JPS5937766B2 - How to measure impedance distribution - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring impedance distribution at an interface between an object to be measured and a transmission wave propagation medium and/or a reflective interface inside the object to be measured.

In recent years, in the fields of medical diagnosis, metal flaw detection, object recognition, etc., transmission waves such as electromagnetic waves and ultrasonic waves are propagated to the measured object, and reflected waves from the measured object are detected and analyzed. It is widely practiced to observe the position, size, shape, internal structure, etc. of

Among these observation methods, ultrasonic tomography is particularly preferred to methods that use X-rays or radiation because it poses less risk to living organisms when the object to be measured is a living organism, and it also allows observation of soft tissue within the living body. It is attracting attention as an alternative.
The conventional method and the method of the present invention will be explained below using ultrasonic tomography as an example, but the method of the present invention is not limited thereto. Conventional ultrasonic tomography has greatly contributed to clinical diagnosis by imaging using the intensity and propagation time of reflected waves as main information. However, little thought has been given to how much information a single reflected wave contains and what can be learned from it. For example, reflected waves from an interface perpendicular to the propagation axis of ultrasound have positive and negative polarities depending on the acoustic impedance of the medium before and after the interface. This is information contained in the phase characteristics of waves, and is one of the important pieces of information that has been overlooked until now.

FIG. 1 is a diagram for explaining information included in the phase characteristics of reflected waves.

In FIG. 1A, the ultrasonic waves sent out from the piezoelectric transducer 1 propagate through the media 10 to N (including the object to be measured) one after another,
The reflected waves reflected at the interfaces 11' to N' of each medium are received by the same piezoelectric transducer 1 or another piezoelectric transducer (not shown). A typical waveform of each reflected wave is shown in FIG. 1B. As shown in the figure, when the interface of the medium is perpendicular to the propagation axis of the ultrasound, the reflection coefficient R of the ultrasound at the l-th interface
i and the transmission coefficient Ti are each Zi; acoustic impedance (real number) of the i-th medium. However, the incident direction of the reflected wave is from Zi-1 to the Z direction.

is given.

At this time, the transmission coefficients are all positive, so if multiple reflections are ignored, the positive and negative polarities of the reflected waves indicate which has the greater acoustic impedance of the medium that constitutes the corresponding reflecting surface. , is one of the important information regarding the internal structure of living organisms. The positive and negative polarities of this reflected wave are included in the phase information of the reflected wave when the information of the reflected wave is divided into amplitude information and phase information, and unlike conventional ultrasonic tomography, the amplitude information is mainly used. This information was overlooked by the previous measurement method.

How can we derive this information from the phase characteristics of the reflected waves?
Examining and realizing the extent to which it can be extracted will require improvements in ultrasonic tomography and tissue characterization (Tis).
This is an important matter for such characters. The present invention has been made based on this knowledge, and an object of the present invention is to provide a method for measuring the impedance distribution of a measured object from phase information contained in reflected waves. The method of the present invention includes a step of propagating a transmitted wave to an object to be measured, a step of receiving a reflected wave from the object to be measured, and a step of determining the phase polarity of the reflected wave. a step of obtaining a Fourier transform value of the reflected wave; a step of obtaining a phase characteristic using the obtained Fourier transform value and a Fourier transform value of the reflected wave from the reference object; and a step of obtaining a phase characteristic using the weighted least squares method. and converting the relationship between the frequency of the reflected wave and the frequency of the reflected wave into a linear equation, and determining the phase polarity based on whether the value of the phase characteristic when the frequency is zero is close to an even number or an odd number, The method is characterized in that a high level of impedance at the reflective interface of the object to be measured is determined based on phase polarity.

Next, the principle of the method of the present invention will be explained using ultrasonic tomography as an example.

In actual measurements, when a living body is exposed to ultrasound, the received waves include many reflected waves, but one reflected wave can be extracted by time gating.

Let's consider how this one reflected wave is expressed in the frequency domain.

If XO(t) is the reflected wave from a reflecting object (hereinafter referred to as the reference object) selected as a reference, then the wave X is shifted by τ in time.

The Fourier transform value of (tz) is, however, f{} indicates the Fourier transform. XO(f): Fourier transform value τ of the reflected wave from the reference object; time shift from the reference wave At this time, the sound speed of the medium of the O propagation path has no frequency dispersion.

O The acoustic impedance of the living body is a real number. If the assumption that the O reflection surface is perpendicular to the ultrasound propagation axis holds, then A(
f) is a positive number indicating the attenuation characteristic of the reflected intensity propagation path, etc., and the positive or negative polarity of the reflected wave is indicated by whether the integer m is an even number or an odd number.

Here, the transfer function H(f) is defined as follows.

The phase characteristic ArgH(f) is obtained from equation (5). The vertical axis is ArgH(f)/π and the horizontal axis is frequency f.
The solid line is a typical measured value, and the dotted line is a weighted least squares method to the measured value, and the estimated values of τ and m are used, and the linear equation (
7) represents a straight line obtained by substituting into the equation. As shown in Figure 2, the phase characteristic of the transfer function is the frequency f of the reflected wave.
, which is a straight line with respect to , which is a relationship that is easy to handle theoretically.

Focusing on this point, the reflected wave is Fourier transformed to ArgH(f
), and by applying the weighted least squares method,
You can find the slope and intercept of a straight line. From these values, estimated values of τ and m? , demand is obtained, and the positive or negative polarity of the reflected wave is determined by whether the rough value is closer to an even number or an odd number. The problem here is that when XO(t) is known, from the output x(t) mixed with additional noise n(t), the output x(
The purpose is to determine whether an integer m indicating the positive or negative polarity of t) is an even number or an odd number.

In this case, equation (5) is where n(t); time-gated self-contained glass noise A; a positive constant indicating the attenuation characteristics of the propagation path, reflection intensity, etc., and the transfer function H(f) is as follows. given to.

However, A is generally a function of frequency, but when considering optimality, it is assumed to be almost constant within the signal band of the reflected wave.

For the sake of simplicity, the phase error of H(f) due to noise is expressed as △θ(f)
Then, it follows from equation (9).

As mentioned earlier, in the absence of noise, θ(f) is a function that shows a straight line with respect to frequency f, and the slope (2πτ) and intercept (mπ) of the straight line are estimated by the weighted least squares method. From these values, the estimated values of τ and m can be obtained. Next, the application of the weighted least squares method will be explained.

The following formula W(f); weighting F2Jl: Upper and lower limits of the signal band of reflected waves The estimated value order, Z, that minimizes is calculated as follows.

A3) Does it satisfy the formula? , given as money as follows:

What is the estimated value when the gate width is sufficiently large when time-gating white glass noise? The optimal weighting function W(f)★ that minimizes the variance of the salmon is determined by the variational method, where c is an arbitrary constant (c=1).

From formula A7), the optimal weighting function is the Fourier transform value X of the reflected wave from the reference object. It can be seen that it is sufficient to use the square of (f). Next, if we consider the estimated value and the variance of the association, what is the estimated value when optimal weighting is applied? The variance of the medical school is σ However,? The power of the noise before being gated TfO; Δf which is the center frequency and satisfies the following formula; and the frequency bandwidth of the reflected wave.

Here, let the standard deviations of the society be △τ and △m.

It becomes like this. The variance of the negative sum of the O estimate does not depend at all on the time shift τ or the phase characteristics of the reference wave. It depends only on the ratio, the frequency bandwidth of the reflected wave, and the center frequency.

The wider the bandwidth defined by equation (a), the higher the accuracy of the estimated value of Oτ, which indicates that the generally speaking distance resolution is determined only by the bandwidth. The estimated value of 0 m is more accurate as the Q (center frequency/bandwidth) is lower, and a transducer with a lower Q is required to determine the polarity of the reflected wave.

0 In commonly used transducers, Q2》1, and the following equation holds true from (self) and (self) equations.

This indicates that, as is clear from the principle of the estimation method, the estimation error of m is mostly due to the estimation error of τ. Under measurement conditions where the standard deviation Δm of the estimated value of 0m exceeds 0.5, it is meaningless to determine whether gold is even or odd.

Therefore, if the measurement condition in which Δm does not exceed 0.5 is found from the equation, it is given as T0-':period of the center frequency.

This indicates that in order to correctly determine the polarity of the reflected wave, τ must be measured with an error within Tc/4. These results hold true when the gate width Tc is large by the force, but the qualitative properties are thought to hold true even when the gate width is relatively narrow. The method of the invention will now be explained by way of examples.

Center frequency F. Up to 5MHZ, Bandwidth △f-0.56MH
Using a Z (Q-9) piezoelectric transducer, the reflected waves from a cow's liver fixed in water were measured using the reflected waves from an acrylic plate placed in water as a reference, and the method of the present invention was applied.

3 to 5 are graphs showing the results actually measured in this example.

Figure 3 shows the reflected wave from the acrylic plate, Figure 4 shows the reflected wave from the interface between water and cow liver, and Figure 5 shows the reflected wave from the interface between cow liver and water. In the diagram, A is X. (t) or X(t) and time gate width [unit: MS], B is X. (f) or X(f) and frequency [MH7J] and c are graphs showing the relationship between ArgXO(f)/π or ArgH(f)/π and frequency [MHZ], respectively. FIG. 4 shows the reflected wave from the interface between water and cow liver, and the straight line obtained by applying the weighted least squares method to the phase characteristics is shown as a broken line in the figure.

Further, the estimated value of m was obtained as 2.02, and it was determined that m was an even number and the polarity was positive. FIG. 5 shows a reflected wave from the interface between the cow's liver and water, and the reflected wave propagates through the water and the cow's liver.

The estimated value of m was determined to be 1.26, and it was determined that m was an odd number and the polarity was negative. In the case of FIG. 5, a result of order=1.26 is obtained, indicating an error of 0.26 for an integer of 1.

Comparing with the simulation results, it does not appear that the error is due to random noise, and when considered together with the experience during measurement (the intensity of the reflected wave changed significantly even when the piezoelectric transducer was slightly tilted), it seems that the reflective surface This is thought to have occurred because it was not perpendicular to the propagation axis of the ultrasound. FIG. 6 shows a block diagram of an embodiment of the method of the present invention, in which 1 is a transducer, 2 is a Fourier transformer, 3 is a reference wave memory, and 4 is a block diagram of an embodiment of the method of the present invention.
5 represents a reflected wave memory, 5 represents an arithmetic circuit, and 6 represents a square circuit.

When the transducer 1 receives a signal from an oscillator (5 MHZ) not shown, it transmits 5 MHZ ultrasonic waves to the specimen X. The reflected wave is received by the transducer 1 and sent to the Fourier transformer 2.

As the Fourier transformer, in addition to the well-known digital operation type Fourier transformer, an analog operation type pulley transformer may be used.

As the output of the Fourier transformer 2, Fourier transform values of frequencies in the reflected wave band (here, 3 to 7M◯, for example, every 0.1 MHz) are obtained.

The Fourier transform value of the reference reflected wave from the medium is stored in the reference wave memory 3. Further, the Fourier transform value of the reflected wave from the medium to be measured is stored in the reflected wave memory 4.

The Fourier transform values of these two memories 3.4 are sent to the arithmetic circuit 5 for each frequency, and the arithmetic circuit calculates the above-mentioned equation (6), (
7) Calculate the equation and output ArgH(f). Based on these outputs, the least squares circuit 6 performs a least squares calculation to determine the slope and intercept of the straight line and outputs them. These can also be executed by a program on a digital computer.

As described above, according to the method of the present invention, it is possible to measure the impedance distribution from the phase characteristics of the reflected wave using a relatively simple method, and by combining it with information obtained from the intensity and propagation time of the reflected wave. Therefore, the tissue of the object to be measured can be observed more accurately.

[Brief explanation of drawings]

FIG. 1 is a diagram for explaining the information included in the phase characteristics of the reflected wave, FIG. 2 is a diagram showing the phase characteristics of the transfer function, and FIGS. 3 to 5 are diagrams for explaining the information included in the phase characteristics of the reflected wave. A diagram showing the actual measurement results and FIG. 6 are diagrams showing a configuration suitable for use in implementing the method of the present invention. 1...Transducer 1, 2...Fourier transformer, 3...Reference wave memory 4...
...Reflected wave memory, 5... Arithmetic circuit, 6...
...Square circuit, 10 or N...
...N types of media.

Claims (1)

[Scope of Claims] 1 The method includes the steps of transmitting a transmission wave to an object to be measured, receiving a reflected wave from the object to be measured, and determining the phase polarity of the reflected wave, and the determining step The method includes the steps of obtaining a Fourier transform value of the reflected wave, obtaining a phase characteristic using the obtained Fourier transform value and a Fourier transform value of the reflected wave from the reference object, and calculating the converting the relationship between the phase characteristic and the frequency of the reflected wave into a linear equation, and determining the phase polarity based on whether the value of the phase characteristic when the frequency is zero is close to an even number or an odd number. A method for measuring an impedance distribution, characterized in that the level of impedance at a reflective interface of the object to be measured is determined based on the phase polarity. 2. The impedance distribution measuring method according to claim 1, wherein the transmitted wave and the reflected wave are ultrasonic waves. 3. The method for measuring impedance distribution according to claim 1 or 2, wherein the object to be measured is a living body.