System and method for radiation treatment optimized for non-coplanar delivery

Abstract

A system or method for radiation treatment optimized for non-coplanar delivery, which includes a first collimator affixed to a gantry and a second collimator movably attached to the gantry to provide the second collimator a translation movement out of a gantry rotation plane. The system or method also includes a third collimator configured to collimate the beam in a direction of a target in the patient's body. The beam collimated by the third collimator is configured to follow the target during treatment. A method of performing rotation setup correction by rotating the treatment beam, without rotating the patient.

Claims

1. A system for radiation treatment, said system comprising: a gantry configured to rotate around a body of a patient positioned along with a longitudinal axis; a radiation treatment source affixed to said gantry, wherein said radiation treatment source is configured to emit an x-ray treatment beam in a direction that is transverse to said longitudinal axis; a first collimator affixed to said gantry, wherein said first collimator is configured to collimate the x-ray treatment beam emitted from said radiation treatment source; and a second collimator movably attached to said gantry, wherein said second collimator is configured to further collimate the x-ray treatment beam collimated by said first collimator and move out of a gantry rotation plane along said longitudinal axis.

2. The system for radiation treatment according to claim 1, wherein said system further comprising a third collimator configured to further collimate the x-ray treatment beam collimated by said second collimator.

3. The system for radiation treatment according to claim 1, wherein said radiation treatment source is configured to emit the x-ray treatment beam in a direction that is substantially perpendicular to said longitudinal axis.

4. The system for radiation treatment according to claim 2, wherein said third collimator comprising: a guiding rail affixed to said gantry; and a cone collimator configured to further collimate the x-ray treatment beam collimated by said second collimator in a direction of a target in the patient's body, wherein said cone collimator is movably attached to said guiding rail and is configured to move along said guiding rail relative to the movement of the patient such that the x-ray treatment beam follows the target while the patient moves along said longitudinal axis.

5. The system for radiation treatment according to claim 2, wherein said third collimator comprising: a rotatable cartridge affixed to said gantry; and a multi-leaf collimator comprising a single layer, wherein said multi-leaf collimator is affixed to said rotatable cartridge, wherein said multi-leaf collimator is configured to further collimate the x-ray treatment beam collimated by said second collimator in a direction of a target in the patient's body, wherein said rotatable cartridge is configured to move with said multi-leaf collimator relative to the movement of the patient such that the x-ray treatment beam follows the target while the patient moves along said longitudinal axis.

6. The system for radiation treatment according to claim 1, wherein said third collimator comprising: a non-rotating cartridge affixed to said gantry; and a multi-leaf collimator comprising a plurality of layers, wherein said multi-leaf collimator is affixed to said non-rotating cartridge, wherein said multi-leaf collimator is configured to further collimate the x-ray treatment beam collimated by said second collimator in a direction of a target in the patient's body, wherein the x-ray treatment beam is collimated to follow the target while the patient moves along said longitudinal axis.

7. The system for radiation treatment according to claim 6, wherein said non-rotating cartridge is configured to translate out of said gantry rotation plane along said longitudinal axis such that said x-ray treatment beam collimated by said multi-leaf collimator follows the target while the patient moves along said longitudinal axis.

8. The system for radiation treatment according to claim 2, wherein said system further comprising: a control unit configured to control rotation movement of said third collimator by rotating said third collimator by a plurality of non-coplanar angles relative to said gantry rotation plane.

9. The system for radiation treatment according to claim 2, wherein a radiation field collimated by said first collimator is larger than a radiation field collimated by said second collimator, wherein said radiation field collimated by said second collimator encompasses at least a partial target volume.

10. The system for radiation treatment according to claim 9, wherein said radiation field collimated by said second collimator is larger than a radiation field collimated by said third collimator, wherein said radiation field collimated by said third collimator defines an actual shape of said radiation field collimated by said third collimator.

11. The system for radiation treatment according to claim 1, wherein said patient is caused to move by a couch that translates along said longitudinal axis.

12. The system for radiation treatment according to claim 1, wherein said radiation treatment source is one of a linear accelerator (LINAC) and co-60.

13. The system for radiation treatment according to claim 1, wherein said gantry is one of a ring gantry or c-arm gantry.

14. The system for radiation treatment according to claim 4, wherein said cone collimator comprising: an iris aperture with a plurality of layers, wherein said layers are configured to move coordinately in order to change an aperture size of said iris aperture at different layer levels such that an edge of each layer follows divergence of the x-ray treatment beam.

15. The system for radiation treatment according to claim 1, wherein said movement of said second collimator comprises one of rotational movement, tilting movement, and translational movement.

16. A method for radiation treatment, said method comprising: rotating a gantry around a body of a patient positioned along with a longitudinal axis; emitting an x-ray treatment beam with a radiation treatment source, wherein the x-ray treatment beam is emitted in a direction that is transverse to said longitudinal axis, wherein said radiation treatment source is affixed to said gantry; collimating the x-ray treatment beam with a first collimator, wherein said first collimator is affixed to said gantry; further collimating the x-ray treatment beam with a second collimator, wherein said second collimator is movably attached to said gantry; and moving said second collimator out of a gantry rotation plane along said longitudinal axis.

17. The method for radiation treatment according to claim 16, wherein said method further comprising: further collimating the x-ray treatment beam with a third collimator, wherein the x-ray treatment beam collimated by said second collimator is collimated in a direction of a target in the patient's body.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) For a better understanding of the present invention, reference may be made to the accompanying drawings in which:

(2) FIG. 1 shows an exemplary embodiment of a conventional LINAC head;

(3) FIG. 2 shows an exemplary embodiment of the system for optimizing non-coplanar delivery without a gimbal head;

(4) FIG. 3 shows a first exemplary embodiment of the third collimator shown in FIG. 2;

(5) FIG. 4(a) shows an exemplary embodiment of an iris aperture;

(6) FIG. 4(b) shows an exemplary embodiment of a multi-layer iris aperture;

(7) FIG. 5 shows a second exemplary embodiment of the third collimator shown in FIG. 2;

(8) FIG. 6 shows a third exemplary embodiment of the third collimator shown in FIG. 2;

(9) FIG. 7 shows an exemplary embodiment for the coordinate system of the system for optimizing non-coplanar delivery without a gimbal head;

(10) FIG. 8 illustrates a flow chart of an exemplary embodiment of the method for optimizing non-coplanar delivery without a gimbal head;

(11) FIG. 9 illustrates a flow chart of an exemplary embodiment of the method for optimizing non-coplanar delivery without a gimbal head in a step-and-shoot delivery mode; and

(12) FIG. 10 illustrates a flow chart of an exemplary embodiment of the method for optimizing non-coplanar delivery without a gimbal head in a continuous helical delivery mode.

(13) Reference characters in the written specification indicate corresponding items shown throughout the drawing figures.

DETAILED DESCRIPTION OF THE INVENTION

(14) In the following detailed description, numerous exemplary specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details, or with various modifications of the details. In other instances, well know methods, procedures, and components have not been described in detail so as not to obscure the present invention.

(15) In order to overcome the disadvantages found in the prior art previously described above, radiation treatment systems that are capable of delivering non-coplanar beams without a gimbal head and perform full six degree positioning are introduced here. In the proposed systems, a treatment head (i.e., a LINAC head) rotates in a gantry when a patient translates during treatment; however, instead of rotating or moving the whole treatment head, only the collimation of the radiation field follows the translation of the patient. In this way, the radiation field center can be configured to follow the movement of the isocenter defined in the patient during treatment planning. The advantages of this system include simpler design/structure and cost reduction. The gantry is mechanically stable and can achieve very high precision in delivery. Moreover, CT imaging can easily be integrated on the system for image guidance. The treatment couch only needs three translational motion freedoms.

(16) FIG. 2 shows an exemplary embodiment of the system for optimizing non-coplanar delivery without a gimbal head. The exemplary embodiment comprises a control unit 205, a gantry 210, a radiation treatment source 220, a first collimator 230, a second collimator 240, a third collimator 250, a patient 260, and a couch 270. The gantry 210 is preferably a rotatable ring gantry; however, the gantry 210 can comprise other types of a gantry such as a C-arm gantry. The gantry 210 is configured to rotate around a body of the patient 260 positioned along with a longitudinal axis 280. The radiation treatment source 220 is preferably a LINAC; however, the radiation treatment source 220 can comprise other types of radiation sources such as co-60. The radiation treatment source 220 is configured to emit the x-ray treatment beam in a direction that is traverse to the longitudinal axis 280. An additional portal imager 296 can be installed for treatment beam and patient setup verification. In one embodiment, the x-ray treatment beam is emitted in a direction that is substantially perpendicular to the longitudinal axis 280.

(17) The first collimator 230 is configured to block peripheral radiation emitted from the radiation treatment source 220. Preferably, the first collimator 230 collimates the x-ray treatment beam to its maximum field size. The second collimator 240 is configured to collimate the x-ray treatment beam collimated by the first collimator 230. The radiation field collimated by the first collimator 230 is larger than the radiation field collimated by the second collimator 240. Preferably, the second collimator 240 can be configured to collimate the x-ray treatment beam to a rectangular shape field that is large enough to enclose the whole target in the patient's body. Alternatively, the second collimator 240 can be configured to collimate the x-ray treatment beam to a field that encompasses at least a partial target volume. The third collimator 250 is configured to collimate the x-ray treatment beam emitted from the second collimator 240. Preferably, the third collimator 250 is configured to collimate the x-ray treatment beam to the actual shape of the radiation field. The radiation field collimated by the second collimator 240 is larger than the field collimated by the third collimator 250.

(18) In operation, the radiation treatment source 220 and the first collimator 230 are affixed to the gantry 210. The second collimator 240 and the third collimator 250 are movably attached to the gantry 210. The couch 270 is configured to translate along the longitudinal axis 280. When the couch 270 moves, the target of the patient also moves with the couch 270 along the longitudinal axis 280. During such movement, the second collimator 240 and third collimator 250 also move along the longitudinal axis 280. The second collimator 240 is preferably configured to move out of a gantry rotation plane 290 along said longitudinal axis 280 such that the second collimator 240 collimates the beam to the third collimator 250. The third collimator 250 is preferably configured to move along with the second collimator 240 such that the beam collimated by the third collimator 250 follows the isocenter 285 while the patient 260 moves along the longitudinal axis 280. The movement of the second collimator 240 and/or third collimator 250 can be in a form of rotational movement, tilting movement, or translation movement. In case of the rotational movement, the second collimator 240 and/or third collimator 250 rotate about a source point of the radiation treatment source 220. In case of tilting movement, the second collimator 240 and/or third collimator 250 tilt on the gantry rotation plane. In case of the translational movement, second collimator 240 and/or the third collimator translate along the longitudinal axis 280. In any movement, the field center always tracks the isocenter 285 in the patient.

(19) The control unit 205 can be configured to control the movement of the second collimator 240 and/or third collimator 250. Preferably, the control unit 205 controls the movement of the second collimator 240 and/or the third collimator 250 by a plurality of non-coplanar angles 295 relative to the gantry rotation plane 290. The non-coplanar angle 295 represents an angle of the center of the x-ray treatment beam aligned with the isocenter of the treatment beams in relative to the gantry rotation plane 290 as shown in FIGS. 2 and 7.

(20) The control unit 205 can reside on the gantry 210 or be a part of the gantry 210. The control unit 205 also can be a separate device, component, or computer that is remotely connected to the gantry 210.

(21) In another embodiment, the control unit 205 can be configured to control not only the third collimator 250 but also other components such as the x-ray radiation source 220, the second collimator 240, and/or the couch 270. In this embodiment, a user or operator can use the control unit 205 to initiate the treatment or adjust the movements of the collimators, x-ray radiation source 220, and couch 270.

(22) In another embodiment, only the first collimator 230 and the second collimator 240 can be used to collimate the x-ray treatment beam. In this embodiment, the third collimator 250 is not used. Instead, the second collimator 240 is configured to collimate the x-ray treatment beam such that the beam follows the isocenter in the patient's body during treatment.

(23) During treatment delivery, the couch translation can be continuous or step-and-shoot. If continuous, the source trajectory is helical in patient's point of view. If step-and-shoot, the source trajectory is multiple circles at different longitudinal positions. As shown in FIG. 2, when the isocenter is out of the gantry rotation plane 290, the treatment beam forms the non-coplanar angle 295 with respect to the gantry rotation plane 290. The treatment beam forms a cone when the source rotates. By rotating or moving the second collimator 240 and/or the third collimator 250, the treatment beam forms a non-coplanar cone shaped beam in a helical mode.

(24) FIG. 3 shows a first exemplary embodiment of the third collimator 250. In this embodiment, the third collimator 250 comprises a guiding rail 310 and a cone collimator 320. The guiding rail 310 is affixed to the gantry 210, shown in FIG. 2. The cone collimator 320 is movably attached to the guiding rail 310. The cone collimator 320 is configured to collimate the x-ray treatment beam collimated by the second collimator 240 in a direction of the isocenter point in the patient's body. Preferably, the cone collimator 320 is configured to move along the guiding rail 310 relative to the movement of the patient. By moving along the guiding rail 310, the beam collimated by the cone collimator 320 can be adjusted to follow the target while the patient moves along the longitudinal axis 280. In this embodiment, the cone collimator 320 is preferably used to treat relatively small targets. For example, the cone collimator 320 can be configured to collimate the beam to a pencil beam. The beam diameter can be determined by the cone collimator insert 322. Preferably, the beam diameter of the cone collimator 320 can be configured to range from 2 mm to 20 mm. However, it should be understood that this is provided only as an example and should not be used to limit the scope of the present invention.

(25) In one embodiment, the cone collimator 320 comprises an iris aperture 408 as shown in FIG. 4(a). In this embodiment, the iris aperture 408 replaces the cone collimator 320 and includes a plurality of layers 410, which can be configured to move in order to change an aperture size 420 of the iris aperture at different layer levels. For example, as shown in FIG. 4(b), the layers can be configured to move in order to gradually change the size of the aperture size at different levels, 430 being a smaller aperture size and 450 being a larger aperture size with 440 being an aperture size between 430 and 450. Only two layers are shown in this example; however, any number of layers can be implemented in order to accomplish this goal. In one embodiment, the control unit 205 can be configured to control the movement of the layers 410.

(26) FIG. 5 shows a second exemplary embodiment of the third collimator 250. In this embodiment, the third collimator 250 comprises a rotatable cartridge 510 and a multi-leaf collimator 520. The rotatable cartridge 510 is preferably mounted on a structure like the guiding rail 310 of FIG. 3 that is affixed to the gantry 210, shown in FIG. 2. The multi-leaf collimator 520 is affixed to the rotatable cartridge 510. The multi-leaf collimator 520 is configured to collimate the x-ray treatment beam collimated by the second collimator 240 in a direction of the target in the patient's body. Preferably, the rotatable cartridge 510 is configured to move relative to the movement of the patient. By having the rotatable cartridge 510 that moves along the patient, the beam collimated by the multi-leaf collimator 520 can be adjusted to follow the target while the patient 260 moves along the longitudinal axis 280. In this embodiment, the multi-leaf collimator 520 is preferably a single-layer multi-leaf collimator. The multi-leaf collimator 520 is preferably used to treat targets that are relatively larger than the targets that can be used for the cone collimator 320 of FIG. 3. For example, the multi-leaf collimator can be configured to collimate the beam to a field size of 20 cm40 cm. However, this should be understood that this is provided only as an example and should not be used to limit the scope of the present invention.

(27) FIG. 6 shows a third exemplary embodiment of the third collimator 250. In this embodiment, the third collimator 250 comprises a non-rotating cartridge (not shown) and a multi-leaf collimator 620. The non-rotatable cartridge is affixed to the gantry 210, as shown in FIG. 2. The multi-leaf collimator 620 is affixed to the non-rotatable cartridge. The multi-leaf collimator 620 is configured to collimate the x-ray treatment beam collimated by the second collimator 240 in a direction of the target in the patient's body. Preferably, the multi-leaf collimator 620 comprises a plurality of layers such that one or more layers can be configured to collimate the beam to follow the movement of the patient 260. The beam collimated by the multi-leaf collimator 620 can be adjusted to follow the target or isocenter 622 while the patient 260 moves along the longitudinal axis 280. In this embodiment, the tips of leaves at different layers may be positioned to follow a divergence angle of the radiation treatment beam so that the radiation beam can have a sharper penumbra at larger non-coplanar angle.

(28) In another embodiment, the non-rotating cartridge can be configured to translate out of the gantry rotation plane along the longitudinal axis 280. The translation movement of the non-rotating cartridge can further expand the range of distance that the beam can travel along the longitudinal axis 280, providing more distance to the range that the leaves of the multi-leaf collimator 620 can translate. Preferably, the control unit 205 is configured to control the movement of the third collimator 250 by rotating the third collimator 250 by a plurality of non-coplanar angles relative to the gantry rotation plane.

(29) FIG. 7 shows an exemplary embodiment for the coordinate system of the system for optimizing non-coplanar delivery without a gimbal head. In this exemplary embodiment, the coordinate system and the beam parameters are defined using International Electrotechnical Commission (IEC) coordinate system convention set forth in Medical Electron AcceleratorsFunctional Performance Characteristics, IEC Performance Standard 976, October 1989. For a patient laying supine on the treatment couch with his/her head towards the gantry, an x-axis 710 runs from patient's right to left, a y-axis 720 runs from inferior to superior direction and a z-axis 730 runs from posterior to anterior direction. The origins of the x, y and z axes are located at an isocenter 740. The longitudinal axis 280 of FIG. 2 is the axis where x=0 and z=0. In the exemplary coordinate system, the gantry 210 of FIG. 2 rotates along a gantry rotation plane 750. The second collimator 240 and/or the third collimator 250 of FIG. 2 are configured to move out of the gantry rotation plane 750 along the longitudinal axis 280, creating a non-coplanar angle 760. The movement of the gantry 210 creates a gantry angle 770.

(30) During radiosurgery, a patient needs to be positioned exactly the same orientation as the simulation CT scans. A full rigid body correction has three translational and three rotational components. Mostly, a treatment couch can only perform translational correction with one degree of rotation correction at most. Rotation angles are often neglected during regular treatments. In order to perform full six degree correction, some LINAC vendors provide special treatment couches that can translate and rotate. Without robotic or hexpod couch, rotation correction can be performed by rotating a couch, gantry and collimator altogether such as one disclosed in A Method to Implement Full Six-Degree Target Shift Corrections for Rigid Body in Image-guided Radiotherapy, Ning J. Yue, Jonathan P. S. Knisely, Hajun Song, and Ravinder Nath, Medical Physics 33, 21-31 (2006). Nevertheless, this method is inconvenient to use, and the patient has to rotate in large angles even for a very small pitch correction.

(31) Another advantage of the system for optimizing non-coplanar delivery without a gimbal head is to perform rotation setup correction by rotating the treatment beam of a patient instead of a treatment couch. The proposed system can be configured to correct a rotational setup error. With the movement of the second and/or third collimator, the patient does not need to rotate. After translated to the isocenter, the rotation components can be corrected by gantry, gimbal and collimator rotations. This eliminates the complex robotic couch. This method is also applicable to the conventional gimbal rotation approaches described in U.S. Pat. No. 6,969,194 or a CyberKnife machine.

(32) In the system for optimizing non-coplanar delivery without a gimbal head, the beam vector B of an x-ray treatment beam can be defined with a gantry angle , non-coplanar angle and collimator angle . Preferably, the collimator angle is an angle by which the third collimator 250 of FIG. 2 rotates about its central axis. In cases where the third collimator 250 is a cone collimator, the collimator angle is irrelevant since the radiation beam is rotational invariable. In cases where the third collimator 250 is a multi-leaf collimator, the collimator angle is a rotation angle of the leaves of the third collimator 250.

(33) For the machines with gimbal rotation capacities, including CyberKnife, and those shown in FIG. 5-7, non-coplanar beams delivery are achieved directly by gimbal rotation. The vector for a beam with gantry angle and gimbal angle is calculated by

(34) $B=R_y^{}.Math.R_x^{}.Math.k=\left(\begin{array}{ccc}\cos & 0& \sin \\ 0& 1& 0\\ -\sin & 0& \cos \end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos & -\sin \\ 0& \sin & \cos \end{array}\right)\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)=\left(\begin{array}{c}\sin \cos \\ -\sin \\ \cos \cos \end{array}\right)$
where R.sub.x.sup., is x rotation matrix.
During an IGRT treatment, 3D image registration between online and reference images determines a setup error with three translational components (x, y and z) and three rotational components (.sub.x, .sub.y and .sub.z). Translational setup error is corrected by shifting the treatment couch, which is straightforward and ignored in the derivation below. To correct rotational setup error, instead of rotating the patient .sub.x.fwdarw..sub.y.fwdarw..sub.z sequentially, one can rotate the treatment beam B in the order .sub.z.fwdarw..sub.y.fwdarw..sub.x. This sequential rotation operation will keep the beam the same orientation with respect to the patient. In the patient's coordinate, the new beam vector B is obtained by,

(35) $B^{}=R_x^{-{}_x}.Math.R_y^{-{}_y}.Math.R_z^{-{}_z}.Math.B=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_x& \sin {}_x\\ 0& -\sin {}_x& \cos {}_x\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{ccc}\cos {}_z& \sin {}_z& 0\\ -\sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}\sin \cos \\ -\sin \\ \cos \cos \end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_x& \sin {}_x\\ 0& -\sin {}_x& \cos {}_x\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{c}\sin \cos \cos {}_z-\sin \sin {}_z\\ -\sin \cos \sin {}_z-\sin \cos {}_z\\ \cos \cos \end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_x& \sin {}_x\\ 0& -\sin {}_x& \cos {}_x\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\sin \cos \cos {}_y\cos {}_z-\sin \cos {}_y\sin {}_z-\\ \cos \cos \sin {}_y\end{array}\\ -\sin \cos \sin {}_z-\sin \cos {}_z\\ \begin{array}{c}\sin \cos \sin {}_y\cos {}_z-\sin \sin {}_y\sin {}_z+\\ \cos \cos {\cos }_y\end{array}\end{array}\right)=\left(\begin{array}{c}\begin{array}{c}\sin \cos \cos {}_y\cos {}_z-\sin \cos {}_y\sin {}_z-\\ \cos \cos \sin {}_y\end{array}\\ \begin{array}{c}\begin{array}{c}-\sin \cos \cos {}_x\sin {}_z-\sin \cos {}_x\cos {}_z+\\ \sin \cos \sin {}_x\sin {}_y\cos {}_z-\sin \sin {}_x\sin {}_y\sin {}_z+\end{array}\\ \cos \cos \sin {}_x\cos {}_y\end{array}\\ \begin{array}{c}\begin{array}{c}\sin \cos \sin {}_x\sin {}_x+\sin \sin {}_x\cos {}_z+\\ \sin \cos \cos {}_x\sin {}_y\cos {}_z-\sin \cos {}_x\sin {}_y\sin {}_z+\end{array}\\ \cos \cos \cos {}_x\cos {}_y\end{array}\end{array}\right)$

(36) The new gantry angle is obtained by,

(37) ${}^{}={\tan }^{-1}\left(\frac{B_x^{}}{B_z^{}}\right)={\tan }^{-1}\left(\frac{\sin \cos \cos {}_y\cos {}_z-\sin \cos {}_y\sin {}_z-\cos \cos \sin {}_y}{\begin{array}{c}\begin{array}{c}\sin \cos \sin {}_x\sin {}_z+\sin \sin {}_x\cos {}_z+\\ \sin \cos \cos {}_x\sin {}_y\cos {}_z-\sin \cos {}_x\sin {}_y\sin {}_z+\end{array}\\ \cos \cos \cos {}_x\cos {}_y\end{array}}\right)$

(38) The new gimbal angle is obtained by,

(39) ${}^{}=-{\sin }^{-1}\left(B_y\right)=-{\sin }^{-1}\left(-\sin \cos \cos {}_x\sin {}_z-\sin \cos {}_x\cos {}_z+\sin \cos \sin {}_x\sin {}_y\cos {}_z-\sin \sin {}_x\sin {}_y\sin {}_z+\cos \cos \sin {}_x\cos {}_y\right)$

(40) The radiation treatment fields are defined by cone or MLC. While cone collimator is rotational invariant, the fields defined by MLC have a rotation angle should also be adjusted to reproduce the same orientation relative to the patient. We define a collimator vector C coinciding with vector j when gantry, gimbal and collimator angles are all zero. For a radiation field with gantry angle , gimbal angle and collimator angle , the collimator vector becomes

(41) $C=R_y^{}.Math.R_x^{}.Math.R_z^{}.Math.j=\left(\begin{array}{ccc}\cos & 0& \sin \\ 0& 1& 0\\ -\sin & 0& \cos \end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos & -\sin \\ 0& \sin & \cos \end{array}\right)\left(\begin{array}{ccc}\cos & -\sin & 0\\ \sin & \cos & 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}0\\ 1\\ 0\end{array}\right)=\left(\begin{array}{c}-\cos \sin +\sin \sin \cos \\ \begin{array}{c}\cos \cos \\ \sin \sin +\cos \sin \cos \end{array}\end{array}\right)$
Similarly to the beam vector, the collimator vector needs to rotate .sub.z.fwdarw..sub.y.fwdarw..sub.x sequentially to correct the rotational setup error. Thereby the new collimator vector C after rotation correction is

(42) $C^{}=R_x^{-{}_x}.Math.R_y^{-{}_y}.Math.R_z^{-{}_z}.Math.C\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_x& \sin {}_x\\ 0& -\sin {}_x& \cos {}_x\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{ccc}\cos {}_z& \sin {}_z& 0\\ -\sin {}_x& \cos {}_x& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}-\cos \cos +\sin \sin \sin \\ \cos \sin \\ \sin \cos +\cos \sin \sin \end{array}\right)$$\left(\begin{array}{c}\begin{array}{c}-\cos \cos \cos {}_y\cos {}_z+\sin \sin \sin \cos {}_y\cos {}_z+\\ \cos \sin \cos {}_y\sin {}_z-\sin \cos \sin {}_y-\cos \sin {\mathrm{sinsin}}_y\end{array}\\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\cos \cos {\cos }_z\sin {}_z-\sin \mathrm{sinsin}\cos {}_z\sin {}_z+\\ \cos \sin \cos {}_z\cos {}_z-\cos \cos \sin {}_z\sin {}_y\cos {}_z+\end{array}\\ \begin{array}{c}\sin \sin \sin \sin {}_z\sin {}_y\cos {}_z+\cos {\mathrm{sinsin}}_z\sin {}_y\sin {}_z+\\ \sin \cos \sin {}_z\cos {}_y-\cos \sin \sin \sin {}_x\cos {}_y\end{array}\end{array}\\ -\cos \cos {\sin }_z\sin {}_z+\sin \sin \sin {\sin }_z\sin {}_z-\end{array}\\ \begin{array}{c}\cos \sin \sin {}_x\cos {}_z-\cos \cos \cos {}_z\sin {}_y\cos {}_z+\\ \begin{array}{c}\begin{array}{c}\sin \sin \sin \cos {}_x\sin {}_y\cos {}_z+\cos \sin \cos {}_z\sin {}_y\sin {}_z+\\ \sin \cos \cos {}_z\cos {}_y+\end{array}\\ \cos \sin \sin \cos {}_x\cos {}_y\end{array}\end{array}\end{array}\right)$

(43) The collimator angle is the angle between gimbal rotation plane and collimator vector. Gimbal rotation plane is represented by a vector G that is perpendicular to the gimbal rotation plane,

(44) $G=R_y^{}.Math.i=\left(\begin{array}{ccc}\cos & 0& \sin \\ 0& 1& 0\\ -\sin & 0& \cos \end{array}\right)\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right)=\left(\begin{array}{c}\cos \\ 0\\ -\sin \end{array}\right)$
The new collimator angle is obtained by

(45) ${}^{}={\cos }^{-1}\left(G.Math.C^{}\right)={\cos }^{-1}(\left(\begin{array}{c}\cos \\ 0\\ -\sin \end{array}\right).Math.\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}-\cos \cos \cos {}_y\cos {}_z+\\ \sin \sin \sin \cos {}_x\cos {}_z+\end{array}\\ \cos \sin \cos {}_y\sin {}_z-\end{array}\\ \sin \cos \sin {}_y-\cos \sin \sin {\sin }_y\end{array}\\ \cos \cos \cos {}_z\sin {}_z-\sin \sin \sin \cos {}_x\sin {}_z+\end{array}\\ \cos \sin \cos {}_z\cos {}_z-\end{array}\\ \cos \cos \sin {}_z\sin {}_y\cos {}_z+\end{array}\\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\sin \sin \sin \sin {}_z\sin {}_y\cos {}_z+\\ \cos \sin \sin {}_x\sin {}_y\sin {}_z+\end{array}\\ \sin \cos \sin {}_z\cos {}_y+\end{array}\\ \cos \sin \sin \sin {}_z\cos {}_y\end{array}\\ -\cos \cos \sin {}_x\sin {}_z+\sin \sin \sin \sin {}_x\sin {}_z-\end{array}\\ \begin{array}{c}\begin{array}{c}\begin{array}{c}\cos \sin \sin {}_x\cos {}_z-\cos \cos {\cos }_x\sin {}_y\cos {}_z+\\ \sin \sin \sin \cos {}_z\sin {}_y\cos {}_z+\end{array}\\ \cos \sin \cos {}_x\sin {}_y\sin {}_z+\end{array}\\ \sin \cos \cos {}_z\cos {}_y-\cos \sin \sin \cos {}_x\cos {}_y\end{array}\end{array}\end{array}\right))={\cos }^{-1}\left(-{\cos }^2\cos \cos {}_y\cos {}_z-\sin \cos \sin \sin \cos {}_y\cos {}_z+\cos \cos \sin \cos {}_y\sin {}_2-\sin \cos \cos \sin {}_y-{\cos }^2\sin \sin \sin {}_{y-}+\sin \cos \cos \sin {}_x\sin {}_z-{\sin }^2\sin \sin \sin {}_x\sin {}_z+\sin \cos \sin \sin {}_x\cos {}_z+\sin \cos \cos \cos {}_x\sin {}_y\cos {}_z-{\sin }^2\sin \sin \cos {}_z\sin {}_y\cos {}_z-\sin \cos \sin \cos {}_z\sin {}_y\sin {}_z-{\sin }^2\cos {\cos }_x\cos {}_y-\sin \cos \sin \sin \cos {}_z\cos {}_y\right)$

(46) Assuming through an image guidance procedure, 3D image registration determines a shift of x, y and z and a rotation correction of .sub.x, .sub.y and .sub.z are needed to set-up the patient properly. The shift is performed by translating the treatment couch, which is straightforward. For rotation correction, instead of rotating the patient, the beam can be rotated .sub.x, .sub.y and .sub.z, so that orientation remains the same with respect to the patient. Thus the new beam vector is obtained by,

(47) $B^{}=R_z^{-{}_z}.Math.R_y^{-{}_y}.Math.R_x^{-{}_x}.Math.B=\left(\begin{array}{ccc}\cos {}_z& -\sin {}_z& 0\\ \sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_x& \sin {}_x\\ 0& -\sin {}_x& \cos {}_x\end{array}\right)\left(\begin{array}{c}\sin \cos \\ -\sin \\ \cos \cos \end{array}\right)=\left(\begin{array}{ccc}{\cos }_z& -\sin {}_z& 0\\ \sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\sin \cos \\ -\cos {}_z\sin +\sin {}_z\cos \cos \end{array}\\ \sin {}_z\sin +\cos {}_x\cos \cos \end{array}\right)=\left(\begin{array}{ccc}\cos {}_z& -\sin {}_z& 0\\ \sin {}_x& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\cos {}_y\sin \cos -\sin {}_y\sin {}_x\sin -\sin {}_y\cos {}_x\cos \cos \\ -\cos {}_x\sin +\sin {}_x\cos \cos \end{array}\\ \sin {}_y\sin \cos +\cos {}_y\sin {}_x\sin +\cos {}_y\cos {}_x\cos \cos \end{array}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\cos {}_z\cos {}_y\sin \cos -\cos {}_x\sin {}_y\sin {}_z\sin -\\ \cos {}_x\sin {}_y\cos {}_z\cos \cos +\sin {}_z\cos {}_x\sin -\end{array}\\ \sin {}_z\sin {}_x\cos \cos \end{array}\\ \sin {}_x\cos {}_y\sin \cos -\sin {}_z\sin {}_y\sin {}_x\sin -\end{array}\\ \sin {}_x\sin {}_y\cos {}_z\cos \cos -\cos {}_z\cos {}_x\sin +\end{array}\\ \cos {}_x\sin {}_z\cos \cos \end{array}\\ \sin {}_y\sin \cos +\cos {}_y\sin {}_x\sin +\end{array}\\ \cos {}_y\cos {}_x\cos \cos \end{array}\right)$
If rotation sequence is defined differently in image registration software, for example, rotate z.fwdarw.y.fwdarw.x, the final equation may be different. Similar equations can be derived in the same principle if rotation correction sequence is defined differently.

(48) The new gantry angle is obtained by,

(49) 0${}^{}={\tan }^{-1}\left(\frac{\begin{array}{c}\cos {}_z\cos {}_y\sin \cos -\cos {}_x\sin {}_y\sin {}_z\sin -\\ \begin{array}{c}\cos {}_x\sin {}_y\cos {}_z\cos \cos +\sin {}_z\cos {}_z\sin -\\ \sin {}_x\sin {}_z\cos \cos \end{array}\end{array}}{\begin{array}{c}\sin {}_y\sin \cos +\cos {}_y\sin {}_x\sin +\\ \cos {}_y\cos {}_x\cos \cos \end{array}}\right)$

(50) The new gimbal or non-coplanar angle is obtained by,
=sin.sup.1(sin .sub.x cos .sub.y sin cos sin .sub.x sin .sub.y sin sin .sub.x sin .sub.y cos .sub.x cos cos cos .sub.x cos .sub.x sin +cos .sub.x sin .sub.x cos cos )

(51) Similarly, a new collimator angle for rotation correction can be derived. With initial collimator vector C with gimbal rotation, the new collimator vector C after rotation correction is

(52) $C^{}=R_z^{-{}_z}.Math.R_y^{-{}_y}.Math.R_z^{-{}_z}.Math.C=\left(\begin{array}{ccc}\cos {}_z& \sin {}_z& 0\\ -\sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos {}_z& \sin {}_z\\ 0& -\sin {}_z& \cos {}_z\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\cos \cos +\sin \sin \sin \\ \cos \sin \end{array}\\ -\sin \cos +\cos \sin \sin \end{array}\right)=\left(\begin{array}{ccc}\cos {}_z& \sin {}_z& 0\\ -\sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{ccc}\cos {}_y& 0& -\sin {}_y\\ 0& 1& 0\\ \sin {}_y& 0& \cos {}_y\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\cos \cos +\sin \sin \sin \\ \cos {}_z\cos \sin -\sin {}_z\sin \cos +\end{array}\\ \sin {}_z\cos \sin \sin \end{array}\\ -\sin {}_z\cos \sin +\cos {}_z\cos \sin \sin \end{array}\right)=\left(\begin{array}{ccc}\cos {}_z& -\sin {}_z& 0\\ \sin {}_z& \cos {}_z& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\cos {}_y\cos \cos +\cos {}_y\sin \sin \sin +\\ \sin {}_y\sin {}_z\cos \sin -\sin {}_y\cos {}_z\cos \sin \sin \end{array}\\ \cos {}_z\cos \sin -\sin {}_z\sin \cos +\end{array}\\ \sin {}_z\cos \sin \sin \end{array}\\ \sin {}_y\cos \cos +\sin {}_y\sin \sin \sin -\end{array}\\ \cos {}_y\sin {}_z\cos \sin +\end{array}\\ \cos {}_y\cos {}_z\cos \sin \sin \end{array}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\cos {}_z\cos {}_y\cos \cos +\cos {}_z\cos {}_y\sin \mathrm{sinsin}+\\ \cos {}_z\sin {}_y\sin {}_x\cos \sin -\end{array}\\ \sin {}_z\sin {}_y\cos {}_x\cos \sin \sin -\end{array}\\ \sin {}_z\cos {}_x\cos \sin +\sin {}_z\sin {}_z\sin \sin -\end{array}\\ \sin {}_z\sin {}_z\cos \sin \sin \end{array}\\ \sin {}_z\cos {}_x\cos \cos +\sin {}_z\cos {}_y\sin \sin \sin +\end{array}\\ \sin {}_z\sin {}_y\sin {}_x\cos \sin -\end{array}\\ \sin {}_z\sin {}_y\cos {}_x\cos \sin \sin +\end{array}\\ \cos {}_x\cos {}_z\cos \sin -\cos {}_x\sin {}_z\sin \sin +\end{array}\\ \cos {}_x\sin {}_x\cos \sin \sin \end{array}\\ \sin {}_x\cos \cos +\sin {}_y\sin \sin \sin -\end{array}\\ \begin{array}{c}\cos {}_y\sin {}_x\cos \cos +\\ \cos {}_y\cos {}_x\cos \sin \sin \end{array}\end{array}\right)$