automatic identification of activity–rest periods based on actigraphy

ORIGINAL ARTICLE

Automatic identification of activity–rest periods basedon actigraphy

Cristina Crespo • Mateo Aboy •

Jose Ramon Fernandez • Artemio Mojon

Received: 15 September 2011 / Accepted: 12 February 2012 / Published online: 1 March 2012

� International Federation for Medical and Biological Engineering 2012

Abstract We describe a novel algorithm for identifica-

tion of activity/rest periods based on actigraphy signals

designed to be used for a proper estimation of ambulatory

blood pressure monitoring parameters. Automatic and

accurate determination of activity/rest periods is critical in

cardiovascular risk assessment applications including the

evaluation of dipper versus non-dipper status. The algo-

rithm is based on adaptive rank-order filters, rank-order

decision logic, and morphological processing. The algo-

rithm was validated on a database of 104 subjects including

actigraphy signals for both the dominant and non-dominant

hands (i.e., 208 actigraphy recordings). The algorithm

achieved a mean performance above 94.0%, with an

average number of 0.02 invalid transitions per 48 h.

Keywords Arterial blood pressure � Actigraphy �Actigraphy algorithms � Cardiovascular risk � Activity/rest

identification

1 Introduction

Ambulatory blood pressure monitoring (ABPM) has been

widely used over casual office blood pressure (BP) read-

ings to improve the diagnosis and treatment of hyperten-

sion and to assess cardiovascular risk [8, 15]. ABPM is a

fully automated technique in which BP measurements are

taken at regular intervals (usually every 15–30 min) over a

24- or 48-h period, providing a continuous BP record

during the patient’s normal daily activities. The use of

ABPM has allowed the observation of a circadian BP

pattern. Typically, there is a decrease in systolic and dia-

stolic BP levels during periods of sleep. Subjects who

exhibit a nocturnal BP drop of at least 10% are classified as

dippers, the ones who do not show this drop are called non-

dippers. Recent studies have shown that non-dipper BP

patterns are associated with an increased frequency of

cardiovascular events, as well as target-organ damage, and

cardiovascular morbidity and mortality [5–7, 9, 10, 19].

The correct assessment of dipper versus non-dipper

requires the ability to accurately identify activity and rest

cycles. Traditionally, determination of activity and rest

cycles has been performed by assuming or imposing a fixed

schedule (for instance, the activity cycle spanning from

7:00 to 23:00 hours, and the rest cycle from 23:00 to

7:00 hours) [3]. This method can prove highly inaccurate

due to individual differences in sleep habits. Another

method involves the use of a diary where the subjects under

study keep a record of their going to sleep and wake up

times. In practice, diaries have proven to be cumbersome

and subjective. Several studies have explored the possi-

bility of using actigraphy to perform identification of sleep/

wake cycles, which provides an objective and non-obtru-

sive method to discriminate between sleep and wake

periods based on recorded activity levels [1, 20, 23]. The

typical actigraphs are wrist-worn devices that use acceler-

ometers to measure and record movement counts at uni-

form time intervals with low sampling frequencies (e.g., 1

sample per minute). The actigraphy signal can be used to

discriminate between sleep and wake cycles, but an auto-

matic algorithm is needed to perform the identification of

activity and rest cycles objectively and accurately.

C. Crespo (&) � M. Aboy

EERE Department, Oregon Institute of Technology,

Portland, OR 97006, USA

e-mail: [email protected]

J. R. Fernandez � A. Mojon

Bioengineering and Chronobiology Laboratories,

University of Vigo, Vigo, Spain

123

Med Biol Eng Comput (2012) 50:329–340

DOI 10.1007/s11517-012-0875-y

Actigraphs are less expensive than inertial measurement

units (IMUs) used in motion tracking applications [17, 18,

26], typically have longer battery life, and are designed to

be wearable during normal activities. In the last 20 years,

several algorithms have been proposed to automatically

identify sleep and wake periods from actigraphy [4, 25,

27]. More recent algorithms use additional signals such as

the electrocardiogram and respiration to achieve better

performance [14]. Most of these algorithms have been

designed as an alternative to polysomnography for the

study of sleep/wake patterns in patients with sleep disor-

ders and other conditions affecting quantity and quality of

sleep [2, 12, 13, 16, 21, 22, 24, 28]. As a consequence, they

exhibit a high sensitivity to sleep disturbances, and tend to

generate multiple wake identifications during main rest

periods. This makes them unsuitable for the identification

of activity and rest cycles in the context of ABPM and

cardiovascular risk assessment, where the objective is not

to detect wake events during periods of sleep, but rather to

determine the boundaries between the main activity and

rest periods. For this reason, short transitions between

states during a main activity or rest cycle are considered

invalid in this application.

In this paper, we describe and assess the performance of

a novel algorithm for automatic identification of activity/

rest periods from actigraphy signals intended for use in

cardiovascular risk applications involving ABPM.

2 Methods

2.1 Algorithm description

The design of an algorithm for the identification of activity/

rest cycles presents several challenges. One of these chal-

lenges is the identification and processing of invalid zeroes.

When working with actigraphy signals, it is common to

find sequences of consecutive zeroes (i.e., points where the

actigraphy signal has a value of zero). During rest periods,

it is more likely to find valid sequences of consecutive

zeroes, whereas during the day this likelihood is small, and

typically when such sequences appear during activity

periods, they correspond to instances where the actigraph

has been removed (to take a shower, for instance). The

algorithm needs to be capable of automatically identifying

the sequences of consecutive zeroes that correspond to

invalid data (i.e., actigraph removal), so that they can be

processed in a way that they do not affect the output of the

algorithm. An empirical probability model was used for

this purpose. The details regarding the methods as well as

the study performed to generate this model are included in

Sect. 2.2. Since the probability of finding valid consecutive

zeroes is different for activity and rest periods, a first stage

in the algorithm using a combined activity/rest probability

model must be able to generate an initial estimate of

activity and rest periods so that the two different proba-

bility models can be later applied to estimated activity and

rest periods separately for a more accurate identification.

Figure 1 shows a block diagram of the proposed algo-

rithm. The algorithm is comprised of two stages: (1) a pre-

processing stage, and (2) a processing and decision stage.

The aim of the first stage is to produce an initial estimate of

the activity and rest periods from the actigraphy signal. The

second stage processes the actigraphy signal using infor-

mation from this initial estimate to produce a binary signal

with the final identification of the activity and rest periods,

where rest periods are represented as a 0 and activity

periods as a 1. During the first stage, the algorithm pro-

cesses regions of consecutive zeroes corresponding to

invalid data using a combined activity/rest probability

model. A rank-order filter is then applied to the signal, and

based on an adaptive threshold, a binary signal is gener-

ated, where rest periods are represented with a 0, and wake

periods with a 1. A morphological filter is finally applied to

the binary signal to eliminate invalid transitions. The sec-

ond stage takes the original actigraphy signal, and using the

initial estimate of activity/rest regions from the pre-pro-

cessing stage, applies separate probability models to esti-

mated activity and rest periods in order to eliminate regions

of invalid zeroes. This signal validation and conditioning

process is followed by an adaptive rank-order filtering and

thresholding operation, which produces a binary signal

corresponding to a more refined estimate of activity/rest

periods. Finally, a morphological filter is applied to the

binary signal to eliminate invalid transitions and obtain the

final activity/rest identification signal. Table 1 provides a

summary of the user-specified input parameters for the

algorithm, as well as their default values. These parameters

are explained in the following section.

Fig. 1 Algorithm block diagram. The algorithm takes an actigraphy

signal s(n) as an input and produces a binary signal o(n) as an output,

where rest periods are represented as binary 0, and wake periods as

binary 1. The algorithm consists of two stages. The purpose of the

preprocessing stage is to produce an initial estimate of the activity/rest

periods from the original actigraphy signal. The processing and

decision stage processes the original actigraphy signal using infor-

mation derived from the initial estimate of activity/rest periods

generated in the preprocessing stage, to produce the final identifica-

tion of activity/rest periods

330 Med Biol Eng Comput (2012) 50:329–340

123

In the following description, we will let s(n) denote the

raw actigraphy signal in discrete time and s ¼ðs1; s2; . . .; sNÞ denote the corresponding vector of length

N, where N represents the number of elements in s(n).

2.1.1 Stage 1: preprocessing

The purpose of this stage is to produce an initial estimate of

the activity and rest periods from the actigraphy signal.

2.1.1.1 Signal conditioning based on empirical probability

model A function Ff�g is applied to s(n) in order to

determine the regions containing more than f consecutive

zeroes,

a ¼ FfsðnÞ; fg ð1Þ

where f is determined from an empirical probabilistic

model and represents the maximum number of consecutive

zeroes considered valid, and a ¼ ða1; a2; . . .; aAÞ denotes

the indices of s(n) containing the invalid zeroes (i.e.,

sequences of more than f consecutive zeroes).

The values of sðnÞ ¼ ðs1; s2; . . .; sNÞ at index locations

a ¼ ða1; a2; . . .; aAÞ are replaced by a value st corre-

sponding to a user-specified percentile t of s(n) which must

be chosen to minimize the impact of invalid zeroes. Per-

centile values above 33% bias the results towards wake

classifications and percentiles below 33% towards rest

classifications assuming a standard 8 h of sleep for every

24 h. The result of this operation is a signal x(n) such that

xðjÞ ¼ st if j 2 asðjÞ if j 62 a

�ð2Þ

Prior to filtering, x(n) is padded at the beginning and at

the end with a sequence of 30� a elements of value m =

max{s(n)}. This is done in order to use a filter window of

user-specified length Lw ¼ ð60� aþ 1Þ centered about

each element of x(n), where a represents the length of the

window in hours (8 by default). Since the subject must be

awake at the moment when the actigraphy recording is

started and stopped the value m used for padding is chosen

as the maximum value in the actigraphy signal so that it

will bias the beginning and the end of the filtered signal

towards an awake state,

xp ¼ ðm; m; . . .; m|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}30�a

; x1; x2; . . .; xN ; m; m; . . .; m|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}30�a

Þ ð3Þ

2.1.1.2 Rank-order processing and decision logic The

padded signal xp is filtered according to the following

nonlinear equation to generate the filtered actigraphy time

series xf(n):

xf ðnÞ ¼ Mfxpðn� 30� aÞ; xpðn� 30� aþ 1Þ; . . .;

xpðn� 1Þ; xpðnÞ; xpðnþ 1Þ; . . .; xpðnþ 30� aÞgð4Þ

where Mf�g denotes the median operator. Larger values of

a result in a lower number of invalid transitions between

the rest and awake states at the expense of larger inaccu-

racies in the determination of the exact transition time.

Large a values resulting in window lengths up to 12 h are

possible due to constraints imposed by the following

thresholding step, which takes into account the user-spec-

ified expected number of rest hours per night (8 h by

default).

A rank-order thresholding operation Tf�g is performed

on the filtered actigraphy signal to obtain the binary signal

y1(n), where y1(n) = 1 for y1(n) [ p and 0 otherwise. The

threshold p is the percentile of xf(n) corresponding to

ðhs=24Þ � 100%; where hs is a user-specified parameter

corresponding to the average number of hours of sleep per

night (8 by default)

y1ðnÞ ¼ T xf ðnÞ� �

ð5Þ

2.1.1.3 Morphological filtering The binary signal y1(n) is

further processed using a closing–opening morphological

filter of user-specified window length Lp in minutes. The

purpose of the morphological filtering is to eliminate

invalid transitions such as short periods of rest during

activity regions and vice versa. The result of this operation

is the binary signal ye(n)

yeðnÞ ¼ ðy1 � LpÞ � Lp ð6Þ

where y1 � Lp represents the morphological closing

operation • on the set y1 by the structuring element

Lp, that is, y1 � Lp = ðy1 � LpÞ � Lp and y1 � Lp represents

the morphological opening operation � on the set y1 by the

structuring element Lp, that is, y1 � Lp ¼ ðy1 � LpÞ � Lp:

The symbols � and � represent the morphological erosion

and dilation operations, respectively:

A� B ¼ fgjðBÞg A ð7Þ

A� B ¼ fgjfðBÞg \ Ag 6¼ ;g ð8Þ

ðBÞ represents the reflection of set B, and (B)g represents

the translation of set B by g elements, which are defined as:

Table 1 Summary of user-specified input parameters for the activity/

rest identification algorithm

Name Symbol Default

Threshold consec. zeroes f 15

Threshold consec. zeroes (wake) fa 2

Threshold consec. zeroes (rest) fr 30

Percentile for invalid zeroes t 33

Median filter window length Lw 60.8 ? 1

Average hours of sleep per night hs 8

Morph. filter window length Lp 60 ? 1

Med Biol Eng Comput (2012) 50:329–340 331

123

B ¼ fwjw ¼ �b; for b 2 Bg ð9ÞðBÞg ¼ fcjc ¼ bþ g; for b 2 Bg ð10Þ

In the case of a one-dimensional signal the operations of

erosion and dilation become the minimum and the

maximum operators, respectively. The output of this first

stage is a binary signal ye(n) containing an initial estimate

of the rest (0) and wake (1) periods.

2.1.2 Stage 2: processing and decision logic

This stage uses information from the previous stage to

produce the final identification of the activity and rest

periods for the input actigraphy signal.

2.1.2.1 Model-based data validation Given the estimated

activity and rest periods for the input actigraphy signal, we

can apply a function Gf�g to the original actigraphy signal

s(n) in order to find sequences of more than fr consecutive

zeroes during estimated rest periods, and sequences of

more than fa consecutive zeroes during estimated wake

periods,

b ¼ GfsðnÞ; fa; frg ð11Þ

where fa and fr are determined from empirical probabi-

listic models and represent the maximum number of

consecutive zeroes considered to be valid during esti-

mated activity and rest periods, respectively, and

b ¼ ðb1; b2; . . .; bBÞ represents the indices of s(n) corre-

sponding to invalid zeroes.

2.1.2.2 Adaptive rank-order processing and decision

logic Prior to filtering, s(n) is padded at the beginning and

at the end with a sequence of length 60 (i.e., 1 h) of values

m = max{s(n)}.This is done in order to bias the beginning

and the end of the filtered signal towards a wake identifi-

cation and avoid multiple invalid transitions close to the

edges.

xsp ¼ ðm; m; . . .; m|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}60

; s1; s2; . . .; sN ; m; m; . . .; m|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}60

Þ ð12Þ

An adaptive median filter Maf�g with a varying window

length is next applied to the padded time series. The

adaptive median filter outputs the median of the values of

s(n) within a moving window whose indices are not

contained in b. The maximum filter window length is the

user-specified parameter Lw. This window is adaptive since

invalid zeroes are not included in the median calculation

and the length of the window starts as 1 h at the edges and

progressively increases to a maximum window length Lw.

This is done in order to be able to maintain a symmetric

window around the current sample at the points where the

distance from the current sample to the end of the padded

signal is less than half of the maximum window length.

The result of this operation is the filtered signal

xfaðnÞ ¼ MafxspðnÞ; bg ð13Þ

The binary output y2(n) is obtained by a rank-order

thresholding operation Tf�g; where y2(n) = 1 (wake) for

y2(n) [ p and 0 (rest) otherwise.The threshold p is the

percentile of xfa(n) corresponding to ðhs=24Þ � 100%;

where hs is a user-specified parameter representing the

average hours of sleep per night (8 by default).

y2ðnÞ ¼ T xfaðnÞ� �

ð14Þ

2.1.2.3 Morphological filtering The binary output y2(n)

is further processed using a closing–opening morphological

filter in order to eliminate invalid transitions such as short

periods of rest in regions of activity and vice versa. This is

the same morphological filtering operation that was applied

at the end of the preprocessing stage, but the window

length is double in size to the one used then (i.e.,

L0p ¼ 2� ðLp � 1Þ þ 1).

oðnÞ ¼ ðy2 � L0pÞ�L0p ¼ fo1; o2; . . .; oNg ð15Þ

The first and last values of the output binary signal are

assigned a binary value of 1 (awake). This heuristic rule is

derived from the constraint that the subject must be in an

awake state when the actigraph is connected or

disconnected.

o1 ¼ oN ¼ 1 ð16Þ

The result of this step is the final discrete binary output

signal of length equal to the original actigraphy signal. A

binary 0 represents a rest state, and a binary 1 represents an

awake state.

2.2 Probability models

When working with actigraphy signals, it is common to

find regions of consecutive zeroes. Some of these corre-

spond to periods of very low activity (mostly during sleep),

and some are the result of momentarily disconnecting the

actigraph (to take a shower, for instance). When using

actigraphy signals to determine activity/rest cycles, it is

necessary to differentiate the regions of consecutive zeroes

representing invalid data (i.e., disconnections) from the

regions of valid consecutive zeroes (i.e., low activity), in

order to avoid misclassifications. A probability model was

developed to determine the threshold between the number

of consecutive zeroes to be considered valid or invalid. The

methodology is described in this section.


123

2.2.1 Probability model definition

Let us assume a situation where we have a perfect data-

base, containing actigraphy signals with true and accurate

information regarding what zeroes correspond to low

activity and are valid data, and what zeroes are invalid. Let

z denote the number of consecutive zeroes. Let Pj(z) denote

the probability of finding z consecutive zeroes that are

valid in a subject j from a sample under study, that is,

j ¼ 1; 2; . . .; J; where J represents the number of subjects in

the sample under study. For each subject j in the sample

under study we can estimate the maximum number of valid

consecutive zeroes fj such that Pjðz fjÞ\0:05; that is,

f jjfP jðz f jÞ\0:05g ð17Þ

where f j represents the maximum number of consecutive

zeroes that are valid for subject j. This estimation can be

done using Monte Carlo methods for each subject j,

f jjfP jðz f jÞ\0:05g� �J

j¼1¼ ðf1; f2; . . .; fJÞ ð18Þ

that is, for subject j = 1, we find that f1 is the maximum

number consecutive zeroes that satisfies P1ðz f1Þ\0:05

and so on for all the subjects in the sample j ¼ 1; 2; . . .; J:

In the simplest probability model for random data (i.e.,

the one-sample model) a single unknown probability dis-

tribution Z produces the data vector f ¼ ðf1; f2; . . .; fJÞ by

random sampling. The notation Z ! f indicates the vector

f contains an independent and identically distributed

sample drawn from Z,

Z ! f ¼ ðf1; f2; . . .; fJÞ ð19Þ

We use the sample f to calculate the statistic of interest

h ¼ sðfÞ: To assess the statistical behavior of the statistic

h we use bootstrap. In this case, the statistic of interest

h ¼ sðfÞ is specific percentile pf (i.e., the 90th percentile).

Once this statistic of interest h ¼ sðfÞ is estimated we can

obtain the 90% confidence interval for h directly using the

percentiles of h�: In order to make use of bootstrap we

must have a probability model for the data. In the case

of the one-sample model Z gives the observed data

f ¼ ðf1; f2; . . .; fJÞ by random sampling, Z ! f: To

perform bootstrap we substitute the unknown probability

distribution Z for the empirical distribution Z� obtained

from the data.

From the empirical distribution Z� we obtain bootstrap

samples by random sampling,

Z� ! f� ¼ ðf�1; f�2; . . .; f�JÞ ð20Þ

These samples enable us to calculate bootstrap

replications of the statistic of interest h� ¼ sðf�Þ; from

which we can perform probabilistic calculations directly

using the bootstrap percentiles, that is, we can use the

histogram of h�kðbÞ; b ¼ 1; 2; . . .; B as an estimate of the

probability density function and bootstrap confidence

intervals for the population are obtained as

hklo¼ 100� athpercentile of h�k’s distribution

hkup¼ 100� ð1� aÞthpercentile of h�k’s distribution

In the context of our problem, we have a three sample

probability model, that is, F = (Z, Za, Zr) where Zr denotes

the probability distribution of the maximum number of

valid consecutive zeroes during rest periods, Za denotes the

probability distribution of the maximum number of valid

consecutive zeroes during activity periods, and Z denotes

the combined activity/rest probability distribution.

Z ! f ¼ ðf1; f2; . . .; fJÞ ð21Þ

Za ! fa ¼ ðfa1; fa2; . . .; faJÞ ð22Þ

Zr ! fr ¼ ðfr1; fr2; . . .; frJÞ ð23Þ

The procedure described above is used to generate an

empirical distribution F* = (Z*, Z*a, Z*r), calculate the

statistic of interest h ¼ sðfÞ for each distribution, and

assess the statistical behavior of the statistic using

bootstrap replicas.

An independent study was conducted using a database

designed for determining the probability model (different

from the database used for algorithm assessment described

in the section below) containing 50 adult healthy subjects,

whose actigraphy signals were monitored for 48 h. The

study took place in Galicia (Spain), and it was approved by

the state Ethics Committee of Clinical Research. All sub-

jects gave written informed consent. The subjects were

diurnally active and nocturnally resting healthy young

adult volunteers, 29.51 ± 11.89 years of age. For the

duration of the experiment, the subjects were asked to keep

an accurate diary of the times when they went to sleep,

woke up, and disconnected the actigraph. In practice, dia-

ries are typically imprecise and subjective. However, in

this case the study included research volunteers motivated

to keep an accurate diary and the need for accuracy in the

diary was strongly emphasized. Using Monte Carlo meth-

ods, a probability model was generated, representing the

probability density function for finding a certain number of

consecutive zeroes in an actigraphy signal. For every

actigraphy signal of length L = 48.60 (i.e., 48 h), 100�L

experiments were performed. Each experiment consisted of

randomly choosing a sequence of length n from the

actigraphy signal, then recording the ratio of the number of

sequences selected where all the elements were equal to

zero. This was done for values of n such that 1 B n B L.

Figures 2 and 3 show the results of the study to determine


123

the probability of having z consecutive zeroes during

activity and rest periods, respectively. The lighter lines

represent the probability model for each actigraphy signal,

the darker line is an average of these probability models

for all the actigraphy signals in the database. Based on

the bootstrap analysis of these results, the algorithm uses

F ¼ ðf; fa; frÞ ¼ ð15; 2; 30Þ by default.

2.3 Algorithm assessment

2.3.1 Assessment database

The algorithm was validated on a database containing ac-

tigraphy recordings of 48 h for 104 subjects. The study

took place in Galicia (Spain), and it was approved by the

state Ethics Committee of Clinical Research. All subjects

gave written informed consent. The subjects were diurnally

active and nocturnally resting healthy young adult volun-

teers, 22.43 ± 1.66 years of age. All participants wore two

actigraphs (Mini-Motion-Logger, Ambulatory Monitoring

Inc., Ardsley, New York, USA), one on each wrist, to

monitor their physical activity every minute. This compact

(about half the size of a wristwatch) device functions as an

accelerometer. During this experiment, ABPM was also

monitored on the non-dominant arm, with ABPM mea-

surements being taken every 20 min between 7:00 and

23:00 hours, and every 30 min between 23:00 and 7:00

hours. The same computer was always used to synchronize

the internal clocks of the two actigraphs. For every subject,

the assessment database includes two actigraphy signals,

corresponding to simultaneous recordings for the dominant

and non-dominant hands, respectively (i.e., 208 record-

ings). The participants agreed to keep an accurate diary of

the times when they went to sleep and woke up for the

duration of the experiment. This diary was used as the

reference for the assessment and evaluation of the algo-

rithm performance. The average number of sleep hours per

night recorded by the subjects included in the validation

database ranged from 5 to 11 h, with 67 out of the 104

subjects recording an average of 8–9 h of sleep per night.

2.3.2 Performance metrics

The assessment of sleep/wake detection algorithms pre-

sented in the literature has been based on metrics that

quantify the amount and quality of sleep [4, 25, 27]. These

are suitable metrics for the study of sleep disorders and

other conditions affecting sleep, but are not relevant or

adequate metrics in the context of cardiovascular risk

assessment using ABPM. For ABPM applications, the

objective is not to assess quantity and quality of sleep, but

to accurately identify the boundaries between the main

activity and rest periods, so that the value of different

ABPM parameters can be calculated separately for activity

and rest BP signals. These parameters include the awake

and sleep systolic, diastolic, and pulse pressure blood

pressure means, and the systolic, diastolic, and pulse

pressure sleep time relative declines. Additionally, ABPM

research and clinical practice is based on the underlying

idea that it is important to record blood pressure during the

normal activity of the subject. Consequently, the gold

standard needs to be adequate for collection over 48 h

periods under ambulatory conditions (i.e., during normal

daily activity over 2 days). This disqualifies the established

gold standard of polysomnography (PSG) used in sleep

research to assess actigraphy algorithms, since it is not

possible to do acquisition during normal life activities over

48 h.

Fig. 2 Results of the study to determine the probability of having

z consecutive zeroes during sleep periods

Fig. 3 Results of the study to determine the probability of having

z consecutive zeroes during wake periods


123

For these reasons, a more adequate reference signal was

chosen, which could be collected under ambulatory con-

ditions, and a new set of metrics was defined which are

more adequate and relevant for the application at hand. The

definition of these metrics uses actigraphy signals for both

dominant and non-dominant hands, as well as a diary of

sleep and wake up times. In order for these metrics to be

valid, it is important that the diary be accurate, and

therefore the participants in the assessment studies must be

motivated and trained to keep an accurate diary. In the

absence of a true gold standard, accurate diaries of strongly

motivated and trained research volunteers were used as the

reference. Diaries have inherent accuracy limitations, and

for this reason the carefully collected diary has not been

labeled as the ‘‘gold standard’’ but rather the ‘‘reference

signal.’’ In ABPM applications, where activity and rest

have typically been determined by assuming a fixed sche-

dule, the best current practice is to use a diary for deter-

mination of main activity and rest cycles, and therefore the

selection of reference signal was made to match the best

current practice.

Three performance metrics (PM) were defined to evaluate

the performance of automatic activity/rest identification

algorithms based on actigraphy for ABPM applications.

These metrics were labeled PM1 through PM3.

• PM1 represents the percent coincidence between the

algorithm output and the desired output (diary) in 1-min

intervals.

• PM2 represents the percent coincidence between the

algorithm output for the dominant versus the non-

dominant hand actigraphy signals in 1-min intervals.

• PM3 represents the average number of invalid transi-

tions per 48-h period.

PM1 provides a measure of the ability of the algorithm to

correctly identify 1-min segments as belonging to an

activity or rest period in comparison to the subject’s diary.

For the application at hand, it is important to have an

accurate identification of activity and rest periods, and there

is no practical difference between inaccuracies due to false

positives or false negatives. For this reason, both types of

errors were lumped into a single metric PM1, as opposed to

separately measuring specificity and sensitivity. Even

though in this experiment it was emphasized that subjects

kept an accurate diary of their going to sleep and getting up

times, there can be more or less of a delay between the time

that a subject records as going to sleep and the time when

the subject falls asleep, as well as between the time the

subject wakes up and the time later recorded as getting up.

PM2 overcomes this limitation by measuring the coinci-

dence between the algorithm output when applied to the

dominant versus the non-dominant hand signals. The cor-

relation between the two hands is an indicator of the

algorithm’s accuracy, since a difference in output between

the two hands indicates an incorrect identification for one of

the signals (i.e., a subject cannot be in an activity cycle

according to one hand, and in a rest cycle at the same time

according to the other hand). PM2 thus provides a measure

of the reliability of the result of the algorithm regardless of

the value of PM1. Low values of PM2 could indicate that

the ABPM monitor is affecting the level of activity in the

non-dominant arm, since the placement of the actigraph

should have no effect on the performance of activity/rest

assessment with actigraphy [11]. This performance metric

is independent of the diary, and therefore will not be

affected by diary inaccuracies. PM3 is also an important

indicator of algorithm performance, as the purpose of the

algorithm is to identify main activity and rest periods. This

implies we want to avoid short transitions between states,

which are sometimes caused by low activity levels during

an activity period (e.g., taking a nap during the day) or high

activity levels during a rest period (e.g., waking up at night

to drink a cup of water). This last metric provides a measure

of the robustness of the algorithm to such events. Better

algorithm performance corresponds to values for PM1 and

PM2 as close as possible to 100%, and values of PM3 as

close as possible to zero.

3 Results

Figure 4 shows an illustrative example of the algorithm

operation on an actigraphy signal selected from the

assessment database. This figure exemplifies some of the

most common difficulties related to processing of actigra-

phy signals to extract the main activity and rest cycles, and

provides a graphical representation of the different steps

performed by the algorithm to produce the binary activity/

rest output signal from the original actigraphy signal. On

the top graph, a representative actigraphy signal is shown

in a light color. During the first stage of the algorithm (i.e.,

preprocessing stage), the sequences of invalid zeroes are

identified and assigned a value equal to the 33% percentile.

In the graph, the invalid zeroes appear as a series of dots

superimposed on the x-axis. A rank-order filter is then

applied to the modified actigraphy signal. The filtered

signal is shown in a darker color, superimposed on the raw

actigraphy signal. A thresholding operation is performed

on the filtered signal, with the threshold set to the appro-

priate percentile, according to the user-specified average

number of sleep hours per night (8 by default). The

threshold appears as a light-colored horizontal line at

around 165 counts/min. The initial binary output estimate

is generated based on this threshold. Values of the filtered

signal lower than the threshold translate into a binary 0 in

the output signal, the rest translate into a binary 1. This


123

initial binary signal is shown in the bottom graph in a

lighter color. Finally, a closing–opening morphological

filter is applied to the binary signal to eliminate transitions

of short duration, which would represent short periods of

rest in a wake region, or short periods of activity in a rest

region. Since the purpose of the algorithm is to detect the

main activity/rest cycle, these short periods are considered

invalid. The filtered binary signal appears in a darker color

superimposed on the unfiltered binary signal. In this case,

an invalid rest period around the 20:00 hours on the first

day was corrected by the morphological filter. The two

gray boxes on the bottom subplot represent the periods of

rest annotated in the diary. A perfect coincidence between

the algorithm output and the diary would correspond to an

output binary signal which has a value of 0 inside the gray

boxes, and a value of 1 everywhere else. Figure 4 illus-

trates the robustness of the algorithm when dealing with

periods of low activity and disconnections of the actigraph

during a wake cycle, such as the period between the 18:00

and 00:00 hours of the first day, due to the ability of the

morphological filter to eliminate invalid transitions. In this

example, the algorithm performed as follows: PM1 (dom-

inant) was 95.7%, PM1 (non-dominant) was 95.6%, PM2

was 95.7%, and PM3 was 0. This type of signal presents

significant challenges for less complex algorithms such as

the classical algorithms (Cole [4], Sadeh [25], and Oakley

[27]) designed for sleep disorders, or simple single-stage

algorithms that do not take into account the empirical

probability model to differentiate valid from invalid zeroes

for a given actigraph.

Table 2 shows the results of the prospective assessment

study of the proposed algorithm on the entire assessment

database. The table summarizes the results using average

values of statistical measures of central tendency and dis-

persion across all the signals in the database. For all the

results presented, the user-specified input parameters to the

algorithm were set to their default values. The performance

metrics shown are the percent coincidence between the

algorithm output and the diary using the actigraphy signal

from the dominant hand and the non-dominant hand,

respectively, and the percent coincidence between the

algorithm output for the dominant versus the non-dominant

hands. The table shows that the mean value for all three

performance metrics is greater than 94.0%, the median is

greater than or equal to 97.3%, and the standard deviation

is no greater than 3.3%. The range of the results over the

104 subjects in the database is between 80.6 and 99.1%

when comparing the algorithm output to the diary (using

the actigraphy signal from either the dominant or the non-

dominant hand), and between 86.9 and 99.7% when mea-

suring the agreement between the output of the algorithm

applied to the dominant versus the non-dominant hand. The

average number of invalid transitions per 48 h is less than

or equal to 0.02.

Fig. 4 Example of results

illustrating the performance of

the algorithm on a real

actigraphy signal collected with

a wrist actigraph. The

actigraphy signal appears in the

top subplot in a lighter color,

with the filtered signal

superimposed in a darker color.

The invalid zeroes are marked

with dots along the horizontal

axis. The horizontal line

represents the threshold used to

discriminate between rest and

activity in the first stage. The

bottom subplot shows the binary

signal (0 = rest, 1 = activity),

before (lighter color) and after

(darker color) the

morphological filtering

operation. The two gray boxesrepresent the periods of rest

recorded in the diary. The

desired algorithm output would

be zero in the region covered by

the gray boxes, and 1

everywhere else


123

4 Discussion

4.1 Algorithm performance

The illustrative example of Fig. 4 shows that the proposed

algorithm is robust to the type of challenges typically

encountered in ABPM research and clinical practice

involving actigraphy signals for objective activity/rest

identification in the context of cardiovascular risk assess-

ment. These challenges include actigraph disconnections,

activity spikes during main rest periods, periods of low

activity during main awake periods, and gradual transitions

between main activity and rest periods. While Fig. 4

exemplifies the algorithm output for a single representative

signal in the assessment database, the results shown in

Table 2 demonstrate that the algorithm performed similarly

for all other signals in the database, both in terms of

accuracy in the identification of the activity/rest regions as

well as the avoidance of invalid transitions.

Currently available algorithms are susceptible to the

technical difficulties mentioned above, resulting in mis-

identifications and invalid transitions. Figure 5 provides a

comparison between the desired output and the output

obtained using the proposed (Crespo) and classical (Cole,

Sadeh, and Oakley) actigraphy algorithms. This example

comparison is shown for illustrative purposes using a rep-

resentative signal from the assessment database. The first

graph shows an actigraphy signal collected with a wrist

actigraph. The second graph corresponds to the activity/rest

periods recorded in the diary (i.e., the desired algorithm

output). The three plots that follow show the output of some

of the classical sleep/wake identification algorithms

(namely, the algorithms proposed by Cole, Sadeh, and

Oakley). Since these algorithms have been tailored to the

study of sleep disorders, they exhibit a high sensitivity to

sleep disturbances, and tend to generate multiple wake

identifications during main rest periods. While this high

sensitivity is a desirable characteristic in the study of sleep

disorders, it makes these algorithms unsuitable for the

identification of activity and rest cycles in the context of

ABPM and cardiovascular risk assessment, where the

objective is not to detect wake events during periods of

sleep, but rather to determine the boundaries between the

main activity and rest periods. For this reason, short tran-

sitions between states during a main activity or rest cycle

are considered invalid in this application. The last plot

corresponds to the output of the proposed algorithm

(Crespo). This example illustrates the advantage of using

the proposed algorithm over the classical ones. It can be

seen that in this example the Crespo algorithm performs a

better identification of the main activity and rest cycles than

any of the classical ones, avoiding the large number of

invalid transitions detected by the classical algorithms

designed for sleep disorder applications.

4.2 Clinical application

While activity/rest identification algorithms based on

actigraphy have applicability in several biomedical appli-

cations, the proposed algorithm was designed to satisfy the

specific requirements of a particular application, namely

cardiovascular risk assessment using ABPM with actigra-

phy. As explained in the introduction, the proper determi-

nation of dipper versus non-dipper, nocturnal versus

diurnal BP, as well as other assessment parameters requires

the ability to identify the major activity and rest cycles

automatically, accurately, and objectively. Researchers in

the ABPM community have relied on actigraphs to aid in

the determination of activity and rest cycles primarily using

a combination of the classical sleep disorder algorithms

previously mentioned, visual inspection of the actigraphy

signal, and patient diaries. The proposed algorithm will

enable researchers to automate the process (i.e., eliminat-

ing subjective visual inspection and inaccurate diaries),

Table 2 This table shows the results of the assessment study for the proposed actigraphy algorithm

PM1 (dominant) PM1 (non-dominant) PM2 (Dom vs. Nond)

Median (%) 94.8 94.8 97.3

Mean (%) 94.3 94.1 96.6

SD (%) 3.3 3.2 2.4

Max (%) 99.1 99.1 99.7

Min (%) 80.6 81.5 86.9

Average PM3 0.02 0.02 –

The performance metrics shown are the percent coincidence between algorithm and diary using the actigraphy signal from the dominant hand,

and the non-dominant hand, respectively, and the percent coincidence between algorithm output for dominant versus non-dominant hands. For

each performance metric, the mean and median values are greater than 94.0%, the standard deviation is no greater than 3.3%, and the range of

performance (min to max) is better than or equal to 80.6–99.1%. In every case, the average number of invalid transitions per 48 h is less than or

equal to 0.02


123

making it faster and more objective without incurring

additional cost. An important constraint in the algorithm

design was to base it exclusively on the type of actigraphy

signals already available in many ABPM studies and built

into some commercial ABPM monitors with integrated

actigraphy, as opposed to basing it on other physiological

signals which would require different hardware, and in

some cases would be inconsistent with the ambulatory,

normal-life conditions required in ABPM clinical practice.

Additionally, the algorithm was designed to be used with

multiple actigraphs and since it is automatic the end user

does not require any specialized technical knowledge. The

algorithm can run very robustly based on ten default

parameters.

4.3 Study limitations

The objective of this paper was to provide a detailed

mathematical description of a new algorithm of activity–

rest identification based exclusively on actigraphy signals

available in ABPM studies, in order to ensure reproduc-

ibility by the scientific community, as well as to provide

illustrative examples of its performance. While the per-

formance of the algorithm was thoroughly assessed using a

prospective database and reported in this article, a scientific

comparison study with respect to the classical algorithms

was not reported here. In this paper, the comparison with

respect to the classical algorithms is limited to a single

illustrative example presented in Fig. 5, and not a complete

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

400Actigraphy Signal (Counts/Min)

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

1

Desired Output (Reference)

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

1

Cole Algorithm

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

1

Sadeh Algorithm

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

1

Oakley Algorithm

12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:000

1

Crespo Algorithm

Fig. 5 Illustrative example of the performance of the proposed

algorithm as compared to some of the currently available actigraphy

algorithms. The first graph shows an actigraphy signal collected with

a wrist actigraph. The second graph corresponds to the activity/rest

periods recorded in the diary (i.e., the desired algorithm output). The

three plots that follow show the output of some of the classical sleep/

wake identification algorithms (namely, the algorithms proposed by

by Cole, Sadeh, and Oakley). The last plot corresponds to the output

of the Crespo algorithm. The classical algorithms exhibit a high

sensitivity to sleep disturbances, and tend to generate multiple wake

identifications during main rest periods. This makes them unsuitable

for the identification of activity and rest cycles in the context of

ABPM and cardiovascular risk assessment. The Crespo algorithm

performs a better identification of the main activity and rest cycles,

avoiding the large number of invalid transitions detected by the

classical algorithms


123

scientific comparative study. Consequently, a more thor-

ough study is needed in order to perform a full assessment,

validation, and characterization of the algorithm, as well as

a comparison with other available algorithms appropriate

for this clinical application (ABPM with actigraphy). This

could include a prospective validation of the algorithm on a

different database, as well as a characterization of algo-

rithm performance over the possible range of variation of

the different user-specified input parameters. Of particular

interest would be to study the variation in algorithm per-

formance when a priori information regarding the average

number of sleep hours per night is available and provided

as an input to the algorithm, versus the case when such

information is not available and the average number of

sleep hours per night is set to the default value of 8. The

preliminary assessment described here was performed on a

homogeneous database of diurnally active and nocturnally

resting healthy young adults. While the validation popu-

lation were young adults, they presented a wide range of

sleep patterns (fragmented sleep, greater periods of quiet

restfulness, naps, and other sleep disturbances). Neverthe-

less, a more thorough assessment could include a charac-

terization of algorithm performance on different

populations. Finally, since the algorithm is intended for

application in the estimation of ABPM parameters such as

activity and rest BP means, a study is needed to determine

the statistical and clinical impact of using the proposed

algorithm in this context.

5 Conclusion

This paper presents a novel algorithm for identification of

activity/rest periods based on actigraphy signals designed

to be used in cardiovascular risk applications involving

ABPM. The algorithm was validated on a database con-

taining 48 h simultaneous actigraphy recordings for the

dominant and non-dominant hands for 104 subjects (i.e.,

208 recordings). When applied to the validation database

with all the input parameters set to their default values, the

algorithm achieved a mean performance above 94.0% with

an average number of invalid transitions per 48 h lower

than 0.02. This performance characteristics make this

algorithm suitable for numerous applications involving the

assessment of cardiovascular risk which take into account

the circadian variability and cardiovascular chronobiology.

Acknowledgments This independent investigator-promoted

research was funded by unrestricted grants from Ministerio de Ciencia e

Innovacion (SAF2009-7028-FEDER); Consellerıa de Economıa e In-

dustria, Direccion Xeral de Investigacion e Desenvolvemento, Xunta de

Galicia (INCITE07-PXI-322003ES; INCITE08-E1R-322063ES;

INCITE09-E2R-322099ES; IN845B-2010/114; 09CSA018322PR);

and Vicerrectorado de Investigacion, University of Vigo.

References

1. Ancoli-Israel S, Cole R, Alessi C, Chambers M, Moorcroft W,

Pollak CP (2003) The role of actigraphy in the study of sleep and

circadian rhythms. Sleep 26: 342–392

2. Blood ML, Sack RL, Percy DC, Pen JC (1997) A comparison of

sleep detection by wrist actigraphy, behavioral response, and

polysomnography. Sleep 20: 388–395

3. Boggia J, Li Y, Thijs L, Hansen TW, Kikuya M, Bjorklund-

Bodegsrd K, Richart T, Ohkubo T, Kuznetsova T, Torp-Pedersen

C et al (2007) Prognostic accuracy of day versus night ambula-

tory blood pressure: a cohort study. Lancet 370: 1219–1229

4. Cole RJ, Kripke DF, Gruen W, Mullaney DJ, Gillin JC (1992)

Automatic sleep/wake identification from wrist actigraphy Sleep

15: 461–469

5. Cuspidi C, Macca G, Sampieri L, Fusi V, Severgnini B, Michev I,

Salerno M, Magrini F, Zanchetti A (2001) Target organ damage

and non-dipping pattern defined by two sessions of ambulatory

blood pressure monitoring in recently diagnosed essential

hypertensive patients. J Hypertens 19: 1539–1545

6. Cuspidi C, Meani S, Salerno M, Valerio C, Fusi V, Severgnini B,

Lonati L, Magrini F, Zanchetti A (2004) Cardiovascular target

organ damage in essential hypertensives with or without repro-

ducible nocturnal fall in blood pressure. J Hypertens 22: 273–280

7. Cuspidi C, Michev I, Meani S, Severgnini B, Fusi V, Corti C,

Salerno M, Valerio C, Magrini F, Zanchetti A (2003) Reduced

nocturnal fall in blood pressure, assessed by two ambulatory blood

pressure monitorings and cardiac alterations in early phases of

untreated essential hypertension. J Hum Hypertens 17: 245–251

8. Dolan E, Stanton A, Thijs L, Hinedi K, Atkins N, McClory S,

Hond ED, McCormack P, Staessen JA, O’Brien E (2005) Supe-

riority of ambulatory over clinic blood pressure measurement in

predicting mortality: the Dublin outcome study. Hypertension 46:

156–161

9. Hermida RC (2007) Ambulatory blood pressure monitoring in the

prediction of cardiovascular events and effects of chronotherapy:

rationale and design of the MAPEC study. Chronobiol Int 24:

749–775

10. Hermida RC, Chayan L, Ayala DE, Mojon A, Domfnguez MJ,

Fontao MJ, Soler R, Alonso I, Fernßndez JR (2009) Association

of metabolic syndrome and blood pressure nondipping profile in

untreated hypertension. Am J Hypertens 22: 307–313

11. Hilten JJV, Middelkoop HA, Kuiper SI, Kramer CG, Roos RA

(1993) Where to record motor activity: an evaluation of com-

monly used sites of placement for activity monitors. Electroen-

cephalogr Clin Neurophysiol 89: 359–362

12. Hyde M, O’Driscoll DM, Binette S, Galang C, Tan SK, Verginis

N, Davey MJ, Horne RSC (2007) Validation of actigraphy for

determining sleep and wake in children with sleep disordered

breathing. J Sleep Res 16: 213–216

13. Jones SH, Hare DJ, Evershed K (2005) Actigraphic assessment of

circadian activity and sleep patterns in bipolar disorder. Bipolar

Disord 7: 176–186

14. Karlen W, Mattiussi C, Floreano D (2008) Improving actigraph

sleep/wake classification with cardio-respiratory signals. Conf

Proc IEEE Eng Med Biol Soc 2008: 5262–5265

15. Krakoff LR (1993) Ambulatory blood pressure monitoring can

improve cost-effective management of hypertension. Am J Hy-

pertens 6: 220–224

16. Krouse HJ, Yarandi H, McIntosh J, Cowen C, Selim V (2008)

Assessing sleep quality and daytime wakefulness in asthma using

wrist actigraphy. J Asthma 45: 389–395

17. Lee JK, Park EJ (2011) 3D spinal motion analysis during stair-

case walking using an ambulatory inertial and magnetic sensing

system. Med Biol Eng Comput 49: 755–764


123

18. Lee JK, Park EJ (2011) Quasi real-time gait event detection using

shank-attached gyroscopes. Med Biol Eng Comput 49: 707–712

19. Liu M, Takahashi H, Morita Y, Maruyama S, Mizuno M, Yuzawa

Y, Watanabe M, Toriyama T, Kawahara H, Matsuo S (2003)

Non-dipping is a potent predictor of cardiovascular mortality and

is associated with autonomic dysfunction in haemodialysis

patients. Nephrol Dial Transplant 18: 563–569

20. Lockley SW, Skene DJ, Arendt J (1999) Comparison between

subjective and actigraphic measurement of sleep and sleep

rhythms. J Sleep Res 8: 175–183

21. Morgenthaler T, Alessi C, Friedman L, Owens J, Kapur V, Bo-

ehlecke B, Brown T, Chesson A, Coleman J, Lee-Chiong T et al

(2007) Practice parameters for the use of actigraphy in the

assessment of sleep and sleep disorders: an update for 2007.

Sleep 30: 519–529

22. Ohinata J, Suzuki N, Araki A, Takahashi S, Fujieda K, Tanaka H

(2008) Actigraphic assessment of sleep disorders in children with

chronic fatigue syndrome. Brain Dev 30: 329–333

23. Sadeh A, Acebo C (2002) The role of actigraphy in sleep med-

icine. Sleep Med Rev 6: 113–124

24. Sadeh A, Hauri PJ, Kripke DF, Lavie P (1995) The role of ac-

tigraphy in the evaluation of sleep disorders. Sleep 18: 288–302

25. Sadeh A, Sharkey KM, Carskadon MA (1994) Activity-based

sleep-wake identification: an empirical test of methodological

issues. Sleep 17: 201–207

26. Schepers HM, Roetenberg D, Veltink PH (2010) Ambulatory

human motion tracking by fusion of inertial and magnetic sensing

with adaptive actuation. Med Biol Eng Comput 48: 27–37

27. Tonetti L, Pasquini F, Fabbri M, Belluzzi M, Natale V (2008)

Comparison of two different actigraphs with polysomnography in

healthy young subjects. Chronobiol Int 25: 145–153

28. ValliFres A, Morin CM (2003) Actigraphy in the assessment of

insomnia. Sleep 26: 902–906


123

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