1. Field of the Invention
The invention concerns a method to determine distortion correction data for distortion correction of magnetic resonance images acquired with a magnetic resonance system, as well as a method to implement such a distortion correction. Moreover, the invention concerns a device to determine distortion correction data and a magnetic resonance system with such a device.
2. Description of the Prior Art
Magnetic resonance tomography is a widespread technique for acquisition of images of the inside of the body of a living examination subject. In order to acquire an image with this method, the body or a body part of the patient or test subject that is to be examined must initially be exposed to an optimally homogeneous, static basic magnetic field which is generated by a basic field magnet of the magnetic resonance system. During the acquisition of the magnetic resonance images, rapidly switched gradient fields that are generated by gradient coils are superimposed on his basic magnetic field for spatial coding. Moreover, radio-frequency pulses of a defined field strength are radiated into the examination subject with radio-frequency antennas. The nuclear spins of the atoms in the examination subject are excited by means of these radio-frequency pulses so as to be deflected by what is known as an “excitation flip angle” from their equilibrium state, parallel to the basic magnetic field. The nuclear spins then precess around the direction of the basic magnetic field. The magnetic resonance signals that are thereby generated are acquired (detected) by radio-frequency acquisition antennas. The magnetic resonance images of the examination subject are finally created on the basis of the acquired magnetic resonance signals. Each pixel in the magnetic resonance image is associated with a small body volume (known as a “voxel”), and every brightness or intensity value of the pixels is linked with the signal amplitude of the magnetic resonance signal that is received from this voxel.
The imaging properties of the magnetic field gradient coils are disadvantageously only approximately linear and one-to-one in the proximity of the isocenter of the basic magnetic field. This volume is designated as a “linearity volume” of the respective gradient coil. In many cases, however, the imaging volume is greater than the linearity volume of a physically realizable gradient coil. The non-ideal magnetic fields outside of the linearity volume therefore lead to imaging errors (typically called “distortions”) in the imaging volume, which are noticeable in, for example, geometric deformations of the spin density images. Limitations thereby arise for such applications in which only slight deviations in the imaging fidelity are allowed, for example stereotaxy applications in the head region. Such deformations are also problematic given a merging of multiple images that image adjoining regions of the examination subject. For example, given a complete spinal column examination it is normally not possible to reconstruct a complete image of the entire spinal column with one measurement. Instead, images of the spinal column are acquired segment-by-segment and these images are subsequently merged to create the complete image. The distortions at the image edges then hinder the combination of the images.
In principle, distortions can be minimized with a subsequent distortion correction. For example, the gradient curve is thereby used for de-skewing in an image plane. In addition to this, a three-dimensional distortion correction is also possible in which additional image errors perpendicular to the image plane are corrected. A spherical function spectrum of the magnetic fields of the three axes of the gradient coil is a foundation for both the two-dimensional and the three-dimensional correction method. For this purpose, a solenoidal spherical volume of radius R in which rotation B disappears is considered. For this the magnetic field B at a location r=r(r, θ, φ) within the sphere can be described by an expansion of the field according to orthogonal spherical functions Ylm up to the order N with the coefficients a(l,m), A(l,m) and B(l,m), as follows:
                                                        B              _                        ⁡                          (                              r                ,                θ                ,                φ                            )                                =                                    ∑                              l                =                0                            N                        ⁢                                          ∑                                  m                  =                                      -                    l                                                                    +                  l                                            ⁢                                                                    (                                                                  a                        ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                    ·                                              r                        l                                                              )                                    ·                                                            Y                      lm                                        ⁡                                          (                                              θ                        ,                        Φ                                            )                                                                      ⁢                                                                  ⁢                with                ⁢                                                                  ⁢                the                ⁢                                                                  ⁢                axial                ⁢                                                                  ⁢                field                ⁢                                                                  ⁢                components                                                    ⁢                                  ⁢                                            B              z                        ⁡                          (                              r                ,                θ                ,                φ                            )                                =                                    ∑                              l                =                0                            N                        ⁢                                          ∑                                  m                  =                                      -                    l                                                                    -                  l                                            ⁢                                                                    (                                          r                      /                      R                                        )                                    l                                ·                                                      P                    lm                                    ⁡                                      (                                          cos                      ⁢                                                                                          ⁢                      θ                                        )                                                  ·                                  [                                                                                    A                        lm                                            ⁡                                              (                                                  cos                          ⁢                                                                                                          ⁢                          m                          ⁢                                                                                                          ⁢                          θ                                                )                                                              +                                                                  B                        lm                                            ⁡                                              (                                                  sin                          ⁢                                                                                                          ⁢                          m                          ⁢                                                                                                          ⁢                          θ                                                )                                                                              ]                                                                                        (        1        )            
The spherical functions Ylm are calculated from the associated Legendre polynomials Plm according to:
                                                        Y              lm                        ⁡                          (                              θ                ,                Φ                            )                                =                                                                                          (                                                                  2                        ⁢                        l                                            +                                        )                                    ⁢                                                            (                                              l                        -                        m                                            )                                        !                                                                    4                  ⁢                                      π                    ·                                                                  (                                                  l                          +                          m                                                )                                            !                                                                                            ·                                          P                lm                            ⁡                              (                                  cos                  ⁢                                                                          ⁢                  θ                                )                                      ·                          exp              ⁡                              (                                  im                  ⁢                                                                          ⁢                  θ                                )                                                    ⁢                                  ⁢        with                            2        )                                                                    P              lm                        ⁡                          (              x              )                                =                                                                      (                                      -                    l                                    )                                m                                                              2                  l                                ⁢                                  l                  !                                                      ⁢                                                            (                                      1                    -                                          x                      2                                                        )                                                  m                  /                  2                                            ·                                                ⅆ                                      l                    -                    m                                                                    ⅆ                                      x                                          l                      -                      m                                                                                            ⁢                                          (                                                      x                    2                                    -                  l                                )                            l                                      ⁢                                  ⁢                  with          ⁢                                          (                                    m              =              0                        ,                          ±                              ,                                  …                  ⁢                                                                          ±                  l                                                              )                                    (        3        )            
For the following considerations it is sufficient to take into account the axial magnetic field component Bz (generally known as the field component in the direction of the basic magnetic field B0).
The following table shows as an example the spherical function expansion terms or, respectively, coefficients A(l,m) and B(l,m) for the first 5 expansion orders in the internal space of a cylindrical gradient coil:
Expansion termAssociationA(0, 0)Constant field (B0 term)A(1, 0)Linear term in z-directionA(1, 1)Linear term in x-directionB(1, 1)Linear term in y-directionA(3, 0)3rd order in z-directionA(3, 1), A(3, 3)3rd order in x-directionB(3, 1), B(3, 3)3rd order in y-directionA(5, 0)5th order in z-directionA(5, 1), A(5, 3), A(5, 5)5th order in x-directionB(5, 1), B(5, 3), B(5, 5)5th order in y-direction
For reasons of symmetry, in ideal gradient coils the terms with even order m in the x- and y-direction and all terms with m>0 in the z-direction (for the longitudinal gradient coil) disappear. For the previous distortion corrections, the expansion coefficients (and thus the magnetic field) have been calculated from the complicated conductor trace structures of the field coils, typically up to the expansion order N=13 (i.e. with l=0 through N). However, in this method production tolerances of the gradient coil have until now remained unconsidered. Such production tolerances lead to the situation that, in addition to the expansion orders calculated from the design, significant additional orthogonal terms occur that should actually not occur for reasons of symmetry. It is also the case that, for example, an x-gradient coil which should actually have only one A(1,1) linear term in the x-direction additionally also generates a B(1,1) term (i.e. a linear term in the y-direction) or a B(2,2) term.
The occurrence of such additional interference terms is more strongly pronounced in magnetic resonance systems with newer, thinner-walled gradient coils. A known method for precise determination of the coefficients is the exact measurement of the magnetic field of each field coil in the MR system. Measurements are thereby obtained with a magnetic field probe at a plurality of locations within the measurement space. Hundreds of measurement points that then serve as nodes for the additional determination of the spherical function coefficients are typical here. This measurement is connected with additional measurement and time costs in the start-up of an MR system, such that typically no individual magnetic field measurement is implemented in present magnetic resonance systems. If the magnetic field measurement should be implemented in customer systems that have already been installed, additional costs arise due to the necessary ordering of the measurement means by the service technician on site.