Information processing device and information processing method

Abstract

To improve image quality.SOLUTION: According to an embodiment, an information processing device includes an acquisition part and a calculation part. The acquisition part acquires a measuring field corresponding to a space distribution of a prescribed physical amount in a measurement object. The calculation part calculates an unknown amount in the measurement object on the basis of a first relational expression between the measuring field and the unknown amount having space dependency, and the measurement place acquired by the acquisition part. The first relational expression is a relational expression acquired on the basis of a second relational expression representing a dual field in which divergence of the dual field can be represented by using the measuring field is represented by using the measuring field and the unknown amount, and Helmholtz decomposition of the dual field.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The embodiments disclosed in the present specification and drawings relate to an information processing device and an information processing method. [Background technology]

[0002] It is conceivable that medical image processing equipment could provide new diagnostic information. For example, unlike the morphological images obtained by ordinary X-ray CT or MRI equipment, it would be possible to calculate and visualize the three-dimensional distribution of unknown quantities, such as electrical properties inside the human body, such as conductivity and dielectric constant, and mechanical properties, such as elasticity and viscosity.

[0003] Examples of these technologies include MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductivity Mapping), MRE (Magnetic Resonance Elastography), etc. These technologies make it possible to measure, for example, cancer and cirrhosis as changes in physical constants.

[0004] In some cases, electrical and mechanical properties are calculated and imaged under the assumption that they change gradually inside the human body (mathematically, they are locally uniform). However, this can result in large estimation errors at the boundaries of abnormal areas. For example, in the case of MREPT, estimation accuracy can decrease when the conductivity changes discontinuously compared to normal tissue, such as in the case of localized solid cancer.

[0005] In addition, the spatial dependence of electrical and mechanical properties can be taken into account by using the finite element method or an integral representation of the electromagnetic field. However, for example, the differential equation to be solved may contain higher-order derivatives of the measurement field, resulting in an ill-posed problem, or the integral equation to be solved may be nonlinear with respect to the unknowns, requiring an iterative method to solve the integral equation, and often resulting in a local optimum if an appropriate initial solution is not provided. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] International Publication No. 2013 / 057655 [Patent Document 2] U.S. Patent No. 5,592,085 [Non-patent literature]

[0007] [Non-Patent Document 1] U. Katscher, et al., “Electric Properties Tomography: Biochemical, Physical and Technical Background, Evaluation and Clinical Applications”, NMR in Biomed., 2017, Vol.30, e3729, pp.1-15 [Non-patent document 2] J. Liu, et al., “Electrical Properties Tomography Based on B1Maps in MRI: Principles, Applications, and Challenges”, IEEE Trans. Biomed. Eng.,2017, Vol.64, No.11, pp.2515-2530 [Non-patent document 3] J. Chi, et al., “Magnetic Resonance-Electrical Properties Tomography by Directly Solving Maxwell's Curl Equation”, Appl. Sci. 2020, Vol.10, No.9, 3318, Summary of the Invention [Problem to be solved by the invention]

[0008] One of the problems to be solved by the embodiments disclosed in this specification and the drawings is to improve image quality. However, the problems to be solved by the embodiments disclosed in this specification and the drawings are not limited to the above problem. Problems corresponding to the effects of each configuration shown in the embodiments described below can also be positioned as other problems. [Means for solving the problem]

[0009] An information processing device according to an embodiment includes an acquisition unit and a calculation unit. The acquisition unit acquires a measurement field corresponding to the spatial distribution of a predetermined physical quantity in a measurement object. The calculation unit calculates the unknown quantity in the measurement object based on a first relational expression between the measurement field and a spatially dependent unknown quantity and the measurement field acquired by the acquisition unit. The first relational expression is a relational expression obtained based on a second relational expression expressing the dual field, in which the divergence of the dual field can be expressed using the measurement field, using the measurement field and the unknown quantity, and Helmholtz decomposition of the dual field. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram showing a magnetic resonance imaging apparatus 100 including an information processing apparatus 130 according to an embodiment. [Figure 2] FIG. 2 is a flowchart illustrating the flow of processing performed by the information processing device 130 according to the embodiment. [Figure 3] FIG. 3 is a flowchart illustrating the flow of processing performed by the information processing device 130 according to the embodiment in the case of MREPT. [Figure 4] FIG. 4 is a flowchart illustrating the flow of processing performed by the information processing device 130 according to the embodiment in the case of QCM. [Figure 5] FIG. 5 is a flowchart illustrating the flow of processing performed by the information processing device 130 according to the embodiment in the case of MRE. [Figure 6] FIG. 6 is a diagram illustrating the processing performed by the information processing device 130 according to the embodiment. [Figure 7] FIG. 7 is a diagram illustrating the processing performed by the information processing device 130 according to the embodiment. [Figure 8] FIG. 8 is a flowchart illustrating the processing performed by the information processing device 130 according to the embodiment. [Figure 9] FIG. 9 is a diagram illustrating the processing performed by the information processing device 130 according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, an information processing apparatus and an information processing method according to an embodiment will be described with reference to the drawings.

[0012] FIG. 1 is a diagram showing a configuration in which an information processing device 130 according to an embodiment is incorporated into a magnetic resonance imaging apparatus 100. However, the embodiment is not limited to the case in which the information processing device 130 is incorporated into the magnetic resonance imaging apparatus 100, and the information processing device 130 may be configured independently of the magnetic resonance imaging apparatus 100. Furthermore, the information processing device 130 may be incorporated into an apparatus of a modality other than the magnetic resonance imaging apparatus 100, such as an ultrasound diagnostic apparatus. For example, the following embodiment describes the case of MRE, which uses the magnetic resonance imaging apparatus 100 to directly vibrate tissue with a vibrating plate or the like to measure elasticity fields. However, the embodiment can also be applied to various modalities that can measure elasticity distribution, such as using an apparatus that directly vibrates tissue to measure elasticity fields.

[0013] 1, the magnetic resonance imaging apparatus 100 includes a static magnetic field magnet 101, a static magnetic field power supply (not shown), a gradient magnetic field coil 103, a gradient magnetic field power supply 104, a bed 105, a bed control circuit 106, a transmission coil 107, a transmission circuit 108, a reception coil 109, a reception circuit 110, a sequence control circuit 120 (sequence control unit), and an information processing device 130. Note that the magnetic resonance imaging apparatus 100 does not include a subject P (e.g., a human body). The configuration shown in FIG. 1 is merely an example. For example, the components in the sequence control circuit 120 and the information processing device 130 may be configured as integrated or separated as appropriate.

[0014] The static magnetic field magnet 101 is a magnet formed in a hollow, approximately cylindrical shape, and generates a static magnetic field in the space inside the cylinder in the direction of its central axis (Z-axis). The static magnetic field magnet 101 is, for example, a superconducting magnet, and is excited by receiving a current from a static magnetic field power supply. The static magnetic field power supply supplies a current to the static magnetic field magnet 101. As another example, the static magnetic field magnet 101 may be a permanent magnet, in which case the magnetic resonance imaging apparatus 100 may not be provided with a static magnetic field power supply. Furthermore, the static magnetic field power supply may be provided separately from the magnetic resonance imaging apparatus 100.

[0015] The gradient magnetic field coil 103 is a hollow, approximately cylindrical coil and is disposed inside the static magnetic field magnet 101. The gradient magnetic field coil 103 is formed by combining three coils corresponding to the mutually orthogonal X, Y, and Z axes, and these three coils are individually supplied with current from a gradient magnetic field power supply 104 to generate gradient magnetic fields whose magnetic field strength in the Z direction varies along each of the X, Y, and Z axes according to the distance from the center of each axis. The gradient magnetic fields of the X, Y, and Z axes generated by the gradient magnetic field coil 103 are, for example, a slicing gradient magnetic field Gs, a phase encoding gradient magnetic field Ge, and a readout gradient magnetic field Gr. The gradient magnetic field power supply 104 supplies current to the gradient magnetic field coil 103.

[0016] The bed 105 includes a top plate 105a on which the subject P is placed, and under the control of a bed control circuit 106, the top plate 105a is inserted into the cavity (imaging port) of the gradient magnetic field coil 103 with the subject P placed thereon. The bed 105 is usually installed so that its longitudinal direction is parallel to the central axis of the static magnetic field magnet 101. Under the control of the information processing device 130, the bed control circuit 106 drives the bed 105 to move the top plate 105a in the longitudinal direction and the up-down direction.

[0017] The transmitting coil 107 is disposed inside the gradient magnetic field coil 103, and generates a radio frequency magnetic field upon receiving RF (Radio Frequency: high frequency magnetic field) pulses from a transmitting circuit 108. The transmitting circuit 108 supplies the transmitting coil 107 with RF pulses corresponding to a Larmor frequency determined by the type of atom of interest and the magnetic field strength.

[0018] The receiving coil 109 is disposed inside the gradient magnetic field coil 103, and receives magnetic resonance signals (hereinafter referred to as "MR signals" as necessary) emitted from the subject P due to the influence of the high frequency magnetic field. Upon receiving the magnetic resonance signals, the receiving coil 109 outputs the received magnetic resonance signals to the receiving circuit 110.

[0019] The above-described transmitting coil 107 and receiving coil 109 are merely examples. They may be configured by combining one or more of a coil having only a transmitting function, a coil having only a receiving function, or a coil having a transmitting and receiving function.

[0020] The receiving circuit 110 detects the magnetic resonance signal output from the receiving coil 109 and generates magnetic resonance data based on the detected magnetic resonance signal. Specifically, the receiving circuit 110 generates the magnetic resonance data by digitally converting the magnetic resonance signal output from the receiving coil 109. The receiving circuit 110 also transmits the generated magnetic resonance data to the sequence control circuit 120. The receiving circuit 110 may be provided on the gantry side including the static magnetic field magnet 101, the gradient magnetic field coil 103, etc.

[0021] The sequence control circuit 120 performs imaging of the subject P by driving the gradient magnetic field power supply 104, the transmission circuit 108, and the reception circuit 110 based on sequence information transmitted from the information processing device 130. Here, the sequence information is information that defines a procedure for performing imaging. The sequence information defines the strength of the current that the gradient magnetic field power supply 104 supplies to the gradient magnetic field coil 103 and the timing of supplying the current, the strength of the RF pulse that the transmission circuit 108 supplies to the transmission coil 107 and the timing of applying the RF pulse, and the timing of detecting a magnetic resonance signal by the reception circuit 110. For example, the sequence control circuit 120 is an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array), or an electronic circuit such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit). Details of the pulse sequence executed by the sequence control circuit 120 will be described later.

[0022] Furthermore, when the sequence control circuit 120 receives magnetic resonance data from the receiving circuit 110 as a result of driving the gradient magnetic field power supply 104, the transmitting circuit 108, and the receiving circuit 110 to image the subject P, the sequence control circuit 120 transfers the received magnetic resonance data to an information processing device 130. The information processing device 130 performs overall control of the magnetic resonance imaging apparatus 100 and generates images. The information processing device 130 includes a memory 132, an input device 134, a display 135, and a processing circuit 150. The processing circuit 150 includes an interface function 131, a control function 133, and a generation function 136.

[0023] In the embodiment, each processing function performed by the interface function 131, the control function 133, the generation function 136, the identification function 137, the acquisition function 138, and the calculation function 139 is stored in the memory 132 in the form of a computer-executable program. The processing circuit 150 is a processor that reads and executes the program from the memory 132 to realize the function corresponding to each program. In other words, the processing circuit 150 in a state in which each program has been read has each function shown in the processing circuit 150 of FIG. 1. Note that, in FIG. 1, the processing functions performed by the interface function 131, the control function 133, the generation function 136, the identification function 137, the acquisition function 138, and the calculation function 139 are described as being realized by a single processing circuit 150. However, the processing circuit 150 may be configured by combining multiple independent processors, and each processor may execute a program to realize the function. In other words, each of the above functions may be configured as a program, and a single processing circuit 150 may execute each program. As another example, a specific function may be implemented in a dedicated, independent program execution circuit. 1, the interface function 131, the control function 133, the generation function 136, the identification function 137, the acquisition function 138, and the calculation function 139 are examples of a reception unit, a control unit, a generation unit, an identification unit, an acquisition unit, and a calculation unit, respectively. Also, the sequence control circuit 120 is an example of a sequence control unit. Specific processing of the identification function 137, the acquisition function 138, and the calculation function 139 will be described later.

[0024] The term "processor" used in the above description refers to circuits such as a CPU (Central Processing Unit), a GPU (Graphical Processing Unit), an Application Specific Integrated Circuit (ASIC), a programmable logic device (e.g., a Simple Programmable Logic Device (SPLD), a Complex Programmable Logic Device (CPLD), and a Field Programmable Gate Array (FPGA)). The processor realizes its functions by reading and executing programs stored in memory 132.

[0025] Furthermore, instead of storing the program in the memory 132, the program may be directly embedded in the processor circuitry. In this case, the processor performs its functions by reading and executing the program embedded in the circuitry. The bed control circuitry 106, the transmission circuitry 108, the reception circuitry 110, etc. are also similarly configured using electronic circuits such as the processor.

[0026] The processing circuitry 150 transmits sequence information to the sequence control circuitry 120 via the interface function 131, and receives magnetic resonance data from the sequence control circuitry 120. Furthermore, upon receiving the magnetic resonance data, the processing circuitry 150 having the interface function 131 stores the received magnetic resonance data in the memory 132.

[0027] The magnetic resonance data stored in the memory 132 is arranged in k-space by the control function 133. As a result, the memory 132 stores the k-space data.

[0028] The memory 132 stores magnetic resonance data received by the processing circuitry 150 having the interface function 131, k-space data arranged in k-space by the processing circuitry 150 having the control function 133, image data generated by the processing circuitry 150 having the generation function 136, etc. For example, the memory 132 is a semiconductor memory element such as a RAM (Random Access Memory), a flash memory, a hard disk, an optical disk, etc.

[0029] The input device 134 accepts various instructions and information input from an operator. The input device 134 is, for example, a pointing device such as a mouse or a trackball, a selection device such as a mode switch, or an input device such as a keyboard. The display 135, under the control of the processing circuit 150 having the control function 133, displays a GUI (Graphical User Interface) for accepting input of imaging conditions, an image generated by the processing circuit 150 having the generation function 136, and the like. The display 135 is, for example, a display device such as a liquid crystal display.

[0030] The processing circuitry 150 performs overall control of the magnetic resonance imaging apparatus 100 using the control function 133, and controls imaging, image generation, image display, etc. For example, the processing circuitry 150 having the control function 133 accepts input of imaging conditions (imaging parameters, etc.) on a GUI and generates sequence information according to the accepted imaging conditions. In addition, the processing circuitry 150 having the control function 133 transmits the generated sequence information to the sequence control circuit 120.

[0031] The processing circuitry 150 uses the generation function 136 to read out the k-space data from the memory 132 and perform reconstruction processing such as Fourier transform on the read out k-space data to generate an image.

[0032] Next, the background of the embodiment will be described.

[0033] It is conceivable that medical image processing equipment will provide new diagnostic information that differs from that of conventional X-ray CT and MRI equipment. For example, unlike the structural images obtained by conventional X-ray CT and MRI equipment, it is conceivable to calculate and visualize the three-dimensional distribution of unknown quantities such as electrical properties inside the human body, such as conductivity and dielectric constant, and mechanical properties, such as elasticity and viscosity.

[0034] Examples of these technologies include MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductivity Mapping), MRE (Magnetic Resonance Elastography), etc. These technologies make it possible to measure, for example, cancer and cirrhosis as changes in physical constants.

[0035] In conventional technology, electrical and mechanical properties are calculated and imaged under the assumption that they change gradually inside the human body (mathematically they are locally uniform). However, assuming that electrical and mechanical properties are locally uniform inside the human body can result in large estimation errors at the boundaries of abnormal areas.

[0036] It is also possible to consider the spatial dependence of electrical and mechanical properties by using the finite element method or an integral representation of the electromagnetic field. However, for example, in the former method, the differential equation to be solved contains higher-order derivatives of the measurement field, which can lead to ill-posed problems, and in the latter method, the integral equation to be solved is nonlinear with respect to the unknowns, which requires an iterative method to solve the integral equation, and if an appropriate initial solution is not provided, it can often fall into a local optimum.

[0037] In view of this background, the information processing device 130 according to the embodiment uses an integral representation that is robust to observation noise, introduces a dual field to the measurement field so that the equation to be solved becomes an integral equation that is linear with respect to the unknown quantity, and calculates the spatially dependent unknown quantity based on a relational expression derived from the Helmholtz decomposition of the dual field.

[0038] Specifically, the information processing device 130 according to the embodiment includes a processing circuit 150. The processing circuit 150 acquires a measurement field corresponding to the spatial distribution of a predetermined physical quantity in the measurement target using an acquisition function 138. The processing circuit 150 also calculates the unknown quantity in the measurement target based on a first relational expression between the measurement field and a spatially dependent unknown quantity and the measurement field using a calculation function 139. Here, the first relational expression is a relational expression obtained based on a second relational expression that expresses a dual field, in which the divergence of the dual field can be expressed using the measurement field, using the measurement field and the unknown quantity, and Helmholtz decomposition of the dual field.

[0039] In addition, the information processing method according to the embodiment includes acquiring a measurement field corresponding to the spatial distribution of a predetermined physical quantity in the measurement object, and calculating the unknown quantity in the measurement object based on a first relational equation between the measurement field and a spatially dependent unknown quantity and the measurement field acquired by the acquisition unit, wherein the first relational equation is a relational equation obtained based on a second relational equation expressing a dual field, in which the divergence of the dual field can be expressed using the measurement field, using the measurement field and the unknown quantity, and Helmholtz decomposition of the dual field.

[0040] According to the information processing device 130 and the information processing method, the image quality can be improved.

[0041] Hereinafter, processing performed by the information processing device according to the embodiment will be described with reference to FIGS. 2 to 7. FIG. 2 is a flowchart illustrating the procedure of processing performed by the information processing device according to the embodiment. FIG. 2 describes the general theory of the procedure of processing performed by the information processing device according to the embodiment, and FIGS. 3 to 5 describe the details of processing when the procedure is applied to individual application examples. Specifically, FIGS. 3 to 5 specifically explain the procedure when processing according to the embodiment is applied to the examples of MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductive Mapping), and MRE (Magnetic Resonance Elastography), respectively. FIG. 6 illustrates the relationship between the measurement field, unknown quantities to be estimated, and fundamental equations, and FIG. 7 illustrates the measurement field, dual field, and the relationship between the measurement field and dual field.

[0042] First, before introducing the dual field, the relationship between the measurement field and unknown quantities in the information processing device 130 according to the embodiment will be described.

[0043] 2, steps S100 to S130 will be described later. First, step S140 will be described. In step S140, processing circuit 150 acquires a measurement field corresponding to the spatial distribution of a predetermined physical quantity in the measurement object using acquisition function 138, and calculates an unknown quantity in the measurement object using calculation function 139 based on the acquired measurement field and the relational expression obtained in step S130. Specifically, processing circuit 150 acquires a measurement field corresponding to the spatial distribution of the predetermined physical quantity in the measurement object using acquisition function 138. Next, processing circuit 150 estimates a spatially dependent unknown quantity in the measurement object using calculation function 139 based on the measurement field acquired by acquisition function 138 and a first relational expression between the measurement field and the spatially dependent unknown quantity obtained in step S130 (to be described later). The first relational expression is an equation derived from a fundamental equation. As will be described later, the first relational equation is a relational equation obtained based on the Helmholtz decomposition of the dual field, and the second relational equation, which expresses the dual field, the divergence of which can be expressed using the measurement field, using the measurement field and the unknown quantity.

[0044] FIG. 6 shows the relationship between these measurement fields and unknown quantities according to the embodiment.

[0045] A first application example of the embodiment is magnetic resonance electrical property tomography (MREPT), which is a method of measuring the amplitude and phase of an RF magnetic field inside a human body using MRI to image the distribution of electrical conductivity and permittivity.

[0046] For MREPT, the processing circuitry 150 receives, via the acquisition function 138, the RF magnetic field H given by the following equation (1): + is obtained as the measurement field.

[0047]

number

[0048] where H xand H y are the RF magnetic fields in the x-axis and y-axis directions, respectively, which are perpendicular to the z-axis.

[0049] Furthermore, Faraday's law given by the following equation (2) and Ampere's law given by the following equation (3) hold true.

[0050]

number

[0051]

number

[0052] where E is the electric field, ω is the Larmor angular frequency, μ is the magnetic permeability of vacuum, and H is the RF magnetic field. Also, λ is the impedance given by the following equation (4).

[0053]

number

[0054] where σe is the electrical conductivity and ε is the dielectric constant.

[0055] In the case of MREPT, the processing circuit 150 uses the calculation function 139 to estimate the electrical conductivity σe, the dielectric constant ε, or the impedance λe given by equation (4) as unknown quantities having spatial dependency.

[0056] That is, in the case of MREPT, as shown in step S140A of FIG. 3, processing circuitry 150 acquires, by acquisition function 138, the RF magnetic field H given by equation (1): + Next, the processing circuit 150 calculates the RF magnetic field H + and the measurement field H obtained in step S130A. +and the spatially dependent unknown quantity λe, the electrical conductivity σe, the dielectric constant ε, or the impedance λe, which is an unknown quantity that varies spatially in the measurement object, is calculated based on the first relational expression between σe, σe, and the spatially dependent unknown quantity λe.

[0057] In other words, in the case of MREPT, the measurement field is the RF magnetic field H + The unknown quantities that vary spatially in the measurement target include the electrical conductivity σe and the permittivity ε. The processing circuit 150 performs MREPT based on the unknown quantities calculated by the calculation function 139.

[0058] In addition, measurement field H + and the unknown quantity λe is derived based on Faraday's law given by equation (2) and Ampere's law given by equation (3). That is, the first relational expression is a relational expression derived from Ampere's law and Faraday's law.

[0059] In the following, the RF magnetic field H + A method for measuring the signal is briefly described below. First, an RF signal is transmitted from the transmission circuit 108 to the transmission coil 107 based on an SE (Spin Echo) method sequence or a GRE (Gradient Echo) method sequence executed by the sequence control circuit 120. The processing circuit 150 acquires the SE signal or GRE signal obtained from the acquisition function 138 from the reception coil 109 via the reception circuit 110.

[0060] Here, the RF magnetic field H + is a complex number, the magnetic resonance imaging apparatus 100 according to the embodiment basically measures the amplitude and phase of the RF magnetic field.

[0061] Several methods are known for measuring the amplitude of an RF magnetic field, and are generally referred to as B1 mapping. The basic principle is that if the signal strength (amplitude) is S, the magnetization at a position (x, y, z) is M0, and the flip angle at which the magnetization is tilted by an RF pulse is α, then S=M0(x, y, z) sin α holds. Therefore, the signal strength (amplitude) is proportional to sin α, where α is the flip angle at which the magnetization is tilted by an RF pulse. Therefore, the processing circuit 150 calculates the flip angle α using the calculation function 139, and calculates sin α based on the calculated flip angle α, thereby calculating the amplitude of the RF magnetic field.

[0062] As an example of measuring the amplitude of an RF magnetic field, the sequence control circuit 120 executes a GRE pulse sequence at two flip angles (hereinafter, referred to as α and 2α) to eliminate the effects of the repetition time in the GRE sequence and the longitudinal relaxation time (T1) of the measurement target. The processing circuit 150 generates GRE images for the two flip angles using the generation function 136 based on the pulse sequence executed by the sequence control circuit 120. Here, if the ratio of signal intensities for each voxel is r, this is given by r = sin α / sin 2α = ½ cos α. Therefore, the processing circuit 150 can calculate the flip angle α based on the ratio r of signal intensities for each voxel obtained from the images generated for the two flip angles using the calculation function 139. Then, the amplitude of the RF magnetic field is measured by calculating sin α based on this.

[0063] The phase of the RF magnetic field can be measured, for example, by having the sequence control circuit 120 execute a pulse sequence for the SE method, and then having the processing circuit 150 use the calculation function 139 to measure the transmit RF phase based on the phase image at the peak of the SE signal from the measurement target. Here, we explain an example in which a quadrature birdcage coil is used to transmit and receive RF magnetic fields. This coil is known to generate a highly uniform RF magnetic field in free space. (See, for example, Convection-Reaction Equation Based Magnetic Resonance Electrical Properties Tomography (cr-MREPT): IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 33, NO. 3, MARCH 2014 777.) When acquiring an SE image with this coil, the echo peak is Fourier transformed at the center of k-space to obtain the SE image. Since this is an SE image, the phase due to static magnetic field inhomogeneity is canceled out, but the phase due to the eddy current magnetic field generated by RF transmission and reception and the driving of the gradient magnetic field remains, and is expressed as shown in Equation (5) below.

[0064]

number

[0065] where φ(r) is the phase of the SE image, r is the position, and φ + (r) is the phase of the transmitted RF magnetic field, φ - (r) is the phase at reception, and ∫γBe(r)dt is the phase due to the eddy current magnetic field. The latter can be canceled by subtracting the phase of the SE image obtained by reversing the gradient magnetic field using the same SE sequence, and φ + (r)+φ - (r) is obtained. On the other hand, in this coil, φ + (r) and φ - (r) is known to be approximately equal to (φ + (r)≒φ - (r)). Therefore, the desired transmit RF phase φ + (r) is (φ + (r)+φ -(r)) / 2. Note that although the measurement method for the amplitude and phase of the RF magnetic field has been described, the scope of the present invention is not limited to those using this measurement method. Other measurement methods or estimation methods may be used as long as they are methods for obtaining information on the amplitude and phase.

[0066] A second application example of the embodiment is QCM (Quantitative Conductivity Mapping), which is a method for imaging the distribution of electrical conductivity based only on the phase distribution of an RF magnetic field.

[0067] In the case of QCM, the processing circuit 150 acquires the measurement field φ given by the following equation (6) using the acquisition function 138.

[0068]

number

[0069] More specifically, the processing circuitry 150, via the acquisition function 138, detects the RF magnetic field H + The measurement field φ is obtained by extracting the phase component of

[0070] In the case of a QCM, the processing circuit 150 uses the calculation function 139 to estimate the electrical conductivity σe or the resistivity ρe given by equation (7) as an unknown quantity having spatial dependency.

[0071]

number

[0072] 4, the processing circuit 150 acquires the measurement field φ given by equation (6) using the acquisition function 138. Then, the processing circuit 150 calculates the electrical conductivity σe or resistivity ρe, which is an unknown quantity that varies spatially in the measurement object, using the calculation function 139, based on the measurement field φ and the first relational expression between the measurement field φ and the spatially dependent unknown quantity ρe obtained in step S130B.

[0073] In other words, in the case of QCM, the measurement field is, for example, an RF magnetic field H + The unknown quantity that varies spatially in the measurement target includes the conductivity σe or the resistivity ρe. The processing circuit 150 performs QCM based on the unknown quantities calculated by the calculation function 139.

[0074] The first relation between the measurement field φ and the resistivity ρe is derived by assuming that the spatial variation of the amplitude of H+ is gradual and that σe>>ωε in Faraday's law given by equation (2) and Ampere's law given by equation (3), which were used in the case of MREPT.

[0075] A third application example of the embodiment is MRE (Magnetic Resonance Elastography), which uses MRI to measure the displacement distribution when external vibration is applied to the human body, and visualizes the distribution of elasticity, viscosity, and other properties inside the human body.

[0076] In the case of MRE, the processing circuitry 150 acquires the displacement u as the measurement field using the acquisition function 138. Note that the displacement u is a vector quantity.

[0077] Furthermore, the equation of motion given by the following equation (8) and Hooke's law given by the following equation (9) hold true.

[0078]

number

[0079]

number

[0080] Here, σm is stress, ω1 is the angular frequency of vibration, ρm is density, and u is displacement. Here, stress σm is a tensor quantity, and displacement u is a vector quantity, so equation (8) adds -ω1 to each component of displacement u. 2This means that the sum of the stress σm multiplied by ρm is equal to the divergence of the vector taken from each row or column of the stress σm. Also, λm and μm are elastic constants, specifically, λm is Lamé's first constant and μm is Lamé's second constant. Also, I represents the identity matrix.

[0081] In the case of MRE, the processing circuit 150 uses the calculation function 139 to estimate the elastic constants λm and μm, and therefore the elastic modulus, viscosity coefficient, etc., as unknown quantities with spatial dependency.

[0082] That is, in the case of MRE, as shown in step S140C of FIG. 5, processing circuitry 150 acquires displacement u as a measurement field using acquisition function 138.

[0083] Next, the processing circuit 150 uses the calculation function 139 to calculate the elastic constants λm and μm, which are unknown quantities that change spatially in the measurement object, based on the displacement u, which is the measurement field, and the first relational equation between the displacement u and the elastic constants λm and μm obtained in step S130C, or calculates the elastic modulus, viscosity coefficient, etc. based on these elastic constants.

[0084] In other words, in the case of MRE, the measurement field is the displacement u, and the unknown quantities that vary spatially in the measurement object include the elastic modulus and the viscosity coefficient. The processing circuitry 150 performs MRE based on the unknown quantities calculated by the calculation function 139.

[0085] The first relational expression between the displacement u, which is the measurement field, and the elastic constants λm and μm is derived based on the equation of motion expressed by equation (8) and Hooke's law given by equation (9). In other words, the first relational expression is a relational expression derived from the equation of motion of an elastic body and Hooke's law.

[0086] Next, returning to FIG. 2, steps S100 and S110 in FIG. 2 will be described with reference to FIG. 7 as needed.

[0087] First, in step S100, a dual field is introduced to the measurement field such that the divergence of the dual field can be expressed using the measurement field. Then, in step S110, the dual field introduced in step S100 is expressed using the measurement field and a space-dependent unknown quantity. That is, in step S110, a second relational expression is introduced that expresses the dual field such that the divergence of the dual field can be expressed using the measurement field, using the measurement field and a space-dependent unknown quantity.

[0088] In the case of MREPT, for example, a field E (a quantity with a tilde) that satisfies the following equation (10) is introduced.

[0089]

number

[0090] where E x ,E y , and E z are the components of the electric field in the x-axis, y-axis, and z-axis directions, respectively, E + =(E x + i E y ) / 2.

[0091] Furthermore, by modifying the formula (2) which is Faraday's law, the following formula (11) is obtained.

[0092]

number

[0093] That is, the divergence of the field E (quantity with a tilde) on the left side of equation (11) is a constant multiple of the measurement field, and this divergence is the measurement field H + Therefore, the field E (a quantity with a tilde) on the left side of equation (11) is expressed as the measurement field H + and the measurement field H + becomes the dual field for

[0094] That is, in the case of MREPT, as shown in FIG. 3, in step S100A, the divergence of the dual field E (the quantity with a tilde) is calculated as the measurement field H + So that the measurement field H + A dual field E (a tilde quantity) for is introduced.

[0095] Furthermore, by transforming Ampere's law, equation (3), we obtain the following equation (12).

[0096]

number

[0097] Here, the operator ∇ C is an operator defined by the following equation (13).

[0098]

number

[0099] That is, in equation (12), the dual field E (the quantity with a tilde) is + and the spatially dependent unknown quantity λe.

[0100] That is, in step S110A, the dual field E (the quantity with a tilde) is converted into the measurement field H + and the unknown quantity λe derived from the electrical conductivity σe / dielectric constant ε.

[0101] In the case of QCM, for example, a field ψ satisfying the following equation (14) is introduced as a dual field to the measurement field φ expressed by equation (5).

[0102]

number

[0103] That is, in the case of QCM, as shown in FIG. 4, in step S100B, a dual field ψ is introduced to the measurement field φ so that the divergence of the dual field ψ is proportional to the zeroth power of the measurement field φ=arg(H+), i.e., a constant.

[0104] Moreover, similarly to the case of MREPT, by transforming the basic equation, the following equation (15) is obtained.

[0105]

number

[0106] That is, in equation (15), the dual field ψ is expressed using the measurement field φ and the unknown quantity ρe that has spatial dependence.

[0107] That is, in the case of QCM, as shown in FIG. 4, in step S110B, the dual field ψ is expressed using the measurement field φ and an unknown quantity derived from the resistivity ρe (conductivity σe).

[0108] In the case of MRE, for example, a field σm that satisfies the following equation (16) is introduced.

[0109]

number

[0110] Here, when comparing Equation (16) with Equation (8), which is the equation of motion, the field σm on the left side of Equation (16) is a stress tensor. Here, the divergence of the field σm on the left side of Equation (16) is expressed in terms of the measurement field u. Therefore, the field σm on the left side of Equation (16) is a dual field to the measurement field u, since its divergence is expressed in terms of the measurement field u. In other words, in MRE, the stress tensor σm becomes a dual field.

[0111] In equation (16), ρm is the density of the elastic body, and ω1 is the angular frequency of the externally applied vibration. In equation (16), the dual field σm is a tensor quantity, and the measurement field u is a vector field. However, as with equation (8), equation (16) means that the divergence of each row vector or column vector of the dual field σm is equal to each component of the measurement field u.

[0112] That is, in the case of MRE, as shown in FIG. 5, in step S100C, a dual field σm is introduced for each component of the displacement u, which is the measurement field, so that the divergence of the dual field σm (each row or column vector) becomes each component of the displacement u.

[0113] Furthermore, Equation (9), which is Hooke's law, can be expressed as it is in the following Equation (17), where the elastic constants λm and μm are the unknown quantities to be estimated, and the dual field σm is expressed using the measurement field u and spatially dependent unknown quantities.

[0114]

number

[0115] That is, as shown in FIG. 5, in step S100C, the dual field σ m is expressed using the measurement field u and the elastic constants λ m and μ m which are unknown quantities.

[0116] Returning to FIG. 2, in step S120, Helmholtz decomposition of the dual field is performed. Here, Helmholtz decomposition is an operation of expressing a three-dimensional vector field as the sum of a rotation-free field and a divergence-free field using Helmholtz's theorem. According to Helmholtz's theorem, it is known that a three-dimensional vector field can be expressed as the sum of a rotation-free field and a divergence-free field. The following equation (18) represents the Helmholtz decomposition of an arbitrary three-dimensional vector field f(r') within a bounded region of interest Ω.

[0117]

number

[0118] where r and r' represent positions, dv is a volume element within the region of interest Ω, dS is an area element at the boundary ∂Ω of the region of interest Ω, and n is a normal vector at the boundary ∂Ω. The first and second terms in equation (18) are the volume integral and surface integral terms, respectively, of a rotation-free vector field. Meanwhile, the third term in equation (18) is a divergence-free vector field. Equation (18) is an identity that holds for any three-dimensional vector field.

[0119] In step S120, the Helmholtz decomposition of the dual field is performed. That is, by substituting the dual field introduced in step S100 into equation (18), the dual field can be decomposed into the sum of a rotation-free vector field and a divergence-free vector field. The volume integral term of the decomposed rotation-free vector field is expressed using the divergence of the dual field.

[0120] For example, in the case of MREPT, the dual field is E (a quantity with a tilde), so substituting this into equation (18) gives the following equation (19).

[0121]

number

[0122] That is, in the case of MREPT, in step S120A of Fig. 3, the dual field E (a tilde-prefixed quantity) is subjected to Helmholtz decomposition. This allows the dual field E (a tilde-prefixed quantity) to be decomposed into the sum of a rotation-free vector field and a divergence-free vector field, as shown in equation (19). Here, the volume integral term of the decomposed rotation-free vector field is expressed using the divergence of the dual field E (a tilde-prefixed quantity).

[0123] In addition, in the case of QCM, the dual field is ψ, so when this is substituted into equation (18), the following equation (20) is obtained.

[0124]

number

[0125] That is, in the case of QCM, the dual field ψ is subjected to Helmholtz decomposition in step S120B of Fig. 4. This allows the dual field ψ to be decomposed into the sum of a rotation-free vector field and a divergence-free vector field, as shown in Equation (20). Here, the volume integral term of the decomposed rotation-free vector field is expressed using the divergence of the dual field ψ.

[0126] In addition, in the case of MRE, the dual field is σm, so when this is substituted into equation (18), the following equation (21) is obtained.

[0127]

number

[0128] 5, the dual field σ is subjected to Helmholtz decomposition. This allows the dual field σ to be decomposed into the sum of a rotation-free vector field and a divergence-free vector field, as shown in Equation (21). Here, the volume integral term of the decomposed rotation-free vector field is expressed using the divergence of the dual field σ.

[0129] Next, the processing of step S130 in FIG. 2 will be described. As described in step S100, the divergence of the dual field is expressed using the measurement field. Therefore, for example, as shown in equations (19) to (21), the volume integral term of the rotation-free vector field obtained by Helmholtz decomposition of the dual field can be expressed using the divergence of the dual field. Therefore, by substituting a relational expression indicating that the divergence of the dual field is the measurement field, the volume integral term of the rotation-free vector field can be expressed using the measurement field. Furthermore, as described in step S110, the dual field can be expressed as a second relational expression using the measurement field and a spatially dependent unknown quantity. Therefore, by substituting this second relational expression into the Helmholtz decomposition equation of the dual field, the processing circuit 150 can obtain, by the calculation function 139, a first relational expression, which is a relational expression between the measurement field and the spatially dependent unknown quantity.

[0130] Thus, in step S130, the processing circuit 150 can obtain, by the calculation function 139, the first relational equation between the measurement field and the spatially dependent unknown quantity based on the second relational equation, which is a relational equation that expresses the dual field using the measurement field and the spatially dependent unknown quantity, and the Helmholtz decomposition of the dual field.

[0131] Considering the advantage of using the divergence of the dual field as the measurement field, for example, in the case of MREPT, if we substitute equation (12) into equation (11) and specifically calculate the left side of equation (11), we get ∇·(λe∇ c H + )=∇λe·∇ C H + +λe∇·(∇ c H +), and the left-hand side of equation (11) is complex, combining a term including ∇λe, i.e., the spatial derivative of a spatially dependent unknown quantity, with the spatial derivative of the measurement field. However, the sum of these forms the right-hand side of equation (11), which is a simple expression consisting of a constant multiple of the measurement field itself. Therefore, by using the divergence of the dual field as the measurement field, the divergence term of the dual field, which appears in the Helmholtz decomposition of the dual field, can be replaced with the measurement field, and the spatial derivative term of the spatially dependent unknown quantity can be eliminated from the integral equation representing the first relational expression. In other words, the first relational expression becomes an integral equation from which the spatial derivative term of the unknown quantity has been removed. As a result, the calculation algorithm becomes numerically stable, and the resulting image quality is stable.

[0132] Next, the processing of step S130 will be described in detail for each application example. For example, in the case of MREPT, if we substitute equation (11) into the divergent part of the dual field E (a quantity with a tilde attached) in the rotation-free vector field in the first term on the right-hand side of equation (19), and then substitute equation (12) into the remaining part of the dual field E (a quantity with a tilde attached), we obtain the following equation (22).

[0133]

number

[0134] That is, in step S130A of FIG. 3, the dual field E (a quantity with a tilde) is converted into the measurement field H + Based on equation (12), which is a relational expression expressed using the spatially dependent unknown quantity λe, and equation (19), which is a Helmholtz decomposition of the dual field E (a quantity with a tilde), the measurement field H + and the spatially dependent unknown quantity λe, we can obtain equation (22).

[0135] Also, for example, in the case of QCM, if we substitute equation (14) into the divergent part of the dual field ψ in the non-rotating vector field in the first term on the right-hand side of equation (20), and then substitute equation (15) into the remaining part of the dual field ψ, we obtain the following equation (23).

[0136]

number

[0137] That is, in step S130B of FIG. 4, based on equation (15), which is a relational expression expressing the dual field ψ using the measurement field φ and the spatially dependent unknown quantity ρe, and equation (20), which is the Helmholtz decomposition of the dual field ψ, equation (23), which is a relational expression between the measurement field φ and the spatially dependent unknown quantity ρe, is derived.

[0138] Also, for example, in the case of MRE, if we substitute equation (16) into the divergent part of the dual field σm in the non-rotating vector field in the first term on the right-hand side of equation (21), and then substitute equation (17) into the remaining part of the dual field σm, we obtain the following equation (24).

[0139]

number

[0140] That is, in step S130C of FIG. 5, based on Equation (17), which is a relational expression expressing the dual field σm using the displacement u, which is the measurement field, and the elastic constants λm and μm, which are spatially dependent unknown quantities, and Equation (21), which is the Helmholtz decomposition of the dual field σm, Equation (24), which is a relational expression between the displacement u, which is the measurement field, and the elastic constants λm and μm, which are spatially dependent unknown quantities, is derived.

[0141] Next, step S140 in Fig. 2 will be described again. In step S140, a measurement field corresponding to the spatial distribution of a predetermined physical quantity in the measurement object is acquired, and an unknown quantity in the measurement object is calculated based on the acquired measurement field and the relational expression obtained in step S130. Specifically, in step S140, processing circuit 150 first acquires, by acquisition function 138, a measurement field corresponding to the spatial distribution of the predetermined physical quantity in the measurement object.

[0142] For example, in the case of MREPT, the processing circuitry 150 receives, via the acquisition function 138, for example, from the receiving circuitry 110, an RF magnetic field H + is obtained as the measurement field by the method described above.

[0143] In the case of QCM, the processing circuitry 150 receives the RF magnetic field H via the acquisition function 138, for example, from the receiving circuitry 110. + The phase of the measured field φ is obtained.

[0144] In the case of MRE, a subject P is placed in the static magnetic field of an MRI apparatus, and a vibration generator (not shown) applies, for example, external sinusoidal transverse vibration to the subject. The sequence control circuit 120 executes, for example, a pulse sequence of a motion probing gradient (MPG) phase shift method in which a gradient magnetic field alternates between positive and negative polarities in synchronization with the external vibration. The processing circuit 150 acquires signals related to the pulse sequence using the acquisition function 138. The processing circuit 150 acquires information related to the displacement u based on the acquired signals using the acquisition function 138.

[0145] Next, the processing circuit 150 uses the calculation function 139 to estimate the spatially dependent unknown quantity based on the acquired measurement field and the first relational equation between the measurement field and the spatially dependent unknown quantity obtained in step S130 described below.

[0146] For example, in the case of MREPT, as shown in step S140A of FIG. 3, processing circuitry 150 calculates the acquired measurement field H + Based on the equation (22), which is the relational expression obtained in step S130A, the impedance λe or the conductivity σe / dielectric constant ε, which is an unknown quantity that varies spatially in the measurement object, is calculated.

[0147] For example, in the case of QCM, as shown in step S140B of FIG. 4, the processing circuit 150 uses the calculation function 139 to calculate the resistivity ρe / conductivity σe, which is an unknown quantity that varies spatially in the measurement object, based on the acquired measurement field φ and equation (23), which is the relational equation obtained in step S130B.

[0148] For example, in the case of MRE, as shown in step S140C of FIG. 5, the processing circuit 150 uses the calculation function 139 to calculate the elastic constants λm, μm, etc., which are unknown quantities that change spatially in the measurement object, based on the displacement u, which is the acquired measurement field, and Equation (24), which is the relational equation obtained in step S130C.

[0149] Next, we will explain the advantages of generating images using equations (22) to (24), which are relational equations that express the dual field using the measurement field and spatially dependent unknown quantities. A feature of these relational equations is that they are all linear integral equations with respect to the unknown quantities. Therefore, solutions can be obtained directly without using iterative methods. On the other hand, if the integral equation is not a linear equation with respect to the unknown quantities, calculations using iterative methods are required, and depending on the initial solution, there is a possibility of falling into a local optimum solution. However, the method according to the embodiment can directly obtain a solution without using iterative methods.

[0150] Furthermore, these equations do not include a term for the second-order derivative with respect to the spatial measurement field. This makes the imaging method robust against noise. For example, in the case of MREPT, even when the conductivity of tissues, such as localized solid tumors, changes discontinuously relative to normal tissue, the measurement accuracy of conductivity and permittivity is less likely to decrease, making it possible to image these tissues with good contrast or perform quantitative evaluations.

[0151] In addition, conventional methods using integral representations sometimes use integral representations of the electromagnetic field over the entire region. In such cases, for example, an MRI coil or the like serving as a source of the electromagnetic field must also be included in the region where the integration is performed. Therefore, in order to eliminate the influence of the MRI coil, it may be necessary to measure or calculate the electromagnetic field under no load. In contrast, the method according to the embodiment can limit the Helmholtz decomposition to a bounded region of interest, eliminating the need to measure or calculate the electromagnetic field under no load.

[0152] In this step in which the processing circuitry 150 calculates the unknown quantities using the calculation function 139 by solving the first relational expressions (22) to (24), etc., a morphological image of the object may be captured to identify the region of interest Ω in the first relational expressions (22) to (24), and step S140 may be performed based on the identified region of interest Ω. This can further improve the accuracy of estimating the unknown quantities.

[0153] An example of the procedure for the process of step S140 in such an embodiment is shown in Figure 8. That is, steps S141 to S143 in Figure 8 are an example of step S140 in Figure 2. Below, an example will be described in which magnetic resonance imaging of the brain region is performed, for example.

[0154] First, the sequence control circuit 120 executes a pulse sequence for performing imaging to generate a morphological image of the measurement target. For example, if the measurement target is a brain, the sequence control circuit 120 executes a pulse sequence for imaging the brain.

[0155] In step S141, the processing circuitry 150 acquires, from the sequence control circuitry 120, magnetic resonance signals collected based on the pulse sequence executed by the sequence control circuitry 120 using the acquisition function 138, and acquires a morphological image of the measurement target based on the acquired magnetic resonance signals. For example, if the measurement target is a brain, the processing circuitry 150 acquires, using the acquisition function 138, a morphological image of the brain region by magnetic resonance imaging based on the magnetic resonance signals generated by the pulse sequence executed by the sequence control circuitry 120.

[0156] Next, in step S142, the processing circuitry 150 performs segmentation processing on the measurement target included in the anatomical image using the identification function 137, thereby identifying a measurement target region Ω (region of interest Ω) from which a measurement field is to be acquired from the measurement target using the acquisition function 138. As an example, when the measurement target is a brain, the processing circuitry 150 uses the identification function 137 to perform segmentation processing to identify a region of the substantial part of the brain as the measurement target region Ω (region of interest Ω) based on the anatomical image acquired in step S141.

[0157] Next, in step S143, the processing circuit 150 acquires the measurement field in the measurement target region Ω (region of interest Ω) measured and acquired by the acquisition function 138, and calculates the unknown quantity based on the measurement field in the measurement target region Ω (region of interest Ω) by the calculation function 139. As an example, the processing circuit 150 acquires the measurement field in a region of a substantial part of the brain by the acquisition function 138, and calculates the unknown quantity by solving the first relational equations, such as Equations (22) to (24), for the measurement target region Ω by the calculation function 139. This can further improve the accuracy of estimating the unknown quantity.

[0158] Another advantage of generating an image using equations (22) to (24) is that they are linear integral equations, so that regularization can be easily introduced.

[0159] In the case of MREPT, at points where the dual field E (the tilde quantity) is zero, both the left and right sides of equation (22) are zero, and λe is not determined. In fact, for example, when using a numerical phantom such as that shown in Figure 9(a), at points where the field E (the tilde quantity) on the left side of equation (22) is zero, as shown in Figure 9(b), artifacts occur in the estimated conductivity image in the corresponding region 10, as shown in Figure 9(c). In particular, when noise is added to the observed data H+, this effect becomes significant, as shown in Figure 9(d).

[0160] In such a case, instead of directly solving the integral equation of equation (22), for example, as in the following equation (25), a function obtained by adding a regularization term R(x) (x is a vector quantity) to the first term, which is the squared error between the left and right sides of the integral equation of equation (22), is used as an evaluation function, and by minimizing the evaluation function, the processing circuit 150 can calculate the unknowns using the calculation function 139.

[0161]

number

[0162] where x is an unknown vector obtained by arranging the unknown quantity λe for the number of pixels, and A and b are the coefficient matrix and right-hand side vector determined from equation (22). The regularization term R(x) is added to make the unknown quantity λe spatially smooth, thereby reducing artifacts and improving image quality.

[0163] In other words, the first relational expression between the measurement field and the unknown quantity, as shown in Equations (22) to (24), may have a singularity around which the numerical calculation becomes unstable, for example, near the zero point of the dual field. In response to this, the processing circuitry 150 can introduce regularization using the calculation function 139, i.e., calculate the unknown quantity based on an evaluation function consisting of a term obtained from the first relational expression and a regularization term. This improves numerical stability around the singularity in the first relational expression, thereby improving image quality.

[0164] Examples of such calculation results are shown in Figures 9(e) and 9(f). Figure 9(e) shows the result when using the following equation (26) where R(x) is the L2 norm of x, and Figure 9(f) shows the result when using the following equation (27) where R(x) is the total variation of x. In both cases, a reduction in artifacts is observed.

[0165]

number

[0166]

number

[0167] It should be noted that the method of giving the regularization term is not limited to these two examples.

[0168] The processing for MREPT has been explained above. In the case of QCM and MRE, similar regularization processing can be performed by deriving equation (25) based on equations (23) and (24), respectively, instead of equation (25) derived based on equation (22).

[0169] That is, in the case of QCM, in equation (25), x in the regularization term R(x) is an unknown vector in which the unknown quantity ρe is arranged for the number of pixels, and A and b are a matrix and a right-hand vector determined from equation (23). The processing circuit 150 calculates the unknown quantity ρe using the calculation function 139 based on equation (25) derived in this way.

[0170] In the case of MRE, in equation (25), x in the regularization term R(x) is an unknown vector in which the unknown quantities λm and μm are arranged for the number of pixels, and A and b are a matrix and a right-hand vector determined from equation (24). The processing circuit 150 uses the calculation function 139 to calculate the unknown quantities λm and μm based on equation (25) derived in this way.

[0171] According to at least one of the embodiments described above, image quality can be improved.

[0172] Although several embodiments have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention.

[0173] For example, in equation (11), the divergence of the field E (quantity with a tilde) on the left side is a constant multiple of the measurement field, and the divergence is the measurement field H + The measurement field H +However, the definition of the dual field is not limited to this. For example, let E, which is a quantity that satisfies both equation (11) derived from Faraday's law and equation (12) derived from Ampere's law, be defined as H + This may also be called the dual field of

[0174] Similarly, in the case of QMC, for example, in equation (14), the divergence of the field ψ on the left-hand side is a constant, and the dual field of the measurement field φ is the field whose divergence is expressed as the zeroth power of the measurement field φ. However, the definition of the dual field is not limited to this. For example, we can call ψ, a quantity that satisfies both equation (14) derived from Faraday's law and equation (15) derived from Ampere's law, the dual field of the measurement field φ.

[0175] Similarly, in the case of MRE, for example, in equation (16), the divergence of the field σm on the left-hand side is a constant multiple of the measurement field, and the divergence expressed in terms of the measurement field u is the dual field of the measurement field u. However, the definition of the dual field is not limited to this. For example, σm, which is a quantity that satisfies both equation (16) derived from the equation of motion and equation (17) derived from Hooke's law, can be called the dual field of the measurement field u.

[0176] These embodiments may be embodied in various other forms, and various omissions, substitutions, modifications, and combinations of embodiments may be made without departing from the spirit of the invention. These embodiments and modifications are intended to be included in the scope of the inventions and their equivalents as defined in the accompanying claims, as well as in the spirit and scope of the inventions. [Explanation of symbols]

[0177] 130 Information processing equipment 131 Interface Functions 133 Control Functions 136 Generation function 137 Specific Functions 138 Acquisition Function 139 Calculation Function 150 Processing Circuit

Claims

1. an acquisition unit that acquires a measurement field corresponding to a spatial distribution of a predetermined physical quantity in a measurement target; a calculation unit that calculates the unknown quantity in the measurement object based on a first relational expression between the measurement field and a spatially dependent unknown quantity and the measurement field acquired by the acquisition unit, the first relational equation is a relational equation obtained based on a second relational equation that expresses the dual field, the divergence of which can be expressed using the measurement field, using the measurement field and the unknown quantity, and a Helmholtz decomposition of the dual field.

2. The information processing apparatus according to claim 1 , wherein the first relational expression is an integral equation from which a term of a spatial derivative of the unknown quantity is removed.

3. The information processing apparatus according to claim 1 , wherein the measurement field is a radio frequency (RF) magnetic field, and the unknown quantity includes at least one of electrical conductivity and dielectric constant.

4. The information processing device according to claim 3 , wherein the measurement field is the amplitude and phase of the RF magnetic field.

5. The information processing apparatus according to claim 4 , wherein magnetic resonance electrical property tomography (MREPT) is performed based on the unknown quantity calculated by the calculation unit.

6. the measurement field is the phase of the RF magnetic field; The information processing device according to claim 3 , wherein QCM (Quantitative Conductivity Mapping) is performed based on the unknown quantity calculated by the calculation unit.

7. The information processing device according to claim 1 , wherein the measurement field is a displacement, and the unknown quantity includes at least one of an elastic modulus or a viscosity coefficient.

8. The information processing device according to claim 1 , wherein the measurement field is a displacement and the dual field is a stress tensor.

9. The information processing apparatus according to claim 1 , wherein MRE (Magnetic Resonance Elastography) is performed based on the unknown quantity calculated by the calculation unit.

10. The information processing device according to claim 1 , wherein the first relational expression is a relational expression derived from Ampere's law and Faraday's law.

11. The information processing apparatus according to claim 1 , wherein the first relational expression is a relational expression derived from an equation of motion of an elastic body and Hooke's law.

12. the acquisition unit acquires a morphological image relating to a measurement object; a specifying unit that specifies a measurement target region for acquiring the measurement field from the measurement target by performing a segmentation process on the measurement target included in the anatomical image, The information processing apparatus according to claim 1 , wherein the calculation unit calculates the unknown quantity based on the measurement field in the measurement target region.

13. the measurement target is a brain, the acquisition unit acquires the morphological image of the brain region by magnetic resonance imaging; the identifying unit identifies a region of a brain parenchyma as the measurement target region based on the anatomical image by the segmentation processing; The information processing device according to claim 12 , wherein the calculation unit calculates the unknown quantity based on the measurement field in a region of the substantial portion.

14. The information processing device according to claim 1 , wherein the calculation unit calculates the unknown quantity based on an evaluation function including a term obtained from the first relational expression and a regularization term.

15. Acquire a measurement field corresponding to the spatial distribution of a predetermined physical quantity in the measurement target; calculating the unknown quantity in the measurement object based on a first relational expression between the measurement field and a spatially dependent unknown quantity and the acquired measurement field; an information processing method, wherein the first relational equation is a relational equation obtained based on a second relational equation that expresses the dual field, the divergence of which can be expressed using the measurement field, using the measurement field and the unknown quantity, and a Helmholtz decomposition of the dual field.

Images