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4. Discussion

4.1 Multivariable Ethoscope Data Follows a Circadian Cycle

Results from section 3.1.1 have shown that all Ethoscope variables follow a circadian cycle. The mean velocity variable directly relates to the activity level (or mobility), and flies with mean velocity below a certain threshold is generally considered as asleep. It is hence found that Drosophila typically sleep during mid-day and the first few hours of the night. Sleep during the day has also been seen in previous fly studies and is known as the mid-day siesta 1, which is thought to be an adaptive response to minimize exposure to heat 2 3 4. Flies also exhibit sleep behaviours during late-night (around hour 20-22) followed by a few hours of low-level activities.

Using the mean velocity as a reference, it is seen that x and phi also follow a similar pattern. Flies tend to be located at x positions around 0.2-0.3 during mid-day siesta and early-night sleep, which is roughly where the food is placed. It is likely because sleep happens after feeding, as food consumption has been thought to induce sleepiness 5. The phi angle is also generally lower (i.e., closer to horizontal) during sleep and consistently higher when active, which is likely due to increased turning when walking back and forth in the tube. Size-related variables including w, h and area all have slightly decreased values during mid-day siesta. Shrinking in size due to fly crouching down when resting has also been observed by previous research 6. However, these measures during the night are less reliable for interpretation in this study as the oval masks are not well assigned in dim lights.

Although the x and phi variables may be useful in distinguishing sleep and awake states, they seem to be less discriminable when trying to identify deep and light sleep stages according to the classification results in section 3.1.2. This study therefore focused on univariate analysis of the mean velocity variable to explore potential indicators of sleep stages.

4.2 Sleep Depth and Burstiness of Activity

In this study, a different way of identifying sleep was developed which allows short bursts of activity during sleep. This is to potentially include more light sleep, that has higher activity levels, into our time series data for analysis. Sleep sessions are extracted from different parts of the day using this method, and results from section 3.3.2 showed that sleep can be relatively well-differentiated between mid-day, early-night and late-night. Time series for mid-day and early-night sleep are generally organised into single clusters, while late-night sleep data is more distributed with a range of characteristics. The hypothesis is that the majority of sleep during early-night is at a deeper stage and the majority for mid-day is at a lighter stage, and both stages can occur during late-night.

Investigation of the time series features in section 3.3.2 revealed that differences between the three classes may be explained by a small amount of simple, location- and spread-dependent features. These top features are also highly correlated and can be narrowed down to a single representative feature: burstiness. Burstiness describes the intermittent short timeframes of activity following long periods of inactivity 7. It is often measured by the Fano factor which is a ratio between the variance and mean of burst counts. The orginal burstiness statistics is proposed by Goh and Barabasi 8 and is defined as

\[ \Delta \equiv \frac{\operatorname{sgn}\left(\sigma_{\tau}-m_{\tau}\right)}{2} \int_{0}^{\infty}\left|P(\tau)-P_{\mathrm{P}}(\tau)\right| d \tau \]

where \(\Delta\) is the burstiness parameter, \(\operatorname{sgn}\) is a function that extracts the sign of a number, \(m_{T}\) and \(\sigma_{T}\) are the mean and standard deviation of \(P(\tau)\), \(P(\tau)\) is the given time series, and \(P_{\mathrm{P}}(\tau)\) is a random, time-independent series that follows an exponential distribution. This equation is adapted by Fulcher and Jones (12) and incorporated into HCTSA with equation

\[ B=\frac{\sigma_{\tau}-m_{\tau}}{\sigma_{\tau}+m_{\tau}} \]

where \(B\) is the burstiness parameter, \(m_{T}\) and \(\sigma_{T}\) are the mean and standard deviation of the time series. For the three classes, late-night sleep yields the highest mean burstiness, and early-night sleep yields the lowest. This suggests that early-night sleep time series have fewer significantly enhanced activity levels, which corresponds to the reduced mobility known for deep sleep 9 10. In addition, sleep has also been associated to increased arousal thresholds (or decreased sensory responsiveness) 6 11, and previous work by the Gilestro Lab Group has shown that late-night sleep exhibits the greatest response to stimuli compared to mid-day siesta and early-night sleep 12. This is concordant to the fact that late-night sleep has the highest burstiness. However, responsiveness of early-night sleep seems to be greater than siesta, which contradicts the order of their burstiness values. More work needs to be carried out to determine whether the arousal threshold is correlated to burstiness of activity during sleep. Overall, burstiness may serve as a possible indicator for sleep depth and help to distinguish sleep stages.

4.3 Limitations and Aspects for Improvements

The use of HCTSA for time series analysis has greatly facilitated our exploration for nuances in sleep. However, it also posed many restrictions to the analysis, particularly during the data curation process. First, most HCTSA operations prefers longer time series as inputs, and so sleep sessions are taken in windows of 60 minutes using the more forgiving sleep metric. This excludes shorter sleep periods which may be more typical for Drosophila sleep. One solution is to obtain per-second data from the Ethoscope database but its downloading and analysis would be more time-consuming and not suitable for this short exploratory project. Secondly, it is known for mammals that sleep stages exists in cycles and have varying lengths 13 14, but HCTSA operations return single statistical values for a given time series which may overlook such details. Lastly, HCTSA only allows single-variate analysis, and multivariable analysis that includes other Ethoscope parameters could potentially improve the classification rate.


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