Determination of geometrical information about a medical treatment arrangement comprising a rotatable treatment radiation source unit

Abstract

A method for determining geometrical information about a medical treatment arrangement that includes a rotatable treatment radiation source unit is provided. The method includes attaching a phantom to a patient support of the medical treatment arrangement, attaching a calibration module to the rotatable treatment radiation source unit to permit the calibration module to rotate together with the rotatable treatment radiation source unit when the rotatable treatment radiation source unit is rotated, obtaining for each of a plurality of rotational positions of the rotatable treatment radiation source unit a projection image of the phantom and of the calibration module by an image detector, while a part of the calibration module is positioned in a radiation propagation zone between the rotatable treatment radiation source unit and the image detector, evaluating the images, obtaining an evaluation result, and determining geometrical information about the medical treatment arrangement from the evaluation result.

Claims

1. A method for determining geometrical information about a medical treatment arrangement including a rotatable treatment radiation source unit, the method comprising: attaching a phantom to a patient support of the medical treatment arrangement; attaching a calibration module to the rotatable treatment radiation source unit to permit the calibration module to rotate together with the rotatable treatment radiation source unit when the rotatable treatment radiation source unit is rotated; obtaining for each rotational position of a plurality of rotational positions of the rotatable treatment radiation source unit, at least one projection image of the phantom and of the calibration module by an image detector of the medical treatment arrangement, while at least a part of the calibration module is positioned in a radiation propagation zone between the rotatable treatment radiation source unit and the image detector; evaluating the at least one projection image obtained for each rotational position of the plurality of rotational positions with respect to coordinates of the calibration module in a coordinate system of the phantom, thereby obtaining an evaluation result; and determining geometrical information about the medical treatment arrangement from the evaluation result.

2. The method of claim 1, further comprising: obtaining for each rotational position of at least a first rotational position and a second rotational position of the rotatable treatment radiation source unit, at least one projection image of the phantom and of the calibration module by the image detector comprises obtaining at least a first projection image corresponding to the first rotational position and a second projection image corresponding to the second rotational position; and evaluating at least the first projection image and the second projection image with respect to coordinates of the calibration module, thereby determining positions of the calibration module in the coordinate system of the phantom for each rotational position of at least the first rotational position and the second rotational position.

3. The method of claim 2, further comprising: determining from the positions of the calibration module in the coordinate system of the phantom, determined for each rotational position of the first rotational position and the second rotational position, at least one of: an angle of rotation of the rotatable treatment radiation source unit or of a part of the rotatable treatment radiation source unit between the first rotational position and the second rotational position, an orientation of a rotation axis around which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has rotated between the first rotational position and the second rotational position, and a straight linear shift which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has performed between the first rotational position and the second rotational position.

4. The method of claim 1, further comprising: determining an orientation of an average rotation axis of the medical treatment arrangement from orientations of rotation axes determined for a plurality of rotation axes around which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has rotated.

5. The method of claim 1, further comprising: determining positions and orientations of a radiation axis of radiation from the rotatable treatment radiation source unit to the image detector for the plurality of rotational positions of the medical treatment arrangement with respect to at least one rotation axis; and determining an isocenter of the medical treatment arrangement with respect to the at least one rotation axis from the determined positions and orientations of the radiation axis.

6. The method of claim 1, wherein: the calibration module includes a set of fiducial markers, and the method further comprises: obtaining the at least one projection image of the phantom and of the calibration module for each rotational position of the plurality of rotational positions of the rotatable treatment radiation source unit by the image detector of the medical treatment arrangement, while the set of fiducial markers of the calibration module is positioned in the radiation propagation zone between the rotatable treatment radiation source unit and the image detector, and evaluating the at least one projection image obtained for each rotational position of the plurality of rotational positions with respect to coordinates of the set of fiducial markers in the coordinate system of the phantom, thereby obtaining the evaluation result.

7. A medical treatment arrangement comprising: a rotatable treatment radiation source unit; a patient support; an image detector arranged to receive a radiation field that has been emitted by the rotatable treatment radiation source unit and that has interacted with any object in between the rotatable treatment radiation source unit and the image detector, the image detector being configured to produce projection images corresponding to the radiation field according to a result of interaction with at least one object; a phantom attached to the patient support; and a calibration module attached to the rotatable treatment radiation source unit to permit the calibration module to rotate together with the rotatable treatment radiation source unit when the rotatable treatment radiation source unit is rotated.

8. The medical treatment arrangement of claim 7, further comprising: a data storage including projection images generated by the image detector and configured to receive projection images of the phantom and of the calibration module obtained by the image detector for each rotational position of a plurality of rotational positions of the rotatable treatment radiation source unit; an evaluation device connected to at least one of the image detector and the data storage while at least a part of the calibration module is positioned in a radiation propagation zone between the rotatable treatment radiation source unit and the image detector, and configured to evaluate the projection images with respect to coordinates of the calibration module in a coordinate system of the phantom, thereby obtaining an evaluation result; and a determination device being at least one of connected to the evaluation device or part of a common unit with the evaluation device, and configured to determine geometrical information about the medical treatment arrangement from the evaluation result.

9. The medical treatment arrangement of claim 8, wherein the evaluation device is configured to evaluate at least a first projection image corresponding to a first rotational position and a second projection image corresponding to a second rotational position with respect to coordinates of the calibration module, thereby determining positions of the calibration module in the coordinate system of the phantom for each rotational position of at least the first rotational position and the second rotational position.

10. The medical treatment arrangement of claim 9, wherein the determination device is configured to determine, from the positions of the calibration module in the coordinate system of the phantom determined by the evaluation device for each rotational position of the first rotational position and the second rotational position, and least one of: an angle of rotation of the rotatable treatment radiation source unit or of a part of the rotatable treatment radiation source unit between the first rotational position and the second rotational position, an orientation of a rotation axis around which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has rotated between the first rotational position and the second rotational position, and a straight linear shift which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has performed between the first rotational position and the second rotational position.

11. The medical treatment arrangement of claim 8, wherein the determination device is configured to determine an orientation of an average rotation axis of the medical treatment arrangement from orientations of rotation axes determined for a plurality of rotation axes around which at least one of the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has rotated.

12. The medical treatment arrangement of claim 8, wherein the determination device is configured to determine: positions and orientations of a radiation axis of radiation from the rotatable treatment radiation source unit to the image detector for the plurality of rotational positions of the medical treatment arrangement with respect to at least one rotation axis, and an isocenter of the medical treatment arrangement with respect to the at least one rotation axis from the determined positions and orientations of the radiation axis.

13. The medical treatment arrangement of claim 7, wherein the calibration module comprises a set of fiducial markers.

14. The medical treatment arrangement of claim 13, wherein the evaluation device is configured to: receive the projection images of the phantom and of the calibration module obtained by the image detector for each rotational position of a plurality of rotational positions of the rotatable treatment radiation source unit, while the set of fiducial markers of the calibration module is positioned in a radiation propagation zone between the rotatable treatment radiation source unit and the image detector, and to evaluate the projection images with respect to coordinates of the set of fiducial markers in a coordinate system of the phantom, thereby obtaining an evaluation result.

15. The medical treatment arrangement of claim 14, wherein the evaluation device is configured to evaluate at least a first projection image and a second projection image with respect to the coordinates of the set of fiducial markers of the calibration module, thereby determining positions of the set of fiducial markers in the coordinate system of the phantom for each rotational position of at least the first rotational position and the second rotational position.

16. The medical treatment arrangement of claim 15, wherein the determination device is configured to determine from the positions of the set of fiducial markers in the coordinate system of the phantom determined by the evaluation device for each rotational position of the first rotational position and the second rotational position at least one of: an angle of rotation of the rotatable treatment radiation source unit or of a part of the rotatable treatment radiation source unit between the first rotational position and the second rotational position, an orientation of a rotation axis around which the rotatable treatment radiation source unit or the part of the rotatable treatment radiation source unit has rotated between the first rotational position and the second rotational position, and a straight linear shift which the rotatable treatment radiation source unit or a part of the rotatable treatment radiation source unit has performed between the first rotational position and the second rotational position.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be described with reference to the drawings wherein:

(2) FIG. 1 shows a schematic side view of a radiation treatment arrangement having a gantry, a patient table and an image detector, wherein a module for determining geometric information is attached to each of these three components of the arrangement,

(3) FIG. 2 shows schematically an exemplary embodiment of a phantom in the form of a cube with six spherical fiducial markers,

(4) FIG. 3 shows schematically an exemplary embodiment of a calibration module in the form of a cube with three spherical fiducial markers,

(5) FIG. 4 shows a three-dimensional view of a projection of one fiducial marker of a phantom and of one fiducial marker of a calibration module from a source onto an image plane,

(6) FIG. 5 shows a three-dimensional view of a projection of three fiducial markers of a calibration module from a source onto an image plane,

(7) FIG. 6 shows a vector diagram with three momentary rotation axes, a mean orientation vector and the errors of the three momentary rotation axes that extend perpendicularly to the mean orientation vector,

(8) FIG. 7 shows the radiation axes, i.e., the central axes of the radiation beam between the source and the image detector, for three rotational positions,

(9) FIG. 8 shows an enlarged view of a target area including the isocenter of the arrangement shown in FIG. 7,

(10) FIG. 9 shows an example of an arrangement comprising three radiation axes and a determined isocenter, wherein projections of the isocenter onto the radiation axes are illustrated, and

(11) FIG. 10 schematically shows a projection of three fiducial marker lines.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

(12) As mentioned above, a plurality of modules, namely the phantom and the calibration module, are used for the determination of the geometrical information about the arrangement. This does not exclude the use of at least one further module, such as a module attached to the image detector for determining the image detector position and image scale (in particular the pixel size of the matrix of pixels of the detector). If the pixel size is known in advance, this module need not to be used and can be omitted. The image detector orientation can be determined using the phantom.

(13) In the following, an arrangement is described that includes three modules. However, the module which is attached to the image detector can be omitted in other exemplary embodiments.

(14) FIG. 1 schematically shows a medical treatment arrangement 1 including a radiation source unit 2, an image detector 6 and a patient support 10 in the form of a patient table. The radiation source unit 2 includes a radiation source 3 and a collimator 4. As indicated by diverging dashed lines 8, the radiation source 3 produces a cone-shaped radiation beam. The collimator 4 shapes and limits the radiation beam that reaches the patient support 10 to a reduced spatial angle, thereby producing a radiation beam that spreads in the example within a pyramidal area having rectangular cross-sections as indicated by dashed lines 7.

(15) The radiation source unit 2 is fixed to a gantry 5. In FIG. 1, an image detector 6 is shown below the patient support 10. The image detector 6 is also fixed to the gantry 5 by a detector support 15. The gantry 5 can be rotated around a first rotation axis 16 that extends in the horizontal direction of FIG. 1. Therefore, the radiation source unit 2 and the image detector 6 can be rotated around the area above the patient support 10 as indicated by a bent arrow. The first rotation axis 16 is not fixed and its position depends on the actual rotational position of the gantry 5.

(16) Furthermore, the radiation source unit 2 can be rotated relative to the gantry 5 (as indicated by a second bent arrow) around a second rotation axis 17 that is coaxial with the central axis of the cone-shaped radiation beam produced by the radiation source unit 2. Patient support 10 rests on a pillar 11 and, as indicated by a third bent arrow, the patient support 10 can be rotated around a third rotation axis that extends perpendicularly to the image plane of FIG. 1. As a result, the surface of the patient support 10 can tilt so that it is no longer horizontally aligned as shown in FIG. 1. Additionally or alternatively, the patient support 10 can be rotated about a fourth rotation axis (not shown) that extends in vertical direction, essentially parallel to the second rotation axis 17.

(17) A computer 21 may be connected to the image detector 6 as indicated by a dashed line in FIG. 1. This connection is understood to be as a virtual connection. In practice, a database may contain the images obtained by the image detector 6 and the computer 21 is connected to the database for evaluation. The computer 21 includes an evaluation device 22 and a determination device 23. The evaluation device 22 is configured to receive images of the phantom M1 and of the calibration module M2 obtained by the image detector 6 for each of a plurality of rotational positions of the rotatable treatment radiation source unit 2, while the at least three fiducial markers 12, 13, and 14 of the calibration module M2 are positioned in a radiation propagation zone between the rotatable treatment radiation source unit 2 and the image detector 6. Furthermore, the evaluation device 22 is configured to evaluate the images with respect to coordinates of the at least three fiducial markers 12, 13, and 14 in a coordinate system of the phantom M1, thereby obtaining an evaluation result. The determination device 23 is part of a common unit (the computer 21) with the evaluation device 22 and is configured to determine geometrical information about the medical treatment arrangement 1 from the evaluation result.

(18) Other exemplary embodiments of the radiation treatment arrangement may differ from the radiation treatment arrangement 1 shown in FIG. 1, in particular with respect to the number and orientation of the rotation axes. Furthermore, at least one additional radiation source unit and an assigned second image detector may be present in such another radiation treatment arrangement, e.g., for image guided therapy and/or examination. The additional radiation source unit may produce (in particular ionizing) invasive radiation that passes through a patient on the patient support 10 and reaches the second image detector in order to provide image information for image guided therapy and/or examination. Additionally or alternatively, the determination device 23 may be connected to a separate evaluation device that is not part of a common unit.

(19) There are three modules M1, M2, and M3 in the radiation treatment arrangement 1 shown in FIG. 1 that are not present when the radiation treatment arrangement 1 is used for treatment of a patient. These three modules are used for determining geometrical information about the radiation treatment arrangement 1. This geometrical information can be used for calibration of the radiation treatment arrangement 1.

(20) The first module is a phantom M1 that is attached to the patient support 10 where a patient would be placed during treatment. As schematically shown in FIG. 1, the phantom M1 includes an arrangement of fiducial markers 18 that includes in the typical example six fiducial markers. According to one exemplary embodiment of the method that will be described in more detail, the coordinates of six points of the set of six fiducial markers are known. This enables the determination of the pairwise distances of the six points. In other words, the mutual positions of the fiducial markers 18 are known. As indicated in FIG. 1, the six fiducial markers 18 may be spheres and the related points may be the center points of the spheres. However, six points may alternatively be defined by another set of fiducial markers 18, for example by a set of three straight lines defining the end points of the straight lines.

(21) The second module is a calibration module M2 rigidly affixed to the radiation source unit 2. For example, a case and/or a support of the collimator 4 may include a standardized mechanical interface (e.g., including guides) for affixing additional equipment to the case and/or a support of the collimator 4. Such additional equipment, for example the calibration module M2, can therefore be attached temporarily to the collimator 4 for (e.g., routinely performed) quality checks. When the projection images intended to be taken for the quality check, in particular for the calibration of the arrangement 1, have been taken, the additional equipment can be removed from the collimator 4. Different additional equipment, such as different kinds of the calibration module, can be provided and each of this additional equipment is shaped and/or there is an adapter that allows for affixing the additional equipment to the mechanical interface, e.g., using the guides mentioned. For example, in order to rigidly fix the calibration module M2 to the radiation source unit 2, the calibration module M2 includes an adapter that fits into these guides. According to an alternative way of temporarily affixing the calibration module to the collimator of the radiation source unit 2, the calibration module M2 is clamped onto the collimator 4, in particular onto the case and/or support, e.g., by inserting projections into corresponding recesses and by continuously loading this connection with a clamping force so that the projections remain in the recesses.

(22) The calibration module M2 includes at least three fiducial markers 12, 13, and 14, which are spherical ball fiducials in the exemplary embodiment. The distances between characteristic points of the at least three fiducial markers 12, 13, and 14 are known. In the exemplary embodiment, the centers of the ball fiducials are the characteristic points.

(23) The third module is a detector module M3 affixed rigidly to the image detector 6. The detector module M3 is used to determine the pixel size of projection images generated by the image detector 6. In the exemplary embodiment, the detector module M3 is a body the shape and size of which is known.

(24) FIG. 2 shows an exemplary embodiment of phantom M1 in the form of a cube. The edges of the cube define a reference coordinate system, i.e., the edges extend in parallel to the coordinate axes e.sub.x,e.sub.y,e.sub.z of the Cartesian coordinate system shown on the left-hand side of FIG. 2. If one of the corners of the cube defines the origin of the coordinate system, the edges starting at the corner extend in line with in each case one of the coordinate axes e.sub.x,e.sub.y,e.sub.z. The six fiducial markers of radiation opaque material that are arranged within the cube are spherical fiducials (i.e., ball markers). The material of the cube in which the fiducial markers are embedded is transparent with respect to the radiation so that projection images of the fiducial markers are obtained by the image detector. For example, one of the six fiducial markers may be placed in the center of the cube or approximately in the center of the cube. From the center point of this central fiducial marker, a vector V extends to each of the center points of the other five fiducial markers. Based on prior knowledge about the constitution of the phantom, the coordinates of the vectors V are precisely known. The arrangement of the fiducials in the volume of the module is arbitrary to some extent, i.e., other phantoms of the same type with a different local distribution of the fiducial markers can be used alternatively. In addition, the number of fiducial markers within the phantom may be different.

(25) FIG. 3 shows an exemplary embodiment of a calibration module M2 in the form of a cube. The three fiducial markers of radiation opaque material that are arranged within the cube of radiation transparent material are spherical fiducials (i.e., ball markers). Typically, none of the three fiducial markers is placed in the center of the cube. The known distances d between the center points of the fiducial markers are shown in the figure. The arrangement of the fiducials in the volume of the module is arbitrary to some extent, i.e., other calibration modules of the same type with a different local distribution of the fiducial markers can be used alternatively. In addition, the number of fiducial markers within the calibration module may be greater than three.

(26) The shapes of the phantom shown in FIG. 2 and/or of the calibration module shown in FIG. 3 may differ in other exemplary embodiments. For example, the shape may be the shape of a cuboid or of a cylinder.

(27) The coordinate system defined by the phantom M1 may be used as the coordinate system in which the geometrical information is determined. For example, all parameters, constants and coefficients that describe the geometrical information can be determined with respect to this coordinate system. For the assumption-free determination of the position of a characteristic point of the radiation source unit (such as the radiation origin point of the central axis of the radiation beam), only the phantom is required, provided that the pixel size of the projection images obtained by using the image detector is known. In other words, the calibration module M2 is not required for the determination of a single characteristic point of the radiation source unit. The same applies to the determination of the distance between the radiation source unit and the image detector and applies to the orientation of the image detector in space.

(28) The calibration module (for example the module shown in FIG. 3) is used to determine the rotation angles and rotation axes of the radiation source unit and/or of a part of the radiation source unit. In particular, the rotation of the radiation source unit may be a rotation around the same rotation axis and with the same rotation angle as a gantry to which the radiation source unit is attached. A part of the radiation source unit that is rotatable around another rotation axis relative to the radiation source may be a collimator. The radiation source unit and (if applicable) the independently rotatable part of the radiation source unit is rotatable relative to the patient support. In practice, the position and orientation of the patient support is represented by the phantom that is attached to the patient support.

(29) There is no need to describe an example of determining the position of the characteristic point of the radiation source unit in detail here, since corresponding methods are known from publications describing applications of the above-mentioned approach (e.g. W. Mao, L. Lee, L. Xing, Development of a QA phantom and automated analysis tool for geometric quality assurance of on-board MV and kV X-ray imaging systems, Med. Phys. 35, 1497-1506 (2008); N. Robert, K. N. Watt, X. Wang, J. G. Mainprize, The geometric calibration of cone-beam systems with arbitrary geometry, Phys Med Biol. 54, 7239-7261 (2009); On-Board Imager (OBI) Advanced Imaging Maintenance Manual, version B502203R01D, Varian Medical Systems, Inc., USA, April 2012, chapter 11, pp. 178-205). In the following, examples of determining the rotation angles and rotation axes will be described.

(30) Because the central axis of radiation may unsteadily move during the rotation, for example as the result of flexing or sagging of the system under its own weight and/or aging of bearing mechanisms, the actual rotation axis and the actual rotation angle (from one rotational position to another rotational position) of the radiation source unit (in particular with respect to the rotation of the complete radiation source unit relative to the patient support or with respect to the rotation of the collimator relative to the patient support) depend on the rotational position. Therefore, the real rotational positions and the real orientation of the radiation source unit may differ from nominal positions and orientation. In other words, the rotation axis is not fixed in space while the rotation is performed.

(31) As shown below, the use of a multi-fiducial calibration module attached to the radiation source unit allows for in particular assumption-free determination of the rotation axis as a function of the rotational position or of the rotation axes as functions of the rotational positions. In particular, an average rotation axis can be determined, such as for collimator rotation while there is no relative rotation of the patient table and the radiation source unit, or for another rotation axis. Furthermore, the position and/or orientation of the radiation axis and/or the radiation isocenter can be determined using the calibration module that is attached to the radiation source unit. From the geometrical information obtained with respect to the rotation of the radiation source unit, with respect to the rotation of the patient support and/or with respect to the rotation of a part of the radiation source unit, the mechanical isocenter can be determined. Determination of an isocenter in particular means that fluctuations of the position of the isocenter during rotation are considered and/or determined.

(32) The following example of a method of determining geometrical information assumes that, for a plurality of rotational positions of the radiation source unit or of a part of the radiation source unit, the normal to the imaging plane of the image detector, the source to detector distance, the source position and the two-dimensional coordinate system (e.g., described by its coordinate axes E.sub.x and E.sub.y, see FIG. 4) in the imaging plane have been determined and/or are known, in particular with respect to the coordinate system of the phantom, based on methods described in published articles (e.g., W. Mao, L. Lee, L. Xing, Development of a QA phantom and automated analysis tool for geometric quality assurance of on-board MV and kV X-ray imaging systems, Med. Phys. 35, 1497-1506 (2008); N. Robert, K. N. Watt, X. Wang, J. G. Mainprize, The geometric calibration of cone-beam systems with arbitrary geometry, Phys Med Biol. 54, 7239-7261 (2009); On-Board Imager (OBI) Advanced Imaging Maintenance Manual, version B502203R01D, Varian Medical Systems, Inc., USA, April 2012, chapter 11, pp. 178-205). In the following, the coordinate system of the phantom or of the patient support with respect to which the geometrical information is given and/or determined and which can be in particular the coordinate system of the phantom, will be referred to as the global coordinate system.

(33) Using the geometrical information mentioned in the preceding paragraph, the coordinates of the projections of the fiducial markers of the phantom can be determined. FIG. 4 illustrates the geometrical situation for one fiducial marker of the phantom and one fiducial marker of the calibration module. Two projection lines from the source Z to the image plane are illustrated by straight lines. There is the characteristic position P of one fiducial marker of the phantom on one of the projection lines and there is the characteristic position Q of one fiducial marker of the calibration module on the other one of the projection lines. The positions of the corresponding projection points are denoted by P and Q. In addition, the vector starting at position P and ending at position Q is denoted by PQ.

(34) The calibration module (in particular the calibration module of FIG. 1 or 3) is rigidly attached to the calibration source unit, for example as described above to the collimator. One task is to find the coordinates of the calibration module fiducials in the global coordinate system. Although these coordinates cannot be assessed directly, the global coordinates of their projections onto the image plane can be determined. For example, in FIG. 4, the global coordinates of position P are known, since all positions and their distances of the fiducial markers of the phantom are known. The global coordinates of the projection position P of the position P can be determined. In addition, for a position Q of a fiducial marker within the calibration module, its projection position Q in the image plane can be determined from the obtained image and the components of the PQ vector can be determined as well in the global coordinate system, as the vectors of the coordinate axes E.sub.x and E.sub.y of the image plane are known. Consequently, the components of the projected position Q in the global coordinate system can be determined as well. Furthermore, it is known that the fiducial marker position Q lies somewhere on the projection line connecting the projection position Q and the source position Z. Therefore, the global coordinates of both positions Q and Z can be determined from the evaluation of the projection images of the fiducial markers of the phantom.

(35) The calibration module includes at least three fiducial markers, corresponding to positions Q.sub.1, Q.sub.2, and Q.sub.3 in FIG. 5. Their mutual distances d.sub.12, d.sub.13, and d.sub.23 are also shown in FIG. 5. Therefore, the following equations (1) apply:
i=1,2,3 t.sub.i(0,1):Q.sub.i=Z+t.sub.iZQ.sub.i
i=1,2,3; j=1,2,3; ij|Q.sub.iQ.sub.j|=d.sub.ij(1)
wherein ZQ is the vector between the position Z of the source and the respective projection point position Q in the image plane. In FIG. 5, the distances of the positions Q are denoted by d followed by the two indices of the respective two positions. According to the second line of equations (1), the distances of the positions Q are equal to the respective known distances d. However, it is typically not possible to find a position on each of the three projection lines for which the pairwise distances are exactly equal to the known distances d.

(36) On the other hand, the first line of equations (1) provides three independent equations for three unknowns, namely the parameters t.sub.1, t.sub.2, and t.sub.3, and these unknowns can be found for example by minimization of the following cost function G:

(37) $\begin{array}{cc}G\left(t_1,t_2,t_3\right)=\underset{i,j=1,2,3;ij}{.Math.}{\left(.Math.\stackrel{\_}{Q_i{Q}_j}.Math.-d_{\mathrm{ij}}\right)}^2& \left(2\right)\end{array}$

(38) To make the determination of the positions Q more robust with the respect to imperfect imaging, a calibration module having a larger number of fiducial markers can be used. In this case, the index variable assumes more than three values and the cost function G includes more than three terms in the summation defined on the right-hand side of the equation (2). In this case, the solution of the minimization problem defined in equation (2) delivers the global coordinates of the fiducial markers of the calibration module.

(39) In the following, a method of determining the rotation angle and the rotation axis using images for two rotational positions of the radiation source unit will be described. In particular, the rotation may be caused by a rotation of the complete radiation source unit corresponding to the rotation of a gantry (if applicable) or the rotation may be caused by a rotation of a part of the radiation source unit, such as a collimator.

(40) The rotation angle is denoted by and the rotation axis is represented by a vector a=(a.sub.x,a.sub.y,a.sub.z), |a|=1, passing through a point P.sub.0=(P.sub.0x,P.sub.0y,P.sub.0z). The position of a fiducial marker of the calibration module prior to rotation (i.e., at the first rotational position) is denoted by X.sub.0=(X.sub.0x,X.sub.0y,X.sub.0z) and after rotation (i.e., at the second rotational position) is denoted by X.sub.N=(X.sub.Nx,X.sub.Ny,X.sub.Nz). The coordinates of X.sub.N in the global coordinate system are given by equation (3):

(41) $\begin{array}{cc}\left(\begin{array}{c}{X}_{\mathrm{Nx}}\\ X_{\mathrm{Ny}}\\ X_{\mathrm{Nz}}\\ 1\end{array}\right)=T\left(X_0\right)=\left(\begin{array}{cccc}1& 0& 0& P_{0x}\\ 0& 1& 0& P_{0y}\\ 0& 0& 1& P_{0z}\\ 0& 0& 0& 1\end{array}\right)R\left(\begin{array}{cccc}1& 0& 0& -P_{0x}\\ 0& 1& 0& -P_{0y}\\ 0& 0& 1& -P_{0z}\\ 0& 0& 0& 1\end{array}\right)\left(\begin{array}{c}{X}_{0x}\\ X_{0y}\\ X_{0z}\\ 1\end{array}\right)R=\left(\begin{array}{cccc}c+a_x^2\left(1-c\right)& a_x{a}_y\left(1-c\right)-a_{z}s& a_x{a}_z\left(1-c\right)+a_{y}s& 0\\ a_x{a}_y\left(1-c\right)+a_{z}s& c+a_y^2\left(1-c\right)& a_y{a}_z\left(1-c\right)-a_{x}s& 0\\ a_x{a}_z\left(1-c\right)-a_{y}s& a_y{a}_z\left(1-c\right)+a_{x}s& c+a_z^2\left(1-c\right)& 0\\ 0& 0& 0& 1\end{array}\right)& \left(3\right)\end{array}$
where T is the rigid-body transformation corresponding to the movement of the complete radiation source unit or to the movement of a part of the radiation source unit, c=cos(), s=sin() and R is the well-known axis-angle representation of the rotation matrix. Then, given a set B={X.sub.0,i, i=1 . . . M} of coordinates X.sub.0,i before rotation and a set A={X.sub.N,i,i=1 . . . M} of corresponding coordinates X.sub.N,i after rotation, the problem of determining the transformation matrix T can be formulated for example as a problem of minimizing the following cost function F(A,B,T):

(42) $\begin{array}{cc}F\left(A,B,T\right)=\underset{i=1}{\overset{M}{.Math.}}{.Math.X_{N,i}-T\left(X_{0,i}\right).Math.}^2& \left(4\right)\end{array}$

(43) Consequently, from the analysis of the projections of fiducial markers of the calibration module, the actual rigid body movement of the radiation source unit or of part of the radiation source unit can be obtained. Then, the average rotation axis of either the complete radiation source unit (which may be equivalent to the rotation of a gantry) or of a part of the radiation source unit (e.g., a collimator) as well as the deviations from the average rotation axis can be derived with the methods described below.

(44) In the following, an exemplary embodiment of a method of determining an average rotation axis for a range of rotational positions or for the whole range of rotational positions (360 degrees, one complete turnaround the rotation axis) is described. Again, the rotation axis may be the rotation axis of the complete radiation source unit or of a part of it, e.g., the collimator.

(45) U.sub.i denotes the orientation of a momentary rotation axis of a rotation between two rotational positions. For each pair of rotational positions, the momentary rotation axis can be determined by performing the method described before. Of course, the orientation U.sub.i of the momentary rotation axis depends on both rotational positions. It is possible to determine the average orientation for a plurality of orientations U.sub.i. The average orientation vector U can be found (e.g., using a least square method) by minimizing the errors H.sub.i of the orientations U.sub.i with the respect to the average orientation U being constrained to unit length (FIG. 6):

(46) $\begin{array}{cc}U=\underset{.Math.U.Math.=1}{\min \arg }\underset{i}{.Math.}{.Math.H_i\left(U\right).Math.}^2=\underset{.Math.U.Math.=1}{\min \arg }\underset{i}{.Math.}{.Math.U_i-\left(U_i.Math.U\right)U.Math.}^2,& \left(5\right)\end{array}$

(47) In FIG. 6, an exemplary embodiment with three momentary rotation axes, i.e., with three orientations U.sub.i is shown. The lines which represent the errors H.sub.i of the three orientations U.sub.i extend perpendicularly to the straight line which is co-linear with the average orientation vector U.

(48) It can be shown that the average orientation vector U is the principal vector corresponding to the maximal principal value of the covariance matrix C of the orientations

(49) $\begin{array}{cc}C=\left(\begin{array}{ccc}\underset{i}{.Math.}{U}_{\mathrm{ix}}{U}_{\mathrm{ix}}& \underset{i}{.Math.}{U}_{\mathrm{ix}}{U}_{\mathrm{iy}}& \underset{i}{.Math.}{U}_{\mathrm{ix}}{U}_{\mathrm{iz}}\\ \underset{i}{.Math.}{U}_{\mathrm{iy}}{U}_{\mathrm{ix}}& \underset{i}{.Math.}{U}_{\mathrm{iy}}{U}_{\mathrm{iy}}& \underset{i}{.Math.}{U}_{\mathrm{iy}}{U}_{\mathrm{iz}}\\ \underset{i}{.Math.}{U}_{\mathrm{iz}}{U}_{\mathrm{ix}}& \underset{i}{.Math.}{U}_{\mathrm{iz}}{U}_{\mathrm{iy}}& \underset{i}{.Math.}{U}_{\mathrm{iz}}{U}_{\mathrm{iz}}\end{array}\right)& \left(6\right)\end{array}$

(50) The principal values and principal directions of the covariance matrix C define a three-axis ellipsoid. The wobbling of the rotation axis is maximal for the principal direction corresponding to the largest principal value of C. The variances of the data with the respect to the principal directions are thus useful information for the quality control in radiotherapy/radiosurgery. In particular, the principal values and principal directions of the covariance matrix C, in particular the largest principal value, represent(s) measures of the undesired variation (movement) of the rotation axis.

(51) In the following, an exemplary embodiment of a method of determining the coordinates of an isocenter (i.e., its position in particular in the global coordinate system) is described. Momentary rotation axes and rotation angles of radiation axes, which are for example determined as described above, can be used as geometrical input information of the determination method. Different isocenters, in particular the isocenters mentioned above, can be determined by the method. Each isocenter can be determined by using a minimization procedure, in particular a least-squares method.

(52) In the exemplary embodiment described here and illustrated in FIG. 7, the mechanical isocenter with respect to the rotation of the radiation source unit and the image detector around their rotation axis is determined. However, the isocenter with respect to any other rotation axis or combination of rotation axes can be determined in a similar manner. As shown in FIG. 7, the radiation axes (center beam propagation lines which may also be the rotation axes of the collimator) are denoted by CAX.sub.i, wherein i denotes the index of the respective radiation axis. For example, if a number of N radiation axes is considered, i assumes the integer values from 1 to N. The positions and orientations of the radiation axes CAX.sub.i have been determined before. The position IS of the isocenter can be determined by solving the following minimization problem:

(53) $\begin{array}{cc}\mathrm{IS}=\underset{W}{\min \arg }\underset{i=1}{\overset{N}{.Math.}}{d}^2\left(W,{\mathrm{CAX}}_i\right),& \left(7\right)\end{array}$
i.e., minimizing the sum of the squares of the distances d of the radiation axes CAX.sub.i to positions W, especially positions within a target area. The target area may be defined as an area of positions, which area most likely contains or for plausibility reasons contains the isocenter position. FIG. 7 and FIG. 8 show an exemplary embodiment for N=3 radiation axes. Each radiation axis CAX.sub.i extends from the radiation source unit 2 to the image detector 6 for the respective rotational position. FIG. 8 shows an enlarged view of the central area VIII of FIG. 7. In the exemplary embodiment, the target area is defined by the triangle, and the edges of which are defined by the radiation axes CAX.sub.i. In case of more radiation axes CAX.sub.i, the target typically has a different shape. In FIG. 8, d(W, CAX.sub.i) denote the distances of an exemplary position W within the target area to the radiation axes.

(54) More generally speaking, if an isocenter position with respect to one rotational axis or more than one rotational axis is to be determined by the minimization procedure, the target area is a volume in space, rather than an area within a plane. This especially applies to the isocenter with respect to two rotational axes. However, this also applies to the exemplary embodiments shown in FIG. 7 and FIG. 8 if the three rotational axes do not intersect each other pairwise. However, in any case, the radiation axis for each combination of rotational positions with respect to the plurality of rotational axes can be determined and the position can be identified for which the sum of the distances or of the square of the distance to the radiation axes is minimal.

(55) In the following, it is shown that the problem defined by equation (7) can be solved analytically, because it is quadratic in the coordinates W.sub.x, W.sub.y, and W.sub.z of an arbitrary point W within the target area. As each radiation axis CAX.sub.i can be represented as a straight line in the three-dimensional space, we have:
CAX.sub.i:{{right arrow over (x)}:{right arrow over (x)}={right arrow over (a.sub.i)}t+{right arrow over (v.sub.0,i)},t}
{right arrow over (a.sub.i)}=(a.sub.x,i,a.sub.y,i,a.sub.z,i)
|a.sub.i|=1
{right arrow over (v.sub.0,i)}=(x.sub.0,i,y.sub.0,i,z.sub.0,i)(8)
wherein t denotes that t is a real number, a denotes a vector having a unit length and extending in the direction of the radiation axis and v.sub.0,i denotes a point in space located where the radiation axis starts at the radiation source.

(56) By taking the derivatives of the cost function

(57) $K\left(V\right)=\underset{i=1}{\overset{N}{.Math.}}{d}^2\left(W,{\mathrm{CAX}}_i\right)$
on the right-hand side of equation (7) with respect to the coordinates of the positions W, it can be shown that the least-squares estimates is.sub.x, is.sub.y, and is.sub.z of the coordinates IS.sub.x, IS.sub.y, and IS.sub.z of the isocenter IS are the solution of the following set of three linear equations:

(58) $\begin{array}{cc}\left(\begin{array}{ccc}N-\underset{i=1}{\overset{N}{.Math.}}{a}_{x,i}{a}_{x,i}& -\underset{i=1}{\overset{N}{.Math.}}{a}_{y,i}{a}_{x,i}& -\underset{i=1}{\overset{N}{.Math.}}{a}_{z,i}{a}_{x,i}\\ -\underset{i=1}{\overset{N}{.Math.}}{a}_{y,i}{a}_{x,i}& N-\underset{i=1}{\overset{N}{.Math.}}{a}_{y,i}{a}_{y,i}& -\underset{i=1}{\overset{N}{.Math.}}{a}_{z,i}{a}_{y,i}\\ -\underset{i=1}{\overset{N}{.Math.}}{a}_{z,i}{a}_{x,i}& -\underset{i=1}{\overset{N}{.Math.}}{a}_{z,i}{a}_{y,i}& N-\underset{i=1}{\overset{N}{.Math.}}{a}_{z,i}{a}_{z,i}\end{array}\right)\left(\begin{array}{c}{\mathrm{is}}_x\\ {\mathrm{is}}_y\\ {\mathrm{is}}_z\end{array}\right)=\left(\begin{array}{c}\underset{i=1}{\overset{N}{.Math.}}\left(x_{0,i}-a_{x,i}{a}_{x,i}{x}_{0,i}-a_{y,i}{a}_{x,i}{y}_{0,i}-a_{z,i}{a}_{x,i}{z}_{0,i}\right)\\ \underset{i=1}{\overset{N}{.Math.}}\left(y_{0,i}-a_{y,i}{a}_{x,i}{x}_{0,i}-a_{y,i}{a}_{y,i}{y}_{0,i}-a_{z,i}{a}_{y,i}{z}_{0,i}\right)\\ \underset{i=1}{\overset{N}{.Math.}}\left(z_{0,i}-a_{z,i}{a}_{x,i}{x}_{0,i}-a_{y,i}{a}_{z,i}{y}_{0,i}-a_{z,i}{a}_{z,i}{z}_{0,i}\right)\end{array}\right)& \left(9\right)\end{array}$

(59) There are at least two reasons for uncertainties in the estimation of the position of the isocenter. The first reason refers to the random measurement errors related to the estimation of the components of the vector a.sub.i and of the point v.sub.0,i and to the actual selection of the orientations of the rotation axis/axes. The second reason are the numerical errors of the minimization procedure performed in order to determine the vector a.sub.i and the point v.sub.0,i. The uncertainties related to the latter reason are the direct consequence of the fact that the results of a minimization procedure may depend on its initialization (in particular defined by a set of start values) and thus are not guaranteed to be Gaussian distributed. Consequently, it is typical to repeat the minimization procedure starting with different initializations in order to estimate and/or to reduce these uncertainties.

(60) When the position of the isocenter IS and the radiation axes CAX.sub.i have been determined, the wobbling of the radiation axes around the isocenter can be assessed. In particular, the isocenter IS can be projected onto each radiation axis CAX.sub.i resulting in a plurality of projection points L.sub.i (FIG. 9). Then, the vectors F.sub.i pointing from the isocenter IS to the respective projection point L.sub.i can be calculated: F.sub.i=L.sub.iIS. Typically, the average orientation vector F for all vectors F.sub.i is calculated as a characteristic of the wobbling. The average orientation vector F can be determined by using a least squares method, e.g., analogue to the least squares method mentioned in connection with FIG. 6 above. FIG. 9 illustrates the projection for an arrangement of three radiation axes CAX.sub.i similar to the arrangement shown in FIG. 7 and FIG. 8. The projection vectors F.sub.i extend perpendicularly to the respective radiation axis.

(61) In order to reliably determine the position of an isocenter and to quantitatively characterize wobbling, the radiation axis CAX.sub.i is to be determined for a plurality of rotational positions with respect to the corresponding rotation axis/axes (e.g., the rotation axis of a gantry and/or of a collimator).

(62) Further geometrical information can be determined using the calibration module that is attached to the radiation source unit. In particular the position of elements (the so-called jaws) of a collimator that is part of the radiation source unit, the size of the radiation field generated by the radiation source unit, movements of the treatment table and/or the natural coordinate system related to the device can be determined. Using geometrical information related to at least one isocenter of the arrangement, geometrical information about other devices of the arrangement can be determined, in particular about room lasers, telemeters, or a light simulation field.

(63) In the following, a second exemplary embodiment for determining the position and/or orientation of the calibration module, and thereby of the radiation source unit, or the respective rotation angle is described.

(64) According to the second exemplary embodiment, there is a plurality of n points of the calibration module which are defined by fiducial markers (e.g., by point markers or by the end points of line markers), wherein n is an integer. A principal difference between the second exemplary embodiment and the first exemplary embodiment described before with reference to FIG. 5, is the fact that the n points of the calibration module and their pairwise distances are fixed, but there is no need to know the coordinates of the points and the distances explicitly.

(65) These n fiducials points are denoted by Q.sub.1, Q.sub.2, . . . , and Q.sub.n. Now, two different rotational positions of the radiation source unit relative to the patient support or relative to any other part of the arrangement are considered, namely an initial position O and a target position N. In the same manner as in the case of the first example, the global coordinates of the projection points Q.sub.O of the fiducial points Q.sub.O for the initial position O and of the projection points Q.sub.N of the fiducial points Q.sub.N for the target position N can be determined. For the initial position O, each of the fiducial points Q.sub.O is located somewhere along the straight line connecting its projection point Q.sub.O and the initial source position Z.sub.O. Similarly, for the target position N, each of the fiducial points Q.sub.N is located somewhere along the straight line connecting its projection point Q.sub.N and the target source position Z.sub.N. The global coordinates of all these points can be determined from an analysis of projection images of the phantom. Since the distances between the fiducials points Q remain constant (although they may be unknown) while rotating, then we have the following conditions:
i=1, . . . ,n t.sub.i,N:Q.sub.i,N=Q.sub.i,N+t.sub.i,N{square root over (Q.sub.i,NZ.sub.N)}
i=1, . . . ,n t.sub.i,O:Q.sub.i,O=Q.sub.i,O+t.sub.i,O{square root over (Q.sub.i,OZ.sub.O)}
i=1, . . . ,n; j=1, . . . ,n; ij|{square root over (Q.sub.i,NQ.sub.j,N)}|=|{square root over (Q.sub.i,OQ.sub.j,O)}|(10)

(66) Herein, t.sub.i,O and t.sub.i,N are parameters describing the position of one of the fiducial points Q on the respective straight line connecting the projection point Q with the source position Z. Therefore, the set of equations (10) includes n(n1)/2 independent equations for the 2n parameters t. In order to determine the fiducial points for the initial rotational position and for the target rotational position in the three-dimensional global coordinate system, n=5 fiducial points Q are required. When these ten fiducial points (five fiducial points of the initial rotational position and five fiducial points of the target rotational position) have been determined, the corresponding transformation that transforms the five fiducial points of the initial rotational position to the five fiducial points of the target rotational position can be calculated and the corresponding rotation angle can be determined.

(67) In the following, a third example of determining the position and/or orientation of the calibration module, and thereby of the radiation source unit, or of the respective rotation angle is described. In this example, straight linear markers and their angles are used instead of fiducial points. When a rigid body like of the radiation source unit together with the calibration module rotates, the angles formed by any three different points remain unchanged. However, the projections of these angles depend on the rotational position.

(68) FIG. 10 schematically shows a projection similar to the projection shown in FIG. 5. While FIG. 5 shows the projection of three fiducial points of a calibration module onto the image plane of the detector, FIG. 10 shows the projection of three fiducial marker lines a, b, and c. The corresponding projected lines are denoted by a, b, and c. In addition, two points a1 and a2 are shown on the projected line a.

(69) The angles between each pair in the set of the three lines a, b, and c are known. For each of the rotational positions of the radiation source unit the lines a, b, and c are projected onto lines a, b, and c, respectively (FIG. 10) and the respective projection image is generated. The coordinates, in particular the positions and orientations, of the projected lines a, b, and c can be determined in each of the projection images, e.g., by applying an image analysis algorithm (for example using a Hough transform) and thenbased on an analysis of the projections of structures of the phantomthe 3-dimensional global coordinates of arbitrary two points (e.g., a1 and a2 in line a) within each projected line a, b, and c are determined. Based on the global coordinates of these points as well as the global coordinates of the source Z, for each of the projected lines a, b, and c the equation of the plane unambiguously defined by the two points and by the source Z can be determined. For example, for line a, the normal line n.sub.a onto the plane is given by the cross product of the vector connecting the point a1 and the source Z and of the vector connecting the second point a2 and the source Z:
n.sub.a=(a.sub.1Z)(a.sub.2Z)(11)

(70) Thus, the plane P.sub.a that includes the projected line a and the source Z is described by:
P.sub.a={XR.sup.3:n.sub.a.Math.(XZ)=0}(12)

(71) wherein X is any point in the plane, i.e., X can assume each set of coordinates of points in the plane. Analogous equations for the plane P.sub.b with respect to the second line b and its projected line b as well as for the plane P.sub.c with respect to the third line c and its projected line c can be set for the other two segments. In these two analogous equations, the normal lines n.sub.b and n.sub.c are used that corresponds to the normal line n.sub.a.

(72) Now, let A be a unit length vector within line a, B a unit length vector within line b, and C a unit length vector within line c, ab be an angle of known size between lines a and b, bc be an angle of known size between lines b and c and ca be an angle of known size between lines c and a. Then, the following set of nine equations for nine unknown components of the vectors A, B, and C can be set-up:
A.Math.n.sub.a=0
B.Math.n.sub.b=0
C.Math.n.sub.c=0
A=1
B=1
C=1
A.Math.B=cos(ab)
A.Math.C=cos(ac)
B.Math.C=cos(bc)(13)

(73) From the set of equations (13), the vector components of A, B, and C can be determined in particular for an initial rotational position and a target rotational position of the radiation source unit relative to any other part of the arrangement. Furthermore, the transformation (e.g., the rotation axis and the rotation angle) between the initial rotational position and the target rotational position can be determined from the vector components of the vectors A, B, and C in the same manner as in the case of the first and the second example.

(74) It is understood that the foregoing description is that of the exemplary embodiments of the invention and that various changes and modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims.

LIST OF REFERENCE SIGNS

(75) a, b, c straight lines (fiducial marker lines) a, b, c projections of straight lines a1 first point on projection line a a2 second point on projection line a d distance e.sub.x,e.sub.y,e.sub.z coordinate axes of coordinate system of phantom E.sub.x,E.sub.y coordinate axes of coordinate system of image plane F.sub.i projection vector IS position of isocenter H.sub.i error of the momentary rotation axes L.sub.i projection point M1 phantom M2 calibration module M3 detector module P position of fiducial marker of phantom P projection of fiducial marker of phantom onto image plane Q position of fiducial marker of calibration module Q projection of fiducial marker of calibration source onto image plane PQ vector from P to Q U average orientation vector U.sub.i momentary rotation axis V vector from fiducial marker to another fiducial marker within phantom Z position of source 1 radiation treatment arrangement 2 radiation source unit 3 radiation source 4 collimator 5 gantry 6 image detector 7 lines indicating narrowed radiation beam 8 diverging lines indicating cone shaped radiation beam 10 patient support 11 pillar 12 first fiducial marker 13 second fiducial marker 14 third fiducial marker 15 detector support 16 first rotation axis 17 second rotation axis 18 arrangement of fiducial markers (within module M1) 20 Image plane of detector