Method for correcting inhomogeneity of the static magnetic field particularly of the static magnetic field generated by the magnetic structure of a machine for acquiring nuclear magnetic resonance images and MRI system for carrying out such method
Method for shimming a magnetic field which is generated by a magnetic structure, and which permeates a volume of space uses the following steps: measuring the magnetic field in a region of a volume of space permeated by the said magnetic field; determining a parameter which is a measure of the homogeneity of the magnetic field; defining a distribution of correction elements including a predetermined number of magnetic dipoles each having a predetermined magnetic charge and a predetermined position relatively to the magnetic structure generating the magnetic field; calculating the charges of each of the dipoles and the position of each of the dipoles of a distribution which minimizes the parameter being a measure of the homogeneity of the magnetic field; using the distribution of dipoles as the shimming distribution of dipoles to be positioned on the magnetic structure.
1 . A method for shimming a magnetic field which is generated by a magnetic structure comprising a plurality of poles, and which permeates a volume of space, the method comprising:
a) defining a shimming field of view comprising a part of a volume of space enclosed by a three-dimensional closed surface permeated by the magnetic field;
b) measuring at least a feature of the magnetic field in a plurality of locations of a three-dimensional grid, along the three dimensional closed surface;
c) defining a positioning surface on each pole of the magnetic structure for positioning one or more correction elements of the magnetic field, depending on the magnet structure;
d) calculating position and magnitude parameters of said one or more correction elements to obtain predetermined target values of the magnetic field characteristics;
in which
e) target values of the magnetic field characteristics are a magnetic field homogeneity;
f) the measured feature of the magnetic field is the field homogeneity on the three-dimensional grid;
g) the correction elements being magnetic dipoles; and
h) a distribution of the position and magnitude parameters of said one or more correction elements on the poles of the magnetic structure being chosen to minimize homogeneity variations of a shimmed magnetic field resulting from an addition of the magnetic field generated by the magnetic structure and a magnetic field generated by the correction elements on the poles of the magnetic structure; and
optionally starting from the magnetic field generated by the magnetic structure with any correction elements already positioned on a pole and iteratively repeating step d) as additional correction elements are added until a predetermined target value is met;
wherein evaluation parameters of the magnetic field homogeneity are a statistical standard deviation of the magnetic field strength inside the volume of space and minimizing homogeneity variations is done by minimizing a standard deviation of the sum of magnetic fields in the volume;
further comprising the steps of:
defining a second three-dimensional closed boundary surface enclosing a part of the volume of space permeated by the magnetic field, the second three-dimensional surface having a different shape than the first three-dimensional closed boundary surface and the volume of space enclosed by the two boundary surfaces being at least partly coincident with each other;
the second three-dimensional closed boundary surface enclosing a part of the volume of space permeated by the magnetic field coinciding with the part of a target body which is represented and visible in an image of the target body;
numerically evaluating the magnetic field in the part of the volume of space inside the second three-dimensional closed boundary surface by applying a field expansion equation; and
calculating from the numerical evaluation of the magnetic field the homogeneity variations of the magnetic field for each iteration of the step d).
2 . The method according to claim 1 , in which the positioning surface of the correction elements is defined by continuous values of position coordinates.
3 . The method according to claim 1 , in which a spherical or spheroidal surface is provided as a first three-dimensional closed boundary surface and a cubic surface is provided as a second three-dimensional closed boundary surface, while the expansion function for calculating the magnetic field in the volume inside the second cubic boundary surface is a spherical or spheroidal harmonic function of the kind:
B
(
ϑ
,
φ
)
=
B
0
+
∑
l
,
m
P
l
,
m
(
cos
ϑ
)
(
a
l
,
m
cos
ϑ
+
b
l
,
m
sin
ϑ
)
in which
B(ϑ, φ) is the magnetic field depending on spherical coordinates ϑ and φ; and
l, m are indexes of the order and degree of the harmonic functions P l,m , and of the coefficients a l,m and b l,m .
4 . The method according to claim 3 , in which maximum values of the index I and of the index m are determined by:
estimating an order of magnitude of error in experimentally measuring the magnetic field in the volume inside the second cubic boundary surface;
and ending the expansion for indexes I and m for which the numerical error is of the same order of magnitude of the error in experimentally measuring the magnetic field.
5 . The method according to claim 1 , in which the step d) is carried out by providing a starting distribution of correction elements,
the starting distribution of correction elements comprising a predetermined number N of correction elements for each pole;
and the position or the magnetic charge of each correction element is determined according to one of the listed ways or by any combination or sub-combination thereof:
i) generation of a predetermined number of different distributions of calculated correction elements of the magnetic field resulting from the adding of the magnetic field generated by the magnetic structure to the magnetic field generated by each different distribution, calculation of a standard deviation for the magnetic field resulting from each different distribution of correction elements and selection as the starting distribution for carrying out step d) or step d) to h) of the distribution of corresponding correction elements leading to the lowest standard deviation;
ii) generation of a population of a predetermined number of randomly generated distributions of correction elements and processing the population by an evolutionary genetic algorithm, selecting as the starting distribution of correction elements for carrying out the step d) or the steps d) to h) the distribution of correction elements generated by the evolutionary genetic algorithm having the lowest standard deviation of the magnetic field;
iii) using a distribution of correction elements which is used and known from one or more magnetic structures which has been subjected to a shimming process in earlier times and which has been saved in a database either directly as a starting distribution or as the predetermined number of populations for applying the evolutionary algorithm.
6 . The method according to claim 1 , in which a specific cost function to be minimized by a nonlinear programming solver algorithm is the following:
min
x
f
(
x
)
such
that
{
c
(
x
)
≤
0
ceq
(
x
)
=
0
A
·
x
≤
b
Aeq
·
x
=
beq
lb
≤
x
≤
ub
,
in which
x is the distribution of the position and magnitude parameters of said one or more correction elements represented by a N×3 matrix in which N is the number of magnetic dipoles, the number 3 is for the following parameters: the X, Z coordinates defining a two dimensional surface of the poles and q is the magnetic charge of each dipole;
c(x) and ceq(x) are functions defining respectively geometric and magnetic constraints to be respected by each distribution x;
lb, ub represents the lower bounds (lb) and upper bounds (ub) for a distribution x relating to the maximum allowed X coordinate, the maximum allowed Z coordinate on the corresponding pole plate and the max allowed magnetic charge of each dipole;
A and Aeq are matrices and b, beq and ceq are vectors in which specific correlation conditions between various dipoles of the distribution x are set and optionally the minimization algorithm may be reduced to the following algorithm:
min
x
f
(
x
)
such
that
{
c
(
x
)
≤
0
lb
≤
x
≤
ub
by describing the geometrical and magnetic constraints and correlations between dipoles N of the same distribution in the functions c(x) and ceq(x) only.
7 . A system for carrying out shimming of magnetic structures for generating a static magnetic field in an MRI apparatus, the system comprising:
a sensor for measuring the magnetic field;
a structure for supporting the sensor, which structure can be displaced at least along three spatial coordinates for positioning the sensor at different spatial positions, the supporting structure having a predetermined position relatively to the magnetic structure;
the supporting structure comprising driving units for displacing the structure along respectively each of the three spatial coordinates and position measuring sensors of the supporting structure along each of the coordinates;
a data collection unit receiving magnetic field measures of the sensor at each spatial position and comprising a memory for saving the data pairs relating to magnetic field strength and spatial position at which the magnetic field strength has been measured;
a processing unit comprising a memory in which at least one model of a three-dimensional grid along a first three-dimensional closed boundary surface provided within a volume of space permeated by a magnetic field, and optionally at least one model of a second three-dimensional closed boundary surface provided within a volume of space permeated by a magnetic field, the coordinate system of the models being registered one with the other and with the coordinate system of the magnetic field;
the processing unit being configured by executing the instructions of a magnetic field measuring program to position the sensor for measuring the magnetic field at each of the positions of the grid along the closed boundary surface by controlling the driving units for displacing the supporting structure as a function of the model of the three-dimensional grid and to register the field at each of the points of the grid and the coordinates of the points;
a processing unit executing a program comprising the instructions for calculating the magnetic field strength in the space inside the second three-dimensional boundary surface and for calculating the magnetic field variations inside the space;
another processing unit executing a program comprising the instructions for carrying out the steps of the method according to claim 1 ;
the magnetic structure comprising at least two magnetic poles generating the magnetic field, the two magnetic poles comprising a surface interfacing a volume of space permeated by the magnetic field and the surface being formed by a pole having a predetermined length and width and being configured to receive a set of magnetic dipoles at different positions on the surface each dipole having a magnetic charge;
a user interface comprising input units and output units, the output units comprising at least a display in which representation of the pole plates of the magnetic poles of the magnetic structure are shown and the representation of each of the magnetic dipoles placed on the poles at their position on the pole and optionally with the corresponding indication of the magnetic charge are shown; and
the input units of the user interface comprising at least input devices for entering data and or commands.
8 . The system according to claim 7 , in which an automatic pick and place device for the positioning of the correction elements is provided, which is provided in combination with a magazine of differently magnetically charged correction elements and a control unit of a robotic arm which controls the pick and place operations of the correction elements on the positioning grid according to the compute distribution and which control unit receives the coordinates of the position of each correction element and the information of which kind of correction element is to be put in place at a certain coordinate on the grid from the processing unit and generates the commands to drive the robotic arm.
9 . The system according to claim 8 , wherein the pick and place device is a robotic arm.
10 . An MRI apparatus comprising a magnetic structure generating a magnetic field permeating the space of a gantry of the MRI apparatus and further comprising a system according to claim 7 .
11 . The MRI apparatus according to claim 10 , wherein the MRI apparatus is provided with a processing unit for executing instructions coded in programs, which processing unit can be the same processing unit controlling the operations of the MRI apparatus or an additional processing unit dedicated to the shimming operations, the programs coding the instructions being saved in a memory on board of the MRI apparatus.
12 . The MRI apparatus according to claim 7 in which the coordinates of the position of the magnetic dipoles on the surface of the poles being configured to receive a set of magnetic dipoles at different positions are continuous.
13 . An MRI apparatus, comprising a magnetic structure generating a magnetic field permeating the space of a gantry of the MRI apparatus and further comprising a system for carrying out shimming of magnetic structures for generating a static magnetic field in an MRI apparatus, the system comprising:
a sensor for measuring the magnetic field;
a structure for supporting the sensor, which structure can be displaced at least along three spatial coordinates for positioning the sensor at different spatial positions, the supporting structure having a predetermined position relatively to the magnetic structure;
the supporting structure comprising driving units for displacing the structure along respectively each of the three spatial coordinates and position measuring sensors of the supporting structure along each of the coordinates;
a data collection unit receiving magnetic field measures of the sensor at each spatial position and comprising a memory for saving the data pairs relating to magnetic field strength and spatial position at which the magnetic field strength has been measured;
a processing unit comprising a memory in which at least one model of a three-dimensional grid along a first three-dimensional closed boundary surface provided within a volume of space permeated by a magnetic field, and optionally at least one model of a second three-dimensional closed boundary surface provided within a volume of space permeated by a magnetic field, the coordinate system of the models being registered one with the other and with the coordinate system of the magnetic field;
the processing unit being configured by executing the instructions of a magnetic field measuring program to position the sensor for measuring the magnetic field at each of the positions of the grid along the closed boundary surface by controlling the driving units for displacing the supporting structure as a function of the model of the three-dimensional grid and to register the field at each of the points of the grid and the coordinates of the points;
a processing unit executing a program comprising the instructions for calculating the magnetic field strength in the space inside the second three-dimensional boundary surface and for calculating the magnetic field variations inside the space;
another processing unit executing a program comprising the instructions for carrying out the steps of the method according to claim 1 ;
the magnetic structure comprising at least two magnetic poles generating the magnetic field, the two magnetic poles comprising a surface interfacing a volume of space permeated by the magnetic field and the surface being formed by a pole having a predetermined length and width and being configured to receive a set of magnetic dipoles at different positions on the surface each dipole having a magnetic charge;
a user interface comprising input units and output units, the output units comprising at least a display in which representation of the pole of the magnetic poles of the magnetic structure are shown and the representation of each of the magnetic dipoles placed on the poles at their position on the poles and optionally with the corresponding indication of the magnetic charge are shown; and
the input units of the user interface comprising at least input devices for entering data and or commands,
wherein the system is configured to carry out the method of claim 1 .
14 . A method for shimming a magnetic field which is generated by a magnetic structure comprising a plurality of poles, and which permeates a volume of space, the method comprising:
a) defining a shimming field of view comprising a part of a volume of space enclosed by a three-dimensional closed surface permeated by the magnetic field;
b) measuring at least a feature of the magnetic field in a plurality of locations of a three-dimensional grid, along the three dimensional closed surface;
c) defining a positioning surface on each pole of the magnetic structure for positioning one or more correction elements of the magnetic field, depending on the magnet structure;
d) calculating position and magnitude parameters of said one or more correction elements to obtain predetermined target values of the magnetic field characteristics;
in which
e) target values of the magnetic field characteristics are a magnetic field homogeneity;
f) the measured feature of the magnetic field is the field homogeneity on the three-dimensional grid;
g) the correction elements being magnetic dipoles; and
h) a distribution of the position and magnitude parameters of said one or more correction elements on the poles of the magnetic structure being chosen to minimize homogeneity variations of a shimmed magnetic field resulting from an addition of the magnetic field generated by the magnetic structure and a magnetic field generated by the correction elements on the poles of the magnetic structure; and
optionally starting from the magnetic field generated by the magnetic structure with any correction elements already positioned on a pole and iteratively repeating step d) as additional correction elements are added until a predetermined target value is met;
in which the minimization of the statistical standard deviation of the magnetic field is calculated by respecting constraints which are geometrical or magnetic constraints which are of the following list:
minimal distance between positions of adjacent dipoles on the corresponding pole or between the position of a dipole and already present magnetic charges on the corresponding pole;
a maximum allowed magnetic charge of each dipole depending on its position on the corresponding magnetic poles; and
the maximum magnetic charge of the dipoles varies as a function from their position on the corresponding magnetic plates;
further comprising the steps of:
defining a second three-dimensional closed boundary surface enclosing a part of the volume of space permeated by the magnetic field, the second three-dimensional surface having a different shape than the first three-dimensional closed boundary surface and the volume of space enclosed by the two boundary surfaces being at least partly coincident with each other;
the second three-dimensional closed boundary surface enclosing a part of the volume of space permeated by the magnetic field coinciding with the part of a target body which is represented and visible in an image of the target body;
numerically evaluating the magnetic field in the part of the volume of space inside the second three-dimensional closed boundary surface by applying a field expansion equation; and
calculating from the numerical evaluation of the magnetic field the homogeneity variations of the magnetic field for each iteration of the step d).
15 . The method according to claim 14 , in which minimizing the standard deviation of the sum of magnetic fields in the volume as a function of the one or more correction elements relative to their position on the corresponding pole and to the magnetic charge of each of the correction elements while respecting the one or more constraints is carried out by a nonlinear programming solver.
16 . The method according to claim 15 , wherein the nonlinear programming solver is a large-scale interior-point algorithm.
17 . The method according to claim 14 , wherein the smaller dipoles are near the central zone of the corresponding pole and the larger dipoles are provided at the peripheral parts of the corresponding magnetic plate.