JP7060226B2 - Frequency analysis method and program of heart rate variability - Google Patents
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本発明は、心拍変動の周波数解析方法に関し、より詳細には、短い観測時間で心拍変動の周波数解析を精度良く行う方法に関する。 The present invention relates to a method for frequency analysis of heart rate variability, and more particularly to a method for accurately performing frequency analysis of heart rate variability in a short observation time.
従来、心拍変動(ＨＲＶ：Heart Rate Variability)の周波数スペクトル特性が自律神経系の指標として用いられており、その周波数解析においては、不等時間間隔のＲＲ間隔を等時間間隔に補正した離散的な時系列データに対して離散フーリエ変換（ＤＦＴ／ＦＦＴ）を実行する方法が一般的である。 Conventionally, the frequency spectrum characteristic of heart rate variability (HRV) has been used as an index of the autonomous nervous system, and in the frequency analysis, the RR interval of the unequal time interval is corrected to the equal time interval in a discrete manner. A method of performing a discrete Fourier transform (DFT / FFT) on time-series data is common.
一方、心拍変動の周波数解析を利用して対象者の状態（心理状態、精神状態、身体状態など）を判定することが種々検討されている（例えば、特許文献１、２）。この場合、対象者の状態の変化を高い時間分解能で判定しようとすれば、心拍データの観測時間をできるだけ短くする必要があるが、一定の時間データ長を基底とする離散フーリエ変換では、観測時間の逆数が周波数分解能となるため、観測時間を短くするほど周波数分解能が低下して解析精度が落ちるというトレードオフの問題が生じる。
On the other hand, various studies have been made to determine a subject's state (psychological state, mental state, physical state, etc.) by using frequency analysis of heart rate variability (for example,
本発明は、上記従来技術における課題に鑑みてなされたものであり、短い観測時間で心拍変動の周波数解析を精度良く行う方法を提供することを目的とする。 The present invention has been made in view of the above-mentioned problems in the prior art, and an object of the present invention is to provide a method for accurately performing frequency analysis of heart rate variability in a short observation time.
本発明者は、短い観測時間で心拍変動の周波数解析を精度良く行う方法につき鋭意検討した結果、以下の構成に想到し、本発明に至ったのである。 As a result of diligent studies on a method for accurately performing frequency analysis of heart rate variability in a short observation time, the present inventor came up with the following configuration and came up with the present invention.
すなわち、本発明によれば、心拍変動の周波数解析方法であって、所定数のＲ波発生時刻からＲＲ間隔を算出するステップと、隣り合う２つのＲ波発生時刻の間隔（ＲＲ間隔）の逆数に基づく階段関数として、当該２つのＲ波発生時刻の間の各時刻の瞬時心拍数を定義した時間関数を定義するステップと、前記時間関数に対するフーリエ変換を適用して連続スペクトルを生成するステップと、を含む周波数解析方法が提供される。
That is, according to the present invention, in the frequency analysis method of heart rate variability, the step of calculating the RR interval from a predetermined number of R wave generation times and the inverse of the interval (RR interval) between two adjacent R wave generation times. As a step function based on, a step of defining a time function that defines an instantaneous heart rate at each time between the two R wave generation times, and a step of applying a Fourier transform to the time function to generate a continuous spectrum. A frequency analysis method including, is provided.
上述したように、本発明によれば、短い観測時間で心拍変動の周波数解析を精度良く行う方法が提供される。 As described above, the present invention provides a method for accurately performing frequency analysis of heart rate variability in a short observation time.
以下、本発明を図面に示した実施の形態をもって説明するが、本発明は、図面に示した実施の形態に限定されるものではない。 Hereinafter, the present invention will be described with reference to the embodiments shown in the drawings, but the present invention is not limited to the embodiments shown in the drawings.
本発明は、心拍数を基底とする心拍変動の周波数解析方法を開示する。以下、本発明の実施形態である心拍変動の周波数解析方法の手順を図１に示すフローチャートに基づいて説明する。なお、以下では、便宜的に、心拍数「６」を基底とする場合を例にとって説明を行う。 The present invention discloses a frequency analysis method for heart rate variability based on heart rate. Hereinafter, the procedure of the frequency analysis method of heart rate variability according to the embodiment of the present invention will be described with reference to the flowchart shown in FIG. In the following, for convenience, the case where the heart rate "6" is used as the basis will be described as an example.
まず、ステップＳ１では、対象者の心拍信号から、時間的に連続する所定数のＲ波のピーク値の発生時刻（以下、Ｒ波発生時刻という）を取得する。 First, in step S1, the occurrence time of the peak value of a predetermined number of R waves continuously in time (hereinafter referred to as the R wave generation time) is acquired from the heartbeat signal of the subject.
本例では、心拍数「６」を基底とするので、図２（ａ）に示すように、６個のＲ波発生時刻ｔ０～ｔ５を取得する。 In this example, since the heart rate “6” is used as the base, six R wave generation times t 0 to t 5 are acquired as shown in FIG. 2 (a).
続くステップＳ２では、検出した６個のＲ波発生時刻から５個のＲＲ間隔を算出する。 In the following step S2, five RR intervals are calculated from the detected six R wave generation times.
本例では、図２（ｂ）に示すように、時刻ｔ１と時刻ｔ０の差分としてＲＲ間隔１（以下、ＲＲ１という）を算出し、時刻ｔ２と時刻ｔ１の差分としてＲＲ間隔２（以下、ＲＲ２という）を算出し、時刻ｔ３と時刻ｔ２の差分としてＲＲ間隔３（以下、ＲＲ３という）を算出し、時刻ｔ４と時刻ｔ３の差分としてＲＲ間隔４（以下、ＲＲ４という）を算出し、時刻ｔ５と時刻ｔ４の差分としてＲＲ間隔５（以下、ＲＲ５という）を算出する。 In this example, as shown in FIG. 2B, the RR interval 1 (hereinafter referred to as RR1) is calculated as the difference between the time t 1 and the time t 0 , and the RR interval 2 is calculated as the difference between the time t 2 and the time t 1 . (Hereinafter referred to as RR2) is calculated, RR interval 3 (hereinafter referred to as RR3) is calculated as the difference between time t3 and time t2 , and RR interval 4 (hereinafter referred to as RR4) is calculated as the difference between time t4 and time t3. ) Is calculated, and the RR interval 5 ( hereinafter referred to as RR5) is calculated as the difference between the time t5 and the time t4.
続くステップＳ３では、算出したＲＲ間隔の逆数を瞬時心拍数とする時間関数を定義する。具体的には、隣り合う２つのＲ波発生時刻の間隔（ＲＲ間隔）の逆数を当該２つのＲ波発生時刻の間の各時刻の瞬時心拍数と推定して、瞬時心拍数の時間関数を定義する。 In the following step S3, a time function is defined in which the reciprocal of the calculated RR interval is used as the instantaneous heart rate. Specifically, the reciprocal of the interval (RR interval) between two adjacent R wave generation times is estimated as the instantaneous heart rate at each time between the two R wave generation times, and the time function of the instantaneous heart rate is obtained. Define.
この例では、ＲＲ１の逆数（ＲＲ１）－１を時刻ｔ０と時刻ｔ１の間の各時刻の瞬時心拍数Ａ１と推定し、ＲＲ２の逆数（ＲＲ２）－１を時刻ｔ１と時刻ｔ２の間の各時刻の瞬時心拍数Ａ２と推定し、ＲＲ３の逆数（ＲＲ３）－１を時刻ｔ２と時刻ｔ３の間の各時刻の瞬時心拍数Ａ３と推定し、ＲＲ４の逆数（ＲＲ４）－１を時刻ｔ３と時刻ｔ４の間の各時刻の瞬時心拍数Ａ４と推定し、ＲＲ５の逆数（ＲＲ５）－１を時刻ｔ４と時刻ｔ５の間の各時刻の瞬時心拍数Ａ５と推定することにより、瞬時心拍数の時間関数として、図２（ｃ）に示すような階段関数が定義される。 In this example, the reciprocal of RR1 (RR1) -1 is estimated to be the instantaneous heart rate A1 at each time between time t 0 and time t 1 , and the reciprocal of RR 2 (RR 2) -1 is time t 1 and time t 2 . Estimate the reciprocal of RR3 ( RR3 ) -1 as the reciprocal of RR3 (RR3) -1 as the reciprocal of RR4 (RR4). -1 is estimated as the instantaneous heart rate A4 at each time between time t 3 and time t 4 , and the reciprocal of RR 5 (RR5) -1 is the instantaneous heart rate A5 at each time between time t 4 and time t 5 . By estimating, a step function as shown in FIG. 2C is defined as a time function of the instantaneous heart rate.
続くステップＳ４では、定義した瞬時心拍数の時間関数に対するフーリエ変換を適用して連続スペクトルを生成する。なお、ここでいう「フーリエ変換」とは、連続的な関数に対するフーリエ変換(FT：Fourier Transform)を意味し、高速フーリエ変換（FFT：Fast Fourier Transform）を含む離散フーリエ変換（DFT：Discrete Fourier Transform）を意味しないことに留意されたい。 In the following step S4, a Fourier transform is applied to the defined instantaneous heart rate time function to generate a continuous spectrum. The "Fourier Transform" here means a Fourier Transform (FT) for a continuous function, and a Discrete Fourier Transform (DFT) including a Fast Fourier Transform (FFT). Note that it does not mean).
ここで、本実施形態では、図２（ｃ）に示す瞬時心拍数の時間関数のフーリエ変換を以下の手順で行う。 Here, in the present embodiment, the Fourier transform of the time function of the instantaneous heart rate shown in FIG. 2C is performed by the following procedure.
瞬時心拍数の時間関数のt0～t1区間をフーリエ変換した関数F1(ω)は、下記式（１）で表される。 The function F1 (ω) obtained by Fourier transforming the t0 to t1 interval of the time function of the instantaneous heart rate is expressed by the following equation (1).
同様に、瞬時心拍数の時間関数のt1～t2区間、t2～t3区間、t3～t4区間、t4～t5間の各々をフーリエ変換した関数F2(ω)、F3(ω)、F4(ω)、F5(ω)は、下記式（２）で表される。 Similarly, the functions F2 (ω), F3 (ω), F4 (ω) obtained by Fourier transforming each of the t1 to t2 section, t2 to t3 section, t3 to t4 section, and t4 to t5 of the time function of the instantaneous heart rate. , F5 (ω) is expressed by the following equation (2).
したがって、フーリエ変換の線形性より、t0～t5区間をフーリエ変換した関数F(ω)は、下記式（３）で表される。 Therefore, from the linearity of the Fourier transform, the function F (ω) obtained by Fourier transforming the t0 to t5 interval is expressed by the following equation (3).
そして、F(ω)の振幅スペクトルA(ω)は、下記式（４）で表される。 The amplitude spectrum A (ω) of F (ω) is expressed by the following equation (4).
つまり、本実施形態では、予め、瞬時心拍数の時間関数（階段関数）のフーリエ変換を実施して一般式を導出しておき、当該一般式にA1～A5、t0～t5などのデータを入力して演算を行うことにより連続関数を生成する。ここで、上記式（４）において、a1～a5、R1～R5、I1～I5のそれぞれの値は、定数であるA1～A5、t0～t5、およびωで構成され、A(ω)は、ω≠0の区間で連続する値を取り、連続スペクトルとなる。 That is, in the present embodiment, the Fourier transform of the time function (step function) of the instantaneous heart rate is performed in advance to derive a general formula, and data such as A1 to A5 and t0 to t5 are input to the general formula. And generate a continuous function by performing the operation. Here, in the above equation (4), each value of a1 to a5, R1 to R5, and I1 to I5 is composed of constants A1 to A5, t0 to t5, and ω, and A (ω) is It takes continuous values in the interval of ω ≠ 0 and becomes a continuous spectrum.
以上、説明したように、本実施形態によれば、心拍変動の周波数解析結果として連続スペクトルが得られるので、短い観測時間でも必要な周波数分解能が確保される。さらに、最新の所定数のＲ波発生時刻について、図１に示すステップＳ１～Ｓ４を出来る限り短い周期で繰り返し実行すれば、心拍変動の経時的変化を高い時間分解能で解析することが可能になる。 As described above, according to the present embodiment, since the continuous spectrum is obtained as the frequency analysis result of the heart rate variability, the required frequency resolution is secured even in a short observation time. Further, if steps S1 to S4 shown in FIG. 1 are repeatedly executed in the shortest possible cycle for the latest predetermined number of R wave generation times, it becomes possible to analyze changes over time in heart rate variability with high time resolution. ..
なお、図１に示した各ステップをコンピュータに実行させるためのプログラムは、任意のプログラム言語で記述することができ、任意の記録媒体に格納して頒布することができ、任意のネットワークを介して伝送することができる。 The program for causing the computer to execute each step shown in FIG. 1 can be written in any programming language, stored in any recording medium and distributed, and can be distributed via any network. Can be transmitted.
以上、本発明について実施形態をもって説明してきたが、本発明は上述した実施形態に限定されるものではなく、当業者が推考しうるその他の実施態様の範囲内において、本発明の作用・効果を奏する限り、本発明の範囲に含まれるものである。 Although the present invention has been described above with embodiments, the present invention is not limited to the above-described embodiments, and the actions and effects of the present invention can be achieved within the scope of other embodiments that can be conceived by those skilled in the art. As long as it works, it is included in the scope of the present invention.
以下、本発明の心拍変動の解析方法について、実施例を用いてより具体的に説明を行なうが、本発明は、後述する実施例に限定されるものではない。 Hereinafter, the method for analyzing heart rate variability of the present invention will be described more specifically with reference to examples, but the present invention is not limited to the examples described later.
下記表１に示す内容の心拍信号を模したサンプルデータを作成し、実施例として、本発明の解析方法による周波数解析を行った。 Sample data imitating the heartbeat signal of the contents shown in Table 1 below was prepared, and as an example, frequency analysis was performed by the analysis method of the present invention.
併せて、比較例として、同じサンプルデータについて、MATLABのFFT関数を使用して周波数解析を行った（サンプリング周波数10Hz）。 At the same time, as a comparative example, frequency analysis was performed on the same sample data using the FFT function of MATLAB (sampling frequency 10 Hz).
図３（ａ）は比較例の解析結果を示す。図３（ａ）に示すように、比較例では、３種類の周波数成分（0.090Hz、0.095Hz、0.10Hz）の振幅ピーク値について最大で２割程度の差が生じる結果となった。これは、比較例の周波数分解能が約0.026Hz（観測時間≒0.39secの逆数）であることから、LF成分に対応するプロット周波数が0.078Hz、0.104Hzとなるところ、サンプルデータのLF成分0.090Hzがその中間にあたるために乖離が大きくなったことが原因と考えられる。 FIG. 3A shows the analysis result of the comparative example. As shown in FIG. 3A, in the comparative example, the difference in the amplitude peak values of the three types of frequency components (0.090Hz, 0.095Hz, 0.10Hz) was about 20% at the maximum. This is because the frequency resolution of the comparative example is about 0.026Hz (reciprocal of observation time ≒ 0.39sec), so the plot frequencies corresponding to the LF component are 0.078Hz and 0.104Hz, but the LF component of the sample data is 0.090Hz. It is considered that the cause is that the divergence became large because it was in the middle.
一方、図３（ｂ）は実施例の解析結果を示す。図３（ｂ）に示すように、実施例では、３種類の周波数成分（0.090Hz、0.095Hz、0.10Hz）のそれぞれの振幅ピーク値が概ね等しかった。この結果から、本発明の解析方法によれば、約39秒という短い観測時間で精度良い結果が得られることが示された。 On the other hand, FIG. 3B shows the analysis results of the examples. As shown in FIG. 3B, in the examples, the amplitude peak values of the three types of frequency components (0.090Hz, 0.095Hz, 0.10Hz) were almost equal. From this result, it was shown that according to the analysis method of the present invention, accurate results can be obtained in a short observation time of about 39 seconds.
Claims (3)
所定数のＲ波発生時刻からＲＲ間隔を算出するステップと、
隣り合う２つのＲ波発生時刻の間隔（ＲＲ間隔）の逆数に基づく階段関数として、当該２つのＲ波発生時刻の間の各時刻の瞬時心拍数を定義した時間関数を定義するステップと、
前記時間関数に対するフーリエ変換を適用して連続スペクトルを生成するステップと、
を含む周波数解析方法。 It is a frequency analysis method for heart rate variability.
A step of calculating the RR interval from a predetermined number of R wave generation times, and
As a step function based on the reciprocal of the interval between two adjacent R wave generation times (RR interval), a step of defining a time function that defines the instantaneous heart rate at each time between the two R wave generation times, and a step of defining the time function.
The step of applying the Fourier transform to the time function to generate a continuous spectrum,
Frequency analysis method including.
（ａ）最新の所定数のＲ波発生時刻からＲＲ間隔を算出するステップ。
（ｂ）隣り合う２つのＲ波発生時刻の間隔（ＲＲ間隔）の逆数に基づく階段関数として、当該２つのＲ波発生時刻の間の各時刻の瞬時心拍数を定義した時間関数を定義するステップ。
（ｃ）前記時間関数に対するフーリエ変換を適用して連続スペクトルを生成するステップ。 A method for analyzing changes in heart rate variability over time, characterized in that the following steps (a) to (c) are repeatedly executed.
(A) A step of calculating the RR interval from the latest predetermined number of R wave generation times.
(B) As a step function based on the reciprocal of the interval (RR interval) between two adjacent R wave generation times, a step of defining a time function that defines the instantaneous heart rate at each time between the two R wave generation times. ..
(C) A step of applying a Fourier transform to the time function to generate a continuous spectrum.
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| JP2016013196A (en) | 2014-06-30 | 2016-01-28 | 株式会社Ｚｍｐ | Server system for heartbeat data analysis |
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