RU2637601C2 - Acoustical method for measurement of arterial pressure and other physical parameters of blood and cardiovascular system - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: acoustic sensor is placed. Continuous infrasound recording is performed with a wideband acoustic sensor. Arterial pressure is measured by a nonlinear relationship between pressure and artery diameter for longitudinal waves according to the Navier-Stokes equation. For this purpose, the acoustic pressure measurement is carried out evenly at a predetermined interval. The obtained values are processed by a digital filter with a finite-impulse response. After digital filtering, the resulting series of numbers form time series of pressure and acoustic pressure values. Further, the arterial pressure is calculated from the obtained time series according to the claimed formula.

EFFECT: device allows non-invasive and continuous measurement of arterial pressure by using a nonlinear relationship between pressure and artery diameter for longitudinal waves according to the Navier-Stokes equation.

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Description

Description of the invention

The cardiovascular system is designed to maintain optimal gas exchange between body tissues and blood. The speed of blood movement in the capillaries is determined by the gas exchange rate, which under normal conditions depends only on the speed of chemical reactions in the body at a certain body temperature. Therefore, the main task of the human cardiovascular system is to reduce the speed of blood in the capillaries to the optimal values necessary for the best gas exchange, and to keep this speed constant if possible.

The human cardiovascular system, as shown in FIG. 1, from the point of view of the physical processes occurring in it, it is a closed hydrodynamic system. The heart acts as a pump. The elastic arteries function as an intermediate reservoir, smoothing out the pulsation of pressure and leveling the speed of blood movement. The reverse movement of blood is prevented by valves. At any point of the cardiovascular system, the condition of continuity of the stream is always satisfied, the mathematical presentation of which is the Bernoulli formula. After complete compression of the heart (systole), at the time of closure of the arterial valves, the amount of blood and pressure in the elastic arteries are maximum. Before the compression of the heart (diastole) begins, the amount of blood and pressure in the elastic arteries are minimal.

In the process, the cardiovascular system produces both sound and infrasound. It is no accident that doctors constantly carry stethoscopes with them, with the help of which they can hear the sounds produced by the cardiovascular system. The sound is formed due to the vibration of the molecules of the substance around a certain equilibrium position, and the infrasound is formed due to the movement of blood. Due to the nature of a person’s hearing, a doctor cannot hear infrasound. Despite the difference in the mechanisms of the formation of pressure changes in the vessel walls, the pressure change itself is always sound pressure. A physical model for recording sound pressure produced by sound / infrasound is shown in FIG. 2.

For the movement of blood through vessels and capillaries in one direction, it is necessary that the blood pressure at the entrance to the vessel is greater than the blood pressure at the exit of the vessel. Moreover, the volume of blood in the cardiovascular system should always be greater than the volume of blood vessels not stretched by blood. This is necessary to maintain positive pressure at any point of the cardiovascular system, as well as to maintain a positive pressure difference at the inlet and outlet of the vessel, which is necessary to ensure the movement of blood. In this case, the acoustic pressure, that is, the change in absolute pressure, is directly proportional to the change in the radius of the artery, while the volume of blood flowing through the artery is directly proportional to the cross-sectional area of the artery. This nonlinear relationship between the change in pressure and the volume of flowing blood underlies the method for measuring blood pressure. If there were no nonlinear dependence, then the measurement of absolute pressure values would be impossible. In addition, since acoustic pressure, which is actually the first derivative of the absolute blood pressure, is recorded, the influence of stationary environmental parameters, such as air pressure, is leveled, since the first derivative of the constant is zero.

For direct measurement of blood pressure and other physical parameters of the blood and cardiovascular system, one could use the Navier-Stokes equations. However, due to the unresolved Cauchy problem for the Navier-Stokes equations, simulation modeling is used, which requires too much computational cost, and it also requires accurate knowledge of the complete physical and geometric configuration of the cardiovascular system as boundary conditions in the Cauchy problem. In this method, simpler cases of the Bernoulli, Kirchhoff and other equations are used. Simplification leads to some decrease in the accuracy of measurements, which, however, is suitable for practical use. For example, the measurement of blood pressure by acoustic means gives an error of the order of 0.2-0.5 mm RT. Art., while the measurement using the cuff method gives an error of the order of 2-3 mm RT. Art.

To significantly reduce the computational cost in the acoustic method, a comparison of the recorded result with the mathematical model of the process, the so-called calibration function, is used. In this case, a comparison is made of what should be with what is recorded by the acoustic sensor. To increase the accuracy of the measurement, it is desirable to tie the parameters of the mathematical expression of the calibration functions to a specific cardiovascular system of the patient. However, the use of averaged calibration functions is quite acceptable, which somewhat reduces the accuracy of measurements. Based on regular residuals, when extraneous random noise is leveled by a large number of observations, the calibration functions can be refined directly in the device so that regular residuals for a particular cardiovascular system are minimal. According to the parameters of mathematical models specified during the observation process, it is possible to more accurately judge the actual physical parameters of the blood and cardiovascular system of a particular patient.

All processes in the cardiovascular system are repeated with a heart rate. This process repeatability makes it easy to filter out random noise influences. For example, a random external sound can be detected by the sensor in one heartbeat period, however, the appearance of the same effect in the same place from the beginning of the cardiac cycle is extremely unlikely. For example, a change in the density and viscosity of blood as a result of the work of the gastrointestinal tract and kidneys changes the shape of the envelope of sound pressure, but this happens much slower than the heart rate, therefore it creates a regular change in the shape of the envelope of sound pressure for several tens or hundreds of periods. For example, the appearance of plaque in the artery leads to turbulence in the blood flow, which leads to the appearance of an additional regular vortex noise in the envelope of the sound wave, which is rigidly tied to the period of heart contractions. For example, with a stroke, rupture of the vessel leads to a fairly rapid compared with the work of the kidneys regular decrease in blood volume at constant density and viscosity.

Acoustic Wave Registration

Acoustic waves of the sound range are a coordinated (synchronous) oscillation of the molecules of a substance in a local zone around a certain equilibrium position, which creates local changes in the density of matter and local changes in pressure. However, the movement of blood in the elastic arteries during the periodicity of processes in the cardiovascular system, as shown in FIG. 2 and FIG. 3 also leads to pressure fluctuations. For acoustic pressure (pressure change) there is no difference how this pressure change is formed, either by the vibration of the molecules around the equilibrium position, or by the movement of the liquid and the expansion / contraction of the vessels. Sound / infrasound can be recorded anywhere where the pulse is heard. However, it is most preferable to place the sensor in the wristband of the watch, since the mobility of the hand promotes more rapid and less noticeable for the patient continuous monitoring of his blood and cardiovascular system. This is clearly seen in the blood density measurement circuit shown in FIG. 4 and FIG. 5.

Acoustic pressure is measured uniformly with an interval Δt. The obtained values are processed by a digital filter with a finite-impulse response (FIR filter) to equalize the amplitude-frequency characteristic (AFC) of the sensor. The use of an FIR filter is necessary so that the overflow of the discharge grid does not occur, which does not insure filters with an infinite-pulse characteristic (IIR filters). Overflow of the discharge grid leads to nonlinearity and, accordingly, to an increase in the noise level in the processed signal. The length of the sequence processed by the filter must exceed the longest period of heart contractions. The resulting sequences of numbers form a time series of pressure and acoustic pressure values, as shown in FIG. 3 in the ranks of Delta Z and dZ / dt.

The primary processing algorithm of the obtained time series

Using the presented algorithm, the pulse (period) and blood pressure are calculated on the basis of the obtained time series. The value of blood pressure, presented in the form of a time series, itself serves as the basis for further calculation of the density, speed of blood movement and other physical parameters of the blood and cardiovascular system.

To describe the algorithm, we introduce the following notation:

i is the measurement number on the processed interval;

p _i - acoustic pressure measured by the sensor for the i-th measurement;

p (t) is the acoustic pressure measured by the sensor as a function of time;

- среднее давление крови в участке артерии на интервале времени между максимальным и минимальным значением давления крови в участке артерии;

- the average blood pressure in the artery section in the time interval between the maximum and minimum values of blood pressure in the artery section;

α is the coefficient of conversion of pressure into the geometric radius of the artery, numerically proportional to the coefficient of elasticity of the walls of the artery;

ΔR (t) is the change in the geometric radius of the artery depending on time;

R ₀ is the geometric radius of the artery in a calm, unstretched state;

V (t) is the geometric volume of blood in the artery, depending on time;

l is the length of the section of the artery, the oscillations of which are recorded by the sensor;

z is the coefficient inverse to the attenuation of the acoustic signal by body tissues located between the artery and the sensor;

t _min - the point in time when the minimum amount of blood is recorded in the artery, corresponds to the minimum value of blood pressure;

t _max - the point in time when the maximum amount of blood is recorded in the artery, corresponds to the maximum value of blood pressure;

t _i - time point of measurement of acoustic pressure by the sensor;

F _K (t) is the calibration function corresponding to the acoustic model of the cardiovascular system.

Heart Rate Calculation

Pulse calculation consists of two steps:

1. Determination of a local minimum or maximum in the time series;

2. Recalculation of time between two nearest minimums or maximums in a pulse.

When determining local minima and maxima, to exclude errors caused by the operation of the heart valves and the reflected pulse wave, it is necessary to use the approximation of the time series section of the third polynomial

P (i) = a ₀ + a ₁ i + a ₂ i ² + a ₃ i ³ by the least squares method.

In the process of recording measurements, we single out monotonically increasing and monotonically decreasing intervals. We select one of the values on a monotonically increasing (decreasing) interval, assigning it an index of 0, we find on the nearest monotonically decreasing (increasing) interval, close in value with the index n. Solving the system of equations, we find the coefficients of the approximating polynomial

According to the first derivative of the polynomial, we find the extremum point lying between these intervals. We recognize the pulse as the reciprocal of the absolute time between the two nearest maximums (minimums).

Blood pressure calculation

The total volume of blood in the cardiovascular system should always be greater than the volume of the cardiovascular system at rest, when the walls of the vessels are not stretched, so that at any time there is an excess positive blood pressure.

We believe that the transformative properties of tissues between the artery wall and the sensor are linear. The formula for calculating blood pressure relates the geometric radius of the artery, the tangential elasticity of the walls of the artery, the change in blood volume in the section of the artery and the weakening of the infrasound pressure by the elastic tissues of the body between the artery wall and the sensor. There is no need to calculate the exact value of the elastic modulus and wall thickness of the artery.

The relationship between the pressure generated by the pulse wave and the change in the radius of the artery section is described by the following formulas:

The volume of blood in the area of the artery, when the walls of the artery are not subject to stretching, is

Accordingly, a blood volume exceeding the blood volume in an unstretched artery and creating a positive pressure in the blood due to stretching of the artery walls is calculated by the following formula:

Substituting in (II) the value of the change in radius (I), we obtain the dependence of the volume on pressure:

Opening the brackets and grouping the terms with respect to the powers of p (t), we obtain

The right-hand side of the equality, since it does not depend on pressure, will be a calibration function that can be measured by other, non-acoustic methods.

From here we obtain the formula relating the calibration function and pressure:

Calibration function F _K (t):

- is determined at the time of binding the acoustic pressure meter to the patient's cardiovascular system;

- in numerical terms, it is proportional to the volume of blood in the area of the artery;

- is a mathematical model of the patient's cardiovascular system, linking the pressure and volume of blood in the artery.

There are two different functions: F _Kup (t) for the interval of increasing pressure (systole) and F _Kdn (t) for the interval of decreasing pressure (diastole). The functions are different because the ascending branch of the time series of acoustic pressure (the front of the pulse wave) has a smooth shape, while the descending part of the time series of acoustic pressure (decay of the pulse wave) has an additional hump due to the reflected pulse wave, as shown in FIG. . 3, Delta Z chart.

The calibration function is set either as a table or as a spline. We introduce additional variables:

In a series of measurements on the upward curve we find the values p (t _min ), p (r _i ), p (t _max ), where t _min <t <t _max . Substituting the corresponding values of the calibration function F _K (t _min ), F _K (t _i ), F _K (t _max ) instead of the blood volume in formula (VII), we obtain a system of three linear algebraic equations with three unknowns for the variables x ₀ , x ₁ x ₂ :

We solve the system and substituting the found values of x ₀ , x ₁ , x ₂ in (VIII), we find:

выбираем такое, чтобы R₀ имело положительное значение.From the two values obtained

choose such that R ₀ has a positive value.

Calculation of other physical parameters of the blood and cardiovascular system

As an example of the use of heart rate and pressure, consider measuring blood density. The condition of the blood and cardiovascular system is repeated periodically in accordance with heart contractions. This is what we use to determine the density of blood. Let the sensor be on the wrist, as shown in FIG. 5. Let us remember the time series of pressures from the beginning of systole to the beginning of diastole (minimum and maximum sound pressure) for a straight arm lowered down as the first time series. Then bend the arm at the elbow so that the bent part of the arm is horizontal. Let us remember the time series of pressures as the second time series. The distance from the elbow joint to the wrist for a particular patient can be easily measured, and it does not change over time. We believe that the speed of blood flow is constant. Since the entrance to the radial artery is at the same height from the heart, due to the continuity of the stream, the equalities

Since the task of the cardiovascular system is to maintain a constant speed of blood in the capillaries, the speed of blood in the artery can be considered constant. That is, v ₁ = v ₂ . By reducing speeds and rearranging the variables, we obtain the following formulas for the cases depicted in FIG. 5:

The difference in the obtained values of blood densities is explained by the action of the difference of the squares of the velocities for the corresponding cases. These differences can be used to calculate the differences of the squares of the blood speed. The remaining formulas for calculating other physical parameters are also a consequence of the obtained time series of the measured blood pressure.

Claims (17)

An acoustic method for non-invasive measurement of blood pressure, including continuous recording of infrasound with a broadband acoustic sensor, characterized in that the acoustic sensor is placed and the blood pressure is measured by the nonlinear dependence between pressure and artery diameter for longitudinal waves according to the Navier-Stokes equation, for which the acoustic pressure is measured evenly with a given interval, the obtained values are processed by a digital filter with a finite-pulse characteristic After digital filtering, the obtained sequences of numbers form time series of pressure and acoustic pressure values, then blood pressure is calculated from the obtained time series using the formula

, wherein a binding calibration function is used

as well as a system of three linear algebraic equations with three unknowns for the variables x ₀ , x ₁ , x ₂

where F _K (t) is the calibration function corresponding to the acoustic model of the cardiovascular system; z is the coefficient inverse to the attenuation of the acoustic signal by body tissues located between the artery and the sensor; p (t) is the acoustic pressure measured by the sensor as a function of time; R ₀ is the geometric radius of the artery in a calm, unstretched state; F _Kup (t) - for the interval of increasing pressure (systole); F _Kdn (t) - for the interval of decreasing pressure (diastole); t _i - time point of measurement of acoustic pressure by the sensor; t _min - the point in time when the minimum amount of blood is recorded in the artery, corresponds to the minimum value of blood pressure; t _max - the point in time when the maximum amount of blood is recorded in the artery, corresponds to the maximum value of blood pressure; p _i - acoustic pressure measured by the sensor for the i-th measurement.

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