JP7473177B2 - Blood vessel stiffness estimation method, blood vessel stiffness estimation device, and program - Google Patents

Description

The present invention relates to a vascular stiffness estimation method, a vascular stiffness estimation device, and a program.

Conventionally, methods have been developed for grasping the state of the body, such as autonomic nerve activity, by using changes in vascular stiffness as an index (for example, Non-Patent Document 1). Non-Patent Document 1 focuses on the correlation between vascular stiffness and muscle sympathetic nerve activity, and discloses a method for evaluating the function of autonomic nerve activity from vascular stiffness.

Hirohiro Hirano and 9 others, "Proposal of a log-linearized peripheral vascular viscoelastic index and its application to sympathectomy", Transactions of the Society of Instrument and Control Engineers, Vol. 48, No. 11, pp. 731-739, 2012

In Non-Patent Document 1, peripheral vascular stiffness is estimated using a log-linear peripheral vascular viscoelasticity model based on the relationship between blood pressure and fingertip volume pulse wave. In addition, the vascular stiffness estimation method in Non-Patent Document 1 calculates vascular stiffness by eliminating stiffness terms including the fingertip volume pulse wave, which is an exponential function, and therefore performs a difference calculation based on the heartbeat, so vascular stiffness is estimated for each heartbeat.

However, in order to accurately grasp the state of the body, it is necessary to estimate vascular stiffness more precisely, i.e., at a higher sampling frequency.

The present invention has been made in consideration of the above circumstances, and aims to provide a vascular stiffness estimation method, a vascular stiffness estimation device, and a program that can estimate vascular stiffness at a sampling frequency higher than the heart rate.

In order to achieve the above object, a blood vessel stiffness estimation method according to a first aspect of the present invention includes:
a first estimation step of estimating an inertia parameter which is a coefficient of the second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of the first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term by a least squares method with a predetermined window width based on a vascular stiffness model which is expressed by the relationship between the volume pulse wave and blood pressure and which includes an inertia term including a second derivative of the volume pulse wave, a viscosity term which is a coefficient of the volume pulse wave, and a stiffness term which is an exponential function of the volume pulse wave;
and a second estimation step of estimating vascular stiffness by substituting the inertial parameters and the viscosity parameters into the vascular stiffness model and using a least squares method with the window width .

The vascular stiffness model is a log-linearized peripheral vascular viscoelasticity model shown below.
where μ is the inertia of the vascular wall, η is the viscosity of the vascular wall, β is the stiffness of the vascular wall, P _b (t) is the arterial blood pressure at time t, P _l (t) is the volume pulse wave at time t, P _bβ0 is the reference blood pressure, and P _bβnl (P _l (t)) is the venous influence.
This may also be the case.

In addition, the vascular stiffness is estimated at a sampling frequency higher than the heart rate.
This may also be the case.

Further, in the second estimation step,
By applying the least squares method to the range above the mean blood pressure,
estimating the vascular stiffness;
This may also be the case.

Furthermore, the window width of the least squares method in the first estimation step and the second estimation step is
longer than the heartbeat interval,
This may also be the case.

Also, a time difference correction step of correcting a time difference between the blood pressure and the volume pulse wave is included.
This may also be the case.

In addition, in the time difference correction step,
calculating a corresponding individual time difference for each heartbeat, and calculating the time difference based on an adjusted individual time difference obtained by multiplying the individual time difference by a weight based on the degree of influence of each heartbeat on a window width of the least squares method in the first estimation step;
This may also be the case.

Further, a blood vessel stiffness estimation device according to a second aspect of the present invention comprises:
a calculation unit that estimates vascular stiffness based on a vascular stiffness model that is expressed by a relationship between a volume pulse wave and a blood pressure, and that includes an inertia term including a second derivative of the volume pulse wave, a viscosity term including a first derivative of the volume pulse wave, and a stiffness term including an exponential function of the volume pulse wave,
The calculation unit is
an inertia parameter which is a coefficient of a second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of a first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term of the vascular stiffness model are estimated by a least squares method with a predetermined window width ;
The estimated inertial parameters and viscosity parameters are substituted into the vascular stiffness model, and the vascular stiffness is estimated by using the least squares method with the window width .

Moreover, a program according to a third aspect of the present invention comprises:
Computer,
Based on a vascular stiffness model expressed by a relationship between a volume pulse wave and a blood pressure, the model including an inertia term including a second derivative of the volume pulse wave, a viscosity term including a first derivative of the volume pulse wave, and a stiffness term including an exponential function of the volume pulse wave,
an inertia parameter which is a coefficient of a second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of a first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term are estimated by a least squares method with a predetermined window width ;
a calculation unit that estimates vascular stiffness by substituting the inertial parameter and the viscosity parameter into the vascular stiffness model and using a least squares method with the window width ;
Function as.

According to the vascular stiffness estimation method, vascular stiffness estimation device, and program of the present invention, the inertial parameter and the viscosity parameter are estimated using the least squares method for each sampling time, and the vascular stiffness is estimated using the estimated inertial parameter and the viscosity parameter. Therefore, it is possible to estimate the vascular stiffness at a sampling frequency higher than the heart rate.

1 is a functional block diagram of a blood vessel stiffness estimation device according to an embodiment of the present invention. FIG. 4 is a flowchart showing a flow of vascular stiffness estimation according to the first embodiment. 13 is a flowchart showing a flow of vascular stiffness estimation according to the second embodiment. FIG. 1 is a conceptual diagram showing the time difference between blood pressure and a volume pulse wave. 13 is a graph showing a measured waveform according to a numerical example. 11 is a graph showing PSD according to a numerical example, where (A) is a graph for a first analysis interval, and (B) is a graph for a second analysis interval.

The following describes a vascular stiffness estimation device 1 according to an embodiment of the present invention, with reference to the drawings. As shown in the block diagram of FIG. 1, the vascular stiffness estimation device 1 includes a sensor 10 and an estimation device main body 20.

The sensor 10 is a detector that is selected according to the type of biosignal to be acquired. The biosignal to be acquired is a time-series signal used to calculate vascular stiffness β, such as an electrocardiogram indicating cardiac activity, blood pressure, or a volume pulse wave indicating changes in the volume of blood vessels.

The estimation device main body 20 is, for example, a computer device, and includes a control unit 21, a memory unit 22, a display unit 23, and an input unit 24.

The control unit 21 is composed of a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a crystal oscillator, etc., and controls the operation of the vascular stiffness estimation device 1. The control unit 21 also calculates vascular stiffness β based on the biosignal acquired by the sensor 10 and a calculation model of vascular stiffness β (hereinafter referred to as the vascular stiffness model) previously stored in the storage unit 22. The control unit 21 loads various operation programs and data stored in the ROM, storage unit 22, etc. of the control unit 21 into the RAM and operates the CPU, thereby realizing each function of the control unit 21 shown in FIG. 1. As a result, the control unit 21 operates as a biosignal acquisition unit 211 and a calculation unit 212.

The biosignal acquisition unit 211 controls the sensor 10 to acquire the biosignal of the subject. It also transmits the acquired biosignal to the memory unit 22 for storage. In this embodiment, multiple sensors 10 are used to simultaneously acquire multiple biosignals, i.e., electrocardiogram, blood pressure, volume pulse wave, etc.

The calculation unit 212 calculates the vascular stiffness β based on the biosignal acquired from the sensor 10 by the biosignal acquisition unit 211 and the vascular stiffness model. The calculation unit 212 also stores the calculated vascular stiffness β as an estimation result in the storage unit 22. Details of the method for estimating the vascular stiffness β will be described later.

The memory unit 22 is a non-volatile memory such as a hard disk or flash memory, and stores the vascular stiffness model, the estimated results of vascular stiffness β calculated by the calculation unit 212, etc.

The display unit 23 is a display device provided in the estimation device main body 20, which is a computer device, and is, for example, a liquid crystal panel. The display unit 23 displays the biosignal acquired by the sensor 10, the vascular stiffness β estimated by the calculation unit 212, etc.

The input unit 24 is an input device for inputting instructions to start and end biosignal acquisition, parameters for estimating vascular stiffness β, etc. The input unit 24 is a keyboard, mouse, etc. provided on the estimation device main body 20.

Next, a method for estimating vascular stiffness using the vascular stiffness estimation device 1 will be specifically described with reference to the flowchart in FIG. 2. In this embodiment, an example will be described in which electrocardiogram, arterial blood pressure, and fingertip volume pulse wave are acquired as biosignals, and vascular stiffness β is estimated based on the biosignals and a vascular stiffness calculation model.

First, in the measurement process, a measurer such as a doctor attaches the sensor 10 for measuring the electrocardiogram, arterial blood pressure, and fingertip volume pulse wave to the subject. The measurer then operates the input unit 24 to start acquiring the electrocardiogram, arterial blood pressure, and fingertip volume pulse wave. The biosignal acquisition unit 211 controls the sensor 10 in response to an instruction to start acquiring the biosignal, and acquires the electrocardiogram, arterial blood pressure, and fingertip volume pulse wave of the subject (step S11). The biosignal acquisition unit 211 transmits the acquired biosignal data to the storage unit 22, and stores it in the storage unit 22 (step S12).

Next, as a first estimation step, the calculation unit 212 performs parameter estimation based on the biosignal data acquired by the biosignal acquisition unit 211 and a calculation model of vascular stiffness β pre-stored in the memory unit 22 (step 13).

Here, the parameter estimation in the first estimation step will be described in detail. The calculation model of the vascular stiffness β in this embodiment is a log-linearized peripheral vascular viscoelasticity model shown in the following formula (1).
Here, μ represents the inertia of the vascular wall, η represents the viscosity of the vascular wall, and β represents the stiffness of the vascular wall (vascular stiffness). In addition, P _b (t) represents the arterial blood pressure at time t, P _l (t) represents the change in vascular volume (fingertip volume pulse wave) at time t, P _bβ0 represents the reference blood pressure, and P _bβnl (P _l (t)) represents the venous influence.

The venous influence term _Pbβnl ( _Pl (t)) is a parameter for taking into consideration influences on the arterial blood pressure and fingertip volume pulse wave measured in the artery of the subject, and takes into consideration, for example, cardiac influences such as hypertension and congestive heart failure, venous influences such as avascularization and gravity, etc. The venous influence _Pbβnl ( _Pl (t)) is appropriately adjusted depending on the subject and the measurement conditions.

The vascular stiffness model in equation (1) is expressed as the relationship between the volume pulse wave and blood pressure, and includes an inertia term including the second derivative of the volume pulse wave, a viscosity term including the first derivative of the volume pulse wave, and a stiffness term including an exponential function of the volume pulse wave.

When the exponential term of the formula (1) is expanded by Maclaurin's expansion around P _l (t)=0 and linearly approximated, the following formula (2) is obtained.
Here, β _A is as follows:

The inertia μ, viscosity η, exp{P _bβnl +P _bβnl (0)}, and stiffness parameter β _A can be estimated by performing a linear least squares method based on equation (2) using the blood pressure P _b (t) and volume pulse wave P _l (t) of an arbitrary window width w.

The calculation unit 212 according to this embodiment uses the arterial blood pressure _Pb (t) and the volume pulse wave _Pl (t) measured by the sensor 10 as a window width w, and estimates the inertia parameter μ, which is the coefficient of the second derivative of the estimated volume pulse wave, the viscosity parameter η, which is the coefficient of the first derivative of the volume pulse wave, the stiffness parameter _βA , which is the coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and the constant term exp{ _Pbβnl + _Pbβnl (0)} by the least squares method. The window width w and the sampling frequency are not particularly limited, but are preferably set to values suitable for estimating the above multiple parameters by the least squares method.

This allows the vascular stiffness estimation device 1 to perform parameter estimation with an arbitrary window width w, and to perform parameter estimation at a sampling frequency higher than the heart rate. That is, unlike the conventional parameter estimation method shown in the following formula, it is not necessary to adjust the timing with the heart rate (R wave) and perform parameter estimation by eliminating the exponential term from the difference between different times, so that the method of the present invention can perform parameter estimation at a higher sampling frequency.

Returning to the flowchart in FIG. 2, in the second estimation step, the calculation unit 212 estimates the vascular stiffness β using the inertia μ and viscosity η estimated in the first estimation step (step S14). The specific estimation method is as follows.

When equation (1) is rearranged into exponential terms and other terms and the natural logarithms are taken on both sides, the following equation (3) is obtained.

Here, each term on the right side can be calculated as a numerical value from the inertia μ and viscosity η estimated in the first estimation step and the measurement data. The calculation unit 212 estimates the vascular stiffness β by substituting the inertia μ and viscosity η into equation (3) and applying the least squares method.

Furthermore, the least squares method is performed within a range that is not affected by veins. Specifically, the least squares method is used to estimate within a range in which the blood pressure P _b (t) is equal to or greater than the mean blood pressure. This makes it possible to estimate the vascular stiffness β and the reference blood pressure P _bβ0 by setting the third term on the left side of equation (3) to 0. The calculation unit 212 then stores the estimated vascular stiffness β and the corresponding sampling time in the storage unit 22.

The calculation unit 212 repeats the process of estimating vascular stiffness β from steps S13 to S14 while advancing the sampling step and shifting the window width w (step S16) until the vascular stiffness estimation process reaches a predetermined end condition (NO in step S15).

When the vascular stiffness estimation process reaches a predetermined end condition (YES in step S15), the control unit 21 ends the estimation of the vascular stiffness β. Then, the control unit 21 causes the display unit 23 to display the vascular stiffness β as the estimation result, and causes the storage unit 22 to store it (step S17).

As described above, in the vascular stiffness estimation method according to this embodiment, in the first estimation step, the parameters of each term are estimated by the least squares method without being restricted by the heart rate. In addition, in the second estimation step, the vascular stiffness β is estimated using the inertia μ and viscosity η estimated in the first estimation step, so that it is possible to estimate the vascular stiffness at a sampling frequency higher than the heart rate.

(Embodiment 2)
In the first embodiment, the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) used in the vascular stiffness model of formula (1) is not taken into consideration, and the vascular stiffness β is estimated using the blood pressure _Pb (t) and the volume pulse wave _Pl (t) at the measured time t. Generally, the measurement location of the blood pressure _Pb (t) and the measurement location of the volume pulse wave _Pl (t) are not the same, and the blood pressure _Pb (t) and the volume pulse wave _Pl (t) are measured by attaching separate measuring instruments to the subject's body.

Therefore, a time error occurs between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) in the change due to blood flow. It is considered that if the estimation interval of the vascular stiffness β is reduced and the sampling frequency is increased, the influence of the time error between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) becomes large. Therefore, in order to estimate the vascular stiffness β with high accuracy, it is required to correct the time difference between the change in the blood pressure _Pb (t) and the change in the volume pulse wave _Pl (t). In this embodiment, a case will be described in which the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) is corrected before estimating the vascular stiffness β.

The vascular stiffness estimation device 1 according to this embodiment differs from embodiment 1 in that the calculation unit 212 corrects the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) as a time difference correction step before estimating vascular stiffness β based on the measured blood pressure _Pb (t) and volume pulse wave _Pl (t). The configurations of the sensor 10, the storage unit 22 of the estimation device main body 20, the display unit 23, and the like according to the vascular stiffness estimation device 1 are the same as those in embodiment 1, so they are denoted by the same reference numerals and detailed description will be omitted.

The vascular stiffness estimation method according to the present embodiment will be specifically described with reference to the flowchart in Fig. 3. The measurement steps in steps S31 to S32 are the same as the measurement steps in steps S11 to S12 in the first embodiment. Next, as a time difference correction step, the calculation unit 212 corrects the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) based on the measurement data stored in the storage unit 22. The measurement data used for the time difference correction may be, for example, the electrocardiogram, the blood pressure _Pb (t), and the volume pulse wave _Pl (t) as shown in Fig. 4.

The window width w according to this embodiment, i.e., the window time used in the least squares method in the first estimation step and the second estimation step, is set to 1.2 seconds. Therefore, since the window width w is usually longer than the heartbeat interval, one or two heartbeats, i.e., R waves, obtained from the electrocardiogram data are present within the window width w. As a time difference correction step, the calculation unit 212 calculates the number of heartbeats _Pk indicating the number of R waves within the window width w for which vascular stiffness estimation is performed (step S33).

Next, the calculator 212 calculates a weight _w1, which is the time from the start time of the window to the first R-wave peak within the window width w (step S34).

If the heart rate P _k is 1 (YES in step S35), the calculator 212 calculates a weight w ₂ which is the time from the first R wave peak to the end time of the window, and sets a weight w ₃ =0 (step S36).

If the number of heartbeats _Pk is 2 (NO in step S35), the calculator 212 calculates a weight _w2 , which is the time from the first R wave peak to the second R wave peak. Furthermore, the calculator 212 calculates a weight _w3 , which is the time from the second R wave peak to the end time of the window (step S37).

Next, the calculation unit 212 calculates the time of the inflection point of the blood pressure _Pb (t). The inflection point is the time when the first derivative of the blood pressure _Pb (t) is maximized. The calculation unit 212 also calculates three times of inflection points: the time ( _φb1 ) of the inflection point that is before the window start time and closest to the window start time, the time ( _φb2 ) of the inflection point that is after the window start time and closest to the window start time, and the time ( _φb3 ) of the inflection point next to _φb2 (step S38).

The calculation unit 212 also calculates the time of an inflection point of the volume pulse wave P _l (t). The inflection point is the time when the first derivative of the volume pulse wave P _l (t) is maximized. The calculation unit 212 also calculates three times of inflection points: the time (φl ₁ ) of the inflection point that is before the window start time and closest to the window start time, the time (φl ₂ ) of the inflection point that is after the window start time and closest to the window start time, and the time (φl ₃ ) of the inflection point next to φl ₂ (step S39).

The calculator 212 calculates the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t) for each of the calculated inflection points (step S40). Specifically, the difference between _φb1 and _φl1 is the first individual time difference φ1, the difference between _φb2 and _φl2 is the second individual time difference φ2, and the difference between _φb3 and _φl3 is the third individual time difference φ3.

The calculation unit 212 calculates the correction value τ from the following equation (4) based on the calculated individual time differences φ1 to φ3 and weights w ₁ to w ₃ .

That is, the calculation unit 212 calculates the corresponding individual time differences φ1 to φ3 for each heartbeat. Then, the calculation unit 212 multiplies the individual time differences by weights _w1 to _w3 based on the degree of influence of each heartbeat on the window width w to calculate adjusted individual time differences corresponding to each term in equation (4). The calculation unit 212 calculates a correction value τ, which is the time difference between the blood pressure _Pb (t) and the volume pulse wave _Pl (t), based on the adjusted individual time differences.

Thereafter, the vascular stiffness estimation device 1 estimates vascular stiffness β in a first estimation step (step S41) and a second estimation step (step S42) similar to those in embodiment 1. At this time, the calculation unit 212 uses the correction value τ calculated in step S40 to correct the time difference between the blood pressure P _b (t) and the volume pulse wave P _l (t). Specifically, as shown in the following equation (5), the vascular stiffness β is estimated using P _b (t) and the volume pulse wave P _l (t-τ).

The vascular stiffness estimation device 1 advances the sampling steps and shifts the window width w (step S44) until a predetermined end condition is reached (NO in step S43). Then, in each sampling step, a time difference correction step, a first estimation step, and a second estimation step are performed to estimate the vascular stiffness β. When the predetermined end condition is reached (YES in step S43), the vascular stiffness estimation device 1 displays the estimation result on the display unit 23 and stores it in the memory unit 22 (step S45).

As described above, the vascular stiffness estimation device 1 according to this embodiment estimates vascular stiffness β by correcting the time difference between blood pressure P _b (t) and the volume pulse wave P _l (t), and therefore can accurately estimate vascular stiffness β regardless of the distance between the measurement point of blood pressure P _b (t) and the measurement point of the volume pulse wave P _l (t).

In this embodiment, the window width w for the first estimation process and the window width w for the second estimation process are the same, but this is not limited to the above. For example, if the window width w for the first estimation process and the window width w for the second estimation process are different, the window width w for either process can be appropriately selected to calculate the correction value τ representing the time difference.

In addition, in this embodiment, the correction value τ is calculated based on three individual time differences, but this is not limited to this. For example, when the window width w is set larger, or when the subject's heart rate is high, the number of individual time differences may be increased according to the heart rate related to the window width w.

(Numerical example)
Hereinafter, an example of estimating vascular stiffness β and calculating the power spectral density (PSD) of vascular stiffness β using the vascular stiffness estimation method of the second embodiment will be described. In this example, 15 patients undergoing thoracoscopic sympathectomy were used as subjects, and biological information was acquired at a sampling frequency of 5 Hz to estimate vascular stiffness β in the right hand. The analysis interval is 30 seconds (first analysis interval) immediately before the right sympathetic trunk blockade and 30 seconds (second analysis interval) 60 seconds after the right sympathetic trunk blockade in the period shown in FIG. 5. In addition, the Burg method is used as the PSD calculation method.

Figure 6 (A) shows the PSD of the first analysis interval during right sympathetic nerve stimulation. More specifically, the graph shown in Figure 6 (A) shows the normalized PSD of 15 subjects based on the PSD normalized by dividing by the total power value. The average of the normalized PSD of the 15 subjects is also shown by the thick line. In the conventional vascular stiffness estimation method, the vascular stiffness β was estimated for each heartbeat, so it was difficult to analyze in detail the frequency components contained in the time change of the vascular stiffness β. However, as shown in the PSD graphs of Figures 6 (A) and (B), the vascular stiffness estimation method of the present invention can perform detailed frequency component analysis. For example, a peak can be confirmed in the vicinity of 1 to 1.5 Hz from the graphs of Figures 6 (A) and (B), and it can be inferred that the vascular stiffness β reflects the heartbeat rhythm.

In addition, from the peak near 0.2 Hz, it can be inferred that vascular stiffness β reflects respiratory rhythm. Furthermore, from the peak near 0.1 Hz, it is possible to analyze the correlation between vascular stiffness β and the low-frequency components of systolic blood pressure.

As described above, the vascular stiffness estimation method and vascular stiffness estimation device according to the present invention can estimate vascular stiffness β at a sampling frequency higher than the heart rate without being restricted by the timing of the heart rate, allowing for more detailed analysis of the physical condition.

The vascular stiffness estimation method according to this embodiment can be realized using a normal computer system. For example, a computer program for executing the above operations can be stored and distributed on a computer-readable recording medium such as a USB memory or a DVD-ROM, and the computer program can be installed on a computer to cause the computer to function as an estimation device that executes the above vascular stiffness estimation method.

In addition, in this embodiment, the vascular stiffness β is estimated by the estimation device main body 20 from the biosignals, such as arterial blood pressure and fingertip volume pulse wave, acquired by the sensor 10, but this is not limited to the above. For example, biosignals previously acquired and stored in the memory unit 22 may be read into the calculation unit 212 to estimate the vascular stiffness β. Furthermore, biosignals may be read from a sensor 10 worn by a subject in a remote location via a network into the estimation device main body 20 to estimate the vascular stiffness β.

The present invention is suitable for estimating vascular stiffness to grasp the state of the body. In particular, the present invention is suitable for estimating vascular stiffness when estimating changes in the state of the body derived from signals of various frequencies from changes in vascular stiffness over time.

1 Blood vessel stiffness estimation device, 10 Sensor, 20 Estimation device main body, 21 Control unit, 211 Biosignal acquisition unit, 212 Calculation unit, 22 Memory unit, 23 Display unit, 24 Input unit

Claims (9)

a first estimation step of estimating an inertia parameter which is a coefficient of the second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of the first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term by a least squares method with a predetermined window width based on a vascular stiffness model which is expressed by the relationship between the volume pulse wave and blood pressure and which includes an inertia term including a second derivative of the volume pulse wave, a viscosity term which is a coefficient of the volume pulse wave, and a stiffness term which is an exponential function of the volume pulse wave;
and a second estimation step of estimating vascular stiffness by substituting the inertial parameter and the viscosity parameter into the vascular stiffness model and using a least squares method with the window width.
A method for estimating blood vessel stiffness comprising: The vascular stiffness model is a log-linearized peripheral vascular viscoelasticity model shown below.
where μ is the inertia of the vascular wall, η is the viscosity of the vascular wall, β is the stiffness of the vascular wall, P _b (t) is the arterial blood pressure at time t, P _l (t) is the volume pulse wave at time t, P _bβ0 is the reference blood pressure, and P _bβnl (P _l (t)) is the venous influence.
The method for estimating blood vessel stiffness according to claim 1 . The vascular stiffness is estimated at a sampling frequency higher than the heart rate.
3. The method for estimating blood vessel stiffness according to claim 1 or 2. In the second estimation step,
By applying the least squares method to the range above the mean blood pressure,
estimating the vascular stiffness;
The method for estimating blood vessel stiffness according to any one of claims 1 to 3. The window width of the least squares method in the first estimation step and the second estimation step is
longer than the heartbeat interval,
The method for estimating blood vessel stiffness according to any one of claims 1 to 4. a time difference correction step of correcting a time difference between the blood pressure and the volume pulse wave,
The method for estimating blood vessel stiffness according to any one of claims 1 to 5. In the time difference correction step,
calculating a corresponding individual time difference for each heartbeat, and calculating the time difference based on an adjusted individual time difference obtained by multiplying the individual time difference by a weight based on the degree of influence of each heartbeat on the window width of the least squares method in the first estimation step;
The method for estimating blood vessel stiffness according to claim 6 . a calculation unit that estimates vascular stiffness based on a vascular stiffness model that is expressed by a relationship between a volume pulse wave and a blood pressure, and that includes an inertia term including a second derivative of the volume pulse wave, a viscosity term including a first derivative of the volume pulse wave, and a stiffness term including an exponential function of the volume pulse wave,
The calculation unit is
an inertia parameter which is a coefficient of a second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of a first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term of the vascular stiffness model are estimated by a least squares method with a predetermined window width ;
the estimated inertial parameter and the estimated viscosity parameter are substituted into the vascular stiffness model, and the vascular stiffness is estimated by using a least squares method with the window width ;
A blood vessel stiffness estimation device comprising: Computer,
Based on a vascular stiffness model expressed by a relationship between a volume pulse wave and a blood pressure, the model including an inertia term including a second derivative of the volume pulse wave, a viscosity term including a first derivative of the volume pulse wave, and a stiffness term including an exponential function of the volume pulse wave,
an inertia parameter which is a coefficient of a second derivative of the volume pulse wave, a viscosity parameter which is a coefficient of a first derivative of the volume pulse wave, a stiffness parameter which is a coefficient of the volume pulse wave obtained by linearly approximating the stiffness term, and a constant term are estimated by a least squares method with a predetermined window width ;
a calculation unit that estimates vascular stiffness by substituting the inertial parameter and the viscosity parameter into the vascular stiffness model and using a least squares method with the window width ;
A program that functions as a