For early detection of Alzheimer dementia (AD), this paper analyzes the features of circadian rhythm of heart rate between healthy people and AD patients, focusing on the circadian rhythm disorder in AD (i.e., unstable circadian rhythm). Focusing on the circadian rhythm estimating log of ADDUCRRaH (the AD detection method based on the stability of estimated circadian rhythms), we analyzed experiments with an elderly AD patient in five months and 21 non-AD people (age from 20-70). Through the experiments confirmed the following implications have been revealed: (1) AD and healthy people show three types of features (cancellation between the rhythms, crossing the sign of the rhythms coefficients and summation of transitions of rhythms coefficients) between unstable and stable circadian rhythms during the estimation in the one day estimated log as well as the final estimated output; (2) the features can be quantified as accumulated values and used together with existing AD detection methods to improve the accuracy of detection.
Recently, World Health Organization reported that the
number of elderly people with dementia is more than 55
million people. In addition, the report estimates that the number
of new patients 10 million
For earlier symptom recognition, the global standard
method of dementia detection called Mini-Mental State
Examination (MMSE)
To tackle these problems, the method that can detect AD
by the biometric data from daily life can be used as the
substitute for the questionnaires tests. In line with this
perspective, the, we proposed the novel AD detection method,
named AD Detection based on Unstable Circadian Rhythm
Ratio of Heart rate (ADDUCRRaH), which focused on the
circadian rhythm (approximately 24 hours cycle) of the
melatonin secretion.
However, ADDUCRRaH has misdetected data with specific patterns in both AD patients and healthy people. Concretely, the patterns are that when misdetecting the AD patients / the healthy people, at the end of the estimation of the trigonometric function, the condition was suddenly to satisfy the conditions which the AD patients / the healthy people detected as healthy people / AD. This is because the estimation is more sensitive to the end stage (i.e., just before waking) heart rate data inputed as a time series. To avoid the misdetection, it is necessary to consider data with long-term. And so this paper additionally analyzes the AD detection prosess to improve the accuracy of the AD detection of ADDUCRRaH. In particular, we will focus on the estimation transitions for the entire of data (one day sleep) in estimating the trigonometric functions and the differences in the features of those AD patients and healthy subjects.
This paper is organized as follows. The next Section “AD Detection based on Unstable Circadian Rhythm Ratio of Heart rate” describes the principle and the problems of ADDUCRRaH. The two analytical experiments and a human subject experiment with AD and healthy people are conducted and the results are discussed in Section “Analytical Experiment 1”, “Analytical Experiment 2” and “Subject Experiment”. Finally, our conclusion is given in Section “Conclusion”.
The AD detection method, AD Detection based on Unstable Circadian Rhythm Ratio of Heart rate (ADDUCRRaH), detects AD based on the hypothesis which the circadian rhythm of the heart rate in AD patients tends to be unstable in comparison with healthy people described in Section “Introduction”. This method has two steps. First, the circadian rhythm is estimated by the modified version of the realtime sleep stage estimation from heart rate data (in Section “Estimation of Circadian Rhythm of Heart rate”). Second is judging whether the estimated circadian rhythm is stable or not (described in Section “Stability of Circadian Rhythm of Heart rate” in detail). At the end of this chapter, We summarize the problems of this method as the arguments against the analysis in this paper (in Section “Problem”).
Real-time Sleep Stage Estimation (RSSE)
fal;c cos mlt + al;s sin mltg + C (1) f (t) = X ml = l2L 2 l the likelihood function used for the maximum likelihood estimation is defined in Eq.(2), where the first term T1 PtT=1fHR(t) f (t)g2 indicates the difference between f (t) and HR(t) (i.e., the heart rate at the time t), and the second term suppresses the overfitting of al;i (coefficients of sine and cosine waves defined from L ) by avoiding a large separation from the one time previous coefficient a^l;i (i.e., the coefficient when time is t 1). The weights the second term (in this paper, = 1:0 in all cases). The coefficients al;i and the constant term C are updated by minimizing J . The value (T ) weights the second term during T (= 600) seconds by changing from 0 (=2) to 1 (i.e., (T ) is set to 0 (=2), decreases until T second, converges to 1 after T second). This is because the initial value of al;i is zero and thus the value may be updated sensitively especially in the first several time during T second. The value d(l; L) is the index of l in L.
fHR(t)
f (t)g2 J = +
T 1 X T t=1
X L j j l2L T = jHRj d(l; L) = the index of l in L (T ) = max(1; (1 0)
+ 0) T
T (T )d(l;L) 1f(al;c a^l;c)2 + (al;s a^l;s)2g (2)
To estimate the circadian rhythm of heart rate, the periods of frequency waves L in this research is set to f25, 24, 23g hours which covers approximately 24 hours, instead of L set to f214=1; :::; 214=14g. Figure 1 shows the example of estimated f (t), where the vertical and horizontal axes respectively indicate the heart rate and time, the blue line indicates the heart rate, and the orange line indicates the estimated f (t) composed of the frequency waves with the L periods. fraction and (ii) the simple sum of the coefficients ai;l in the denominator. In the case of the stable estimated circadian rhythm which coefficients tend to have the same sign, the two types of sum values are expected to be the same, which means that Ri is expected to be 1.0. In the case of unstable ones which coefficients tend to have the different sign, on the other hands, the absolute sum is expected to be larger than the simple sum, which means that Ri is expected to be larger than 1.0. Considering that R is calculated by the average of Rc for the cosine wave and Rs for the sine wave, the proposed AD detection method judges as the non-AD person when R is 1.0 because of having the stable circadian rhythm of heart rate, while it judges as the AD patient when if R > 1.0 because of having the unstable circadian rhythm of heart rate.
Ri = R =
P
l2L jal;ij P
l2L al;i Rc + Rs 2 (3)
As mentioned in the “Introduction”, the factor for ADDUCRRaH misdetection of AD patients / healthy people is found to be that when misdetecting the healthy people, at the end of the estimation of the trigonometric function, the condition was suddenly to detect the AD patients / the healthy people as healthy people / AD satisfied. For this perspective, we focused not only on the end of the estimation, but also on the its transitions, and conducted an analytical experiment on the differences in features between AD and healthy subjects. Specifically, we use the trajectory of the estimation 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/negative). The coefficients at the last time of the graph (red line on the right side of the graph) are used for f (t) (described in “Estimation of Circadian Rhythm of Heart rate”) which is used for AD detection (described in “Stability of Circadian 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 following 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 University and the University of Electro-Communications approved this study, and all the subjects signed their consent.
Figure 8 and Figure 9 represent respectively the examples of AD patients / the healthy person data which detected as healthy people / AD because the coefficients (of the cosine waves) are emphasized each other / cancelled out at the end of the estimation (red circle on the right side of the figure). However, when focusing on the transition of the estimation, it can be seen that the coefficients crosses positive and negative many times (as shown blue circle) and occurs cancellation for a long time (as shown green arrow) in Figure 8, and the coefficients of sine waves in particular is negative and stable over a long period of time in Figure 9.
In Figure 8, the reason why the coefficients crosses positive and negative many times and occurs long cancellation is that cancellation occurs for unstable heart rate and can occur periodically even during estimation (i.e., a part of heart rate).
While, in Figure 9, the reason why the coefficient of the sine wave is negative and stable can be explained as shown in Figure 7. The top graph shows the estimated f (t) for one day of a healthy person, where the blue and orange lines in the graphs respectively indicate the heart rate and the estimated f (t), and the equations under the graphs indicates the sine and cosine waves in f (t). The sine and cosine portions of f (t) are respectively represented by the red and yellow lines in the bottom figure. The heart rate of healthy people decreases monotonically from the time they fall asleep until dawn, and the amount of decrease is gradually reduced to zero. For such the transitions, it is easy to improve the likelihood of the entire f(t) by combining cosine waves based on sine waves with negative coefficients that has the form represented by the red line. As a result, the sine waves transitions are more likely to be negative and stable for healthy people. (7) (8) (9) (10) (11) al;i(x) are the extenstion of al;i as the coefficients at the time x in the estimation transition. Eq.(9) is the time average of the count that cancelation (i.e., i the signs of i group coefficients are different between plus and minus signs) occurred. Eq.(10) is the count that the coefficients crossed zero line (i.e., the sign of the sum of i group coefficients switches). Eq.(11) is the approximately area of the red and blue regions represented in Figure 9. al;i(t) is the coefficient during estimation at the time t. Si(i 2 fs; cg) is the area average of the sum of the coefficients divided respectively by the time T on the horizontal axes and the standard deviation (PT
x=0 A(x; i)) with the time series coefficients al;i(x) (l 2 L; x = f0; 1; :::; T g) on the vertical axes. A large positive value of Si means that the coefficients are positive for a long time, and a large negative value means that they are negative for a long time.
This experiment employs the same heart rate data of “Analysis Experiment 1”. And, the differences of Ci, Oi and Si between healthy people and AD patients were analyzed.
The results were as shown in Figure 10, Figure 11 and Figure 12. The horizontal axis represents each data, and the left and right sides from the black line are respectively for AD patients and healthy people, and the vertical axis represents the value of Ci (, Oi and Si). The blue and orange bars represent respectively the C (, O and S) value of the sine waves Cs (, Os and Ss) and that of cosine waves Cc (, Oc and Sc).
Both of Ci have large values in about half of AD patients, At least one of Oi has a possibility to reach over ten, and Ss has a large negative value in most of the data of healthy people.
Ci and Oi tend to be higher in AD, but not enough to clearly separate it from healthy people. It is clear that Ss is able to visualize the feature of healthy people obtained from the analysis experiment as numerical values. In particular, Ss smaller than -500 was obtained only for the healthy people, which suggests that this feature can be used for AD detection. However, these features were not found in all healthy people and must be used in conjunction with other AD detection.
In addition, this feature-based detection can be added to or replaced by the second mechanism “Stability of Circadian Rhythm of Heart rate” of ADDUCRRaH. And that means that the detection by the second mechanism is also the features-based detection of the final coefficients of f (t).
Focusing on the features obtained from “Analysis Experiment 1” and “Analysis Experiment 2”, we examine an example of an AD detection method that combines the obtained features (C , O and S) and that of the second mechanism of ADDUCRRaH R. Specifically, the following procedure is used to detect AD.
To investigate the effectiveness of this AD detection method the human subject experiments were conducted by comparing with our previous method, ADDUCRRaH. This experiment employs the same heart rate data of “Analysis Experiment 1” and “Analysis Experiment 2”. As the evaluation criteria, this experiment employs the accuracy of AD detection (i.e., the percentage of AD detection for AD patients and that of the non-AD detection for healthy subjects).
Figure 13 shows the accuracy of AD detection of healthy people (blue bar) and ADDUCRRaH (orange bar). Note that the accuracy of the AD patients is the percentage of AD detection, while that of the healthy subjects is the percentage of non-AD detection. From this figure, we found that both of the features-based accuracies of AD and healthy people (76.4% and 83.3%) is higher than those of ADDUCRRaH (66.7% and 76.7%) and the accuracies are improved.
In this paper, since the misdetection of ADDUCRRaH occurred 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 patients. The analysis experiments revealed the following implications: (1) unstable heart rate in AD patients causes continuous censoring and zero line crossing; (2) the coefficients of the sine waves continue to be negative because they fit the stable heart rate of healthy people; and (3) it is possible that these features can be quantified and utilized for AD detection.
The future works include that (1) an analysis of new features of coefficient transitions; and (2) a consideration of an AD detection method that summarize the obtained features, especially non-threshold detection.