Sleep Science 7 (2014) 158–164
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Nonparametric methods in actigraphy: An update
Bruno S.B. Gonçalvesa,c,d,n, Paula R.A. Cavalcantib, Gracilene R. Tavaresb,
Tania F. Camposb, John F. Araujoa,b,c
a
Programa de Pós-Graduação em Psicobiologia, UFRN, Natal, RN, Brazil
Programa de Pós-Graduação em Fisioterapia, UFRN, Natal, RN, Brazil
c
Laboratório de Neurobiologia e Ritmicidade Biológica, UFRN, Natal, RN, Brazil
d
Instituto Federal Sudeste de Minas Gerais, Campus Barbacena, Barbacena, MG, Brazil
b
ar t ic l e in f o
Available online 29 September 2014
abs tra ct
Circadian rhythmicity in humans has been well studied using actigraphy, a method of
Keywords:
measuring gross motor movement. As actigraphic technology continues to evolve, it is
Actigraphy
important for data analysis to keep pace with new variables and features. Our objective is to
Fragmentation
study the behavior of two variables, interdaily stability and intradaily variability, to describe
Synchronization
rest activity rhythm. Simulated data and actigraphy data of humans, rats, and marmosets
Amplitude
were used in this study. We modified the method of calculation for IV and IS by modifying
Activity
the time intervals of analysis. For each variable, we calculated the average value (IVm and
Rest
ISm) results for each time interval. Simulated data showed that (1) synchronization analysis
depends on sample size, and (2) fragmentation is independent of the amplitude of the
generated noise. We were able to obtain a significant difference in the fragmentation
patterns of stroke patients using an IVm variable, while the variable IV60 was not identified.
Rhythmic synchronization of activity and rest was significantly higher in young than adults
with Parkinson's when using the ISM variable; however, this difference was not seen using
IS60. We propose an updated format to calculate rhythmic fragmentation, including two
additional optional variables. These alternative methods of nonparametric analysis aim to
more precisely detect sleep–wake cycle fragmentation and synchronization.
& 2014 Published by Elsevier B.V. on behalf of Brazilian Association of Sleep.
Background
The rest–activity rhythm in humans is commonly studied using
actigraphy, a technology which measures gross motor movement. Adjusting a cosine function to actigraphic data provides
parameters that are used in circadian rhythmicity studies. The
parameters that describe rhythm characteristics include: amplitude, mesor, acrophase, and period. However, as the rest–
activity rhythm does not behave exactly as a cosine function,
other variables have been studied and new methodologies have
been developed. Since these variables are not associated with
parameters of a known function, they are called nonparametric.
In 1990, such nonparametric variables were primarily
proposed by Witting et al., who had studied the effect of
age and Alzheimer's disease on rest–activity rhythm [12].
These variables quantify the main characteristics of the rest–
activity circadian rhythm, such as intradaily variability (IV),
which quantifies the rhythm fragmentation; interdaily
n
Corresponding author at: to: Rua Monsenhor José Augusto, no. 204, Bairro São José, CEP: 36205-018 Barbacena, MG, Brazil.
Tel.: þ55 3233335703.
E-mail address: brunocrono@hotmail.com (B.S.B. Gonçalves).
http://dx.doi.org/10.1016/j.slsci.2014.09.013
1984-0063/& 2014 Published by Elsevier B.V. on behalf of Brazilian Association of Sleep.
Sleep Science 7 (2014) 158–164
stability (IS), which quantifies the synchronization to the 24-h
light–dark cycle; the average activity during the least active 5h period, or nocturnal activity (L5); and the average activity
during the most active 10-h period, or daily activity (M10).
Rhythmic fragmentation and synchronization are measured,
respectively, by IV and IS. Intradaily variability quantifies the
frequency and extent of transitions between periods of rest and
activity on an hourly basis [12,10,11]. High IV values indicate the
occurrence of daytime naps and/or nocturnal activity episodes.
Interdaily stability quantifies rhythm's synchronization to zeitgeber's 24-h day–night (or light–dark) cycle.
Studies have shown that IV is an excellent variable for
analysis, as it serves as a marker of sleep–wake cycle disturbances [6]. Assessment of interdaily variability in an elderly
population shows a more fragmented rest–activity rhythm (high
IV values) [6]. Researchers have also observed higher values of IV
in patients with Alzheimer's disease when compared to controls
[12,5]. Aging and Alzheimer's disease are factors that contribute
to the degeneration of the suprachiasmatic nucleus [9,13], which
may explain rhythm fragmentation. Furthermore, it was demonstrated that high IV (high rhythm fragmentation) is associated
with decreased sleep quality [3], decreased cognitive functions [7]
and decreased circadian rhythm amplitude [12,10].
On the other hand, high IS values indicate good synchronization of zeitgeber's 24 h cycle, and good operation of the
circadian timing system's (CTS) components, which are connected to photic and nonphotic synchronizations. This synchronization can be influenced by age, neurological disorders,
and lifestyle. In terms of aging, the synchronization to
zeitgeber's cycle increases the CTS maturity level [14]. The
rhythm stability measured by IS has a direct relationship
with quality of life measures. Studies have shown that IS is
directly related to rhythm amplitude and light exposure
[12,10], Mini Mental State Examination [4], and sleep quality
[3]. A well synchronized rhythm is associated with less
fragmentation, less nocturnal activity, and better cognitive,
behavioral, and emotional functioning [12,4].
Studies using the nonparametric approach, such as those
cited above, have calculated the fragmentation and stability
of rhythm using a 1 h interval for analysis. However, new
actimetry sensor models have been developed, and with the
increase in storage capacity, limitations on sampling rates
have been overcome. Now that current actimetry sensors are
able to record data at a variety of intervals instead of only 1 h,
it is possible for rhythm fragmentation data to be analyzed at
different intervals. For this reason, we propose a new method
of quantifying fragmentation and synchronization data by
extracting sampling intervals from 1 min to 60 min. In our
study, we used a simulated time series of human and
experimental animal rest–activity records obtained by the
use of three different devices.
159
were obtained using three different devices, data from
human studies, and animal models.
Simulated series
To construct the simulated data we used two types of time
series: (i) random data with normal distribution (equal to 1
mean) known in physics as noise, and (ii) a sinusoidal wave
with amplitude equal to 1 and whose negative values were
replaced with zeros. The duration of these series corresponded to 60 cycles of 1440 min each, thus simulating 60
days with a sampling rate of 1 min.
Based on these two types of time series, we created three
types of simulated data. The first consisted of a sinusoidal wave
with a period equal to 1440 min multiplied by a noise (mean¼ 1
and standard deviation varied). The second set was similar to the
first; however, the mean of the noise (which in previous conditions was equal to 1) varied every 30 min. The third set consisted
of sinusoids with periods of 480, 1440, 1470, and 1500 min.
Experimental data
Our data were obtained from three different systems: (i) an
actimetry sensor Actiwatchs-16, trademarked by Mini-Mitter
Co., which recorded the acceleration variation in three axes at a
32 Hz frequency and stored the accumulated value each minute; (ii) an actimetry sensor by Tempatilumi, CE Brasil, which
recorded the variation in acceleration that occurred each
minute; and (iii) infrared motion sensors that recorded the
locomotor activity and stored the total movements every 5 min.
These three systems were used to verify the behavior of
variables IV and IS in connection with the proposed method
to analyze the data obtained by different devices. In addition,
we have used two different animal models, rat (nocturnal and
polyphasic) and marmoset (daytime and biphasic).
The Actiwatch was used to record the locomotor activity
during one week in two groups: (i) 24 healthy people (38–69
years), and (ii) 52 patients with cerebrovascular accident (55–
75 years). The motor activity of 26 patients with Parkinson's
disease (42–76 years) and 24 healthy young individuals (18–23
years) were analyzed using Tempatilumi during one week. In
the animal studies, the motor activity of 6 rats and 8
marmosets was recorded during one week using the sensor
system as they remained in cages. The animals were kept in
light conditions with a cycle of 12 h light and 12 h dark.
The study was approved by the Federal University of Rio
Grande do Norte's Institutional Review Board (CEP-HUOL: the
University Hospital Onofre Lopes' research ethics committee
code: 048/09 and 302/09), and conducted in accordance with
the criteria established by Resolution 196/96 of the Brazilian
National Health Council.
Data analysis
Methods
In the present study we used an artificially created time
series with known behavior and data recorded from human
and experimental animal studies. The simulated data
allowed us to verify the performance and robustness of the
new methodology. The rest–activity experimental records
From the actigraphy experimental data, four nonparametric
variables were calculated: IS, IV, M10, and L5 [12]. In our study
we modified the method of calculation for IV and IS by
modifying the time intervals of analysis. The fragmentation
(IV) was calculated as the ratio of the mean squares of the first
derivative and its population variance. The interdaily variability
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Sleep Science 7 (2014) 158–164
(IV) was calculated for resampled ranges between 1 and 60 min.
The IV, calculated with a 1 h interval, was named IV60. Based
on the IV profile, we estimated two parameters of interest: (i)
mean IV for each sampling interval (IVm); and (ii) IV for an
interval equal to 60 min (IV60). The existing normalization in IV
calculation can make this index insensitive to large variations
in data amplitude. To verify this, two time series formed by
simple noise were used with variance equal to 0.05 and 0.5.
Interdaily stability (IS) was calculated with data sampled
every 60 min (IS60); and the mean IS for the sampling
intervals divisors of 1440 between 1 and 60 min (ISm). The
intervals were 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30,
32, 36, 40, 45, 48 and 60 min.
We used various sizes of simulated data to verify variable
IS behavior. The analysis was performed in two sine functions: one with a period equal to 1470 and the other at
1500 min. Moreover, in this data, IS was calculated simulating
different records sizes.
Results
Simulated data
The first analysis was performed using two random data
groups with a normal distribution. Both presented a mean of
1, but the first group's variance was 0.05 and the other
presented variance equal to 0.5. The IV calculation (Fig. 1A)
showed noise amplitude and sampling rate independence.
There were no significant differences between groups regarding the sampling method (n ¼100).
Interdaily variability was calculated for each simulated time
series group: the pure rectified sinusoid function, sinusoid with
simple noise, and sinusoid with compound noise (Fig. 1B). For all
calculated IV intervals, the time series with compound noise
showed the highest values, whereas the series with pure
sinusoid showed the lowest IV values. An increase in the
compound noise IV profile was observed after 30 min.
In order to evaluate the noise effect on IV values, we
changed the noise value modulated by sinusoid variance
from 0 to 2, and calculated IVm and IVerror. By increasing
the noise variance value, we also increased IVm and IVerror
(Fig. 1C).
Nonparametric variables were also calculated for different
periods of sine functions: 8, 24 and 24.5 h (Table 1). The IV
profile for sin24 and sin24.5 were found to be similar;
however, it differed from the sin8 IV profile (Fig. 2A). In order
to evaluate rest–activity rhythm stability, IS60 and ISm were
calculated for series of the same amplitude but with different
periods and durations. IS60 and ISm values were equal to 1
for both sin8 and sin24, as the other variables presented
different values; this is explained because 8 h is a multiple of
Fig. 1 – Calculation of fragmentation simulated data in different conditions. (A) Profile IV calculated for randomly distributed
data with equal variances 0.05 and 0.5; (B) IV calculated for three types of simulated signals, pure sine wave, sine and noise
with single sinusoid plus noise compound; (C) analysis of behavior of IVerro and IVm parameters for different intensities of
noise modulated by a sinusoid.
Sleep Science 7 (2014) 158–164
Table 1 – Values of non-parametric variables for the three
sine waves with period equal to 24, 24.5 and 8 h.
Variable
T ¼24
T ¼ 24.5
T¼ 8
IS60
ISm
IV60
IVm
M10
L5
1
1
0.0680
0.0233
1043.8
21.2004
0.5517
0.5518
0.0658
0.0225
1049.7
20.361
1
1
0.5835
0.2033
709.6933
160.3758
24 h. Functions sin24 and sin24.5 presented different IS
values, although the other variables presented similar values.
In addition, the IS60 value for sin24.5 and sin25 were reduced
by increasing the length of time analyzed, suggesting that
IS60 values depend on the analyzed time series size (Fig. 2B).
Experimental data
The results obtained using the Actiwatch showed that
patients with cerebrovascular disease have reduced activity
compared to the control group (Table 2). Analyzing IVm, we
found that these patients' rhythm was more fragmented. On
the other hand, when using IV60, no significant difference
was found between groups (Student's t-Test). The IV profile
was calculated for the control group and patients with
cerebrovascular disease (Fig. 3A). In all calculated intervals,
the mean IV was higher for the patient group. There were
significant differences for different intervals using Student's
t-Test, shown in Fig. 3B.
Analysis of the Tempatilumi data demonstrated that
people with Parkinson's disease (PD) showed reduced activity
compared to young individuals (Table 3). The rhythm of the
oldest population was more fragmented when analyzing the
following variables: IVm, IVerror, and IV60. As for synchronization, we found a tendency (p ¼0.0583) between groups, as
the young individuals were more synchronized to zeitgeber's
24 h cycle. The IV profile was calculated for each group
(Fig. 4A). In all calculated intervals, the mean IV was higher
for patients with PD. There were significant differences for
different intervals (Fig. 4B) (Table 4).
Analysis of the data obtained from animals using infrared
sensor showed that rats' rhythm was more fragmented at
intervals 15, 20, 25, 30, and 35 (Fig. 5A). Rats presented higher
values for M10 and L5 when compared to marmosets.
Discussion
The main contribution of this study is the implementation of
alternative methods of nonparametric variables analysis
which aims to more precisely detect sleep–wake cycle fragmentation and synchronization. The statistical analysis of
the simulated data showed its methodological ability to
detect fragmentation in known intervals. In addition, the IS
calculation, using different re-samplings, enables a higher
sensitivity of this methodology. In regards to the time series
size, we observed that it is important to be careful when
using IS index.
161
It was not possible to detect rhythm fragmentation in
patients with cerebrovascular disease using the classical IV
calculation with a 60 min sampling. However, when using
different sampling rates, it was observed that patient rhythm
was more fragmented than in the control group. As in other
studies [10], the use of variable IV60 was not efficient to
detect differences in sleep fragmentation in both groups. We
propose that by utilizing only the IV calculated for the 60 min
interval, one may lose the sensitivity needed to determine
rhythm fragmentation. The new method appears to be more
sensitive to rhythm fragmentation. Moreover, by calculating
IVm and IVerror, significant differences were observed
between the groups, with the IV60 p-value approximately 14
times greater than that calculated for IVm and IVerror. This
greater sensitivity shall encourage the use of this new
method. Furthermore, to our knowledge there are no reports
demonstrating that IV calculated by hourly sampled data is
the best method to identify rhythm fragmentation.
The IV profile on the data collected with the Tempatilumi
device showed a greater fragmentation at sampling intervals
of 1–8 min. This pattern is similar to the one observed in the
noise profileþsin24. This is likely due to the equipment's
recording methodology, which measures acceleration in
three axes, then repeats the procedure at 1 min and records
the acceleration variation. This method ignores the movements which occur between one measurement and another.
This should create a type of noise that is modulated by the
circadian rhythm, such as the simulated data.
In the animal data, fragmentation calculated every hour
showed no significant differences in rhythm between rats
and marmosets. In addition, neither of new variables IVm
identified a significant difference in fragmentation, only
a tendency (both with p-value equal to 0.0628). However, in
sampling intervals of 15–35 min, the rhythm fragmentation
in rats was greater than that found in marmosets. This may
be explained by the alternation in rats' sleep phases, which
occur in periods of 15–35 min [1,2].
The simulated data analysis has shown the proposed method
robustness. Noise analysis, even with different amplitudes, was
not significantly different. The compound noise analysis showed
that it is possible to identify a distinct peak at 30 min of a known
interval. The pure sinusoid presented the lowest IV values and
by increasing the modulated noise amplitude using sinusoid,
there was an increase in IV.
Similarly to Van Someren et al., we have also found IV
random data values next to two [10]. The method robustness
was demonstrated with the simulated data analysis. Random
data with different amplitudes showed high IV in all intervals, and no significant differences. This can be explained by
the IV equation in which the denominator is the data
population variance.
Pure sinusoid showed the lowest IV value, as there was
a small variation between measurements. Ortiz-Tudela et al.
have also found IV60 close to zero for sine wave [8]. IV values
grew as we increased noise multiplied by the sinusoid. OrtizTudela et al. calculated IV equal to zero for sine wave, which
increased as noise was included [8].
Our study demonstrated that the calculation of the synchronization to the 24-h light–dark cycle (IS) was significantly
related to the length of the time series analyzed. Simulated
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Sleep Science 7 (2014) 158–164
Fig. 2 – Calculation of fragmentation and the stability of the rhythm in sinusoids with different periods of simulated data.
(A) IV measured profile for the three sinusoids with a period of 8.24 h and 24.5; (b) behavior of is 24.5 for two sinusoids of
different lengths and 25 h in days.
Table 2 – Values of non-parametric variables for the control group and patients with stroke.
Control
IS60
ISm
IV60
IVm
L5
0.6381
0.5267
0.8162
0.6648
3.438e5
10,805
AVE
(0.0907)
(0.0822)
(0.2090)
(0.1626)
(1.098e5)
(7769)
p-Value
0.6182
0.4940
0.9190
0.7834
2.466e5
10,564
(0.1442)
(0.1142)
(0.2649)
(0.1769)
(1.203e5)
(833.06)
0.5361
0.2119
0.0983
0.0068
4.0341e 13
0.7894
Fig. 3 – Calculation of fragmentation of the circadian rhythm of activity and rest recorded at Actiwatch. (A) Calculation of
profile IV data of the control group and patients with stroke; (B) level of statistic difference between the control groups. For
each re-sampling values of the two groups IV and were calculated by two-tailed t-test value was obtained from p.
Table 3 – Values of non-parametric variables of the young and oldest group with Parkinson's.
Young
IS60
ISm
IV60
IVm
M10
L5
0.5498
0.4254
0.6069
0.5970
76,148
5781
(0.1287)
(0.1028)
(0.6069)
(0.0683)
(7015)
(883.67)
data showed that this relationship is greater as the free-running
period approaches 1440 min. This finding can be applied for
both simulated and experimental data. IS was calculated by
Oldest þParkinson
p-Value
0.4871
0.3688
0.7336
0.7182
68,800
5936
0.0647
0.0349
o0.0001
o0.0001
o0.0001
0.4891
(0.1053)
(0.0812)
(0.0435)
(0.0288)
(1011)
(688.92)
dividing data into 1440 min intervals (light–dark cycle external
period); therefore, to calculate the mean IS (ISm), it was applied
interval divisors of 1440. Our data showed that in all studies,
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Sleep Science 7 (2014) 158–164
Fig. 4 – Calculation of fragmentation of the circadian rhythm of activity and rest recorded at Tempatilumi. (A) Calculation of
profile IV data of young and old with Parkinson's; (B) level of statistic difference between groups. For each resampling the IV
values of the two groups and were calculated by two-tailed t test was obtained p value.
Table 4 – Values of non-parametric variables for the group of rats and marmosets.
IS60
ISm
IV60
IVm
IVerror
M10
L5
Marmoset
Rat
0.6111
0.5067
0.8571
0.6951
0.6694
5041
0.6656
0.4455
0.3529
0.9834
0.9198
0.8941
12,132
823.433
(0.1529)
(0.1436)
(0.3275)
(0.2052)
(0.2052)
(1737.4)
(0.8381)
p-Value
(0.1435)
(0.1061)
(0.3259)
(0.1613)
(0.1613)
(5463.2)
(529.5)
0.0781
0.0643
0.5121
0.0628
0.0628
o0.01
o0.01
Fig. 5 – Calculation of fragmentation of the circadian rhythm of activity and rest recorded with infrared sensor. (A) Calculation
of rats and marmosets IV profile; (B) Level of statistical difference between groups. For each resampling the IV values of the
two groups and were calculated by two-tailed t test was obtained p value.
ISm value is more sensitive and can even present a significant
difference when compared to IS60.
Our study proposes the use of a more sensitive method for
circadian rhythm analysis that may improve the study of the
rest–activity rhythm in humans. Traditional 60 min data analysis
of IV calculation (IV60) in cerebrovascular disease patients was
not able to detect significant differences between groups. The
same results were obtained by many other studies that adopted
the same method of analysis. With the implementation of the
proposed method of analysis, it will be possible to increase the
sensitivity of the circadian rhythm fragmentation and synchronization measurements.
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Sleep Science 7 (2014) 158–164
Conclusions
The results of this study suggest new variables for circadian
rhythm studies: mean IV for each sampling interval (IVm)
and mean IS for sampling intervals divisors of 1440, between
1 and 60 min (ISm). In our knowledge this is the first study to
propose a more sensitive method of detecting circadian
rhythm alterations.
Competing interests
The authors declare no competing interests.
Acknowledgments
We thank CNPq – 305290/2009-6 and FAPERN – 20231195722003
for financial support.
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