The complexity of daily life walking in older adult community-dwelling fallers and non-fallers

Author’s Accepted Manuscript The complexity of daily life walking in older adult community-dwelling fallers and non-fallers Espen A.F. Ihlen, Aner Weiss, Alan Bourke, Jorunn L. Helbostad, Jeffrey M. Hausdorff www.elsevier.com/locate/jbiomech

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S0021-9290(16)30254-8 http://dx.doi.org/10.1016/j.jbiomech.2016.02.055 BM7620

To appear in: Journal of Biomechanics Received date: 12 September 2015 Revised date: 22 February 2016 Accepted date: 29 February 2016 Cite this article as: Espen A.F. Ihlen, Aner Weiss, Alan Bourke, Jorunn L. Helbostad and Jeffrey M. Hausdorff, The complexity of daily life walking in older adult community-dwelling fallers and non-fallers, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2016.02.055 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Original article:

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The complexity of daily life walking in older adult community-dwelling fallers and non-

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fallers

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Espen A. F. Ihlen1*, Aner Weiss2, Alan Bourke1, Jorunn L. Helbostad1,3, Jeffrey M.

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Hausdorff2,4

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Department of Neuroscience, Norwegian University of Science and Technology, Trondheim,

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Norway 2

Center for the study of Movement, Cognition, and Mobility, Department of Neurology, Tel

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Aviv Sourasky Medical Center, Tel Aviv, Israel 3

Clinic for Clinical Services, St. Olavs Hospital, Trondheim University Hospital, Trondheim,

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Norway 4

Department of Physical Therapy, Sackler School of Medicine and Sagol School of

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Neuroscience, Tel Aviv University, Tel Aviv, Israel

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Word count: 3499

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Address for correspondence:

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Espen A. F. Ihlen

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Department of Neuroscience

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Norwegian University of Science and Technology

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N-7489 Trondheim

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Norway

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E-mail: [email protected]

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Abstract

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Complexity of human physiology and physical behavior has been suggested to decrease with

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aging and disease and make older adults more susceptible to falls. The present study

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investigates complexity in daily life walking in community-dwelling older adult fallers and

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non-fallers measured by a 3D inertial accelerometer sensor fixed to the lower back.

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Complexity was expressed using new metrics of entropy: refined composite multiscale

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entropy (RCME) and refined multiscale permutation entropy (RMPE). The study re-analyses

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data of 3 days daily-life activity originally described by Weiss et al (2013). The data set

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contains inertial sensor data from 39 older persons reporting less than 2 falls and 32 older

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persons reporting two or more falls during the previous year. The RCME and the RMPE were

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derived for trunk acceleration and velocity signals from walking epochs of 50 seconds using

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mean and variance coarse graining of the signals. Discriminant abilities of the entropy metrics

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were assessed using a partial least square discriminant analysis. Both RCME and RMPE

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successfully distinguished between the daily-life walking of the fallers and non-fallers (AUC

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> 0.8) and performed better than the 35 conventional gait features investigated in Weiss et al.

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(2013). Higher complexity was found in the vertical and mediolateral directions in the non-

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fallers for both entropy metrics. These findings suggest that RCME and RMPE can be used to

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improve the assessment of fall risk in older people.

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Keywords: gait, complexity, multiscale entropy, variability, falls, aging, older adults,

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accelerometer

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1.0

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Efforts have been made to develop accurate fall risk assessment tools for older persons

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(Nandy et al., 2004; Oliver et al., 1997; Raiche et al., 2004; Tromp et al., 2001). Features of

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acceleration signals during daily life activities, e.g. lying, sitting, standing and walking, and

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the transition between these activities have shown to differentiate between older adult fallers

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and non-fallers (Iluz et al., 2015; Rispens et al., 2015; Weiss et al., 2013). Aging of the

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neuromuscular system and age-related diseases make older adults less adaptable to changes in

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heterogeneous conditions of daily life activities and more susceptible to falls (Lipsitz, 2002;

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Lipsitz and Goldberger, 1992). The lack of adaptability has been associated with loss of

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complexity and increased regularity in the dynamics of daily life activities (Paraschiv-Ionescu

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et al., 2011).

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Introduction

The complexity of acceleration signals during daily-life walking has previously been

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assessed by entropy analysis (Cavanaugh et al., 2010). The loss of complexity in the

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acceleration signals can be indicated by a more regular, resulting in a decreased entropy

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metric. A decrease in entropy has been found for the variation of minimum toe clearance and

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trunk acceleration during treadmill walking for elderly at risk of falling (Karmakar et al.,

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2007; Riva et al., 2013). Furthermore, higher entropy has been found in the step counts in

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physical active older adults, compared to inactive older adults (Cavanaugh et al., 2010). These

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findings support the hypothesis that functional decline in older people leads to loss of

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complexity in the gait dynamics and consequently reduces the adaptability of daily life

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walking. To date, however, entropy analysis has not been applied to daily living walking and

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its association with fall history among older adults.

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Increased risk of falling in older adults can be seen as a symptom of age-related degeneration of the neuromuscular system that causes functional decline. Entropy analysis 3

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may identify changes in the regularity of the acceleration signals from body-worn inertial

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sensors that might be early warning signs of decline in the gait function of older adults.

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However, no study has compared the performance of entropy analyses of daily life walking in

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distinguishing between elderly fallers and non-fallers. Thus, the main aim of the present study

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is to evaluate how well entropy metrics of daily life walking distinguish between elderly

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fallers and elderly non-fallers. Based on the idea a higher entropy value reflects greater health,

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adaptability and more resilient physiologic processes (Lipsitz, 2002; Lipsitz and Goldberger,

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1992), we hypothesized that acceleration signals from inertial sensor recordings during daily

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life walking would have higher entropy (i.e., are more complex) across multiple temporal

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scales for elderly non-fallers as compared to elderly fallers.

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2.0

Methods

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2.1

Participants and data collection

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Inertial sensor data recorded during daily-life walking, previously studied by Weiss et al.

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(2013), were re-analyzed in the present study. The data can be downloaded at

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www.physionet.org. The data consists of acceleration signals of all of the ≥ 60 seconds

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walking bouts during 3-day data recording of 32 older fallers and 39 older non-fallers (mean

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age: 78.36 ± 4.71 yrs; range : 65-87 yrs) in the anterioposterior (AP), mediolateral (ML)

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and vertical (V) directions (3D-acceleration). Participants reporting at least 2 falls in the year

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prior to testing were considered as fallers; this definition was used to ensure a clear distinction

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between the two groups and to focus on (multiple) fallers and non-fallers, excluding older

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adults who may be in an intermediate, less well defined, and more ambiguous state with

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respect to their fall history. Although the self-report fall questionnaire included questions

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about the causes of the falls and if they resulted in injury, this data was not assessed as part of 4

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this scope of work. The 3D-acceleration signals were sampled at 100 Hz by a small sensor

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worn in an elastic belt over the lower back (DynaPort Hybrid, McRoberts, The Hague,

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Netherlands; 87 × 45 × 14 mm, 74 g); the sensor has range and resolution of ±6 g and ±1 mg,

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respectively.

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2.2

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A threshold-based algorithm was applied to extract the walking bouts within the 3-day

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recordings of the 3D-acceleration signals (Weiss et al., 2011). Walking bouts with a duration

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of at least 60 second (number of bouts per person; mean = 28.3, SD = 17.2, range: 5 to 90)

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were identified, identical to those originally analyzed by Weiss et al. (2013). The walking

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bouts were all divided into 50 seconds (i.e. 5000 samples) walking epochs to provide a

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consistent sample size for the computation of the entropy measures. The 3D-velocity was

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estimated by a numerical integration of detrended acceleration signals. The 3D-acceleration

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signals were detrended using an orthogonal wavelet procedure that preserved intra-step

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variation in the 3D-velocity, but removed inter-stride nonlinear trends (Lin et al., 2012). This

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detrending procedure provides stationary 3D-velocity data which is a necessary assumption

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for entropy measures (Kantz and Schreiber, 2004). The reader is referred to Weiss et al.

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(2013) for further details about the participants, protocols, and pre-processing of the 3D-

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acceleration data.

Preparation of data

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2.3

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Entropies define the average level of irregularity (i.e., complexity) in a time series. The

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regularity of a time series has been suggested to be measured by the Komologorov-Sinai

Multiscale entropy measures

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entropy, but this demands long time series with a low level of noise, which cannot be obtained

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in physiological time series (Kantz and Schreiber, 2004; Kolmogorov, 1958; Sinai, 1959).

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More recently, the approximate entropy (Pincus, 1991), the sample entropy (Richman and

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Moorman, 2000) and the permutation entropy (Bandt and Pompe, 2002) have been proposed

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as measures for short noisy time series from physiological processes. The sample entropy and

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the permutation entropy have later been extended to multiscale entropies that are able to

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quantify aspects of complexity on multiple temporal scales of the underlying dynamics of the

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time series (Costa et al., 2002; Li et al., 2010; Wu et al., 2014). Multiscale entropies

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determine the entropy as a function of scale and thus express how complexity in a time series

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changes with its temporal resolution. Multiscale entropy has assessed the difference in

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complexity of the stride time variation between younger and older adults and in the trunk

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acceleration of older adults (Costa et al., 2003; Riva et al., 2013). However, the original

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computation of multiscale entropies yields errors for small sample size and the robustness of

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results for human gait may be questionable. Wu et al. (2014) recently introduced a refined

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version of multiscale entropy that produces more accurate results for small sample sizes and,

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thus, are more suitable to investigate complexity of daily-life walking. The present study

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compared two different multiscale entropy metrics: 1) The refined composite multiscale

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entropy (RCME) (Costa et al., 2002; Wu et al., 2014), and 2) The refined multiscale

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permutation entropy (RMPE) (Aziz and Arif, 2005; Li et al., 2010). Both RCME and RMPE

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quantify the regularity of the signals on multiple scales, but RCME is influenced by the

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magnitude of the sample-to-sample increments in the signals whereas RMPE quantify the

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magnitude-independent structure. Both entropy measures were applied to trunk acceleration

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and velocity signals in the anterioposterior (AP), mediolateral (ML), and vertical (V)

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directions. Both RCME and RMPE include multiscale analysis that coarse grains the trunk

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acceleration and velocity signals by computing the mean and variance for windows (i.e., 6

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scales) containing τ = 1 to 20 samples (Costa and Goldberger, 2015; Wu et al., 2014; see Eq.

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1 and 2 in Appendix A). The mean provides a low-pass moving average filter revealing signal

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trends, whereas the variance reveals the change in variation around these moving averages.

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Further technical details of the computational steps and parameter settings of RCME and

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RMPE together with Matlab codes used in the present study are provided in Appendix A and

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B, respectively. The improved performance of RMPE, developed for the present study,

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compared to the conventional multiscale permutation entropy is shown in Appendix C.

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2.4

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Median RCME and median RMPE was computed across all walking epochs for each person.

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The discriminatory ability of median RCME and median RMPE was assessed by a partial

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least square discriminatory analysis (PLS-DA), using a backward feature selection procedure

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(see Wold et al. (2001) and Westerhuis et al. (2008) for further technical details on PLS-DA).

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The PLS-DA identifies low-dimensional latent factors from a large number of noisy and

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collinear variables. A response matrix was constructedfor both the RCME and the RMPE for

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trunk accelerations and velocity based on the mean and variance coarse graining (Eq. 1 and

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2), providing a total of eight response matrices. The RCME or the RMPE for scale 1 to 20 in

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the AP, ML, and V directions were combined into to a total of 60 metrics for each matrix. The

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faller and non-faller status of the participants was set as the response variable.

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Discriminatory analysis and statistics

Backward feature selection was performed by the following four step procedure: First,

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the error (i.e., 1 – accuracy) was defined by PLS-DA with a 10-fold cross-validation by

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leaving one of the N = 60 RCME or RMPE metrics out of the response matrix. The maximum

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number of latent vectors to search for in the response matrix was below one-third of the

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number of variables. Second, the excluded metrics that caused the lowest error were removed 7

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from the response matrix, that after the removal contained N – 1 metrics. Third, the first and

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second steps were repeated until all except two metrics had been removed. Fourth, the number

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of metrics that provided the lowest error was selected and the sensitivity, specificity and AUC

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computed. Target projection loading scores of the PLS-DA were used to rank the influence of

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each of the selected metrics in the classification of fallers and non-fallers (Kvalheim and

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Karstang, 1989). A loading score close to -1 or 1 indicates that the metrics distinguish

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perfectly between fallers and non-fallers, whereas a loading score close to 0 indicates no

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distinction.

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3.0

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Figure 1 shows that the RCME’s were higher for the elderly non-fallers compared to the

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fallers for AP, ML and V acceleration and velocity for both the coarse grained mean and the

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variance (see Eq. 1 and 2 in Appendix A). In contrast, Figure 2 shows that the RMPE for

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trunk acceleration in the ML direction was higher for the non-fallers compared to fallers in the

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intermediate and large scales and lower for the non-fallers considering the same scales in the

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V direction (see the middle and right upper panel in Figure 2A). The RMPE for trunk velocity

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in the ML direction also showed scale dependency with larger values for non-fallers at the

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smaller scales and larger values for the fallers at the larger scales (see middle panels in Figure

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2B). Both the RCME and the RMPE based on the coarse grained means were able to classify

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elderly fallers with high precision (AUC > 0.8) using both the acceleration and velocity

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signals (see Table 1). The precision for the coarse grained variance was, however, lower

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(AUC = 0.6 to 0.8). The target projection loading score indicated that the RCME of the V

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direction was most influential in distinguishing between fallers and non-fallers for both

Results

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acceleration and velocity signals and for coarse grained mean and variance (see red bars in

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Figure 3).

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The target projection loading score indicated that the RMPE in the ML direction was

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most influential in distinguishing between fallers and non-fallers for both the mean and

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variance coarse graining of both the acceleration and velocity signals (see green bars in Figure

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4). However, the difference in both RCME and RMPE between fallers and non-fallers was

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most significant for the ML direction (see horizontal black lines and asterix in Figure 1 and 2,

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respectively). In summary, RCME demonstrated a decrease in complexity of trunk

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acceleration and velocity signals for the fallers in the AP, ML and V directions, while the

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RMPE demonstrated decrease in complexity in trunk acceleration and velocity signals in the

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ML direction and increase in complexity in the trunk acceleration and velocity in V direction

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for the fallers.

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--Insert Figure 1, 2, 3, 4--

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--Insert Table 1--

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4.0

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The main purpose of the present study was to evaluate the ability of two multiscale entropy

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metrics to distinguish elderly fallers from elderly non-fallers based on trunk acceleration and

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velocity of daily life walking. The larger RCME and RMPE indicate that the trunk

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acceleration and velocity assessed by the inertial sensor recordings are more irregular and

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complex for the elderly non-fallers when compared to the fallers. This result is supported by a

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recent result by Cone (2015) which indicates that tripping exposure to in-lab gait in younger

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adults improves their reaction to tripping and increases their sample entropy of step width

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variation. The fallers included in the present study were not clinically diagnosed with gait

Discussion

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instabilities or balance disorders (Weiss et al., 2013). Thus, decreases in RCME and RMPE,

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especially in the V and ML directions, may be important features for improvements of early

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fall risk assessment.

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Several studies have shown a close relationship between local dynamic stability of gait

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kinematics, measured by Lyapunov exponents, and increased risk of falling (e.g., Bruijn et al.,

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2013; Rispens et al., 2015). According to mathematical theory based on dynamical systems,

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there should be a close relationship between entropy measures and measures of local dynamic

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instability (i.e., Lyapunov exponents) (Kantz and Schreiber, 2004). A recent study by Ihlen et

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al. (in press) on the same data set supports this relationship indicating higher local dynamic

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instability in the daily-life walking of elderly non-fallers, compared with elderly fallers. These

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findings were in contradiction with previous in-lab gait studies where local dynamic

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instability was higher in healthy older adults compared with healthy younger adults, and

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elderly fallers exhibited higher local dynamic instability as compared to elderly non-fallers

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(Ihlen et al., 2012; Kang and Dingwell, 2003; Lockhart and Liu, 2008). Higher complexity in

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a standardized in-lab setting might reflect neuromuscular noise causing decay in the ability to

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regulate and control the gait. In contrast, higher complexity in daily-life walking may reflect

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better adaptability and adaptation to changing environmental conditions. Thus, these contrasts

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might be explained by a less heterogeneous and complex regulation of the gait dynamics in

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in-lab gait compared to daily life walking.

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The present study found differences between RCME and RMPE as measures of

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complexity. The significantly higher RCME values found for non-fallers in V and AP

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direction vanished when considering RMPE, whereas the differences in ML direction were

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present for both measures. Weiss et al. (2013) have shown that fallers had increased V

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variability, reflecting impaired regulation of the step timing, and decreased ML variability, 10

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indicating less adaptability to gait context in this direction. The main difference between

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RMPE and RCME is that RMPE considers the magnitude-independent structure of the trunk

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acceleration and velocity whereas the RCME also considers the influence of magnitude of the

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signal increments on the structure (Bandt and Pompe, 2002; Richman and Moorman, 2000).

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Thus, RCME indicated that the difference in the complexity of the V and AP acceleration and

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velocity between the elderly fallers and non-fallers are both influenced by increases in signal

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magnitude as well as their structure. In contrast, the RMPE indicated that the differences in

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ML trunk acceleration and velocity between elderly fallers and non-fallers were due to a

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magnitude-independent change in the signal structure. Thus, RCME and RMPE may represent

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different aspects of the complexity of gait variability and may be critical characteristics of

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impaired regulation of step timing and adaptability to the environmental context (Weiss et al.,

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2013). Further, experimental gait perturbation studies as well as studies on physiological

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correlates of gait are necessary to gain further knowledge about the difference in RMPE and

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RCME between elderly fallers and non-fallers and underlying mechanisms for the scale-

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dependent changes in RMPE and RCME.

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and RMPE for the trunk acceleration distinguished between elderly fallers and non-fallers.

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Based on the same dataset, the RCME and RMPE reported in this study performed as good

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and better as the 36 gait features reported in Weiss et al. (2013). This finding was similar to

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what was observed for the 8 phase-dependent local dynamic stability metrics tested in Ihlen et

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al. (2015). This might reflect the close mathematical association between stability and

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complexity metrics. However, the state space reconstruction used to compute the RCME and

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RMPE consider the AP, ML, and V directions individually whereas the local dynamic

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stability metrics combined all of the directions into the same state space. Thus, further

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development of the RCME and RMPE analyses are needed to evaluate state space

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reconstruction methods of the stability metrics used in Ihlen et al. (2015) and more fully

The results in Table 2 and 3 indicate that RCME

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investigate the relationship between the concept of complexity and local dynamic instabilities

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in both in-lab gait and daily life walking.

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The present study introduces both RCME and RMPE as new measures of complexity

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of the trunk acceleration and velocity in daily life walking. RCME and RMPE analysis

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improves the accuracy of the conventional multiscale entropy analysis, especially for short

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time series (< 10 000 samples). Thus, both RCME and RMPE analysis are important

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extensions for analysis of daily life walking because a large portion of walking bouts are of

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short duration (Del Din et al., 2015). However, there are several limitations in the present

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study. First, a single measure of complexity of gait dynamics does not exist. RCME and

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RMPE used in the present study are only two out of a plethora of entropy metrics in the

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literature that claim to measure complexity. Other variants of multiscale entropies have been

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suggested as alternative quantifications of complexity and group differences have been shown

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to be dependent on the choice of entropy metrics (Humeau-Heurtier, 2015; Rhea et al., 2011).

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Further studies are necessary to determine if other variants of the complexity metrics improve

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the discrimination between elderly fallers and non-fallers.

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Second, the present study only investigated the entropy of the acceleration signals for

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bouts of walking. Other entropy measures, like wavelet entropy (Rosso et al., 2001), could

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assess changes in complexity in transitions between activities, like sit-to-stand transitions

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(Illuz et al., 2015). Furthermore, the Lempel-Ziv complexity and normalized information

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entropy have been used to assess the complexity of pattern of activity distribution throughout

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several days (Paraschiv-Ionescu et al., 2011). Further studies should investigate if there is a

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relationship between the complexity of the activity pattern and the structure of the

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acceleration signals of specific activities like walking.

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Third, the present study did not investigate changes in RCME and RMPE for different

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phases of the step cycle or for possible asymmetry in these measures between left and right

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steps. RCME and RMPE of different phases could provide more detailed information about

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possible critical phases within the step cycle where the differences in RCME and RMPE

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between fallers and non-fallers may be at its maximum. Furthermore, patients groups within

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the older cohort with neurodegenerative diseases and stroke might have substantial

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asymmetry in their gait and asymmetry of the RCME and RMPE values for the left and right

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steps might be important for fall risk assessment in these groups. However, these extensions

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of the present study need a robust identification of step cycles and/or internal sensors worn on

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the lower extremities which was not included in the present study.

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Finally, the present study suggests that RCME and RMPE are related to the fall status

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of older adults and might therefore be important to include in future fall risk assessments.

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Several studies indicate that including features of daily life walking improves fall risk

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assessment when compared to assessments and models based on clinical tests and fall history

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(Iluz et al., 2015; Rispens et al., 2015; Weiss et al., 2013). Thus, further application of RCME

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and RMPE in prospective studies on falls is needed to determine their influence in fall risk

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assessments.

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5.0

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Trunk acceleration and velocity signals were more irregular and complex in elderly non-

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fallers compared to the fallers, especially for the refined composite multiscale entropy

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(RCME) in all directions and refined multiscale permutation entropy (RMPE) in the ML

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direction. These results indicate that RCME and RMPE during gait might be important

Conclusions

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indicators of fall risk amongst community dwelling older persons. The present results set the

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stage for follow-up prospective studies in larger cohorts and clinical feasibility studies to

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further assess the potential of these metrics for prediction and outcome assessment.

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6.0

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The long-term recordings on which the present analyses were made are available at

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www.physionet.org, the National Institutes of Health-sponsored Research Resource for

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Complex Physiologic Signals. The Matlab codes for RCME and RMPE is represented in

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Appendix A and B, respectively. The RMPE code is an extension of a code for multiscale

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permutation entropy developed by Li et al. (2010) and available at

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http://www.mathworks.com/matlabcentral/fileexchange/37288-multiscale-permutation-

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entropy--mpe-. The RCME code is an extension of code for sample entropy developed by

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Kijoon Lee and available at http://www.mathworks.com/matlabcentral/fileexchange/35784-

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sample-entropy. This work was funded by the Norwegian Research Council (FRIMEDBIO,

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Contract No. 230435) and in part by the European Commission (FP7 project V-TIME-

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278169 and WIISEL, FP7-ICT-2011-7-ICT-2011.5.4-Contract No. 288878).

Acknowledgments

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Conflict of interest statement

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The authors declare that no conflict of interests is associated with the present study.

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Kang, H.G., Dingwell, J.B., 2008. Effects of walking speed, strength and range of motion on gait stability in healthy older adults. Journal of Biomechanics 41 (14), 2899–2905. Kantz, H., Schreiber, S., 2004. Nonlinear time series analysis (2nd edition). Cambridge, UK: Cambridge University Press. Karmakar, C.K., Khandoker, A.H., Begg, R.K., Palaniswami, M., Taylor, S., 2007. Understanding ageing effects by approximate entropy analysis of gait variability.

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Lipsitz, L.A., Goldberger, A.L., 1992. Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence. JAMA 267, 1806-1809. Lockhart, T., Liu, J. 2008. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 51(12), 1860-1872. Nandy, S., Persons, S., Cryer, C., Underwood, M., Rashbrook, E., Carter, Y., Eldridge, S.,

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entropy and sample entropy. American Journal of Physiology: Heart and Circulation

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Physiology 278, H2039-H2049.

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Rispens, S.M., 2014. Walking on the wild side: fall risk assessment from daily-life gait. PhD thesis, VU University in Amsterdam, The Netherlands. Rispens, S.M., van Schooten, K.S., Pijnappels, M., Daffertshofer, A., Beek, P.J., van Dieën,

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Metabolics 4(1), 81-89.

449 450 451 452

Wold, S., Sjöström, L., Erikson, L., 2001. PLS regression: a basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems 58, 37–52. Wu, S.D., Wu, C.W., Lin, S.G., Lee, K.Y., Peng, C.K., 2014. Analysis of complex time series using refined composite multiscale entropy, Physical letters A 378 (20), 1369-1374.

453 454

20

455

Appedix A

456

Refined composite multiscale entropy (RCME)

457

The computation of the refined composite multiscale entropy is illustrated by the flowchart in

458

Figure A1 by the following seven steps:

459

Step 1 (Coarse graining): The trunk acceleration and velocity signal xi was coarse grained

460

into twenty scales τ by either the following mean or variance (Costa et al., 2002, Wu et al.,

461

2014; Costa and Goldberger, 2015):

462

463



yk , j 

yk , j 

1

 1



j  k 1



i  ( j 1)  k

xi

(1)

j  k 1

  x  y 

i  ( j 1)  k

i

2

(2)

k, j

464

where j is the index of non-overlapping time windows of size τ and k = 1, 2…, τ is the sample-

465

by-sample translation of these windows to provide the τ possible version of the coarse

466

graining. The variance (i.e., Eq. 2) has been suggested to improve the quantification of

467

complexity of intermittent large signal components that frequently appears during the walking

468

bouts.

469

Step 2 (Template creation): Two template vectors, X k ,m, j   yk , j , yk , j 1 , yk , j 2 ,..., yk , j  m1  and

470

X k ,m1, j   yk , j , yk , j 1 , yk , j 2 ,..., yk , j  m  were created for coarse grained signal yk , j of each

471

segment j and each sample k. The parameter m is the number of dimensions (i.e., lags)

472

considered.

473

Step 3 (Template matching): Template matching was performed by the computation of

474

Chebyshev distance d  X k ,m, j , X k ,m,i   max X k ,m, j  X k ,m,i

475

d  X k ,m1, j , X k ,m1,i   max X k ,m1, j  X k ,m1,i for all segments where j ≠ i. The template





 and



21

476

vectors X k ,m, j and X k ,m,i are similar when d  X k ,m, j , X k ,m,i   r which implies that all

477

absolute values of differences, [ yk , j  yk ,i , yk , j 1  yk ,i 1 ,..., yk , j m  yk ,i m ] , are all below

478

magnitude r.

479

Step 4 (Count of template matches): The average number of pairs, nk ,m, j and nk ,m1, j ,

480

with d  X k ,m, j , X k ,m,i   r and d  X k ,m1, j , X k ,m1,i   r , respectively, was counted across all

481

segments where i ≠ j:

482

nk ,m, j 

483

nk ,m1, j 

484

where N is the sample size of the time series and where the heavyside step function is given

485

by the following equation:

486

0, d  r (d )   1, d  r

487

The mean number of pairs across all template vectors j was then defined as the following two

488

equations for nk ,m, j and nk ,m1, j , respectively:

489

nk ,m 

490

Step 5 (k - iteration): The four steps above was iterated for all k = 1, 2, …, τ versions of the

491

non-overlapping yk , j of Eq 1 or Eq 2.

492

Step 6 (Computation of RCME): The refined composite multiscale entropy is defined by the

493

following equation [32]:

1 N m  d  X k ,m, j , X k ,m,i   N  m i 1





(3)

N  m 1 1  d  X k ,m1, j , X k ,m1,i   N  m  1 i 1

1 N m   nk ,m, j N  m j 1





(4)

and

nk ,m1 

N  m 1 1 nk ,m1, j  N  m  1 j 1

(5)

22

494



RCMEm,r

 nm 1    ln     nm 

(6)

495

Where nm and nm 1 is the average count across all k = 1, 2, …, τ versions of the non-

496

overlapping yk , j of Eq 1 or Eq 2:

497

nm 

1





 nk ,m

and

k 1

nm 1 

1



n   k 1

k , m 1

498

Step 7 (Scale – iteration): Step 1 to 6 was then iterated for all scales τ = 1, 2, …, 20

499

considered in the present study.

500

(7)

--Insert Figure A1--

501

In the present study, parameter settings m = 4 and r = 0.3 SD had minimum mean square

502

errors according to a procedure suggested by Lake et al. (2002). SD was set as the median of

503

standard deviations of the acceleration signal across all walking bouts for all elderly fallers

504

and non-fallers. The Matlab code of RCME is presented below and is an extension of the

505

Matlab code of sample entropy developed by Kijoon Lee and available at

506

http://www.mathworks.com/matlabcentral/fileexchange/35784-sample-entropy.

507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529

function RCME = RCMEn(X,dim,t,r,Scale) %Inputs-------------------------------------------%X________Data series %m________Number of time lags in the template vector %(m = 4 was used in the present study) %r________Similarity threshold for template vector pairs %(r = 0.3*SD was used in the present study) %t________Time lag(t=1 was used in the present study) %Scale____Number of scales %Output--------------------------------------------%RMPE_____Refined composite multiscale entropy RCME=[]; for tau=1:Scale %Step 7: Scale-iteration n = zeros(2,tau); for k=1:tau %Step 5: k-iteration X1 = X(1+k:length(X)-Scale+k); %Step 5: k-iteration; data = Multi(X1,tau); % Step 1: Coarse graining N = length(data); dataMat = zeros(dim+1,N-dim);

23

530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568

if t > 1, % Step 1: Coarse graining and downsampling data = downsample(data, t); end for i = 1:dim+1 % Step 2: Template vector creation dataMat(i,:) = data(i:N-dim+i-1); end for m = dim:dim+1 % Step 2: Iteration for template vectors with m and m+1 time lags count = zeros(1,N-dim); tempMat = dataMat(1:m,:); for j = 1:N-m % Step 3: Template matching; calculate Chebyshev distance and excluding self% matching cases i=j dist=max(abs(tempMat(:,j+1:N-dim)-repmat(tempMat(:,j),1,N-dim-j))); % Step 3: Template matching; find similar template vectors (Eq. 4) D = (dist < r); % Step 4: Average count of template matches for each template vector j(Eq. 3) count(j) = sum(D)/(N-dim); end % Step 4: Mean count of template matches across all template vectors j (Eq.5) n(m-dim+1,k) = sum(count)/(N-dim); end end %Step 6: Definition of refined composite multiscale entropy (Eq.6) %by mean count n across all k iterations (Eq. 7) saen=log(mean(n(1,:))/mean(n(2,:))); RCME=[RCME saen]; end function M_Data = Multi(Data,S) L = length(Data); J = fix(L/S); for i=1:J M_Data(i) = mean(Data((i-1)*S+1:i*S)); %(Eq. 1) %M_Data(i) = var(Data((i-1)*S+1:i*S)); %(Eq. 2) end

24

569

Appendix B

570

Refined multiscale permutation entropy (RMPE)

571

The computation of refined multiscale permutation entropy is illustrated by the flow chart in

572

Figure A2 by the following seven steps:

573

Step 1 and 2 (Coarse graining and Template creation): These steps were identical to the Step

574

1 and 2 for RCME (see Appendix A) with exception that only template vector X k ,m, j was

575

created.

576

Step 3 (Template matching): The order of the entities of X k ,m, j was identified for all non-

577

overlapping segments j and compared to a permutation list containing all i = 1,2,…,m!

578

possible orderings of the m entities in X k ,m, j .

579

Step 4 (Count of template matches): The number nk ,m,i of matches with the ith ordering in the

580

permutation list was counted across all non-overlapping segments j.

581

Step 5 (k - iteration): Identical to the computation of RCME, the four steps above was iterated

582

for all k = 1, 2, …, τ versions of the non-overlapping yk , j of Eq 1 and 2.

583

Step 6 (Computation of RMPE): The refined multiscale permutation entropy (RMPE) was

584

defined as the Shannon entropy:

585

RMPEm   pm,i ln  pm,i  m!

(6)

i 1

586

where pm ,i is the probability of finding the ordering of the template vector X k ,m, j to be equal

587

to the ith ordering of the permutation list. The probability pm ,i was defined as:

25

588

nm ,i



pm,i 

(7)

1 m!   nm,i m ! i 1

589

Where nm ,i is the mean count for each of the ith ordering of the permutation list across all k

590

= 1, 2, …, τ versions of the non-overlapping yk , j of Eq 1 or Eq 2:

591

nm ,i 

1



n   k 1

(8)

k , m ,i

592

Step 7 (Scale - iteration): Step 1 to 6 was then iterated for all scales τ = 1, 2, …, 20 considered

593

in the present study. Small values of RMPE are a result of a narrow probability distribution

594 595

pm ,i which indicates a regular acceleration pattern where only a few possible orderings of the entities in X k ,m, j are present.

596

--Insert Figure A2--

597

RMPE used in the present study was an extension of the method developed by Li et al. (2010)

598

which prevents artificial changes in RMPE on larger scales due to down sampling of the data

599

series (see Appendix B for the performance of Eq. 5 compared with the method suggested by

600

Li et al., 2010). The dimension m = 4 was chosen which resulted in m! = 24 possible

601

orderings in the permutation list. This choice of dimension prevented too few or too many

602

possible orderings in permutation list according to the sample size of the walking epochs. The

603

Matlab code below is an extension of the Matlab code of multiscale permutation entropy

604

developed by Li et al. (2010) and available at

605

http://www.mathworks.com/matlabcentral/fileexchange/37288-multiscale-permutation-

606

entropy--mpe-.

607 608 609 610 611

function RMPE = RMPEn(X,m,t,Scale) %Inputs--------------------------------------------

26

612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647

%X________Data series %m________Number of time lags in the template vector (m=4 was used in the present study) %t________Time lag(t=1 was used in the present study) %Scale____Number of scales %Output--------------------------------------------%RMPE_____Refined multiscale permutation entropy permlist = perms(1:m); %Creation of the permutation list RMPE=[]; for tau=1:Scale, %Step 7: Scale-iteration n(1:length(permlist),1:tau)=0; for k=1:tau; %Step 5: k-iteration X1 = X(k:length(X)-Scale+k); %Step 5: k-iteration Xs = Multi(X1,tau); %Step 1: Coarse graining (see Multi function in Appendix A) ly = length(Xs); for j=1:ly-t*(m-1) [a,iv]=sort(Xs(j:t:j+t*(m-1))); %Step 2: Template creation and ordering for i=1:length(permlist) if (abs(permlist(i,:)-iv))==0 %Step 3: Template matching with %permutation list n(i,k) = n(i,k) + 1 ;%Step 4: Count of template matches end end end end M_n=mean(n,2); %Step 6: Mean count n across all k iterations (Eq.8) M_n=M_n(M_n~=0); p = M_n/sum(M_n); %Step 6: Probability of finding a template vector with entity %order equal to the orderings of the permutation list (Eq.7) PE = -sum(p .* log(p)); %Step 6: Refined multiscale permutation entropy (Eq.6) RMPE=[RMPE PE]; end

27

648

Appendix C

649

Comparison of multiscale permutation entropy (MPE) with refined multiscale

650

permutation entropy (RMPE)

651

Refined multiscale permutation entropy (RMPE) developed in the present study is an

652

extension of multiscale permutation entropy (MPE) (Aziz and Arif, 2005; Li et al., 2010). In

653

MPE, the coarse graining in Step 1 suggested by Costa et al. (2002) is used instead of Eq. 1

654

and 2 in the main text. In this procedure, means or variances in N/τ non-overlapping samples

655

are computed by the following equation:

656

yj 

657

yj 

1

 1



j 1



i  ( j 1)

xi

(A1)

j 1

   x  y 

i  ( j 1)

i

2

j

(A2)

658

In the present study, multiscale entropy measures were computed for walking epochs of 50

659

seconds (i.e., 5000 samples). Equation A1 and A2 provides only N/τ = 5000/20 = 250 samples

660

for the largest scale τ = 20 and the computation of multiscale permutation entropy is

661

susceptible to errors due to small sample size. In contrast, Eq. 1 and Eq. 2 in the main text

662

preserve the sample size by considering a moving mean and variance by index k (Wu et al.,

663

2014). The mean number of orderings, nm ,i , will improve the numerical stability of the

664

estimation of permutation entropy on the larger scale (see Eq. 6 in the main text). The

665

improved numerical stability of RMPE is illustrated for white noise in Figure A3 where the

666

Matlab code of RMPE represented in Appendix B was compared with the Matlab code for

667

MPE available at http://www.mathworks.com/matlabcentral/fileexchange/37288-multiscale-

668

permutation-entropy--mpe-. Furthermore, the improved numerical stability of RMPE and

669

RCME compared to MPE and multiscale entropy (ME), respectively, appear to have provided 28

670

an improved classification of fallers and non-fallers (see Table A1). However, the differences

671

is smaller than expected due to the stabilizing effect of computing the median ME and median

672

MPE across all walking epochs of each person before the employment of PLS-DA. Figure A4

673

shows substantial differences in the epoch-to-epoch variation between RCME and ME (see

674

panel A) and between RPME and MPE (see panel B) even though the median entropy values

675

are similar. Thus, larger differences between RCME and ME and between RPME and MPE in

676

the classification of fallers might be apparent for data sets with fewer walking epochs per

677

person. Nonetheless, additional work is needed to more fully determine if these differences

678

help in the clinical assessment of fall risk.

679

(--Insert Figure A3, A4 and Table A1--)

680

29

681

Figure captions

682

Fig. 1: The mean ± 1 standard error of RCME for elderly fallers (red traces) and non-fallers

683

(blue traces). (A) RCME for trunk acceleration in AP (left panels), ML (middle panels) and V

684

directions (right panels) based on coarse grained mean (upper panels) and variance (lower

685

panels). (B) RCME for trunk velocity in AP (left panels), ML (middle panels) and V

686

directions (right panels) based on coarse grained mean (upper panels) and variance (lower

687

panels). Note that horizontal black lines and asterix indicate the scales with significant

688

difference in RCME between elderly fallers and non-fallers where * is p < 0.05 and ** is p <

689

0.005 by an independent-sample t-test. Note also that scales τ marked in red are RCME

690

selected by the backward selection procedure used in the present study.

691

Fig. 2: The mean ± 1 standard error of RMPE for elderly fallers (red traces) and non-fallers

692

(blue traces). (A) RMPE for trunk acceleration in AP (left panels), ML (middle panels) and V

693

directions (right panels) based on coarse grained mean (upper panels) and variance (lower

694

panels). (B) RCME for trunk velocity in AP (left panels), ML (middle panels) and V

695

directions (right panels) based on coarse grained mean (upper panels) and variance (lower

696

panels). Note that horizontal black lines and asterix indicate the scales with significant

697

difference in RMPE between elderly fallers and non-fallers where * is p < 0.05 and ** is p <

698

0.005 by an independent-sample t-test. Note that scales τ marked in red are RMPE selected by

699

the backward selection procedure used in the present study.

700

Fig. 3: The absolute value of the partial least square (PLS) loading scores in ascending order

701

(from lowest to highest) of the selected scales by the backward selection procedure for RCME

702

of (A) trunk acceleration based on coarse grained mean and (B) coarse grained variance, and

703

(C) trunk velocity based on coarse grained mean and (D) coarse grained variance. The blue,

30

704

green, and red bars define the scale-dependent RCME in AP, ML, and V direction,

705

respectively.

706

Fig. 4: The absolute value of the partial least square (PLS) loading scores in ascending order

707

(from lowest to highest) of the selected scales by the backward selection procedure for RMPE

708

of (A) trunk acceleration based on coarse grained mean and (B) coarse grained variance, and

709

(C) trunk velocity based on coarse grained mean and (D) coarse grained variance. The blue,

710

green, and red bars define the scale-dependent RMPE in AP, ML, and V direction,

711

respectively.

712

Fig. A1: A flow chart that summarize the computation of refined composite multiscale

713

entropy (RCME). In Step 1, the accelerometer signal (blue trace) is coarse grained by a non-

714

overlapping mean (red horizontal lines) or variance (not shown in the figure). In Step 2,

715

template vectors

716

signal (red trace) and matched with all template vectors X k ,m,i and

717

j ≠ i. In Step 3, the template vector pairs are matched by computing the Chebyshev’s distance

718

d  X k ,m, j , X k ,m,i   max X k ,m, j  X k ,m,i

719

are below a magnitude r. In Step 4, the mean number

720

assessed across all template pairs with j ≠ i (black boxes). In Step 5, Step 1 to 4 are iterated τ

721

times for the index k by translating the non-overlapping intervals by one sample (from blue

722

dashed lines to red lines). In Step 6, the refined composite multiscale entropy (RCME) are

723

computed by first define the mean number of template matches across all τ iterations in Step 5

724

before taking the logarithm of the ratio of these two (blue trace and equation below the trace).

725

In Step 7, Step 1 to 6 are iterated increasing the scale (i.e. sample size of the non-overlapping

726

window) by one sample (red arrow and red dashed trace).

X k ,m, j



and

X k ,m1, j

(left dashed boxes) are constructed from coarse grained X k ,m1,i ,

respectively, for all

 (red arrows). The vector pairs are similar if d  X nk ,m

and

nk ,m1 of

 k , m, j

, X k ,m,i 

and

template matches are

31

727

Fig. A2: A flow chart that summarize the computation of refined multiscale permutation

728

entropy (RMPE). In Step 1, the accelerometer signal (blue trace) is coarse grained by a non-

729

overlapping mean (red horizontal lines) or variance (not shown in the figure). In Step 2,

730

template vector

731

In Step 3, the ordering of the m = 4 entities in the template vector (numbers above the red

732

trace) is matched with one of the ith orderings of the permutation list (blue numbers). The

733

permutation list illustrated in the figure is for m = 4 with m! = 24 possible orderings. In Step

734

4, the number

735

permutation list is counted (black boxes). In Step 5, Step 1 to 4 are iterated τ times for the

736

index k by translating the non-overlapping intervals by one sample (from blue dashed lines to

737

red lines). In Step 6, the mean number of template matches across all τ iterations in Step 5 is

738

defined before the probability of finding a template vector with entity order equal to the ith

739

entity of the permutation list (black boxes). These probabilities are used to define refined

740

multiscale permutation entropy (RMPE) for scale τ (blue trace and equation below the trace).

741

In Step 7, Step 1 to 6 are iterated increasing the scale (i.e. sample size of the non-overlapping

742

window) by one sample (red arrow and red dashed trace).

743

Fig. A3: (A) The mean ± 1 SD of multiscale permutation entropy (red traces) and refined

744

multiscale permutation entropy (RMPE, blue traces) for 100 series of white noise for (A) m =

745

3 and (B) m =6. The multiscale permutation entropy shows an artificial decrease and a larger

746

SD due to the down sampling provided by Eq. A1 when compared to RMPE. The left panels

747

in (A) and (B) shows how the numerical stability of permutation entropy converges with

748

increasing sample size and indicates that multiscale permutation entropy needs about five

749

times the number of samples to perform as well as RMPE.

X k ,m, j

nk ,m,i

(left dashed box) is constructed from coarse grained signal (red trace).

of template matches for all j templates and all ith ordering of the

32

750

Fig. A4: A comparison of the epoch-to-epoch variation of (A) RCME (solid line) and ME

751

(dashed line) and (B) RMPE (solid line) and MPE (dashed line) of daily life walking for an

752

older person with similar median values of these metrics. Both ME and MPE shows larger

753

epoch-to-epoch variation compared to RCME and RMPE, respectively, on larger scales. Note

754

that only scale, j = 20, is displayed in the figure.

755 756

Table 1: The performance of refined composite multiscale entropy (RCME) and refined

757

multiscale permutation entropy (RMPE) in distinguishing between elderly fallers and non-

758

fallers. Features

Factors

Sensitivity

Specificity

AUC

Error

RCME: Trunk acceleration Mean (Eq. 1)

30

9

0.84

0.85

0.81

0.15

Variance (Eq. 2)

27

4

0.63

0.92

0.75

0.21

RCME: Trunk velocity Mean (Eq. 1)

14

5

0.78

0.90

0.83

0.15

Variance (Eq. 2)

11

4

0.59

0.82

0.69

0.28

RMPE: Trunk acceleration Mean (Eq. 1)

35

12

0.88

0.90

0.88

0.11

Variance (Eq. 2)

17

6

0.75

0.79

0.76

0.23

RMPE: Trunk velocity

759

Mean (Eq. 1)

41

14

0.75

0.87

0.82

0.18

Variance (Eq. 2)

17

6

0.71

0.77

0.72

0.25

Note that Eq. 1 and 2 are found in Appendix A

760 761 33

762

Figure 1

A

Trunk acceleration 1.2

Mean (see Eq. 1 in Appendix A) 1.2

RCME

1

*

0.8

1.2

ML

AP

**

1

*

V

**

*

*

1

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.2

Non-fallers Fallers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

** * *

0.4

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Variance (see Eq. 2 in Appendix A) 1.2

1.2

*

1

*

0.8

RCME

1.2

ML

AP 1

*

*

0.8

V 1

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

B

*

0.8

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

Scale ( in samples)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

Trunk velocity Mean (see Eq. 1 in Appendix A) 1 0.9

1

AP

0.9

0.8

0.8

*

RCME

0.7

0.7

1

ML

*

0.9

**

*

0.8 0.7

0.6

0.6

0.6

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

V

*

Non-fallers Fallers

0.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Variance (see Eq. 2 in Appendix A) 0.45 0.4

0.45

AP

*

RCME

0.35

0.4

0.45

ML

0.4

0.35

0.3

0.3

0.3

0.25

0.25

0.25

0.2

0.2

0.2

0.15

0.15

0.15

0.1

0.1

0.1

0.05

0.05

0.05

0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

0

V

0.35

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

763 764 765 766

Figure 2

34

A

Trunk acceleration

Mean (see Eq. 1 in Appendix A)

3.4 3.2

3.4

AP

RMPE

3

Non-fallers Fallers

3.2

3.4

ML

* **

*

**

3.2

3

3

2.8

2.8

2.8

2.6

2.6

2.6

2.4

2.4

2.4

2.2

2.2

2.2

2

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2

V

*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Variance (see Eq. 2 in Appendix A) 3.2

3.2

AP

3.15

RMPE

3.1

*

3.2

ML

3.15 3.1

3.1

3.05

3.05

3.05

3

3

3

2.95

2.95

2.95

2.9

2.9

2.9

2.85

2.85

2.85

2.8 2.75

2.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2.75

Scale ( in samples)

B 3 2.8

*

RMPE

2.6

2.75

Scale ( in samples)

2.8 2.6

3

ML

* **

2.8

*

2.4

2.4

2.2

2.2

2.2

2

2

2

1.8

1.8

1.8

1.6

1.6

1.6

1.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

V

2.6

2.4

1.4

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Mean (see Eq. 1 in Appendix A) 3

AP

2.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

Trunk velocity

V

3.15

Non-fallers Fallers

1.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Variance (see Eq. 2 in Appendix A) 3.2

AP

3.2

ML

RMPE

*

3.2

*

3.1

3.1

3.1

3

3

3

2.9

2.9

2.9

2.8

2.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

V

2.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Scale ( in samples)

767 768

35

769

Figure 3 Trunk acceleration: Mean (Eq. 1)

A

0.8

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.7

PLS loading scores (absolute values)

AUC = 0.81 0.6

0.5

0.4

0.3

0.2

0.1

0

B

10 3 20 13 5 17 19 6 13 12 18 1

7 20 16 14 4 7 Scale ( in samples)

9

2 15 14 17 10 13 18 15 9 10 12

Trunk acceleration: Variance (Eq. 2) 0.8

0.7

PLS loading scores (absolute values)

AUC = 0.75

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.6

0.5

0.4

0.3

0.2

0.1

0

7

14

8

6

18 15

9

19

5

11 20

8 12 4 9 10 3 Scales ( in samples)

1

14 15 11

7

8

9

14 16 15

Trunk velocity: Mean (Eq. 1)

C

0.8

Anterioposterior (AP) 0.7

PLS loading scores (absolute values)

AUC = 0.85

Mediolateral (ML) Vertical (V)

0.6

0.5

0.4

0.3

0.2

0.1

0

D

7

20

19

3

20

2

15 16 3 Scale ( in samples)

4

13

9

12

11

Trunk velocity: Variance (Eq. 2) 0.8

0.7

PLS loading scores (absolute values)

AUC = 0.69

Mediolateral (ML) Vertical (V)

0.6

0.5

0.4

0.3

0.2

0.1

0

770 771

18

6

17

14

14 18 9 Scales ( in samples)

1

2

4

12

Figure 4

36

Trunk acceleration: Mean (Eq. 1)

A

0.9 0.8

PLS loading scores (absolute values)

AUC = 0.88

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

B

6 4

6 7 1

5 3 16 13 20 9 5 17 12 10 8 8 20 19 9 18 10 16 15 10 11 17 12 12 11 20 18 17 14 15 Scales ( in samples)

Trunk acceleration: Variance (Eq. 2) 0.9 0.8

PLS loading scores (absolute values)

AUC = 0.76

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

6

14

7

15

12

20

10

16 8 8 Scale ( in samples)

2

17

9

10

20

19

20

Trunk velocity: Mean (Eq. 1)

C

0.9 0.8

PLS loading scores (absolute value)

AUC = 0.82

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

D

17 20 19 20 19 16 18 14 17 8 16 20 15 19 18 14 17 16 15 13 1 14 11 11 10 12 13 4 9 10 3 5 7 6 9 3 8 5 4 5 6 Scale ( in samples)

Trunk velocity: Variance (Eq. 2) 0.9 0.8

PLS loading scores (absolute values)

AUC = 0.72

Anterioposterior (AP) Mediolateral (ML) Vertical (V)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

772

13

18

19

2

6

16

10

15 14 15 Scale ( in samples)

6

7

8

2

6

11

5

773 774

37