Patent Publication Number: US-2023148873-A1

Title: Physiological state index calculation system, physiological state index calculation method, and non-transitory computer readable medium

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from Japanese patent application No. 2021-187848, filed on Nov. 18, 2021, the disclosure of which is incorporated herein in its entirety by reference. 
     BACKGROUND 
     The present disclosure relates to a physiological state index calculation system, a physiological state index calculation method, and a non-transitory computer readable medium for calculating physiological state indices of a living body. 
     In related art, various techniques for calculating physiological state indices of a living body have been proposed. As an example of these techniques, a disease condition determination apparatus disclosed in International Patent Publication No. WO 2018/056137 determines a disease condition of a subject based on a degree of separation of two kinds of blood flow information based on loads different from each other, amplitude of a change in a hemoglobin concentration of a cerebral blood flow, and a phase of the change in the hemoglobin concentration of the cerebral blood flow. 
     SUMMARY 
     There is a problem in the disease condition determination apparatus disclosed in International Patent Publication No. WO 2018/056137 that it is impossible to capture subtle changes in the physiological state of a subject since this disease condition determination apparatus statistically processes the amplitude and the phase, which are directly detected from a change in the amount of the cerebral blood flow from a subject to which two types of load tasks are given, and determines a disease condition based on the magnitude of the change in the amount of the cerebral blood flow. 
     The present disclosure has been made in order to solve the aforementioned problem and an object of the present disclosure is to provide a physiological state index calculation system, a physiological state index calculation method, and a non-transitory computer readable medium storing a physiological state index calculation program for capturing subtle changes in a physiological state of a living body. 
     A physiological state index calculation system configured to calculate a physiological state index of a living body according to one aspect of the present disclosure includes:
     a waveform information generation unit configured to measure a cerebral blood flow of a living body, which is time series data, in at least one part of a brain to generate blood flow amount waveform information; and   a band-pass filter configured to filter the blood flow amount waveform information in at least one frequency band and an arithmetic unit configured to convert the filtered blood flow amount waveform information into a complex number.   

     The arithmetic unit may obtain a logarithmic value of blood flow amount waveform information converted into the complex number as one oscillator for at least one frequency band, and the real part of this logarithmic value may be an instantaneous amplitude, the imaginary part of the logarithmic value may be an instantaneous phase, and the time differential value thereof may be an instantaneous frequency. 
     The arithmetic unit is further able to aggregate the instantaneous amplitude during a period in which the living body can be regarded as being in a physiologically steady state to calculate a probability distribution. This distribution becomes a monomodal distribution such as a Gaussian distribution. If the instantaneous frequency is aggregated to calculate the probability distribution, this distribution becomes a monomodal distribution such as a Gaussian distribution. 
     Last, the arithmetic unit is able to calculate an average value, a variance and the like from the monomodal distribution shapes of the instantaneous amplitude and the instantaneous frequency by fitting. They serve as feature amounts representing the physiological state. 
     According to the aforementioned method, the number of frequency bands × the number of cerebral blood flow measurement parts × 4 (two amplitudes + two frequencies) mathematically independent feature amounts can be obtained and the physiological state can thus be treated as a multi-dimensional data space. By performing analysis using this method for physiological experiments, subtle changes in his/her physiological state, which have not been discerned in the physiological indices so far, can be statistically discerned. 
     Regarding the frequency band for performing band-pass filter, if tNIRS-1 non-invasive cerebral oxygen monitor C12707 (sampling frequency 0.2 Hz) manufactured by Hamamatsu Photonics K.K. is used, the physiological feature amount can be calculated in bands of 4-15 mHz (VLF2), 15-40 mHz (VLF1), and 0.04-0.15 Hz (LF). 
     Further, if NIRO-200NX manufactured by Hamamatsu Photonics K.K. is used, although the accuracy of the measurement of the cerebral blood flow is low, the sampling frequency is 20 Hz. Therefore, bands of 0.4-4 mHz (VLF2), 0.15-0.4 Hz (VLF1), 0.04-0.15 Hz (LF), 0.15-0.4 Hz (HF), 0.4-1.5 Hz (δ1), 1.5-4 Hz (δ2), and 4-8 Hz (θ) are available. By using an apparatus having a high sampling frequency, the physiological feature amounts of α waves or larger of electroencephalogram can be calculated. 
     According to the present disclosure, it is possible to provide a physiological state index calculation system, a physiological state index calculation method, and a non-transitory computer readable medium storing a physiological state index calculation program for capturing subtle changes in a physiological state of a living body. More specifically, the cerebral blood flow waveform information converted into a complex number by a complex number conversion unit represents the physiological state of the living body using the distribution shapes of the instantaneous amplitude and the instantaneous frequency of each band waveform of the cerebral blood flow as feature amounts, whereby it is possible to capture subtle changes in a physiological state of a living body. 
     The above and other objects, features and advantages of the present disclosure will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus are not to be considered as limiting the present disclosure. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a diagram showing results of analyzing measurement data of a blood flow of a frontal lobe of a subject by FFT; 
         FIG.  2    is a diagram showing an algorithm according to one aspect of the present disclosure; 
         FIG.  3    is a diagram showing one example of a hemoglobin concentration in a blood flow of right and left frontal lobes of the subject; 
         FIG.  4    is a diagram showing one example of a distribution density of an instantaneous amplitude a 1 k for each frequency band of the left frontal lobe of the subject; 
         FIG.  5    is a diagram showing one example of a distribution density of an instantaneous frequency ω 1 k for each frequency band of the left frontal lobe of the subject; 
         FIG.  6    is a diagram showing one example of a distribution density of an instantaneous amplitude a 2 k for each frequency band of the right frontal lobe of the subject; 
         FIG.  7    is a diagram showing one example of a distribution density of an instantaneous frequency ω 2 k for each frequency band of the right frontal lobe of the subject; 
         FIG.  8    is a diagram showing a protocol of a fatigue experiment conducted for subjects; 
         FIG.  9    is a diagram showing results of an analysis of variance of feature amounts according to one aspect of the present disclosure; 
         FIG.  10    shows a QQ plot and a box-and-whisker diagram of a feature amount mw1 according to one aspect of the present disclosure; 
         FIG.  11    shows a QQ plot and a box-and-whisker diagram of a feature amount sw1 according to one aspect of the present disclosure; 
         FIG.  12    shows a QQ plot and a box-and-whisker diagram of a feature amount swfl according to one aspect of the present disclosure; 
         FIG.  13    shows a QQ plot and a box-and-whisker diagram of a feature amount mw2 according to one aspect of the present disclosure; 
         FIG.  14    is a diagram showing results of a stepwise multiple regression analysis; 
         FIG.  15    is a diagram showing a correlation relation between objective variables (subjective indices and behavioral indices) and explanatory variables (feature amounts of physiological indices); 
         FIG.  16    is a diagram showing a correlation between VAS (feeling of tiredness) and the feature amount swfl and a regression coefficient; 
         FIG.  17    is a diagram showing a correlation between pleasant (pleasantness) and the feature amount sw1 and a regression coefficient; 
         FIG.  18    is a diagram showing a correlation between relax_(opposite of relaxed) and the feature amount sw1 and a regression coefficient; 
         FIG.  19    is a diagram showing a correlation between fatigue (weariness) and the feature amount swfl and a regression coefficient; 
         FIG.  20    is a diagram showing a correlation between anxiety (anxious) and the feature amount sw1 and a regression coefficient; 
         FIG.  21    is a diagram showing a correlation between stress (stressed) and feature amount mw1 and a regression coefficient; 
         FIG.  22    is a diagram showing a correlation between res_m (an average of a reaction time of PVT) and the feature amount mw1 and a regression coefficient; 
         FIG.  23    is a diagram showing a correlation between res_s (a standard deviation of a reaction time of PVT) and the feature amount mw1 and a regression coefficient; 
         FIG.  24    is a diagram showing one example of a physiological state index calculation system according to one aspect of the present disclosure; 
         FIG.  25    is a diagram showing one example of a physiological state index calculation program according to one aspect of the present disclosure; and 
         FIG.  26    is a flowchart showing one example of processing executed in the physiological state index calculation system according to one aspect of the present disclosure. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Fast Fourier Transform (FFT) Analysis of Cerebral Blood Flow Data 
     Hereinafter, with reference to the drawings, one aspect of the present disclosure will be described.  FIG.  1    is a diagram showing results of measuring the blood flow of the frontal lobe of a subject using a non-invasive cerebral oxygen monitor (tNIRS-1 manufactured by Hamamatsu Photonics K.K.) and analyzing the measurement data by FFT. The sampling frequency at this time is 0.2 Hz and the measurement time is 60 minutes. 
     “O 2 Hb+HHb” shown in  FIG.  1   , which represents the sum of an oxygenerated hemoglobin concentration and a deoxygenerated hemoglobin concentration, corresponds to a total hemoglobin concentration. The total hemoglobin concentration is proportional to the amount of the blood flow that flows through arteries of the frontal lobe of a subject. It is seen from  FIG.  1    that the frequency spectrum of the total hemoglobin concentration (O 2 Hb+HHb) is on the ⅟f line. 
     Proposal of Ak-ωk Analysis Method of Cerebral Blood Flow Data 
     In one aspect of the present disclosure, an ak-ωk analysis method of measurement data of the total hemoglobin amount in the cerebral blood flow by a non-invasive cerebral oxygen monitor is proposed. In one aspect of the present disclosure, as shown in  FIG.  2   , waveform information indicating a total hemoglobin amount φ1(t) in the cerebral blood flow of the left frontal lobe of the subject and a total hemoglobin amount φ2(t) in the cerebral blood flow of the right frontal lobe of the subject that have been measured is subjected to band-pass filter processing in predetermined frequency bands. The predetermined frequency bands include, for example, a Low Frequency (LF) [0.04:0.15] Hz (blood pressure fluctuation), Very Low Frequency (VLF) 1 [15:40] mHz (first autonomic neurogenic fluctuation), and VLF 2  [4:15] mHz (second autonomic neurogenic fluctuation). The LF is related to blood pressure fluctuation and VLF 1  and VLF 2  are related to autonomic neurogenic fluctuation. 
     Next, the waveform information in each frequency band is converted into a complex number. In this embodiment, Hilbert transformation is employed as a complex number conversion method. By converting the waveform information into a complex number in each frequency band, oscillation waveform expressions as shown in the following Equations 1 and 3 can be obtained. The symbol k represents each frequency band, like k = 1 (VLF2), k = 2 (VLF1), and k = 3 (LF). Equations 1 and 2 are equations regarding the left brain. The real part a 1 k(t) of the logarithm in the oscillation waveform expression shown in Equation 1 represents the instantaneous amplitude and the imaginary part ψ 1 k(t) thereof represents an instantaneous phase. The part ω 1 k(t) shown in Equation 2, which represents the instantaneous frequency, corresponds to a time differentiation of the instantaneous phase. Equations 3 and 4 are equations regarding the right brain. The real part a 2 k(t) of the logarithm in the oscillation waveform expression shown by Equation 3 represents the instantaneous amplitude and the imaginary part ψ 2 k(t) thereof represents an instantaneous phase. The symbol ω 2 k(t) shown in Equation 4, which represents the instantaneous frequency, corresponds to a time differentiation of the instantaneous phase. 
     
       
         
           
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     While Equations 1 and 2 show the cerebral blood flow in the left frontal lobe and Equations 3 and 4 show the cerebral blood flow in the right frontal lobe, it is possible to concurrently measure the cerebral blood flow of the temporal lobe, the parietal lobe, the occipital lobe other than the frontal lobe and perform similar analysis using a multi-channel non-invasive cerebral oxygen monitor. 
     Method of Processing Total Hemoglobin Waveform Data 
       FIG.  3    is a diagram showing the hemoglobin concentration in the blood flow of the right and left frontal lobes of the subject during a period in which the living body can be regarded as being in a physiologically steady state (hereinafter a “physiologically steady period”). In the example shown in  FIG.  3   , the physiologically steady period was set to seven minutes. In  FIG.  3   , the cerebral blood flow of the right and left frontal lobes of the subject was measured.  FIG.  3    shows each of the first cerebral blood flow information (oxygenerated hemoglobin concentration in the blood flow: O 2 Hb), the second cerebral blood flow information (deoxygenerated hemoglobin concentration: HHb), and the total hemoglobin concentration (O 2 Hb+HHb), which is the total of them. 
     As a result of deriving the aforementioned Equations 1-4 based on the data of the total of the oxygenerated hemoglobin concentration and the deoxygenerated hemoglobin concentration, aggregating the time series data shown in Equations 1-4 during the period in which the living body can be regarded as being in the physiologically steady state, and calculating the distribution densities, results shown in  FIGS.  4 - 7    were obtained. The above Equations 1-4 may be derived based on one of data of the oxygenerated hemoglobin concentration and data of the deoxygenerated hemoglobin concentration.  FIG.  4    is a diagram showing the distribution density (logarithm normal distribution) of the instantaneous amplitude a 1 k in the frequency bands (LF, VLF 1 , and VLF 2 ) of the left frontal lobe of the subject.  FIG.  5    is a diagram showing the distribution density (normal distribution) of the instantaneous frequency ω 1 k in the frequency bands (LF, VLF 1 , and VLF 2 ) of the left frontal lobe of the subject.  FIG.  6    is a diagram showing the distribution density (logarithm normal distribution) of the instantaneous amplitude a 2 k in the frequency bands (LF, VLF 1 , and VLF 2 ) of the right frontal lobe of the subject.  FIG.  7    is a diagram showing the distribution density (normal distribution) of the instantaneous frequency ω 2 k in the frequency bands (LF, VLF 1 , VLF 2 ) of the right frontal lobe of the subject. As shown in  FIGS.  4 - 7   , the distribution densities of the time series data shown in Equations 1-4 can be approximated by a Gaussian distribution. 
     Feature amounts representing the physiologically stable state of the subject in the aforementioned measurement period may be obtained by fitting the distribution densities of the instantaneous amplitude a 1 k, the instantaneous amplitude a 2 k, the instantaneous frequency ω 1 k, and the instantaneous frequency ω 2 k by a normal distribution (solid line in the drawings) and calculating the average and the standard deviation of the distribution. 
     By using a non-invasive cerebral oxygen monitor such as NIRO-200NX (sampling frequency 20 Hz) manufactured by Hamamatsu Photonics K.K. in which the upper limit of the sampling frequency is higher than that of the non-invasive cerebral oxygen monitor used in this experiment, High Frequency (HF) [0.15:0.4] Hz band, δ [0.4:1.5] Hz, θ [1.5:4] Hz, α [4:13] Hz bands may also be analyzed although the accuracy of the measurement is lower than that in the case in which the non-invasive cerebral oxygen monitor used in this experiment is employed. Further, if an apparatus having a high sampling frequency is used, physiological feature amounts equal to or larger than α waves can be calculated. 
     Further, if it is possible to hold the physiologically steady state for a long time (e.g., several tens of minutes) and measure the cerebral blood flow, a ULF band ([0.4:1.5] mHz, [1.5:4] mHz), which is further lower than the VLF band, may also be analyzed, and indices representing the state of the living body of, for example, an immune system, for a longer period may be derived. 
     The aforementioned description is based on a case in which the probability density distribution function for approximating the distribution is a normal distribution when it can be considered that the instantaneous amplitude a i k and the instantaneous frequency ω i k, (i=1,2,...) are in the physiologically steady state. However, the distribution is not limited to the normal distribution. This distribution may instead be approximated by other monomodal distributions such as a gamma distribution or a Lorentz distribution. When the distribution is approximated by a monomodal distribution other than the normal distribution, a shape parameter such as a variance value or a half-value width may be used in place of the standard deviation. 
     While the feature amounts are extracted by regarding the oscillation waveform, which is obtained by band-pass filtering one cerebral blood flow data piece and converting the filtered data piece into a complex number, as one oscillator in the aforementioned description, there is also a case in which a distribution is multimodal, which is a superposition of a plurality of oscillators. This case may include the following two cases, that is, a case in which the physiological state has been changed in a period in which the distributions are aggregated and a case in which there are a plurality of oscillators in the downstream of the arteries in the brain of the part to be measured. In the former case, the time interval for aggregating the distributions is divided to obtain a monomodal distribution. In the latter case, bandwidth to be band-pass filtered needs to be divided or the part to be measured needs to be moved to a downstream area of the arteries in the brain so that the distribution becomes monomodal as one oscillator. 
     Analysis of Cerebral Blood Flow Data in Fatigue Experiment 
     Method of Experiment 
       FIG.  8    is a diagram showing a protocol of a fatigue experiment conducted for  10  subjects. In order to evaluate the fatigue states of the subjects, as psychological indices, subjective evaluation such as tiredness and awakening subjective evaluation Roken Arousal Scale (RAS), or transient stress subjective evaluation Perceived Stress Scale (PSS) was conducted. Further, as behavioral indices, reaction time test Psychomotor Vigilance Task (PVT) was conducted before and after the fatigue task. Specifically, a 4-digit digital counter runs at random intervals of 2-10 seconds, and a reaction time to press the button on the hand of each subject to stop the movement of the counter was measured. Further, an N-back task (three-back, 20 minutes) was performed as the fatigue task. Further, as the physiological indices, the brain activity based on the cerebral blood flow was measured in the measurement in rest 1 and rest 2, and biochemical systems were measured by a salivary biomarker. 
     Subjects 
     The subjects were 10 healthy adult men, ranging in age from 20 to 44 years old, with a mean age was 28.5 years old. 
     Design of Experiment 
     For the purpose of searching objective indices regarding daily feeling of tiredness, a relation between the brain activity of the frontal lobe and the autonomic nerve activity before and after a fatigue load task, and results of subjective evaluation such as feeling of tiredness and task score of behavioral indices is considered. In this experiment, two meeting rooms were used, and two men or two women joined the experiments in each of the rooms. Each of the subjects participated in the experiment in one of the time schedule of 14:00-15:30 and 15:30-17:00. Measurement for five minutes in a sitting rest state (rest 1) was performed in a state in which each subject wears various electrodes and a non-invasive cerebral oxygen monitor (tNIRS-1 manufactured by Hamamatsu Photonics K.K., hereinafter, “NIRS”) that measures the cerebral blood flow, and measurement for 10 minutes in a sitting rest state (rest 1) was performed in a state in which each subject does not wear the NIRS. Next, a task that will be described later was executed for a total of 30 minutes, and then measurement for seven minutes in a sitting rest state (rest 2) was performed. Until rest 2 for seven minutes is ended after the task, the right and left cerebral blood flow was measured in a state in which sensors of the NIRS apparatus were attached to the right and left forehead part of 10 men subjects. The environment of the experiment was adjusted in such a way that the room temperature was kept 25° C.±1° C. by changing the settings of air conditioners in the meeting rooms. 
     Tasks and Behavioral Indices 
     As a mental fatigue load task, using an n-back task, which is a working memory task in which the subjects answer whether the currently presented stimulus is the same as the stimulus presented n times before, 3-back task was performed on the subjects for 20 minutes (about 260 questions). Just before and just after the 3-back task, PVT was performed for five minutes. Regarding PVT, the score at the first PVT before the 3-back task was compared with the score at the second PVT after the 3-back task. 
     Subjective Evaluation 
     As a subjective evaluation, before and after the rest 1 and after the rest 2, feeling of tiredness was evaluated by Visual Analog Scale (VAS) and pleasant/unpleasant and awakening/drowsiness were evaluated by the affect grid method. Further, mood conditions related to tiredness and stress were evaluated using RAS and PSS. 
     Measurement of Cerebral Blood Flow by Non-invasive Cerebral Oxygen Monitor, Ak-ωk Analysis, and Analysis of Variance 
     The time series data of the total hemoglobin in the cerebral blood flow for five minutes (five minutes from the start) of each of rest 1 (five minutes) and rest 2 (one-six minutes) of 10 men whose cerebral blood flow was measured in rest 1 (five minutes), task, and rest 2 (seven minutes) was processed in the flow shown in  FIG.  2   , distribution densities of the instantaneous amplitude a 1 k, the instantaneous frequency ω 1 k, the instantaneous amplitude a 2 k, and the instantaneous frequency ω 2 k were calculated, and these distribution densities were fit by a normal distribution. Accordingly, 24 feature amounts, that is, 2 (ak, ωk) × 2 (left brain and right brain) × 3 (LF, VLF 1 , VLF 2 ) × 2 (average µ, standard deviation σ), were obtained. 
     By performing, using the levels of ri ( r   1 : rest 1,  r   2 : rest 2) and id (10 subjects), analysis of variance (one-way analysis of variance of the level of ri and two-way analysis of variance of the level of ri+id) on these feature amounts, the results shown in  FIG.  9    were obtained. Three feature amounts ( mw   1 ,  sw   1 ,  mw   2 ) where 95% significance was reached and one feature amount ( swfl ) where 90% significance was reached as a result of the task (five minutes of PVT + 3 - 20 minutes of Back + five minutes of PVT) were extracted from the 24 feature amounts. 
     The feature amount  mw   1  is a feature amount representing the average µ of the values of the instantaneous amplitude a 1 k in the complex number waveform expression of VLF 2  derived from the total hemoglobin of the left brain frontal lobe of the subject. The feature amount  sw   1  is a feature amount representing the standard deviation σ of the values of the instantaneous amplitude a 1 k in the complex number waveform expression of VLF 2  derived from the total hemoglobin of the left brain frontal lobe of the subject. The feature amount  mw   2  is a feature amount representing the average µ of the values of the instantaneous amplitude a 2 k in the complex number waveform expression of VLF 2  derived from the total hemoglobin of the right brain frontal lobe of the subject. The feature amount  swfl  is a feature amount representing the standard deviation σ of the values of the instantaneous frequency ω 1 k, which is the time differential value of the instantaneous phase ψ 1 k in the complex number waveform expression of VLF 2  derived from the total hemoglobin of the left brain frontal lobe of the subject. 
     The symbol “m” shown in  FIG.  9    represents an average µ of the distribution. The symbol “s” represents a standard deviation σ of the distribution. The symbol “1” represents the amplitude of the LF band. The symbol “1f” represents the frequency of the LF band. The symbol “v” represents the amplitude of the VLF 1  band. The symbol “vf” represents the frequency of the VLF 1  band. The symbol “w” represents the amplitude of the VLF 2  band. The symbol “wf” represents the frequency of the VLF 2  band. The symbol “1” represents the left brain and the symbol “2” represents the right brain. 
       FIGS.  10 - 13    each show one-way analysis of variance before and after the fatigue task.  FIG.  10    shows a QQ plot and a box-and-whisker diagram of the feature amount  mw   1  in each of rest 1 and rest 2.  FIG.  11    shows a QQ plot and a box-and-whisker diagram of the feature amount  sw   1  in each of rest 1 and rest 2.  FIG.  12    shows a QQ plot and a box-and-whisker diagram of the feature amount  swfl  in each of rest 1 and rest 2.  FIG.  13    shows a QQ plot and a box-and-whisker diagram of the feature amount mw2 in each of rest 1 and rest 2. 
     Multiple Regression Analysis of Subjective Evaluation (RAS, PSS, VAS) and Behavioral Indices (PVT), and Feature Amounts of Ak-ωk Analysis Method 
     Multiple regression analysis has been performed using four feature amounts ( mw   1 ,  sw   1 ,  swfl ,  mw   2 ), which are physiological indices which have become significant as a result of the analysis of variance, as explanatory variables, and subjective indices (RAS, PSS, VAS, the affect grid (pleasant/unpleasant and awakening/drowsiness)) and the behavioral indices (PVT) as objective variables. 
     In order to reduce fluctuations in the subjective indices, the behavioral indices, and the feature amounts ( mw   1 ,  sw   1 ,  swfl ,  mw   2 ) of physiological indices in individuals, the difference between the subjective indices, the behavioral indices, and the feature amounts of the physiological indices before the task and those after the task was calculated, and stepwise multiple regression analysis was performed. Here, an operation of excluding explanatory variables in which p values exceed 10% as a result of the stepwise multiple regression and leaving only explanatory variables in which p values are equal to or lower than 10% was performed.  FIG.  14    shows results of the stepwise multiple regression analysis.  FIG.  15    shows a correlation relation between the objective variables (subjective indices and behavioral indices) and the explanatory variables (feature amounts of physiological indices). 
     The index VAS is an index indicating the strength of the tiredness expressed by a numerical value of 0-100. The indices pleasant (pleasantness) and arousal (awakening) are indices expressed by numerical values based on the affect grid. The indices sleepy (drowsiness), active_ (the opposite of active), relax_ (opposite of relaxed), strainR (nervous), concentrate (concentrated state), and motivation (motivated state) are indices which are based on the results of the response in RAS. The indices fatigue (weariness), Pleasant_P (unpleasant), angry (anger), anxiety (anxious), stress (stressed state), strainP (nervous) are indices which are based on the results of the response in PSS. The index res_m represents an average of the reaction time of PVT and res_s represents a standard deviation of a reaction time of PVT. 
       FIGS.  16 - 23    show a correlation between each of the objective variables (subjective indices and behavioral indices) and explanatory variables (feature amounts of physiological indices) and a regression coefficient.  FIG.  16    shows a correlation between VAS (feeling of tiredness) and the feature amount  swfl  and a regression coefficient.  FIG.  17    shows a correlation between pleasant (pleasantness) and the feature amount  sw   1  and a regression coefficient.  FIG.  18    shows a correlation between relax_ (opposite of relaxed) and the feature amount  sw   1  and a regression coefficient.  FIG.  19    shows a correlation between fatigue (weariness) and the feature amount  swfl  and a regression coefficient.  FIG.  20    shows a correlation between anxiety (anxious) and the feature amount  sw   1  and a regression coefficient.  FIG.  21    shows a correlation between stress (stressed) and the feature amount  mw   1  and a regression coefficient.  FIG.  22    shows a correlation between res_m (average of a reaction time of PVT) and the feature amount  mw   1   and a regression coefficient.  FIG.  23    shows a correlation between res_s (a standard deviation of the reaction time of PVT) and the feature amount  mw   1  and a regression coefficient. 
     It is seen from  FIG.  15    that the feature amount  swfl  (fluctuation in the frequency in the VLF 2  band of the left forehead part) increases as VAS (tiredness), fatigue (weariness), anxiety (anxious), and stress (stressed) increase. It is further seen that the feature amount  mw   1  (the frequency average value in the VLF 2  band of the left forehead part) increases as VAS (tiredness), relax_(opposite of relaxed), and stress (stressed) increase and the feature amount  mw   1  increases as Pleasant (pleasantness) decreases. It seems opposite in terms of the fatigue effect that the feature amount  mw   1  increases as res_m (PVT reaction time average) and res_s (PVT reaction time standard deviation) decrease. However, it can be interpreted that those who seriously engaged in the PVT task had a faster reaction time but were fatigued as a result, whereas those who did not engage in the task seriously had a slower reaction time but were not fatigued. By performing the ak-ωk analysis in this manner, it was found that the increase in the tiredness appeared as the increase in the feature amount  swfl  and the feature amount  mw   1 . 
       FIG.  24    shows one example of a physiological state index calculation system 1 according to one aspect of the present disclosure. The physiological state index calculation system 1 includes an information processing apparatus  10  and a cerebral oxygen monitor  20 . Specific examples of the information processing apparatus  10  include a Personal Computer (PC), a server, a raspberry pi, a smartphone, a wearable terminal, a tablet terminal or the like. These apparatuses correspond to a computer. 
     Specific examples of the cerebral oxygen monitor  20  include the aforementioned tNIRS-1, NIRO-200NX or the like. Note that the function that the information processing apparatus  10  includes may be implemented in the cerebral oxygen monitor  20  and the physiological state index calculation system 1 may be formed as one apparatus. 
     The information processing apparatus  10  includes an arithmetic apparatus  11 , a communication interface (I/F)  12 , a storage apparatus  13 , and a display apparatus  14 . 
     The arithmetic apparatus  11  is an apparatus configured to control the entire information processing apparatus  10 . Specific examples of the arithmetic apparatus  11  include a Central Processing Unit (CPU), a Micro Processing Unit (MPU), an Electronic Control Unit (ECU) or the like. The arithmetic apparatus  11  also corresponds to a computer. 
     The arithmetic apparatus  11  executes the physiological state index calculation program  100 , the registration unit  110 , and the output unit  120 . The arithmetic apparatus  11  implements a physiological state index calculation method by executing the physiological state index calculation program. The details of the physiological state index calculation program  100  will be described later. 
     The registration unit  110  is a program for registering the physiological state indices that the physiological state index calculation program  100  has calculated in a database of the storage apparatus  13 . The registration unit  110  may register the physiological state indices in a database constructed in an external apparatus. 
     The output unit  120  is a program for outputting the physiological state indices that the physiological state index calculation program  100  has calculated. The output unit  120  is able to output the physiological state indices to the display apparatus  14  to cause the display apparatus  14  to display the physiological state indices. Further, the output unit  120  is able to output the physiological state indices to an external apparatus via the communication interface  12 . 
     Note that semiconductor devices such as a Field-Programmable Gate Array (FPGA) and an Application Specific Integrated Circuit (ASIC) may execute the physiological state index calculation program. These semiconductor devices also correspond to a computer. 
     The communication interface (I/F)  12  is an apparatus that communicates data with an external apparatus. The communication interface (I/F)  12  acquires cerebral blood flow information from the cerebral oxygen monitor  20 . The communication interface (I/F)  12  is able to acquire the cerebral blood flow information from the cerebral oxygen monitor  20  connected to the communication interface (I/F)  12  via a dedicated line. Further, the communication interface (I/F)  12  may acquire the cerebral blood flow information from the cerebral oxygen monitor  20  via a network that can be formed of a Local Area Network (LAN) and/or a Wide Area Network (WAN). 
     The display apparatus  14  is an apparatus configured to display various kinds of information such as physiological state indices calculated by the arithmetic apparatus  11 . The storage apparatus  13  is a storage apparatus that stores various kinds of information such as the physiological state index calculation program. 
       FIG.  25    is a diagram showing one example of the physiological state index calculation program  100 . The physiological state index calculation program  100  generates the cerebral blood flow waveform information using at least one of cerebral blood flow information representing the amount of the blood flow of the left brain of the living body and cerebral blood flow information representing the amount of the blood flow of the right brain of the living body, which are time series data. Next, the physiological state index calculation program  100  filters the cerebral blood flow waveform information in at least one frequency band. 
     The physiological state index calculation program  100  calculates the logarithm of the converted waveform information which is the complex number, and aggregates the real part of the logarithm, which is an instantaneous amplitude, the imaginary part of the logarithm, which is an instantaneous phase, and the time differential value of the instantaneous phase, which is an instantaneous frequency, during a period in which the living body can be considered as being in a physiologically rest state. These distributions are like a Gaussian distribution. The physiological state index calculation program  100  approximates them with a normal distribution to calculate the average value µ and the standard deviation σ as physiological state indices of the living body. Specifically, the physiological state index calculation program  100  calculates, for the above predetermined frequency band, the instantaneous amplitude a i k(t) and the instantaneous frequency ω i k(t) (i=1,2) of the complex equation in information on right and left cerebral blood flow waveforms in accordance with Equations (1)-(4), aggregates the instantaneous amplitude and the instantaneous frequency during a period in which the living body can be regarded as being in a physiologically steady state to calculate the probability density distribution, fits them by a normal distribution, and calculates the average value and the standard deviation for each band. 
     The physiological state index calculation program  100  includes a waveform information generation unit  101 , a band-pass filter  102 , a complex number conversion unit  103 , a first distribution calculation unit  104 , an instantaneous frequency calculation unit  105 , a first feature amount calculation unit  106 , a second distribution calculation unit  107 , and a second feature amount calculation unit  108 . 
     The waveform information generation unit  101  is a program configured to generate the cerebral blood flow waveform information using at least one of cerebral blood flow information representing the amount of the blood flow of the left brain of the living body and cerebral blood flow information representing the amount of the blood flow of the right brain of the living body, which are time series data. The cerebral blood flow information is obtained by measuring the blood flow at one or more parts of the body. Specific examples of the cerebral blood flow information include the concentration of the total hemoglobin, the oxygenerated hemoglobin concentration, or the deoxygenerated hemoglobin concentration in the intracerebral blood that reflects the amount of the blood flow in the brain of the living body. While the target brain regions are right and left frontal lobes in Examples, the target brain regions may be other brain regions such as a temporal lobe or an occipital lobe that may reflect the physiological state of the living body. Further, by measuring arteries that flow into the brain such as the internal carotid artery, the cerebral blood flow information may be obtained. 
     The band-pass filter  102  is a program for filtering the cerebral blood flow waveform information generated by the waveform information generation unit  101  in at least one frequency band. Specifically, the band-pass filter  102  divides the converted cerebral blood flow waveform information by a frequency band that can be regarded as at least one oscillator. This frequency band includes, for example, at least one of bands of 4-15 mHz (VLF 2 ), 15-40 mHz (VLF 1 ), and 0.04-0.15 Hz (LF). Further, the frequency band may include at least one of bands of 0.4-1.5 mHz (UHF2), 1.5-4 mHz (UHF1), 0.15-0.4 Hz (HF), 0.4-1.5 Hz (δ1 waves), 1.5-4 Hz (δ2 waves), 4-8 Hz (θ waves), 8-13 Hz (α waves), 13-30 Hz (β waves), and 30 Hz- (γ waves). Further, the band-pass filter  102  may divide, if a plurality of oscillators are found in the aforementioned frequency band, the aforementioned frequency band into a plurality of bands that correspond to these respective oscillators. Note that the frequency that corresponds to the boundary between the aforementioned frequency bands may be included in any band. For example, 15 mHz may belong to one of VLF 1  and VLF 2 . 
     The cerebral blood flow waveform information includes first cerebral blood flow waveform information and second cerebral blood flow waveform information identified based on optical characteristics of blood. The band-pass filter  102  is able to filter cerebral blood flow waveform information obtained by adding the first cerebral blood flow waveform information and the second cerebral blood flow waveform information. Further, the band-pass filter  102  is able to filter one of the first cerebral blood flow waveform information and the second cerebral blood flow waveform information. 
     The complex number conversion unit  103  is a program for converting the cerebral blood flow waveform information filtered by the band-pass filter  102  into a complex number and generating the converted cerebral blood flow waveform information which is the complex number. Specifically, the complex number conversion unit  103  calculates the converted cerebral blood flow waveform information which is the complex number for the aforementioned predetermined frequency band. The complex number conversion unit  103  may employ, for example, Hilbert transformation as a complex number conversion method. Note that the complex number conversion method is not limited to Hilbert transformation and may be a desired complex number conversion method. The converted cerebral blood flow waveform information which is the complex number is an oscillator that reflects the physiological state of the living body. 
     The first distribution calculation unit  104  is a program for aggregating the real part of the logarithm in the oscillation waveform expression representing the cerebral blood flow waveform information converted into the complex number by the complex number conversion unit  103 , which corresponds to the instantaneous amplitude, in a physiologically steady period to calculate a probability density distribution of the instantaneous amplitude. Specifically, the first distribution calculation unit  104  aggregates the real parts a 1 k(t) and a 2 k(t) of the logarithm shown by Equations 1 and 3 in the physiologically steady period to calculate the probability density distribution of the instantaneous amplitude. The distribution data is normally distributed like a Gaussian distribution. 
     The instantaneous frequency calculation unit  105  is a program for calculating the instantaneous frequency by obtaining the time differential value of the imaginary part of the logarithm in the oscillation waveform expression representing the cerebral blood flow waveform information converted into the complex number by the complex number conversion unit  103 . The imaginary part of the logarithm in the oscillation waveform expression represents the instantaneous phase. Specifically, imaginary parts ψ 1 k(t) and ψ 2 k(t) of the logarithm shown by Equations 1 and 3 each represent the instantaneous phase. The instantaneous frequency calculation unit  105  calculates the instantaneous frequency by obtaining the time differential value of the imaginary parts ψ 1 k(t) and ψ 2 k(t) of the logarithm according to Equations 2 and 4. The instantaneous frequency may be used to calculate the time differential value. 
     The second distribution calculation unit  107  is a program for aggregating the instantaneous frequency calculated by the instantaneous frequency calculation unit  105  in a physiologically steady period to calculate the probability density distribution of the instantaneous frequency. The distribution data is normally distributed like a Gaussian distribution. 
     The first feature amount calculation unit  106  is a program that approximates a probability density distribution of the instantaneous amplitude calculated by the first distribution calculation unit  104  by a specific distribution and calculates at least one of the average value µ and the standard deviation σ of the specific distribution as a feature amount. The specific distribution includes a normal distribution and other distributions such as a gamma distribution or an exponential distribution. The first feature amount calculation unit  106  calculates a feature amount for each frequency band. The feature amounts calculated by the first feature amount calculation unit  106 , that is, the average value and the standard deviation of the distribution of the instantaneous amplitude based on the right and left cerebral blood flow in the aforementioned frequency band, may be physiological state indices. 
     The second feature amount calculation unit  108  is a program that approximates the probability density distribution of the instantaneous frequency calculated by the second distribution calculation unit  107  by a specific distribution and calculates at least one of the average value µ and the standard deviation σ of the specific distribution as a feature amount. The specific distribution includes a normal distribution and other distributions such as a gamma distribution or an exponential distribution. The second feature amount calculation unit  108  calculates the feature amount for each frequency band. The feature amount calculated by the second feature amount calculation unit  108 , that is, the average value and the standard deviation of the distributions of the instantaneous frequency based on the right and left cerebral blood flow in the above frequency band may be physiological state indices. 
     The output unit  120  outputs the average value and the standard deviation of the distributions of the instantaneous amplitude of the right and left cerebral blood flow in the above frequency band and the average value and the standard deviation of the distributions of the instantaneous frequency that have been calculated by the physiological state index calculation program  100  as the physiological state indices. 
       FIG.  26    is a flowchart showing one example of processing executed in the physiological state index calculation system 1 according to one aspect of the present disclosure. 
     In Step S 101 , the waveform information generation unit  101  generates cerebral blood flow waveform information using cerebral blood flow information representing the amount of the blood flow of the left brain of the living body and cerebral blood flow information representing the amount of the blood flow of the right brain of the living body, which are time series data. 
     In Step S 102 , the band-pass filter  102  filters the cerebral blood flow waveform information in the above predetermined frequency band. In Step S 103 , the complex number conversion unit  103  converts the filtered cerebral blood flow waveform information into a complex number. 
     In Step S 104 , the first distribution calculation unit  104  calculates the probability density distribution of the instantaneous amplitude using the converted cerebral blood flow waveform information which is the complex number. In Step S 105 , the first feature amount calculation unit  106  calculates the feature amount based on the probability density distribution of the instantaneous amplitude. 
     In Step S 106 , the instantaneous frequency calculation unit  105  calculates the instantaneous frequency using the converted cerebral blood flow waveform information. In Step S 107 , the second distribution calculation unit  107  calculates the probability density distribution of the instantaneous frequency using the instantaneous frequency. In Step S 108 , the second feature amount calculation unit  108  calculates the feature amount based on the probability density distribution of the instantaneous frequency. 
     In Step S 109 , the registration unit  110  registers the physiological state indices calculated in the aforementioned processing in a database. Specifically, the registration unit  110  is able to register at least one of the converted cerebral blood flow waveform information which is the complex number, the feature amount based on the probability density distribution of the instantaneous amplitude, and the feature amount based on the probability density distribution of the instantaneous frequency in a database. 
     In Step S 110 , the output unit  120  outputs the physiological state indices calculated in the aforementioned processing and the processing of  FIG.  26    is ended. Specifically, the output unit  120  is able to output at least one of the converted cerebral blood flow waveform information which is the complex number, the feature amount based on the probability density distribution of the instantaneous amplitude, and the feature amount based on the probability density distribution of the instantaneous frequency. 
     In the aforementioned embodiment, the waveform information generation unit  101  generates, for each of parts to be measured, blood flow amount waveform information representing the amount of the blood flow of the brain of the living body, which is time series data. Next, the band-pass filter  102  filters the blood flow amount waveform information in at least one frequency band. Next, the complex number conversion unit  103  converts the filtered blood flow amount waveform information into a complex number and generates blood flow amount waveform information, which can be regarded as at least one oscillator. Then, the distribution calculation units  104  and  107  aggregate, for the at least one oscillator, the distributions of the instantaneous amplitude and the instantaneous frequency during the period in which the living body can be regarded as being in a physiologically steady state, and the feature amount calculation units  106  and  108  fit each of the distributions by a normal distribution and calculate the average value and the standard deviation of the amplitude and the frequency as feature amounts representing the physiological state. Then the output unit  120  forms the calculated feature amounts in the form of a database, and externally outputs the calculated feature amounts. 
     As described above, by conducting physiological experiments as described in the aforementioned embodiment using the feature amounts derived from the cerebral blood flow information of the living body and performing statistical processing as well as having the subject answer a psychological questionnaire, it is possible to capture subtle changes in a physiological state of a living body. 
     In the aforementioned examples, the program includes instructions (or software codes) that, when loaded into a computer, cause the computer to perform one or more of the functions described in the embodiments. The program may be stored in a non-transitory computer readable medium or a tangible storage medium. By way of example, and not a limitation, non-transitory computer readable media or tangible storage media can include a random-access memory (RAM), a read-only memory (ROM), a flash memory, a solid-state drive (SSD) or other types of memory technologies, a CD-ROM, a digital versatile disc (DVD), a Blu-ray disc or other types of optical disc storage, and magnetic cassettes, magnetic tape, magnetic disk storage or other types of magnetic storage devices. The program may be transmitted on a transitory computer readable medium or a communication medium. By way of example, and not a limitation, transitory computer readable media or communication media can include electrical, optical, acoustical, or other forms of propagated signals. 
     From the disclosure thus described, it will be obvious that the embodiments of the disclosure may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the disclosure, and all such modifications as would be obvious to one skilled in the art are intended for inclusion within the scope of the following claims.