MAGNETIC RESONANCE NUMERICAL SIMULATION APPARATUS AND METHOD
A processing circuitry inputs, in regard to an isochromat, a value before update of magnetization, and a value before update of a partial differential for the magnetization in each of a spatial direction and/or an angular frequency direction. The processing circuitry executes an arithmetic operation of an update formula representing a time-dependent behavior of magnetic resonance, by using a part of the values before update of the magnetization, and the values before update of the partial differential, and compute, in regard to the isochromat, a value after update of the magnetization, and a value after update of the partial differential for the magnetization in a computation target direction of the spatial direction and/or the angular frequency direction.
1 . A magnetic resonance numerical simulation apparatus comprising processing circuitry configured to:
input, in regard to an isochromat, a numerical value before update of magnetization, and a numerical value before update of a partial differential for the magnetization in each of a spatial direction and/or an angular frequency direction; and
execute an arithmetic operation of an update formula representing a time-dependent behavior of magnetic resonance, by using a part of the numerical values before update of the magnetization, and the numerical values before update of the partial differential, and compute, in regard to the isochromat, a numerical value after update of the magnetization, and a numerical value after update of the partial differential for the magnetization in a computation target direction of the spatial direction and/or the angular frequency direction.
2 . The magnetic resonance numerical simulation apparatus of claim 1 , wherein the processing circuitry is configured to:
execute the arithmetic operation of the update formula by using the numerical value before update of the magnetization, without using the numerical value before update of the partial differential, and compute the numerical value after update of the magnetization, and
execute the arithmetic operation of the update formula by using the numerical value before update of the partial differential in the computation target direction, without using the numerical value before update of the partial differential in a non-computation target direction of the spatial direction and/or the angular frequency direction, and compute the numerical value after update of the partial differential in the computation target direction.
3 . The magnetic resonance numerical simulation apparatus of claim 2 , wherein
the update formulae include a magnetization update formula, a spatial partial differential update formula, and an angular frequency partial differential update formula, which are separated from each other, and
the processing circuitry is configured to:
execute an arithmetic operation of the magnetization update formula by referring to the numerical value before update of the magnetization, thereby to compute the numerical value after update of the magnetization;
execute an arithmetic operation of the spatial partial differential update formula by referring to the numerical value before update of the magnetization and the numerical value before update of the partial differential in the spatial direction of the computation target direction, thereby to compute the numerical value after update of the partial differential in the spatial direction of the computation target direction; and
execute an arithmetic operation of the angular frequency partial differential update formula by referring to the numerical value before update of the magnetization and the numerical value before update of the partial differential in the angular frequency direction, thereby to compute the numerical value after update of the partial differential in the angular frequency direction.
4 . The magnetic resonance numerical simulation apparatus of claim 3 , wherein the processing circuitry is configured to:
compute a magnetization rotation term value by executing an arithmetic operation of a rotation term in the magnetization update formula by referring to the numerical value before update of the magnetization; and
compute the numerical value after update of the magnetization by applying a relaxation term in the magnetization update formula to the magnetization rotation term value.
5 . The magnetic resonance numerical simulation apparatus of claim 4 , wherein the processing circuitry is configured to:
compute a partial differential rotation term value by executing an arithmetic operation of a rotation term in the spatial partial differential update formula and/or the angular frequency partial differential update formula by referring to the numerical value before update of the magnetization and the numerical value before update of the partial differential in the computation target direction; and
compute the numerical value after update of the partial differential in the computation target direction by applying a relaxation term in the spatial partial differential update formula and/or the angular frequency partial differential update formula to the partial differential rotation term value.
6 . The magnetic resonance numerical simulation apparatus of claim 5 , wherein the spatial partial differential update formula includes a first term that depends on an effective magnetic field vector component in an orthogonal direction to a slice selection gradient magnetic field direction, a second term that depends on an effective magnetic field vector component in the slice selection gradient magnetic field direction, and a third term that does not depend on the effective magnetic field vector components, the first term, the second term and the third term being separated from each other.
7 . The magnetic resonance numerical simulation apparatus of claim 6 , wherein the processing circuitry is configured to:
execute an arithmetic operation of the first term, the second term and the third term in an application period of an RF pulse; and
execute an arithmetic operation of the second term and third term in a nonapplication period of the RF pulse.
8 . The magnetic resonance numerical simulation apparatus of claim 6 , wherein the processing circuitry is configured to execute an arithmetic operation of the first term, the second term and the third term in an application period and a nonapplication period of an RF pulse.
9 . The magnetic resonance numerical simulation apparatus of claim 6 , wherein the processing circuitry is configured to:
compute a first rotation term value by executing an arithmetic operation of a rotation term of the first term by referring to the numerical value before update of the magnetization and the numerical value before update of the spatial partial differential in the computation target direction, compute a second rotation term value by executing an arithmetic operation of a rotation term of the second term by referring to the numerical value before update of the magnetization and the numerical value before update of the spatial partial differential in the computation target direction, and compute a third rotation term value by executing an arithmetic operation of a rotation term of the third term by referring to the numerical value before update of the magnetization and the numerical value before update of the spatial partial differential in the computation target direction, thereby to compute the numerical value after update of the spatial partial differential in the computation target direction; and
compute the numerical value after update of the spatial partial differential in the computation target direction by applying a relaxation term in the spatial partial differential update formula to an addition value of the first rotation term value, the second rotation term value and the third rotation term value.
10 . The magnetic resonance numerical simulation apparatus of claim 2 , wherein the update formula is a combined transition matrix in which a plurality of transition matrices each describing a time-dependent behavior of the magnetization and a time-dependent behavior of the partial differential in each of a plurality of time steps are combined.
11 . The magnetic resonance numerical simulation apparatus of claim 10 , wherein
a first matrix element contributing to an arithmetic operation of a time-dependent behavior of magnetic resonance in the combined transition matrix has a nonzero value,
a second matrix element not contributing to the arithmetic operation of the time-dependent behavior of the magnetic resonance in the combined transition matrix has a zero value, and
the processing circuitry is configured to not execute an arithmetic operation of the second matrix element having the zero value.
12 . The magnetic resonance numerical simulation apparatus of claim 11 , further comprising a memory configured to store the combined transition matrix,
wherein the memory is configured to store the first matrix element and to not store the second matrix element.
13 . The magnetic resonance numerical simulation apparatus of claim 10 , wherein the processing circuitry is configured to compute each of matrix elements of the combined transition matrix, based on an output vector acquired by applying to the update formula an input vector including a predetermined numerical value of magnetization and a numerical value of a spatial partial differential of magnetization in each of the spatial directions.
14 . The magnetic resonance numerical simulation apparatus of claim 10 , further comprising a memory configured to store a combined transition matrix in regard to each of sequence segments of a pulse sequence,
wherein the processing circuitry is configured to:
determine whether a combined transition matrix corresponding to a sequence segment of an arithmetic operation target is stored in the memory;
read out and use the combined transition matrix corresponding to the sequence segment of the arithmetic operation target, in a case where the combined transition matrix is determined to be stored; and
compute a combined transition matrix corresponding to the sequence segment of the arithmetic operation target, in a case where the combined transition matrix is determined to be not stored, and use the computed combined transition matrix.
15 . The magnetic resonance numerical simulation apparatus of claim 1 , wherein, in a case of computing a prediction output value of an A/D converter, the processing circuitry is configured to not compute the numerical value after update of the partial differential in the computation target direction for a magnetization component of a slice selection gradient magnetic field direction, but configured to compute the numerical value after update of the partial differential in the computation target direction for a magnetization component of a gradient magnetic field direction other than the slice selection gradient magnetic field direction.
16 . A magnetic resonance numerical simulation method comprising:
inputting, in regard to an isochromat, a numerical value before update of magnetization, and a numerical value before update of a partial differential for the magnetization in each of a spatial direction and/or an angular frequency direction; and
executing an arithmetic operation of an update formula representing a time-dependent behavior of magnetic resonance by using a part of the numerical values before update of the magnetization and the numerical values before update of the partial differential, and computing, in regard to the isochromat, a numerical value after update of the magnetization, and a numerical value after update of the partial differential for the magnetization in a computation target direction of the spatial direction and/or the angular frequency direction.