=Paper=
{{Paper
|id=Vol-3276/SSS-22_FinalPaper_128
|storemode=property
|title=Analysis of Circadian Rhythm Estimation Process for
Improving the Accuracy of Alzheimer Dementia Detection
|pdfUrl=https://ceur-ws.org/Vol-3276/SSS-22_FinalPaper_128.pdf
|volume=Vol-3276
|authors=Naoya Matsuda,Taiki ,Senju,Iko
Nakari,Keiki Takadama
|dblpUrl=https://dblp.org/rec/conf/aaaiss/MatsudaSNT22
}}
==Analysis of Circadian Rhythm Estimation Process for
Improving the Accuracy of Alzheimer Dementia Detection==
https://ceur-ws.org/Vol-3276/SSS-22_FinalPaper_128.pdf
Analysis of Circadian Rhythm Estimation Process for Improving the Accuracy of
Alzheimer Dementia Detection
Naoya Matsuda, Taiki Senju, Iko Nakari, Keiki Takadama
The University of Electro-Communications
1-5-1 Chofugaoka, Chofu, Tokyo, Japan
matsuda.naoya@cas.lab.uec.ac.jp, senju@cas.lab.uec.ac.jp, iko0528@cas.lab.uec.ac.jp, keiki@inf.uec.ac.jp
Abstract To tackle these problems, the method that can detect AD
For early detection of Alzheimer dementia (AD), this paper
by the biometric data from daily life can be used as the
analyzes the features of circadian rhythm of heart rate be- substitute for the questionnaires tests. In line with this per-
tween healthy people and AD patients, focusing on the circa- spective, the, we proposed the novel AD detection method,
dian rhythm disorder in AD (i.e., unstable circadian rhythm). named AD Detection based on Unstable Circadian Rhythm
Focusing on the circadian rhythm estimating log of ADDU- Ratio of Heart rate (ADDUCRRaH), which focused on the
CRRaH (the AD detection method based on the stability of circadian rhythm (approximately 24 hours cycle) of the
estimated circadian rhythms), we analyzed experiments with melatonin secretion. (Matsuda, Nakari, and Takadama 2021)
an elderly AD patient in five months and 21 non-AD people Concretely, the melatonin secretion of the healthy people
(age from 20-70). Through the experiments confirmed the fol- (including the non-AD elderly persons) have stable (i.e.,
lowing implications have been revealed: (1) AD and healthy clear) circadian rhythm while the AD patients have unstable
people show three types of features (cancellation between the
rhythms, crossing the sign of the rhythms coefficients and
circadian rhythm (e.g., a phase shift of the circadian rhythm,
summation of transitions of rhythms coefficients) between a change of the circadian rhythm period, and a reduction
unstable and stable circadian rhythms during the estimation of circadian rhythm amplitude) (Zhdanova and Tucci 2003).
in the one day estimated log as well as the final estimated However, the melatonin secretion is hard to be obtained in
output; (2) the features can be quantified as accumulated val- the daily life. So our method focused on the fact that the
ues and used together with existing AD detection methods to circadian rhythm is also represented in heart rate (Boudreau
improve the accuracy of detection. et al. 2012)(Massin et al. 2000). Since heart rate is easily
to acquire from the mattress sensor (placed under the mat-
Introduction tress) in the daily life, it can be used to measure its circadian
Recently, World Health Organization reported that the num- rhythm instead of melatonin. From these perspectives, AD-
ber of elderly people with dementia is more than 55 mil- DUCRRaH detects AD from the instability of the circadian
lion people. In addition, the report estimates that the number rhythm estimated from the heart rate. For detail, circadian
of new patients 10 million(Organization 2012) each year. rhythms are estimated by the regression of a trigonometric
And more than half of these dementias are classified as function which have waves with a period of around 24 hours
Alzheimer dementia (AD). However, no treatment for AD with the maximum likelihood estimation.
is currently available other than medication to slow its pro- However, ADDUCRRaH has misdetected data with spe-
gression. And when the symptoms (due to wandering, vio- cific patterns in both AD patients and healthy people. Con-
lence, and so on) become so severe that it is difficult to care cretely, the patterns are that when misdetecting the AD pa-
for the patient, the patient has to be hospitalized and stay in tients / the healthy people, at the end of the estimation of the
bed. For the facts, early detection is essential to slow down trigonometric function, the condition was suddenly to satisfy
the progression of dementia. However, it is difficult to detect the conditions which the AD patients / the healthy people de-
dementia early because it takes a long time (e.g., ten years) tected as healthy people / AD. This is because the estimation
for the symptoms to appear (Mioshi et al. 2010). is more sensitive to the end stage (i.e., just before waking)
For earlier symptom recognition, the global standard heart rate data inputed as a time series. To avoid the misde-
method of dementia detection called Mini-Mental State Ex- tection, it is necessary to consider data with long-term. And
amination (MMSE) (Folstein, Folstein, and McHugh 1975), so this paper additionally analyzes the AD detection prosess
which is a questionnaire-based screening test, is widely em- to improve the accuracy of the AD detection of ADDUCR-
ployed. However, this method has problems in that the de- RaH. In particular, we will focus on the estimation transi-
tection accuracy may decrease due to habituation when the tions for the entire of data (one day sleep) in estimating the
test is taken many times. In addition, people who others have trigonometric functions and the differences in the features of
pointed out that they may have dementia are difficult to ac- those AD patients and healthy subjects.
cept the fact and the test result, or are possible not to take This paper is organized as follows. The next Section “AD
the test. Detection based on Unstable Circadian Rhythm Ratio of
___________________________________
In T. Kido, K. Takadama (Eds.), Proceedings of the AAAI 2022 Spring Symposium
“How Fair is Fair? Achieving Wellbeing AI”, Stanford University, Palo Alto, California,
USA, March 21–23, 2022. Copyright © 2022 for this paper by its authors. Use permitted
under Creative Commons License Attribution 4.0 International (CC BY 4.0).
81
Heart rate” describes the principle and the problems of AD- and thus the value may be updated sensitively especially in
DUCRRaH. The two analytical experiments and a human the first several time during ∆Tγ second. The value d(l, L)
subject experiment with AD and healthy people are con- is the index of l in L.
ducted and the results are discussed in Section “Analytical
Experiment 1”, “Analytical Experiment 2” and “Subject Ex- T
periment”. Finally, our conclusion is given in Section “Con- 1X
J= {HR(t) − f (t)}2
clusion”. T t=1
λ X
AD Detection based on Unstable Circadian + γ(T )d(l,L)−1 {(al,c − aˆl,c )2 + (al,s − aˆl,s )2 }
|L|
Rhythm Ratio of Heart rate l∈L
Overview T = |HR|
The AD detection method, AD Detection based on Unsta- d(l, L) = the index of l in L
ble Circadian Rhythm Ratio of Heart rate (ADDUCRRaH), T
γ(T ) = max(1, (1 − γ0 ) + γ0 )
detects AD based on the hypothesis which the circadian ∆Tγ
rhythm of the heart rate in AD patients tends to be unsta- (2)
ble in comparison with healthy people described in Section
“Introduction”. This method has two steps. First, the circa- To estimate the circadian rhythm of heart rate, the periods
dian rhythm is estimated by the modified version of the real- of frequency waves L in this research is set to {25, 24, 23}
time sleep stage estimation from heart rate data (in Section hours which covers approximately 24 hours, instead of L set
“Estimation of Circadian Rhythm of Heart rate”). Second is to {214 /1, ..., 214 /14}. Figure 1 shows the example of esti-
judging whether the estimated circadian rhythm is stable or mated f (t), where the vertical and horizontal axes respec-
not (described in Section “Stability of Circadian Rhythm of tively indicate the heart rate and time, the blue line indicates
Heart rate” in detail). At the end of this chapter, We summa- the heart rate, and the orange line indicates the estimated
rize the problems of this method as the arguments against f (t) composed of the frequency waves with the L periods.
the analysis in this paper (in Section “Problem”).
Estimation of Circadian Rhythm of Heart rate
Real-time Sleep Stage Estimation (RSSE) (Harada et al.
2016) estimates six sleep stages (i.e., Wake, REM, Non-
REM1, 2, 3, and 4) by the regression of the heart rate.This
method is based on the fact that there is a correlation be- Figure 1: An example of heart rate (blue) and the estimated
tween sleep stages and heart rate. The regression model f (t) f (t) (orange).
is computed by synthesizing the frequency waves as shown
in Eq. (1), where al,i (i.e., i ∈ {c, s}) is a coefficients of
cos/sin waves, l is the period of the frequency waves (i.e.,
Stability of Circadian Rhythm of Heart rate
l ∈ L = {214 /1, ..., 214 /13, 214 /14} second), and C is con-
stant term of f (t). Figure 2 and Figure 3 respectively show the estimated f (t)
for one day with the stable and unstable circadian rhythms
X of heart rate, where the blue and orange lines in the graphs
f (t) = {al,c cos ml t + al,s sin ml t} + C respectively indicate the heart rate and the estimated f (t),
l∈L and the equations under the graphs indicates the sine and co-
(1)
2π sine waves in f (t). When the heart rate gradually decreases
ml = and finally increases as shown in Figure 2, the estimated
l
f (t) shows the stable circadian rhythm and coefficients al,i
the likelihood function used for the maximum likeli- of the sine and cosine waves are the large enough with the
hood estimation is defined in Eq.(2), where the first term same sign. When the heart rate repeatedly increases and de-
1
PT 2
T t=1 {HR(t) − f (t)} indicates the difference between creases in a certain short periods as shown in Figure 3, on the
f (t) and HR(t) (i.e., the heart rate at the time t), and the other hand, the estimated f (t) shows the unstable circadian
second term suppresses the overfitting of al,i (coefficients of rhythm and the coefficients al,i of the sine and cosine waves
sine and cosine waves defined from L ) by avoiding a large are relatively smaller than those in Figure 2. In such case,
separation from the one time previous coefficient aˆl,i (i.e., these coefficients al,i become the positive and negative to
the coefficient when time is t − 1). The λ weights the second cancel the waves each other, which weakens the amplitude
term (in this paper, λ = 1.0 in all cases). The coefficients al,i of f (t).
and the constant term C are updated by minimizing J. The From these differences, the proposed AD detection
value γ(T ) weights the second term during ∆Tγ (= 600) method evaluates the stability of the estimated circadian
seconds by changing from γ0 (=2) to 1 (i.e., γ(T ) is set to rhythm using the numerical value R calculated as shown in
γ0 (=2), decreases until ∆Tγ second, converges to 1 after Eq.(3). Ri is calculated by the absolute value of the ratio
∆Tγ second). This is because the initial value of al,i is zero between (i) the absolute sum of the coefficients |ai,l | in the
82
as shown in Figure 5 and Figure 4, where the horizontal and
vertical axes respectively indicate the time and the value of
the estimated sine/cosine waves coefficients ai,l for 23, 24,
and 25 hours. The upper/lower graphs are the coefficients of
the sine/cosine (as,25 , as,24 and as,23 /ac,25 , ac,24 and ac,23 ).
Figure 5/4 is the example of the AD patient/healthy person
which detected as AD/healthy person (true positive/nega-
tive). The coefficients at the last time of the graph (red line
Figure 2: Stable circadian rhythm of heart rate in estimated on the right side of the graph) are used for f (t) (described
f (t). in “Estimation of Circadian Rhythm of Heart rate”) which
is used for AD detection (described in “Stability of Circa-
dian Rhythm of Heart rate”). Figure 6 shows the relationship
between the estimation transition and f (t). It is possible to
draw f (t) from the coefficients ai,l at each time. Basically,
f (t) will follow the heart rate that you input.
This experiment employs the heart rate data of the follow-
ing subjects: (a) one elderly AD patient in the care house (72
days); (b) 21 healthy (i.e., non-AD) persons (20s ∼ 70s, 30
days in total). The ethics community of St.Marianna Uni-
versity and the University of Electro-Communications ap-
Figure 3: Unstable circadian rhythm of heart rate in esti- proved this study, and all the subjects signed their consent.
mated f (t).
Result
fraction and (ii) the simple sum of the coefficients ai,l in the Figure 8 and Figure 9 represent respectively the examples
denominator. In the case of the stable estimated circadian of AD patients / the healthy person data which detected as
rhythm which coefficients tend to have the same sign, the healthy people / AD because the coefficients (of the cosine
two types of sum values are expected to be the same, which waves) are emphasized each other / cancelled out at the end
means that Ri is expected to be 1.0. In the case of unstable of the estimation (red circle on the right side of the figure).
ones which coefficients tend to have the different sign, on However, when focusing on the transition of the estimation,
the other hands, the absolute sum is expected to be larger it can be seen that the coefficients crosses positive and nega-
than the simple sum, which means that Ri is expected to be tive many times (as shown blue circle) and occurs cancella-
larger than 1.0. Considering that R is calculated by the av- tion for a long time (as shown green arrow) in Figure 8, and
erage of Rc for the cosine wave and Rs for the sine wave, the coefficients of sine waves in particular is negative and
the proposed AD detection method judges as the non-AD stable over a long period of time in Figure 9.
person when R is 1.0 because of having the stable circadian
rhythm of heart rate, while it judges as the AD patient when Discussion
if R > 1.0 because of having the unstable circadian rhythm
of heart rate. In Figure 8, the reason why the coefficients crosses positive
and negative many times and occurs long cancellation is that
P cancellation occurs for unstable heart rate and can occur pe-
|al,i | riodically even during estimation (i.e., a part of heart rate).
Ri = Pl∈L
l∈L al,i (3) While, in Figure 9, the reason why the coefficient of the
Rc + Rs sine wave is negative and stable can be explained as shown
R= in Figure 7. The top graph shows the estimated f (t) for one
2
day of a healthy person, where the blue and orange lines in
Analytical Experiment 1 the graphs respectively indicate the heart rate and the esti-
mated f (t), and the equations under the graphs indicates the
Experimental Setup sine and cosine waves in f (t). The sine and cosine portions
As mentioned in the “Introduction”, the factor for ADDU- of f (t) are respectively represented by the red and yellow
CRRaH misdetection of AD patients / healthy people is lines in the bottom figure. The heart rate of healthy people
found to be that when misdetecting the healthy people, at the decreases monotonically from the time they fall asleep until
end of the estimation of the trigonometric function, the con- dawn, and the amount of decrease is gradually reduced to
dition was suddenly to detect the AD patients / the healthy zero. For such the transitions, it is easy to improve the like-
people as healthy people / AD satisfied. For this perspective, lihood of the entire f(t) by combining cosine waves based
we focused not only on the end of the estimation, but also on sine waves with negative coefficients that has the form
on the its transitions, and conducted an analytical experi- represented by the red line. As a result, the sine waves tran-
ment on the differences in features between AD and healthy sitions are more likely to be negative and stable for healthy
subjects. Specifically, we use the trajectory of the estimation people.
83
Figure 4: The exmaple of the estimation transition of the AD patients data detected as the AD (true positive).
Figure 5: The exmaple of the estimation transition of the healty person data detected as the healthy person (true negative).
Figure 6: Relation between the estimation transition and es-
timating f (t). Figure 7: The reason healthy people’ heart rate are easily
fitted based on minus sine waves.
Analytical Experiment 2 ( AAbs(x,i)
Experimental Setup 1 AbsA(x,i) > 1.0
cancel(x, i) = AAbs(x,i) (7)
Focusing on the features obtained from “Analysis Exper- 0 AbsA(x,i) = 1.0
iment 1”, we formulate the following equation Eq.(9),
1
(
(A(x,i)>0∧A(x−1,i)<0)
Eq.(10) and Eq.(11)
cross(x, i) = ∨(A(x,i)<0∧A(x−1,i)>0) (8)
X 0 otherwise
A(x, i) = al,i (x) (4) T
X
l∈L Ci = cancel(x, i)/T (9)
X x=0
AbsA(x, i) = |A(x, i)| = al,i (x) (5) T
X
l∈L Oi = cross(x, i) (10)
X
AAbs(x, i) = |al,i (x)| (6) x=0
PT
l∈L x=0 A(x, i)
Si = PT (11)
T σ( x=0 A(x, i))
84
Figure 8: The exmaple of the estimation transition of the AD patients data detected as the healthy people (false negative).
Figure 9: The exmaple of the estimation transition of the healty person data detected as the AD (false positive).
al,i (x) are the extenstion of al,i as the coefficients at the Cs (, Os and Ss ) and that of cosine waves Cc (, Oc and Sc ).
time x in the estimation transition. Eq.(9) is the time aver- Both of Ci have large values in about half of AD patients,
age of the count that cancelation (i.e., i the signs of i group At least one of Oi has a possibility to reach over ten, and
coefficients are different between plus and minus signs) oc- Ss has a large negative value in most of the data of healthy
curred. Eq.(10) is the count that the coefficients crossed people.
zero line (i.e., the sign of the sum of i group coefficients
switches). Eq.(11) is the approximately area of the red and Discussion
blue regions represented in Figure 9. al,i (t) is the coeffi- Ci and Oi tend to be higher in AD, but not enough to clearly
cient during estimation at the time t. Si (i ∈ {s, c}) is the separate it from healthy people. It is clear that Ss is able
area average of the sum of the coefficients divided respec- to visualize the feature of healthy people obtained from the
tively by the time T on the horizontal axes and the standard analysis experiment as numerical values. In particular, Ss
PT
deviation σ( x=0 A(x, i)) with the time series coefficients smaller than -500 was obtained only for the healthy people,
al,i (x) (l ∈ L, x = {0, 1, ..., T }) on the vertical axes. A which suggests that this feature can be used for AD detec-
large positive value of Si means that the coefficients are pos- tion. However, these features were not found in all healthy
itive for a long time, and a large negative value means that people and must be used in conjunction with other AD de-
they are negative for a long time. tection.
This experiment employs the same heart rate data of In addition, this feature-based detection can be added to
“Analysis Experiment 1”. And, the differences of Ci , Oi and or replaced by the second mechanism “Stability of Circa-
Si between healthy people and AD patients were analyzed. dian Rhythm of Heart rate” of ADDUCRRaH. And that
means that the detection by the second mechanism is also
Result the features-based detection of the final coefficients of f (t).
The results were as shown in Figure 10, Figure 11 and Fig- Subjects Experiment
ure 12. The horizontal axis represents each data, and the left
and right sides from the black line are respectively for AD Experimental Setup
patients and healthy people, and the vertical axis represents Focusing on the features obtained from “Analysis Experi-
the value of Ci (, Oi and Si ). The blue and orange bars rep- ment 1” and “Analysis Experiment 2”, we examine an exam-
resent respectively the C (, O and S) value of the sine waves ple of an AD detection method that combines the obtained
85
Figure 10: The calculated result of Ci of AD patients (left side) and healthy people (right side)
Figure 11: The calculated result of Oi of AD patients (left side) and healthy people (right side)
Figure 12: The calculated result of Si of AD patients (left side) and healthy people (right side)
86
features (C , O and S) and that of the second mechanism of the sine waves continue to be negative because they fit
of ADDUCRRaH R. Specifically, the following procedure the stable heart rate of healthy people; and (3) it is possi-
is used to detect AD. ble that these features can be quantified and utilized for AD
1. As and f (t) are estimated with the ADDUCRaH’s first detection.
mechanism “Estimation of Circadian Rhythm of Heart The future works include that (1) an analysis of new fea-
rate” tures of coefficient transitions; and (2) a consideration of an
AD detection method that summarize the obtained features,
2. Ci , Oi and Ss are calculated.
especially non-threshold detection.
3. If Cs > 5 ∧ Cc > 5 then the input data is detected as AD.
If not, move on to the next step.
References
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Figure 13: The accuracy of AD detection.
Conclusion
In this paper, since the misdetection of ADDUCRRaH oc-
curred at the end of the estimation of f (t), we focused on
the transition of the estimation of its coefficients al,i (t) and
analyzed the difference between healthy people and AD pa-
tients. The analysis experiments revealed the following im-
plications: (1) unstable heart rate in AD patients causes con-
tinuous censoring and zero line crossing; (2) the coefficients
87