Computerized Assessment of Communication for Cognitive Stimulation for People with Cognitive Decline Using Spectral-Distortion Measures and Phylogenetic Inference

Therapeutic communication and interpersonal relationships in care homes can help people to improve their mental wellbeing. Assessment of the efficacy of these dynamic and complex processes are necessary for psychosocial planning and management. This paper presents a pilot application of photoplethysmography in synchronized physiological measurements of communications between the care-giver and people with dementia. Signal-based evaluations of the therapy can be carried out using the measures of spectral distortion and the inference of phylogenetic trees. The proposed computational models can be of assistance and cost-effectiveness in caring for and monitoring people with cognitive decline.


Introduction
Communication is a complex and dynamic process to comprehend words or signals between two or more participants. The ability to communicate with people whose speech or hearing is impaired by cognitive decline is a skill that can be developed over time with practice. Care-givers use communication skills to provide individuals with professional care, establish supportive relationships, obtain information, and assist with changing behavior. Thus, therapeutic communication is a basis of the nurse-client relationship [1].
A decline in cognitive ability severe enough to interfere with daily life is seen in dementia, which is caused by damage to brain cells. In addition to drug treatments, there are other interventions that can treat or manage the symptoms of dementia. These include a range of therapies such as talking therapies, reminiscence therapy, cognitive stimulation therapy and vital changes in the body for detecting how an individual performs, feels, and responses [21]. Furthermore, it was reported that stress can be detected with the increase of finger pulse rate and decrease of pulse wave amplitude [20]; and finger PPG can be used to capture, with great precision, the immediate physiological response to a stimulus [23]. Because this PPG-based evaluation for cognitive intervention is a signal-based approach, the assessment of the influence of the care-giver on the participant can be analytically evaluated using spectral-distortion measures, which has been found useful for analysis of biological data [24], and the inference of phylogenetic tree reconstruction methods. Using these computational models for cognitive stimulation therapy assessment, the research suggests that the proposed therapeutic assessment is economically feasible. Experimental results are reproducible. Such reproducibility of intervention assessments can also be helpful for reaching agreement among experts in the presence of uncertainty around standardization of the course and outcome of cognitive stimulation therapy for cognitive impairment.

Methods Participants
The study was carried out in Shosha Himawari (Japan) care home, and involved 48 participants (5 males and 43 females). After receiving an explanation about the study, those who understood the purpose of the study and agreed to participate were asked to sign the written informed consent form in the presence of the care-home manager. When a participant was considered incapable of providing consent, the consent form was signed by either a family member of or the nurse caring for that particular participant. This study was approved by the Himeji Himawari Nursing Home Ethics Committee.
The mean age of the participants was 85.23 years (standard deviation = 6.93 years, and range = 66-100 years). These elderly participants were clinically diagnosed with dementia. There are 5 grades ranging from 1 to 5 (the higher the more severe), indicating the severity of dementia evaluated by a geriatric psychiatrist. The grades of these 48 participants were from 1 to 4 (mean = 3.16, and standard deviation = 0.69). There are 5 levels of care given by the care home, designating the intensity of professional care that clients require for their needs. The participants involved all 5 levels of care (mean = 3, and standard deviation = 1.5) at the time of recordings of their finger pulse waves (finger PPG). The qualified care-giver, was a female familiar with the daily living activities of the participants, who was 45 years old at the time of the experimental PPG measurement.

Spectral-distortion measures
Before the calculation of the spectral distortion between the finger pulse waves of the care-giver and each of the participants, which indicates the degree of matching between the pair of people during the cognitive-function stimulating therapy, the pre-processing of the PPG signals were carried out to remove the trend (baseline shift resulting from sensor drift) to represent the true amplitude of the pulse waves by fitting a low order polynomial (degree 6 was used in this study) to the signal for detrending (by subtracting the value of the polynomial from the signal), and smoothed by using the Savitzky-Golay filter [25].
Spectral distortion measures are designed to compute the dissimilarity or distance between two (power) spectra [26] (the power spectrum of a signal describes how the variance of the data is distributed over the frequency components into which the signal may be decomposed, and the most common way of generating a power spectrum is by using a discrete Fourier transform) of the two feature vectors, originally developed for comparison of speech patterns [27]. Three methods of spectral-distortion measures were used in this study, based on their popular applications in signal processing: Itakura distortion (ID), log spectral distortion (LSD), and weighted cepstral distortion (WCD) [27]. Unlike the Itakura distortion, both log spectral distortion (distance) and weighted cepstral distortion (distance) are symmetric.
Consider two signals S and S 0 , and their two spectral representations S(ω) and S 0 (ω), respectively, where ω is normalized frequency ranging from −π to π.
The Itakura-Saito distortion (ISD) between S and S 0 is defined as [28] ISDðS; S 0 Þ ¼ where jSðoÞj 2 ¼ s 2 j1 þ a 1 e Àjo þ a 2 e Àj2o þ Á Á Á þ a p e Àjpo j 2 ; where σ and a i , i = 1, . . ., p, are the gain and ith linear-predictive-coding coefficients of the pthorder LPC model [27], respectively (in digital signal processing, linear prediction is often called linear predictive coding (LPC) that estimates future values of a discrete-time signal as a linear function of previous samples, used for representing the spectral envelope of a digital signal in a compressed form).
The distortion defined in Eq. (4) is known as the Itakura distortion. It is also known as the log-likelihood ratio distortion or the gained-optimized Itakura-Saito distortion that can be derived as follows [29,30]: where σ 02 is the prediction error of S 0 produced by the linear predictive coding (LPC) [27], a is the vector of LPC coefficients of S, R 0 the LPC autocorrelation matrix of S 0 . It is shown that ID (S, S 0 ) 6 ¼ ID(S 0 , S), hence to make the measure symmetrical, a natural expression of its symmetrized version, denoted as ID s (S, S 0 ), is The log spectral distortion distance between two signals S and S 0 is defined as [27] LSDðS; S 0 Þ ¼ where m = 1 gives the mean absolute log spectral distortion, m = 2 defines the root-meansquare log spectral distortion that has been widely applied in speech signal processing and also used in this study, when m approaches 1 Eq. (7) reduces to the peak log spectral distortion, and V(ω) is the difference between the two spectra S(ω) and S 0 (ω) on a log magnitude versus frequency scale and defined by The weighted cepstral distortion between S and S 0 is defined by [27] WCDðS; S 0 Þ ¼ where w(n) is a lifter function and given as in which h is usually chosen as L/2, L is the truncated term and taken as p − 1 in this study, where p is the LPC number of poles, and the cepstral coefficients c n is derived with the following recursion [27]: where a n , n = 1, . . ., p, are the LPC coefficients, a 0 = 1, a k = 1 for k > p, c 0 = log σ 2 , and c −n = c n .

Phylogenetic tree reconstruction
Molecular biology suggests that if genomes change slowly by the gradual accumulation of mutations, then the amount of difference in a nucleotide sequence between a pair of genomes should indicate how recently those two genomes shared a common ancestor [31]. In other words, it is expected that the dissimilarity of two genomes that diverged in the recent past would be less than a pair of genomes whose common ancestor is more ancient. Based on this hypothesis of evolution, molecular phylogenetics aims to infer the evolutionary relationships between three or more genomes by comparing their DNA sequences for classifying molecular data. Plotting a phylogenetic tree is helpful because one can easily visualize the evolutionary relationships between species. The notion of phylogenetic tree reconstruction has been applied to partition MRI white-matter-lesion patterns into similar groups, which can be helpful for studying age-related diseases [32].
Phylogenetic tree reconstruction can be done using a number of different tree-building models. A popular choice is the use of the dissimilarity/similarity matrix based approach, such as the unweighted pair-group method using arithmetic averaging (UPGMA) [33] for linking the tree nodes. UPGMA, which is a hierarchical cluster analysis, generates nested hard clusters in dataset X by merging the two clusters at each step based on the minimization of a dissimilarity measure. The UPGMA algorithm mathematically works as follows [34]: 2. At step k, k = 1, . . ., n − 1, c = n − k + 1, using U c to directly solve the measure of hard-cluster similarity (hard clustering means that each data point is a member of one and only one cluster) by minimizing the following function to identify the minimum distance as the similarity between any two data points in X: where u j , u k denote the j-th and k-th rows of U c , u ji 2 [0, 1], and d: X × X ! R + is any measure of dissimilarity on X, and d was used as a spectral-distortion measure in this study.
3. Let (u r , u s ) c solve Eq. (12). Merge u r and u s , thus constructing from U c the updated partition Merge the two remaining clusters, set , and stop.

Results and Discussion
The preprocessed PPG data of the care-giver and 18 selected participants were used to calculate the three spectral-distortion measures (ID, LSD, and WCD) between the care-giver and each of the participants before, during and after the therapeutic session. The 12th-order LPC model (p = 12) was used to calculate the LPC coefficients. The dissimilarity matrices of the PPG data between the care-giver and the participants obtained from the three distortion measures were then used to construct the "phylogenetic" trees with the UPGMA algorithm. Figs. 1-18 show the trees of the PPG data of 18 participants and the care-giver, in which the terms Care-giver, Before care, During care, and After care in the tree nodes denote the care-giver, the participated individual before, during, and after the therapeutic session, respectively. A phylogenetic tree is composed of branches (edges) and nodes. Branches connect nodes each of which is the point at which two (or more) branches diverge. In the case of molecular phylogeny, trees are built for assigning similar species into the same groups. A node is a clade or a monophyletic group. All members of a tree node are assumed to have inherited a set of unique common characters [35]. Thus, based on the inference of the phylogenetic tree reconstruction, the evidence of influence of the care-giver over a particular participant is when the PPG patterns of the care-giver and the participant during the session belong to the same node. The three distortion measures were applied to construct the trees and used as the consensus of evidence for validating the computerized assessment. Among the selection of 18 participants, the influence of the care-giver over Participant #8 is supported by all three distortion measures (3 out of 3 = 100%), as shown in Fig. 8. Support of the care-giver's influence is partial over Participant #1, as Fig. 1 shows that the spectral patterns of the care-giver and participant during care are in the same node using ID and WCD (2 out of 3 = 67%). The effectiveness of the care-giver over Participant #2 is only supported by the ID measure (1 out of 3 = 33% as shown in Fig. 2). Although the PPG patterns of the care-giver and Participant #7 (Fig. 7) are not located in the same node, the pattern of the care giver is closer to those of the participant's during-care and after-care branches that connect the same node, this topology should be considered as an evidence of the influence of the care-giver over the participant. The influence of the care-giver over Participant #9 is clearly supported by the WCD measure, based on the topology of the tree shown in the bottom of Fig. 9, which also shows the support of the LSD measure (middle tree of Fig. 9). The influence of the care-giver over Participant #10 has the same consensus rate (67%) with Participant #9, but the former was supported by the ID and LSD measures (Fig. 10). The LSD measure gives evidence that the patterns of the care-giver and Participant #13 are best-matched among other patterns (middle tree in Fig. 13), while there is a lack of support from the results given by the other two distortion measures (top and bottom trees of Fig. 13). The pattern of support of the influence over Participant #14, which is given by the ID measure (top tree shown in Fig. 14, is similar to that of Participant #7, given by the LSD measure (middle tree shown in Fig. 7). No obvious support by any of the three distortion measures can be found in the trees of the care-giver and Participants #3 (Fig. 3), #4 (Fig. 4), #5 (Fig. 5), #6 (Fig. 6), #11 (Fig. 11), #12 (Fig. 12), and #15-#18 ( Fig. 15-Fig. 18).
It should be pointed out that, for the comparison of DNA or protein sequences, a popular and simple test of phylogenetic accuracy is usually carried out by the bootstrap method [35,36]. Bootstrap analysis essentially tests whether the whole dataset supports the tree by means of creating multiple pseudo-datasets that are randomly sampled with replacement. Individual phylogenetic trees are then reconstructed from each of the pseudo-datasets, which are finally used to find the consensus of support for the data grouping. In principle, the bootstrap procedure randomly selects samples with replacement from a dataset, given a condition that the number of elements in each bootstrap sample equals the number of elements in the original dataset. Thus, a particular data point from the original dataset has a chance to appear multiple times in a bootstrap sample. Unlike DNA or protein sequences, the PPG patterns in this study are represented with vectors of spectral coefficients, and the application of the bootstrap method for these type of data is not simply applicable. Therefore, several distortion measures of the PPG patterns are applied to validate the results obtained from the tree topologies. Table 1 shows the consensus of support (%) of the care-giver's influence over the 18 participants during cognitive stimulation therapy, including each participant's identity number (ID), age, gender, as well as the spectral-distortion method(s) supporting the evidence.

Conclusion
Cognitive stimulation therapy has been widely discussed in literature, in particular for people with dementia [37]- [41]. This study adopted the use of synchronized PPG measurement for assessing the effectiveness of the communication for cognitive stimulation therapy based on the computational models of spectral distortion and phylogenetic inference. Experimental results of this pilot study show its potential application as an assistive computer-technology tool for assessing the efficacy of cognitive therapy. Because the PPG measurements can be synchronized among the care-giver or therapist and multiple participants, the approach can also be applied for the assessment of the effectiveness of group therapy.
Furthermore, research findings have suggested that the increase in the sense of life quality of disabled elderly is an important psychological factor for alleviating care-givers' burden in      Dissimilarities of PPG data between care-giver and participant were determined by spectral-distortion measures: Itakura distortion (a), log spectral distortion (b), and weighted cepstral distortion (c). Matrices of dissimilarity are used to construct trees of relationships between PPG data of care-giver and participant before, during and after synchronized communication.
doi:10.1371/journal.pone.0118739.g008     Dissimilarities of PPG data between care-giver and participant were determined by spectral-distortion measures: Itakura distortion (a), log spectral distortion (b), and weighted cepstral distortion (c). Matrices of dissimilarity are used to construct trees of relationships between PPG data of care-giver and participant before, during and after synchronized communication.
doi:10.1371/journal.pone.0118739.g017 Dissimilarities of PPG data between care-giver and participant were determined by spectral-distortion measures: Itakura distortion (a), log spectral distortion (b), and weighted cepstral distortion (c). Matrices of dissimilarity are used to construct trees of relationships between PPG data of care-giver and participant before, during and after synchronized communication. doi:10.1371/journal.pone.0118739.g018 Japan [42], the use of this proposed methodology can be applied as a feasible and cost-effective analysis for quantifying the relationship between life quality and burden among care-givers. Three computational models, which are known as spectral-distortion measures, were applied in this pilot study to obtain the consensus of the "phylogenetic" tree results. The inclusion of other potential methods for pattern matching of PPG data between the care-giver and participants is feasible and would increase the reliability of the therapeutic assessment.

Supporting Information
Matlab codes are for the calculations of the three spectral-distortion measures and phylogenetic tree reconstruction of the PPG signals. Preprocessed finger pulse-wave data (3 minutes of recording) are synchronized PPG signals of the care-giver and 18 selected participants. The data also include the preprocessed finger PPG measurements (3 minutes of recording) of the 18 participants, recorded before and after the synchronized cognitive therapy.