JP2007319255A - Ultrasonograph - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an ultrasonograph capable of measuring precise and reliable IMT (Intima-Media thickness) values of the anterior wall and the posterior wall of the blood vessel by ultrasonic waves without bothering an operator. <P>SOLUTION: This ultrasonograph is provided with: a receiving section 2 receiving ultrasonic echo signals reflected by the blood vessel; a boundary position detecting section 8 detecting the boundary position between the blood flow area and the tunica intima, and the boundary position between the tunica media and the tunica externa of the anterior wall and the posterior wall of the blood vessel respectively; an IMT value calculation section calculating the IMT values of the anterior wall and the posterior wall of the blood vessel from the boundary position detected in the boundary position detecting section 8; and a reliability determination section 12 determining the reliability of the detected boundary position based on the feature quantity of the long shaft direction of the blood vessel of the boundary position. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an ultrasonic diagnostic apparatus for diagnosing a blood vessel state using ultrasonic waves.

  Diagnosis of arteriosclerosis is performed by measuring the intima-media thickness (hereinafter referred to as IMT) of the blood vessel. Here, the carotid artery has an IMT value that is larger from the initial stage of arteriosclerosis than other parts, and is known to be effective in detecting arteriosclerosis. The carotid artery is compared to 2 to 3 cm from the skin surface. Because of its shallow depth, the carotid artery is often used as a measurement target for diagnosing arteriosclerosis.

  Conventionally, as a method of measuring the IMT value of the carotid artery blood vessel by ultrasound, the luminance signal in B-mode image data based on ultrasound reflected by the blood vessel, assuming that it has a standard vascular structure A method for measuring the IMT value of the blood vessel wall based on the maximum peak value and the second peak value is known (for example, see Patent Document 1).

  However, in this method, since the echo intensity is used, when the intimal luminance of the blood vessel wall to be measured is low or the luminance information includes a lot of noise, the blood flow-intimal boundary position or There is a problem in that the medial-external membrane boundary position cannot be accurately detected, and the accurate IMT value of the blood vessel wall cannot be measured.

In addition, since it is a precondition that the structure of the blood vessel wall to be measured is in a normal state, if there is a local lesion such as an atheroma in the blood vessel to be measured, the boundary position is accurately determined. There was a problem that it could not be measured.

  As a technique that can avoid this problem, the IMT value of the blood vessel wall is measured by detecting the blood flow-intima boundary position and the medial position based on the tissue hardness calculated from the phase change of the ultrasonic echo signal. Has been proposed (see, for example, Patent Document 2 below).

  When a cross-section parallel to a blood vessel is observed in these conventional ultrasonic diagnostic apparatuses, two blood vessel walls on the side closer to and far from the subject's skin surface are depicted for one blood vessel. In general, echo data from the blood vessel wall on the skin surface side (hereinafter referred to as the front wall) close to the ultrasonic probe is easily affected by multiple reflections of ultrasonic waves, and the resulting B-mode image tends to have an unclear outline. . For this reason, the IMT value of the blood vessel wall (hereinafter referred to as the rear wall) far from the skin surface is often measured.

  However, depending on the measurement conditions, it may be better to use the blood vessel wall of the front wall as the measurement target. Therefore, the operator determines from the B-mode image whether the measurement target is the front wall or the rear wall. It was necessary to set an appropriate region of interest with a mouse or the like. Such judgments and operations are troublesome, and in the case of making a diagnosis on a large number of subjects such as a periodic health check, it has been a cause of extending the total diagnosis time.

  In addition, if there are plaques or noise that cannot be clearly determined by the B-mode image in the vicinity of the blood vessel wall selected as the IMT value measurement target, the blood flow-intima and media-outer membrane boundary of the blood vessel are accurately Therefore, an incorrect IMT value is measured. As a method for solving this, a method has been proposed in which the region of interest to be set is set so that both the front wall and the rear wall are included, and the IMT values of the front wall and the rear wall are measured (for example, Patent Documents). 3).

Japanese Patent Laid-Open No. 11-318896 International Publication No. 2004/112568 Pamphlet JP 2004-357892 A

However, even in the conventional method, when the operator is immature and the method of applying the ultrasonic probe is inappropriate, the correct position of the blood flow-intima / intima boundary is not detected. There is a risk of misdiagnosis.

  The present invention has been made in view of the above-described conventional circumstances, and an object thereof is to provide an ultrasonic diagnostic apparatus capable of measuring an IMT value with accuracy and reliability.

An ultrasonic diagnostic apparatus according to the present invention includes: a transmitter that transmits ultrasonic pulses from a body surface of a subject toward a plurality of points along a major axis direction of a blood vessel inside the subject; and the plurality of points A receiving unit that receives an ultrasonic echo signal reflected from the ultrasonic echo signal, and a boundary position between a blood flow region and an intima in each of the front wall and the rear wall of the blood vessel at the plurality of points, and A boundary position detection unit that detects a boundary position between the media and outer membrane; an IMT value calculation unit that calculates an IMT value of the blood vessel based on the boundary position detected by the boundary position detection unit; A reliability determination unit that determines the reliability of the boundary position detected by the boundary position detection unit from the feature amount in the major axis direction of the blood vessel at the boundary position detected at this point.
According to the above configuration, when the operator is immature and the ultrasonic probe is improperly applied, etc., it is possible to grasp the possibility of not detecting the correct position of the bloodstream-intima / media-media boundary This makes it possible to accurately and reliably measure the IMT value. In the above configuration, the IMT value may be calculated only when reliability is high as a result of the reliability determination, or the IMT value is calculated regardless of the reliability determination result of the boundary position, and the reliability of the IMT value calculation result is calculated. You may determine as.

The ultrasonic diagnostic apparatus according to the present invention further includes notification means for performing notification based on the determination result of the reliability determination unit.
According to the above configuration, when the reliability determination unit determines that the reliability is low, the fact can be notified, so that the correct position of the bloodstream-intima / media-media boundary is detected. The operator can easily confirm that this is not done.

In addition, the ultrasonic diagnostic apparatus according to the present invention processes the phase information of the ultrasonic echo signal and sends out at least one of the phase information processing results to the boundary position detection unit; An amplitude information processing unit that processes amplitude information of the sound wave echo signal and sends at least one of the amplitude information processing results to the boundary position detection unit, wherein the boundary position detection unit A boundary position between the blood flow region and the intima in each of the front wall and the rear wall of the blood vessel at the plurality of points, and the media and the outer from at least one of the amplitude information processing results The boundary position with the film is detected.
According to the above configuration, it is possible to accurately detect the boundary position.

Further, the ultrasonic diagnostic apparatus according to the present invention includes a moving speed of a living tissue that is one of the phase information processing results and an intensity of an ultrasonic echo signal that is one of the amplitude information processing results. A blood flow region through which blood in the blood vessel flows using at least one of the blood vessel region, and a boundary position between the blood flow region and the intima for each of the front wall near the body surface of the blood vessel and the rear wall far from the body surface, And a region-of-interest setting unit that sets a region of interest necessary for detecting the boundary position between the media and the outer membrane.
According to the above configuration, it is possible to accurately detect the boundary position.

In the ultrasonic diagnostic apparatus according to the present invention, the feature amount is an average value and a standard deviation of the boundary position, or an average value and a variance.
According to the above configuration, the reliability of the detected boundary position can be easily determined.

In the ultrasonic diagnostic apparatus according to the present invention, the feature amount is a degree of inconsistency between the approximate function estimated by regarding the boundary position as a function in the long axis direction of the blood vessel and the boundary position.
According to the above configuration, the reliability of the detected boundary position can be easily determined.

In the ultrasonic diagnostic apparatus according to the present invention, the approximate function is a linear function.
According to the above configuration, the reliability of the detected boundary position can be easily determined.

In the ultrasonic diagnostic apparatus according to the present invention, the approximate function is a linear function.
According to the above configuration, the reliability of the detected boundary position can be easily determined.

In the ultrasonic diagnostic apparatus according to the present invention, the approximate function is a polynomial function.
According to the said structure, the reliability of the detected boundary position can be determined more correctly.

In the ultrasonic diagnostic apparatus according to the present invention, the approximation method for estimating the approximate function is a linear least square method.
According to the above configuration, the reliability of the detected boundary position can be easily determined.

In the ultrasonic diagnostic apparatus according to the present invention, the approximation method for estimating the approximation function is a nonlinear least square method.
According to the said structure, the reliability of the detected boundary position can be determined more correctly.

In the ultrasonic diagnostic apparatus according to the present invention, the approximate function is a nonlinear function.
According to the said structure, the reliability of the detected boundary position can be determined more correctly.

Furthermore, in the ultrasonic diagnostic apparatus according to the present invention, the approximation method for estimating the approximation function is a nonlinear least square method.
According to the said structure, the reliability of the detected boundary position can be determined more correctly.

  According to the present invention, when the operator is immature and the ultrasonic probe is improperly applied, etc., it is possible to grasp the possibility that the correct position of the blood flow-intima / media-outer membrane boundary is not detected. This makes it possible to accurately and reliably measure the IMT value.

  Hereinafter, an ultrasonic diagnostic apparatus according to an embodiment of the present invention will be described with reference to the drawings.

(Embodiment 1)
FIG. 1 is a block diagram showing a schematic configuration of the ultrasonic diagnostic apparatus according to the first embodiment of the present invention. However, FIG. 1 also shows a B-mode image received by this ultrasonic diagnostic apparatus. The B-mode image is an image when an ultrasonic pulse is transmitted toward the blood vessel.

  In a B-mode image, 30 is a blood vessel, 31 is a front wall of the blood vessel, 32 is a rear wall of the blood vessel, 33 is a blood flow region, 301 is an outer membrane of the front wall, 302 is an inner media of the front wall, and 303 is a rear wall. , 304 is the posterior wall adventitia, 310 is the anterior wall media-endocardium boundary, 311 is the anterior wall blood flow-intima boundary, 312 is the posterior wall blood flow-intima boundary, 313 Indicates the medial-external membrane boundary of the back wall.

  The transmission unit 1 generates an ultrasonic pulse and supplies it to the ultrasonic probe 101. Here, the transmission unit 1 transmits ultrasonic pulses from the body surface of the subject toward a plurality of points along the long axis direction of the blood vessel inside the subject. The ultrasonic probe 101 transmits the ultrasonic pulse supplied from the transmission unit 1 from the skin surface 20 of the living body toward the blood vessel 30 in the living body. The blood vessel 30 has a blood vessel wall configured to surround a blood flow region 33 through which blood flows, and has a front wall 31 on the side close to the skin surface and a rear wall 32 on the far side. An atheroma 306 which is a local lesion is formed inside the blood vessel wall.

  The ultrasonic pulse reflected by the blood vessel 30 is received by the ultrasonic probe 101 and supplied to the amplitude information processing unit 5 and the phase information processing unit 6 via the reception unit 2 and the delay synthesis unit 3. The amplitude information processing unit 5 sends at least one feature amount extracted from the amplitude information of the ultrasonic echo signal, and the phase information processing unit 6 sends at least one feature amount extracted from the phase information of the ultrasonic echo signal. To do.

  The region-of-interest setting unit 7 uses at least one of the amplitude intensity of the ultrasonic echo signal sent from the amplitude information processing unit 5 and the moving speed of the living tissue sent from the phase information processing unit 6 to blood in the blood vessel 30. The interest necessary for detecting the flow region 33 and detecting the blood flow-intima boundary positions 311 and 312 and the medial-adventricular boundary positions 310 and 313 of the anterior wall 31 and the posterior wall 32 of the blood vessel 30, respectively. Set the area.

  In the boundary position detection unit 8, the region of interest on the front wall 31 and the rear wall 32 sent from the region of interest setting unit 7 and the processing result sent from the amplitude information processing unit 5 and the phase information processing unit 6, the blood flow-intima boundary positions 311 and 31 and the medial-outer membrane boundary positions 310 and 313 of the front wall 31 and the rear wall 32 are detected based on at least one of the processing results sent out from 6. To do.

  The IMT value calculation unit 9 determines whether the boundary position between the intima of the blood vessel 30 and the blood flow region 33 changes from the intima to the intima based on the temporal change in one heartbeat cycle and the temporal change in the position of the media. Measure the thickness IMT (Intima-Media Thickness) to the film. The IMT calculation unit 9 calculates at least one of the maximum value, the minimum value, and the average value of IMT values in one heartbeat cycle.

  In this case, the IMT value calculation unit 9 uses the tissue hardness value converted by the hardness value conversion based on the ultrasonic echo signal obtained by receiving the ultrasonic echo reflected by the blood vessel 30. A hardness value change waveform when detecting the boundary position between the intima and the blood flow region 33, and a point indicating the maximum peak value and a second peak value of the hardness value change waveform May be detected as an IMT value.

  The blood flow-intima boundary positions 311 and 31 and the medial-examinal boundary positions 310 and 313 in the front wall 31 and the rear wall 32 detected by the boundary position detection unit 8, and the IMT value calculation unit 9 The IMT value calculated in the above is sent to the image composition unit 10.

  The B-mode processing unit 4 generates image information representing a cross section of the blood vessel 30 based on the ultrasonic echo signal supplied via the delay synthesis unit 3 and supplies the image information to the image synthesis unit 10. The image composition unit 10 synthesizes the image information supplied from the B mode processing unit 4 and the result supplied from the boundary position detection unit 8 and displays the result on the display unit 11.

  Since there may be a slight shift between the B-mode image displayed on the monitor and the detected boundary position, the blood flow-intima of the detected front wall 31 and rear wall 32 is detected by the boundary position detection unit 8. A fixed value may be added or subtracted as an offset value 802 to the boundary positions 311 and 31 and the media-outer membrane boundary positions 310 and 313.

  In the ultrasonic diagnostic apparatus according to the present embodiment, the offset setting 802 is performed on the boundary position extraction unit 8, but the present invention is not limited thereto. Any configuration may be used as long as the boundary displayed on the monitor is very close to the case where the operator visually determines. Further, the IMT value calculated by the IMT value calculation unit 9 can be displayed in the image composition unit 10 as necessary, but the present invention is not limited to this.

  The reliability determination unit 12 determines the reliability of the boundary position from the feature amount in the major axis direction of the blood vessel 30 at the boundary position detected by the boundary position detection unit 8. Below, the specific content of the reliability determination method is demonstrated. In the following description, the rear wall 32 of the blood vessel 30 will be described. However, the reliability of the front wall 31 of the blood vessel 30 can be determined by the same procedure, and thus the description thereof will be omitted.

  FIG. 2 shows the boundary position detection of the blood flow-intima boundary position and the medial-examinal boundary position of the posterior wall of the blood vessel located substantially perpendicular to the depth H from the skin surface along the acoustic scanning line H. FIG. 8 is a schematic diagram of a result detected by the unit 8, where a blood flow-intima boundary position along a certain acoustic scanning line H is B0 (H), and a medial film-outer membrane boundary position is B1 (H).

  If the average values of B0 (H) and B1 (H) are MB0 and MB1, respectively, and their standard deviations are SDB0 and SDB1, respectively, the distribution of the respective boundary positions is MB0 ± SDB0 and MB1 ± SDB1. Usually, since the boundary between the blood flow and the intima is not so complicated, the distribution of the boundary position is not so wide.

  Therefore, in the reliability determination unit 12 in the present embodiment, either the standard deviation SDB0 of the blood flow-intima boundary position B0 (H) or the standard deviation SDB1 of the medial-intima boundary position B1 (H) is: When the reliability threshold value 121 set in advance is exceeded, it is determined that the boundary position of the measurement is low in reliability, the reliability determination result is transmitted to the image composition unit 10, and the boundary position is not displayed on the display unit 11 on the monitor. Take action. Here, although the example in which the reliability determination unit 12 determines the reliability from the average value and the standard deviation of the boundary position has been shown here, the reliability is determined using the average value and the variance of the boundary position. Also good.

In the above description, when the reliability of the boundary position is low, this is transmitted to the image composition unit 10 and the display unit 11 does not display the boundary position on the display monitor. However, the present invention limits this. is not. For example, if the display unit 11 is configured to allow the operator to determine whether the reliability of the boundary position obtained by the measurement is low or high, such as displaying a letter indicating that the reliability of the detected boundary position is low. Any configuration is acceptable.
The IMT value calculation unit 9 may calculate the IMT value only when reliability is high as a result of the reliability determination by the reliability determination unit 12. The value calculation unit 9 may calculate the IMT value and perform notification such as a monitor display so that the operator can grasp the reliability of the IMT value calculation result.

  In addition, the value of the reliability threshold 121 described above may be set in advance as an appropriate value in consideration of the normal blood vessel structure.

  As described above, according to the present embodiment, when the operator is immature and the ultrasonic probe is improperly applied, the correct position of the blood flow-intima boundary and intima-media boundary is detected. The operator can be surely notified of the absence. Therefore, it is possible to provide an ultrasonic diagnostic apparatus capable of measuring an accurate and reliable IMT value on the front wall and the rear wall of a blood vessel.

(Embodiment 2)
Hereinafter, a second embodiment of the present invention will be described with reference to the drawings. A block diagram showing a schematic configuration of the second embodiment of the present invention is the same as that of FIG. 1, and the same components as those of the first embodiment are denoted by the same reference numerals and description thereof is omitted.

  The method of setting the region of interest, the method of detecting the blood flow-intima boundary positions 311 and 312 and the medial-adventricular boundary positions 310 and 313 of the anterior wall 31 and the posterior wall 32 of the blood vessel 30, etc. Since it is the same as that of form 1, description is abbreviate | omitted.

  The difference between the present embodiment and the first embodiment is that the boundary position or IMT value calculation unit 9 calculates the feature amount in the major axis direction of the blood vessel 30 at the boundary position detected by the boundary position detection unit 8. The method of determining the reliability of the IMT value is different. Below, the specific content of the reliability determination method is demonstrated.

  In the following description, the rear wall 32 of the blood vessel 30 will be described. However, the reliability of the front wall 31 of the blood vessel 30 can be determined by the same procedure, and thus the description thereof will be omitted.

  FIG. 3 is a schematic diagram showing the blood flow-intima boundary position and the medial-outer membrane boundary position of the rear wall 32 of the blood vessel 30 as in the first embodiment. FIG. 4 is a schematic diagram of the result detected in FIG. 2, where the blood flow-intima boundary position on an acoustic scanning line H is B0 (H), and the media-outer membrane boundary position is B1 (H).

Here, when the blood vessel 30 is not positioned parallel to the direction perpendicular to the acoustic scanning line H as shown in FIG. 3 and is present at an inclination, or a lesion such as atheroma 306 is present in the intima as shown in FIG. When the blood flow-intima boundary position is meandering, using the determination method described in the first embodiment, the boundary position is detected even though the accurate boundary position is detected. In this case, it is determined that the reliability is low. Therefore, in the present embodiment, reliability is determined by the following procedure.

  A straight line having a certain inclination in the direction perpendicular to the acoustic scanning line H of B0 (H), that is, the depth H direction is assumed, and the approximate straight line L0 (H) = a0H + b0 is estimated by linear regression. Similarly, a straight line having a certain slope in the depth H direction of B1 (H) is assumed, and the approximate straight line L1 (H) = a1H + b1 is estimated by linear regression.

In this case, the degree of coincidence X0 between B0 (H) and L0 (H) defined by the following equation and the degree of coincidence X1 between B1 (H) and L1 (H) are calculated.
X0 = Σ | B0 (H) Σ L0 (H) | ² (1)
X1 = Σ | B1 (H) Σ L1 (H) | ² (2)
If the value of X0 or X1 exceeds the reliability threshold value 121 set in advance, the measurement result is regarded as having low reliability.

  In the above description, the boundary position is regarded as a straight line having a certain inclination with respect to the direction perpendicular to the acoustic scanning line, and the approximate straight line is estimated by linear regression. However, the present invention limits this. Instead, for example, the boundary position may be approximated by a polynomial or a nonlinear function. Further, the present invention does not limit the estimation method of an approximate line or approximate curve to linear regression, and any approximation method such as a nonlinear least square method may be used.

  As described above, according to the present embodiment, it is possible to reliably notify the operator that the correct position of the blood flow-intima or intima-media boundary is not detected due to the shape of the blood vessel. Therefore, it is possible to provide an ultrasonic diagnostic apparatus capable of measuring an accurate and reliable IMT value on the front wall and the rear wall of a blood vessel.

  The present invention grasps the possibility of not detecting the correct position of the blood flow-intima / intima boundary of the blood vessel when the operator is immature and the ultrasonic probe is improperly applied. Therefore, it is possible to accurately and reliably measure the IMT value, which is useful for displaying images and diagnosing blood vessels using ultrasonic echoes in the medical field.

The block diagram which shows schematic structure in embodiment of this invention Schematic diagram for explaining an operation example of the reliability determination unit in the first embodiment of the present invention. The schematic diagram for demonstrating the operation example of the reliability determination part in Embodiment 2 of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Transmission part 2 Reception part 3 Delay synthetic | combination part 4 B mode process part 5 Amplitude information processing part 6 Phase information processing part 7 Region of interest setting part 8 Boundary position detection part 9 IMT value calculation part 10 Image composition part 11 Display part 12 Reliability Determination unit 20 Subject skin surface 30 Blood vessel 31 Blood vessel front wall 32 Blood vessel rear wall 33 Blood flow region 51, 52 Amplitude information processing result 61, 62 Phase information processing result 101 Probe 301 Outer membrane 302 of front wall Inner media 303 Inner membrane of the rear wall 304 Outer membrane of the rear wall 310 Medial membrane-outer membrane boundary 311 of the front wall Blood flow-intima boundary of the front wall 312 Blood flow of the rear wall-intima boundary 313 of the rear wall Middle-outer membrane boundary 801 threshold 802 offset

Claims (13)

A transmitter that transmits ultrasonic pulses from a body surface of the subject toward a plurality of points along the longitudinal direction of a blood vessel inside the subject;
A receiver for receiving ultrasonic echo signals reflected from the plurality of points;
A boundary position for detecting a boundary position between the blood flow region and the intima and a boundary position between the media and the outer membrane in each of the front wall and the rear wall of the blood vessel at the plurality of points from the ultrasonic echo signal. A detection unit;
An IMT value calculation unit that calculates an IMT value of the blood vessel based on the boundary position detected by the boundary position detection unit;
A reliability determination unit that determines the reliability of the boundary position detected by the boundary position detection unit from the feature amount in the major axis direction of the blood vessel at the boundary position detected at the plurality of points;
An ultrasonic diagnostic apparatus comprising:   The ultrasonic diagnostic apparatus according to claim 1, further comprising notification means for performing notification based on a determination result of the reliability determination unit. A phase information processing unit for processing phase information of the ultrasonic echo signal and sending at least one of phase information processing results to the boundary position detection unit;
An amplitude information processing unit that processes amplitude information of the ultrasonic echo signal and sends at least one of the amplitude information processing results to the boundary position detection unit;
With
The boundary position detection unit includes a blood flow region in each of the front wall and the rear wall of the blood vessel at the plurality of points from at least one of the phase information processing results and at least one of the amplitude information processing results. The ultrasonic diagnostic apparatus according to claim 1, wherein a boundary position between the inner membrane and a boundary position between the media and the outer membrane is detected.   The blood of the blood vessel flows using at least one of the moving speed of the living tissue that is one of the phase information processing results and the intensity of the ultrasonic echo signal that is one of the amplitude information processing results. The blood flow region is detected, and the boundary position between the blood flow region and the intima and the boundary position between the media and the outer membrane are determined for each of the front wall near the body surface and the rear wall far from the body surface. The ultrasonic diagnostic apparatus according to claim 3, further comprising a region-of-interest setting unit configured to set a region of interest necessary for detection.   The ultrasonic diagnostic apparatus according to claim 1, wherein the feature amount is an average value and standard deviation of the boundary position, or an average value and variance.   5. The ultrasonic diagnosis according to claim 1, wherein the feature amount is a degree of inconsistency between an approximate function estimated by regarding the boundary position as a function in a long axis direction of a blood vessel and the boundary position. 6. apparatus.   The ultrasonic diagnostic apparatus according to claim 6, wherein the approximate function is a linear function.   The ultrasonic diagnostic apparatus according to claim 7, wherein the approximate function is a linear function.   The ultrasonic diagnostic apparatus according to claim 7, wherein the approximate function is a polynomial function.   The ultrasonic diagnostic apparatus according to claim 6, wherein an approximation method for estimating the approximation function is a linear least square method.   The ultrasonic diagnostic apparatus according to claim 6, wherein an approximation method for estimating the approximate function is a nonlinear least square method.   The ultrasonic diagnostic apparatus according to claim 6, wherein the approximate function is a nonlinear function. The ultrasonic diagnostic apparatus according to claim 6 or 12, wherein an approximation method for estimating the approximation function is a nonlinear least square method.

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