Electric tomography method and electric tomography device

Abstract

This electric tomography device visualizes, by utilizing a complex sensitivity matrix, at least one of the distribution of the dielectric constant and the distribution of the conductivity of a measurement object.

Description

Electrical tomography method and electrical tomography apparatus

[0001] The present invention relates to an electrical tomography method and an electrical tomography apparatus.This application claims priority to Japanese Patent Application No. 2023-170589, filed on September 29, 2023, the contents of which are incorporated herein by reference.

[0002] Cell and tissue imaging technology is an important technology in many fields. In the medical field, imaging the structure and function of cells and tissues in vivo is expected to contribute to the diagnosis of diseases and the development of treatments. In the field of drug discovery, imaging technology is applied to observe how drugs are taken up into cells and at what site they exert their effects in order to understand how drugs act within cells. Furthermore, cell and tissue imaging technology is also used to find disease-specific targets.

[0003] Common cell and tissue imaging techniques include fluorescence microscopy, electron microscopy, and super-resolution microscopy. These techniques are used to analyze cell morphology and function, protein localization (determining the location and amount of specific proteins and analyzing their function and interactions within the cell), cell motility (observing cell movement and morphological changes to analyze physiological or pathological processes in cells), and drug testing and discovery research (analyzing intracellular pharmacokinetics and interactions to evaluate the efficacy and toxicity of new drugs). However, these techniques have the following drawbacks:

[0004] The first issue is the limited resolution. Optical microscopy has a resolution limit due to the wavelength constraints of visible light. Although the development of super-resolution microscopy has overcome some of these limitations, there are still limitations on resolution.

[0005] Second, it is invasive: fluorescence microscopy requires the attachment of fluorescent dyes or protein tags to the specimen, which can potentially affect physiological processes and interactions within the cells.

[0006] The third issue is the limitation of temporal resolution. When observing cellular dynamics and physiological processes, high temporal resolution is required, but some techniques have limitations in terms of temporal resolution.

[0007] Due to the problems described above, conventional imaging technologies have difficulty in providing rapid, real-time, non-invasive imaging on-site, preventing their use at the point of care or accelerating the drug discovery process. Therefore, imaging using electrical tomography (ET) technology may be a solution to these problems. ET technology plays an important role in process management and control in industrial plants, and in recent years, its application to cell or tissue observation in medical care and drug discovery has been explored.

[0008] For example, as a technique for applying ET technology to imaging of cells and tissues, Non-Patent Document 1 discloses a technique for imaging cell concentration and dead cells in cell culture using a printed circuit board. Also, Non-Patent Document 2 discloses a technique for imaging the distribution of extracellular ion concentration due to ion transport inside and outside of cells.

[0009] Y. Yang, J. Jia, S. Smit, N. Jamil, W. Gamal, and P. O. Bagnaninchi, “A Miniature Electrical Impedance Tomography Sensor and 3-D Image Reconstruction for Cell Imaging”, IEEE Sensors Journal, Vol. 17(2), 514-523, 2017. Daisuke Kawashima, Yuki Tsubasa, Songshi Li, Masahiro Takei, “Non-invasive imaging of ion concentration distribution around cell spheroids by electrical impedance tomographic sensor printed on circuit board under temporal compensation by ion transport impedance model”, Biosensors and Bioelectronics, Elsevier, Vol. 212(15), 114432, 2022.

[0010] The technology described in Non-Patent Documents 1 and 2 uses a multi-electrode sensor mounted on a printed circuit board to measure impedance changes caused by cellular or extracellular conductivity distribution, and by reconstructing the conductivity distribution using inverse problem analysis, it has been successful in imaging cellular concentrations and extracellular ion concentrations.

[0011] However, conventional ET techniques have limitations in their sensitivity and accuracy, primarily due to the sensitivity matrix representation used in image reconstruction. The sensitivity matrix used in conventional ET techniques is based on electrical conductivity and is not generalized to dielectric spectroscopy. In dielectric spectroscopy, phenomena should be expressed using two physical properties, electrical conductivity and permittivity, in the frequency range used in ET. However, sensitivity matrices currently do not include permittivity, resulting in reconstructed images that do not accurately reflect the true phenomena. This leads to the following problems: 1) the inability to reconstruct the permittivity; 2) the inability to reflect the frequency characteristics of permittivity and conductivity; and 3) the inability to reconstruct images that accurately reflect the dielectric properties of the target object (cells, cytoplasm, nuclei, and other cellular components), making it impossible to observe detailed cellular information (e.g., cell structure and pharmacokinetics).

[0012] The present invention has been made in consideration of the above circumstances, and aims to provide an electrical tomography method and an electrical tomography device that can image at least one of the conductivity distribution and the permittivity distribution of an object to be measured by utilizing a sensitivity matrix expressed in complex numbers, which has not been taken into account in conventional electrical tomography.

[0013] In order to solve the above problems, the present invention proposes the following means. [1] An electrical tomography method according to one aspect of the present invention uses a complex sensitivity matrix to visualize at least one of a dielectric constant distribution and a conductivity distribution of a measurement object. [2] In the electrical tomography method described in [1] above, the complex sensitivity matrix may be expressed by the following equation (1): In the formula (1), J com : complex sensitivity matrix, R: resistance component (real part of complex impedance), X: reactance component (real part of complex impedance), σ: conductivity, ε: permittivity, ω: angular frequency, ε ０: permittivity of vacuum, T: transpose symbol. [3] In the electrical tomography method described in [2] above, the complex sensitivity matrix may be calculated by partial derivatives of a complex sensitivity matrix based on the Geselowitz theory. [4] In the electrical tomography method described in [3] above, the complex sensitivity matrix may be calculated by partial derivatives of a complex sensitivity matrix derived from equation (2) which expresses the relationship between complex impedance and a complex potential field obtained by modifying the Geselowitz theory. In the above formula (2), Z ｍ * : Complex impedance measured at the mth electrode pattern expressed by equation (3), φ * : Complex potential distribution expressed by equation (4), σ n * : Complex conductivity of the nth mesh expressed by equation (5), Ω n : the area of ​​the nth mesh, and in the above formula (3), R ｍ : Resistance component of the complex impedance measured at the mth electrode pattern, X ｍ : the reactance component of the complex impedance measured in the mth electrode pattern, in the above formula (4), φ': the value of the real part of the potential, φ'': the value of the imaginary part of the potential, in the above formula (5), σ ｎ : conductivity of the nth mesh, ω: angular frequency, ε ０ : dielectric constant of vacuum, ε ｎ：is the permittivity of the nth mesh, and in the above formulas (3) to (5), j represents the imaginary unit. [5] In the electrical tomography method described in [2] above, the complex sensitivity matrix may be calculated using partial derivatives derived from perturbations of the permittivity and conductivity. [6] In the electrical tomography method described in any of [1] to [5] above, the distribution of at least one of the permittivity and conductivity of the object to be measured in multiple dimensions may be visualized. [7] In the electrical tomography method described in [6] above, the multiple dimensions may be two or more dimensions selected from the group consisting of frequency, time, and three-dimensional space. [8] In the electrical tomography method described in any of [1] to [7] above, the object to be measured may be a biological or non-biological substance. [9] In the electrical tomography method described in [8] above, the biological substance may be one or more selected from the group consisting of cells, tissues, living organisms, and biological constituents.

[10] In the electrical tomography method described in [8] above, the non-biological substance may be any one or more selected from the group consisting of a liquid containing bubbles, a powder, a slurry, and a plastic.

[11] In the electrical tomography method described in any one of [1] to

[10] above, the measurement object may be a cell or tissue, and the concentration of ions flowing in and out of ion channels in the measurement object may be visualized by applying a potential-controlled stimulus to the measurement object from outside the measurement object.

[12] In the electrical tomography method described in

[11] above, the movement and activity of the measurement object may be controlled by applying a constant voltage or a periodically changing voltage to the measurement object using a single or multiple electrodes.

[0014]

[13] According to another aspect of the present invention, an electrical tomography apparatus is provided with three or more electrodes, and includes a calculation unit that calculates a complex sensitivity matrix, and a display unit that displays at least one of a dielectric constant distribution and a conductivity distribution of a measurement object based on the complex sensitivity matrix.

[14] In the electrical tomography apparatus described in

[13] above, the complex sensitivity matrix may be expressed by the following equation (1): In the formula (1), J com : complex sensitivity matrix, R: resistance component (real part of complex impedance), X: reactance component (real part of complex impedance), σ: conductivity, ε: permittivity, ω: angular frequency, ε ０ : permittivity of vacuum, T: transpose symbol.

[15] In the electrical tomography apparatus described in

[14] above, the calculation unit may calculate the complex sensitivity matrix using a partial derivative of the complex sensitivity matrix based on the Geselowitz theory.

[16] In the electrical tomography apparatus described in

[15] above, the calculation unit may derive the partial derivative of the complex sensitivity matrix from equation (2) which expresses the relationship between the complex impedance and the complex potential field obtained by modifying the Geselowitz theory. In the above formula (2), Z ｍ * : Complex impedance measured at the mth electrode pattern expressed by equation (3), φ * : Complex potential distribution expressed by equation (4), σ n * : Complex conductivity of the nth mesh expressed by equation (5), Ω n : the area of ​​the nth mesh, and in the above formula (3), R ｍ : Resistance component of the complex impedance measured at the mth electrode pattern, X ｍ : the reactance component of the complex impedance measured in the mth electrode pattern, in the above formula (4), φ': the value of the real part of the potential, φ'': the value of the imaginary part of the potential, in the above formula (5), σ ｎ : conductivity of the nth mesh, ω: angular frequency, ε ０ : dielectric constant of vacuum, ε ｎ：is the permittivity of the nth mesh, and in the above formulas (3) to (5), j represents the imaginary unit.

[17] In the electrical tomography apparatus described in

[14] above, the calculation unit may calculate partial derivatives derived from perturbations of the permittivity and conductivity, and calculate the complex sensitivity matrix from the partial derivatives.

[18] In the electrical tomography apparatus described in any of

[13] to

[17] above, the display unit may display at least one of a multidimensional permittivity distribution and a multidimensional conductivity distribution of the object to be measured.

[19] In the electrical tomography apparatus described in

[18] above, the multidimensional may be two or more dimensions selected from the group consisting of five dimensions: frequency, time, and three-dimensional space.

[20] In the electrical tomography apparatus described in any of

[13] to

[19] above, the object to be measured may be a biological or non-biological substance.

[21] In the electrical tomography apparatus described in

[20] above, the biological substance may be one or more selected from the group consisting of cells, tissues, living organisms, and biological constituents.

[22] In the electrical tomography apparatus described in

[20] above, the non-biological substance may be one or more selected from the group consisting of a liquid containing bubbles, a powder, a slurry, and a plastic.

[23] The electrical tomography apparatus described in any of

[13] to

[22] above may include a potential control unit that controls the potential of the electrodes, the measurement object being a cell or tissue, the potential control unit applying a potential-controlled stimulus to the measurement object from outside the measurement object, and the display unit displaying the distribution of ion concentrations flowing in and out of the ion channels of the measurement object.

[24] In the electrical tomography apparatus described in

[23] above, the potential control unit may apply a constant or periodically changing voltage to the measurement object using a single or multiple electrodes to control the movement and activity of the measurement object.

[0015] According to the above aspect of the present invention, by utilizing a sensitivity matrix expressed in complex numbers, which was not taken into account in conventional electrical tomography, it is possible to image at least one of the conductivity distribution and the permittivity distribution of the object to be measured.

[0016] 1 is a diagram showing an outline of the configuration of an electrical tomography apparatus according to an embodiment of the present invention. It is a functional block diagram of the electrical tomography apparatus 1 according to the embodiment. It shows the J when m and n are changed at a frequency f=1000 Hz, 0.1 MHz, or 1 MHz. R,σ m , n , J R,ε m , n , J X,σ m , n , and J. X,ε m , n 1 is a graph showing the change in the spatial average value of the dielectric constant <Δε> with frequency for each homogeneous field in the inventive example of Example 1; and FIG. 2 is a graph showing the change in the spatial average value of the dielectric constant <Δε> with frequency for each homogeneous field in the comparative example of Example 1. (a) is a microscope image of the cell spheroid in Example 2A, (b) is a stereomicroscope image of the cell spheroid placed on the measurement area of ​​the electrical tomography device and the electrodes arranged around the measurement area, and (c) is a stereomicroscope image of the cell spheroid placed on the measurement area of ​​the electrical tomography device at time t １ , t ２ , t ３ , and t ４ 1 is a contour diagram showing the distribution of the reconstructed conductivity Δσ and permittivity Δε at time t for each frequency in Example 2B. １ , t ２ , t ３ , and t ４1 is a contour diagram showing the distribution of the reconstructed electrical conductivity Δσ and permittivity Δε in Example 4. (a) is a microscopic image of a single cell in Example 3, (b) is an image of a single cell imaged by the electrical tomography method of the present invention, and (c) is an image obtained by superimposing (a) and (b). (a) is a diagram of a printed circuit board in the electrical tomography device used in Example 4, and (b) is a diagram showing multiple electrodes and measurement areas on the printed circuit board. (b) is a graph showing the time-dependent change in the voltage applied to the potential control electrode and the measured impedance in Example 4, where (a) is a graph showing the change in impedance in the absence of an inhibitor, and (b) is a graph showing the change in impedance in the presence of an inhibitor. (c) is a contour diagram showing the image of the ion concentration based on the impedance in Example 4. (d) is a graph showing the inhibitor concentration C in hERG inhibition in Example 5. ｄ 1 is a graph showing the change in conductivity over time for each sample. 2 is a graph showing inhibition curves for an example of the present invention and a conventional example in Example 5.

[0017] <Electrical tomography apparatus> An electrical tomography apparatus according to a first embodiment of the present invention will be described with reference to the drawings. Note that the dimensions and ratios of each component in the drawings do not represent the actual dimensions and ratios of each component.

[0018] 1 is a diagram showing the general configuration of an electrical tomography apparatus 1 according to this embodiment. The electrical tomography apparatus 1 includes a current application device 11, a multiplexer 12, a printed circuit board 13, a plurality of electrodes 14, a connector 15, a display 16, a control device 17, and electrical wires 18.

[0019] The current application device 11 is a device that applies a current to the electrodes 14 arranged on the printed circuit board 13. The current application device 11 is, for example, an impedance analyzer that has a function of applying a current to the electrodes 14 while changing the frequency and amplitude.

[0020] The multiplexer 12 is a device that switches between the electrodes 14 to which current is applied by the current application device 11 among the plurality of electrodes 14. The multiplexer 12 has a function of determining a current application voltage measurement pattern (a pattern in which two electrodes 14 are selected in order from the plurality of electrodes 14, a current is applied, and a voltage is measured sequentially). That is, two of the electrodes 14 are selected, a current is applied, and two of the electrodes 14 are further selected, and a voltage is measured.

[0021] A plurality of electrodes 14 and electric wires 18 connecting each electrode 14 to the multiplexer 12 are mounted on the printed circuit board 13. The electric wires 18 and the printed circuit board 13 are connected by a connector 15.

[0022] The number of electrodes 14 is, for example, three or more, with no particular upper limit, and the more electrodes 14 there are, the higher the resolution of the image that can be displayed by the display 16. The number of electrodes 14 is preferably eight or more, and more preferably sixteen or more. The number of electrodes 14 may be 32 or less, or may be 16 or less.

[0023] The placement of the electrodes 14 is not particularly limited as long as they are arranged around the object to be measured and can be determined according to the shape of the object to be measured. However, to suppress variations in the measured voltage, it is preferable that the electrodes 14 be arranged at equal intervals. However, some of the electrodes 14 may be arranged unevenly around the object to be measured, and the spacing between the electrodes 14 may be even or uneven. The unevenness or non-uniformity of the electrodes 14 is corrected in the calculation of a sensitivity matrix expressed in complex numbers (complex sensitivity matrix). In FIG. 1, eight electrodes are arranged at equal intervals around the measurement area A.

[0024] Furthermore, the electrode 14 can also be used to control the potential of cells or tissues. In this case, the electrode 14 is placed, for example, within the measurement region A. The electrode 14 can image at least one of the permittivity and the conductivity while controlling the ion channel activity.

[0025] The display 16 displays an image of at least one of the dielectric constant distribution and the conductivity distribution of the object to be measured. The display 16 may be a known display, but preferably has sufficient resolution according to the number of meshes.

[0026] The control device 17 controls various operations of the electrical tomography apparatus 1. The control device 17 includes a storage device such as a central processing unit (CPU), a read-only memory (ROM), a random access memory (RAM), or a hard disk drive (HDD) / solid state drive (SSD). The control device 17 is realized, for example, by the CPU executing a predetermined program. The program may be acquired via a recording medium or a network. Alternatively, a dedicated hardware configuration may be used to realize the configuration of the electrical tomography apparatus 1. Each component will be described below.

[0027] 2 is a functional block diagram of the electrical tomography apparatus 1 according to this embodiment. As shown in FIG. 2, the electrical tomography apparatus 1 includes a control unit 21, a calculation unit 22, a display unit 23, and a storage unit 24.

[0028] The control unit 21 has a function of controlling the overall operation of the electrical tomography apparatus 1. The control unit 21 is realized, for example, by causing a CPU included in the control device 17 to execute a program.

[0029] The calculation unit 22 calculates the complex sensitivity matrix, which will be described in detail in the description of the electrical tomography method.

[0030] The display unit 23 displays at least one of the dielectric constant distribution and the conductivity distribution of the object to be measured based on the complex sensitivity matrix. The display unit 23 is realized by the display 16, for example.

[0031] The storage unit 24 stores information necessary for the calculations performed by the calculation unit 22, information related to the calculation process, and calculation results. The storage unit 24 also stores programs for the control unit 21 to perform various controls. The storage unit 24 is realized by a ROM, a RAM, and a HDD or SSD, etc.

[0032] <Electrical Tomography Method> Next, an electrical tomography method according to a second embodiment of the present invention will be described. The electrical tomography method utilizes a complex sensitivity matrix to visualize at least one of the permittivity distribution and the conductivity distribution of a measurement object. The complex sensitivity matrix indicates how much the measured voltage changes when a current is applied in response to a change in the spatially distributed electrical properties (conductivity, permittivity) relative to a reference, and has an imaginary component. The complex sensitivity matrix is ​​expressed by the permittivity, conductivity, and the real and imaginary parts of the complex impedance. The complex sensitivity matrix varies depending on the spatial distribution of the electrical properties of the measurement object, and the electrical property distribution can be calculated by knowing the complex sensitivity matrix. The complex sensitivity matrix is ​​calculated based on a predetermined current application / voltage measurement pattern, mesh coordinates, and coordinates of multiple electrodes.

[0033] A current application voltage measurement pattern refers to a pattern in which two electrodes are selected in sequence from a plurality of (three or more) electrodes, a current is applied, and the potential difference between the electrodes is measured. The number of current application voltage measurement patterns varies depending on the method for measuring the potential difference, such as the adjacent method, the reference method, or the two-terminal method. Hereinafter, the total number of current application voltage measurement patterns is designated as M. Hereinafter, a pattern may be referred to as the mth current application voltage measurement pattern, where m is an integer between 1 and M.

[0034] Next, how to determine mesh coordinates will be explained. For example, to obtain an appropriate resolution, the area where the measurement object is placed (measurement area) is divided into a two-dimensional mesh according to the number of electrodes. For example, if there are eight electrodes, the measurement area can be divided into 64 areas in the x direction and approximately 64 areas in the y direction, resulting in a total of 4096 points, to create a mesh. A mesh refers to each divided area, and the coordinates of each mesh are the mesh coordinates. In the above example, the number of meshes N is 4096. Hereinafter, a mesh may be referred to as the nth mesh among multiple meshes, where n is an integer between 1 and N (the number of meshes).

[0035] An example of a complex sensitivity matrix will be given below to explain an electrical tomography method for visualizing (displaying) the distribution of conductivity and permittivity in five dimensions: frequency, time, and three-dimensional space. Note that the frequency is the frequency of the AC current flowing from the electrodes.

[0036] The linear equation for the inverse problem of five-dimensional electrical tomography is expressed by equation (1), similarly to conventional electrical impedance tomography (EIT).

[0037]

[0038] In formula (1), Z com is a column vector of complex impedances in multiple current application / voltage measurement patterns, and J com is the complex sensitivity matrix, σ com is a column vector of the distribution of complex conductivity. Δ represents the difference from the reference value. The reference value is the value for the measurement area A in a state where no measurement object is placed. For example, if the measurement object is a cell, the value in a state where only the culture medium is placed in the measurement area A is used as the reference value. ΔZ in equation (1) com is expressed as (2), and Δσ com is defined by equation (3).

[0039]

[0040] In equation (2), ΔR is a column vector of the difference between the resistance and the reference value, and ΔX is a column vector of the difference between the reactance and the reference value. In equation (3), Δσ is a column vector of the difference between the conductivity and the reference value, and Δε is a column vector of the difference between the relative permittivity and the reference value. ω is the angular frequency, ε is the ０ is the dielectric constant of a vacuum. Furthermore, M in equation (2) is the total number of current application and voltage measurement patterns, and N in equation (3) is the total number of meshes into which the conductivity distribution is discretized. The sizes of the matrices ΔR, ΔX, Δσ, and Δε are defined as follows, respectively, by equations (4) to (7).

[0041]

[0042] Therefore, Z com , σ com , and the complex sensitivity matrix J com The matrix sizes of are defined as in equations (8) to (10).

[0043]

[0044] From equations (1) to (3), the complex sensitivity matrix J com is expressed by four components as shown in equation (11).

[0045]

[0046] In the above formula (11), J com : complex sensitivity matrix, R: resistance component (real part of complex impedance), X: reactance component (real part of complex impedance), σ: conductivity, ε: permittivity, ω: angular frequency, ε ０ : dielectric constant of vacuum, T: transposition symbol. From equations (1) to (3) and (11), the following equation (12) is obtained.

[0047]

[0048] Complex sensitivity matrix J com A sensitivity matrix formula based on the Geslowitz theory can be applied to derive each component of (13). By modifying the Geslowitz theory, the relationship between the complex impedance and the complex potential field is expressed as follows:

[0049]

[0050] (13) In the formula, Z ｍ * is the complex impedance measured in the m-th current application voltage measurement pattern, and is expressed by equation (14). ｍ is the resistance component of the complex impedance measured at the mth electrode pattern, and X ｍ is the reactance component of the complex impedance measured at the mth electrode pattern. * is the complex potential distribution expressed by equation (15), and φ * (i e ) represents the complex potential field generated by passing current i through the e-th electrode, and φ * (i m ) represents the complex potential field generated by passing current i through the m-th electrode. In equation (15), φ' is the value of the real part of the potential, and φ'' is the value of the imaginary part of the potential. In equation (13), σ ｎ * is the complex conductivity of the nth mesh, and is expressed by equation (16). In equation (16), σ ｎ is the conductivity of the nth mesh, ω is the angular frequency, ε ０ is the dielectric constant of a vacuum, and ε ｎ is the permittivity of the nth mesh. In equation (13), Ω ｎ is the area of ​​the nth mesh. In equations (14) to (16), j represents the imaginary unit. Also, the applied current I ０ Since is a constant value in all measurements, I in equation (13) ０ ２ is ignored in the calculation of the sensitivity matrix. Therefore, by deriving four partial derivatives from equation (13), the complex sensitivity matrix J in equation (11) can be calculated as follows: com These four partial derivatives satisfy the Cauchy-Riemann relationship, that is, the complex sensitivity matrix J com The relationship between the four components is expressed as in equation (17).

[0051]

[0052] From the above, equation (12) can be rewritten as equation (18). In equation (18), J R,σ m , n , J R,ε m , n , J X,σ m , n , and J. X,ε m , n are respectively expressed by equations (19) to (22). In addition, Φ' in equations (19) and (22) indicates the real part on the left side of equation (23), and Φ'' in equations (20) and (21) indicates the imaginary part on the left side of equation (23).

[0053]

[0054] The complex conductivity is imaged by solving the inverse problem of equation (18). As an example, the complex conductivity is imaged by image reconstruction using Tikhonov regularization or Gauss-Newton numerical optimization. Note that the method for imaging the complex conductivity is not limited to these. The real part of the complex conductivity represents the conductivity, and the imaginary part represents the permittivity. Figure 3 shows the J when m and n are changed at a frequency f = 1000 Hz, 0.1 MHz, or 1 MHz. R,σ m , n , J R,ε m , n , J X,σ m , n , and J. X,ε m , n The graph shows the values ​​of J R,σ m , n , J R,ε m , n , J X,σ m , n , and J. X,ε m , n varies with frequency, and the complex sensitivity matrix J com It is shown that is a function of frequency.

[0055] In this embodiment, the target may be a biological substance or a non-biological substance.

[0056] The biological substance is, for example, one or more selected from the group consisting of cells, tissues, living organisms, and biological constituents, such as ions, proteins, organelles, and cell nuclei.

[0057] Non-biological substances are not substances collected from living organisms, but are generated, for example, during the manufacturing process of industrial products. Examples of non-biological substances include liquids, powders, slurries, and plastics containing gas bubbles. Therefore, the biological substance may be one or more selected from the group consisting of liquids, powders, slurries, and plastics containing gas bubbles.

[0058] In the electrical tomography method according to this embodiment, the subject is a cell or tissue, and potential-controlled stimulation is applied to the subject from outside the subject, thereby making it possible to visualize the ion concentration flowing in and out of the subject's ion channels. Furthermore, the stimulation may be achieved by constant or periodic potential control of multiple electrodes. Therefore, in the electrical tomography method according to this embodiment, a constant or periodically changing voltage may be applied to the subject via a single or multiple electrodes to control the movement and activity of the subject. Furthermore, the electrical tomography apparatus according to one embodiment of the present invention may include a potential control unit that controls the potential of the electrodes. The potential control unit may apply a constant or periodically changing voltage to the subject via a single or multiple electrodes to control the movement and activity of the subject.

[0059] The electrical tomography method and apparatus described above enable the observation of various intracellular structures and dynamics, revealing phenomena that were difficult to observe using conventional techniques, such as the activity of intracellular ion channels and the distribution of intracellular fluids. Furthermore, because this technology is non-invasive, observations can be made while maintaining the physiological state of cells. The application of such electrical tomography has many potential applications in the fields of life science and medicine, such as detailed analysis of cellular pathological changes and drug responses. It will also be useful for observing the electrical activity of neurons, cardiac myocytes, and other cells.

[0060] The present invention has been described above using the present embodiment. However, the technical scope of the present invention is not limited to the above embodiment, and various modifications can be made without departing from the spirit of the present invention.

[0061] For example, in the above-described embodiment, the complex sensitivity matrix is ​​calculated using the partial derivative of the complex sensitivity matrix based on the Geselowitz theory, but the complex sensitivity matrix may also be calculated using the partial derivative derived from the perturbation of the permittivity and conductivity.

[0062] In the above-described embodiment, the distribution of conductivity and the distribution of permittivity are visualized in a total of five dimensions, namely, frequency, time, and three-dimensional space, but the dimensions for visualization are not limited to these. Therefore, the electrical tomography method of the present disclosure may visualize at least one distribution of permittivity and conductivity of an object in multiple dimensions.

[0063] The distribution of conductivity and the distribution of permittivity may be visualized in two or more of the five dimensions of frequency, time, and three-dimensional space. In other words, the multiple dimensions may be two or more dimensions selected from the group consisting of the five dimensions of frequency, time, and three-dimensional space.

[0064] In the above-described embodiment, the four partial derivatives of the complex sensitivity matrix are derived based on the Geselowitz theory, but the invention is not limited to this and derivation by other methods is also possible. For example, the invention can be applied to a general sensitivity matrix derivation method, such as a method that uses perturbation (ΔR, ΔX) of complex impedance due to perturbation (Δσ, Δε) of conductivity and permittivity.

[0065] In the above-described embodiment, a case where a current is applied to the electrodes and a voltage is measured has been described, but electrical tomography may also be performed by applying a voltage to the electrodes and measuring the current. In this case, the electrical tomography apparatus includes a voltage application device instead of a current application device.

[0066] Electrical tomography devices can be used with not only concentric multiple electrode arrays as shown in Figure 1, but also linear electrode arrays and two-dimensional and three-dimensional multilayered arrays. By devising an electrode array, it is possible to image frequency and two-dimensional and three-dimensional spatiotemporal distributions.

[0067] The electrodes can be mounted on glass substrates, rigid printed circuit boards, or flexible printed circuit boards. They can also be mounted on wearable materials, piping, chambers, and other devices, allowing for designs tailored to the application.

[0068] The effects of one embodiment of the present invention will be explained in more detail using examples. However, the conditions in the examples are merely examples adopted to confirm the feasibility and effects of the present invention. The present invention is not limited to these examples. Various conditions may be adopted in the present invention as long as they do not deviate from the gist of the present invention and achieve the object of the present invention.

[0069] (Example 1) In circular fields (homogeneous fields) 1 to 3 (measurement objects 1 to 3 in Table 1) having homogeneous conductivity and permittivity as shown in Figure 4, assuming that the permittivity of the field fluctuates uniformly, the spatial average value <Δε> of the permittivity reconstructed by the electrical tomography method of the present invention and the conventional electrical impedance tomography method was obtained by electric field simulation. In this simulation, eight electrodes were arranged at equal intervals along the periphery of the homogeneous field. The frequency range was 1 kHz to 1 MHz. The conductivity σ of the homogeneous fields (measurement objects) 1 to 3 ｎ and dielectric constant ε ｎ , and their reference values ​​are shown in Table 1.

[0070]

[0071] [Example of the Invention] In the electrical tomography method of the example of the invention, the permittivity change Δε was calculated by solving the inverse problem of equation (18) using the complex sensitivity matrices of equations (19) to (22) obtained as partial derivatives of equation (13). The results are shown in Figure 5. Figure 5 is a graph showing the change in the spatial average value <Δε> of the permittivity with frequency for each homogeneous field in the example of the invention.

[0072] Comparative Example The following method was adopted as the conventional electrical impedance tomography method: com and J com Instead, the imaginary part of the impedance (reactance ΔX) and the imaginary part of the complex conductivity (dielectric constant) were calculated based on equation (24) described by the conventional Jacobian matrix J.

[0073]

[0074] The results are shown in Figure 6. Figure 6 is a graph showing the change in the spatial average value <Δε> of the dielectric constant with frequency for each homogeneous field in the comparative example.

[0075] As shown in Figures 5 and 6, the conventional electrical impedance tomography method showed unstable permittivity, with variations in the reconstructed permittivity for each frequency. On the other hand, the electrical tomography method of the present invention reconstructed a stable permittivity at any frequency. The conventional method of the comparative example did not take into account the theoretical correlation between the real part (resistance) and imaginary part (reactance) of the impedance and the complex conductivity. Therefore, it is presumed that the behavior of the reactance, which changes significantly depending on the frequency, was reflected in the reconstructed permittivity, resulting in unstable behavior.

[0076] Example 2A: Cell spheroids were used as measurement objects, and the conductivity and permittivity of the cell spheroids were imaged. The experimental apparatus consisted of an impedance analyzer, a multiplexer, a sensor, and a control PC. A printed circuit board was used as the sensor, with eight electrodes arranged at equal concentric intervals on the board. The impedance between each electrode pair (28 patterns in total) was measured by selecting and switching two of the eight electrodes using the multiplexer. Cell spheroids formed on a well plate using MRC-5 human fetal lung fibroblasts were used in the experiment. The experimental protocol consisted of first placing the cell spheroid at the center of the sensor, and then dripping a deionized sucrose solution with adjusted osmotic pressure around it. This created a system in which ions were transported from the cell spheroid to the surrounding sucrose solution. At this time, impedance measurement was initiated between each electrode pair, and the time-dependent changes in impedance associated with ion transport around the cell spheroid were obtained. In Example 2A, ωε ０ In other words, in the complex sensitivity matrix expressed by equation (11), ０ was set to 1. Furthermore, the four partial derivatives in the complex sensitivity matrix expressed by equation (11) were calculated from R and X at a frequency of 1 kHz without taking into account frequency changes.

[0077] FIG. 7(a) is a microscopic image of a cell spheroid, and is a reference image for the shape and diameter of the cell spheroid. FIG. 7(b) is a stereomicroscope image of a cell spheroid placed on the measurement area of ​​an electrical tomography device and electrodes arranged around the measurement area. In FIG. 7(b), the area inside the circle labeled "sensor area" indicates the area where the sensor is placed, and the circle labeled "Cell spheroid" represents the boundary of the cell spheroid, and the area inside the circle is the area where the cell spheroid is captured. FIG. 7(c) is a stereomicroscope image of a cell spheroid placed on the measurement area of ​​an electrical tomography device at time t １ , t ２ , t ３ , and t ４ t is a contour diagram showing the distribution of the reconstructed conductivity Δσ and permittivity Δε. １ ~t ４ In Fig. 7(c), time passes in the order of Δσl and Δε l are the imaged diagrams of the conductivity distribution and the permittivity distribution in the low frequency band (1 kHz), respectively, and Δσ ｈ and Δε ｈ are images of the conductivity distribution and permittivity distribution in the high frequency band (1 MHz), respectively. The ellipse placed inside in Fig. 7(c) corresponds to the circle marked "Cell spheroid" in Fig. 7(b).

[0078] Δσ in FIG. l Each contour plot shows the distribution of extracellular conductivity. It can be seen that the extracellular conductivity increases over time. This increase in conductivity is due to an increase in the extracellular ion concentration caused by the movement of ions from inside the cell to outside the cell. Furthermore, the intracellular conductivity was almost zero because low-frequency current cannot pass through the cell membrane.

[0079] Δε l As shown in each contour map, the distribution of the dielectric constant outside the cells was shown. This is because the extracellular ion concentration increased due to ion movement caused by the extracellular solution, and the extracellular dielectric constant decreased over time.

[0080] Δσ h The distribution of intracellular conductivity is shown in each contour map. The distribution of intracellular conductivity is due to the ability of high-frequency current to pass through the cell membrane and the presence of many free ions within the cell. The intracellular conductivity decreased over time due to the movement of ions to the outside.

[0081] Δε h As shown in each contour map, the dielectric constant distribution within the cell was shown, and it was shown to decrease over time.

[0082] As described above, the electrical tomography method of the present invention made it possible to image the distribution of electrical conductivity and the distribution of permittivity in five dimensions: frequency, time, and space.

[0083] (Example 2B) The experimental apparatus and protocol were the same as those in Example 2A, and the impedance change over time associated with ion transport occurring around the cell spheroid was acquired. In this Example 2B, ωε was calculated based on the acquired 28 patterns of impedance. ０ Furthermore, by taking R and X into consideration as functions of frequency (or each frequency ω), the complex sensitivity matrix expressed by equation (11) was used to reconstruct images of the spatiotemporal and frequency distributions of the conductivity and permittivity inside and outside the cell spheroid.

[0084] FIG. 8 shows the time t for each frequency (f=1 kHz, 10 kHz, 1 MHz) in Example 2B. １ = 2.5s, t ２ = 5.0 s, t ３ = 7.5s, and t ４ 10.0 s.

[0085] Using the complex sensitivity matrix expressed by equation (11), ωε ０ By treating R and X as frequency functions, it was possible to reconstruct more accurate and more stable images of the dielectric constant distribution and the spatiotemporal and frequency distribution of the conductivity of the object to be measured, as shown in Figure 8.

[0086] Example 3: A single cell was imaged using the electrical tomography method of the present disclosure. Specifically, a current frequency in the MHz range was used, and changes in the internal conductivity of the cell were measured using multiple electrodes. For this measurement, a microelectrode array was placed around the cell. By adjusting the frequency range, a weak current flowed inside the cell, and image reconstruction was performed based on the measured impedance. Figure 9(a) is a microscopic image of a single cell, Figure 9(b) is an image of a single cell imaged using the electrical tomography method of the present disclosure, and Figure 9(c) is a superimposed image of Figures 9(a) and 9(b). In these images, the area within the solid line represents the single cell, and the area within the dashed line represents the cell nucleus of the single cell. As shown in Figures 9(a) to 9(c), high-resolution single-cell images were obtained, demonstrating that the internal structure of a single cell can be imaged.

[0087] Example 4: To evaluate pharmacological hERG inhibition, we imaged changes in impedance and extracellular ion concentrations with and without the addition of an hERG inhibitor, focusing on the voltage-gated potassium channel (hERG), an ion channel present in cardiomyocytes. Figure 10(a) shows the printed circuit board of the electrical tomography device used in this example, and Figure 10(b) shows multiple electrodes and the measurement area on the printed circuit board. As shown in Figure 10(b), 16 electrodes were arranged concentrically and equidistantly within the plane of the measurement area on the printed circuit board. A potential-control electrode was also provided at the center of the measurement area. A pulse potential was applied to the potential-control electrode to control the membrane potential required for channel activation. The experimental device consisted of a sensor, an impedance analyzer (IM3570, manufactured by Hioki E.E. Corporation), a multiplexer, a function generator, and a PC for control and data collection. Current application and voltage measurement were repeated over time across multiple electrode pairs, and the time-dependent changes in impedance across the multiple electrode pairs were obtained. After a certain time had elapsed since the start of measurement, a pulse signal output from a function generator was applied to the potential-controlling electrode to control the cell membrane potential. HEK293 cells (human embryonic kidney cells 293) expressing hERG were used. A -70 mV rectangular pulse wave was applied to the potential-controlling electrode of HEK293 cells seeded on the sensor to measure hERG activity. Furthermore, for hERG inhibition experiments, astemizole, a well-known hERG inhibitor, was dissolved in DMSO (dimethyl sulfoxide) medium and mixed with the HEK293 cell suspension in advance, and measurements were performed in the same manner as above.

[0088] Figure 11 shows the change over time in the voltage applied to the potential-controlled electrode and the measured impedance. Figure 11(a) shows the change in impedance in the absence of an inhibitor, and it was confirmed that the impedance rapidly decreased after applying a -70 mV rectangular pulse wave. This is because the application of the potential caused hERG activation, which released potassium ions into the extracellular fluid, increasing the ion concentration in the extracellular fluid.

[0089] 11(b) shows the change in impedance when an inhibitor was added. When an inhibitor was added, the change in impedance before and after the application of the pulse potential was relatively small, indicating the hERG inhibition caused by the addition of astemizole.

[0090] Next, the results of tomography of ion concentration based on impedance data obtained with multiple current application and voltage measurement patterns are shown in Figure 12. As shown in Figure 12, we were able to image the changes in extracellular ion concentration before and after hERG activation.

[0091] (Example 5) The toxicity of the inhibitor was evaluated by imaging the extracellular ion concentration to determine the change in extracellular ion concentration over time and plotting an inhibition curve showing the relationship between the inhibitor concentration and ion channel activity. Different concentrations of hERG inhibitors were added, and the change in conductivity over time was measured. In this example, the same electrical tomography device as in Example 4 was used to acquire the change in conductivity over time. The same cells as in Example 4 were used, and E-4031 was used as the hERG inhibitor, and the inhibitor concentration c ｄ The cell suspension was pre-mixed with a hERG inhibitor so that the amount of each was different.

[0092] Furthermore, the inhibition curves obtained by the patch clamp method as disclosed in Z. Zhou et al., "Properties of HERG Channels Stably Expressed in HEK 293 Cells Studied at Physiological Temperature," Biophysical Journal, 74, 1998, 230-241, were used as a conventional example to compare the examples of the present invention with the conventional example.

[0093] FIG. 13 shows the inhibitor concentration C ｄ13 is a graph showing the change in conductivity over time for each sample. FIG. 14 is a graph showing the inhibition curves for an example of the present invention and a conventional example. In FIG. 13 , the white areas without plots indicate the time during which voltage was applied. In the example of the present invention, the inhibition curve in FIG. 14 was created using the conductivity measured after the fifth voltage application from the start of measurement (after 200 seconds had elapsed since the start of measurement). In FIG. 14 , the curve shown by the solid line is the inhibition curve for the example of the present invention, and the curve shown by the dashed line is the inhibition curve for the conventional example.

[0094] In the present invention, for example, the inhibitor concentration c when the activity is 50% (IR = 0.50) ｄ is calculated to be 2 nM, and the inhibitor concentration c ｄ The calculated value was 7 nM. This level of difference is generally considered acceptable. Therefore, it was found that the present invention can non-invasively evaluate the 50% inhibitory concentration (IC50) while maintaining the physiological state of the cells. Furthermore, because the evaluation was easier than in the past, the operator was able to perform the process accurately with fewer errors.

[0095] The electrical tomography apparatus and method disclosed herein have been described. The electrical tomography apparatus and method disclosed herein are capable of reconstructing an image of permittivity. Furthermore, the electrical tomography apparatus and method disclosed herein are capable of reflecting the frequency characteristics of permittivity and conductivity. Furthermore, the electrical tomography apparatus and method disclosed herein are capable of reconstructing images that accurately reflect the dielectric properties of cellular components such as cells, cytoplasm, and nuclei, thereby enabling the observation of detailed cellular information (such as cell structure and pharmacokinetics). Specifically, for example, five-dimensional imaging of at least one of the conductivity distribution and permittivity distribution of biological or non-biological substances is possible. This enables rapid and real-time analysis of pharmacokinetics of cultured cells, artificial stem cells, membrane proteins such as ion channels, and biological tissues, as well as the detection of cancer cells, thereby providing innovative imaging technology in the fields of medicine and drug discovery. The present disclosure also has applicability to process management and control in chemical plants and other applications, contributing to the achievement of the SDGs, including energy issues.

[0096] REFERENCE SIGNS LIST 1 Electrical tomography device, 11 Current application device, 12 Multiplexer, 13 Printed circuit board, 14 Electrode, 15 Connector, 16 Display, 17 Control device, 18 Electric wire, 21 Control unit, 22 Calculation unit, 23 Display unit, 24 Memory unit

Claims

1. An electrical tomography method that utilizes a complex sensitivity matrix to visualize at least one of the distribution of permittivity and the distribution of conductivity of a measurement object.

2. The electrical tomography method according to claim 1, wherein the complex sensitivity matrix is ​​expressed by the following equation (1). In the formula (1), J com : complex sensitivity matrix, R: resistance component (real part of complex impedance), X: reactance component (real part of complex impedance), σ: conductivity, ε: dielectric constant, ω: angular frequency, ε ０ : dielectric constant of a vacuum, T: transposition symbol, 3. The electrical tomography method according to claim 2, wherein the complex sensitivity matrix is ​​a complex sensitivity matrix calculated by partial derivatives of a complex sensitivity matrix based on the Geselowitz theory.

4. The electrical tomography method according to claim 3, wherein the complex sensitivity matrix is ​​calculated by taking partial derivatives of a complex sensitivity matrix derived from equation (2) which expresses the relationship between complex impedance and a complex potential field obtained by modifying the Geselowitz theory. In the formula (2), Z ｍ * φ is the complex impedance measured at the m-th electrode pattern expressed by equation (3). * : Complex potential distribution expressed by equation (4), σ ｎ * : Complex conductivity of the nth mesh expressed by equation (5), Ω ｎ R is the area of ​​the nth mesh, and in the formula (3), ｍ : Resistance component of the complex impedance measured in the mth electrode pattern, X ｍ m is the reactance component of the complex impedance measured in the m-th electrode pattern, and in the above formula (4), φ′ is the value of the real part of the potential, and φ″ is the value of the imaginary part of the potential, and in the above formula (5), σ ｎ : Conductivity of the nth mesh, ω: Angular frequency, ε ０ : Dielectric constant of vacuum, ε ｎ： is the dielectric constant of the nth mesh, and in the above formulas (3) to (5), j represents the imaginary unit.

5. An electrical tomography method according to claim 2, wherein said complex sensitivity matrix is ​​a complex sensitivity matrix calculated by partial derivatives taken from perturbations of permittivity and conductivity.

6. An electrical tomography method according to any one of claims 1 to 5, which visualizes the distribution of at least one of the multi-dimensional permittivity and conductivity of the object to be measured.

7. An electrical tomography method as claimed in claim 6, wherein said multiple dimensions are two or more dimensions selected from the group consisting of the five dimensions of frequency, time and three-dimensional space.

8. The electrical tomography method according to claim 1, wherein the object to be measured is a biological or non-biological substance.

9. An electrical tomography method according to claim 8, wherein the biological material is at least one selected from the group consisting of cells, tissues, living organisms, and biological constituents.

10. An electrical tomography method according to claim 8, wherein the non-biological material is at least one selected from the group consisting of a liquid containing gas bubbles, a powder, a slurry, and a plastic.

11. An electrical tomography method according to any one of claims 1 to 5, wherein the object to be measured is a cell or tissue, and the concentration of ions flowing in and out of an ion channel of the object to be measured is visualized by applying a potential-controlled stimulus to the object to be measured from outside the object to be measured.

12. The electrical tomography method of claim 11, wherein a constant or periodically varying voltage is applied to the object to be measured by one or more electrodes to control the movement and activity of the object to be measured.

13. An electrical tomography device having three or more electrodes, comprising: a calculation unit that calculates a complex sensitivity matrix; and a display unit that displays at least one of a distribution of permittivity and a distribution of conductivity of a measurement object based on the complex sensitivity matrix.

14. An electrical tomography apparatus according to claim 13, wherein the complex sensitivity matrix is ​​expressed by the following equation (1). In the formula (1), J com : complex sensitivity matrix, R: resistance component (real part of complex impedance), X: reactance component (real part of complex impedance), σ: conductivity, ε: dielectric constant, ω: angular frequency, ε ０ : dielectric constant of a vacuum, T: transposition symbol, 15. The electrical tomography apparatus according to claim 14, wherein the calculation unit calculates the complex sensitivity matrix by partial derivatives of the complex sensitivity matrix based on the Geselowitz theory.

16. The electrical tomography apparatus according to claim 15, wherein the calculation unit derives a partial derivative of a complex sensitivity matrix from equation (2) which expresses the relationship between complex impedance and a complex potential field obtained by modifying the Geselowitz theory. In the formula (2), Z ｍ * φ is the complex impedance measured at the m-th electrode pattern expressed by equation (3). * : Complex potential distribution expressed by equation (4), σ ｎ * : Complex conductivity of the nth mesh expressed by equation (5), Ω ｎ R is the area of ​​the nth mesh, and in the formula (3), ｍ : Resistance component of complex impedance measured in the mth electrode pattern X ｍ m is the reactance component of the complex impedance measured in the m-th electrode pattern, and in the above formula (4), φ′ is the value of the real part of the potential, and φ″ is the value of the imaginary part of the potential, and in the above formula (5), σ ｎ : Conductivity of the nth mesh, ω: Angular frequency, ε ０ : Dielectric constant of vacuum, ε ｎ： is the dielectric constant of the nth mesh, and in the above formulas (3) to (5), j represents the imaginary unit.

17. The electrical tomography apparatus according to claim 14, wherein the calculation unit calculates partial derivatives derived from perturbations of permittivity and conductivity, and calculates the complex sensitivity matrix from the partial derivatives.

18. An electrical tomography device according to any one of claims 13 to 17, wherein the display unit displays at least one of a multi-dimensional distribution of dielectric constant and a multi-dimensional distribution of conductivity of the object to be measured.

19. An electrical tomography apparatus as described in claim 18, wherein said multiple dimensions are two or more dimensions selected from the group consisting of the five dimensions of frequency, time, and three-dimensional space.

20. An electrical tomography apparatus according to claim 13, wherein the object to be measured is a biological or non-biological substance.

21. An electrical tomography apparatus according to claim 20, wherein the biological material is at least one selected from the group consisting of cells, tissues, living organisms, and biological constituents.

22. An electrical tomography apparatus according to claim 20, wherein the non-biological material is at least one selected from the group consisting of a liquid containing gas bubbles, a powder, a slurry, and a plastic.

23. An electrical tomography device as described in any one of claims 13 to 17, comprising a potential control unit that controls the potential of the electrodes, the object to be measured is a cell or tissue, the potential control unit applies a potential-controlled stimulus to the object to be measured from outside the object to be measured, and the display unit displays the distribution of ion concentrations flowing in and out of ion channels of the object to be measured.

24. An electrical tomography apparatus according to claim 23, wherein the potential control unit applies a constant voltage or a periodically changing voltage to the object to be measured via a single or multiple electrodes to control the movement and activity of the object to be measured.

Images