Device and method for detecting elastic force of thrombus in micro-metal tube based on L(0,1) longitudinal modal guided wave

Abstract

The present invention discloses a device and method for detecting thrombus elasticity of a micro-metal tube based on L(0,1) longitudinal modal waveguide. The device includes a device housing, a temperature control module, a micro-metal tube, and a magnetostrictive component. The housing is externally connected to the temperature control module to achieve internal constant temperature, and a replaceable micro-metal tube is installed inside. A magnetostrictive component composed of a permanent magnet and a coil is provided at one end outside the tube. L(0,1) longitudinal modal waveguide is excited on the micro-metal tube. When the viscosity of the liquid in the tube changes, the energy attenuation of the waveguide propagating along the tube is different. The waveguide energy attenuation is defined by the attenuation rate of multiple echo peak values, which can reflect the change in blood viscosity. The present invention overcomes the defects of traditional thrombus elasticity measurement devices, such as poor real-time performance, large collection volume, and poor portability. It can achieve real-time and accurate measurement of thrombus elasticity, with a small amount of blood sampling and simple detection method operation.

Description

Technical Field

[0001] The patent of this invention relates to a parameter detection device and method in the field of thrombus elasticity measurement, and specifically to a device and method for detecting thrombus elasticity using longitudinal modal ultrasonic guided waves. Background Art

[0002] Human coagulation function includes coagulation and fibrinolysis, which are closely related to coagulation factors, fibrinogen and platelets in the blood. If the coagulation function is abnormal, it will cause thrombotic or hemorrhagic diseases, endangering health and even life. Therefore, it is very important to realize real-time detection of the patient's coagulation function during surgery. This indicator not only reflects the patient's current physiological condition, but can also be used to guide doctors to formulate appropriate treatment plans. The main thrombus elasticity measurement devices on the market are Sonoclot, TEG and ROTEM. The public document "Application and Progress of Viscoelastic Coagulation Function Monitoring Technology" points out that these devices are only slightly different in technical implementation solutions. However, due to the limitations of probe size and sensitivity, the three devices require a large amount of blood and a long detection time. Usually, 1 ml of blood and more than 1 hour of detection time are required, which cannot meet the real-time detection needs of coagulation function in some surgical environments.

[0003] Therefore, developing a thrombus elasticity measurement technology that requires a small sample size and is fast and convenient to detect has very important research and practical value.

[0004] The invention patent with patent number CN202110378292.2 proposes a rapid detection device and method for blood viscosity based on ultrasonic guided waves in micro-metal tubes. The correlation between the T(0,1) torsional mode guided wave signal and liquid viscosity is analyzed through deep learning, which realizes the rapid measurement of blood viscosity to a certain extent. However, its excitation method is complicated, and it is necessary to spray magnetostrictive powder or install strips on the micro-metal tube, which has high production costs; the magnetic field distribution of the excitation is uneven, and the excited T(0,1) guided waves are not pure, causing measurement errors, and the blood viscosity value measured without temperature is less accurate; the device has high requirements on the sensor technology used for excitation and reception, which is not conducive to practical application and popularization. At the same time, this patent can only obtain static blood viscosity values, and does not realize dynamic thrombus elasticity measurement, and cannot analyze the correlation between blood viscosity changes and time. Summary of the invention

[0005] In order to solve the current problems of large amount of blood required for thrombus elasticity measurement and low real-time performance, the present invention utilizes the correlation between the propagation attenuation of longitudinal ultrasonic guided waves in micro-metal tubes and liquid viscosity to propose a thrombus elasticity measurement device and method that is easy to operate, has better real-time performance and requires less blood.

[0006] The present invention generates L(0,1) longitudinal modal ultrasonic guided waves, and based on the correlation between energy attenuation in the guided wave propagation process and the viscosity of the liquid in the micro-metal tube, obtains the attenuation rate of the guided wave signal by processing, thereby achieving real-time and accurate measurement of the elasticity of the thrombus.

[0007] The present invention is achieved through the following technical solutions:

[0008] 1. A micro-metal tube thrombus elasticity detection device based on L(0,1) longitudinal modal guided wave:

[0009] It includes a device housing, a fine metal tube and a magnetostrictive component;

[0010] A fine metal tube installed inside the device housing and containing a blood sample;

[0011] The magnetostrictive component is arranged at one end of the fine metal tube and includes a permanent magnet and a hollow coil.

[0012] A permanent magnet is arranged at the end of the fine metal tube;

[0013] The air-core coil is arranged near the end of the fine metal tube.

[0014] It also includes an excitation receiving module, and the hollow coil is electrically connected to the excitation receiving module.

[0015] It also includes a data processing module and a display module. The excitation receiving module is connected to the data processing module, and the data processing module is connected to the display module.

[0016] It also includes a temperature control module installed on the device shell, the temperature control module includes a temperature detection module and a heating module that are electrically connected, the temperature detection module is connected to the device shell or the fine metal tube, and the heating module is also connected to the device shell or the fine metal tube.

[0017] The magnetostrictive assembly is installed at one end of the fine metal tube, the permanent magnet is directly connected to the end face of the fine metal tube through magnetism, the hollow coil is sleeved outside the fine metal tube, the inner wall of the coil does not contact the outer wall of the metal tube, and the difference between the inner diameter of the coil and the outer diameter of the metal tube is less than 1.0 mm. The fine metal tube can be directly disassembled and replaced by plugging and unplugging.

[0018] The fine metal tube is made of magnetic material, and the permanent magnet is magnetically adsorbed on the end of the fine metal tube.

[0019] The material of the fine metal tube is a magnetic conductive material such as nickel, iron, iron-nickel alloy, iron-aluminum alloy and iron-cobalt alloy.

[0020] 2. A method for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal guided wave, the method steps are as follows:

[0021] 1) According to the structural geometric parameters and material mechanical characteristics of the micro-metal tube, the waveguide dispersion curve of the micro-metal tube is calculated, and the frequency point with the smallest dispersion degree is selected as the excitation frequency according to the waveguide dispersion curve; the small dispersion degree is defined as the frequency range of Δv / Δf<0.25m / (s*kHz), Δv is the phase velocity change, Δf is the frequency change, and for the L(0,1) mode waveguide, the range is f<250kHz.

[0022] 2) When the micro-metal tube is empty, the hollow coil on the micro-metal tube is excited to generate L(0,1) mode guided wave, which propagates back and forth between the two end surfaces of the micro-metal tube until the energy is exhausted. The tube length is d meters. The hollow coil collects the first k reciprocating processes, and the total echo signal of k*2d meters is used as the empty tube reference signal w 0 ;

[0023] 3) Fill the micro-metal tube with an isolated blood sample and obtain an echo signal as a filling detection signal in the same manner as step 2). The i-th filling detection signal is w i ;

[0024] 4) Air traffic control reference signal w 0 And each filling detection signal w i Take the envelope to obtain the respective envelope signals, and take n echo peaks from the envelope signals for fitting to obtain their respective attenuation rates b 0 and b i , according to the decay rate b 0 and b i Combined with the relationship between the relative blood viscosity and attenuation rate of the blood sample obtained in advance, the filling detection signal w is obtained for each filling i The corresponding relative blood viscosity is expressed by b i / b 0 Reflects the relative blood viscosity at the i-th test;

[0025] In the present invention, a positive correlation is established between the relative blood viscosity and the attenuation rate of the blood sample.

[0026] 5) Set the sampling times m and the sampling interval Δt for the test, and after the blood sample is filled into the micro-metal tube, continuously repeat steps 3) and 4) to perform sampling and obtain the relative blood viscosity of each test, thereby drawing a curve of the relative blood viscosity of the blood sample within the time m*Δt as a thromboelastogram to achieve thromboelastogram measurement.

[0027] The innovation of the present invention is that a micro-metal tube is provided for measuring blood samples to obtain thrombus elasticity test results. The echo signal obtained by the measurement is subjected to specific echo peak processing to obtain an accurate attenuation rate, and the relationship between the attenuation rate and the relative blood viscosity of the blood sample is discovered and established, and this relationship is used to obtain an accurate thrombus elasticity test result.

[0028] In step 4), the specific method of taking n echo peaks from the envelope signal is: selecting a suitable first threshold l according to the envelope signal 1 and the second threshold l 2 , the interval between them is l = l 1 -l 2 , the starting point x selected from the envelope signal 0 The first threshold l 1 At the location, we start to build n consecutive intervals of length l, that is, the interval [x 0 , x 0 +l],[x 0 +l,x 0 +2l]……[x 0 +(n-1)l,x 0 +nl], so that each interval contains only one peak, the peak in each interval is extracted as the echo peak, and all peaks in n intervals are extracted as the final selected n echo peaks, numbered 1-n.

[0029] In step 4), the specific fitting method of the echo peak attenuation rate is that the attenuation rate is obtained by fitting according to the following formula:

[0030] y=a*b x

[0031] Wherein, x represents the sequence number of the echo peak, y is the value of the echo peak, b is the attenuation rate of the echo peak, and a represents the amplitude normalization coefficient.

[0032] The method of the present invention has a fast data transmission speed. Through the method of the present invention, in the step 5), the relative blood viscosity collected at each interval Δt time will be updated in real time on the display module without waiting until all sampling is completed before displaying the test results.

[0033] The method of the present invention obtains the echo peak attenuation rate by adopting a specific processing method. Compared with parameters such as amplitude attenuation and flight time in the prior art, it can better and more accurately reflect the thrombus elasticity parameter results; and the method of the present invention only establishes a nonlinear relationship between the echo peak attenuation rate and the relative blood viscosity, which can better and more accurately detect and obtain the thrombus elasticity results.

[0034] The detection device of the invention comprises a device shell, a temperature control module, a fine metal tube, a magnetostrictive component, an excitation receiving module, a data processing module and a display module.

[0035] The shell is connected to an external temperature control module to achieve internal constant temperature, and a replaceable fine metal tube is installed inside; a magnetostrictive component consisting of a permanent magnet and a coil is provided at one end outside the tube;

[0036] The magnetostrictive component is connected to the excitation receiving module, and the excitation receiving module is connected to the data processing module and the display module.

[0037] The present invention excites L(0,1) longitudinal modal guided waves on a micro-metal tube. When the viscosity of the liquid in the tube changes, the energy attenuation of the guided waves propagating along the tube is different. The guided wave energy attenuation is defined by the attenuation rate of multiple echo peaks, which can reflect the change of blood viscosity.

[0038] The present invention overcomes the defects of the traditional thrombus elasticity measuring device, such as poor real-time performance, large blood sampling volume and poor portability, and can realize the real-time and accurate measurement of thrombus elasticity, with a small blood sampling volume and simple and convenient detection method operation.

[0039] The beneficial effects of the present invention are:

[0040] The present invention can detect blood viscosity by utilizing the correlation between the peak attenuation rate of the L(0,1) longitudinal modal guided wave echo and the change of blood viscosity. Data collection and processing are simple. A micro-metal tube is used as a carrier during the detection process. A small amount of blood is required and the overall measurement time is short. This effectively overcomes the problems of poor real-time performance and large collection volume of traditional thrombus elastic devices.

[0041] The detection device proposed in the present invention has high integration, small size, and portability, and can update the blood viscosity changes during the measurement process in real time on the host computer display module. It can be used on-site and help medical staff understand the patient's condition in a timely and convenient manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a structural diagram of the thrombus elasticity measurement device;

[0043] Figure 2 It is the air traffic control detection signal;

[0044] Figure 3 It is the liquid filling detection signal diagram;

[0045] Figure 4 It is the envelope of the filling detection signal;

[0046] Figure 5 Schematic diagram for setting threshold;

[0047] Figure 6 This is the effect diagram of thrombus elasticity measurement. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings and specific implementations.

[0049] like Figure 1 As shown, it includes a device housing 1, a fine metal tube 2 and a magnetostrictive component;

[0050] The fine metal tube 2 is installed inside the device housing 1 and serves as a container for the liquid to be tested and a carrier for wave transmission. The device housing 1 and the fine metal tube 2 are in contact and connected, and contain an in vitro blood sample.

[0051] The magnetostrictive component is arranged at one end of the fine metal tube 2, and includes a permanent magnet 3 and a hollow coil 4. The permanent magnet 3 is used to provide a longitudinal constant magnetic field, and the hollow coil 4 is used to provide a dynamic longitudinal magnetic field and receive an echo signal when powered.

[0052] The permanent magnet 3 is arranged at the end of the fine metal tube 2 to provide a longitudinal constant magnetic field;

[0053] The hollow coil 4 is arranged near the end of the fine metal tube 2 and can be hollowly sleeved outside the fine metal tube 2 for providing a dynamic longitudinal magnetic field and receiving echo signals when energized.

[0054] It also includes an excitation receiving module 8, and the air-core coil 3 is electrically connected to the excitation receiving module 8.

[0055] It also includes a data processing module 9 and a display module 10 . The excitation receiving module 8 is connected to the data processing module 9 , and the data processing module 9 is connected to the display module 10 .

[0056] The excitation receiving module 8 generates multiple periodic pulse signals, which are applied to the excitation receiving module 8 of the magnetostrictive component. The hollow coil 4 is energized through the excitation receiving module 8 to generate a dynamic longitudinal magnetic field, while the permanent magnet 3 is fixed to generate a longitudinal constant magnetic field.

[0057] Under the combined effect of the longitudinal constant magnetic field generated by the permanent magnet 3 and the dynamic longitudinal magnetic field generated by the power supply of the air-core coil 4, the micro-metal tube 2 is deformed based on the magnetostrictive effect, thereby generating an L(0,1) modal guided wave that is affected by the blood sample in the micro-metal tube 2 and propagates on the micro-metal tube 2;

[0058] The hollow coil 4 receives the echo signal after propagation based on the magnetostrictive inverse effect, collects it through the excitation receiving module 8, transmits it to the data processing module 9 for data processing such as filtering, amplification and sampling, and finally uploads it to the display module 10 for display.

[0059] It also includes a temperature control module 5 installed on the device housing 1, the temperature control module 5 includes a temperature detection module 6 and a heating module 7 which are electrically connected, the temperature detection module 6 is connected to the device housing 1 or the fine metal tube 2, and the heating module 7 is also connected to the device housing 1 or the fine metal tube 2 to achieve an internal constant temperature of 37°C to simulate the internal environment of blood in the human body.

[0060] The temperature detection module 6 detects the temperature of the fine metal tube 2 in real time through the temperature sensor inside itself, and drives the heating module 7 to work and heat to achieve constant temperature of human blood when the temperature changes.

[0061] The magnetostrictive component is installed at one end of the fine metal tube 2, the permanent magnet 3 is directly connected to the end face of the fine metal tube 2 through magnetism, the hollow coil 4 is sleeved on the outside of the fine metal tube 2, the inner wall of the coil does not contact the outer wall of the metal tube, and the difference between the inner diameter of the coil and the outer diameter of the metal tube is less than 1.0mm. The fine metal tube 2 can be directly disassembled and replaced by plugging and unplugging.

[0062] The fine metal tube 2 is made of magnetic material, and the permanent magnet 3 is magnetically adsorbed on the end of the fine metal tube 2 .

[0063] In a specific implementation, the fine metal tube 2 is made of magnetic conductive materials such as nickel, iron, iron-nickel alloy, iron-aluminum alloy and iron-cobalt alloy. The inner diameter of the fine metal tube 2 is very fine, with a length not exceeding 200 mm and an inner diameter not exceeding 1.5 mm.

[0064] The embodiments of the complete method according to the above invention content of the present invention are as follows:

[0065] In a specific embodiment, the fine metal tube 2 is a fine carbon steel tube with a length of 200 mm, an outer diameter of 3 mm, and an inner diameter of 1 mm; the coil 4 is 15 mm long, 4 mm in inner diameter, 1500 turns, and a wire diameter of 0.1 mm; the permanent magnet 3 is a circular magnet magnetized in the thickness direction, with a diameter of 10 mm and a height of 5 mm.

[0066] In addition, the heating module 7 selects a heating sheet with a power of 0.02W to be attached to the inner wall of the device housing 1; the excitation receiving module 8 excites the L(0,1) longitudinal mode guided wave.

[0067] 1) According to the inner and outer diameters of the selected fine metal tube 2, the density, elastic modulus and Poisson's ratio of iron, the L(0,1) dispersion curve is calculated to find the best excitation frequency around 87 kHz.

[0068] 2) In the empty pipe state, collect the echo signal of the reciprocating reflection with a distance of 5 meters. Figure 2 shown.

[0069] 3) Push the blood sample to be tested into the horizontally placed fine metal tube 2 from one end through a medical injection needle, and the tube is considered full when blood flows out from the other end. Then, one end of the fine metal tube 2 is adsorbed with a circular magnet to block it, and the other end is sealed with a silicone plug.

[0070] For the selected micro-metal tube 2 with a length of 200 mm, an outer diameter of 3 mm, and an inner diameter of 1 mm, only about 157 ul of blood is theoretically required when it is filled, which is far less than the amount of blood required for traditional thromboelastometry testing.

[0071] 4) After the filling is completed, the echo signal is collected again, and the filling detection signal is obtained through data processing. Figure 3 As shown, the signal envelope is Figure 4 shown.

[0072] 5) Set the threshold according to the signal and take the echo peak value within 10 intervals, such as Figure 5 As shown, the decay rate was calculated and the relative blood viscosity was calculated. The samples were continuously sampled 500 times with a sampling interval of 5 seconds.

[0073] The measurement results are as follows: Figure 6 As shown in the figure, relative blood viscosity increases first and then decreases over time, which is consistent with the whole process of blood coagulation and fibrinolysis in vitro. Therefore, it can be used as the result image of thrombus elasticity measurement. Parameters further calculated based on the image, such as viscosity drop, total rise time, slope, viscosity turn-up inflection point time, etc., can help medical staff understand the specific situation of the patient's coagulation function. Figure 6 As a result, the relative blood viscosity reached the lowest point after about 900 seconds, that is, the entire coagulation process took about 15 minutes to measure, which was significantly shorter than the traditional thrombus elasticity measurement device and had better real-time performance.

[0074] Comparative Example 1

[0075] Compared with the existing methods, the method proposed in the present invention has higher measurement accuracy. The six viscosity liquids with viscosities of 4.8cp, 21.2cp, 48.2cp, 98.5cp, 198cp, and 476cp were used for verification experiments. The attenuation rates of 4.8cp, 48.2cp, 98.5cp, and 476cp viscosity liquids were calculated according to the method of the present invention to be 0.9946, 0.9331, 0.8967, and 0.8122. The function related to viscosity and attenuation rate obtained by power function fitting is as follows:

[0076] y=-0.0534*x 0.2591 +1.075

[0077] Where y represents the attenuation rate, and x represents the liquid viscosity value. The remaining two viscosity liquids of 21.2cp and 198cp are taken, and the attenuation rates are calculated to be 0.9559 and 0.8667 according to the method of the present invention. The liquid viscosities are inferred to be 22.0973cp and 191.3934cp according to the fitting formula, and the measurement errors are 4.23% and 3.34%, which are less than 5%.

[0078] According to the invention patent with existing patent number CN202110378292.2, the device and method for rapid detection of blood viscosity based on micro-metal tube ultrasonic guided waves were predicted, and the viscosities of the two liquids to be tested were predicted, with results of 23.9043cp and 209.0347cp, and measurement errors of 12.76% and 5.57%, respectively, both of which were greater than the errors obtained by the method of the present invention.

[0079] The above specific implementation modes are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A micro-metal tube thrombus elastic force detection device based on L(0,1) longitudinal modal guided wave, characterized by: It comprises a device housing (1), a fine metal tube (2) and a magnetostrictive component; A fine metal tube (2) is installed inside the device housing (1) and contains a blood sample; The magnetostrictive component is arranged at one end of the fine metal tube (2), and comprises a permanent magnet (3) and an air-core coil (4). A permanent magnet (3) is arranged at the end of the fine metal tube (2); A hollow coil (4) is arranged near the end of the fine metal tube (2); It also includes an excitation receiving module (8), and the hollow coil (4) is electrically connected to the excitation receiving module (8); The magnetostrictive component is installed at one end of a fine metal tube (2), the permanent magnet (3) is directly connected to the end face of the fine metal tube (2) through magnetism, the hollow coil (4) is sleeved outside the fine metal tube (2), the inner wall of the coil does not contact the outer wall of the metal tube, the inner diameter of the coil differs from the outer diameter of the metal tube by less than 1.0 mm, and the fine metal tube (2) can be directly disassembled and replaced by plugging and unplugging.

2. According to claim 1, a micro-metal tube thrombus elastic force detection device based on L(0,1) longitudinal modal guided wave, characterized in that: It also includes a data processing module (9) and a display module (10), the excitation receiving module (8) is connected to the data processing module (9), and the data processing module (9) is connected to the display module (10).

3. The device for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal waveguide according to claim 1, characterized in that: The device also includes a temperature control module (5) installed on the device housing (1), wherein the temperature control module (5) includes a temperature detection module (6) and a heating module (7) which are electrically connected to each other, wherein the temperature detection module (6) is connected to the device housing (1) or the fine metal tube (2), and the heating module (7) is also connected to the device housing (1) or the fine metal tube (2).

4. The device for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal waveguide according to claim 1, characterized in that: The fine metal tube (2) is made of magnetic material, and the permanent magnet (3) is magnetically adsorbed on the end of the fine metal tube (2).

5. A micro-metal tube thrombus elastic force detection device based on L(0,1) longitudinal modal waveguide according to claim 1 or 4, characterized in that: The material of the fine metal tube (2) is a magnetic conductive material such as nickel, iron, iron-nickel alloy, iron-aluminum alloy and iron-cobalt alloy.

6. A method for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal guided wave applied to any one of the devices described in claims 1-5, characterized in that: The steps are as follows: 1) calculating the waveguide dispersion curve of the fine metal tube (2) according to the structural geometric parameters and material mechanical characteristics of the fine metal tube (2), and selecting a frequency point with a small dispersion degree as the excitation frequency according to the waveguide dispersion curve; 2) When the micro-metal tube (2) is an empty tube, the hollow coil (4) on the micro-metal tube (2) is excited to generate L (0, 1) mode guided waves that propagate back and forth between the two end surfaces of the micro-metal tube (2) until the energy is exhausted. The tube length is d meters. The hollow coil (4) collects the first k reciprocating processes, and the total echo signals of k*2d meters are used as the empty tube reference signal w0; 3) Fill the micro-metal tube (2) with a blood sample, and obtain an echo signal as a filling detection signal in the same manner as step 2). The i-th filling detection signal is w i ; 4) Empty pipe reference signal w0 and each filling detection signal w i Take the envelope to obtain the respective envelope signals, and take n echo peaks from the envelope signals for fitting to obtain their respective attenuation rates b0 and b i , according to the decay rates b0 and b i Combined with the relationship between the relative blood viscosity and attenuation rate of the blood sample obtained in advance, the filling detection signal w is obtained for each filling i The corresponding relative blood viscosity; 5) Setting the number of sampling times m and the sampling interval Δt for the test, after the blood sample is filled into the micro-metal tube (2), steps 3) and 4) are continuously repeated to perform sampling and obtain the relative blood viscosity of each test, thereby drawing a curve of the relative blood viscosity of the blood sample within the time m*Δt as a thromboelastogram, thereby achieving thromboelastogram measurement.

7. The method for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal waveguide according to claim 6, characterized in that: In step 4), the specific method of taking n echo peaks from the envelope signal is: select the first threshold l1 and the second threshold l2 according to the envelope signal, the interval between the two is l=l1-l2, and start to establish n consecutive intervals of length l from the starting point x0 selected on the envelope signal, that is, the position of the first threshold l1, that is, the interval [x 0， x0+l],[x0+l ， x0+2l]……[x0+(n-1)l ， x0+nl], so that each interval contains only one peak, the peak in each interval is extracted as the echo peak, and all the peaks in n intervals are extracted as the final selected n echo peaks.

8. The method for detecting elastic force of thrombus in a micro-metal tube based on L(0,1) longitudinal modal waveguide according to claim 6, characterized in that: In step 4), the attenuation rate is obtained by fitting according to the following formula: y=a*b x Wherein, x represents the sequence number of the echo peak, y is the value of the echo peak, b is the attenuation rate of the echo peak, and a represents the amplitude normalization coefficient.

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