Participants and recruitment

Participants were recruited from stroke or motor disease patients admitted to a rehabilitation facility between June 1, 2018, and May 30, 2021. These patients were transferred from an acute care hospital to the rehabilitation facility. In order to be included in the study, participants needed to be at least 65 years old and score 24 or higher on the mini-mental state examination (MMSE) [25]. Those with severe immobility, significant memory defects, aphasia, or consciousness disturbance were excluded from the study. Ultimately, 34 patients met the inclusion criteria and provided informed consent to participate. The study protocol was approved by the local ethical committee of Hospital A in Toyonaka, Japan (ethical numbers: 2018–06 and 2019–04). Data collection for each individual began one month after hospitalization to allow participants to become familiar with the hospital's daily schedule.

The daily schedule and environment

The subjects spent their hospitalization following the hospital's schedule. At 7 a.m., the lights came on, and they proceeded to the dining room on the same floor of the ward to have breakfast by 7:30 a.m.. For those who were unable to move independently, hospital staff assisted them in moving to the dining room. After breakfast, they brushed their teeth and used the restroom before returning to their rooms. Between 9 a.m. and 12 p.m., the subjects received one rehabilitation session. During the time outside of rehabilitation sessions, they spent their time lying down or sitting on the bed in their rooms. At 12 p.m., they went to the dining room for lunch. After lunch, they brushed their teeth and used the restroom before returning to their rooms. From 1 p.m. to 5 p.m., two rehabilitation sessions were conducted. During the time outside of these sessions, they rested on their beds or sat in their rooms. At 6 p.m., they had dinner in the dining room, and after brushing their teeth and using the restroom, they returned to their rooms. They settled into bed by the lights-out time at 10 p.m.. Rehabilitation sessions, such as OT and PT, were conducted for 40 to 60 min per session. The subjects engaged in physical activities like stretching, strength training, and walking exercises, as well as activities of daily living (ADL) training. In their rooms, they had the freedom to engage in leisure activities, such as watching TV, listening to the radio, or reading around the bed area. However, for safety reasons, they were not allowed to freely go outdoors.

The illuminance in the hospital was measured using a digital lux meter (HOLDPEAK 881E, HOLDPEAK, Chaina). The illuminance in the hospital rooms was 300–350 Lux at eye level when lying in bed or sitting in bed during the day, and 1–5 Lux at eye level when lying in bed late at night. The illuminance in the platform or corridor of rehabilitation room during the day was 400–450 Lux at eye level when in a chair-sitting or standing position.

Patients’ background characteristics

The data included as basic characteristics: the age, sex, body mass index (BMI), diagnosis, MMSE, presence of sleep medication, presence of psychotropic medication and the motor subtotal rating score of functional independence measure (motor FIM) were obtained from the medical records. The motor FIM consists of 13 items with a 7-point scale for independence [26]. The total motor FIM scores range from 13 to 91 points. The higher motor FIM scores indicate greater the level of ADL independence. The level of ADL independence refers to the degree of independence in activities such as eating, dressing, toileting, changing, bathing, and transferring. The participants were divided into two groups according to the locomotive faculty, either independent or dependent. The former could freely move around the wards by themselves, and the latter required assistance to move around.

Amount of physical activity and sleep state

We used wrist actigraphs to measure sleep status and physical activity levels. We opted for wrist-type devices because waist-type activity monitors can sometimes come off when patients use the restroom, change clothes, or turn over in bed during sleep. Additionally, wearing two devices-one on the wrist and another on the waist-could be physically and mentally burdensome for elderly inpatients. Thus, to minimize discomfort, we chose to measure their physical activity solely with wrist-type actigraphs.

All participants were equipped with a wrist actigraph (Life Microscope, Hitachi, Tokyo, Japan) from Monday to Friday. Since weekends often included family visits that could disrupt participants' regular routines, we decided to collect actigraphy data continuously on weekdays and not on weekends. The actigraph was worn on the non-dominant hand. In cases where the non-dominant hand was paralyzed, the device was worn on the dominant hand instead. This wrist actigraph detects acceleration changes of 0.01 G/Rad/sec or more within the 2 to 3 Hz range. It calculates the amount of activity based on the acceleration change every 1 s and determines exercise intensity as metabolic equivalents (METs) [27, 28]. METs is a units of activity intensity. One METs indicates a resting state in the sitting position [29]. For example, easy work in a sitting position is about 1.5 METs, walking in the house is 2.0 METs [30].

Actigraphy was designed as a tool to monitor sleep conditions, and its accuracy has been confirmed through multiple studies [2, 31, 32]. This device used the Cole-Kripke algorithm to determine whether the person was in a state of sleep or wakefulness [33]. The sleep-related data included nocturnal sleep hours, sleep efficiency, waking time, and bedtime. To calculate sleep efficiency, the time spent in arousals during the sleep period was subtracted from the total nightly sleep time. This value was then divided by the total nightly sleep time. The data collected over five days were averaged to represent one day's worth of sleep information.

Exercise intensity classification assessment of physical activity

The amount of physical activity was classified into three categories according to exercise intensity; 1.0 to 1.5 METs of activity was classified as sedentary behavior (SB), 1.6–2.9 METs as light-intensity physical activity (LIPA), and 3.0 METs and above were defined as Moderate-to-Vigorous Physical Activity (MVPA) [34]. The total SB, LIPA and MVPA hours per day were calculated from the averaged activity data. SB was calculated even after lights-off at night. Daytime SB hours were also calculated, except the hours from 22:00 h to 07:00 h the next morning.

Synthetic periodic regression analysis

The 24-h and 12-h periods were examined for their appropriateness for this participants activity data, the therapists fitted 720 period components ranging from 24-h cycles to 3.3333E-8-h cycles to the subject's activity data. As a result, the 24-h and 12-h cycles fit the original data the best by the multiple contribution rate (R2). The multiple contribution rate, denoted as R2, is a statistical measure used to assess quantitatively how well the analyzed model fits the original data. It takes values between 0 and 1. A higher R2 value indicates that the regression model is better at capturing and explaining the patterns and the variation in the data.

A synthetic periodic regression analysis with 24-h and 12-h cycles was used [22, 23, 35]. The synthetic periodic regression curve is “ y = M + A1・cos (ω1・t–θ1) + A2・cos (ω2・t–θ2).” M (mesor) is the mean value of the synthetic periodic regression curve. A (amplitude) is the difference between the value from the mesor and the maximum or minimum value. A1 indicates the amplitude of the 24-h, and A2 indicates the amplitude of the 12-h periodic regression curve. θ (acrophase) is the phase angle of the maximum value in the periodic regression curve. θ1 indicates the acrophase of the 24-h, and θ2 indicates the acrophase of the 12-h periodic regression curve. The synthetic periodic regression analysis was conducted with advice from a statistics expert who has written many books on statistics in Japan.

The CAR

The CAR was defined by six parameters. The mesor represented the average amount of activity in the day. The maximum value represented the highest level of activity. The maximum phase time represented the peak time of the day's activity [36]. The minimum value represented the lowest level of activity. The minimum phase time represented the calmest time of the day's activity [36]. The range represented the difference between the maximum and minimum values. A higher range value represented a greater balance of rest and activity in a day [36].

Data analysis

The parameters of the CAR and sleep states were compared between the two groups: male and female, cerebrovascular and orthopedic disease, locomotive independent and dependent, and taking hypnotics and non-taking hypnotics. Welch’s test or the Mann–Whitney test was used. The relationship between the parameters of the CARs or sleep states and age, BMI, MMSE, motor FIM, total sleep time, sleep efficiency, waking time and sleeping time was analyzed with Pearson’s correlation or Spearman’s rank correlation.

The relationship between evaluation according to physical activity classification and the parameters of CAR as well as sleep states was analyzed with Spearman’s rank correlation coefficient. Significant correlations were found between SB, LIPA, and MVPA and the mesor, maximum, and range, respectively. For those parameters, single regression analysis with SB, LIPA, and MVPA was performed. Several confounding factors influencing Mesor, Maximum, and Range were examined using statistical methods such as intergroup comparisons and correlation. As a result, nocturnal sleep duration was found to be a confounding factor affecting the relationship between Mesor and either SB or LIPA. Therefore, we conducted multiple regression analyses considering the influence of nocturnal sleep duration in the relationship between Mesor and either SB or LIPA. Since Mesor was a time series data, the presence of autocorrelation using the Durbin-Watson test was verified. A Durbin-Watson statistic value close to 2 indicated no autocorrelation. The IBM SPSS Statistics 28.0.0.0 (IBM Corp., Armonk, N.Y., USA) was used to perform the statistical analyses. A p-value of less than 0.05 was considered evidence for statistical significance.