健康支援
第25巻1号 11‑17，2023
doi：10.57438/jshp.20220729̲1

A potentially new evaluation method to visualize rest-activity
rhythm based on inpatient activity amount
Yuki NAKAGAWA １）２），Kaoru YAMANO １），Kazue NODA ２），
Hiroaki NARITOMI ３），Hiroshi FURUKAWA １）

入院患者の活動量を指標とした休息活動リズムを視覚化する可能性のある新しい手法中川友紀１）２）、山野

薫１）、野田和惠２）、成富

博章３）、古川宏１）

Abstract
BACKGROUND：A 24 -hour periodic regression analysis is often conducted for the humansʼ rest-activity rhythm
indexed by activity amount. However, this analysis cannot be said to accurately capture the rest-activity rhythm of
inpatients. OBJECTIVE：We preliminarily developed a new evaluation method to accurately visualize the complex
24 -h rest-activity rhythms of inpatient life. METHODS：Physical activity of one male inpatient was measured. The
periodic regression analysis in a 24 - or 12 -h cycle as well as a synthetic 24 - and 12 -h cycle were applied to the activity
amount data. RESULTS：A periodic regression analysis with only a 24 -h period resulted in y = 1 . 19352 + 0 . 115537
× cos（15・t- 183 . 662）. The multiple contribution ratio（R２）was 0 . 76 . A periodic regression analysis with only a 12 -h
period resulted in y = 1 . 19352 + 0 . 0444696 × cos（30・t- 273 . 522）. The R２ was 0 . 11 . The results of the synthetic
periodic regression curve combining the 24 - and 12 -h periodic components were y = 1 . 19352 + 0 . 115537 × cos（15・t- 183 . 662）+ 0 . 0444696 × cos（30・t- 273 . 522）. The R２ was 0 . 87 . The synthetic periodic regression curves were able
to capture the subjectʼs rest-activity rhythms more accurately. CONCLUSION：The synthetic periodic regression
analysis on the activity amount was able to capture more accurately the rest-activity rhythm of the subject. In the
future, it is necessary to examine the reliability and validity of the rest-activity rhythm based on synthetic periodic
regression analysis by increasing the number of subjects.
Keywords：Circadian rhythm, Physical activity, Periodic regression analysis, Rehabilitation, Patients
１）Faculty of Health Sciences, Osaka University of Human Sciences
1‑4‑1 Shojaku, Settsu-shi, Osaka‑fu, 566‑8501 Japan
大阪人間科学大学保健医療学部
２）Graduate School of Health Sciences, Kobe University
7‑10‑2 Tomogaoka Suma‑ku, Kobe‑shi, Hyogo‑ken 654‑0142 Japan神戸大学大学院保健学研究科
３）Department of Rehabilitation, Kyowakai Medical Corporation Senri-chuo Hospital
1‑4‑3 Shinsenri Higashimachi, Toyonaka-shi, Osaka‑fu 560‑0082 Japan
医療法人協和会千里中央病院リハビリテーション部門
Corresponding author：Yuki Nakagawa Faculty of Health Sciences, Osaka University of Human Sciences
1‑4‑1 Shojaku, Settsu-shi, Osaka‑fu, 566‑8501 Japan
Phone：06‑6383‑6441 Fax：06‑6383‑6472 E-mail：yuki-nakagawa@kun.ohs.ac.jp
Received：2022.3.18，Accepted：2022.7.29

J‑STAGE Advance published date：2023.1.12

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Introduction

recent years, the evaluation of rest-activity rhythms

Humans have a 24 -h daily rhythm. We generallyusing periodic regression analysis of activity amounts

awaken in the morning, perform activities during thein a 24 - or 12 -h cycle has become the main method. 11 - 13）day, and sleep at night. Various human physiologicalHowever, the evaluation of rest-activity rhythms bysystems also have 2 4 -h rhythms, such as blood

periodic regression analysis of the 24 - or 12 -h cycle

pressure, heart rate, and body temperature. 1）

caused a gap between the subjectʼs actual rest-activity

Various health problems occur when rest-activity

rhythm and the analytical results. The results in therhythms are disrupted. Lifestyle disruptions lead toperiodic regression analysis of the 24 -h or 12 -h cycle

increased mortality 2）and increased susceptibility to

do not fit the original data well. Notably, there is a wide

ischemic heart disease 3）and metabolic syndrome. 4）

gap in the time of peak activity（acrophase）between

Rest-activity rhythms reportedly change with age.

the original data and the analysis result. The reason

Since the elderly go to bed earlier and awaken earlier,

may be that humans do not simply have only one cycle

their rest-activity rhythms advance in phase andof daily activity. 14 , 15）In addition to the 24 -hour cycle,

5）decrease in amplitude. Such age-related changes inhuman daily activity also has a 12 -hour circasemidian

rest-activity rhythms may be among the causes ofrhythm. 14 , 15）Therefore, it is essential to develop a system

the increased prevalence of cardiovascular diseases

that can accurately evaluate both rest-activity rhythms

due to aging. Therefore, it is important to accuratelyof the 24 -h and 12 -h cycle, simultaneously. This study

understand the rhythm of human life and restore an

aimed to identify a new evaluation method for complex

appropriate rhythm to maintain health and prevent

human rest-activity rhythms and accurately visualize

various diseases. In addition, people with dementia

human rest-activity rhythms.

have decreased daily activities, including an increase
Materials and Methods

in nighttime arousal and a gradual decrease in daytime
6）

arousal. As dementia progresses, irregular restactivity rhythms worsen further, 6）and if nighttime

As a preliminary study, only one subject was

wakefulness leads to nighttime wandering, caregiverincluded in this study. We used the data of one patientburden increases. To reduce caregiver burden andwith a cerebellar tumor who had been admitted tocorrect disordered rest-activity rhythms, it is important

Hospital A in Japan for more than one month. The firstto accurately understand the daily rhythms of people

criterion for the selection of the subject was normal

with dementia, such as the time of day when they are

cognitive function with a cut-off score of 24 points ormost active and the time of day when they are mosthigher on the Mini-Mental State Examination. 16）The

likely to sleep.

second criterion was absence of delirium, meaning that

There are currently several methods for assessing

the patient was able to live in accordance with therest-activity rhythm, including self-administeredhospitalʼs daily schedule. Moreover, the subject did not

7）

perform independent training irregularly because thesubjective assessments using questionnaires,
8）electroencephalography（EEG）, and activity-basednecessary exercise was secured by physical therapy

assessments. 9）However, self-administered methods are（PT）and occupational therapy（OT）. The patient

unreliable for collecting data from patients who are

was transferred to our hospital for PT and OT after

elderly and have dementia and do not accurately assesspassing the acute stage of the cerebellar tumor. He

their 24 -h rest-activity rhythms. EEG cannot evaluate

was an 81 -year-old man who was able to walk with aa subjectʼs actual rhythm of life because it is difficult

cane. The content of the study was explained to him,

for the subject to lead a normal life while wearing theand he agreed with the ethical considerations before

device. The evaluation method based on activity amountevaluation. The study was approved by the hospitalʼs

is quantitative and can evaluate the actual living

ethics committee（approval number : 2018 - 06）.

conditions. However, simply looking at the averageamount of daily activity or the maximum or minimum
values does not evaluate the rest-activity rhythm.

The subject wore a wristband-type life recorder,

10）

In

a Life Microscope（manufacturer : A&D, Inc.）, to
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collect data on his physical activity and sleep status

multiple contributions. The periodic regression curve

17 , 18）

The device was a 3 -axis accelerationfor 24 h was expressed by the equation y = M + A

wristwatch lifestyle monitoring device that calculatescos（ωt - 㸦）. From the equation, we could obtain three

for 7 days.

exercise intensity as metabolic equivalents（METs）.

19）

parameters of the rest-activity rhythm : mesor（M）

Sleep status was automatically determined using

was the mean value, amplitude（A）was the value froman automatic sleep-wake discrimination algorithm

the mesor to the maximum or minimum value, andproposed by Cole et al.

20）

Because this device was notacrophase（㸦）was the phase angle of the maximum

water-resistant, it was removed during bathing. The

value in the cosine curve. The acrophase wassubject was asked to write down his bed and waking

converted to time, which was defined as the maximum

times on a behavioral record sheet.

phase time. The phase time at which the minimum

The subject was asked to live according to his usual

value was taken was called the minimum phase time.

daily schedule. His morning schedule consisted ofSecond, considering that humans do not operate in a

waking up at 6 : 00 a.m., getting ready for the morning

single cycle of 24 h per day, but in two 12 -h cycles, 14 , 15）such as changing and dressing after the lights came on

we performed a cyclic regression analysis in a single

at 7 : 00 a.m., and having breakfast in the dining room

cycle of 12 h to find the best-fitting cyclic regression

at 7 : 30 a.m. After breakfast, he returned to his room

curve. 13）The 12 -h cyclic regression curve was shownand spent time lying in bed or watching TV until hisby the equation y = M + A cos（ωt - 㸦）equation. Frommorning physical and occupational therapy sessions

the equation, we could obtain three parameters of thebegan. PT and OT were conducted 40 min to 1 h

rest-activity rhythm : mesor（M）, amplitude（A）, andbetween 9 and 12 oʼclock, during which muscle strength

acrophase（㸦）. The acrophase was converted to time,training and gait training were performed with thewhich was defined as the maximum phase time. The

therapists. Afterwards, he returned to his room to lie

phase time at which the minimum value was taken

down in bed and rest before having lunch in the dining

was called the minimum phase time.

room at 12 : 00 . After lunch, he lay down to rest. The

Third, considering that humans have both a 24 - andafternoon schedule consisted of a second PT and OT

12 -h cycle, 14 , 15）we performed a periodic regression

session after 1 : 00 p.m., followed by a third PT and OT

analysis with a synthetic periodic regression thatsession after a break of approximately 1 h. The patient

combined a 24 -h cycle with a 12 -h cycle to obtain theleft his room at 6 : 00 p.m. to eat dinner in the dining

best-fit periodic regression curve. 21 , 22）The synthetic

room. After dinner, he returned to his room, changed

periodic regression curve was shown by the equation

his clothes, and brushed his teeth. The patient went toy = M + A 1 cos（ω 1 t - 㸦 1）+ A 2 cos（ω 2 t - 㸦 2）,

bed after the lights were turned off at 10 : 00 p.m. The

where the parameters of the 2 4 -hour cycle were

subject followed a similar schedule for the 7 -day data

the amplitude A 1 and the acrophase 㸦 1 , while thecollection period. Bathing was provided twice during

parameters of the 12 -h cycle were the amplitude A 2

the week and lasted 20 minutes each time.

and the acrophase 㸦 2 . The mean mesor value of thesynthetic periodic regression curve was M. The point

For the subjectʼs 7 -day activity METs value data,

occupying the highest value in the synthetic periodic

the average value of the data at the same time wasregression curve was the maximum value, and thecalculated for each minute. Periodic regression analysis

time at which the maximum value was taken was

was applied to the moving METs average. Periodic

the maximum phase time. The point that occupies

regression analysis was first performed for a single

the lowest value was the minimum value, while the

24 -h period and the best-fit periodic regression curve

minimum value was taken as the minimum phase time.

was obtained.

11 , 12）The percentage of agreement of

The range was defined as the maximum value minus

the periodic regression curve with the data of thethe minimum value.

original METs values was calculated using the multiple
contribution rate（R 2）.12）The significance of the periodic

Results

regression equation was confirmed by the results of

The first was a periodic regression analysis with
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only a 24 -h period, and the periodic regression equation
resulted in y = 1.19352 + 0 .115537 × cos（15・t-183 . 662）.
The mesor was 1 . 19 with an amplitude of 0 . 12 , theacrophase was 183 . 7 , the maximum phase time was
12 . 24（12 :14 p.m.）, and the minimum phase time was0(7V0 . 24（0 :14 a.m.）. The multiple contribution ratio（R 2）was
0 . 76（Table 1, Figure 1）. The test results of the periodic
regression equation were significant（p < 0 . 001）.

0HDVXUHGYDOXHVKSHULRG

Table 1. Measured physical activity（METs）and 24 - and 12 -h
periodic regression analyses
Mesor [METs]
Amplitude [METs]*1
Range [METs]*2

24-h

12-h

24- and 12-h

1.19

1.19

1.19
Time (h)

1

1

0.12*

0.76

R



2

0.04*

Maximum phase time 12:14 p.m.
2

PHVRU

0.28*

9:07 a.m.
9:07 p.m.
0.11

















Fig. 2 . Measured physical activity（METs）and 12 -h
periodic regression curve.

10:22 a.m.

Third, the result of the synthetic periodic regression

0.87

curve combining the 24 - and 12 -h periodic components

1* 24-h or 12-h periodic regression analysis shows Amplitude.

was y = 1 .19352 + 0 .115537*2 24-h and 12-h synthetic periodic regression shows Range.

0 . 0444696 × cos（30・t- 273 . 522）. The mesor was 1 .19 ,× cos（15・t- 183 . 662）+

the maximum value was 1 . 33 , and the maximum phasetime was 10 . 37（10 : 22 a.m.）, the minimum value was
1 . 05 , and the minimum phase time was 1 . 97（1 : 58 a.m.）.
The range was 0 . 28 . The multiple contribution ratio
（R 2）

0(7V

was 0 . 87（Table 1 , Figure 3）.

0HDVXUHGYDOXHVKSHULRG

0(7V

PHVRU

0HDVXUHGYDOXHV
KKSHULRG

Time (h)
















KSHULRG

Fig. 1. Measured physical activity（METs）and 2 4 -hperiodic regression curve.

KSHULRG

PHVRUSecond, the result of the periodic regression equation of
the periodic regression analysis with only a 12 -h period
was y = 1.19352 + 0 . 0444696 × cos（30・t- 273 . 522）.The
mesor was 1.19 , the amplitude was 0 . 04 , the acrophase

Time (h)was 273 . 5 , the maximum phase times were 9 .12（9 : 07

Fig. 3 . Measured physical activity（METS）and 24 h and
12 h periodic regression curve.

a.m.）and 21 . 12（9 : 07 p.m.）, and the minimum phasetimes were 15 .12（3 : 07 p.m.）and 3 .12（3 : 07 a.m.）. The
multiple contribution ratio（R 2）was 0 .11（Table 1, Figure

Discussion2）. The test results of the periodic regression equation

The results of the 24 -h periodic regression curve

were significant（p < 0 . 001）.

showed that the mesor was 1 . 19 , the amplitude was
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0 . 12 , the maximum phase time was 12 : 14 p.m., and thethey have a simple cycle of two 12 -h periods.

2minimum phase time was 0 : 14 a.m. The R indicatesConsidering that human activity has a 24 -hour cycle

the degree of agreement between the original data

and a 12 -hour cycle, 14 , 15）we constructed a synthetic

and the periodic regression curve. Because the R 2 wasperiodic regression curve that combines the 24 -h and

0 . 76 , only 76 % of the original data could be used to

12 -h periodic regression curves. The results of theshow the rhythm of the subjectʼs activity in the 24 -hsynthetic periodic regression curve showed that theperiodic regression curve. The peak of the activity ofmesor was 1 . 19 , the range was 0 . 28 , the maximum

the original data comes at 10 : 00 p.m. The maximum

value was 1 . 33 , and the maximum phase time atphase time of the 24 -h period regression curve, that is,

the maximum value was 10 : 22 a.m., the minimum

the peak of the activity, is approximately 12 : 15 p.m.

value was 1 . 05 , and the minimum phase time at the

The peak of the activity of the original data and thatminimum value was 1 : 58 a.m. The R 2 of 0 . 87 indicatedof the 24 -h cyclic regression curve deviate from eachthat the synthetic cyclic regression curve showed 87 %other by approximately 2 h, and the result of the 24 -hof the original data in the subjectʼs activity rhythm.

cyclic regression curve is not consistent with the data

When the resulting graph was compared with theof the original subjects. In other words, the 24 -h cycle

subjectʼs routine, the synthetic periodic regression

regression curve does not accurately capture the daily

curve also had a steep upward curve at that timerhythms of human activity. Humans did not have ain accordance with the 6 : 00 a.m. waking, 7 : 00 a.m.

14）This could be the rationale thatmorning preparation after turning on the lights, andthe 24 -hour cyclic regression curve cannot accurately

7 : 30 a.m. breakfast. Then, in accordance with the

explain the rest-activity rhythm of human activity.

rehabilitation at 9 : 00 a.m. to 10 : 00 a.m. and lunch atsimple 24 -hour cycle.

14 , 15）We

12 : 00 p.m., rehabilitation at 1 : 00 p.m. to 2 : 00 p.m. andcalculated a 12 -h cycle regression curve. The results

3 : 00 p.m. to 4 : 00 p.m., a mountain peak was created inof the 12 -hour cycle regression curve showed thatthe synthetic periodic regression curve that descended

the mesor was 1 . 19 , the amplitude was 0 . 04 , and thegently in the evening. This was followed by a gradualmaximum phase times were 9 : 07 a.m. and 9 : 07 p.m.,

downward curve that coincided with dinner at 6 : 00 p.m.

Humans have 12 -h circasemidian rhythm.

2respectively. Because the R is 0 . 11 , only 11 % of theand a steep downward curve with bedtime after theoriginal data could show the rhythm of the subjectʼs

removal of lights at 9 : 00 p.m. The valley phase time

activity in the 12 -h cyclic regression curve. On theof around 02 : 00 a.m. occurred during the nighttime

resulting graph, the peak of activity in the original
data came at 10 : 00 a.m. The maximum phase time of
the 12 -h periodic regression curve, that is, the peakof activity, was approximately 9 : 00 a.m. and 9 : 00 p.m.
The peak of activity in the original data and the firstpeak of activity around 9 : 00 a.m. in the 12 -h cyclic0(7V

regression curve deviated by approximately 1 h. The
second peak of activity in the 12 -h cyclic regression

0HDVXUHGYDOXHV
KKSHULRG

9:00-12:00 a.m.
PT or OT once

curve was approximately 9 : 00 p.m. However, around9 : 00 p.m. is the time when people lie down to sleep,

Lunch
Brecfast

and the original graph shows a gradual decrease in

1:00-4:00 p.m.
PT or OT twice
Dinnerthe amount of activity and no peak in the amount of

Waking up
Going to bed

activity. Therefore, the results of the 12 -h periodic
regression curve did not match the subjectʼs originaldata. In other words, the 12 -h cyclic regression curve
cannot accurately capture the rest-activity rhythm of

7LPH K

human activity. This may be because humans do not

Fig. 4 . 24 - and 12 -h periodic regression curves and thesubjectʼ s daily life schedule.

have the same activity pattern twice per day, nor do
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period before waking up, and the curve rose sharply in

results may become more complicated because thetime with waking at 6 : 00 a.m.（Fig. 4）. The maximum

synthetic periodic regression analysis covers more

phase time at which the maximum value was obtained

parameters than the 24 -h or 12 -h periodic regression

was approximately 10 : 30 a.m. and coincided with theanalyses.

peak activity of the original data. The synthetic cyclic

for each parameter in the synthetic periodic regression.

regression analysis fits the original data of the subjects

This range may be useful in interpreting the results ofbetter than the 24 -h or 12 -h cycle regression analyses.

the synthetic periodic regression analysis easily.

Next stage will determine a normal range

Therefore, the synthetic periodic regression curve wasconsidered able to accurately capture the daily activity

Conclusion

rhythms of the subject.

The synthetic periodic regression analysis could

The method of synthetic cyclic regression analysis

capture the rest-activity rhythms of this subject

by adding a 12 -h cyclic component to the 24 -h cyclic

accurately. In the future, it is necessary to examinecomponent has been used to examine the rhythm of

the reliability and validity of the synthetic periodic

human blood pressure. 21 , 22）This method has been used

regression analysis by increasing the number ofto understand the normal blood pressure rhythm,

subjects.

understand the standard of normal subjects, andexamine the effect of blood pressure medication. 21）

Acknowledgments and conflicts of interest

Since the synthetic periodic regression analysis

The authors are grateful to a statistics teacher.

was conducted for blood pressure, this method is

The authors report no conflicts of interest.

appropriate. The fact that the rest-activity rhythmsof the subjects can be captured more accurately

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