JP7744253B2 - Information processing device and information processing method - Google Patents

Description

The embodiments disclosed in this specification and drawings relate to an information processing device and an information processing method.

It is conceivable that medical image processing devices could provide new diagnostic information. For example, unlike the morphological images obtained with conventional X-ray CT or MRI devices, it is conceivable that unknown quantities could be electrical properties such as conductivity and dielectric constant inside the human body, and mechanical properties such as elasticity and viscosity, and the three-dimensional distribution of these unknown quantities could be calculated and visualized.

Examples of these technologies include MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductivity Mapping), and MRE (Magnetic Resonance Elastography). These techniques make it possible to measure conditions such as cancer and cirrhosis as changes in physical constants.

In some cases, electrical and mechanical properties are calculated and images are generated 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 conductivity changes discontinuously compared to normal tissue, such as in the case of localized solid cancer.

In addition, the spatial dependence of electrical and mechanical properties can sometimes 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 unknown quantities, requiring iterative methods to solve the integral equation, and often resulting in a local optimum if an appropriate initial solution is not provided.

International Publication No. 2013/057655 U.S. Pat. No. 5,592,085

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 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 J. Chi, et al., “Magnetic Resonance-Electrical Properties Tomography by Directly Solving Maxwell's Curl Equation”, Appl. Sci. 2020, Vol.10, No.9, 3318,

One of the problems that the embodiments disclosed in this specification and drawings attempt to solve is improving image quality. However, the problems that the embodiments disclosed in this specification and drawings attempt to solve 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.

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 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 Helmholtz decomposition of the dual field.

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

The information processing device and information processing method according to the embodiment will be described below with reference to the drawings.

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

As shown in FIG. 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 various components of the sequence control circuit 120 and the information processing device 130 may be integrated or separated as appropriate.

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 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 does not need to be equipped with a static magnetic field power supply. The static magnetic field power supply may also be provided separately from the magnetic resonance imaging apparatus 100.

The gradient magnetic field coil 103 is a hollow, approximately cylindrical coil and is placed 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. These three coils are individually supplied with current from the gradient magnetic field power supply 104 and generate gradient magnetic fields along the X, Y, and Z axes whose magnetic field strength in the Z direction varies depending on the distance from the center of each axis. The gradient magnetic fields for the X, Y, and Z axes generated by the gradient magnetic field coil 103 are, for example, a slice 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.

The bed 105 includes a top plate 105a on which the subject P is placed, and under the control of the 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 typically 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 and vertical directions.

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

The receiving coil 109 is positioned 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 radio frequency magnetic field. When the receiving coil 109 receives the magnetic resonance signals, it outputs the received magnetic resonance signals to the receiving circuit 110.

Note that the above-mentioned transmitting coil 107 and receiving coil 109 are merely examples. The coil may be configured by combining one or more of a coil with only a transmitting function, a coil with only a receiving function, or a coil with both a transmitting and receiving function.

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 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 also be provided on the gantry side, which includes the static magnetic field magnet 101, gradient magnetic field coil 103, etc.

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

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 the 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.

In this embodiment, the processing functions performed by the interface function 131, control function 133, generation function 136, identification function 137, acquisition function 138, and calculation function 139 are stored in memory 132 in the form of computer-executable programs. The processing circuit 150 is a processor that reads and executes the programs from memory 132 to realize the functions corresponding to each program. In other words, the processing circuit 150, after reading each program, has each of the functions shown in the processing circuit 150 in FIG. 1. Note that while FIG. 1 illustrates a single processing circuit 150 realizing the processing functions performed by the interface function 131, control function 133, generation function 136, identification function 137, acquisition function 138, and calculation function 139, the processing circuit 150 may also 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. In FIG. 1, the interface function 131, control function 133, generation function 136, identification function 137, acquisition function 138, and calculation function 139 are examples of a reception unit, control unit, generation unit, identification unit, acquisition unit, and calculation unit, respectively. The sequence control circuit 120 is an example of a sequence control unit. Specific processing by the identification function 137, acquisition function 138, and calculation function 139 will be described later.

The term "processor" used in the above description refers to circuits such as a CPU (Central Processing Unit), GPU (Graphical Processing Unit), or an application-specific integrated circuit (ASIC), programmable logic device (e.g., Simple Programmable Logic Device (SPLD), Complex Programmable Logic Device (CPLD), and Field Programmable Gate Array (FPGA)). The processor performs functions by reading and executing programs stored in memory 132.

In addition, instead of storing the program in memory 132, the program may be configured to be directly embedded in the processor circuitry. In this case, the processor realizes its functions by reading and executing the program embedded in the circuitry. Note that the bed control circuitry 106, transmission circuitry 108, reception circuitry 110, etc. are also similarly configured using electronic circuits such as the processors described above.

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

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

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 RAM (Random Access Memory), flash memory, a hard disk, an optical disk, etc.

The input device 134 accepts various instructions and information input from the operator. The input device 134 is, for example, a pointing device such as a mouse or 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, images 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.

The processing circuitry 150 uses the control function 133 to perform overall control of the magnetic resonance imaging apparatus 100, controlling imaging, image generation, image display, etc. For example, the processing circuitry 150 with 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. The processing circuitry 150 with the control function 133 also transmits the generated sequence information to the sequence control circuit 120.

The processing circuitry 150 uses the generation function 136 to read the k-space data from the memory 132 and generate an image by performing reconstruction processing such as a Fourier transform on the read k-space data.

Next, we will explain the background to the embodiments.

It is conceivable that medical image processing devices could provide new diagnostic information that differs from that of conventional X-ray CT and MRI devices. For example, unlike the structural images obtained with conventional X-ray CT and MRI devices, it is conceivable that unknown quantities could be electrical properties such as conductivity and dielectric constant inside the human body, and mechanical properties such as elasticity and viscosity, and the three-dimensional distribution of these unknown quantities could be calculated and visualized.

Examples of these technologies include MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductivity Mapping), and MRE (Magnetic Resonance Elastography). These technologies also make it possible to measure conditions such as cancer and cirrhosis as changes in physical constants.

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

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, with the former method, the differential equation to be solved contains higher-order derivatives of the measurement field, which can result in an ill-posed problem. With the latter method, the integral equation to be solved is nonlinear with respect to the unknown quantities, requiring iterative methods to solve the integral equation, and if an appropriate initial solution is not provided, it can often result in a local optimum.

In light 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 quantities, and calculates the spatially dependent unknown quantities based on a relational expression derived from the Helmholtz decomposition of the dual field.

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

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 expression between the measurement field and a spatially dependent unknown quantity and the measurement field acquired by the acquisition unit, where 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.

This information processing device 130 and information processing method can improve image quality.

The processing performed by the information processing device according to the embodiment will be described below using Figures 2 to 7. Figure 2 is a flowchart illustrating the processing procedure performed by the information processing device according to the embodiment. Figure 2 describes the general principles of the processing procedure performed by the information processing device according to the embodiment, while Figures 3 to 5 describe the details of the processing when the procedure is applied in individual application cases. Specifically, Figures 3 to 5 specifically explain the procedures when the processing according to the embodiment is applied in the examples of MREPT (Magnetic Resonance Electrical Property Tomography), QCM (Quantitative Conductive Mapping), and MRE (Magnetic Resonance Elastography), respectively. Figure 6 shows the relationship between the measurement field, unknown quantities to be estimated, and the fundamental equations, while Figure 7 explains the measurement field, dual field, and the relationship between the measurement field and dual field.

First, before introducing the dual field, we will explain the relationship between the measurement field and unknown quantities in the information processing device 130 according to the embodiment.

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

Figure 6 shows the relationship between these measurement fields and unknown quantities in this embodiment.

A first application example of this embodiment is MREPT (Magnetic Resonance Electrical Property Tomography). MREPT is a method that uses MRI to measure the amplitude and phase of RF magnetic fields inside the human body and visualize the distribution of electrical conductivity and permittivity.

In the case of MREPT, the processing circuit 150 acquires, via the acquisition function 138, an RF magnetic field H ⁺ given by the following equation (1) as a measurement field.

Here, H _x and H _y are the RF magnetic fields in the x-axis and y-axis directions, respectively, which are orthogonal to the z-axis.

Faraday's law, given by the following equation (2), and Ampere's law, given by the following equation (3), also hold true.

where E is the electric field, ω is the Larmor angular frequency, μ ₀ is the magnetic permeability of a vacuum, H is the RF magnetic field, and λ is the impedance given by the following equation (4):

Here, σe is the conductivity and ε is the permittivity.

In addition, in the case of MREPT, the processing circuit 150 uses the calculation function 139 to estimate the conductivity σe, the permittivity ε, or the impedance λe given by equation (4) as unknown quantities with spatial dependence.

3, in the case of MREPT, processing circuitry 150 acquires the RF magnetic field H ⁺ given by equation (1) as a measurement field using acquisition function 138. Next, processing circuitry 150 calculates the electrical conductivity σe, dielectric constant ε, or impedance λe, which are unknown quantities that vary spatially in the measurement object, using calculation function 139, based on the RF magnetic field H ⁺ , which is the measurement field, and the first relational expression between the measurement field H ⁺ and the spatially dependent unknown quantity λe obtained in step S130A.

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

The first relational expression between the measurement field ^H and the unknown quantity λ 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 derived from Ampere's law and Faraday's law.

A method for measuring the RF magnetic field H ⁺ in each voxel of the measurement target will be 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.

Here, since 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.

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

As an example of measuring the amplitude of the 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 object being measured. The processing circuitry 150, using the generation function 136, generates GRE images for the two flip angles based on the pulse sequence executed by the sequence control circuitry 120. Here, if the ratio of signal intensities per voxel is r, then r = sin α/sin 2α = 1/2 cos α. Therefore, the processing circuitry 150 can calculate the flip angle α based on the ratio r of signal intensities per voxel obtained from the images generated for the two flip angles using the calculation function 139. Then, by calculating sin α based on this, the amplitude of the RF magnetic field is measured.

In addition, 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 the processing circuit 150 use the calculation function 139 to measure the transmitted RF phase based on the phase image at the peak of the SE signal from the measurement target. Here, we will explain an example in which a quadrature birdcage coil is used to transmit and receive the RF magnetic field. This coil is known to generate a very uniform RF magnetic field in free space. (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 gradient magnetic field drive remains, and is expressed as shown in equation (5) below.

Here, φ(r) is the phase of the SE image, r is the position, φ ₊ (r) is the phase of the transmit 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 it from the phase of the SE image obtained by reversing the gradient magnetic field using the same SE sequence, yielding φ ₊ (r) + φ _- (r). Meanwhile, it is known that in this coil, φ ₊ (r) and φ _- (r) are nearly equal (φ ₊ (r) ≒ φ _- (r)). Therefore, the desired transmit RF phase φ ₊ (r) can be calculated as (φ ₊ (r) + φ _- (r))/2. While 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 or estimation methods may be used as long as they can obtain amplitude and phase information.

A second application example of this embodiment is QCM (Quantitative Conductivity Mapping). QCM is a method for imaging the distribution of electrical conductivity based solely on the phase distribution of an RF magnetic field.

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.

More specifically, processing circuitry 150 acquires, via acquisition function 138, the measurement field φ by extracting the phase component of the RF magnetic field H ⁺ .

In addition, in the case of a QCM, the processing circuit 150 uses the calculation function 139 to estimate the conductivity σe or the resistivity ρe given by equation (7) as an unknown quantity with spatial dependence.

That is, in the case of a QCM, as shown in step S140B of FIG. 4, the processing circuitry 150 acquires the measurement field φ given by equation (6) using the acquisition function 138. Next, the processing circuitry 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.

In other words, in the case of QCM, the measurement field is, for example, the phase φ of the RF magnetic field H ⁺ , and the unknown quantities that vary spatially in the measurement object include the conductivity σ or the resistivity ρ. The processing circuit 150 performs QCM based on the unknown quantities calculated by the calculation function 139.

The first relation between the measurement field φ and the resistivity ρe is derived by assuming that the spatial variation of the H+ amplitude 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.

A third application example of this embodiment is MRE (Magnetic Resonance Elastography). MRE is a method of using MRI to measure the displacement distribution when external vibrations are applied to the human body, and to visualize the distribution of elasticity, viscosity, and other properties inside the human body.

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.

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

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) means that multiplying each component of displacement u by _-ω1 ² ρm is equal to the divergence of the vector taken from each row or column of 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 unit matrix.

In addition, in the case of MRE, the processing circuitry 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 dependence.

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

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.

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 viscosity. The processing circuitry 150 performs MRE based on these unknown quantities calculated by the calculation function 139.

The first relational equation 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 in equation (8) and Hooke's law given in equation (9). In other words, the first relational equation is derived from the equation of motion of an elastic body and Hooke's law.

Next, returning to Figure 2, steps S100 and S110 in Figure 2 will be explained with reference to Figure 7 as appropriate.

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 spatially dependent unknown quantity. That is, in step S110, a second relational equation 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 spatially dependent unknown quantity.

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

where E _x , E _y , and E _z are the components of the electric field in the x-, y-, and z-axis directions, respectively;
E ⁺ = (E _x + i E _y )/2.

Furthermore, by transforming Faraday's law, equation (2), we obtain the following equation (11).

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 expressed in terms of the measurement field H ⁺ . Therefore, the divergence of the field E (quantity with a tilde) on the left side of equation (11) is expressed in terms of the measurement field H ⁺ , and it becomes a dual field to the measurement field H ⁺ .

That is, in the case of MREPT, as shown in FIG. 3, in step S100A, a dual field E (a tilde quantity) is introduced for the measurement field H ⁺ such that the divergence of the dual field E (a tilde quantity) becomes the measurement field H ⁺ .

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

Here, the operator ∇ _C is an operator defined by the following equation (13).

That is, in equation (12), the dual field E (the quantity with a tilde) is expressed using the measurement field H ⁺ and the unknown quantity λ e that has spatial dependence.

That is, in step S110A, the dual field E (a quantity with a tilde) is expressed using the measurement field H ⁺ and the unknown quantity λ e derived from the conductivity σ e /dielectric constant ε.

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

That is, in the case of QCM, as shown in Figure 4, in step S100B, a dual field ψ is introduced relative 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.

Furthermore, as in the case of MREPT, by transforming the fundamental equation, we obtain the following equation (15).

In other words, in equation (15), the dual field ψ is expressed using the measurement field φ and the spatially dependent unknown quantity ρe.

In other words, in the case of a QCM, as shown in Figure 4, in step S110B, the dual field ψ is expressed using the measurement field φ and unknown quantities derived from the resistivity ρe (conductivity σe).

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

Comparing equation (16) with equation (8), which is the equation of motion, the field σm on the left side of equation (16) is the 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.

In equation (16), ρ is the density of the elastic body, and _ω is the angular frequency of the externally applied vibration. In equation (16), the dual field σ 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 σ is equal to each component of the measurement field u.

In other words, in the case of MRE, as shown in Figure 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.

Furthermore, Hooke's law, equation (9), can be directly expressed as equation (17) below, in which 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.

That is, as shown in Figure 5, in step S100C, the dual field σm is expressed using the measurement field u and the unknown elastic constants λm and μm.

Returning to Figure 2, in step S120, Helmholtz decomposition of the dual field is performed. Here, Helmholtz decomposition is an operation that uses Helmholtz's theorem to express a three-dimensional vector field as the sum of a rotation-free field and a divergence-free field. 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.

Here, 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 the 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. On the other hand, 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.

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 rotation-free vector field decomposed in this way is expressed using the divergence of the dual field.

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

That is, in the case of MREPT, in step S120A of Figure 3, the dual field E (the tilde-prefixed quantity) is subjected to Helmholtz decomposition. This allows the dual field E (the 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 rotation-free vector field decomposed in this way is expressed using the divergence of the dual field E (the tilde-prefixed quantity).

Also, in the case of a QCM, the dual field is ψ, so substituting this into equation (18) gives the following equation (20).

That is, in the case of QCM, the dual field ψ is subjected to Helmholtz decomposition in step S120B of Figure 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 rotation-free vector field decomposed in this way is expressed using the divergence of the dual field ψ.

Also, in the case of MRE, the dual field is σm, so substituting this into equation (18) gives the following equation (21).

Here, in step S120C of Figure 5, the dual field σm is subjected to Helmholtz decomposition. This allows the dual field σm 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 rotation-free vector field decomposed in this way is expressed using the divergence of the dual field σm.

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 circuitry 150, using the calculation function 139, can obtain a first relational expression, which is the relational expression between the measurement field and the spatially dependent unknown quantity.

In this way, in step S130, the processing circuit 150, using the calculation function 139, can obtain a 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.

Furthermore, 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-hand side of equation (11), the formula for vector analysis becomes ∇・( _λe∇c H ⁺ )＝∇λe・_∇C H ⁺ +λe∇・( _∇c H ⁺ ), and the left-hand side of equation (11) has a complex form due to the combination of a term including ∇λe, that is, the spatial derivative term of an unknown quantity with space dependence, and the spatial derivative of the measurement field, but the sum of these becomes the right-hand side of equation (11), which is a simple formula that is 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 that appears in the Helmholtz decomposition of the dual field can be replaced with the measurement field, and the term of the spatial derivative of the unknown quantity that has space dependency can be eliminated from the integral equation that expresses the first relational expression. That is, the first relational expression becomes an integral equation from which the term of the spatial derivative of the unknown quantity has been removed, and as a result, the calculation algorithm becomes numerically stable, and the image quality that can be obtained becomes stable.

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 tilde quantity) 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 tilde quantity), we obtain the following equation (22).

That is, in step S130A of FIG. 3, based on equation (12), which is a relational equation expressing the dual field E (a quantity with a tilde) using the measurement field H ⁺ and the spatially dependent unknown quantity λe, and equation (19), which is the Helmholtz decomposition of the dual field E (a quantity with a tilde), equation (22), which is a relational equation between the measurement field H ⁺ and the spatially dependent unknown quantity λe, can be obtained.

Also, for example, in the case of a 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).

That is, in step S130B of FIG. 4, equation (23), which is the relational equation between the measurement field φ and the spatially dependent unknown quantity ρe, is derived based on equation (15), which is the relational equation 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.

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).

That is, in step S130C of FIG. 5, equation (24), which is the relational equation between the displacement u, which is the measurement field, and the elastic constants λm and μm, which are spatially dependent unknown quantities, is derived based on equation (17), which is the relational equation 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.

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 the 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, the processing circuit 150 first uses the acquisition function 138 to acquire a measurement field corresponding to the spatial distribution of the predetermined physical quantity in the measurement object.

For example, in the case of MREPT, the processing circuitry 150 acquires an RF magnetic field H ⁺ as a measurement field by the acquisition function 138, for example, from the receiving circuitry 110, in the manner described above.

In the case of QCM, the processing circuit 150 acquires the phase of the RF magnetic field H ⁺ as the measurement field φ from, for example, the receiving circuit 110 via the acquisition function 138 .

In the case of MRE, the subject P is placed in the static magnetic field of the MRI device, 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, which alternates between positive and negative polarities in synchronization with the external vibration. The processing circuitry 150 acquires signals related to the pulse sequence using the acquisition function 138. The processing circuitry 150 acquires information about the displacement u based on the acquired signals using the acquisition function 138.

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, which will be described later.

For example, in the case of MREPT, as shown in step S140A of FIG. 3, the processing circuit 150 uses the calculation function 139 to calculate the impedance λ or the conductivity σ/dielectric constant ε, which are unknown quantities that vary spatially in the measurement target, based on the acquired measurement field H ⁺ and equation (22), which is the relational equation obtained in step S130A.

For example, in the case of a 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 are unknown quantities that vary spatially in the measurement object, based on the acquired measurement field φ and equation (23), which is the relational equation obtained in step S130B.

For example, in the case of MRE, as shown in step S140C of Figure 5, the processing circuit 150 uses the calculation function 139 to calculate the elastic constants λm, μm, etc., which are unknown quantities that vary 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.

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 characteristic of these relational equations is that they are all linear integral equations related to the unknown quantities. Therefore, a solution can be found directly without using iterative methods. In contrast, if the integral equation is not a linear equation related 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. However, the method according to the embodiment can find a solution directly without using iterative methods.

Furthermore, these equations do not include terms for second-order derivatives with respect to the space of the measurement field. This makes them an imaging method that is robust against noise. For example, in the case of MREPT, even when the conductivity changes discontinuously relative to normal tissue, such as in the case of localized solid tumors, 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.

Furthermore, conventional methods using integral representations sometimes used integral representations of the electromagnetic field over the entire region. In such cases, for example, an MRI coil or the like, which serves 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 at 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 at no load.

In this step, in which the processing circuitry 150 calculates the unknown quantities using the calculation function 139 by solving the first relational equations (22) to (24), etc., it is also possible to identify the region of interest Ω in the first relational equations (22) to (24) by capturing a morphological image of the object, and then perform step S140 based on the identified region of interest Ω. This can further improve the accuracy of estimating the unknown quantities.

Figure 8 shows an example of the processing procedure for step S140 in such an embodiment. That is, steps S141 to S143 in Figure 8 are an example of step S140 in Figure 2. Below, we will explain an example of performing magnetic resonance imaging of the brain region.

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

In step S141, the processing circuitry 150 uses the acquisition function 138 to acquire magnetic resonance signals collected from the sequence control circuitry 120 based on the pulse sequence executed by the sequence control circuitry 120, and acquires a morphological image of the measurement target based on the acquired magnetic resonance signals. For example, if the measurement target is the brain, the processing circuitry 150 uses the acquisition function 138 to acquire 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.

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

Next, in step S143, the processing circuitry 150 acquires the measurement field in the measurement target region Ω (region of interest Ω) using the acquisition function 138, and calculates the unknown quantity based on the measurement field in the measurement target region Ω (region of interest Ω) using the calculation function 139. As an example, the processing circuitry 150 acquires the measurement field in a region of the brain's substantial part using 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 using the calculation function 139. This can further improve the accuracy of estimating the unknown quantity.

Another advantage of generating images using equations (22) to (24) is that they are linear integral equations, making it easy to introduce regularization.

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, if we use a numerical phantom such as the one shown in Figure 9(a), as shown in Figure 9(b), at points where the field E (the tilde quantity) on the left side of equation (22) is zero, as shown in Figure 9(c), artifacts will appear in the estimated conductivity image in the corresponding region 10. This effect will be particularly noticeable when noise is added to the observed data H+, as shown in Figure 9(d).

In such cases, instead of directly solving the integral equation of equation (22), the processing circuit 150 can use the evaluation 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), as in equation (25) below, and minimize the evaluation function, thereby allowing the calculation function 139 to calculate the unknowns.

Here, x is the 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 spatially smooth the unknown quantity λe, thereby reducing artifacts and improving image quality.

In other words, the first relational equation, which is the relational equation between the measurement field and the unknown quantity, as shown in equations (22) to (24), may have singular points around which the numerical calculation becomes unstable, such as 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 equation and a regularization term. This improves numerical stability around the singular points in the first relational equation, thereby improving image quality.

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

Note that the method for assigning the regularization term is not limited to these two examples.

The above describes the processing for MREPT, but 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).

In other words, 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 the matrix and right-hand side vector determined from equation (23). The processing circuit 150 uses the calculation function 139 to calculate the unknown quantity ρe based on equation (25) derived in this way.

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 the matrix and right-hand side vector determined from equation (24). The processing circuitry 150 uses the calculation function 139 to calculate the unknown quantities λm and μm based on equation (25) derived in this way.

At least one of the embodiments described above can improve image quality.

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

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 expressed by the measurement field H ⁺ is the dual field of the measurement field H ⁺ . However, the definition of the dual field is not limited to this. For example, E tilde, which is a quantity that satisfies both equation (11) derived from Faraday's law and equation (12) derived from Ampere's law, may be called the dual field of H ⁺ .

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 a dual field is not limited to this. For example, ψ, which is a quantity that satisfies both equation (14) derived from Faraday's law and equation (15) derived from Ampere's law, can also be called the dual field of the measurement field φ.

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 a 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 also be called the dual field of the measurement field u.

These embodiments may be embodied in a variety of 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 their variations are within the scope and spirit of the invention, as well as the inventions and their equivalents as set forth in the claims.

130 Information processing device 131 Interface function 133 Control function 136 Generation function 137 Identification function 138 Acquisition function 139 Calculation function 150 Processing circuit

Claims (15)

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. The information processing device of claim 1, wherein the first relational expression is an integral equation in which a term representing the spatial derivative of the unknown quantity has been removed. The information processing device of claim 1, wherein the measurement field is an RF (radio frequency) magnetic field, and the unknown quantity includes at least one of conductivity or dielectric constant. The information processing device of claim 3, wherein the measurement field is the amplitude and phase of the RF magnetic field. The information processing device according to claim 4, wherein MREPT (Magnetic Resonance Electrical Property Tomography) is performed based on the unknown quantities calculated by the calculation unit. 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. The information processing device of 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. The information processing device of claim 1, wherein the measurement field is a displacement and the dual field is a stress tensor. The information processing device according to claim 1, wherein MRE (Magnetic Resonance Elastography) is performed based on the unknown quantities calculated by the calculation unit. The information processing device of claim 1, wherein the first relational expression is a relational expression derived from Ampere's law and Faraday's law. The information processing device of claim 1, wherein the first relational expression is a relational expression derived from the equation of motion of an elastic body and Hooke's law. 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. 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. The information processing device according to any one of claims 1 to 13, wherein the calculation unit calculates the unknown quantity based on an evaluation function consisting of a term obtained from the first relational expression and a regularization term. 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.