expanded population. The assessment of
this method in different groups is not yet known. In the present study, we recruited
different populations, testing healthy young adults and older adults, healthy individuals
in the older, and patients with cognitive decline or impairment. It was found that thediscrimination index was significantly different between healthy young and old people.
And there was also a significant difference between normal older adults and patientswith cognitive decline or impairment, respectively.

68

Chapter 5 Application Evaluation for Difference Group People
5.1 Background

The haptic sorting test system standardizes the sorting test method, simplifies thetesting process for experimentalists and subjects, and improves the testing efficiency.
To further test the system and evaluate the test of the method on different populations,
we recruited two different groups of subjects for the test. To further evaluate thecomparison of the sorting method in cognitively different populations, we also
compared healthy individuals with cognitively different populations with Alzheimer's
disease.

5.2 Experiment (Exp.3: Young and Old)

5.2.1 Participants

Fifty-one healthy volunteers, including 30 young from Okayama University
students (26 males and 4 females, ranging in age from 20-23 years with a mean age of
21.7 years, 2 males are left-handed, and the rest are right-hand) and 21 elderly retirees(6 males and 15 females, ranging in age from 64-88 years with a mean age of 72.9 years,
4 females are left-handed and the rest are right-hand), consented to participate in angle
sorting test. Handedness was confirmed by the Edinburgh Handedness Inventory. The
research was approved by the ethics committee of Okayama University, and allparticipants signed informed consent forms. No participants had prior experience withhaptic angle sorting devices.

5.2.2 Prudence

The haptic angle sorting device was horizontally placed on the table directly in69

Chapter 5 Application Evaluation for Difference Group People
front of the participant, who was asked the paradigm of the sorting angle, as describedin Section 2.1. The same angle stimulus is selected for a 2° angle difference (20°, 22°,24°, 26°, 28°, 30°, 32°, among them, 20° and 32° are reference angles.). The angle
sorting experiment was repeated 3 times for each participant. The angle sorting 3 times
for each participant was 12 to 15 minutes.

5.2.3 Result and Discussion

The haptic angle sorting device automatically calculates the result of each trial
sorting according to the evaluation method in chapter 3 section 3.3.1, the result of which
includes the maximum probability of the sorting 𝑃(𝜎, 𝐴𝑆𝑛 ), and the discriminationindex of 𝜎, as shown in Figure 4.6. There was also no invalid σ for all participants ineach sorting. Independent Samples T-Test was used to determine whether there were
any statistically significant differences in the discrimination thresholds between the twogroups. T-Test analyses were performed using SPSS version 26.0.

70Chapter 5 Application Evaluation for Difference Group People

Figure 4.6. The average of discrimination index from angle sorting in the young
and old groups showed that the performance of young participants was significantly
better than that of old participants. Values are means ± SEM.(*p<0.05).

The experimental results show that young and old groups have significant
differences in the performance of angle sorting tasks, as shown in Figure 12. Moreover,compared with the younger group, the performance of the elderly group has
experienced a significant decline [ 𝑡22.79 = −2.784 , 𝑝 = 0.011 , Cohen's 𝑑 =−1.141], which consistency with previous research that the ability to discern the angle
decreases with age [45,46].
It is well known and confirmed that since cognitive ability declines with age, theangle discrimination ability of elderly subjects is significantly weaker than that ofyounger participants [47–49]. The results of the experiment are the same as our
expectations, which is significant differences in the performance of the angle sortingtask between participants of different ages. And the same as the previous study, thediscrimination threshold of angle sorting of the elderly is also significantly lower than71

Chapter 5 Application Evaluation for Difference Group People
that of the young. This result is very good to support our aim of this device that we want
to use it for cognitive diagnosis and the like. At the same time, it also proves theconvenience and stability that relatively stable results can be obtained in a short time.

5.3 Experiment (Exp.4: Normal, MCI and AD)

5.3.1 Participants

Seventy-six old volunteers, mean age of 78.6 years old, who are 18 Alzheimer's
disease (AD), 12 Mild Alzheimer's disease (Mild AD), 23 Mild cognitive impairment(MCI), and 24 Normal Controls (NC), consented to participate in angle sorting test.
Two of the AD patients did not complete the sequencing test due to physical conditions.
The research was approved by the ethics committee of Okayama University, and allparticipants signed informed consent forms. No participants had prior experience withhaptic angle sorting devices.

5.3.2 Prudence

The haptic angle sorting device was horizontally placed on the table directly infront of the participant, who was asked the paradigm of the sorting angle, as describedin chapter 3 section 3.3.1. According to previous studies, the Angle discriminationthreshold of the aged and cognitively impaired population is significantly different fromthat of the normal population. Thus, the angle stimulus is selected for a 5° angle
difference (60°, 65°, 70°, 75°, 80°, 85°, 90°, among them, 60° and 90° are reference
angles). The angle sorting experiment was repeated one time for each participant. The
angle sorting one time for each participant was 5 to 10 minutes.
72

Chapter 5 Application Evaluation for Difference Group People
5.3.3 Result and Discussion

The haptic angle sorting device automatically calculates the result of each trial
sorting according to the evaluation method in chapter 3 Section 2.3, the result of which
includes the maximum probability of the sorting 𝑃(𝜎, 𝐴𝑆𝑛 ) and the discriminationindex of 𝜎. Among all the subjects, there were two AD, two Mild AD and one NC who
could not be tried with the angle difference (5°) of the current test. The results were all
invalid. In the group data analysis, the results of these subjects were not included in thestatistical analysis.
To examine whether the patients with AD, Mild AD, MCI, and NC showed any
decline in angle discrimination, we further examined the angle discrimination index.
We performed a one-way ANOVA and a multiple comparison using the Tukey HSD
correction ( 𝛼 = 0.05 ) on mean discrimination index. As shown in Figure 4.7,
differences in the mean discrimination index among patients with AD (8.31 ± 1.41),
Mild AD (8.42 ± 2.61) or MCI (6.52 ± 0.98) and NC subjects (2.83 ± 0.99) weresignificant [F (3,72) = 6.093, p < 0.001], with a larger discrimination index in patientswith AD compared to patients with NC (p = 0.004). The discrimination index in patientswith Mild AD was also larger compared to NC with sufficient statistical significance (p= 0.0118). In addition, the index in patients with MCI was also larger compared to NC
with sufficient statistical significance (p = 0.0374). These results indicated that the
decline of ability to discriminate angle in patients with AD, Mild AD and MCI was
significant compared to NC group.

73Chapter 5 Application Evaluation for Difference Group People

Figure 4.7. The average discrimination index from angle sorting in the four
different groups showed that the performance of NC groups was significantly better
than the other three groups. Values error bars represent means ± SEM (*p<0.05,**p<0.01).

5.4 General Discussion

The current two studies showed that there were differences in the ability to
distinguish haptic angle between groups of healthy subjects with age differences andbetween groups of healthy, MCI, mild AD or AD patients. The current study compared
the performance of angle discrimination in young and old subjects, as well as NC, MCI,
mild AD and AD subjects. The results of this study show that there are significant groupdifferences in the ability of angle. As shown in Figure 4.6 and figure 4.7, the average
discrimination index of the elderly is significantly lower than that of the young; themean discrimination index of mild AD, ad and MCI patients were significantly lower
than that of NC individuals.
74Chapter 5 Application Evaluation for Difference Group People
All subjects were asked to actively perceive the angle of movement under the rightindex finger, distinguished the order of each angle in the five angles, and arranged it inorder from small to large. In the process of angle sorting, it includes two reference
angles for fixed positions and five angles to determine positions. The angle recognition
task is a typical tactile assisted shape recognition process. The sensory feedback is the
key to active touch shape recognition, which is generated by four mechanical sensing
systems located in the skin [108]. In addition, previous studies [55,108] have shownthat tactile shape perception can be defined as the sum of skin mechanical receptor
functions. However, in Experiment 1, there were significant differences in angle
discrimination between healthy young people and the elderly. With age, many
anatomical and morphological changes will occur in hands and fingers. The density ofmechanical receptors in the skin decreases [109,110], and the conduction velocity of
peripheral nerves decreases significantly with age [111]. On a practical level, thereduced touch sensitivity of the elderly can lead to a series of problems [112,113],
including impaired ability to recognize objects through touch and to detect objects incontact with the skin. Therefore, compared with normal young subjects, normal elderly
subjects naturally have worse ability to distinguish angles. For example, the average
discrimination index of young subjects is 1.49, that of the elderly is 2.63 (such as
Experiment 1) or that of NC population is 2.83 (such as Experiment 2). The average
discrimination index of healthy elderly subjects in the two groups was 1.77 times and1.90 times higher than that of young people, respectively.
In Experiment 2, the angle discrimination defects were observed in patients with
MCI, Mild AD and AD. The results of the study showed that healthy elderly subjects
and MCI, mild AD and AD patients were able to complete the angle sorting task,
excluding the special situation where the physical state and the angle difference of the75

Chapter 5 Application Evaluation for Difference Group People
angle sorting could not be correctly distinguished. Almost all subjects in the experimentcan clearly perceive the angle difference between stimuli and complete the sorting task
in accordance with the test. One of the earliest symptoms of AD is impaired working
memory [114–116]. In addition, previous studies have observed that compared withhealthy aging patients, the memory process of MCI patients is also impaired [117–119].
In those experiment, all subjects were required to perform a sorting task from multiple
angles through active touch discrimination. To perform this task, the subject must
remember the composition characteristics of each angle, and then compare these angles
to make a judgment. The working memory contributes to the performance ofsomatosensory discrimination [86,120]. Therefore, current research shows that the
decline and impairment of working memory is a factor leading to the decline in angle
discrimination. Firstly, AD, Mild AD is a neurodegenerative encephalopathy. Unlike
MCI patients, these patients have more severe working memory impairment [121].
Secondly, the isolated memory impairment found in MCI patients is more severe thanthat observed in healthy elderly individuals, while other cognitive functions remain
normal [117–119]. In contrast, AD patients have further deficiencies, planning andproblem solving in the field of spatial learning and memory [122–124]. These severe
cognitive impairments in AD patients can explain the more serious angle discrimination
deficits in AD patients.
In addition, the process of spatial discrimination activates a widely distributed
brain network (Bodegård et al., 2001b; Kitada et al., 2006; Roland et al., 1998; Wu etal., 2010). The results of these neuroimaging studies also support our above findings.
In terms of standing posture, the parietal groove (located on the outer surface of theparietal lobe) participates in multi-sensory spatial processing during the grasping andshape classification process. In fact, the parietal sulcus is an advanced area for
76

Chapter 5 Application Evaluation for Difference Group People
calculation and fine shape construction [120]. Some neuroimaging studies[125–128]

have shown that abnormalities in the frontal, temporal, and parietal cortex lead tofunctional defects in AD patients. Therefore, our research results show that comparedwith MCI patients and NC patients, AD patients' working memory impairment andspatial discrimination are the reasons for the lowest discernibility angle.
5.5 Conclusions
When comparative evaluation between young and old groups, it found that theresults are very significant.Through the two experiments of the current study, thesystem evaluation, and the comparison of population differences, it shows thepracticality of the system. It also shows that the new method may have potential
application value in the evaluation of haptic discrimination ability, haptic cognitive
function, and even early clinical evaluation.

77

Chapter 6 General Conclusion and Future Projections

Chapter 6 General Conclusion and Future Projections

SummaryThis thesis proposed an angle sorting evaluation method and developed anevaluation system based on this method. In addition, the performance of this systemand the evaluation method are also tested and compared with different groups of people.
In this chapter, our findings are summarized as follows. In addition, some future
predictions are also included.

78

Chapter 6 General Conclusion and Future Projections
6.1 General Conclusions

This thesis includes three aspects of research, respectively, from the previous
improvement of the haptic angle evaluation method, the improvement of the evaluation
analysis and calculation method, and the development and application of the new
method of the haptic angle sorting evaluation system. The first experiment was the basisof the paper. The 2AFC method used angle discrimination threshold and discriminationindex to compare angle evaluation. The second study was the analysis of the calculationof the mathematical model of the design of the evaluation experimental paradigm andthe evaluation calculation method. In the third study, we developed an angle sorting
evaluation system and discussed the application of evaluation methods and haptic angle
sorting devices in different groups of people.
Chapter 2 described how the angle discrimination threshold and discriminationindex were calculated through different function distributions, and the significance of
two different evaluation parameters in evaluating the angle discrimination ability. The
2AFC experiment usually uses two stimulus selection methods to test the individual's
discrimination performance, and the logical growth curve was fitted to the correct rateof the response, and the 75% position of the parameter was evaluated as thediscrimination threshold. The method of logical growth curve measurement
discriminative performance is often used in previous evaluations. However, in theanalysis, the functions of Gaussian distribution and Gaussian cumulative distribution
are also used in the psychophysical evaluation model, and the logical growth curve issimilar to the Gaussian cumulative function. In this chapter, we use the Gaussian
cumulative function to fit the correct rate to obtain the variance of each person's fitting
Gaussian function. This parameter is also used to evaluate the discrimination ability of79

Chapter 6 General Conclusion and Future Projections
different testers. On the one hand, the data measured in the same experiment was used
to fit the logistic growth curve and the Gaussian cumulative function curve, and themeasured data are used to calculate the evaluation parameters of each subject using
these two different analysis methods, which is Discrimination threshold anddiscrimination index. By comparing the values of SSE and R-square obtained by thefitting function in the experimental data, it was found that the fitting quality was very
good, and the values were the same or very close. In addition, we also established themathematical relationship between these two evaluation models. Specifically, theextremely high similarity between the logical growth curve and the Gaussian
cumulative function is that they can be converted to each other by mathematical
relationships. Especially when the logical growth curve is transformed into theGaussian cumulative distribution function, more properties similar to the Gaussianfunction can be obtained. When the subjects repeat the test, the results obtained are also
in line with the central limit theorem, that is, in accordance with the Gaussian
distribution. Such analysis also proves that the discrimination threshold anddiscrimination index used in the evaluation can be converted mutually, and there is no
doubt that the discrimination index can also be used to evaluate the angle discrimination
ability.
Chapter 3 proposed an angle sorting evaluation method. It does not use multiple
repeated tests similar to the 2AFC test paradigm to calculate the correct answer rate.
Instead, it requires a series of angle stimuli with the same difference to be sorted andcompleted according to each time. Calculating the discrimination index based on thesorting results. And according to the discriminant index difference to evaluate theparticipant’s angle discrimination performance. In the analysis of the sorting results, we
proposed that the recognition of the angle is to recognize the size of the angle according80Chapter 6 General Conclusion and Future Projections
to the way. For example, in the angle 22°, 24°, 26°, 28°, 30°, the intensity of the
response to the angle of the channel 22 to the CH22 is in accordance with the Gaussian
positive. The state distribution is 𝑓(𝑥 = 22, 𝜇 = 22, 𝜎), and the response intensity ofchannel CH22 from other angles is 𝑓(𝑥 = 24, 𝜇 = 22, 𝜎) , 𝑓(𝑥 = 26, 𝜇 = 22, 𝜎) ,𝑓(𝑥 = 28, 𝜇 = 22, 𝜎) , 𝑓(𝑥 = 30, 𝜇 = 22, 𝜎) , especially for the same subject thediscrimination index 𝜎 is constant. Therefore, the probability of the angle of thesorting result can be calculated at each position, and the probability of the sorting result
can also be calculated according to the final sorting. This probability is driven by thevariance of the Gaussian distribution, the discrimination index (𝜎), in other words, eachsigma corresponds to a different probability. In this way, we can get the relationshipbetween the probability of the sorting result and the variance of the Gaussian
distribution. In this relationship, the optimal solution is the 𝜎 corresponding to the
maximum probability, and this value is also the discrimination index evaluated fromthe sorting result. At the same time, we also use the discrimination index as a measureof the participant’s perspective discrimination performance. The larger thediscrimination index, the worse the angle discrimination performance; the smaller thediscrimination index, the worse the performance.
Chapter 4 described the design and development of the haptic angle evaluation
system, the evaluation of the performance of the device, and its practical application indifferent groups of people. The application groups include healthy elderly and young
people, healthy elderly and patients with mild cognitive impairment, patients with mild
Alzheimer’s disease, and patients with Alzheimer’s disease. The development of theevaluation system included the design of hardware and software respectively. The
hardware design system included an angle recognition and conversion module for angle
stimuli. The binary codes are used to recognize different angle stimuli and convert these81Chapter 6 General Conclusion and Future Projections
codes into actual angle values. The system also has a main control module, which
accepts the angle value of the conversion module, and then calculates the discriminationindex according to the evaluation method in Chapter 3. After the calculation iscompleted, not only the result is displayed, but this data will be also saved. At the sametime, the calculation module has the calculation function and other operation functions,such as recalling historical results, transmitting data, and it is a simple operation method
through the touch screen. In addition, in the software design of the system, it is mainly
designed in accordance with the flow of the test task - output tester information, start
the test, the subject completes the test, calculate the result, display the result, and store
it. According to this process, the software is designed into three steps. The first step isthat the tester needs to enter the tester's information in the software and confirm thestart of the test; the second step is to include the participant to complete the sequence
and adjust the order, and then confirm; The third step involves displaying the results
and storing them. After the completion of the system, we tested healthy elderly andyoung people, healthy elderly, patients with mild cognitive impairment, patients withmild Alzheimer's disease, and patients with Alzheimer's disease. Through thecomparison of the two sets of data, it is found that such a system and method have ahigh reference value for early clinical screening of cognitive decline and impairment.

6.2 Future Projections

In the developed equipment, the angle difference of different series is stillinsufficient. In order to adapt to a wider and larger group of people, it is necessary to
make more series of stimulation angles with different angles. The normal people
currently tested use a 2° angle difference for testing, while the cognitive decline andimpairment people have a 5° angle difference. Among all the subjects in the paper, very82

Chapter 6 General Conclusion and Future Projections
few subjects will appear in these two series. A test that cannot obtain a valid result froman angle. To further measure the effective evaluation data, more series of stimulation
angles will be added in the future, such as 3°, 4°, 5°, 6°, 7°, 9°. Such improvements
attempt to further expand the equipment test population.
In the current improved method proposed and the equipment developed for the
method, the method has been preliminarily perfected for practical application. At thattime, there was still a deeper level of research that deserves more investigation.
First, in the current study, the evaluation method is based on reasonable
mathematical modeling derivation and verification with less sample data. Moreover,further evaluation and investigation of diverse groups and large sample data are needed.
Unlike the 100HUE TEST, which has a large amount of data to verify, the angle sorting
evaluation method is established based on mathematical modeling. We still need toobtain a large amount of data in practical applications to verify and improve this method.
In contrast, the actual data in this article can support the change trend of themathematical model, and the amount of such data is still slightly insufficient for morein-depth and extensive difference evaluation. In the future, we plan to use this method
to evaluate the need for more data for more in-depth and detailed evaluation, such asmeasuring the grading threshold of population differences, especially the identificationof differences in cognitive decline or impairment. Although our current research findsthat there are more significant results for these evaluations, such results still require
more data and a wider range of populations to be evaluated. From these evaluations, acritical evaluation range that can be used to differentiate levels can be derived. Such
research objectives are of great significance for evaluating cognitive changes,
especially for early clinical screening of cognitive decline and impairment.
In addition, there are clear evaluation parameters for this method in the test result
83Chapter 6 General Conclusion and Future Projections
analysis and difference evaluation. However, the intermediate process of such anevaluation task is currently unclear, especially the difference in the strategy that thehuman brain needs to compare and sort in this. Whether such differences will also be
manifested through the results of the evaluation. And when different strategies are
adopted, whether they will be shown through the evaluation results, such as sortingfrom big to small, from small to big, or without specific restrictions. Whether the
optimization of strategies may improve the results, such research is conducive toimproving people's cognitive process of external things. And it has high reference
significance for the exploration of artificial intelligence.
Moreover, evaluating the sorting method of the human brain is of greatsignificance to improving the method of computing operation. Because the sorting
method has always been used in computer algorithms, this method is used to normalize
data to improve its readability. Most of the current research and improvement of sorting
methods are derived from human behavior and life experience, and their purpose is totry to use a more intelligent way, that is, with a lower computational load and low
resource consumption, to complete the sorting accurately and efficiently. In the future,
the research on the strategy and process of advancing human brain sorting will havehigh reference value for the improvement and promotion of such methods.
In the current sorting method of the tactile angle discrimination test, we use asingle angle as the stimulus in the one-dimensional Gaussian model, whether theperception of other stimuli will also be applicable. Because of the high efficiency of thesorting test method, it is more suitable for the actual degree test. Moreover, when theperception method is changed and the stimulus dimension is increased, the sorting
evaluation method in the multidimensional Gaussian model is still used, which can
improve and increase the evaluation of multi-channel interaction and can also test
84

Chapter 6 General Conclusion and Future Projections
whether the cognition of the human brain exists in different stimulus dimensions, forinstance, to promote or inhibit. The improvement of evaluation methods has a goodreference for psychophysical test evaluation.

85

Appendix

Appendix●

報告書番号 No.
2020.3.26 版

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2021 年

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86

Publications

Publications
1. Journal paper[1] Yulong Liu, Jiajia Yang, Yinghua Yu, Yiyang Yu, Wu Wang, Huazhi Li, Satoshi
Takahashi, Yoshimichi Ejima, Qiong Wu, and Jinglong Wu. 2021. "A New Methodfor Haptic Shape Discriminability Detection" Applied Sciences 11, no. 15: 7049.
https://doi.org/10.3390/app11157049[2] Huazhi Li; Jiajia Yang; Yinghua Yu; Wu Wang; Yulong Liu; Mengni Zhou;
Qingqing Li; Jingjing Yang; Shiping Shao; Satoshi Takahashi; Yoshimichi Ejima;
Jinglong Wu.2021. "Global surface features contribute to human haptic roughness
estimations" Experimental Brain Research
2. International conference paper[3] Yulong Liu, Jiajia Yang, Qiong Wu, Hongtao Yu, Satoshi Takahashi, Yoshimichi
Ejima & Jinglong Wu. Research and Development of the Synchronization Deviceof fMRI Scanning Cycle and External Stimulus Presentation Equipment. 2020
IEEE International Conference on Mechatronics and Automation (ICMA 2020). pp.
1431-1436, (2020).
[4] Qiong Wu, Yang Liu, Yulong Liu, Jinglong Wu & Ritsu Go. Development andperformance evaluation of automatic measuring apparatus for sorting haptic angle
stimulus. 2020 IEEE International Conference on Mechatronics and Automation(ICMA 2020), pp. 1467-1472, (2020).
[5] Yiyang Yu, Yang Feng, Meng Wang, Qiong Wu, Yulong Liu, Jiajia Yang, Satoshi
Takahashi, Yoshimichi Ejima & Wu Jinglong. A Reading Assistant System ofChinese Text for Persons with Central Visual Field Loss. In 2019 IEEE
International Conference on Mechatronics and Automation (ICMA). pp. 11021107, (2019).
87

Acknowledgements

Acknowledgements
Firstly, I would like to express my sincerely gratitude to Prof. Jinglong Wu for thecontinuous support during my Ph.D studies and related researches. Prof. Jinglong Wu
helped me in all my research design and writing of this thesis. I could not complete mystudy of doctor course and finish this thesis successfully without his enlightening
instruction. Impressive kindness and patience. His diligence gives me power not only
during my present PhD scours, but also in my future life. In addition, Prof. Wu also
helps me also for my daily life, and let my life in Japan much easier.
Secondly, I also want to express my sincerely gratitude to my supervisor Prof.
Satoshi Takahashi. I got a lot of comments from Prof. Satoshi Takahashi during I makemy study plan, conduct my experiments.
Thirdly, I would like to thank Prof. Yoshimichi Ejima for his insightful comments
and encouragement. Prof. Yoshimichi Ejima also helped me a lot in my research design,
and in writing published papers and this thesis.
Last but not the least, I would also like to express my sincere thanks to Professor
Jiajia Yang, who provided me a lot of comments during I write my papers. I thank myfellow lab mates in for the stimulating discussions and for all the fun we have had
together during these years. I would like to thank my parents and friends for supportingme spiritually throughout writing this thesis and my life general.

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