Magnetic resonance simulation device, magnetic resonance simulation method, magnetic resonance simulation program, and magnetic resonance imaging device

Abstract

To reduce a calculation time in quantum mechanical magnetic resonance simulation.SOLUTION: A magnetic resonance simulation device includes an acquisition unit, a calculation unit, and an output unit. The acquisition unit updates and acquires a density matrix of the electronic spin and a spatial partial differential value of the density matrix on the basis of a pulse sequence on the collection of a magnetic resonance signal on each of a plurality of voxels. The calculation unit calculates an observation corresponding value corresponding to a predetermined observation using the density matrix and the spatial partial differential value of the density matrix on each of the plurality of voxels in a collection period of the magnetic resonance signal in the pulse sequence, and calculates the spatial partial differential value of the observation corresponding value on the basis of the pulse sequence. The output unit calculates and outputs a signal value corresponding to a sum total of the magnetic resonance signals over the plurality of voxels on the basis of the observation corresponding value and the spatial partial differential value of the observation corresponding value.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The embodiments disclosed in this specification and the drawings relate to a magnetic resonance simulation apparatus, a magnetic resonance simulation method, a magnetic resonance simulation program, and a magnetic resonance imaging apparatus. [Background technology]

[0002] Conventionally, magnetic resonance simulation can be realized by, for example, numerically solving the Bloch equations, which phenomenologically describe magnetic resonance, for the magnetization of a virtual hydrogen atom, which is a collection of multiple hydrogen atoms contained in one voxel of a static magnetic field. Because the Bloch equations are described in terms of classical mechanics, there is a problem in that it is not possible to simulate, for example, spin-spin interactions, and the physics of the virtual hydrogen atom cannot be accurately represented.

[0003] In order to express the quantum mechanical physics of the virtual hydrogen atom, for example, a magnetic resonance simulation can be performed using a density matrix related to the electrons of the virtual hydrogen atom. When the quantum mechanical physics of the virtual hydrogen atom is calculated for a large number of isochromats, for example, 100×100×100, arranged in a three-dimensional space, there is a problem that the calculation time is long. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] AHMED J. ALLAMI, MARIA GRAZIA CONCILIO, PAVAN LALLY, AND ILYA KUPROV, Quantum mechanical MRI simulations: Solving the matrix dimension problem, SCIENCE ADVANCES, 19 July 2019, Vol 5, Issue 7 DOI: 10.1126 / sciadv.aaw8962, https: / / www.science.org / doi / 10.1126 / sciadv.aaw8962 [Non-Patent Document 2] Thies H. Jochimsen, Andreas Schafer, Roland Bammer, Michael E. Moseley, Efficient simulation of magnetic resonance imaging with Bloch-Torrey equations using intra-voxel magnetization gradients, Journal of Magnetic Resonance 180 (2006) 29-38, [Non-Patent Document 3] Hidenori Takeshima, A fast and practical computation method for magnetic resonance simulators, Magnetic Resonance in Medicine, 15 April 2023, https: / / doi.org / 10.1002 / mrm.29646 Summary of the Invention [Problem to be solved by the invention]

[0005] One of the problems to be solved by the embodiments disclosed in this specification and the drawings is to reduce the calculation time in quantum mechanical magnetic resonance simulation. 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 later can also be positioned as other problems. [Means for solving the problem]

[0006] A magnetic resonance simulation apparatus according to an embodiment includes an acquisition unit, a calculation unit, and an output unit. The acquisition unit updates and acquires a density matrix of electron spins and a spatial partial derivative of the density matrix for each of a plurality of voxels based on a pulse sequence related to the acquisition of magnetic resonance signals. The calculation unit calculates an observation corresponding value corresponding to a predetermined observation for each of the plurality of voxels during an acquisition period of the magnetic resonance signals in the pulse sequence, using the density matrix and the spatial partial derivative of the density matrix, and calculates a spatial partial derivative of the observation corresponding value based on the pulse sequence. The output unit calculates and outputs a signal value corresponding to the sum of the magnetic resonance signals across the plurality of voxels based on the observation corresponding value and the spatial partial derivative of the observation corresponding value. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a block diagram showing an example of a magnetic resonance simulation apparatus according to a first embodiment. [Diagram 2] FIG. 2 is a diagram showing an example of a pulse sequence in a spin echo technique according to the first embodiment. [Diagram 3] FIG. 3 is a flowchart showing an example of a procedure of an MR simulation process according to the first embodiment. [Figure 4] FIG. 4 is a diagram showing an example of the configuration of a magnetic resonance imaging apparatus according to the second embodiment. [Diagram 5] FIG. 5 is a flowchart showing an example of an MR simulation analysis process according to the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] Hereinafter, embodiments of a magnetic resonance (hereinafter referred to as MR (Magnetic Resonance)) simulation device, an MR simulation method, an MR simulation program, and a magnetic resonance imaging (hereinafter referred to as MRI (Magnetic Resonance Imaging)) device will be described in detail with reference to the drawings. Fig. 1 is a block diagram showing an example of an MR simulation device 1.

[0009] (First embodiment) For the sake of concrete explanation, the MR simulation device 1 acquires and updates the density matrix of electron spins and the spatial partial derivative of the density matrix (hereinafter referred to as the density partial derivative) for each of a plurality of voxels based on a pulse sequence for collecting magnetic resonance signals, and calculates an output physical value corresponding to the sum of the magnetic resonance signals (hereinafter referred to as the MR (Magnetic Resonance) signals) across the plurality of voxels using the density matrix and the density partial derivative.

[0010] In the MR simulation that numerically calculates the magnetic resonance phenomenon, a virtual molecule is set at the center of each of a plurality of voxels. Each of the plurality of voxels may correspond to, for example, an isochromat. The MR simulation in this embodiment is performed by simulating a differential equation according to quantum mechanics. The MR simulation using a density matrix may be called a density matrix simulation.

[0011] The density matrix is ​​defined, for example, by applying a state vector to the Schrödinger equation. For example, a molecule consisting of n spins (conceptually corresponding to atoms) is expressed in a density matrix basis generated based on the direct product of a Pauli matrix and a unit matrix. The density matrix is, for example, a matrix that corresponds to the quantum mechanical physical state of a single molecule viewed collectively. The density matrix is ​​used when dealing with quantum mechanical behavior.

[0012] A density matrix describes the average behavior of many molecules, rather than the behavior of a single molecule. Density matrices are used in the analysis of Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Spectroscopy (MRS), and in the generation of spectral analysis bases (reference waveform patterns).

[0013] Quantum mechanical time evolution (time-series state transition) is given by, for example, a solution of a differential equation based on the Schrodinger equation. The time-series state transition is given by a Hamiltonian at each time point in the MR simulation. The Hamiltonian is set in advance by a pulse sequence related to the acquisition of MR imaging. The Hamiltonian has interactions specific to quantum mechanics, such as spin-spin interactions. The pulse sequence is, for example, information (sequence information) that defines a procedure for performing imaging.

[0014] The pulse sequence defines, for example, the strength of the current supplied by a gradient magnetic field power supply to a gradient magnetic field coil in a magnetic resonance imaging device (hereinafter referred to as an MRI (Magnetic Resonance Imaging) device) and the timing of supplying the current, the strength of the RF pulse supplied by a transmission circuit in the MRI device to a transmission coil and the timing of applying the RF pulse, and the timing at which a receiving circuit in the MRI device detects an MR signal.

[0015] The magnetic resonance simulation device 1 includes, for example, an input interface 11, an output interface 13, a memory 15, and a processing circuit 17. The magnetic resonance simulation device 1 may include an external storage device (for example, various storages, various memories, etc.) that stores programs that realize various functions executed in the processing circuit 17 and / or output results by an output function 177.

[0016] The external storage device may be, for example, a drive device that reads and writes various information between a semiconductor memory element such as a hard disk drive (HDD), a solid state drive (SSD), a random access memory (RAM), a flash memory, etc., an optical disc such as a compact disc (CD) or a digital versatile disc (DVD), a portable storage medium, etc.

[0017] The input interface 11 is electrically connected to, for example, a pulse sequence input function 2 in the MRI apparatus. In this case, the input interface 11 is connected to an output end of the pulse sequence input function 2 of the MRI apparatus.

[0018] The input interface 11 is not limited to being connected to an MRI device, and may be connected to an external device (e.g., a sequence generating device) capable of generating and outputting pulse sequence data related to MR imaging. The input interface 11 may be connected to various devices that are input sources of pulse sequences via a network.

[0019] The input interface 11 may also have an input device that accepts various instructions and information input from a user. In this case, the input interface 11 corresponds to an input device such as a pointing device such as a mouse or a trackball, or a keyboard. For example, the input interface 11 inputs a pulse sequence to be subjected to MR simulation in response to an instruction from a user.

[0020] Furthermore, the input interface 11 may input, by a user's operation, an output instruction regarding the result of the MR simulation by the MR simulation device 1. The output instruction is, for example, an instruction to output the result of the MR simulation to various external devices and / or displays that are the output destinations of the output interface 13. The input interface 11 corresponds to an input unit.

[0021] FIG. 2 is a diagram showing an example of a pulse sequence in the spin echo method. In FIG. 2, Txreal indicates a real part of a transmit RF pulse. The waveform of the imaginary part of the transmit RF pulse may be the same as or different from that of the real part of the transmit RF pulse. Gz indicates a slice selection gradient magnetic field. Gy indicates a phase encoding gradient magnetic field. Gx indicates a readout gradient magnetic field. In the pulse sequence shown in FIG. 2, after the lapse of an echo time (TE) from the application of a 90° RF pulse, MR signals are collected together with the application of a readout gradient magnetic field.

[0022] The MR signal is converted into a digital signal by an analog-to-digital converter (ADC). Although not shown in FIG. 2, various pulses such as a preparation pulse may be appropriately applied depending on the type of pulse sequence.

[0023] As shown in Fig. 2, a pulse sequence is expressed by a combination of application of a gradient magnetic field (Gradient), application of a gradient magnetic field and an RF pulse (RF&Gradient), application of a gradient magnetic field and analog-to-digital conversion (Gradient&ADC), and a time without application of a gradient magnetic field (No-Gradient). For example, in the case of the spin echo method shown in Fig. 2, a combination of Gradient, RF&Gradient, Gradient&ADC, and No-gradient is repeated over the number of phase encoding steps. For each phase encoding, the Gradient shown in Fig. 2 is calculated once, and the Gradient&ADC is repeated the number of times (the number of samplings) of ADC. These calculations are realized with fewer calculations than, for example, RF&Gradient.

[0024] The pulse sequence input function 2 inputs a gradient such as a pre-pulse, an RF&Gradient, a gradient such as a crusher, an RF&Gradient, a Gradient&ADC, and a No-Gradient in chronological order to the input interface 11. The input interface 11 outputs the gradient, the RF&Gradient, the RF&Gradient, and the Gradient&ADC to the processing circuit 17 in chronological order.

[0025] The pulse sequence according to the present embodiment is not limited to the pulse sequence shown in FIG. 2. In a general pulse sequence, combinations of RF&Gradient, Gradient, Gradient&ADC, and No-Gradient are appropriately repeated. The input interface 11 may be connected to, for example, an output end of a transmission circuit and an output end of a gradient magnetic field power supply in an MRI apparatus. At this time, the input interface 11 receives inputs from the MRI apparatus of a current and voltage corresponding to the strength of the gradient magnetic field, application timing of the gradient magnetic field, application timing of the current and RF pulse supplied to the transmission coil, detection timing of the MR signal, and the like.

[0026] The output interface 13 is connected to, for example, a sampling data output function 3 of a sequence control circuit in an MRI apparatus. The output interface 13 outputs a signal value calculated by the output function 217 to the sampling data output function 3 under the control of the control function 171. Note that the connection destination of the output interface 13 is not limited to the sequence control circuit, and may be various devices (for example, various displays, various analysis devices, various image generating devices, etc.) that can use the output value for display, analysis, processing, etc. Also, the connection between the output interface 13 and various devices to which the output value is output may be connected via a network. Also, the output interface 13 may have a display that displays the output value, etc. under the control of the control function 171. In this case, the display is, for example, a known display device such as a liquid crystal display.

[0027] The memory 15 is, for example, a storage device such as an HDD (Hard disk Drive), an SSD (Solid State Drive), or an integrated circuit storage device that stores various information. In addition to an HDD or SSD, the memory 15 may be a portable storage medium such as a CD (Compact Disc), a DVD (Digital Versatile Disc), or a flash memory, or a drive device that reads and writes various information between the portable storage medium and a semiconductor memory element such as a RAM (Random Access Memory), etc.

[0028] The memory 15 stores various programs related to the execution of, for example, the control function 171, the acquisition function 173, the calculation function 175, the output function 177, etc. The memory 15 also stores various data generated by the execution of, for example, the control function 171, the acquisition function 173, the calculation function 175, the output function 177, etc.

[0029] For example, the memory 15 stores a pulse sequence inputted via the input interface 11. The memory 15 also stores a Hamiltonian set by the acquisition function 173 along the time series of the pulse sequence based on the pulse sequence. The memory 15 stores a density matrix and a density partial differential calculated according to quantum mechanical time evolution using the Hamiltonian for each of a plurality of voxels according to updates. The memory 15 also stores an observation corresponding value and a partial differential of an observation value (hereinafter referred to as an observation partial differential) calculated based on the density matrix and the density partial differential during an acquisition period of an MR signal in the pulse sequence in association with each of a plurality of voxels. The memory 15 also stores a signal value corresponding to the sum of MR signals over a plurality of voxels. The memory 15 also stores various calculation algorithms related to calculation of the density matrix, the density partial differential, the observation corresponding value, and the observation partial differential. The memory 15 corresponds to a storage unit.

[0030] The processing circuitry 17 controls the overall operation of the MR simulation device 1 in response to an electrical signal of an input operation output from the input interface 11. For example, the processing circuitry 17 has, as hardware resources, a processor such as a central processing unit (CPU), a micro processing unit (MPU), or a graphics processing unit (GPU), and a memory such as a read only memory (ROM) or a RAM. The processing circuitry 17 may also be realized by an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), another complex programmable logic device (CPLD), a simple programmable logic device (SPLD), or the like.

[0031] The processing circuitry 17 has, for example, a control function 171, an acquisition function 173, a calculation function 175, and an output function 177. The control function 171, the acquisition function 173, the calculation function 175, and the output function 177 are stored in the memory 15 in the form of a program executable by a computer. The processing circuitry 17 executes the control function 171, the acquisition function 173, the calculation function 175, and the output function 177 by a processor that executes the program deployed in the memory.

[0032] That is, the processing circuit 17 corresponds to a processor that realizes a function corresponding to each program by reading and executing the program from the memory 15. In other words, the processing circuit 17 in a state in which each program has been read has a function corresponding to the read program. Note that each function in the control function 171, the acquisition function 173, the calculation function 175, and the output function 177 is not limited to being realized by a single processing circuit. A processing circuit may be configured by combining multiple independent processors, and each processor may execute a program to realize each function in the control function 171, the acquisition function 173, the calculation function 175, and the output function 177. The processing circuit 17 that realizes the control function 171, the acquisition function 173, the calculation function 175, and the output function 177 is an example of a control unit, an acquisition unit, a calculation unit, and an output unit.

[0033] The processing circuitry 17 controls each function of the processing circuitry 17 by a control function 171. Specifically, the processing circuitry 17 reads out a control program stored in the memory 15, expands it on the memory in the processing circuitry 17, and controls each part of the MR simulation device 1 according to the expanded control program. An acquisition function 173, a calculation function 175, and an output function 177 realized by the processing circuitry 17 will be described later along with a procedure for executing a process for executing MR simulation (hereinafter referred to as MR simulation process).

[0034] Above is a description of the overall configuration of the MR simulation device 1. Below is a description of the procedure of the MR simulation processing. Fig. 3 is a flowchart showing an example of the procedure of the MR simulation processing.

[0035] (MR simulation processing) (Step S301) The processing circuitry 17 acquires a pulse sequence related to MR imaging by the acquisition function 173. The pulse sequence may be generated by a user's instruction via the input interface 11. The acquisition function 173 stores the acquired pulse sequence in the memory 15.

[0036] (Step S302) The processing circuit 17 sets a Hamiltonian by the acquisition function 173 based on a pulse sequence related to the collection of MR signals. For example, in the pulse sequence shown in FIG. 2, a Hamiltonian is set in each of a plurality of periods corresponding to the application of a gradient magnetic field (Gradient), the application of a gradient magnetic field and an RF pulse (RF&Gradient), the application of a gradient magnetic field and analog-to-digital conversion (Gradient&ADC), and the time when no gradient magnetic field is applied (No-Gradient) in the pulse sequence. The acquisition function 173 stores the set Hamiltonian in the memory 15. Setting of a Hamiltonian based on a pulse sequence can be realized by a known method, and therefore a description thereof will be omitted. The set Hamiltonian is used in step S303 for calculating the update of the quantum state of the electron spin in each of a plurality of voxels, that is, for calculating the time evolution of the spin density matrix.

[0037] (Step S303) When the MR simulation is started, the processing circuit 17 updates and acquires a density matrix and a density partial differential for each of a plurality of voxels based on a pulse sequence by the acquisition function 173. For example, the acquisition function 173 updates and acquires a density matrix and a density partial differential for each of a plurality of voxels by quantum mechanical time evolution using a set Hamiltonian. Specifically, when the pulse sequence is as shown in FIG. 2, the acquisition function 173 updates the density matrix by multiplying the density matrix by a Hamiltonian corresponding to the pulse sequence along the time axis.

[0038] Specifically, the processing circuit 17 uses an arbitrary initial matrix set, for example, a density matrix and a density partial differential corresponding to the state of electron spin in an equilibrium state, as initial values ​​by the acquisition function 173. The acquisition function 173 calculates the time evolution of the density matrix and the density partial differential from the density matrix and the density partial differential as the initial values, using a Hamiltonian. The acquisition function 173 updates the calculated density matrix and density partial differential every time the density matrix and the density partial differential are calculated, and stores them in the memory 15.

[0039] An example of the quantum mechanical calculation for obtaining the density matrix and density partial derivative using the Hamiltonian and the update will be described later using equations. In the calculation of the density partial derivative according to this embodiment, the model for the Hamiltonian uses, for example, a constant Hamiltonian for each of a plurality of voxels.

[0040] (Step S304) In the pulse sequence, if the MR simulation is not in the acquisition period of the MR signal (No in step S304), the process of step S303 is repeated. This causes the density matrix and the density partial differential to be calculated and updated according to the pulse sequence. In the pulse sequence, if the MR simulation is in the acquisition period of the MR signal (Yes in step S304), the process of step S305 is executed.

[0041] (Step S305) The processing circuit 17 calculates, with the calculation function 175, an observation corresponding value corresponding to a predetermined observation for each of a plurality of voxels during the acquisition period of MR signals in the pulse sequence, using a density matrix and a density partial differential. The calculation of the observation corresponding value is a quantum mechanical calculation, and an example will be described later using a formula. In addition, the calculation function 175 calculates an observation partial differential indicating a spatial partial differential of the observation corresponding value for each of a plurality of voxels, based on the pulse sequence related to the acquisition period of MR signals. For example, the calculation function 175 calculates the spatial partial differential of the observation corresponding value using the spatial partial differential of the density matrix calculated using the pulse sequence.

[0042] In this embodiment, a model is used in which the observation partial differential is constant for each of a plurality of voxels regardless of the position within the voxel. The predetermined observation is, for example, transverse magnetization. An example of quantum mechanical calculation for obtaining the observation corresponding value and the observation partial differential will be described later using formulas.

[0043] (Step S306) The processing circuitry 17 calculates a signal value corresponding to the sum of MR signals over multiple voxels based on the observed corresponding value and the observed partial differential by the output function 177. For example, the output function 177 calculates the signal value by calculating the observed corresponding value and the observed partial differential using the formula described in Non-Patent Document 2. An example of the calculation of the signal value using the formula described in Non-Patent Document 2 will be described later.

[0044] (Step S307) The processing circuitry 17 causes the output function 177 to store the calculated output value in the memory 15 in association with the time point at which the simulation of the observation is performed. This causes the signal value to be associated with the time point at which step S305 is performed during the acquisition period of the MR signal in the pulse sequence.

[0045] (Step S308) If the MR simulation for the pulse sequence is not completed (No in step S308), the process from step S303 onwards is repeated. This causes the density matrix and density partial differentials to be calculated and updated according to the pulse sequence. If the MR simulation for the pulse sequence is completed (Yes in step S308), the process of step S309 is executed.

[0046] (Step S309) The processing circuitry 17 outputs the signal values ​​by the output function 177. For example, the output function 177 outputs a plurality of signal values ​​associated with the time points at which the observation was performed to the memory 15. As a result, the memory 15 stores a plurality of signal values ​​indicating a time-series change in the MR signal during the collection period of the MR signal. The output function 177 may output the plurality of signal values ​​to an external device such as an MRI device or an analysis device, and / or a display.

[0047] The outline of the procedure of the MR simulation process has been described above. An example of an equation used in each step of the MR simulation process will be described below. For the sake of concrete explanation, the quantum mechanical time evolution using the Hamiltonian will be described using, for example, the Schrödinger equation. Note that the quantum mechanical time evolution using the Hamiltonian is not limited to the following Schrödinger equation (1), and may be described using the Heisenberg equation of motion.

[0048] The Schrödinger equation using the time-dependent wave function |ψ(t)> is given by the following equation (1).

[0049]

number

[0050] The left side of equation (1) indicates the partial time derivative of the wave function |ψ(t)>. The right side of equation (1) indicates that the operator (the hat of H) of the Hamiltonian H as an operator and a negative imaginary number are applied to the wave function |ψ(t)>. The hat is a symbol indicating an operator. In Japanese, the operator is called an operator. In step S302, the Hamiltonian H is generated by the acquisition function 173 along a time series based on the pulse sequence.

[0051] The spin density operator is defined by the ket and bra of the wave function as shown in the following equation (2). The spin density operator is expressed, for example, by a matrix.

[0052]

number

[0053] In this case, the Schrödinger equation for the spin density operator is expressed as follows:

[0054]

number

[0055] From equation (3), the update equation (time evolution) of the spin density operator for a small time Δt is expressed by the following equation (4).

[0056]

number

[0057] Equation (4) is used in step S303 to calculate the update of the quantum state of the electron spin in each of the multiple voxels, i.e., to calculate the time evolution of the density matrix. The argument t of the Hamiltonian H in equation (4) may be (t+1 / 2Δt). Also, the Hamiltonian H in equation (4) may be approximated by the average of the Hamiltonian from t to (t+1 / 2Δt).

[0058] The spatial partial differential ∂ p (p is a spatial coordinate axis), and considering the derivative of the composition operator, we obtain the following equation (5). In equation (5), the spatial coordinate axis p∈{x, y, z} is assumed, and the partial derivative with respect to the spatial coordinate axis p is abbreviated as ∂ / ∂p≡∂p.

[0059]

number

[0060] In one example of the model in this embodiment, the Hamiltonian is constant within a voxel, that is, the spatial partial derivative of the Hamiltonian is zero within a voxel. In this case, equation (5) can be expressed as the following equation (6).

[0061]

number

[0062] According to equation (6), the spatial partial differential (density partial differential) of the spin density operator is updated with respect to a small time interval Δt as shown in the following equation (7).

[0063]

number

[0064] As another example, when the RF pulse of the Hamiltonian is constant within a voxel and the gradient magnetic field is linear, the linear coefficient of the gradient magnetic field in the p direction is G p When expressing it as, for example, the following equation (8) may be considered as the spatial partial derivative of the Hamiltonian.

[0065]

number

[0066] In the above equation (8), I k、p represents the kth spin in the p direction.

[0067] Equation (7) is used in step S303 to calculate the update of the spatial partial derivative of the electron spin in each of the multiple voxels, i.e., to calculate the time evolution of the density partial derivative. The argument t of the Hamiltonian H in equation (7) may be (t+1 / 2Δt). Also, the Hamiltonian H in equation (7) may be approximated by the average of the Hamiltonian from t to (t+1 / 2Δt).

[0068] The period during which the magnetic resonance signals are collected and converted to analog digital form while applying the gradient magnetic field (Gx) along the X-direction (Gx Gradient & ADC) corresponds to the observation period of the macroscopic magnetization. The real component of the magnetization is I x , the imaginary component of magnetization is I y Then, the observed value of the real component of magnetization and the observed value of the imaginary component of magnetization can be calculated by the following equation (9).

[0069]

number

[0070] In equation (9), I x hat and I y The hats in the equation represent the summation of operators in the density matrix basis in the x and y directions over all spins. For example, the transverse magnetization M xy is the real component of magnetization I x and the imaginary component of magnetization is I y Using and, M xy =I x +iI y Therefore, the transverse magnetization M xy The observed value of can be calculated by the following formula (10): Formula (10) is used in step S305 to calculate an observed corresponding value for each of a plurality of voxels using a density matrix and a spatial partial derivative of the density matrix.

[0071]

number

[0072] The purpose of MR simulation is to calculate the macroscopic magnetization of the entire voxel with volume. A model is used in which the observation partial differential, which indicates the spatial partial differential of the observation corresponding value, is constant for each of multiple voxels regardless of the position within the voxel. Below, we will explain the calculation of a general observation A hat for the calculation of the observation partial differential. The observation of the spatial differential for the observation A hat is expressed by the following formula (11).

[0073]

number

[0074] On the right-hand side of equation (11), the spatial partial differential of coordinate p, ∂ p By applying Leibniz's law to, we obtain the following equation (12).

[0075]

number

[0076] Since the observation partial differential is constant, the first term on the right side of equation (12) becomes zero. Therefore, equation (12) reduces to the following equation (13).

[0077]

number

[0078] In step S305, the equation (13) is used to calculate an observation partial differential for each of a plurality of voxels using the density matrix and the spatial partial differential of the density matrix. For example, the processing circuit 17 calculates an observation partial differential (a spatial partial differential of an observation corresponding value) by the equation (13) using the spatial partial differential of the density matrix calculated by the calculation function 175 using the pulse sequence.

[0079] An example of the multiple equations used in step S306 will be described below. The value in the following equation (14) is calculated using the observed corresponding value calculated by equation (10) and the partial differential of the transverse magnetization (observed partial differential) calculated by equation (13). The symbols in the following equations (14) to (16) conform to Non-Patent Document 2, so their explanation will be omitted as appropriate.

[0080]

number

[0081] Equation (14) is used as an argument of the sinc function in the following equation (15). k corresponds to the length of each axis k.

[0082]

number

[0083] Using equations (14) and (15), the MR signal of each of the multiple voxels is calculated using the following equation (16).

[0084]

number

[0085] The signal value in step S306 is calculated by taking the sum of the MR signals calculated by equation (16) for all voxels. * and T2' corresponds to the difference between T2' and T2', for example, 1 / T2 * =1 / T2+1 / T2 ’ is given by the relationship:

[0086] The MR simulation device 1 according to the first embodiment described above updates and acquires the density matrix of electron spins and the spatial partial differential of the density matrix for each of a plurality of voxels based on a pulse sequence related to the acquisition of MR signals, calculates an observation corresponding value corresponding to a predetermined observation for each of a plurality of voxels using the density matrix and the spatial partial differential of the density matrix during the acquisition period of the MR signals in the pulse sequence, calculates the spatial partial differential of the observation corresponding value based on the pulse sequence, and calculates and outputs a signal value corresponding to the sum of MR signals over a plurality of voxels based on the observation corresponding value and the spatial partial differential of the observation corresponding value. The MR simulation device 1 according to the first embodiment calculates the spatial partial differential of the observation corresponding value using the spatial partial differential of the density matrix calculated using the pulse sequence.

[0087] In the MR simulation device 1 according to the first embodiment, the spatial partial derivative of the observation corresponding value is constant in each of the multiple voxels. In the MR simulation device 1 according to the first embodiment, a predetermined observation corresponds to transverse magnetization. Also, in the MR simulation device 1 according to the first embodiment, the Hamiltonian is constant or the spatial partial derivative of the Hamiltonian is constant in each of the multiple voxels.

[0088] From these facts, according to the MR simulation device 1 of the first embodiment, by performing MR simulation using a density matrix describing a quantum mechanical physical process and a spatial partial differential of the density matrix, it is possible to track observations of the density matrix, and for example, it is possible to obtain observation results of the time evolution of quantum mechanical transverse magnetization with reduced calculation time. As a result, according to the MR simulation device 1 of the first embodiment, since a quantum mechanical MR simulation is performed, it is possible to obtain more accurate observation results including quantum phenomena such as the Zeeman effect compared to classical mechanical MR simulation, and it is possible to obtain observation results in a shorter time than conventional quantum mechanical MR simulation. Furthermore, according to the MR simulation device 1 of the first embodiment, it is possible to reduce calculation errors due to discretization in MR simulation.

[0089] (Modification) This modification is to calculate the observation partial differential (spatial partial differential of the observation corresponding value) without using the density matrix and the spatial partial differential of the density matrix. For example, the processing circuit 17 calculates the spatial partial differential of the observation corresponding value by using the calculation function 175 of classical mechanics calculation based on the pulse sequence. Specifically, the calculation function 175 calculates the observation partial differential by numerically solving the Bloch equation using various parameters in the pulse sequence. Since the method described in Non-Patent Document 2 can be applied to numerically solving the Bloch equation, a description thereof will be omitted.

[0090] The MR simulation device 1 according to the modification of the first embodiment calculates the spatial partial differential of the observed corresponding value by using classical mechanical calculation based on the pulse sequence. As a result, according to this modification, the accuracy is inferior to the first embodiment when the spatial partial differential of the density matrix is ​​used, but the calculation time can be reduced by omitting the calculation of the spatial partial differential of the density matrix. Other advantageous effects are the same as those of the first embodiment, and therefore the description will be omitted.

[0091] Second embodiment In the second embodiment, the MR simulation process using the various functions realized by the MR simulation device 1 described in the first embodiment is realized by an MRI device. The MRI device according to the second embodiment has various components related to the execution of the MR simulation process. Fig. 4 is a diagram showing an example of the configuration of an MRI device 100 according to the second embodiment.

[0092] As shown in FIG. 4, the MRI apparatus 100 includes a static magnetic field magnet 101, a static magnetic field power supply 102, 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, and a computer 130 (also called an image processing device, an information processing device, etc.). The MRI 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 sequence control circuit 120 and each part in the computer 130 may be appropriately integrated or separated. The computer 130 is mounted on a console, for example.

[0093] The static magnetic field magnet 101 is a magnet formed in a hollow, approximately cylindrical shape, and generates a static magnetic field in the internal space. 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 102. The static magnetic field power supply 102 supplies a current to the static magnetic field magnet 101. Note that the static magnetic field magnet 101 may be a permanent magnet, and in this case, the MRI apparatus 100 does not need to include the static magnetic field power supply 102. Also, the static magnetic field power supply 102 may be provided separately from the MRI apparatus 100.

[0094] The gradient magnetic field coil 103 is a hollow coil formed in a substantially cylindrical shape, 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 changes along the X, Y, and Z axes. The gradient magnetic fields of 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.

[0095] 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 a computer 130, the bed control circuit 106 drives the bed 105 to move the top plate 105a in the longitudinal direction and up and down directions.

[0096] The transmission coil 107 is disposed inside the gradient magnetic field coil 103, and generates a high-frequency magnetic field upon receiving an RF pulse from a transmission circuit 108. The transmission circuit 108 supplies the transmission coil 107 with an RF pulse corresponding to a Larmor frequency determined by the type of target atom and the magnetic field strength.

[0097] The receiving coil 109 is disposed inside the gradient magnetic field coil 103, and receives an MR signal emitted from the subject P due to the influence of a high frequency magnetic field. Upon receiving the MR signal, the receiving coil 109 outputs the received MR signal to a receiving circuit 110.

[0098] The above-mentioned transmitting coil 107 and receiving coil 109 are merely examples. The transmitting coil 107 and receiving coil 109 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.

[0099] The receiving circuit 110 detects the MR signal output from the receiving coil 109, and generates MR data based on the detected MR signal. Specifically, the receiving circuit 110 generates MR data by digitally converting the MR signal output from the receiving coil 109. The receiving circuit 110 also transmits the generated MR data to the sequence control circuit 120. The receiving circuit 110 may be provided on the side of a gantry device including the static magnetic field magnet 101, the gradient magnetic field coil 103, and the like.

[0100] The sequence control circuit 120 drives the gradient magnetic field power supply 104, the transmission circuit 108, and the reception circuit 110 based on sequence information transmitted from the computer 130, thereby imaging the subject P. For the sake of concrete explanation, the sequence information will be described below as a pulse sequence related to the subject P, and a pulse sequence for obtaining MR spectroscopy from the subject P. The pulse sequence is generated in advance or generated by a user's instruction via the input device 141 and stored in the memory circuit 132.

[0101] A known pulse sequence for obtaining MR spectroscopy can be used, and therefore a description thereof will be omitted. For example, the sequence control circuit 120 executes a pulse sequence for generating MR spectroscopy to collect MR data from the subject P. The sequence control circuit 120 stores the collected MR data in the memory circuit 132.

[0102] The sequence control circuit 120 drives the gradient magnetic field power supply 104, the transmission circuit 108, and the reception circuit 110 to image the subject P, and receives MR data from the reception circuit 110. The sequence control circuit 120 transfers the received MR data to the computer 130. The sequence control circuit 120 is realized by an integrated circuit such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA), a CPU, an MPU, or other electronic circuit. The sequence control circuit 120 corresponds to a sequence control unit.

[0103] The computer 130 performs overall control of the MRI apparatus 100, generates images, etc. The computer 130 includes a memory circuitry 132, an input device 141, a display 143, and a processing circuitry 150. The processing circuitry 150 includes an interface function 131, a control function 133, a generation function 134, an acquisition function 173, a calculation function 175, an output function 177, and an analysis function 137.

[0104] Each processing function performed by the interface function 131, the control function 133, the generation function 134, the acquisition function 173, the calculation function 175, the output function 177, and the analysis function 137 is stored in the storage circuitry 132 in the form of a program executable by the computer 130. The processing circuitry 150 is a processor that realizes a function corresponding to each program by reading the program from the storage circuitry 132 and executing it. In other words, the processing circuitry 150 in a state in which each program has been read has each function shown in the processing circuitry 150 in FIG.

[0105] 4, the processing functions performed by the interface function 131, the control function 133, the generation function 134, the acquisition function 173, the calculation function 175, the output function 177, and the analysis function 137 are realized by a single processing circuit 150, but the processing circuit 150 may be configured by combining a plurality of independent processors, and each processor may execute a program to realize the function. In other words, each of the above-mentioned functions may be configured as a program, and one processing circuit 150 may execute each program, or a specific function may be implemented in a dedicated independent program execution circuit.

[0106] The term "processor" used in the above description means a circuit such as a CPU, a GPU, an application specific integrated circuit, 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 functions by reading and executing a program stored in the memory circuit 132.

[0107] Instead of storing the program in the memory circuitry 132, the program may be directly built into the circuitry of the processor. In this case, the processor realizes the function by reading and executing the program built into the circuitry. The bed control circuitry 106, the transmission circuitry 108, the reception circuitry 110, the sequence control circuitry 120, etc. are also similarly composed of electronic circuits such as the above-mentioned processor.

[0108] The memory circuitry 132 stores MR data received by the processing circuitry 150 having the interface function 131, various data acquired by the acquisition function 173, various image data generated by the generation function 134, programs related to calculation processing used in the calculation function 175, calculation results calculated by the calculation processing, programs related to output processing used in the output function 177, output results output by the output function 177, programs related to analysis processing used in the analysis function 137, and the like.

[0109] For example, the memory circuitry 132 stores a density matrix and density partial differentials acquired by the acquisition function 173. The memory circuitry 132 stores observed corresponding values ​​and observed partial differentials calculated by the calculation function 175. The memory circuitry 132 stores signal values ​​calculated by the output function 177. The memory circuitry 132 stores analysis results analyzed by the analysis function 137.

[0110] Moreover, the memory circuitry 132 stores MR data (also referred to as k-space data) arranged in k-space by the control function 133. For example, the memory circuitry 132 is realized by a semiconductor memory element such as a random access memory (RAM) or a flash memory, a hard disk, an optical disk, or the like. The memory circuitry 132 may be referred to as a memory.

[0111] The input device 141 accepts various instructions and information input from a user. The input device 141 is realized by, for example, a trackball, a switch button, a mouse, a keyboard, a touch pad that performs an input operation by touching an operation surface, a touch screen in which a display screen and a touch pad are integrated, a non-contact input circuit using an optical sensor, and a voice input circuit. The input device 141 is electrically connected to the processing circuit 150, and converts an input operation received from a user into an electrical signal and outputs it to the processing circuit 150.

[0112] In this specification, the input device 141 is not limited to one equipped with physical operation parts (input interface) such as a mouse and a keyboard. For example, an example of the input device 141 includes an electric signal processing circuit that receives an electric signal corresponding to an input operation from an external input device provided separately from the MRI apparatus 100 and outputs the electric signal to a control circuit. The input device 141 corresponds to an input unit, and may be called an input interface, an operation device, or the like.

[0113] The display 143 displays a GUI (Graphical User Interface) for receiving input of imaging conditions and the like, and an image generated by the processing circuit 150 having the generation function 134, under the control of the processing circuit 150 having the control function 133. The display 143 also displays an analysis result, which will be described later, by the analysis function 137. The display 143 is realized by, for example, a display device such as a CRT display, a liquid crystal display, an organic EL display, an LED display, a plasma display, or any other display or monitor known in the art. The display 143 corresponds to a display unit.

[0114] The processing circuit 150 transmits sequence information to the sequence control circuit 120 and receives MR data from the sequence control circuit 120 through the interface function 131. Furthermore, upon receiving MR data, the processing circuit 150 having the interface function 131 stores the received MR data in the memory circuit 132. The processing circuit 150 that realizes the interface function 131 corresponds to an interface unit.

[0115] The processing circuitry 150 performs overall control of the MRI apparatus 100 using the control function 133, and controls imaging, image generation, image display, and the like. 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 conditions of a saturation pulse set by 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. The processing circuitry 150 that realizes the control function 133 corresponds to a control unit.

[0116] The processing circuitry 150 reads the k-space data from the storage circuitry 132 using the generating function 134, and performs reconstruction processing such as Fourier transform on the read k-space data to generate an image. For example, the generating function 134 generates an MR spectroscopy of the subject P based on the MR data. The generating function 134 stores the generated MR spectroscopy in the storage circuitry 132. Since a known method can be appropriately used to generate the MR spectroscopy, a description thereof will be omitted. The processing circuitry 150 that realizes the generating function 134 corresponds to a generating unit.

[0117] The processing circuitry 150 acquires the pulse sequence executed in the sequence control circuitry 120 from the memory circuitry 132 by the acquisition function 173. Based on the acquired pulse sequence, the acquisition function 173 updates and acquires the density matrix of electron spins and the spatial partial differential (density partial differential) of the density matrix for each of a plurality of voxels. The acquisition process for updating and acquiring the density matrix and the density partial differential is similar to that of the first embodiment except that the pulse sequence executed in the sequence control circuitry 120 is used, and therefore a description thereof will be omitted.

[0118] The processing circuit 150 calculates, with the calculation function 175, an observation corresponding value corresponding to a predetermined observation for each of a plurality of voxels using a density matrix and a spatial partial differential of the density matrix during an acquisition period of MR signals in a pulse sequence executed in the sequence control circuit 120. The calculation function 175 also calculates a spatial partial differential of the observation corresponding value based on the pulse sequence executed in the sequence control circuit 120. The calculation process for calculating the observation corresponding value and the observation partial differential is similar to that of the first embodiment except that the pulse sequence executed in the sequence control circuit 120 is used, and therefore a description thereof will be omitted.

[0119] The processing circuitry 150 calculates a signal value corresponding to the sum of MR signals across multiple voxels based on the observation corresponding value calculated by the calculation function 175 and the spatial partial differential of the observation corresponding value using the output function 177, and outputs the signal value to, for example, the storage circuitry 132. The output process related to the calculation and output of the signal value is similar to that of the first embodiment, and therefore will not be described.

[0120] The processing circuitry 150 outputs an analysis result indicating molecular information on the subject P by fitting the MR spectroscopy generated by the generation function 134 to a signal value by the analysis function 137. Specifically, the analysis function 137 fits the MR spectroscopy generated by MR imaging of the subject P to a signal value calculated according to the pulse sequence used for the MR imaging. As a result, the analysis function 137 outputs an analysis result indicating molecular information on the subject P. The processing circuitry 150 that realizes the analysis function 137 corresponds to an analysis unit.

[0121] The analysis result corresponds to, for example, a percentage of error for a molecule corresponding to the degree of agreement between MR spectroscopy and a signal value. The analysis processing realized by the analysis function 137 can be realized by various known software, applications, models, etc., and therefore a description thereof will be omitted. The software, applications, models, etc. that realize the analysis processing are stored in the storage circuitry 132 in advance.

[0122] The MR simulation process and analysis process (hereinafter, referred to as MR simulation analysis process) executed by the MRI apparatus 100 of this embodiment configured as above will be described. Fig. 5 is a flowchart showing an example of the procedure of the MR simulation analysis process. Prior to the execution of the MR simulation analysis process, a pulse sequence related to MR imaging of the subject P is set in advance, for example, by a user's instruction via the input device 141 or by a separate sequence generation device.

[0123] (MR simulation analysis processing) (Step S501) The processing circuitry 150 acquires a pulse sequence related to MR imaging performed on the subject P by the acquisition function 173. As a result, the processing circuitry 150 executes MR simulation processing and outputs a plurality of signal values. The execution of the MR simulation processing and the output of the signal values ​​are similar to the MR simulation processing shown in FIG. 3 in the first embodiment, and therefore a description thereof will be omitted.

[0124] (Step S502) The sequence control circuit 120 executes MR imaging of the subject P in accordance with the pulse sequence. Through the MR imaging, the sequence control circuit 120 acquires MR data. The sequence control circuit 120 stores the MR data in the storage circuitry 132.

[0125] (Step S503) The processing circuitry 150 generates an MR spectroscopy of the subject P based on the MR data by the generation function 134. The generation function 134 stores the generated MR spectroscopy in the storage circuitry 132. As shown in Fig. 5, the process of step S501 and the processes of steps S502 and S503 are processed in parallel in time.

[0126] (Step S504) The processing circuitry 150 applies MR spectroscopy to a plurality of signal values ​​using the analysis function 137, and outputs an analysis result indicating molecular information regarding the subject P. In this way, the analysis function 137 identifies the molecular information in the MR spectroscopy, including errors.

[0127] (Step S505) The display 143 displays the analysis results. The display 143 may further display MR spectroscopy and a plurality of signal values ​​in addition to the analysis results. For example, the display 143 may display the signal values ​​superimposed on the MR spectroscopy together with the analysis results.

[0128] The MRI apparatus 100 according to the second embodiment described above executes a pulse sequence for generating MR spectroscopy to collect MR data from the subject P, generates MR spectroscopy for the subject P based on the MR data, updates and acquires the density matrix of electron spins and the spatial partial derivative of the density matrix for each of a plurality of voxels based on the pulse sequence, calculates an observation corresponding value corresponding to a predetermined observation for each of a plurality of voxels using the density matrix and the spatial partial derivative of the density matrix during an MR signal acquisition period in the pulse sequence, calculates the spatial partial derivative of the observation corresponding value based on the pulse sequence, calculates and outputs a signal value corresponding to the sum of MR signals over a plurality of voxels based on the observation corresponding value and the spatial partial derivative of the observation corresponding value, applies MR spectroscopy to the signal value, outputs an analysis result indicating molecular information for the subject P, and displays the analysis result.

[0129] As a result, the MRI apparatus 100 according to the second embodiment can execute an MR simulation using parameters in a pulse sequence related to the generation of an MR spectroscopy during the execution of the pulse sequence. As a result, the MRI apparatus 100 according to the second embodiment can perform fitting between the MR spectroscopy and the output signal value after MR imaging of the subject P, and can present to the user the result of matching between the MR spectroscopy generated by MR imaging of the subject P and the signal value that is the quantum mechanical calculation result.

[0130] From these facts, the MRI apparatus 100 according to the second embodiment can present the analysis result of the MR spectroscopy on the subject P to the user with high resolution and in a short time, thereby improving the throughput of the examination and diagnosis on the subject P. Other effects are similar to those of the first embodiment, and therefore will not be described.

[0131] When the technical idea of ​​the embodiment is realized by a magnetic resonance simulation method, the magnetic resonance simulation method calculates, for each of a plurality of voxels, a density matrix of electron spins and a spatial partial differential of the density matrix based on a pulse sequence related to the collection of MR signals, an observation corresponding value corresponding to a predetermined observation using the density matrix and the spatial partial differential of the density matrix for each of a plurality of voxels during the collection period of MR signals in the pulse sequence, calculates, for each of a plurality of voxels, a spatial partial differential of the observation corresponding value based on the pulse sequence during the collection period of MR signals in the pulse sequence, and calculates and outputs a signal value corresponding to the sum of MR signals over a plurality of voxels based on the observation corresponding value and the spatial partial differential of the observation corresponding value. The procedure and effect of the MR simulation process are the same as those of the first embodiment, so a description thereof will be omitted.

[0132] When the technical idea of ​​the embodiment is realized by a magnetic resonance simulation program, the magnetic resonance simulation program causes a computer to update and acquire, for each of a plurality of voxels, a density matrix of electron spins and a spatial partial derivative of the density matrix based on a pulse sequence for collecting MR signals, calculate, for each of the plurality of voxels, an observation corresponding value corresponding to a predetermined observation using the density matrix and the spatial partial derivative of the density matrix during a period for collecting MR signals in the pulse sequence, calculate, for each of the plurality of voxels, a spatial partial derivative of the observation corresponding value based on the pulse sequence during a period for collecting MR signals in the pulse sequence, and calculate and output a signal value corresponding to the sum of magnetic resonance signals over the plurality of voxels based on the observation corresponding value and the spatial partial derivative of the observation corresponding value.

[0133] For example, the MR simulation process can be realized by installing a magnetic resonance simulation program in a computer in the MRI apparatus 100 or various simulation servers and developing the program in memory. In this case, the program that can cause the computer to execute the process can be stored in a storage medium such as a magnetic disk (hard disk, etc.), an optical disk (CD-ROM, DVD, etc.), or a semiconductor memory and distributed. The distribution of the MR simulation program is not limited to the above-mentioned medium, and may be distributed using an electric communication function, such as downloading via the Internet. The processing procedure and effects of the MR simulation process using the MR simulation program are similar to those in the first embodiment, and therefore will not be described.

[0134] According to at least one of the embodiments and modifications described above, it is possible to reduce the calculation time in a quantum mechanical magnetic resonance simulation.

[0135] Although some embodiments have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, substitutions, modifications, and combinations of embodiments can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope of the invention and its equivalents as described in the claims, as well as in the scope and spirit of the invention. [Explanation of symbols]

[0136] 1. Magnetic resonance simulation device 2 Pulse sequence input function 3. Sampling data output function 11 Input Interface 13 Output Interface 15 Memory 17 Processing circuit 100 Magnetic resonance imaging device 101 Static magnetic field magnet 102 Static magnetic field power supply 103 Gradient magnetic field coil 104 Gradient magnetic field power supply 105 Bed 105a Tabletop 106 Bed control circuit 107 Transmitting Coil 108 Transmitting circuit 109 Receiving coil 120 Sequence control circuit 130 Computer 131 Interface Functions 132 Memory circuit 133 Control Functions 137 Analysis Function 141 Input Devices 143 Display 150 Processing circuit 171 Control Functions 173 Acquisition Function 175 Calculation function 177 Output Function

Claims

1. an acquisition unit that acquires, for each of a plurality of voxels, an electron spin density matrix and a spatial partial differential of the density matrix by updating the density matrix based on a pulse sequence related to the acquisition of magnetic resonance signals; a calculation unit that calculates, for each of the plurality of voxels, an observation corresponding value corresponding to a predetermined observation using the density matrix and a spatial partial derivative of the density matrix during an acquisition period of the magnetic resonance signals in the pulse sequence, and calculates the spatial partial derivative of the observation corresponding value based on the pulse sequence; an output unit that calculates and outputs a signal value corresponding to the sum of the magnetic resonance signals across the plurality of voxels based on the observed corresponding value and a spatial partial differential of the observed corresponding value; A magnetic resonance simulation device comprising:

2. In each of the plurality of voxels, a spatial partial derivative of the observed corresponding value is constant.

2. The magnetic resonance simulation apparatus according to claim 1.

3. The predetermined observation corresponds to a transverse magnetization.

2. The magnetic resonance simulation apparatus according to claim 1.

4. In each of the plurality of voxels, a Hamiltonian based on the pulse sequence is constant.

2. The magnetic resonance simulation apparatus according to claim 1.

5. The calculation unit calculates a spatial partial derivative of the observed corresponding value using a spatial partial derivative of the density matrix calculated using the pulse sequence.

5. The magnetic resonance simulation device according to claim 1.

6. The calculation unit calculates a spatial partial derivative of the observed corresponding value using a classical mechanical calculation based on the pulse sequence.

5. The magnetic resonance simulation device according to claim 1.

7. Acquiring, for each of a plurality of voxels, a density matrix of electron spins and a spatial partial differential of the density matrix by updating them based on a pulse sequence for acquiring magnetic resonance signals; calculating, for each of the voxels during an acquisition period of the magnetic resonance signals in the pulse sequence, an observation corresponding value corresponding to a predetermined observation using the density matrix and a spatial partial differential of the density matrix; calculating a spatial partial derivative of the observed corresponding value based on the pulse sequence for each of the plurality of voxels during an acquisition period of the magnetic resonance signal in the pulse sequence; calculating and outputting a signal value corresponding to a sum of the magnetic resonance signals across the plurality of voxels based on the observed corresponding values ​​and the spatial partial derivatives of the observed corresponding values; A magnetic resonance simulation method comprising:

8. On the computer, Acquiring, for each of a plurality of voxels, a density matrix of electron spins and a spatial partial differential of the density matrix by updating them based on a pulse sequence for acquiring magnetic resonance signals; calculating, for each of the voxels during an acquisition period of the magnetic resonance signals in the pulse sequence, an observation corresponding value corresponding to a predetermined observation using the density matrix and a spatial partial differential of the density matrix; calculating a spatial partial derivative of the observed corresponding value based on the pulse sequence for each of the plurality of voxels during an acquisition period of the magnetic resonance signal in the pulse sequence; calculating and outputting a signal value corresponding to a sum of the magnetic resonance signals across the plurality of voxels based on the observed corresponding values ​​and the spatial partial derivatives of the observed corresponding values; A magnetic resonance simulation program that makes this possible.

9. a sequence control unit that executes a pulse sequence related to the generation of magnetic resonance spectroscopy to collect magnetic resonance data from a subject; A generating unit that generates a magnetic resonance spectroscopy of the subject based on the magnetic resonance data; an acquisition unit that updates and acquires an electron spin density matrix and a spatial partial derivative of the density matrix for each of a plurality of voxels based on the pulse sequence; a calculation unit that calculates, for each of the plurality of voxels, an observation corresponding value corresponding to a predetermined observation using the density matrix and a spatial partial derivative of the density matrix during an acquisition period of a magnetic resonance signal in the pulse sequence, and calculates the spatial partial derivative of the observation corresponding value based on the pulse sequence; an output unit that calculates and outputs a signal value corresponding to the sum of the magnetic resonance signals across the plurality of voxels based on the observed corresponding value and a spatial partial differential of the observed corresponding value; an analysis unit that applies the magnetic resonance spectroscopy to the signal value to output an analysis result indicating molecular information regarding the subject; A display unit that displays the analysis results; A magnetic resonance imaging apparatus comprising:

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