Correcting geometry and intensity distortions in MR data

Details Correcting geometry and intensity distortions in MR data Correcting geometry and intensity distortions in MR data

2003-06-25

2004-09-07

Shrivastav, Brij B. (Department: 2859)

Electricity: measuring and testing

Particle precession resonance

Spectrometer components

C324S318000

Reexamination Certificate

active

06788062

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Technical Field
The invention relates to the field of Magnetic Resonance Imaging (MRI). In particular, the invention relates to a method, a computer program product and an apparatus which allow the correction of geometrical and intensity distortions inherent in Magnetic Resonance (MR) data.
2. Description of the Prior Art
MRI is a powerful technology for acquiring images with high tissue contrast. Besides the high tissue contrast, the potential for tumor localization and the possibility to scan in any plane orientation have made MRI a useful tool in many fields of medicine.
MRI relies on the principle that an arbitrary object of interest is magnetized by a strong and homogenous static magnetic field B
0
. The homogeneity of the static magnetic field B
0
is a very important aspect of MRI because any perturbations of the homogeneity lead to geometry and intensity distortions in the image plane as well as to displacement, warp and tilt of the image plane itself.
In reality, the static magnetic field B
0
is never homogeneous but perturbed. One reason for perturbations of the magnetic field B
0
is the object of interest itself which is placed in the magnetic field B
0
.
When an object having a specific magnetic susceptibility distribution
102
(x) is placed in the homogeneous and static magnetic field B
0
, the object becomes magnetized and the homogenous static magnetic field B
0
is distorted giving rise to an induced magnetic field B. For an analysis of the geometry and intensity distortions caused by an object placed in the homogeneous static magnetic field B
0
, the field B has to be determined.
In order to determine B, the Maxwell equations have to be solved. For a magnetostatic problem the Maxwell equations reduce to the Laplace equation
div(&mgr;&Dgr;&PHgr;
M
)=0.  (1)
Here &PHgr;
M
is the magnetic scalar potential in [Wb/m] and &mgr;=1+
&khgr;
is the dimensionless magnetic permeability. If the susceptibility distribution
102
(x) of an object is known, &PHgr;
M
is determined by solving equation (1). From &PHgr;
M
the magnetic field H in [H/m]
H
=−∇&PHgr;
M
  (2)
and the induced magnetic field B in [T]
B=&mgr;
0
&mgr; H  (3)
can be deduced. &mgr;
0
denotes the permeability of vacuum and has a value of &mgr;
0
=4&pgr;×10
−7
H/m.
Equation (1) can be solved analytically for very simple objects such as cylinders and spheres. For more complex objects equation (1) can be solved only numerically. An exemplary numerical analysis of the magnetic field B for arbitrary magnetic susceptibility distributions
&khgr;
(x) in two and three dimensions is discussed in R. Bhagwandien: “Object Induced Geometry and Intensity Distortions in Magnetic Resonance Imaging”, PhD thesis, Universiteit Utrecht, Faculteit Geneeskunde, 1994, ISBN: 90-393-0783-0.
Susceptibility related distortions in MRI are usually in the millimeter range and have therefore no influence on diagnostic applications. However, in certain applications like Radio Therapy Planning (RTP) the geometric accuracy of an MR image is of high importance because accurate beam positioning is essential for optimal tumor coverage and sparing healthy tissues surrounding the tumor as much as possible.
Based on a numerical solution of equation (1), various methods have been proposed to reduce susceptibility induced distortions in MR images.
In the Bhagwandien document a correction method is described which is based on just one image, namely the distorted MR image. According to this correction method, the distorted MR image is first converted into a magnetic susceptibility distribution by segmenting the MR image into air and water equivalent tissue. In a next step the susceptibility distribution thus obtained is used to numerically calculate the field B. Finally, the corrected MR image is calculated on the basis of a read out gradient that is reversed with respect to the read out gradient used to acquire the distorted MR image. If for example a gradient field of a specific strength G
z
has been applied during acquisition of the distorted MR image to define the image plane in z-direction, the corrected MR image is calculated for a gradient field of the strength-G
z
.
A major draw back of all methods hitherto used to correct distortions in MR data is the computational complexity involved in generating corrected MR data. Consequently, there is a need for a method, a computer program product and an apparatus for correcting distortions in MR data faster.
SUMMARY OF THE INVENTION
This need is satisfied according to the invention by a method of correcting distortions in MR data, the method comprising the steps of providing distorted MR data of an object of interest and distortion parameters for one or more generic objects, determining transformation parameters correlating the object of interest and one or more of the generic objects, and processing the distorted MR data taking into account the distortion parameters and the transformation parameters to obtain corrected MR data.
By using generic distortion parameters, i.e. distortion parameters derived for generic objects, the corrected MR data for the object of interest can be generated faster. The reason for this is the fact that the Laplace equation (1) has not necessarily to be solved individually for every set of distorted MR data.
The distortion parameters for a particular generic object may be determined in various ways. The distortion parameters for a particular generic object may for example be derived from magnetic field inhomogenities which result from the specific magnetic susceptibility distribution of this particular generic object when the object is placed in a homogeneous static magnetic field. According to a first variant, the magnetic field inhomogenities caused by the generic object are determined by way of measurements. According to a second variant, the magnetic field inhomogenities are derived by way of calculations from distorted MR data of the generic object, i.e. from distorted generic MR data.
Preferably, the magnetic field inhomogenities, i.e. the distortion parameters, are derived from distorted generic MR data. Generic MR data may be obtained for e.g. a specific part of the human body from commercial databases. However, the generic MR data may also be generated using available generic objects during a data acquisition phase preceding the actual acquisition of the distorted MR data of the object of interest.
Deriving the magnetic field inhomogenities from generic MR data may include two separate steps. In a first step the magnetic susceptibility distribution of the generic object may be determined from the distorted generic MR data. To that end an image generated on the basis of the distorted generic MR data may be segmented automatically or manually to obtain areas of common or similar magnetic susceptibility. Then, an appropriate susceptibility value may be automatically or manually assigned to each area having the same or a similar magnetic susceptibility.
Once the magnetic susceptibility distribution of the generic object has been determined, the magnetic field inhomogenities are derived from the determined susceptibility distribution in a second step. The second step may include a numerical approach in order to solve the Laplace equation (1) for the determined susceptibility distribution. The numerical approach may for example be based oh transforming the Laplace equation (1) into a diffusion equation and on solving this diffusion equation by means of a diffusion technique. Preferably, however, a multi-grid approach is used to solve the Laplace equation (1) for the determined susceptibility distribution. By means of a multi-grid algorithm the computational complexity is reduced since the iterations that normally take place on a fine grid are replaced by iterations on a coarser grid.
The multi-grid approach is not restricted to solving the Laplace equation (1) in context with determining the distortion parame

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