JP2019092697A - Heartbeat fluctuation frequency analysis method and program - 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 of frequency analysis of heart rate variability, and more particularly to a method of accurately performing frequency analysis of heart rate variability with 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: Heart Rate Variability) is used as an index of the autonomic nervous system, and in its frequency analysis, discrete RR intervals of unequal time intervals are corrected to equal time intervals. It is common to perform discrete Fourier transform (DFT / FFT) on time series data.
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 the condition (psychological condition, mental condition, physical condition, etc.) of a subject using frequency analysis of heart rate variability (eg, Patent Documents 1 and 2). In this case, it is necessary to shorten the observation time of heart rate data as much as possible if it is intended to judge the change of the state of the subject with high time resolution, but in discrete Fourier transform based on a fixed time data length, the observation time Since the reciprocal of is the frequency resolution, there is a trade-off problem that the frequency resolution is lowered and the analysis accuracy is lowered as the observation time is shortened.
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 problems in the above-mentioned prior art, and it is an object of the present invention to provide a method for performing frequency analysis of heart rate variability with high accuracy 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 intensive studies on a method of accurately performing frequency analysis of heart rate variability in a short observation time, the present inventor has arrived at the present invention, considering the following configuration.
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、各前記ＲＲ間隔の逆数を瞬時心拍数とする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, there is provided a frequency analysis method of heart rate fluctuation, wherein a step of calculating an RR interval from a predetermined number of R wave generation times and a time function having an inverse number of each RR interval as an instantaneous heart rate are defined. A frequency analysis method is provided comprising the steps of: performing a Fourier transform on the time function to generate a continuous spectrum.
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, according to the present invention, there is provided a method of 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 the embodiment 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 method for frequency analysis of heart rate variability based on heart rate. Hereinafter, the procedure of the frequency analysis method of the heart rate fluctuation which is an embodiment of the present invention will be described based on the flowchart shown in FIG. In the following, for convenience, a case where the heart rate is "6" 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 generation time (hereinafter referred to as R-wave generation time) of the peak value of a predetermined number of R-waves continuous in 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 is “6”, six R wave generation times t 0 to t 5 are acquired as shown in FIG. 2A.
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 subsequent 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. 2 (b), the RR interval 1 as the difference time t 1 and time t 0 (hereinafter, referred to as RR1) is calculated, the time t 2 and time t 1 of the RR interval 2 as the difference (hereinafter, referred to as RR2) calculates, RR interval 3 as the difference of time t 3 and time t 2 (hereinafter, referred to as RR3) calculates, as the difference of time t 4 and time t 3 RR interval 4 (hereinafter, RR4 calculating a) that, RR interval 5 as the difference time t 5 and time t 4 (hereinafter, calculates a) of RR5.
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 an instantaneous heart rate. Specifically, the inverse function of the interval (RR interval) between two adjacent R wave occurrence times is estimated as the instantaneous heart rate at each time between the two R wave occurrence times, and the time function of the instantaneous heart rate is 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, estimates an instantaneous heart rate A1 of the time between the reciprocal of RR1 (RR1) -1 time t 0 and time t 1, the time t 1 the reciprocal (RR2) -1 of RR2 and time t 2 each time the instantaneous heart rate A2 and estimates of the reciprocal of RR3 between (RR3) -1 estimates the instantaneous heart rate A3 at each time between the time t 2 and time t 3, the inverse of RR4 (RR4) -1 estimates the instantaneous heart rate A4 at each time between the time t 3 and time t 4, the instantaneous heart rate A5 in the time between times t 4 and time t 5 the inverse of RR5 (RR5) -1 As a time function of the instantaneous heart rate, a step function as shown in FIG. 2 (c) is defined.
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 continuous spectrum is generated by applying a Fourier transform to the time function of the defined instantaneous heart rate. Here, "Fourier transform" means Fourier transform (FT: Fourier Transform) for a continuous function, and discrete Fourier transform (DFT: Discrete Fourier Transform) including fast Fourier transform (FFT). Note that 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 in 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 ((omega)) which Fourier-transformed the t0-t1 area of the time function of an instantaneous heart rate is represented by following formula (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, functions F2 (ω), F3 (ω) and F4 (ω) obtained by Fourier transforming each of t1 to t2, t2 to t3, t3 to t4, and t4 to t5 of the time function of the instantaneous heart rate , F5 (ω) are represented by the following formula (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, a function F (ω) obtained by Fourier transforming t0 to t5 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, Fourier transformation of the time function (step function) of the instantaneous heart rate is performed in advance to derive a general expression, and data such as A1 to A5 and t0 to t5 are input to the general expression. A continuous function is generated by performing the operation. Here, in the above-mentioned formula (4), the respective values of a1 to a5, R1 to R5, and I1 to I5 are constituted by constants A1 to A5, t0 to t5, and ω which are constants, and A (ω) is A continuous spectrum is obtained by taking continuous values in the interval of ω ≠ 0.
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 a continuous spectrum is obtained as a result of frequency analysis of heartbeat fluctuation, a necessary frequency resolution is secured even in a short observation time. Furthermore, if steps S1 to S4 shown in FIG. 1 are repeatedly executed as short as possible at the latest predetermined number of R wave generation times, it is possible to analyze temporal changes in heart rate fluctuation 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。 A program for causing a computer to execute each step shown in FIG. 1 can be described in any program language, can be stored and distributed in any recording medium, and can be transmitted via any network. It 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 by way of the embodiments, the present invention is not limited to the above-described embodiments, and the functions and effects of the present invention can be included within the scope of other embodiments that can be conceived by those skilled in the art. As long as it plays, 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, although the analysis method of the heart rate fluctuation of the present invention is explained more concretely using an example, the present invention is not limited to the example mentioned below.
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。 The sample data which imitated the heartbeat signal of the contents shown in the following Table 1 was created, and the frequency analysis by the analysis method of the present invention was performed as an example.
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）。 In addition, as a comparative example, frequency analysis was performed using the FFT function of MATLAB (sampling frequency 10 Hz) for the same sample data.
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, a difference of about 20% at the maximum occurs with respect to amplitude peak values of three types of frequency components (0.090 Hz, 0.095 Hz, 0.10 Hz). This is because the frequency resolution of the comparative example is about 0.026 Hz (reciprocal of observation time 0.3 0.39 sec), the plot frequency corresponding to the LF component is 0.078 Hz, 0.104 Hz, and the LF component 0.090 Hz of the sample data It is considered that the cause is that the divergence is increased because
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. 3 (b) shows the analysis result of the embodiment. As shown in FIG. 3B, in the example, the respective amplitude peak values of the three types of frequency components (0.090 Hz, 0.095 Hz, 0.10 Hz) were approximately equal. From these results, it was shown that according to the analysis method of the present invention, accurate results can be obtained with 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、
各前記ＲＲ間隔の逆数を瞬時心拍数とする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 of heart rate fluctuation, and
Calculating an RR interval from a predetermined number of R-wave occurrence times;
Defining a time function in which the reciprocal of each of the RR intervals is an instantaneous heart rate;
Applying a 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）各前記ＲＲ間隔の逆数を瞬時心拍数とする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 of analyzing temporal change of heart rate fluctuation, wherein the following steps (a) to (c) are repeatedly performed.
(A) calculating an RR interval from the latest predetermined number of R-wave occurrence times;
(B) defining a time function in which the reciprocal of each of the RR intervals is an instantaneous heart rate.
(C) applying a Fourier transform to the time function to generate a continuous spectrum.
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| JP2023032476A (en) * | 2021-08-27 | 2023-03-09 | Kddi株式会社 | Cardiac beat data analysis device and program |
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| JP2008264138A (en) * | 2007-04-18 | 2008-11-06 | Delta Tooling Co Ltd | Sleep state judgement apparatus, sleep state judgement method and computer program |
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