Discovery and Application of New Index for Cognitive Psychology Mayumi Oyama-Higa Member, IEEE , Teijun Miao Abstract— Fingertip pulsations (plethysmograms) were found to obey chaotic dynamics [1]. We applied chaos theory to analysis of the time series of plethysmograms under various human physio-psychological conditions. It found out that the largest Lyapunov exponent of the time series could be used to characterize physio-psychological status. In addition, the Lyapunov index can use as an index of the cognitive psychology. A visual representation method based on constellation graphs was developed to indexing the changes in the largest Lyapunov exponent.
M
I. INTRODUCTION
OST biological systems that exist in the natural world are believed to be complex systems with chaotic fluctuations. Chaotic systems appear to be very complex and to behave in a random and unstable manner. But in fact they are systems that change according to deterministic rules. Measuring fingertip pulse waves, which are biological signals, is easier than electroencephalography because it is less restrictive and more convenient. We have measured fingertip pulse waves of subjects belonging to different age groups. Recently there were a lot of investigations showing the effectiveness of the plethysmography in studying of the physio-psychological changes. The plethysmography was used to analyzing psychological changes in relation to work load. It was also employed to examing physio-psychological changes of firm employers working on morning, midday and evening. The study of physio-psychological changes caused by decline in communication skill with aging demonstrated the effectiveness of the plethysmography. All of the facts promoted the present study by the use of the plethysmography. We concentrated on the temporal changes in the largest Lyapunov exponent, in relating to indexing physio-psychological status and mental immunity, on the basis of experimental results. In this study the temporal changes of Lyapunov exponents of the time series, which was used as a physio-psychological index, is taken as a measure of mental immunity (mental toughness. Mental immunity here is defined as the adaptability to external environment, communication skill and a certain level of flexibility (divergence). Humans skillfully avoid various changes, contacts and assaults of the external environment. In some cases, they deal with them, cope with them, and maintain their lives while expressing themselves. This is true mental immunity. Just as one becomes sick with the decline in physical immunity, mental
Mayumi Oyama-Higa Ph.D.is with Graduate School of Humanities and Department of Integrated Psychological Sciences Kwansei Gakuin University, Japan (e-mail:
[email protected]) Teijyun Miao Ph.D. is with Chaous Technical Research Laboratory and CCI Incorporation (e-mail: T-miao`Tokyo.cci-web.co.jp)
immunity may well signify “spiritedness,” which has been so far described vaguely. “Spiritedness” could not be quantified until now. But we feel that we could grasp an image of it in the present study. II. METHOD A. Method of measurement Pulse waves were measured using a photoplethysmography sensor (CCI BC2000) in the following manner. The subjects were allowed to become accustomed to their surroundings for at least 10 minutes in a room maintained at 25ºC. They were allowed to sit comfortably in a chair with both hands placed in a relaxed manner on a desk (at a height that was comfortable for writing). The subjects kept their eyes open while measurements were made on the left index finger for a minimum of 60 sec to a maximum of 180 sec. The signals were A/D converted. Digital data sampled at a frequency of 200 Hz and a resolution of 12 bits was recorded on a computer. B. Method of chaos analysis and calculation of the largest Lyapunov exponent For the time series data x(i), with i=1,…, N obtained from the fingertip pulse waves, the phase space was reconstructed using the method of time delays. Assuming that we create a d-dimensional phase space using a constant time delay τ, the vectors in the space are generated as d-tuples from the time series and are given by: X(i) = ( x(i),..., x(i − (d − 1)τ )) = {x k (i )} (1) where x k (i ) = x(i − ( k − 1)τ ) , with k=1,...,d. To reconstruct the phase space correctly, the parameters of delay (τ) and embedding dimensions (d) should be chosen optimally [4]. In time series data recorded from human finger photoplethysmograms, we chose the parameters τ=50 ms and d=4, as in references [1] and [2]. In the reconstructed phase space, one of the important measures of complexity is the largest Lyapunov exponent λ1 . If X(t ) is the evolution of some initial orbit X(0) in the phase space, with time, then
1 t →∞ ε →0 t
λ1 = lim lim ln
| δX ε (t ) | |ε |
(2)
where
δX ε (t ) = X(t ) − X ε (t ) ε = X(0) − X ε (0) for almost all initial difference vectors We estimate
λ1
ε = X(0) − X ε (0) .
using the algorithm of Sano and Sawada [3],
where λ1 describes the divergence and instability of the orbits in phase space. The largest Lyapunov exponents ( λ1 ) were calculated for a basic window of 8,000 points (40 sec). The n sec (n*200 points) were covered by sequentially sliding, 200 points (1 sec) at a time and λ1 was determined for each window. Figure 1 presents the plethysmogram and attractor obtained from a 180-sec measurement and the Lyapunov exponents determined by the sliding procedure.
graph. The line is straighter when the standard deviation is small and kinkier and bent when it is large. III. RESULTS A. Measurement of pulse waves and representation of the physio-psychological index Informed consent was obtained from all the subjects beforehand. B. Changes in physio-psychological status caused due to work load Subjects: 2 adult males (one in his 20’s and the other in his 40’s) Measuring procedure: A Kraeplin’s test was performed for 15 minutes and the pulse waves were measured under the resting condition before and after the test, for 1 minute each time. Representation of the results: Figure 2 shows the changes in the condition. 2 replicate measurements were made with each subject (4 trials comprising 8 measurements in total). Pulse wave data of the subjects before (4 green lines) and after (4 orange lines) the work are shown in the Figure. After the Kraeplin’s test, a task involving brain work, the data shifted towards the left. This suggests that the physio-psychological condition had been activated.
Fig. 1. Plethysmogram (upper), chaotic attractor (middle) and temporal changes of the largest Lyapunov exponents (bottom)
C. Representation of the physio-psychological index through constellation graphs We can observe changes in the physio-psychological index if we could visually represent the changes in the Lyapunov exponent obtained by a method using sliding window. This study developed constellation graphs method to visually describe the temporal variations of the Lyapunov exponents. In these constellation graphs, the numerical data of a time series was converted into angles (minimum=0°, maximum=180°), and the vectors of the same length were joined together and depicted on a semicircular graph. The maximum and minimum values could be set automatically or manually from the values of the Lyapunov exponents. Each line on the graph represents the data of one measurement. The smaller the value of the Lyapunov exponent, the closer the vector is to the bottom right of the constellation graph. As the value of the exponent increases, the line shifts to the left in the
Fig. 2 Lyapunov exponents before and after brain work Orange: After the work, Green: Before the work
Note: The subjects commented that their head became clearer after the Kraeplin’s test, a calculation task. C. Changes in physio-psychological index in firm employees during a working day (morning, midday and evening) Subjects: 8 employees aged 26 to 34 (mean: 30.25 ) Measuring procedure: Measurements were made, for 3 minutes at a time, soon after the employee reached the office (in the morning), at least 1 hour after lunch (midday) and when leaving office (evening). Representation of the results: Figure 3 shows the results of measurements made in the morning, at midday and in the evening with the 8 subjects. Measurements were made for 3 minutes at a time in all the cases. Discussion: In the constellation graphs, the physio-psychological condition is better when the line is closer to the left and poorer when it is closer to the right.
Subject No.1 had a normal physio-psychological condition from morning to evening, but the condition was better in the morning than in the evening, the order being morning>midday>evening. The physio-psychological condition of Subject No. 2 was very good from morning to evening, but the trend was evening> midday>morning. Subject No. 3 had a normal physio-psychological condition from morning to evening and the trend was evening>midday>morning. Subject No. 4 had a normal physio-psychological condition but the condition at midday was better than in the morning or evening. Subject No. 5 cannot be considered to have been in a good condition at any time of the day, from morning to evening. But the condition was relatively better at midday compared to morning or evening. Subject No. 6 was in a good condition in the morning and evening but not at midday. Subject No. 7 showed the same trend as No. 5 but had more subtle changes. Subject No. 8 was fine in the morning, slightly sluggish at midday and not in a good condition in the evening.
Fig. 3 Changes in physio-psychological index in firm employees during a working day (morning, midday and evening)
Note: On reaching office (morning): Yellow While working (midday): Red When leaving office (evening): Green
D. Changes caused by decline in communication skill with ageing Subjects: 179 persons (139 females and 40 males) aged 65 to 100 (mean: 83.4) Measuring procedure: Temperature, systolic and diastolic blood pressure and pulse rate were measured before measuring pulse waves. Photoplethysmograms were recorded for 3 minutes.
For estimating the communication skill of aged persons, we used data of Activities of Daily Living (ADL) indices recorded by health care professionals who were looking after the subjects in an old people’s home. The communication skill was assigned to one of the three levels: a. Be able to communicate normally; b. Be able to communicate to some extent; and c. Hardly or disable communicate. Representation of results: Measured results: As shown in Figure 4, the Lyapunov exponent decreased with decline in communication skill. For this Figure, all the subjects were grouped into one of the 3 categories of communication skill and sorted within each group according to the values of the Lyapunov exponent, and 10 subjects closest to the median value of each group were selected and are shown in the Figure. Discussion: The results show that the value of the physio-psychological index declined with decline in communication skill.
Fig. 4 The relationship between communication skill and the Lyapunov exponents of the time series
E. Interpretation of the results In this study the temporal changes of Lyapunov exponents of the time series, which was used as a physio-psychological index, is taken as a measure of mental immunity(mental toughness. Mental immunity here is defined as the adaptability to external environment, communication skill and a certain level of flexibility (divergence). Humans skillfully avoid various changes, contacts and assaults of the external environment. In some cases, they deal with them, cope with them, and maintain their lives while expressing themselves. This is true mental immunity. Just as one becomes sick with the decline in physical immunity, mental immunity may well signify “spiritedness,” which has been so far described vaguely. “Spiritedness” could not be quantified until now. But we feel that we could grasp an image of it in the present study. F.
What we can find out from these measurements？
It is believed that physical immunity is important for humans in order to maintain good health, and that reduced immunity leads to various diseases. We pay attention to our diets, rest or take medicine as needed, and train our body to increase stamina levels so that our resistance to disease increases and we can protect ourselves better. Mental
immunity is also very important for humans, but no methods for studying such a phenomenon are available. Here, we suggest that the value of the largest Lyapunov exponent is related to mental immunity, which is discussed below. G. Mental immunity Mental immunity is associated with our ability to adapt to changes in the external environment, changes that are continuously present in our lives; it also involves our communication skills, capabilities for self-expression, appropriate psychological flexibility (divergence), etc. Through self-expression, human beings maintain their lives by skillfully fending off numerous types of change, contact, and assault from the external environment; they can also confront such influences and try to cope with them. This kind of adaptability constitutes true mental immunity, a phenomenon that constantly changes with respect to degree during our daily lives . Mental immunity is a very important index, and it varies depending on our state of mind. In short, it naturally changes with the emotions that we experience in our daily lives, such as happiness, anger, and sorrow. Mental immunity is always in a state of flux. For instance, when presented with some task, we may at times feel that we cannot actively cope with it; at other times, however, we may welcome the opportunity to take on such a task. Alternatively, we may feel unable to communicate well with a person we do not like, but can enjoy a pleasant conversation with a person whose company we enjoy. Nevertheless, we can say that a person who can proactively face a situation that cannot be avoided has a high level of mental immunity. The value of mental immunity, as a parameter, fluctuates ceaselessly. When the value remains high or low without variation, it is an abnormal state. It tends to remain high continuously under extreme tension or stress, while it tends to remains low continuously during depression and senile dementia. We previously reported that the Lyapunov exponent decreased when communication skills decreased and dementia advanced with age. IV. .CONCLUTION Advancement of computers has made it easy to perform complexity and chaos analysis. We believe that studies on chaotic nature of human body can make much progress in future researches. In our earlier studies, we found that the value of Lyapunov exponent decreased in aged persons with severe dementia. This phenomenon is similar to depressive psychosis. We plan to advance this area of research by obtaining detailed data on the changes in mental immunity with growth from birth to early childhood and also in all sorts of situations that humans have to face in order to live. REFERENCES [1]. Tsuda I, Tahara T, Iwanaga I (1992) Chaotic pulsation in capillary vessels and its dependence on mental and physical conditions. Int J Bifurcation and Chaos 2: 313-324.
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