X-ray or gamma ray systems or devices – Source support – Including movable source
Reexamination Certificate
2001-12-18
2003-06-24
Dunn, Drew A. (Department: 2882)
X-ray or gamma ray systems or devices
Source support
Including movable source
C378S196000, C378S185000, C378S015000
Reexamination Certificate
active
06582120
ABSTRACT:
BACKGROUND
1. Field of the Invention
The invention relates to a method for the acquisition of a set of projection images for the reconstruction of a three-dimensional image data set of an object to be examined that is arranged in an examination zone, said acquisition being performed by means of an X-ray device that includes an X-ray source and an X-ray detector, the X-ray source being displaced along a trajectory around the examination zone, said trajectory being situated essentially on a spherical surface, in order to acquire the projection images. The invention also relates to an X-ray device that is suitable for carrying out such a method.
2. Description of Related Art
The so-called cone beam-computed tomography technique aims to reconstruct a three-dimensional image of an object to be examined from a set of cone beam projections of this object. An examination device that is provided with a punctiform X-ray source as well as with a flat X-ray detector is used for the measurement of the cone beam projections. The object is situated between the source and the detector. While the object remains stationary, the source and the detector are moved around the object; during this displacement cone beam projections are measured at short intervals in space or in time. The source and the detector are usually rigidly coupled to one another and the connecting line between the source and the center of the detector always passes through a defined point that is referred to as the isocenter. The trajectory of the source also determines the trajectory of the detector in such a case. Moreover, when small mechanical inaccuracies are ignored, the trajectory of the source is situated on the surface of a sphere whose center constitutes the isocenter. The trajectory of the source can be described by an image a: [s
−
,s
+
]→R
3
, where s is a real parameter and a(s) denotes the position vector of the trajectory relative to a Cartesian system of co-ordinates, the center of which is situated at the isocenter. The reconstructed image of the object represents the spatial distribution of the X-ray attenuation coefficient in the examination zone. The image is calculated from the measured set of cone beam projections by means of a computer and a reconstruction algorithm.
Numerous conditions must be satisfied so as to enable an exact reconstruction of the X-ray attenuation coefficient. One of these conditions is indicated and substantiated, for example, by P. Grangeat in “Mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform”, in G. T. Herman, A. K. Louis and F. Natterer, Mathematical Methods in Tomography, Vol. 1497 of the Lecture Notes in Mathematics, Springer Verlag, 1991, pp. 66 to 97. This condition is known as the completeness condition which stipulates that each plane that intersects the examination zone should also intersect the trajectory of the X-ray source. A trajectory that satisfies the completeness condition in relation to an examination zone will be deemed to be complete in relation to this examination zone hereinafter.
In the case of an isocentric examination device the examination zone is preferably an isocentric sphere B(r
max
) having the radius r
max
. The completeness condition can also be formulated differently for a spherical examination zone. In order to derive such an alternative formulation, first the set of all planes that intersect an arbitrary but fixed point a(s) of the trajectory as well as the sphere B(r
max
) is considered. Each of these planes is unambiguously characterized by its normal vector in relation to the center of the sphere B(r
max
), that is, the isocenter. Simple geometrical considerations that can be understood on the basis of
FIG. 1
demonstrate that such normal vectors form a spherical cap U(a(s),r
max
) where the associated sphere has the center a(s)/2 and the radius |a(s)/2|. When the parameter s is varied, and hence also the point a(s), the spherical cap U(a(s),r
max
) is also varied. When the parameter s traverses the interval [s
−
,s
+
], a corresponding number of spherical caps is obtained. From a construction point of view this number of spherical caps contains exactly those normal vectors that are associated with those planes that intersect the trajectory as well as the spherical examination zone B(r
max
). Thus, in order to satisfy the completeness condition, this number of spherical caps must fill the sphere B(r
max
) completely. This is because if a void were present, the planes that are associated with the normal vectors in this void would intersect the examination zone but not the trajectory.
For a given trajectory and a given sphere B(r
max
), a dense sub-set of the set comprising all spherical caps can be calculated and graphically represented by means of a computer and a suitable computer program, after which it can be visually checked whether these spherical caps fill the sphere B(r
max
) without voids or not. As opposed to the first formulation of the completeness condition, the second formulation thus enables a visual test as to whether or not a given trajectory is complete in relation to a given sphere B(r
max
).
It is to be noted that a plane trajectory, that is, a trajectory that is situated completely within one plane, cannot be complete. This is because all planes that extend parallel to the plane of the trajectory and differ therefrom do not intersect the trajectory. Notably a circular trajectory or a segment thereof cannot be complete. However, there are trajectories that are composed of plane segments and are complete. These trajectories include, for example two circles that have the same diameter and the same center and whose axes enclose an angle that is large enough relative to one another.
When the trajectory of the X-ray source is not complete, it can nevertheless be attempted to reconstruct an image of the object to be examined. Generally speaking, however, shortcomings in the image quality will have to be accepted in such a case.
The examination device, however, must also be capable of realizing the trajectory of the X-ray source. In medical applications the object to be examined is a part of a patient who is accommodated on an examination table and it must be ensured that the X-ray source and the X-ray detector do not collide with the object to be examined or with the support for the object.
The Philips INTEGRIS V5000 is an examination device in conformity with the state of the art. This examination device has a C-arm, one end of which supports an X-ray source while an X-ray detector is mounted at its other end. The object to be examined is arranged between the X-ray source and the X-ray detector. The C-arm is supported by a circular rail, so that it can be rotated about its axis. This so-called C-arm axis extends perpendicularly to the plane that contains the C-arm. The support for the C-arm is connected, via a pivot joint, to a so-called L-arm which itself is connected, via a further pivot joint, to a suspension device that is mounted on the ceiling. This suspension device can be displaced rectilinearly and horizontally. The three axes mentioned always intersect one another in one point, that is, the isocenter. An electric motor provides the controllable rotation of the X-ray source and the X-ray detector about the C-arm axis. Rotations about the other two axes are assisted by servomotors, but cannot be controlled. The acquisition of a set of cone beam projections of the object to be examined takes place during a revolution of the C-arm about the C-arm axis. Because of the absence of control, rotations about the other two axes are not possible during the acquisition of cone beam projections in the INTEGRIS V5000. The rotation of the C-arm about its C-arm axis leads to a semi-circular trajectory of the X-ray source. As has already been stated, such a trajectory is not complete.
A complete trajectory could in principle be composed from a plurality of semi-circles. The C-arm would then be positioned anew between the
Dunn Drew A.
Vodopia John
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