Identifying Characteristic Physiological Patterns of Mentally Ill

Patients using Nonlinear Analysis of Plethysmograms

Yuyu Hu, Wenbiao Wang, Takashi Suzuki and Mayumi Oyama-Higa

Department of Systems Innovation, Osaka University, Toyonaka, Osaka 560-8531, Japan

Keywords: Plethysmogram, Mental Illness, Largest Lyapunov Exponent, Autonomic Nerve Balance.

Abstract: We measured the pulse waves of 195 mentally ill patients and 113 healthy students. Using heartbeat

changes, we calculated the values which represent the intensity of their sympathetic and parasympathetic

activities, and the values of their autonomic nerve balance (ANB). In addition, we obtained the largest

Lyapunov exponents (LLE) by non-linear analysis of plethysmograms. Values were analyzed by group. The

results revealed a significant relationship between LLE and ANB. The sympathetic nerve values in the

patient group were significantly higher than those in the student group, whereas the LLE values were

significantly lower. Furthermore, we illustrated the dynamic change in the results for single participants

over several testing times. The measurement of pulse waves is easy and economical and does not put a

strain on the subject. Additionally, these values are likely to provide information that is more accurate than

medical examination obtained from an interview. Our study contributed to the existing methodology in this

field, and future data collection and measurement will be carried out. We hope that our study will be useful

for neurologists and psychotherapists in their detection and treatment of mental illnesses.

1 INTRODUCTION

The total number of people suffering from

depression in Japan which was 433,000 in 1996 and

1,041,000 in 2008, has increased to 2.4 times over

the 13 years according to “the patient investigation”

held every three years by Japanese Ministry of

Health, Labour and Welfare. Depression, a mental

disorder marked by sudden feelings of melancholia,

anxiety, and worthlessness, which is closely related

to suicide, has become a serious social problem.

Early detection of depression is therefore

necessary for sustained mental health in everyday

life. Motivated by this urgent need, we examined in

this study how physiological data of depression

sufferers differed from those of individuals in good

health.

This study has succeeded in identifying the

characteristic patterns of mentally disease sufferers

in terms of certain physiological indexes.

Furthermore, a self-check system has been

developed, enabling people to check their status of

mental health in a convenient and economical way.

The next section will describe the experiment

and explain the method, namely, chaos analysis,

which is essential in this study and has been

effectively applied in numerous previous studies.

Then the following section will give the analysis and

results in details.

2 EXPERIMENT AND METHOD

2.1 Subjects

A professional counsellor helped measure the pulse

waves of the mentally ill patients, whose ages and

names of diseases are shown in Table 1. The gender

is undisclosed.

The students’ data were collected from healthy

university students of Kwansei Gakuin University in

Nishinomiya, Japan. They include 42 males and 71

females, with the average age of 19.61 and the

standard deviation of 1.90. Informed consent was

obtained from all participants in the study. Table 1

also presents the number of times the pulse waves

were measured, and the total duration of the pulse

waves measurement in a sub-sample of the patient

group.

Hu Y., Suzuki T., Wang W. and Oyama-Higa M. (2012).

Identifying Characteristic Physiological Patterns of Mentally Ill Patients using Nonlinear Analysis of Plethysmograms.

In Proceedings of the Sixth International Symposium on e-Health Services and Technologies and the Third International Conference on Green IT

Solutions, pages 69-73

DOI: 10.5220/0004474300690073

 SciTePress

Table 1: Partial list of the mentally ill patients included in

the calculations.

2.2 Procedure

After obtaining informed consent, we measured the

pulse waves using a photoplethysmography sensor

(CCI BC2000). The room temperature was 25°C.

Each subject was asked to sit in a chair and keep

his or her eyes open during the measurements, which

were taken using a cuff attached to the left index

finger. For each time of the measurement, the pulse

waves of each subject were measured for at least

three minutes, since the measurement for more than

two minutes is necessary to correctly calculate the

autonomic nerve balance (ANB), which is an

important parameter in our study and will be

explained in Section 3.1.

2.3 Method of Chaos Analysis—The

Calculation of Largest Lyapunov

Exponent

It has been evidenced that time series data with

deterministic chaos can be constituted by fingertip

plethysmograms (Tsuda, Tahara and Iwanaga, 1992).

Let

denote the time series data. By the method of delays,

the phase space is reconstructed, which contains

vectors in the form of

(1)

where τ is a constant delay, d is the embedding

dimension and

(2)

In order to reconstruct the phase space correctly, the

parameters of the delay τ and the dimension d should

be chosen optimally (Abarbanel et al., 1993). In our

study, considering the time series recorded from

fingertip pulse waves, it has been shown that the

optimal choice is τ = 50 ms and d = 4 (Sano and

Sawada, 1985; Sumida et al., 2000).

The largest Lyapunov exponent (LLE) is one of

the essential measures of complexity in the

reconstructed phase space, which reflects the

divergence of the attractor trajectory. Considering

X(t) as the evolution with time from some initial

trajectory X(0), LLE is given by

(3)

where

(4)

and the initial difference vector

(5)

in the phase space. LLE is estimated by applying the

algorithm of Sano and Sawada (1985).

Figure 1 shows the plethysmogram and attractor

obtained from the measurements, and LLE obtained.

Figure 1: Plethysmogram (top), attractor (right) and LLE

(bottom).

Previous studies (Imanishi and Oyama-Higa,

2006; Oyama-Higa and Miao, 2006; Oyama-Higa,

EHST/ICGREEN 2012

Miao and Mizuno-Matsumoto, 2006) have shown

that LLE serves as a significant indicator of mental

immunity. The values of LLE of a mentally healthy

individual fluctuate within a reasonable scope. When

LLE is abnormally high, the mental immunity of the

individual is so strong that he or she is likely to go to

extremes, such as committing crime. On the other

hand, when it is abnormally low, the mental

immunity is so weak that the individual is prone to

mental illnesses.

3 ANALYSIS AND RESULT

3.1 Analysis of Plethysmograms using

“Lyspect”

We analyzed the plethysmograms using a software

called Lyspect, developed by Chaos Technology

Research Lab in Shiga, Japan. Lyspect is able to

perform chaos analysis and analysis of ANB, using

finger plethysmograms as input data.

The top panel shows the pulse wave. In the

middle panel, three semicircles display, from the left,

LLE, blood vessel balance, and ANB, respectively.

Each semicircular graph represents a normalized

scale of 0–10, and a value for each time is shown by

the angle of the line drawn in yellow. The line graph

in the bottom panel shows changes in values for the

low frequency of heartbeat period (LF, in red) and

high frequency (HF, in blue) with respect to time.

To put it concretely, HF is referred to in the scale

of 0.15-0.40 Hz, which reflects the parasympathetic

activity; LF is in the domain of 0.04-0.15 Hz, which

is influenced by both sympathetic and

parasympathetic nerves. ANB is defined as

normalized value:

(6)

ANB < 5 indicates parasympathetic predominance,

and ANB > 5 indicates sympathetic predominance.

The patients in Figures 2 and 3 are diagnosed

with schizoaffective disorder and post-traumatic

stress disorder, respectively. In both graphs, LLE is

low, and ANB is greater than 5.

Notice that the values shown in Figures 2 and 3

are averages obtained through several measurements.

That is, results of several measurement times are

shown in the figures. Through several times of

measurements for each patient, LLE and ANB tend

to be stable, so we are confident that the results of

the repeated measurements are reliable.

Figure 2: Results for patient A (Schizoaffective Disorder).

Figure 3: Results for patient B (Post-traumatic Stress

Disorder).

3.2 Identification of Characteristic

Patterns in Mentally Ill Patients

The values of LLE and ANB are found to reflect

data characteristic of the mentally ill patients. Figure

4 shows the relationship between LLE and ANB in

the patient and student groups.

Figure 4: The relationship between LLE and ANB [All the

data are shown. Mental ill patients’ group (red) and

healthy students’ group (blue) are shown with an

establishment oval of 95%].

Identifying Characteristic Physiological Patterns of Mentally Ill Patients using Nonlinear Analysis of Plethysmograms

3.3 Autonomic Nerve Balance Analysis

Figure 5 shows the results of a one-way ANOVA on

the ANB.

Figure 5: Comparison of the average ANB and LLE

between a mentally ill patient and a healthy individual.

3.4 Detection of Mental Illnesses using

Pulse Waves

Figure 6 shows the rules for distinguishing mentally

ill patients from mentally healthy individuals using

partition analysis.

Figure 6: The distinction rule for the mentally ill patients

and mentally healthy individuals using partition analysis.

Recall that the total sample size is 308, including

195 mentally ill patients and 113 mentally healthy

students. For partition analysis,

Rule 1. LLE ≥ 4.84: the number of mentally

healthy students is 87;

Rule 2. 3.73 ≤ LLE < 4.84: the numbers of

mentally healthy students and mentally ill patients

are 23 and 15 respectively;

Rule 3. LLE < 3.73 and ANB < 5.40: the

numbers of students and patients are 3 and 21

respectively;

Rule 4. LLE < 3.73 and ANB ≥ 5.40: the number

of patients is 158.

3.5 Discriminant Analysis

In this subsection, discriminant analysis is carried

out with the help of statistical software.

Table 2: Discriminant weights of the variables.

Function

LLE 0.911

ANB -0.436

Table 3: Discriminant loadings of the variables.

Function

LLE 0.900

ANB -0.414

Tables 2 and 3 show the discriminant weights

and discriminant loadings respectively, which reflect

the contribution of the two variables to the function.

Table 4: Unstandardized coefficients.

Function

LLE 0.696

ANB -0.306

Constant -0.734

Table 4 shows the unstandardized coefficients,

which enabled us to directly calculate the

unstandardized function:

(7)

Table 5: Unstandardized canonical discriminant functions.

V Function

0 -1.221

1 2.108

Table 5 shows the unstandardized canonical

discriminant functions evaluated at the group means,

where V is a two-valued notation, which equals 0 or

1, representing a mentally ill participant or a healthy

participant, respectively; the right side shows their

magnitudes. Thus, using the number of mentally ill

and healthy participants, the critical value can be

obtained:

EHST/ICGREEN 2012

(8)

We judged whether a participant suffered from

mental illnesses by comparing the values of f and y:

the participant was classified as mentally ill if f < y

and as mentally healthy if f > y.

Table 6: Classification results.

Predicted

group

membership

Total

0 1

Original Count 0 190 5 195

1 10 103 113

Percentage 0 97.4 2.6 100.0

1 8.8 91.2 100.0

Cross-

validated

Count 0 189 6 195

1 10 103 113

Percentage 0 96.9 3.1 100.0

1 8.8 91.2 100.0

Table 6 presents the classification results for the

participants. We were able to correctly classify

97.4% of the mentally ill patients and 91.2% of the

mentally healthy students in our sample.

4 CONCLUSIONS AND REMARK

To conclude, this study has identified characteristic

physiological patterns of mentally ill patients using

pulse waves measurement. From the results of the

analysis, we obtained a significant difference

between these groups in LLE and ANB.

Notably, this system can display the activity of

sympathetic nerves, parasympathetic nerves, and

LLE at the same time, which enables us to assess the

mental status of patients when measuring their

fingertip pulse waves. Furthermore, the

methodology is simple and the operation is

economical. It can be used for early detection of

mental illnesses.

We hope that this system can contribute to

promoting better medical care. We will strive to

collect and analyze more data of mentally illness

sufferers, and intend to continue relevant studies in

the future.

ACKNOWLEDGEMENTS

We are deeply thankful to Dr. Oshima, president and

psychological counsellor at the Insight Counselling

Corporation (Tokyo, Japan) who helped provide the

pulse waves measurements of the mentally ill

patients and diagnoses of their mental illnesses. We

thank Dr. Shomura who provided the English names

of the mental illnesses.

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Identifying Characteristic Physiological Patterns of Mentally Ill Patients using Nonlinear Analysis of Plethysmograms