Magnetic resonance simulation apparatus, magnetic resonance simulation method, and magnetic resonance imaging apparatus
A magnetic resonance (MR) simulation apparatus according to an embodiment includes processing circuitry. The processing circuitry updates and obtains, for each of voxels, an electron-spin density matrix based on a pulse sequence for acquisition of MR signals. For each of the voxels, the processing circuitry computes, during an acquisition period for the MR signals in the pulse sequence, an observation value representing a predetermined observation by using the density matrix, and computes a spatial partial differential of the observation value based on the pulse sequence. The processing circuitry computes a signal value for output based on the observation value and the spatial partial differential of the observation value. The signal value represents a sum of the MR signals in the voxels.
1 . A magnetic resonance simulation apparatus comprising processing circuitry configured to:
update and obtain, for each of a plurality of voxels, a density matrix of electron spin, based on a pulse sequence for acquisition of magnetic resonance signals;
compute, for each of the plurality of voxels, during an acquisition period for the magnetic resonance signals in the pulse sequence,
an observation value by using the density matrix, the observation value representing a predetermined observation, and
a spatial partial differential of the observation value based on the pulse sequence; and
compute a signal value for output based on the observation value and the spatial partial differential of the observation value, the signal value representing a sum of the magnetic resonance signals in the plurality of voxels.
2 . A magnetic resonance simulation method comprising:
updating and obtaining, for each of a plurality of voxels, a density matrix of electron spin, based on a pulse sequence for acquisition of magnetic resonance signals;
computing, for each of the plurality of voxels, during an acquisition period for the magnetic resonance signals in the pulse sequence, an observation value by using the density matrix, the observation value representing a predetermined observation;
computing, for each of the plurality of voxels, during the acquisition period for the magnetic resonance signals in the pulse sequence, a spatial partial differential of the observation value based on the pulse sequence; and
computing a signal value for output based on the observation value and the spatial partial differential of the observation value, the signal value representing a sum of the magnetic resonance signals in the plurality of voxels.
3 . A magnetic resonance imaging apparatus comprising:
sequence control circuitry configured to perform a pulse sequence for generation of magnetic resonance spectroscopy to acquire magnetic resonance data of a subject;
processing circuitry configured to:
generate magnetic resonance spectroscopy of the subject based on the magnetic resonance data,
update and obtain, for each of a plurality of voxels, a density matrix of electron spin, based on the pulse sequence,
compute, for each of the plurality of voxels, during an acquisition period for magnetic resonance signals in the pulse sequence,
an observation value by using the density matrix, the observation value representing a predetermined observation, and
a spatial partial differential of the observation value based on the pulse sequence,
compute a signal value for output based on the observation value and the spatial partial differential of the observation value, the signal value representing a sum of the magnetic resonance signals in the plurality of voxels, and
generate an analysis result for output by applying the magnetic resonance spectroscopy to the signal value, the analysis result representing molecule information as to the subject; and
a display that displays the analysis result.
4 . The magnetic resonance simulation apparatus according to claim 1 , wherein
the spatial partial differential of the observation value is constant in each of the plurality of voxels.
5 . The magnetic resonance simulation apparatus according to claim 1 , wherein
the predetermined observation corresponds to transverse magnetization.
6 . The magnetic resonance simulation apparatus according to claim 1 , wherein
a Hamiltonian based on the pulse sequence is constant in each of the plurality of voxels.
7 . The magnetic resonance simulation apparatus according to claim 1 , wherein
the processing circuitry configured to:
update and obtain a spatial partial differential of the density matrix, for each of the plurality of voxels, based on the pulse sequence, and
compute the observation value by using the density matrix and the spatial partial differential of the density matrix.
8 . The magnetic resonance simulation apparatus according to claim 1 , wherein
the processing circuitry is configured to compute the spatial partial differential of the observation value by classical-mechanical computation based on the pulse sequence.
9 . The magnetic resonance simulation apparatus according to claim 7 , wherein
the processing circuitry is configured to compute the spatial partial differential of the observation value by using the spatial partial differential of the density matrix computed based on the pulse sequence.