People with multiple sclerosis (pwMS) are less physically active compared to healthy individuals (Motl et al., 2005; Ng and Kent-Braun, 1997; Blikman et al., 2015; Motl et al., 2008; Bollaert and Motl, 2019; Rietberg et al., 2014). While early work documented these changes via self-report, in recent years, wearable sensors have been used to quantify daily-living activity and mobility outcomes in pwMS (Shema-Shiratzky et al., 2020; Dasmahapatra et al., 2018; Sandroff et al., 2012). These efforts have produced valuable insights into the effects of MS on the quality of life of patients and on the association of physical activity levels with disease severity and disability level (Motl et al., 2008; Bollaert and Motl, 2019; Rietberg et al., 2014). However, most of the work quantifying and studying physical activity in free-living environments has focused on the amount of activity, rather than the patterns of activity and active-sedentary behavior throughout the day.

The fragmentation of rest and activity patterns is altered in a wide variety of clinical conditions. For example, rest-activity patterns are altered in preclinical Alzheimer's disease (Musiek et al., 2018), Parkinson's disease (Chastin et al., 2010), and older adults with cognitive impairments (Lim et al., 2012) and with fatigability (Palmberg et al., 2020). Activity fragmentation was also previously associated with mortality rates in older adults (Di et al., 2017; Wanigatunga et al., 2019; Zuurbier et al., 2015). Together, these studies suggest that there is clinically relevant information that can be gleaned from investigating how physical activity changes during the day and that fragmentation provides a measure that is, at least theoretically, independent of the total volume of activity (e.g., see Fig. 1 in the supplementary material, SM).

Due to the impaired mobility of pwMS, which potentially affects the ability to sustain physical activity for long periods, one can speculate that the fragmentation patterns are altered in pwMS. In their pilot study, Blikman et al. reported differences in the active-sedentary patterns of fatigued pwMS compared to healthy controls (Blikman et al., 2015). Although the study was limited to severely fatigued patients, these findings hint at the possibility of extracting potentially valuable information from outcomes related to rest-activity fragmentation in pwMS.

Fractal analysis of human motor activity provides an alternative means of examining the changes in physical activity during the day. This approach evaluates correlations in the temporal fluctuations of the activity signal over varying time scales (Hu et al., 2004; Scafetta et al., 2009). When applied to recorded accelerometer data, measures based on fractal analysis predict frailty, disability, and mortality (Li et al., 2019) as well as cognitive decline and Alzheimer's disease (Li et al., 2018) in older adults. Li et al. found that the degradation of motor fractal regulation, which occurs in association with aging (Hausdorff et al., 1997; Hausdorff et al., 2001; Raichlen et al., 2019; Hu et al., 2009), is accelerated in Alzheimer's disease, and that acceleration worsens after diagnosis of cognitive impairment and worsens further after the clinical onset of Alzheimer's dementia (Li et al., 2019). In a pilot study, differences in the scaling exponent derived from the fractal analysis were observed between groups of patients with different self-reported disability level and ambulatory status, and an association with patient-rated walking impairment measures were also observed, with a lower scaling exponent being linked to greater impairment (Sosnoff et al., 2010). These preliminary results suggest that fluctuations in physical activity during the day are not simply noise; rather, they may provide important information about MS-related physical activity patterns.

The circadian rhythm amplitude (the maximum range of daily activity) decreases with aging (Huang et al., 2002) and was associated with an increased risk of developing Parkinson's and Alzheimer's disease (Leng et al., 2020; Li et al., 2020). There is, however, little information about circadian amplitude metrics in pwMS. Nonetheless, due to the general decrease in physical activity that is associated with disease progression among pwMS, a relationship similar to what is seen in older adults might emerge in pwMS. Preliminary evidence of a negative relationship between circadian amplitude and disability level, as assessed by the Expanded Disability Status Scale (EDSS) (Merkelbach et al., 2011) provides some initial support for this possibility. Together, these findings, along with those related to aging and Parkinson's disease, suggest that measures of circadian activity amplitude could potentially be valuable in the study of pwMS.

To explore these largely unaddressed questions in the context of MS, we evaluated daily-living activity patterns in pwMS and healthy controls. We aimed to (1) identify which fragmentation, fractal, and circadian amplitude measures differ between pwMS and healthy controls, (2) evaluate the relationship between fragmentation, fractal, and circadian amplitude measures and disease severity, and (3) begin to assess the added value of those measures compared to more conventional volume-based measures of physical activity (e.g., signal vector magnitude (SVM)).