This observational cross-sectional study was performed at Arizona Center on Aging, Tucson, AZ. Participants in this study were from primary, secondary, and tertiary health-care settings within our academic network and also from community providers and aging service organizations. DPA was recorded from eligible volunteers for 48 hours and the walking data from the DPA was processed to study the gait performance parameters and associate these characteristics with frailty.
Participants
Older adults (65 years or older), without severe mobility disorder and the ability to walk at least 10m with or without an assistive device, were considered eligible for the study. Participants with dementia identified by a Mini-Mental State Examination (MMSE) (18) score of <23 or terminal illness were excluded. All the eligible participants signed a written consent form according to the principles expressed in the Declaration of Helsinki (19), approved by the Institutional Review Board of the University of Arizona.
Demographic and Clinical Measures
The recorded clinical measures included self-reported history of falls, use of assistive device and the number of prescriptions. Interviewer-administered questionnaires included the MMSE, Mobility-Tiredness Scale (20), Center for Epidemiologic Studies Depression Scale (CES-D) (21), Falls Efficacy Scale-International (22), and Barthel Activity of Daily Living (ADL) Scale (23).
Gold Standard Frailty Assessment
Frailty was assessed using the five criteria proposed by Fried et al (3), including: self-reported weight loss, weakness measure by the grip strength, self-reported exhaustion, slowness measure by the walking test, and self-reported low energy expenditure. A score of one point was given for each criterion recorded, totaling a score in the range of 0–5. Frailty was categorized as follows: non-frail (score 0), pre-frail (score 1–2), and frail (score 3–5).
Sensor-Based Daily Physical Activity Assessment
DPA was quantified for two consecutive days (48 hours) using a tri-axial accelerometer sensor (PAMSys, BioSensics Cambridge, MA, USA) fixed in a tee-shirt, with a device pocket located at the sternum. PAMSys is a small (5.1 x 3 x 1.6 cm), light (24g) recording system containing inertial sensors. We used a previously validated algorithm to identify walking bouts (PAMWare, BioSensics Cambridge, MA, USA). Briefly, walking bouts were defined by a minimum of three successive steps (24), where steps were estimated by the detection of an acceleration peak beyond a predefined threshold after filtering the signal (25). Using this software several gait parameters were derived including: the duration of walking, walking bout times (duration of each walking episodes), number of steps per walking bout, and walking cadence per bout. PAMWare is 87% sensitive and 87% specific for gait detection (24,26). Within the current study we further refined the PAMSys algorithm to derive assess purposeful walking, as well as gait performance parameters.
Purposeful Walking Bouts
To provide sufficient sample size, purposeful walking bouts, defined as 60 seconds or longer, were used for extraction of gait performance parameters (27,28). This assured that for each analyzed walking event, the participant is commuting with the purpose of getting to a certain destination point, rather than random daily walking. Gait performance parameters including time- and frequency-domain gait variability, gait asymmetry, and gait irregularity were extracted from purposeful walking bouts, continuous for 60 seconds or longer with no pauses longer than 1.7s between gait cycles (12). Allowable 1.7s pause between gait cycles was conservatively selected based on the average plus standard deviation stride time duration observed in frail participants (12). All the sensor-based gait performance outcome measures are shown in Table 1. For each purposeful walking bout, the raw vertical acceleration signal was filtered using a second order Butterworth filter (cut-off frequency of 2.5Hz (29)), and the peaks of the filtered acceleration signal were detected using a peak-detection algorithm. The time-interval between two consecutive peaks was defined as the step-time, and the time-interval between alternate peaks was defined as the stride-time.
Gait Variability: We defined gait variability as the stride-to-stride fluctuation in walking cycles, which has been associated with high risk of fall and cognitive impairments in elders (5,30–32). Gait variability reflects inconsistency in physiological systems that regulate walking, including neuromuscular, reflexive postural control, and cardiovascular systems (33). We used two methods to assess gait variability: 1) step- and stride-time variability using time-domain; and 2) power spectral density (PSD) using frequency-domain analysis (34,35). Step- or stride-time variability was calculated as the coefficient of variation of the series of step- or stride-times for each purposeful walking bout. For PSD analysis, the power spectrum of the acceleration data was calculated using Welch’s averaged modified periodogram method (36), to represent the frequency components of the acceleration signal (37). We used a window size of 512 samples and an FFT length of 2-times the next higher power of the window size (36). An overlap of 50% was considered between the windows. The locomotion band between 0.5–3.0Hz was analyzed (36). PSD components were extracted from the raw acceleration signal, including: maximum PSD peak, PSD width (full width at half maximum height), PSD slope (PSD width to the peak) and dominant walking frequency. A higher variability in walking was identified by a shorter and wider PSD peak.
Gait Asymmetry: When gait becomes less automatic due to sarcopenia and cognitive aging, left-right step coordination may require more effort, especially among frail individuals (12,38,39). Further, studies showed that no strong association between gait variability and asymmetry exists, suggesting that asymmetry reflects an independent measure of gait impairments due to distinct pathological causes (12,38). Here, step asymmetry was obtained from the autocorrelation function of the vertical acceleration signal (12,38), represented by a sequence of autocorrelation coefficients over increasing time lags.

where Ad1 and Ad2 are the prominence of the first and the second peaks respectively after the central (zero lag) peak (40).
Gait Irregularity: Results from supervised gait studies showed that irregularity measures can describe predictability of walking cycles, which can be influenced by both neurological and neuromuscular diseases (41–44). Further, within in-lab settings, it has been demonstrated that gait irregularity can differ between non-frail and pre-frail older adults (16). We used Sample Entropy (SampEn) assessment defined as equation (2), where A was defined as the number of matches in the filtered acceleration signal length m+1 (distance function smaller than tolerance r: d[Xm+1(i),Xm+1(j)]<r) and B as the number of matches of length m: (d[Xm(i),Xm(j)]<r) (45–49).

The time-delay of the signal was calculated using mutual information method for all the purposeful walks (50), and the average time-delay of all the purposeful walks was used to calculate the SamplEn for each volunteer. We used embedding dimension m = 3, and tolerance r = 0.2 times the standard deviation of the signal, which are commonly used to compute sample entropy of gait signal (45–49).
Table 1. Sensor based outcome measures
Parameter
|
Description
|
Reference
|
Step/stride time
|
Time-interval between two consecutive/alternate acceleration peaks
|
|
Gait Variability
|
Step/stride time variability
|
Coefficient of variation (%), standard deviation of step/stride time over mean step/stride time
|
(12)
|
PSD max
|
Maximum height of the PSD distribution curve representing the amount of walking that occurs at the dominant frequency
|
(36,51)
|
PSD width
|
The width of the PSD curve at half of the maximum height representing the range of walking frequencies
|
(36,51)
|
PSD slope
|
The slope of the PSD curve from the peak to the width representing the rate of change of walking frequencies
|
(36,51)
|
Dominant frequency
|
The frequency at which the PSD curve attains its peak, representing the frequency at which most of the walking cycles occur
|
(36,51)
|
Gait Asymmetry
|
|
Unbiased auto-correlation coefficients of gait signal, representing left-right step coordination
|
(10,52)
|
Gait Irregularity
|
|
Sample entropy, representing the predictability of walking cycles
|
(45,53,54)
|
Purposeful Walking Quantitative Measures
|
|
|
No. of purposeful walks
|
Total number of purposeful walks during 48 hours
|
|
Total continuous walking duration
|
Total duration of continuous purposeful walks during 48 hours
|
|
Max walking bout
|
Maximum bout of purposeful continuous walking in 48 hours
|
|
Max no. of continuous steps
|
Maximum number of continuous steps in the longest continuous walking bout in 48 hours
|
|
Walking bout variability
|
Coefficient of variation (%), standard deviation of walking bouts over mean walking bout
|
|
PSD – Power Spectral Density
Purposeful Walking Quantitative Measures: In addition to the above-mentioned features, we extracted the following parameters in each purposeful continuous walking event: maximum walking bout, maximum number of continuous steps, walking-bout variability (coefficient of variation in walking bouts duration within 48 hours), and total duration of purposeful walks. Of note, the parameters extracted here were only obtained for continuous purposeful walking events with no pause of 1.7s or longer, as described above.
Statistical Analysis
Separate analysis of variance (ANOVA) models were performed to compare sociodemographic parameters between the three Fried frailty groups. To explore differences in gait performance parameters among frailty categories, univariate ANOVA models were used with each gait performance parameter as the dependent variable, and the Fried frailty categories (non-frail, pre-frail, and frail) as the independent variable. Subsequently, gait performance parameters were used in a single multivariable nominal logistic model to assess the association between frailty categories and DPA gait performance parameters. In this model we combined pre-frail and frail groups, due to the limited number of frail participants. The model was developed following these steps: 1) univariate nominal logistic model analysis of the gait performance parameters as independent variables was performed. Gait performance parameters with significant association with frailty were considered for subsequent steps; 2) collinearity between the various gait performance parameters was tested using the variance inflation factor (VIF) index. VIF value greater than 10 represented the presence of collinearity (55); and 3) gait performance and demographic parameters were selected based on Akaike information criterion (AIC) values. Participants who exhibited no 60-second purposeful walk were automatically categorized as frail. All analyses were done using JMP (Version 11; SAS Institute Inc., Cary, NC, USA), and statistical significance was concluded when p<0.05.