RU2662079C1 - Method of microwave ultra high-resolution tomography - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention relates to a medical technique, namely to methods for scanning and further processing the resultant image for tomographic examination. Method of microwave ultra high-resolution tomography of a tissue without disturbing its integrity comprises the steps of placing a microwave power source and microwave receiving and transmitting antennas, controlling microwave receiving and transmitting antennas, placing a matching medium between the microwave transmitting and receiving antennas, placing a tissue to be irradiated, receiving inside the separating medium the microwave radiation by the transmitting and receiving antennas after interaction with the tissue and measuring the change in microwave radiation after interaction with the tissue, processing the measurement results and constructing a three-dimensional tomographic image of the tissue, wherein the transmitting and receiving antennas are controlled so that each of them emits microwave radiation, axis of the radiation pattern of which discretely changes its angular position in the radiation plane, that is, with the help of each transmitting and receiving antenna, several measurements are made corresponding to each angular position of the axis of the radiation pattern, wherein the step to which the direction of the axis of the radiation pattern of the scanning radiation changes, corresponds to the magnitude of the required resolving power, a set of tomograms is constructed, each of tomograms corresponds to a certain radiation pattern, further they are summed up and the obtained result is processed using an inverse filter, the final tomographic image of the tissue is constructed in accordance with formula:

, where T(x,y,z) – is a superposition of individual images; K(x,y,z) – analytic approximation of a two-dimensional spatial filter; x,y,z – spatial variables; u – Fourier variable conjugate to x; v – Fourier variable conjugate to y;

– two-dimensional Fourier images of corresponding functions T and K with respect to variables x and y; α – regularization parameter; Ω=u²+v² – regularizing operator; * is a complex conjugate sign.

EFFECT: use of the invention provides the improved quality of images obtained with the help of microwave tomography by increasing their spatial resolution up to 1 mm or more.

1 cl, 5 dwg

Description

The invention relates to the field of research of materials using electromagnetic radiation, followed by obtaining an image of the investigated object, and in particular to methods of scanning and subsequent processing of the obtained image for tomographic studies in the medical, space fields, etc.

It is known that living tissues in different conditions differ in their dielectric properties, local measurements of which lead to the possibility of three-dimensional visualization of biological objects, including organs of the human body. X-ray tomography (RT) is the most well-known method of three-dimensional imaging. Being extremely useful, x-rays, however, have very low sensitivity to soft tissues. This significantly limits their use for the diagnosis of many diseases.

The best quality of medical images is achieved using magnetic resonance imaging (MRI). This method allows you to see the functional state of living tissues, but it also has its limitations. First, MRI is, in essence, a “slow” method. It can only be used to study stable objects or very slowly progressing processes. Secondly, this method is still very expensive and cannot be used for low-budget research, in a regular medical office or for mass medical examination. MW (Microwave Tomography) uses electromagnetic radiation in the frequency range from 500 MHz to 5 GHz instead of x-rays. There are several advantages of MW over RT. For example, M / W does not use ionizing radiation, which makes it completely harmless; MVT is sensitive to the functioning processes of living tissues, which makes it useful for a wide range of studies and diagnostics. MW is also superior to MRI, as it can be performed in the mode of high speed measurement and image processing. It can visualize the heartbeat and other rapidly progressing processes, which cannot be done with MRI. For example, it was determined that microwave tomography is able to detect changes in myocardial blood supply, tissue hypoxia, myocardial ischemia and heart attack, that is, it is suitable for functional imaging.

However, the disadvantage of existing MW methods and devices is the relatively low spatial resolution, limited by the wavelength of the radiation used. All known experimental devices show a spatial resolution of the order of 1 cm. This is still useful for some applications, but it is far behind the capabilities of modern MRI.

So, the well-known "System and method for non-destructive functional imaging and mapping of the electrical excitation of biological tissues using electromagnetic tomography and spectroscopy" according to US patent No. 7239731 (IPC G06K 9/00, published 03.07.2007).

The known invention relates to electromagnetic tomography and spectroscopy, and, in particular, to non-invasive functional imaging, detection and mapping of the electrical excitation of biological tissue using electromagnetic tomography and spectroscopy using a sensitive material (solution) with the introduction into the biological tissue or circulation system, about which it is known that it has dielectric properties, which is a function of the electric field produced by biological excited tissue. The invention includes several versions of the system that distinguish based on the multiple frequency, polarization and types of sensitive material (solution) used. In addition, the invention includes computer-implemented software specifically designed and adapted for a system and method for non-invasively detecting and mapping the electrical excitation of biological tissue with a graphical and three-dimensional tomographic imaging interface.

A microwave tomographic device for spectroscopy is known and a method for its implementation (application RU No. 96124805 for an invention, applicant Dze Carolinas Hart Institute (US), IPC АВВ 5/05, published on 02.27.1999). A method for microwave tomographic spectroscopy of tissue without violating its integrity comprises the steps of: placing a microwave radiation power source; placing multiple microwave emitters-receivers; controlling a plurality of microwave receiver emitters so that the plurality of receiver emitters are capable of emitting multi-frequency microwave radiation from a power source to a plurality of receiver emitters that receive microwave radiation; placing a separation medium between the emitting and receiving microwave emitters-receivers; the premises of the test tissue, which will be exposed to radiation, inside the separation medium; transmission of microwave radiation from microwave emitters-receivers; reception of microwave radiation by microwave emitters-receivers after its interaction with tissue; measuring changes in microwave radiation after interaction with tissue. The measurement step includes solving the inverse problem for calculating the tomographic image of the tissue, based on the measured change in microwave radiation, and this solution to the inverse problem contains the steps of: determining the component of the functional formation; using a gradient forming component; calculation of the minimization parameter "tau"; as well as performing the calculation of ε *.

A known electromagnetic tomograph and image acquisition method (application WO 2011027127 for an invention, applicants Univ Keele (GB), Semenov Serguei (GB), IPC: A61B 5/053, G01N 23/04, publ. 03/10/2011). A method of obtaining an image on electromagnetic radiation with a frequency in the range from 0.05 to 10 GHz, comprising emitting electromagnetic radiation with a frequency in the range from 0.05 to 10 GHz from a selected one of the many emitters, measuring data representing electromagnetic radiation received by a plurality of receivers after interacting with the object, and obtaining an image based on measurement data. At the same time, when receiving the image, they are not taken into account: the measured data in the period t ₂ , the duration of the second period of time t ₂ , and are set in such a way that the electromagnetic radiation includes that radiation that does not pass through the object.

However, a common drawback of the known methods and devices is the obtaining of an image with insufficiently high spatial resolution, which is due to the physical principle - the diffraction limit. This limitation can be circumvented only due to additional measurements and special processing of the received information.

There is another method of tomographic research of microscopic objects and a scanning microscope for its implementation (patent RU No. 2413204 for an invention, patent holder Limited Liability Company "Center for Innovative Technologies-ES", IPC G01N 23/04, publ. 02.27.2011). The invention relates to the field of research of materials using electromagnetic radiation, followed by obtaining an image of the object under study, namely, scanning methods and devices for tomographic study of the two-dimensional structure of flat objects. The method includes scanning the monitoring object with a beam of electromagnetic radiation with a discrete change in the angular position of the monitoring object relative to the electromagnetic radiation beam, registering the intensity of radiation transmitted through the monitoring object during scanning, and processing the received information with subsequent restoration of the structure of the object based on it. When scanning, a beam of electromagnetic radiation is formed with discretely variable dimensions of the beam cross section, while one of the cross sections of the beam is changed by a value corresponding to the required resolution, the radiation intensity is recorded after each change in the cross section of the beam section, and the difference is calculated during processing two successively recorded intensities to obtain the set of values used to recover structure of the object. EFFECT: increased resolution of a scanning microscope. Thus, in the known technical solution through the use of discretely variable dimensions of the cross section of the beam of electromagnetic radiation, it is possible to achieve an increase in resolution. But this method is not applicable for obtaining three-dimensional images, since it is applicable only for thin films.

Closest to the claimed invention is a microwave tomographic device for spectroscopy and a method for its implementation (Patent RU No. 2238033 for an invention, patentee Dze Carolinas Hart Institute (US), IPC АВВ 5/05, published on October 20, 2004), which was selected as a prototype . The known invention relates to medical equipment, namely to devices and methods for obtaining an internal structural image of biological tissues. A device for microwave tomographic tissue spectroscopy includes a plurality of microwave emitters-receivers spatially oriented to tissue, a matching medium, a control device for selective control through a channel forming subsystem, the encoder of which is configured to encode microwave radiation and decode the received signal from a plurality of emitters-receivers. Moreover, when implementing the method for identifying discrete signals with respect to antenna arrays, decoding is carried out with the possibility of determining the emitter-receiver emitting it. When carrying out microwave tomographic spectroscopy, a plurality of emitters-receivers are controlled so that they emit multi-frequency microwave radiation through the channel forming system. Using the invention allows a quick assessment of the biological function and anatomical structure in real time.

The disadvantage of the prototype is also the low spatial resolution of images obtained using it, which imposes serious limitations on the use of this method, since it does not allow to detect a large number of changes in tissues and organs.

The main factor determining the spatial resolution of the MW is the diffraction resolution limit, which depends on the wavelength of the probe radiation. An improvement in spatial resolution can theoretically be achieved by reducing the wavelength of the probe radiation. However, in practice, this leads to an increase in the absorption of radiation in biological objects and the inability to shine through them. The optimal frequency range for MW is 1-3 GHz.

Thus, the technical problem that currently exists is the insufficient quality of images obtained using microwave tomography, which greatly limits the possibilities of its application. The creation of the proposed technical solution is aimed at solving this technical problem, namely the creation of a method of microwave tomography ultra-high resolution.

The technical result of the claimed invention is to improve the quality of images obtained using MW by increasing their spatial resolution to 1 mm or more.

The specified technical result is achieved due to the fact that in the method of microwave tomography of ultra-high resolution of the tissue without violating its integrity, comprising the steps of placing a microwave radiation power source, placing transmitting and receiving antennas of microwave radiation, controlling receiving and transmitting antennas of microwave radiation, placing matching the medium between the transmitting and receiving microwave transmitting and receiving antennas, place tissue that will be irradiated inside of the dividing medium, the microwave radiation is received by the transceiver antennas after its interaction with the tissue and the change in the microwave radiation after the interaction with the tissue is measured, the measurement results are processed and a three-dimensional tomographic image of the tissue is constructed, it is proposed:

- control the transmit-receive antennas so that each of them emits microwave radiation, the axis of the radiation pattern of which discretely changes its angular position in the plane of radiation, that is, with the help of each transmit-receive antenna, make several measurements corresponding to each angular position of the axis of the radiation pattern radiation, and the step by which the direction of the axis of the radiation pattern of the scanning radiation corresponds to the required resolution,

- build a set of tomograms, each of which corresponds to a certain radiation pattern,

- summarize the set of tomograms and process the result using the inverse filter,

- the final tomographic image of the tissue to build in accordance with the formula:

where T (x, y, z) is the superposition of individual images,

K (x, y, z) is the analytical approximation of a two-dimensional spatial filter,

x, y, z are spatial variables,

u - Fourier variable conjugate to x,

v is the Fourier variable conjugate to y,

- двумерные Фурье образы соответствующих функций Т и K по переменным х и у,

- two-dimensional Fourier images of the corresponding functions T and K with respect to the variables x and y,

α is the regularization parameter,

Ω = u ² + v ² is a regularizing operator,

* - a sign of complex pairing.

Superhigh resolution in this context refers to methods for obtaining images with a resolution that exceeds the diffraction limit. Such methods are known in radio astronomy and optics, but they were not used in the MVT.

For example, in two-dimensional images obtained using conventional digital photography, spatial resolution is limited not by diffraction, but by the size of the detector in the photomatrix. The larger the size of the detector, the worse the resolution. If you take many photographs of the same object taken from slightly different angles, then combining them together and applying a special image processing method called the inverse filter, you can repeatedly improve the spatial resolution of the original photo.

In the claimed invention, the authors propose to use a similar principle for microwave tomography.

In the theory of signal processing, a filter refers to a linear transformation of a signal of the form:

where Φ (y) is the signal function, K (x) is the filter core function, F (x) is the signal function after filtering. The inverse filter is the procedure of "restoration" of the signal Ф (y) from the known filtered signal F (x). The inverse filter can be represented as a convolution:

where the function of the inverse filter core can be expressed in terms of the function of the direct filter and the noise characteristics of the measurement.

Consider the proposed technical solution in more detail.

The invention is illustrated by the following figures: FIG. 1, which shows a conventional radiation pattern of a transceiver antenna; FIG. 2, which shows the radiation patterns of the antenna, in which the direction of the axis changes sequentially with a certain step; FIG. 3, which shows the investigated object in the radiation field of the antenna with a constant radiation pattern; FIG. 4, which shows the investigated object in the radiation field of an antenna with a varying radiation pattern; FIG. 5, which shows the location of the transceiver antennas relative to the investigated object, where: 1 - antenna; 2 - object; d, d1-d5 - radiation pattern.

A conventional transceiver antenna emits an electromagnetic field with some radiation pattern d (see Fig. 1). The radiation pattern is the radiation intensity as a function of angle (intensity in polar coordinates). The radiation pattern is usually symmetrical about the axis. In studies, it is desirable to have a narrow diagram, but there is a limitation associated with the diffraction phenomenon. The authors propose to control a number of transmitting and transmitting antennas so that each of them emits microwave radiation, the axis of the radiation pattern of which discretely changes its angular position in the plane of radiation, that is, with the help of each transmitting and transmitting antenna, several measurements are made corresponding to each angular position of the axis radiation patterns.

In FIG. 2 antenna 1 has five different positions (configurations) d1-d5 for the radiation pattern. Those. The radiation pattern is as if rotated in the direction of the arrow. In this case, measurements are made for each fixed position of the radiation pattern separately. The more such provisions, the better.

If the object 2, having dimensions smaller than the wavelength of the incident radiation, enters the field of the antenna 1 (see Fig. 3), then it scatters the electromagnetic field as a dipole. The internal structure of this object does not affect the scattered radiation, so it cannot be restored using the scattered radiation received from the antenna 1 with a fixed radiation pattern d. However, if several measurements are used with a varying (“scanning”, “rotating”) radiation pattern d, this changes the matter (see Fig. 5). Measurements with a diagram in position “1” more cover the “upper” part of the object. Measurements with a diagram in position “2” more cover the “lower” part of the object, therefore together they carry information about the internal structure of object 2, which is described by the distribution of dielectric constant:

This function is the subject of tomographic research and reflects the anatomical and physiological structure of a biological object.

Microwave radiation is described by the electric field vector

The vector of the electric field can be represented as the sum of the incident field and the scattered field:

The incident field is generated by antenna 1 in the tomograph without object 2. Information about object 2 is contained in the scattered field. The incident field is calculated, knowing the design of the antenna 1, the geometry of the tomograph and the boundary conditions. Typically, the Kirchhoff integral is used for these purposes.

Knowing the distribution of the dielectric constant of the medium and the object, the scattered field can be calculated by solving the direct problem for Maxwell's equations or for an inhomogeneous wave equation:

where i, j are the indices of the transmitting and receiving antennas.

The heterogeneity of the object is described by the formulas:

ω is the circular frequency of the incident radiation, and c is the speed of light. Hereinafter, the GHS system of units is used. As a rule, the tomograph is filled with an immersion fluid for better electrical contact at the object boundary. In view of this, the scattered electric field can be considered incapable of reflection from the surface of the tomograph. Therefore, the reflectionless boundary conditions were used to solve the system of equations (3).

The authors of [1] have developed an effective and quick way to solve (3) with reflectionless and zero boundary conditions. Comparison with exact solutions confirmed the reliability of this method for solving direct problems in different conditions, including cases of solving equations with discontinuous coefficients.

To describe the operation of the receiving antennas, the principle of reciprocity was used. The signal of the receiving antenna number j, when only the transmitting antenna number i, - S _{i, j is} working, is calculated using the solution of equation (3) for the direct wave and the solution of a similar equation for the backward propagating wave [1].

In order to solve the inverse problem, that is, knowing the measured values of the signals at the antennas S _{i, j} , to calculate the distribution values of the dielectric constant in the volume of the object, the variational approach was applied [2].

should be minimized due to variations in the dielectric constant ε. The indices T and E mean theoretical and experimental. Amounts are taken for all transmitting and receiving antennas.

Functional (5) is proposed to be minimized by the gradient descent method. It was shown in [1, 2] that the gradient of functional (5) can be expressed in terms of a combination of solutions of the direct problem for directly propagating and back propagating waves, based on the numerical solution of equation (3) with reflectionless and fixed boundary conditions.

As noted earlier, the optimal frequency range is 1-3 GHz.

For each direction of radiation of the antennas with number j, the scattered radiation signal S _{mnj is recorded} , where the first two indices number the transmitting and receiving antennas.

Due to the sensitivity of the solution to this problem, instead of minimizing the functional (5), its regularized version should be minimized:

where: α is the regularization parameter, Λ is the second-order stabilizing operator [7].

This minimization and solution is carried out in the following iterative process:

вычисляется по формуле:Functional Gradient

calculated by the formula:

- обратно распространяющаяся рассеянная волна, * - комплексное сопряжение.where: A is the normalization constant,

- backscattered scattered wave, * - complex conjugation.

Directly propagating and backward propagating waves are solutions of the equations:

The source of the backward-propagating wave field is calculated by the formula:

- функция Грина для однородного пространства,

- фазовые центры пронимающих антенн.Where:

- Green's function for homogeneous space,

- phase centers of penetrating antennas.

The step of the iterative process (7) is calculated by the formula:

The parameter β is selected empirically from the interval (0,1). The parameter γ has an initial value of unity. If the value of the functional decreases at one iterative step, then this parameter increases by 20%, otherwise it decreases by 20%. The process (7) is terminated if the solution is stabilized.

After the image is obtained for each configuration of the emitting field, the superposition of all images is calculated:

where: T is the superposition of individual images ε _j . N is the number of elements in superposition.

By analogy with the subpixel super-resolution method [7], the superposition T can be approximately represented as a convolution of the true distribution of dielectric constant with a core of a known type:

The analytical form of the core of this equation is quite complex and depends on the antenna pattern. We propose using an analytical approximation in the form of a two-dimensional Gaussian function with an empirically selected dispersion parameter. Equation (7) should be solved using regularization and the choice of the regularization parameter by the residual method [7]. The final formula for a high-resolution three-dimensional MB tomogram is:

и

- двумерные фурье образы соответствующих функций Т и K по переменным x и y. Знак * означает комплексное сопряжение. Параметр регуляризации а выбирается в соответствии с шумом измерения [7]. Регуляризущий оператор Ω=u²+ν².Where

and

are two-dimensional Fourier images of the corresponding functions T and K with respect to the variables x and y. The sign * means complex conjugation. The regularization parameter a is selected in accordance with the measurement noise [7]. The regularizing operator Ω = u ² + ν ² .

The measurements are carried out as follows. The axes of the radiation patterns of all antennas are set to the extreme left position. One 3-dimensional tomogram is calculated. For this, an iterative method is used (formula 7). After that, all the diagrams are rotated a small step to the right, and the process repeats. After the diagrams have reached the extreme right position, the process is completed. The result is a set of tomograms, each of which corresponds to a specific position of the antenna diagram. Then they are simply summed up (formula 13). All tomograms, both individual and total, have a spatial resolution no better than the wavelength of the probe radiation. However, the total tomogram is a mathematical convolution (convolution) of an ideal image and a known function (formula 14). To extract an ideal (actually improved) image, you need to mathematically reverse this convolution (make deconvolution). The best way to do this is to use the inverse filter method (formula 15).

Thus, due to the restoration of the high-frequency components of the spatial spectrum of the image of the object achieved by using angular scanning of the radiation pattern of the transmitting antennas, a high spatial image of the object under study is achieved. The initial loss of the high-frequency components of the spatial spectrum is due to diffraction of microwave radiation.

The management of transceiver antennas is implemented using software. The radiation parameters (carrier frequency, pulse repetition rate and duty cycle) are determined in advance and set using a personal computer. Antennas are pre-numbered and served in turn by the program, as well as receiving antennas. Microwave (microwave) voltage is generated by the generator (s), after which it is fed to switches (keys), which redirect it via microwave channels to transmitting antennas. Transmitting antennas convert a microwave signal into an electromagnetic wave. The receiving path works in the reverse order: antenna-microwave signal-switch-low-frequency signal-analog-to-digital converter (ADC) -computer program-computer memory.

In addition to the measuring channel, a control channel with known losses and phase incursion is used. The control channel is a microwave channel (for example, a coaxial cable) between the generator and the receiving antenna, bypassing the transmitting antennas and the monitoring object. It is mixed with a useful signal and allows you to measure changes in the amplitude and phase of the signal that occur due to the object, and not due to the passage of the signal through the cables. In this case, a heterodyne registration method is used.

Next, the resulting image is processed using a digital inverse filter.

Bibliography

1. Bulyshev A.E., Semenov S.Y., Souvorov A.E., Svenson R.H., Nazarov A.G., Sizov Y.E., Tatsis G.P. "Three dimensional microwave tomography. Theory and computer experiments in scalar approximation", Inverse Problems, 2000, 16, 863-875.

2. Bulyshev A.E., Souvorov A.E., Semenov S.Y., Posukh V.G., Sizov Y.E. "Three-dimensional Vector Microwave Tomography. Theory and Computational experiments", Inverse Problems, 2004, 20, No. 4, 1238.

3. Semenov S.Y., Svenson R.H., Bulyshev A.E., Souvorov A.E., Nazarov A.G., Sizov Y.E., Posukh V.G., Pavlovsky A.V., Repin P.N., Tatsis G.P. "Spatial resolution of microwave tomography for detection of the myocardial ischemia and infarction. Experimental study on two-dimensional models", IEEE Trans MTT, 2000, 48, 4, 538-544.

4. Semenov S.Y., Svenson R.H., Boulyshev A.E., Souvorov A.E., Nazarov A.G., Sizov Y.E., Posukh V.G., Pavlovsky A., Repin P.N., Starostin A.N., Voinov B., Tatsis G.P., Baranov V.Y. "Three-dimensional microwave tomography: initial experimental imaging of animals", IEEE Trans B ME, 2002, 49, 1, 55-63.

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Claims (3)

A method of microwave tomography of ultra-high resolution tissue without violating its integrity, comprising the steps of placing a microwave radiation power source and microwave transmitting and receiving antennas, controlling microwave transmitting and receiving antennas, placing a matching medium between transmitting and receiving microwave antennas, placing tissue, which will be irradiated, inside the separating medium, receive microwave radiation with transceiver antennas after interaction its interaction with the tissue and measure the change in microwave radiation after interacting with the tissue, process the measurement results and build a three-dimensional tomographic image of the tissue, characterized in that the transceiver antennas are controlled so that each of them emits microwave radiation, the axis of the radiation pattern of which would discretely change its angular position in the plane of radiation, that is, with the help of each transceiver antenna, several measurements are carried out corresponding to each angular position the axis of the radiation pattern, and the step by which the direction of the axis of the scanning radiation pattern corresponds to the required resolution, a set of tomograms are built, each of which corresponds to a certain radiation pattern, then they are summed up and the result is processed using the inverse filter, The final tomographic image of the tissue is constructed in accordance with the formula:

where T (x, y, z) is a superposition of individual images; K (x, y, z) is the analytical approximation of a two-dimensional spatial filter; x, y, z are spatial variables; u is the Fourier variable conjugate to x; v is the Fourier variable conjugate to y;

- two-dimensional Fourier images of the corresponding functions T and K with respect to the variables x and y; α is the regularization parameter; Ω = u ² + v ² is the regularizing operator; * - a sign of complex pairing.

Images