Objective Characterization of Activity, Sleep, and Circadian Rhythm Patterns Using a Wrist-Worn Actigraphy Sensor: Insights Into Posttraumatic Stress Disorder

Background Wearables have been gaining increasing momentum and have enormous potential to provide insights into daily life behaviors and longitudinal health monitoring. However, to date, there is still a lack of principled algorithmic framework to facilitate the analysis of actigraphy and objectively characterize day-by-day data patterns, particularly in cohorts with sleep problems. Objective This study aimed to propose a principled algorithmic framework for the assessment of activity, sleep, and circadian rhythm patterns in people with posttraumatic stress disorder (PTSD), a mental disorder with long-lasting distressing symptoms such as intrusive memories, avoidance behaviors, and sleep disturbance. In clinical practice, these symptoms are typically assessed using retrospective self-reports that are prone to recall bias. The aim of this study was to develop objective measures from patients’ everyday lives, which could potentially considerably enhance the understanding of symptoms, behaviors, and treatment effects. Methods Using a wrist-worn sensor, we recorded actigraphy, light, and temperature data over 7 consecutive days from three groups: 42 people diagnosed with PTSD, 43 traumatized controls, and 30 nontraumatized controls. The participants also completed a daily sleep diary over 7 days and the standardized Pittsburgh Sleep Quality Index questionnaire. We developed a novel approach to automatically determine sleep onset and offset, which can also capture awakenings that are crucial for assessing sleep quality. Moreover, we introduced a new intuitive methodology facilitating actigraphy exploration and characterize day-by-day data across 49 activity, sleep, and circadian rhythm patterns. Results We demonstrate that the new sleep detection algorithm closely matches the sleep onset and offset against the participants' sleep diaries consistently outperforming an existing open-access widely used approach. Participants with PTSD exhibited considerably more fragmented sleep patterns (as indicated by greater nocturnal activity, including awakenings) and greater intraday variability compared with traumatized and nontraumatized control groups, showing statistically significant (P<.05) and strong associations (|R|>0.3). Conclusions This study lays the foundation for objective assessment of activity, sleep, and circadian rhythm patterns using passively collected data from a wrist-worn sensor, facilitating large community studies to monitor longitudinally healthy and pathological cohorts under free-living conditions. These findings may be useful in clinical PTSD assessment and could inform therapy and monitoring of treatment effects.


Characterizing activity, sleep, and circadian rhythm patterns
Following the pre-processing of the actigraphy data as mentioned in the main manuscript, the aim is to extract characteristic patterns. These can be broadly clustered into three categories: activity, sleep, and circadian rhythm patterns.

Activity patterns
Many studies have focused on extracting Physical Activity (PA) characteristics from actigraphy data, for example see Blume et al. [1]. Traditionally, some of the simplest approaches used are: • M10, computed as the maximum average activity over 10 consecutive hours in a 24h day. It can be thought of as a measure of diurnal activity during the day. It was computed using minute-wise assessments, as described in Blume et al. [1].
• L5, computed as the least average activity over 5 consecutive hours (this was practically used to determine nocturnal activity without relying on estimates of bed times) in a 24h day. It was computed using minute-wise assessments, as described in Blume et al. [1].
• Relative Amplitude (RA) jointly expresses the information contained in M10 and L5, and has the following form: = ( 10 − 5) ( 10 + 5) • Mean Diurnal Activity (MDA), mean activity during the 24h when the participant is not sleeping (see the following section for details on how sleep is detected).
• Mean Nocturnal Activity (MNA), mean activity during bed time. We would expect that groups with pathologies which affect sleep may exhibit elevated levels of MNA compared to healthy controls.
• Mean Activity (MA), mean activity across the 24h day considering diurnal and nocturnal components, computed as in Faedda et al. [2]: where is the averaged 5 minute epoch activity during sleep, is the sleep duration in minutes, is the averaged 5 minute epoch activity during awake hours, is the total time in minutes not spent in sleep.
• Diurnal skewness, is simply the skewness of the probability distribution of activity values during the period from rise time to bed time. It is a standard statistical descriptor which here provides a measure of the asymmetry in the activity.
Skewness quantifies the extent to which a probability distribution differs from a normal distribution.
• Percentile diurnal activity, where we compute the 5 th , 25 th , 50 th , 75 th and 95 th activity percentile from rise time to bed time • Percent nocturnal activity (%NA), which is the ratio of nocturnal activity over the total sum activity.
• Inter-day stability (IS) expresses the stability of activity across days. It lies in the range 0 to 1, with values close to 1 indicating strong coupling with external zeitgebers (sunlight, social interactions). We can reasonably expect that IS would be lower in groups with pathologies compared to healthy controls.
where ̅ ℎ is the mean activity sampled over instances, is the activity at the th minute of the day, and ̅ is the overall average activity. We used the classical definition for IS taking averages over 1 hour, and also over 1 hour with 30 minute overlap.
• Intra-day variability (IV) quantifies the fragmentation of the diurnal rhythm and is complementary to IS.
where is the number of samples used to analyse the variability for each day that we have recorded data. Here we used = 1440 (using the minute-wise summarized activity), = 24 (using 1-hour summarized activity), and = 48 (using 1-hour summarized activity with a 30 minute window overlap).
• Time dependent Coefficient of Variation (TD-COV), measures the variability across epochs during the period from rise time to bed time, and is computed as: We also borrow standard generic concepts from other fields to introduce new actigraphy measures: the Teager-Kaiser Energy Operator (TKEO), defined in Eq. (6), and the Root Mean Squared Successive Differences (RMSSD), defined in Eq. (7)).
Specifically, we introduce the following new activity measures: • Activity TKEO, computing the variability of the time series in 5 minute and 30 minute intervals from rise time to bed time. The TKEO has the property of quantifying both amplitude and frequency variation in the time series, and has worked across different applications [3]. Finally, we computed the ratio of diurnal activity over the overall activity: where is the number of samples from rise time to bed time, and is the number of samples during sleep. used it both to evaluate the entire time series (using all days) computing CMSE at 5, 30, 60, 120 minutes, and also to evaluate the complexity of the activity separately for each day at 5, 30, and 60 minutes.

Sleep patterns
Having extracted the segments corresponding to sleep for each day using the algorithm described in the preceding section, we computed the following: • Sleep onset, the time detected of (nocturnal) sleep start.
• Sleep offset, the time detected of (nocturnal) sleep end.
• Number of awakenings, number of times detected that nocturnal sleep was interrupted.
• Wake After Sleep Onset (WASO), average time (in minutes) required to go back to sleep after wake, if awakening occurred.
• Sleep duration, the difference between sleep offset and sleep onset minus interim time awake (total duration of awakenings).
• Sleep entropy, the entropy of activity using only the segment marked as sleep time (in general, entropy quantifies the uncertainty (variability) in the data).
• Percentile sleep activity, where we compute the 5 th , 25 th , 50 th , 75 th and 95 th activity percentile from sleep onset to sleep offset.

Circadian rhythm patterns
Circadian rhythms impose an approximately 24-hour cycle in the physiological processes of humans, and sleep can be considered to be a consequence of circadian rhythms. Strictly speaking, circadian rhythms are endogenous, entrainable processes; chronobiologists prefer the use of the more general term diurnal rhythm to describe self-sustained, repeated processes with 24h oscillations when their endogenous nature cannot be confirmed. We will use the former expression as an umbrella term for simplicity since we use both intrinsic processes (temperature) and activity to express daily variability measures which we may expect to have a roughly 24h repeating pattern.
Specifically, the following measures were computed: • Sleep zenith temperature, the maximum temperature during sleep.
• Sleep zenith temperature time, the time that the maximum temperature during sleep occurs.
• Sleep nadir temperature, the minimum temperature during sleep.
• Sleep nadir temperature time, the time that the minimum temperature during sleep occurs.
• Sleep temperature range, the difference between the maximum and minimum temperature values during sleep.
• Sleep onset phase, the difference in sleep onset over two successive nights.
• Sleep offset phase, the difference in sleep offset over two successive nights.

Summarizing the extracted patterns
Ultimately, we characterize each Geneactiv recording with 49 patterns (measures) across each of the days data was collected, and hence characterize each participant. The aim is to capitalize on those patterns to get a better understanding into how groups differ and potentially get a tentative insight into PTSD using these objective data to complement selfreported scores. Table 2 in the manuscript provides a succinct summary of the extracted characteristics along with their description (for convenience and easier reference presented here as Table S1).

Additional results
This section presents additional results to complement findings reported in the main manuscript.

Sleep detection
Here we present some further illustrations to demonstrate the accuracy of the proposed   Subsequently, we present an example from a participant where it could be argued that sleep appears to be erroneously reported on the basis of the actigraphy data (see Fig. S2).
The algorithm has detected periods where the actigraphy visually looks very much like standard sleep (e.g. compare with Fig. S1). In contrast, periods that the participant has marked as sleep appear to be dominated by movement, sharp decreases in temperature, and non-zero light for considerable time, all indicators of standard physical activity.
Although this is an extreme example of major disagreement between the algorithmic estimate and the self-reported sleep in the current dataset, it demonstrates a possible problem with self-report and the reliability of certain sleep entries they are when they differ drastically from typical sleep actigraphy patterns.   Table S2 provides an overview of some indicative descriptive statistics of the variables that are reported in Table 4 of the manuscript. We provide a more detailed overview of the descriptive statistics for all variables used in the study in the additional Supplementary Material 'Statistical comparisons of features across cohorts.xlsx', which is an Excel file. The entries are summarized in the form median ± interquartile range. Statistical comparisons of the results and the reporting of correlation coefficients appear in Table 4 of the manuscript.