Patent Publication Number: US-11642027-B2

Title: Methods and apparatus for the planning and delivery of radiation treatments

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 15/707,931, filed Sep. 18, 2017, which is a continuation of U.S. patent application Ser. No. 15/382,469, filed Dec. 16, 2016, now U.S. Pat. No. 9,788,783, issued Oct. 17, 2017, which is a continuation of U.S. patent application Ser. No. 14/710,485, filed May 12, 2015, now U.S. Pat. No. 9,630,025, issued Apr. 25, 2017, which is a continuation of U.S. patent application Ser. No. 14/202,305, filed Mar. 10, 2014, now U.S. Pat. No. 9,050,459, issued Jun. 9, 2015, which is a continuation of U.S. patent application Ser. No. 12/986,420, filed Jan. 7, 2011, now U.S. Pat. No. 8,696,538, issued Apr. 15, 2014, which is a continuation of U.S. patent application Ser. No. 12/132,597, now U.S. Pat. No. 7,880,154, issued Feb. 1, 2011, which is a continuation-in-part of U.S. patent application Ser. No. 11/996,932, filed Jan. 25, 2008, now U.S. Pat. No. 7,906,770, issued Mar. 15, 2011, which is a 35 U.S.C. § 371 application which claims benefit of International Application No. PCT/CA2006/001225, filed Jul. 25, 2006, which claims benefit of U.S. Provisional Patent Application No. 60/701,974, filed Jul. 25, 2005, all of which are incorporated by reference herein. 
    
    
     TECHNICAL FIELD 
     This invention relates to radiation treatment. The invention relates particularly to methods and apparatus for planning and delivering radiation to a subject to provide a desired three-dimensional distribution of radiation dose. 
     BACKGROUND 
     The delivery of carefully-planned doses of radiation may be used to treat various medical conditions. For example, radiation treatments are used, often in conjunction with other treatments, in the treatment and control of certain cancers. While it can be beneficial to deliver appropriate amounts of radiation to certain structures or tissues, in general, radiation can harm living tissue. It is desirable to target radiation on a target volume containing the structures or tissues to be irradiated while minimizing the dose of radiation delivered to surrounding tissues. Intensity modulated radiation therapy (IMRT) is one method that has been used to deliver radiation to target volumes in living subjects. 
     IMRT typically involves delivering shaped radiation beams from a few different directions. The radiation beams are typically delivered in sequence. The radiation beams each contribute to the desired dose in the target volume. 
     A typical radiation delivery apparatus has a source of radiation, such as a linear accelerator, and a rotatable gantry. The gantry can be rotated to cause a radiation beam to be incident on a subject from various different angles. The shape of the incident radiation beam can be modified by a multi-leaf collimator (MLC). A MLC has a number of leaves which are mostly opaque to radiation. The MLC leaves define an aperture through which radiation can propagate. The positions of the leaves can be adjusted to change the shape of the aperture and to thereby shape the radiation beam that propagates through the MLC. The MLC may also be rotatable to different angles. 
     Objectives associated with radiation treatment for a subject typically specify a three-dimensional distribution of radiation dose that it is desired to deliver to a target region within the subject. The desired dose distribution typically specifies dose values for voxels located within the target. Ideally, no radiation would be delivered to tissues outside of the target region. In practice, however, objectives associated with radiation treatment may involve specifying a maximum acceptable dose that may be delivered to tissues outside of the target. 
     Treatment planning involves identifying an optimal (or at least acceptable) set of parameters for delivering radiation to a particular treatment volume. Treatment planning is not a trivial problem. The problem that treatment planning seeks to solve involves a wide range of variables including:
         the three-dimensional configuration of the treatment volume;   the desired dose distribution within the treatment volume;   the locations and radiation tolerance of tissues surrounding the treatment volume; and   constraints imposed by the design of the radiation delivery apparatus.
 
The possible solutions also involve a large number of variables including:
   the number of beam directions to use;   the direction of each beam;   the shape of each beam; and   the amount of radiation delivered in each beam.       

     Various conventional methods of treatment planning are described in:
         S. V. Spirou and C.-S. Chui.  A gradient inverse planning algorithm with dose - volume constraints , Med. Phys. 25, 321-333 (1998);   Q. Wu and R. Mohand.  Algorithm and functionality of an intensity modulated radiotherapy optimization system , Med. Phys. 27, 701-711 (2000);   S. V. Spirou and C.-S. Chui.  Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators , Med. Phys. 21, 1031-1041 (1994);   P. Xia and L. J. Verhey.  Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments , Med. Phys. 25, 1424-1434 (1998); and   K. Otto and B. G. Clark.  Enhancement of IMRT delivery through MLC rotation ,” Phys. Med. Biol. 47, 3997-4017 (2002).       

     Acquiring sophisticated modern radiation treatment apparatus, such as a linear accelerator, can involve significant capital cost. Therefore it is desirable to make efficient use of such apparatus. All other factors being equal, a radiation treatment plan that permits a desired distribution of radiation dose to be delivered in a shorter time is preferable to a radiation treatment plan that requires a longer time to deliver. A treatment plan that can be delivered in a shorter time permits more efficient use of the radiation treatment apparatus. A shorter treatment plan also reduces the risk that a subject will move during delivery of the radiation in a manner that may significantly impact the accuracy of the delivered dose. 
     Despite the advances that have been made in the field of radiation therapy, there remains a need for radiation treatment methods and apparatus and radiation treatment planning methods and apparatus that provide improved control over the delivery of radiation, especially to complicated target volumes. There also remains a need for such methods and apparatus that can deliver desired dose distributions relatively quickly. 
     SUMMARY 
     One aspect of the invention provides a method for planning delivery of radiation dose to a target area within a subject. The method comprises: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; specifying an initial plurality of control points along an initial trajectory, the initial trajectory involving relative movement between a radiation source and the subject in a source trajectory direction; and iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals to determine one or more radiation delivery parameters associated with each of the initial plurality of control points. For each of the initial plurality of control points, the one or more radiation delivery parameters may comprise positions of a plurality of leaves of a multi-leaf collimator (MLC). The MLC leaves may be moveable in a leaf-translation direction. During relative movement between the radiation source and the subject along the initial trajectory, the leaf-translation direction is oriented at a MLC orientation angle φ with respect to the source trajectory direction and wherein an absolute value of the MLC orientation angle φ satisfies 0°&lt;|φ|&lt;90°. 
     Another aspect of the invention provides a method for delivering radiation dose to a target area within a subject. The method comprises: defining a trajectory for relative movement between a treatment radiation source and the subject in a source trajectory direction; determining a radiation delivery plan; and while effecting relative movement between the treatment radiation source and the subject along the trajectory, delivering a treatment radiation beam from the treatment radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject. Delivering the treatment radiation beam from the treatment radiation source to the subject comprises varying at least one of: an intensity of the treatment radiation beam; and a shape of the treatment radiation beam over at least a portion of the trajectory. 
     Varying at least one of the intensity of the treatment radiation beam and the shape of the treatment radiation beam over at least the portion of the trajectory, may comprise varying positions of a plurality of leaves of a multi-leaf collimator (MLC) in a leaf-translation direction. During relative movement between the treatment radiation source and the subject along the trajectory, the leaf-translation direction may be oriented at a MLC orientation angle φ with respect to the source trajectory direction wherein an absolute value of the MLC orientation angle φ satisfies 0°&lt;|φ|&lt;90°. 
     Varying at least one of the intensity of the treatment radiation beam and the shape of the treatment radiation beam over at least the portion of the trajectory may comprise varying a rate of radiation output of the radiation source while effecting continuous relative movement between the treatment radiation source and the subject along the trajectory. 
     Other aspects of the invention provide program products comprising computer readable instructions which, when executed by a processor, cause the processor to execute, at least in part, any of the methods described herein. Other aspects of the invention provide systems comprising, inter alia, controllers configured to execute, at least in part, any of the methods described herein. 
     Further aspects of the invention and features of embodiments of the invention are set out below and illustrated in the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The appended drawings illustrate non-limiting example embodiments of the invention. 
         FIG.  1    is a schematic view of an exemplary radiation delivery apparatus in conjunction with which the invention may be practised. 
         FIG.  1 A  is a schematic view of another exemplary radiation delivery apparatus in conjunction with which the invention may be practised. 
         FIG.  2    is a schematic illustration of a trajectory. 
         FIG.  3 A  is a schematic cross-sectional view of a beam-shaping mechanism. 
         FIG.  3 B  is a schematic beam&#39;s eye plan view of a multi-leaf collimator-type beam-shaping mechanism. 
         FIG.  3 C  schematically depicts a system for defining the angle of leaf-translation directions about the beam axis. 
         FIG.  4 A  is a flow chart illustrating a method of optimizing dose delivery according to a particular embodiment of the invention. 
         FIG.  4 B  is a schematic flow chart depicting a method for planning and delivering radiation to a subject according to a particular embodiment of the invention. 
         FIGS.  5 A,  5 B and  5 C  illustrate dividing an aperture into beamlets according to a particular embodiment of the invention. 
         FIG.  6    graphically depicts the error associated with a dose simulation calculation versus the number of control points used to perform the dose simulation calculation. 
         FIG.  7    graphically depicts dose quality versus the number of optimization iterations for several different numbers of control points. 
         FIG.  8    represents a flow chart which schematically illustrates a method of optimizing dose delivery according to another embodiment of the invention where the number of control points is varied over the optimization process. 
         FIG.  9    graphically depicts the dose distribution quality versus the number of iterations for the  FIG.  8    optimization method where the number of control points is varied over the optimization process. 
         FIG.  10    is a depiction of sample target tissue and healthy tissue used in an illustrative example of an implementation of a particular embodiment of the invention. 
         FIGS.  11 A and  11 B  respectively depict the initial control point positions of the motion axes corresponding to a trajectory used in the  FIG.  10    example. 
         FIGS.  12 A- 12 F  depict a dose volume histogram (DVH) which is representative of the dose distribution quality at various stages of the optimization process of the  FIG.  10    example. 
         FIG.  13    another graphical depiction of the optimization process of the  FIG.  10    example. 
         FIGS.  14 A- 14 D  show the results (the motion axes parameters, the intensity and the beam shaping parameters) of the optimization process of the  FIG.  10    example. 
         FIG.  15    plots contour lines of constant dose (isodose lines) in a two-dimensional cross-sectional slice of the target region in the  FIG.  10    example. 
         FIGS.  16 A and  16 B  show examples of how the selection of a particular constant MLC orientation angle may impact treatment plan quality and ultimately the radiation dose that is delivered to a subject. 
         FIG.  17    schematically depicts how target and healthy tissue will look for opposing beam directions. 
         FIGS.  18 A and  18 B  show an MLC and the respective projections of a target and healthy tissue for opposing beam directions corresponding to opposing gantry angles. 
         FIGS.  18 C and  18 D  show an MLC and the respective projections of a desired beam shape for opposing beam directions corresponding to opposing gantry angles. 
     
    
    
     DESCRIPTION 
     Throughout the following description specific details are set forth in order to provide a more thorough understanding to persons skilled in the art. However, well known elements may not have been shown or described in detail to avoid unnecessarily obscuring the disclosure. Accordingly, the description and drawings are to be regarded in an illustrative, rather than a restrictive, sense. 
     This invention relates to the planning and delivery of radiation treatments by modalities which involve moving a radiation source along a trajectory relative to a subject while delivering radiation to the subject. In some embodiments the radiation source is moved continuously along the trajectory while in some embodiments the radiation source is moved intermittently. Some embodiments involve the optimization of the radiation delivery plan to meet various optimization goals while meeting a number of constraints. For each of a number of control points along a trajectory, a radiation delivery plan may comprise: a set of motion axes parameters, a set of beam shape parameters and a beam intensity. 
       FIG.  1    shows an example radiation delivery apparatus  10  comprising a radiation source  12  capable of generating or otherwise emitting a beam  14  of radiation. Radiation source  12  may comprise a linear accelerator, for example. A subject S is positioned on a table or “couch”  15  which can be placed in the path of beam  14 . Apparatus  10  has a number of movable parts that permit the location of radiation source  12  and orientation of radiation beam  14  to be moved relative to subject S. These parts may be referred to collectively as a beam positioning mechanism  13 . 
     In the illustrated radiation delivery apparatus  10 , beam positioning mechanism  13  comprises a gantry  16  which supports radiation source  12  and which can be rotated about an axis  18 . Axis  18  and beam  14  intersect at an isocenter  20 . Beam positioning mechanism  13  also comprises a moveable couch  15 . In exemplary radiation delivery apparatus  10 , couch  15  can be translated in any of three orthogonal directions (shown in  FIG.  1    as X, Y, and Z directions) and can be rotated about an axis  22 . In some embodiments, couch  15  can be rotated about one or more of its other axes. The location of source  12  and the orientation of beam  14  can be changed (relative to subject S) by moving one or more of the movable parts of beam positioning mechanism  13 . 
     Each separately-controllable means for moving source  12  and/or orienting beam  14  relative to subject S may be termed a “motion axis”. In some cases, moving source  12  or beam  14  along a particular trajectory may require motions of two or more motion axes. In exemplary radiation delivery apparatus  10 , motion axes include:
         rotation of gantry  16  about axis  18 ;   translation of couch  15  in any one or more of the X, Y, Z directions; and   rotation of couch  15  about axis  22 .       

     Radiation delivery apparatus  10  typically comprises a control system  23  capable of controlling, among other things, the movement of its motion axes and the intensity of radiation source  12 . Control system  23  may generally comprise hardware components and/or software components. In the illustrated embodiment, control system  23  comprises a controller  24  capable of executing software instructions. Control system  23  is preferably capable of receiving (as input) a set of desired positions for its motion axes and, responsive to such input, controllably moving one or more of its motion axes to achieve the set of desired motion axes positions. At the same time, control system  23  may also control the intensity of radiation source  12  in response to input of a set of desired radiation intensities. 
     While radiation delivery apparatus  10  represents a particular type of radiation delivery apparatus in conjunction with which the invention may be implemented, it should be understood that the invention may be implemented on different radiation delivery apparatus which may comprise different motion axes. In general, the invention may be implemented in conjunction with any set of motion axes that can create relative movement between a radiation source  12  and a subject S, from a starting point along a trajectory to an ending point. 
     Another example of a radiation delivery apparatus  10 A that provides an alternative set of motion axes is shown in  FIG.  1 A . In exemplary apparatus  10 A, source  12  is disposed in a toroidal housing  26 . A mechanism  27  permits source  12  to be moved around housing  26  to irradiate a subject S from different sides. Subject S is on a table  28  which can be advanced through a central aperture  29  in housing  26 . Apparatus having configurations like that shown schematically in  FIG.  1 A  are used to deliver radiation in a manner commonly called “Tomotherapy”. 
     In accordance with particular embodiments of the invention, beam positioning mechanism  13  causes source  12  and/or beam  14  to move along a trajectory while radiation dose is controllably delivered to target regions within subject S. A “trajectory” is a set of one or more movements of one or more of the movable parts of beam position mechanism  13  that results in the beam position and orientation changing from a first position and orientation to a second position and orientation. The first and second positions and the first and second orientations are not necessarily different. For example, a trajectory may be specified to be a rotation of gantry  16  from a starting point through an angle of 360° about axis  18  to an ending point in which case the beam position and orientation at the starting and ending points are the same. 
     The first and second beam positions and beam orientations may be specified by a first set of motion axis positions (corresponding to the first beam position and the first beam orientation) and a second set of motion axis positions (corresponding to the second beam position and the second beam orientation). As discussed above, control system  23  of radiation delivery apparatus  10  can controllably move its motion axes between the first set of motion axis positions and the second set of motion axis positions. In general, a trajectory may be described by more than two beam positions and beam orientations. For example, a trajectory may be specified by a plurality of sets of motion axis positions, each set of motion axis positions corresponding to a particular beam position and a particular beam orientation. Control system  23  can then controllably move its motion axes between each set of motion axis positions. 
     In general, a trajectory may be arbitrary and is only limited by the particular radiation delivery apparatus and its particular beam positioning mechanism. Within constraints imposed by the design of a particular radiation delivery apparatus  10  and its beam positioning mechanism  13 , source  12  and/or beam  14  may be caused to follow an arbitrary trajectory relative to subject S by causing appropriate combinations of movements of the available motion axes. A trajectory may be specified to achieve a variety of treatment objectives. For example, a trajectory may be selected to have a high ratio of target tissue within the beam&#39;s eye view compared to healthy tissue within the beam&#39;s eye view or to avoid important healthy organs or the like. 
     For the purpose of implementing the present invention, it is useful to discretize a desired trajectory into a number of “control points” at various locations along the trajectory. A set of motion axis positions can be associated with each such control point. A desired trajectory may define a set of available control points. One way to specify a trajectory of radiation source  12  and/or beam  14  is to specify at a set of discrete control points at which the position of each motion axis is defined. 
       FIG.  2    schematically depicts a radiation source  12  travelling relative to a subject S along an arbitrary trajectory  30  in three-dimensions while delivering radiation dose to a subject S by way of a radiation beam  14 . The position and orientation of radiation beam  14  changes as source  12  moves along trajectory  30 . In some embodiments, the changes in position and/or direction of beam  14  may occur substantially continuously as source  12  moves along trajectory  30 . While source  12  is moving along trajectory  30 , radiation dose may be provided to subject S continuously (i.e. at all times during the movement of source  12  along trajectory  30 ) or intermittently (i.e. radiation may be blocked or turned off at some times during the movement of source  12  along trajectory  30 ). Source  12  may move continuously along trajectory  30  or may move intermittently between various positions on trajectory  30 .  FIG.  2    schematically depicts a number of control points  32  along trajectory  30 . In some embodiments, the specification of trajectory  30  defines the set of available control points  32 . In other embodiments, the set of control points  32  are used to define trajectory  30 . In such embodiments, the portions of trajectory  30  between control points  32  may be determined (e.g. by control system  23 ) from control points  32  by a suitable algorithm. 
     In general, control points  32  may be specified anywhere along trajectory  30 , although it is preferable that there is a control point at the start of trajectory  30 , a control point at the end of trajectory  30  and that the control points  32  are otherwise spaced-apart along trajectory  30 . In some embodiments of the invention, control points  32  are selected such that the magnitudes of the changes in the position of a motion axis over a trajectory  30  are equal as between control points  32 . For example, where a trajectory  30  is defined as a 360° arc of gantry  16  about axis  18  and where the number of control points  32  along trajectory  30  is 21, then control points  32  may be selected to correspond to 0° (a starting control point), 360° (an ending control point) and 19 other control points at 18° intervals along the arc of gantry  16 . 
     Although trajectory  30  may be defined arbitrarily, it is preferable that source  12  and/or beam  14  not have to move back and forth along the same path. Accordingly, in some embodiments, trajectory  30  is specified such that it does not overlap itself (except possibly at the beginning and end of trajectory  30 ). In such embodiments, the positions of the motion axes of the radiation delivery apparatus are not the same except possibly at the beginning and end of trajectory  30 . In such embodiments, treatment time can be minimized (or at least reduced) by irradiating subject S only once from each set of motion axis positions. 
     In some embodiments, trajectory  30  is selected such that the motion axes of the radiation delivery device move in one direction without having to reverse directions (i.e. without source  12  and/or beam  14  having to be moved back and forth along the same path). Selection of a trajectory  30  involving movement of the motion axes in a single direction can minimize wear on the components of a radiation delivery apparatus. For example, in apparatus  10 , it is preferable to move gantry  16  in one direction, because gantry  16  may be relatively massive (e.g. greater than 1 ton) and reversing the motion of gantry  16  at various locations over a trajectory may cause strain on the components of radiation delivery apparatus  16  (e.g. on the drive train associated with the motion of gantry  16 ). 
     In some embodiments, trajectory  30  is selected such that the motion axes of the radiation delivery apparatus move substantially continuously (i.e. without stopping). Substantially continuous movement of the motion axes over a trajectory  30  is typically preferable to discontinuous movement, because stopping and starting motion axes can cause wear on the components of a radiation delivery apparatus. In other embodiments, the motion axes of a radiation delivery apparatus are permitted to stop at one or more locations along trajectory  30 . Multiple control points  32  may be provided at such locations to allow the beam shape and/or beam intensity to be varied while the position and orientation of the beam is maintained constant. 
     In some embodiments, trajectory  30  comprises a single, one-way, continuous 360° rotation of gantry  16  about axis  18  such that trajectory  30  only possibly overlaps itself at its beginning and end points. In some embodiments, this single, one-way, continuous 360° rotation of gantry  16  about axis  18  is coupled with corresponding one-way, continuous translational or rotational movement of couch  15 , such that trajectory  30  is completely non-overlapping. 
     Some embodiments involve trajectories  30  which are effected by any combination of motion axes of radiation delivery apparatus  10  such that relative movement between source  12  and/or beam  13  and subject S comprises a discrete plurality of arcs, wherein each arc is confined to a corresponding plane (e.g. a rotation of up to 360° of gantry  16  about axis  18 ). In some embodiments, each arc may be non-self overlapping. In some embodiments, each arc may overlap only at its beginning and end points. In the course of following such a trajectory  30 , the motion axes of radiation delivery apparatus  10  may be moved between individual arcs such that the corresponding planes to which the arcs are confined intersect with one another (e.g. by suitable rotation of couch  15  about axis  22 ). Alternatively, the motion axes of radiation delivery apparatus  10  may be moved between individual arcs such that the corresponding planes to which the arcs are defined are parallel with one another (e.g. by suitable translational movement of couch  15 ). In some cases, radiation may not be delivered to subject S when the motion axes of radiation delivery apparatus  10  are moved between individual arcs. 
     Radiation delivery apparatus, such as exemplary apparatus  10  ( FIG.  1   ) and  10 A ( FIG.  1 A ), typically include adjustable beam-shaping mechanisms  33  located between source  12  and subject S for shaping radiation beam  14 .  FIG.  3 A  schematically depicts a beam-shaping mechanism  33  located between source  12  and subject S. Beam-shaping mechanism  33  may comprise stationary and/or movable metal components  31 . Components  31  may define an aperture  31 A through which portions of radiation beam  14  can pass. Aperture  31 A of beam-shaping mechanism  33  may define a two-dimensional border of radiation beam  14 . In particular embodiments, beam shaping mechanism  33  is located and/or shaped such that aperture  31 A is in a plane orthogonal to the direction of radiation from source  12  to the target volume in subject S. Control system  23  is preferably capable of controlling the configuration of beam-shaping mechanism  33 . 
     One non-limiting example of an adjustable beam-shaping mechanism  33  comprises a multi-leaf collimator (MLC)  35  located between source  12  and subject S.  FIG.  3 B  schematically depicts a suitable MLC  35 . As shown in  FIG.  3 B , MLC  35  comprises a number of leaves  36  that can be independently translated into or out of the radiation field to define one or more apertures  38  through which radiation can pass. Leaves  36 , which may comprise metal components, function to block radiation. In the illustrated embodiment, leaves  36  are translatable in the leaf-translation directions indicated by double-headed arrow  41 . Leaf-translation directions  41  may be located in a plane that is orthogonal to beam axis  37  (i.e. a direction of the radiation beam  14  from source  12  to the target volume in subject S). In the  FIG.  3 B  view, beam axis  37  extends into and out of the page. The size(s) and shape(s) of aperture(s)  38  may be adjusted by selectively positioning each leaf  36 . 
     As shown in the illustrate embodiment of  FIG.  3 B , leaves  36  are typically provided in opposing pairs. MLC  35  may be mounted so that it can be rotated to different orientations about beam axis  37 —i.e. such that leaf-translation directions  41  and the direction of movement of leaves  36  may be pivoted about beam axis  37 . Dotted outline  39  of  FIG.  3 B  shows an example of an alternate orientation of MLC  35  wherein MLC  35  has been rotated about beam axis  37  such that leaf-translation directions  41  are oriented at an angle that is approximately 45° from the orientation shown in the main  FIG.  3 B  illustration. 
     It will be appreciated that the angle φ of leaf-translation directions  41  about beam axis  37  may be defined relative to an arbitrary reference axis.  FIG.  3 C  schematically depicts a system for defining the angle φ of leaf-translation directions  41  about beam axis  37 . In the  FIG.  3 C , the angle φ of leaf-translation directions  41  about beam axis  37  is defined to be an angle in a range of −90°&lt;φ&lt;=90° relative to a reference axis  43 .  FIG.  3 C  illustrates a first leaf-translation direction  41 A wherein the angle φA is greater than zero and a second leaf-translation direction  41 B wherein the angle φB is less than zero. The angle φ of leaf-translation directions  41  about beam axis  37  (as defined relative to reference axis  43  in the above-described manner) may be referred to as the MLC orientation angle φ. In particular embodiments, the reference axis  43  may be selected to coincide with the direction of motion of beam axis  37  as beam positioning mechanism  13  moves source  12  and/or beam  14  relative to subject S along trajectory  30 . Reference axis  43  may therefore be referred to herein as source trajectory direction  43 . 
     A configuration of MLC  35  can be specified by a set of leaf positions that define a position of each leaf  36  and an MLC orientation angle φ of MLC  35  about beam axis  37 . The control system of a radiation delivery device (e.g. control system  23  of radiation delivery device  10 ) is typically capable of controlling the positions of leaves  36  and the MLC orientation angle φ. MLCs can differ in design details, such as the number of leaves  36 , the widths of leaves  36 , the shapes of the ends and edges of leaves  36 , the range of positions that any leaf  36  can have, constraints on the position of one leaf  36  imposed by the positions of other leaves  36 , the mechanical design of the MLC, and the like. The invention described herein should be understood to accommodate any type of configurable beam-shaping apparatus  33  including MLCs having these and other design variations. 
     The configuration of MLC  35  may be changed (for example, by moving leaves  36  and/or rotating the MLC orientation angle φ of MLC  35  about beam axis  37 ) while radiation source  12  is operating and while radiation source  12  is moving about trajectory  30 , thereby allowing the shape of aperture(s)  38  to be varied dynamically while radiation is being delivered to a target volume in subject S. Since MLC  35  can have a large number of leaves  36 , each of leaves  36  can be placed in a large number of positions and MLC  35  can be rotated about beam axis  37 , MLC  35  may have a very large number of possible configurations. 
       FIG.  4 A  schematically depicts a method  50  according to an example embodiment of this invention. An objective of method  50  is to establish a radiation treatment plan that will deliver a desired radiation dose distribution to a target volume in a subject S (to within an acceptable tolerance), while minimizing the dose of radiation delivered to tissues surrounding the target volume or at least keeping the dose delivered to surrounding tissues below an acceptable threshold. This objective may be achieved by varying: (i) a cross-sectional shape of a radiation beam (e.g. beam  14 ); and (ii) an intensity of the radiation beam, while moving radiation source  12  and/or beam  14  along a trajectory  30  relative to subject S. In some embodiments, as discussed above, these objectives are achieved while radiation source  12  and/or beam  14  are caused to move continuously along trajectory  30 . 
     Method  50  may be performed, at least in part, by a treatment planning system  25  (e.g. treatment planning system  25  of  FIG.  1   ). In the illustrated embodiment, treatment planning system  25  comprises its own controller  25 A which is configured to execute suitable software  25 B. In other embodiments, control system  23  and treatment planning system  25  may share a controller. Controller  25  may comprise one or more data processors, together with suitable hardware, including, by way of non-limiting example: accessible memory, logic circuitry, drivers, amplifiers, A/D and D/A converters and like. Such a controller may comprise, without limitation, a microprocessor, a computer-on-a-chip, the CPU of a computer or any other suitable microcontroller. Controller  25  may comprise a plurality of data processors. 
     A desired amount of radiation dose to be delivered to the target volume (referred to as the “desired dose distribution”) and a suitable trajectory  30  may be defined in advance. Method  50  derives the shape that beam  14  ought to have during movement of source  12  and/or beam  14  along trajectory  30  and the intensity with which radiation ought to be delivered during movement of source  12  and/or beam  14  along trajectory  30 . The shape of beam  14  may be determined by a suitable configuration of a beam-shaping mechanism  33 , such as MLC  35 . 
     In block  52 , method  50  obtains a set of optimization goals  61  and trajectory data  62  defining a desired trajectory  30 . Optimization goals  61  comprise dose distribution data  60 , which defines a desired dose distribution, and may comprise other optimization goals  63 . Optimization goals  61  and/or trajectory data  62  may have been developed by health professionals, such as a radiation oncologist in consultation with a radiation physicist, for example. Optimization goals  61  and/or trajectory data  62  may be specified by an operator as a part of block  52 . 
     The person or persons who develop trajectory  30  may have reference to factors such as:
         the condition to be treated;   the shape, size and location of the target volume;   the locations of critical structures that should be spared; and   other appropriate factors.
 
Trajectory  30  may be selected to minimize treatment time.
       

     Radiation delivery apparatus according to some embodiments of the invention may provide one or more pre-defined trajectories. For example, in some embodiments, a pre-defined trajectory  30  may comprise a single, one-way, continuous 360° rotation of gantry  16  about axis  18  such that trajectory  30  overlaps itself only at its beginning and end points. In such cases, block  52  may comprise selecting a pre-defined trajectory  30  or a template that partially defines a trajectory  30  and can be completed to fully define the trajectory  30 . 
     As discussed above, optimization goals  61  comprise dose distribution data  60  and may comprise other optimization goals  63 . Other optimization goals  63  may be specified by an operator as a part of block  52 . By way of non-limiting example, other optimization goals  63  may comprise a desired uniformity of dose distribution in the target volume (or a desired precision with which the dose distribution in the target volume should match desired dose distribution data  60 ). Other optimization goals  63  may also define volumes occupied by important structures outside of the target volume and set limits on the radiation doses to be delivered to those structures. Other optimization goals  63  may define a maximum time required to deliver the radiation based on an individual patient&#39;s ability to stay still during treatment. For example, a child may be more likely to move during treatment than an adult and such movement may cause incorrect dose delivery. Consequently, it may be desirable to lower the maximum dose delivery time for the child to minimize the risk that the child may move during treatment. Other optimization goals  63  may also set priorities (weights) for different optimization goals. 
     Other optimization goals  63  may have any of a variety of different forms. For example, a biological model may be used in the computation of a metric which estimates a probability that a specified dose distribution will control a disease from which the subject is suffering and/or the probability that a specified dose delivered to non-diseased tissue may cause complications. Such biological models are known as radiobiological models. Other optimization goals  63  may be based in part on one or more radiobiological models. The physical limitations of a particular radiation delivery apparatus may also be taken into account as another example of an optimization goal  63 . As mentioned above, gantry  12  can be relatively massive and controlled movement of gantry  12  may be difficult and may cause strain to various components of the radiation delivery apparatus. As a particular example, one optimization goal  63  may be to have gantry  16  move continuously (i.e. without stopping) over the specified trajectory  30 . 
     Method  50  then proceeds to an optimization process  54 , which seeks desirable beam shapes and intensities as a function of the position of source  12  and/or beam  14  along trajectory  30 . In the illustrated embodiment of method  50 , optimization process  54  involves iteratively selecting and modifying one or more optimization variables affecting the beam shape or the beam intensity. For example, the optimization variable(s) may comprise a position of a leaf  36  in a MLC  35  at a control point  32  (which determines a shape of beam  14 ), a MLC orientation angle φ of MLC  35  about axis  37  at a control point  32  (which determines a shape of beam  14 ) and/or an intensity of beam  14  at a control point  32 . The quality of the dose distribution resulting from the modified optimization variable(s) is evaluated in relation to a set of one or more optimization goals. The modification is then accepted or rejected. Optimization process  54  continues until it achieves an acceptable set of beam shapes and intensities or fails. 
     In the illustrated method  50 , optimization process  54  begins in block  56  by establishing an optimization function. The block  56  optimization function is based, at least in part, on optimization goals  61 . The set of optimization goals  61  includes the desired dose distribution data  60  and may include one or more other optimization goals  63 . The block  56  optimization function may comprise a cost function. Higher costs (corresponding to circumstances which are farther from optimization goals  61 ) may be associated with factors such as:
         deviations from the desired dose distribution data  60 ;   increases in the radiation dose delivered outside of the target volume;   increases in the radiation dose delivered to critical structures outside of the treatment volume;   increases in the time required to deliver the radiation treatment; and/or   increases in the total radiation output required for the delivery of the treatment.
 
Lower costs (corresponding to circumstances which are closer to optimization goals  61 ) may be associated with factors such as:
   radiation doses that come closer to matching specified thresholds (which may be related to desired dose distribution data  60 );   no radiation doses exceeding specified thresholds;   reductions in radiation dose outside of the target volume;   reductions in radiation dose delivered to critical structures outside of the target volume;   decreases in the time required to deliver the radiation treatment; and/or   decreases in the total radiation output required for the delivery of the treatment.
 
These factors may be weighted differently from one another. Other factors may also be taken into account when establishing the block  56  optimization function.
       

     The result of block  56  is an optimization function which takes as input a dose distribution and produces an output having a value or values that indicate how closely the input dose distribution satisfies a set of optimization goals  61 . 
     Block  58  involves initializing beam shapes and intensities for a number of control points  32  along trajectory  30 . The initial beam shapes and intensities may be selected using any of a wide variety of techniques. Initial beam shapes may be selected by specifying a particular configuration of MLC  35 . By way of non-limiting example, initial beam shapes specified in block  58  may be selected by any of:
         setting the beam shape at each control point  32  along trajectory  30  to approximate a beam&#39;s eye view outline of the target volume (taken from control point  32 );   setting the beam shape so that radiation is blocked from healthy tissue structures only;   initializing leaves  36  of MLC to be in a specified configuration such as fully open, fully closed, half-open, or defining a shape for aperture  38  (e.g. round, elliptical, rectangular or the like); and   randomizing the positions of leaves  36  of MLC. The particular way that the beam shapes are initialized is not critical and is limited only by the beam-shaping mechanism  33  of particular radiation delivery apparatus.       

     By way of non-limiting example, the initial beam intensities specified in block  58  may be selected by any of:
         setting all intensities to zero;   setting all intensities to the same value; and   setting intensities to random values.       

     In some embodiments, the beam shapes are initialized in block  58  to shapes that match a projection of the target (e.g. to approximate a beam&#39;s eye view outline of the target volume from each control point  32  along trajectory  30 ) and the intensities are initialized in block  58  to all have the same value which may be set so that the mean dose in the target volume will equal a prescribed dose. 
     In block  64 , method  50  involves simulating the dose distribution resulting from the initial beam shapes and initial beam intensities. Typically, the block  64  simulation comprises a simulated dose distribution computation which is discussed in more detail below. Method  50  then determines an initial optimization result in block  65 . The block  65  determination of the initial optimization result may comprise evaluating the block  56  optimization function on the basis of the block  64  simulated dose distribution. 
     In block  66 , method  50  alters the beam shapes and/or intensities at one or more control points  32 . The block  66  alteration of beam shapes and/or intensities may be quasi-random. The block  66  alteration of beam shapes and/or intensities may be subject to constraints. For example, such constraints may prohibit impossible beam shapes and/or intensities and may set other restrictions on beam shapes, beam intensities and/or the rate of change of beam shapes and/or beam intensities. In each execution of block  66 , the alteration of beam shapes and/or intensities may involve a single parameter variation or multiple parameter variations to beam shape parameter(s) and/or to beam intensity parameter(s). The block  66  alteration of beam shapes and/or intensities and may involve variation(s) of these parameter(s) at a single control point  32  or at multiple control points  32 . Block  68  involves simulating a dose distribution that would be achieved if the block  66  altered beam shapes and/or intensities were used to provide a radiation treatment. Typically, the block  68  simulation comprises a simulated dose distribution computation which is discussed in more detail below. 
     In some embodiments, the block  66  alteration of beam shapes and/or intensities is not chosen randomly, but rather is selected to give priority to certain parameter(s) that have large impacts on dose distribution quality. “Dose distribution quality” may comprise a reflection of how closely a simulated dose distribution calculation meets optimization goals  61 . For example, where the beam is shaped by a MLC  35 , certain leaves  36  or positions of leaves  36  may be given priority for modification. This may be done by determining a priori which leaves of MLC  35  have the most impact on dose distribution quality. Such an a priori determination of particularly important MLC leaves may be based, for example, on a calculation of the relative contributions to the block  56  optimization function from each voxel in the target region and the surrounding tissue and by a projection of beam ray lines intersecting a particular voxel to the plane of MLC  35 . 
     In block  70 , method  50  determines a current optimization result. The block  70  determination may comprise evaluating the block  56  optimization function on the basis of the block  68  simulated dose distribution. In block  72 , the current optimization result (determined in block  70 ) is compared to a previous optimization result and a decision is made whether to keep or discard the block  66  alteration. The first time that method  50  arrives at block  72 , the previous optimization result may be the block  65  initial optimization result. The block  72  decision may involve:
         (i) deciding to preserve the block  66  alteration (block  72  YES output) if the current optimization result is closer to optimization goals  61  than the previous optimization result; or   (ii) deciding to reject the block  66  alteration (block  72  NO output) if the current optimization result is further from optimization goals  61  than the previous optimization result.
 
Other optimization algorithms may make the block  72  decision as to whether to keep or discard the block  66  alteration based on rules associated with the particular optimization algorithm. For example, such optimization algorithms may, in some instances, allow preservation of the block  66  alteration (block  72  YES output) if the current optimization result is further from the optimization goals  61  than the previous optimization result. Simulated annealing is an example of such an optimization algorithm.
       

     If block  72  determines that the block  66  alteration should be preserved (block  72  YES output), then method  50  proceeds to block  73 , where the block  66  altered beam shapes and intensities are updated to be the current beam shapes and intensities. After updating the beam shapes and intensities in block  73 , method  50  proceeds to block  74 . If block  72  determines that the block  66  alteration should be rejected (block  72  NO output), then method  50  proceeds directly to block  74  (i.e. without adopting the block  66  alterations). 
     Block  74  involves a determination of whether applicable termination criteria have been met. If the termination criteria have been met (block  74  YES output), method  50  proceeds to block  75 , where the current beam shapes and intensities are saved as an optimization result. After block  75 , optimization process  54  terminates. On the other hand, if the termination criteria have not been met (block  74  NO output), method  50  loops back to perform another iteration of blocks  66  through  74 . 
     By way of non-limiting example, block  74  termination criteria may include any one or more of:
         successful achievement of optimization goals  61 ;   successive iterations not yielding optimization results that approach optimization goals  61 ;   number of successful iterations of blocks  66  through  74  (where a successful iteration is an iteration where the block  66  variation is kept in block  73  (i.e. block  72  YES output));   operator termination of the optimization process.       

     The illustrated method  50  represents a very simple optimization process  54 . Optimization process  54  may additionally or alternatively include other known optimization techniques such as:
         simulated annealing;   gradient-based techniques;   genetic algorithms;   applying neural networks; or   the like.       

     Method  50  may be used as a part of an overall method for planning and delivering radiation dose to a subject S.  FIG.  4 B  schematically depicts a method  300  for planning and delivering radiation dose to a subject S according to a particular embodiment of the invention. Method  300  begins in block  310 , which, in the illustrated embodiment, involves obtaining a desired trajectory  30  and desired optimization goals  61 . Method  300  then proceeds to block  320  which involves optimizing a set of radiation delivery parameters. In one particular embodiment, the block  320  optimization process may comprise an optimization of the beam shape and beam intensity parameters in accordance with optimization process  54  of method  50 . The result of the block  320  optimization process is a radiation delivery plan. In block  330 , the radiation delivery plan is provided to the control system of a radiation delivery apparatus (e.g. control system  23  of radiation delivery device  10  ( FIG.  1   )). In block  340 , the radiation delivery apparatus delivers the radiation to a subject in accordance with the radiation treatment plan developed in block  320 . 
     Method  50  involves the simulation of dose distribution that results from a particular set of beam shapes, beam intensities and motion axis positions (e.g. in blocks  64  and  68 ). Simulation of the dose distribution may be performed in any suitable manner. Some examples of dose calculation methods that may be employed to simulate dose distribution results comprise:
         pencil beam superposition;   collapsed cone convolution; and   Monte Carlo simulation.       

     In some embodiments, the dose that would be delivered by a treatment plan is simulated (as in blocks  64  and  68  of method  50 ) by adding a contribution to the dose from each control point  32 . At each of control points  32 , the following information is known:
         a position of source  12  and an orientation of beam  14  relative to subject S including the target volume (as determined by the positions of the available motion axes);   a beam shape (as determined, for example, by a MLC orientation angle φ and/or a configuration of the leaves  36  of a MLC  35 ); and   a beam intensity.       

     In some embodiments, the contribution to the dose at each control point  32  is determined by pencil beam superposition. Pencil beam superposition involves conceptually dividing the projected area of beam  14  into many small beams known as “beamlets” or “pencil beams”. This may be done by dividing a cross-sectional beam shape (e.g. aperture  38  of MLC  35 ) into a grid of square beamlets. The contribution to an overall dose distribution from a particular control point  32  may be determined by summing the contributions of the beamlets. The contribution to a dose distribution by individual beamlets may be computed in advance. Such contributions typically take into account radiation scattering and other effects that can result in the radiation from one beamlet contributing to dose in regions that are outside of the beamlet. In a typical MLC  35 , there is some transmission of radiation through leaves  36 . Consequently, when performing a dose simulation calculation, it is often desirable add some smaller contribution to the dose from outside of the beam shaping aperture  38  to account for transmission through leaves  36  of MLC  35 . 
       FIG.  5 A  shows an aperture  38  of an MLC  35  divided into a plurality of beamlets  80 . In general, it is desirable for beamlets  80  to be fairly small to permit precise modelling of the wide range of configurations that aperture  38  may have. Beamlets  80  may be smaller than the widths of the leaves  36  (not shown in  FIG.  5 A ) of MLC  35 . In  FIG.  5 A , 105 beamlets  80  are required to cover aperture  38  and, consequently, for a particular control point  32  having the aperture configuration shown in  FIG.  5 A , a dose simulation calculation (e.g. a portion of the block  68  dose simulation) involves a superposition of the dose contributed by 105 beamlets  80 . 
     Some embodiments achieve efficiencies in this dose simulation computation by providing composite beamlets  82  that are larger than beamlets  80 . A range of composite beamlets  82  having different sizes, shapes and/or orientations may be provided.  FIG.  5 B  shows a number of composite beamlets  82 A,  82 B,  82 C (collectively, beamlets  82 ) having different sizes and shapes. It can be seen from  FIG.  5 B , that composite beamlets  82  can be used in the place of a plurality of conventionally sized beamlets  80 . An example application of composite beamlets  82  is shown in  FIG.  5 C . For a given shape of aperture  38 , composite beamlets  82  are used in place of some or all of smaller beamlets  80 . In the particular configuration of aperture  38  of  FIG.  5 C  (which is the same as the configuration of aperture  38  of  FIG.  5 A ), the area of aperture  38  is covered by 28 composite beamlets  82  (24  82 A, one  84 B, three  84 C) and one smaller beamlet  80 . Consequently, for a particular control point  32  having the aperture configuration of  FIG.  5 B , a dose simulation calculation (e.g. a portion of the block  68  dose simulation) is reduced to a superposition of the dose contributed by 29 beamlets  82 ,  80 . Dose contributed by composite beamlets  82  may be determined in advance in a manner similar to the advance dose contribution from conventional beamlets  80 . 
     The size and shape of composite beamlets  82  may be selected to reduce, and preferably minimize, the number of beamlets required to cover the area of aperture  38 . This can significantly reduce calculation time without significantly reducing the accuracy of dose simulation. The use of composite beamlets is not limited to pencil beam superposition and may be used in other dose simulation calculation algorithms, such as Monte Carlo dose simulation and collapsed cone convolution dose simulation, for example. 
     The use of composite beamlets  82  to perform a dose simulation calculation assumes that there are only small changes in the characteristics of the tissue over the cross-sectional dimension of the composite beamlet  82 . As composite beamlets are made larger, this assumption may not necessarily hold. Accordingly, the upper size limit of composite beamlets  82  is limited by the necessary calculation accuracy. In some embodiments, at least one dimension of composite beamlets  82  is greater than the largest dimension of conventional beamlet  80 . In some embodiments, the maximum dimension of composite beamlets  82  is less than 25 times the size of the largest dimension of conventional beamlet  80 . 
     The dose simulation computation (e.g. the block  68  dose simulation) is performed at a number of control points  32 . Based on calculations for those control points  32 , an estimated dose distribution is generated for a radiation source  12  that may be continuously moving over a trajectory  30  and continuously emitting a radiation beam  14 , where the radiation beam  14  may have a continuously varying shape and intensity. Where a dose distribution is computed by summing contributions from discrete control points  32 , the accuracy with which the computed dose will match the actual dose delivered by continuous variation of the position of source  12 , the orientation of beam  14 , the beam shape and the beam intensity will depend in part upon the number of control points  32  used to perform the dose simulation computation. If there are only a few control points  32 , then it may not be possible to obtain accurate estimates of the delivered dose. The dose delivered by source  12  over a continuous trajectory  30  can be perfectly modelled by summing contributions from discrete control points  32  only at the limit where the number of control points  32  approaches infinity. Discretization of the dose simulation calculation using a finite number of control points  32  will therefore degrade the accuracy of the modelled dose distribution. 
     This concept is graphically illustrated in  FIG.  6   , which plots the dose simulation error against the number of control points  32 .  FIG.  6    clearly shows that where the dose simulation computation makes use of a large number of control points  32 , the resultant error (i.e. the difference between simulation dose distribution and actual dose distribution) is minimized. 
     In some embodiments of the invention, constraints are imposed on the optimization process (e.g. block  54  of method  50 ). Such constraints may be used to help maintain the accuracy of the discretized dose simulation calculation to within a given tolerance. In some embodiments, these optimization constraints are related to the amount of change in one or more parameters that may be permitted between successive control points  32 . Examples of suitable constraints include:
         Radiation source  12  cannot travel further than a maximum distance between consecutive control points  32 . This may be achieved entirely, or in part, by imposing a maximum change in any motion axis between consecutive control points  32 . Separate constraints may be provided for each motion axis. For example, a maximum angular change may be specified for gantry angle, maximum changes in displacement may be provided for couch translation etc.   Parameters affecting beam shape cannot change by more than specified amounts between consecutive control points  32 . For example, maximum values may be specified for changes in the positions of leaves  36  of a MLC  35  or changes in MLC orientation angle φ of MLC  35 .   Parameters affecting beam shape cannot change by more than a specified amount per unit of motion axis change. For example, maximum values may be specified for changes in the positions of leaves  36  of a MLC  35  for each degree of rotation of gantry  16  about axis  18 .   The source intensity cannot change by more than a specified amount between control points  32 .   The source intensity cannot change by more that a specified amount per unit of motion axis change.   The source intensity cannot exceed a certain level.
 
It will be appreciated that where a dose simulation calculation is based on a number of discretized control points, constraints which force small changes of motion axes parameters, beam shape parameters and/or beam intensity parameters between control points can produce more accurate dose simulation calculations.
       

     In addition to improving the accuracy of the dose simulation calculation, the imposition of constraints may also help to reduce total treatment time by accounting for the physical limitations of particular radiation delivery apparatus. For example, if a particular radiation delivery apparatus has a maximum radiation output rate and the optimization solution generated by method  50  involves a desired radiation intensity that results in a radiation output rate higher than this maximum radiation output rate, then the rate of movement of the motion axes of the radiation delivery apparatus will have to slow down in order to deliver the intensity prescribed by the block  54  optimization process. Accordingly, a constraint imposed on the maximum source intensity during the block  54  optimization can force a solution where the prescribed intensity is within the capability of the radiation delivery apparatus (e.g. less than the maximum radiation output rate of the radiation delivery apparatus) such that the motion axes of the radiation delivery apparatus do not have to slow down. Since the motion axes do not have to slow down, such a solution can be delivered to subject S relatively quickly, causing a corresponding reduction in total treatment time. Those skilled in the art will appreciate that other constraints may be used to account for other limitations of particular radiation delivery apparatus and can be used to reduce total treatment time. 
     An example of how such constraints may be defined is “For an estimated dose to be within 2% of the actual dose distribution, the following parameters should not change by more than the stated amounts between any two consecutive control points  32 :
         intensity—10%;   MLC leaf position—5 mm;   MLC orientation φ—5%;   gantry angle—1 degree; and   couch position—3 mm.”       

     The number of control points  32  used in optimization process  54  also impacts the number of iterations (and the corresponding time) required to implement optimization process  54  as well as the quality of the dose distribution.  FIG.  7    graphically depicts the dose distribution quality as a function of the number of iterations involved in a block  54  optimization process for various numbers of control points  32 . 
       FIG.  7    shows plots for 10 control points, 50 control points, 100 control points and 300 control points on a logarithmic scale. It will be appreciated by those skilled in the art that the number of iterations (the abscissa in  FIG.  7   ) is positively correlated with the time associated to perform the optimization.  FIG.  7    shows that when the number of control points  32  is relatively low, the quality of the dose distribution improves rapidly (i.e. over a relatively small number of iterations). However, when the number of control points  32  is relatively low, the quality of the resultant dose distribution is relatively poor and, in the cases of 10 control points and 50 control points, the quality of the dose distribution does not achieve the optimization goals  61 . Conversely, if a relatively large number of control points  32  is used, the block  54  optimization requires a relatively large number of iterations, but the quality of the dose distribution eventually achieved is relatively high and exceeds the optimization goals  61 . In some cases, where the number of control points  32  is relatively high, the number of iterations required to achieve a solution that meets the optimization goals  61  can be prohibitive (i.e. such a solution can take too long or can be too computationally expensive). 
     The impact of the number of control points  32  on the block  54  optimization process may be summarized as follows. If a relatively small number of control points  32  are used:
         there may be relatively large changes in the motion axes parameters (i.e. beam position and beam orientation), the beam shape parameters (e.g. positions of leaves  36  of MLC  35  and/or MLC orientation angle φ) and beam intensity between control points  32  (i.e. the constraints on the motion axes parameters, the beam shape parameters and the beam intensity will be relatively relaxed as between control points  32 );   because of the relatively relaxed constraints and the large range of permissible changes to the beam shape and intensity parameters, it is possible to explore a relatively large range of possible configurations of the beam intensity and beam shape during optimization process  54 ;   because of the ability to explore a relatively large range of possible beam shape and intensity configurations, the block  54  optimization process will tend to approach the optimization goals  61  after a relatively small number of iterations;   because there are fewer control points available at which the beam shape parameters and/or beam intensity parameters may be varied, it may be difficult or impossible for the block  54  optimization process to derive a dose distribution that meets or exceeds optimization goals  61 ; and   the accuracy of dose simulation computations based on the relatively small number of control points  32  will be relatively poor and may be outside of an acceptable range.       

     If a relatively large number of control points  32  are used:
         the possible magnitudes of the changes in the motion axes parameters (i.e. beam position and beam orientation), the beam shape parameters (e.g. positions of leaves  36  of MLC  35  and/or MLC orientation angle φ) and beam intensity between control points  32  are relatively low (i.e. the constraints on the motion axes parameters, the beam shape parameters and the beam intensity will be relatively restrictive as between control points  32 );   because of the relatively restrictive constraints and the small range of permissible changes to the beam shape and intensity parameters, only a relatively small range of possible beam shape and beam intensity configurations may be explored during optimization process  54 ;   because of the limited range of possible beam shape and intensity configurations, it may take a relatively large number of iterations for the block  54  optimization process to approach the optimization goals  61 ;   because there are more control points available at which the beam shape and/or the beam intensity may be varied, it may be easier to derive a dose distribution that meets or exceeds optimization goals  61 ; and   the accuracy of dose simulation computations based on the relatively large number of control points  32  will be relatively good.       

     In some embodiments, the benefits of having a small number of control points  32  and the benefits of having a large number of control points  32  are achieved by starting the optimization process with a relatively small number of control points  32  and then, after a number of initial iterations, inserting additional control points  32  into the optimization process. This process is schematically depicted in  FIG.  8   . 
       FIG.  8    shows a method  150  of optimizing dose delivery according to another embodiment of the invention. Method  150  of  FIG.  8    may be used as a part of block  320  in method  300  of  FIG.  4 B . In many respects, method  150  of  FIG.  8    is similar to method  50  of  FIG.  4 A . Method  150  comprises a number of functional blocks which are similar to those of method  50  and which are provided with reference numerals similar to the corresponding blocks of method  50 , except that the reference numerals of method  150  are proceeded by the numeral “1”. Like method  50 , the objective of method  150  is to establish a radiation treatment plan that will deliver a desired radiation dose distribution to a target volume in a subject S (to within an acceptable tolerance), while minimizing the dose of radiation delivered to tissues surrounding the target volume or at least keeping the dose delivered to surrounding tissues below an acceptable threshold. This objective may be achieved by varying: (i) a cross-sectional shape of radiation beam  14 ; and (ii) an intensity of beam  14 , while moving radiation source  12  and/or beam  14  along a trajectory  30  relative to subject S. 
     The principal difference between method  50  of  FIG.  4 A  and method  150  of  FIG.  8    is that the optimization process  154  of method  150  involves a repetition of the optimization process over a number of levels. Each level is associated with a corresponding number of control points  32  and the number of control points  32  increases with each successive level. In the illustrated embodiment, the total number of levels used to perform the block  154  optimization (or, equivalently, the final number of control points  32  at the conclusion of the block  154  optimization process) may be determined prior to commencing method  150 . For example, the final number of control points  32  may be specified by an operator depending, for example, on available time requirements, accuracy requirements and/or dose quality requirements. In other embodiments, depending on termination conditions explained in more detail below, the final number of control points  32  may vary for each implementation of method  150 . 
     Method  150  starts in block  152  and proceeds in the same manner as method  50  until block  158 . In the illustrated embodiment, block  158  differs from block  58  in that block  158  involves the additional initialization of a level counter. In other respects, block  158  is similar to block  58  of method  50 . Initialization of the level counter may set the level counter to 1 for example. When the level counter is set to 1, method  150  selects a corresponding level 1 number of control points  32  to begin the block  154  optimization process. The level 1 number of control points  32  is preferably a relatively low number of control points. In some embodiments, the level 1 number of control points  32  is in a range of 2-50. As discussed in more detail below, the level counter is incremented during the implementation of method  150  and each time the level counter is incremented, the corresponding number of control points  32  is increased. 
     Using a number of control points  32  dictated by the level counter, method  150  proceeds with blocks  164  through  174  in a manner similar to blocks  64  through  74  of method  50  discussed above. Block  174  differs from block  74  in that block  174  involves an inquiry into the termination conditions for a particular level of method  150 . The termination conditions for a particular level of method  150  may be similar to the termination conditions in block  74  of method  50 . By way of non-limiting example, the termination conditions for block  174  may comprise any one or more of:
         successful achievement of optimization goals  61  to within a tolerance level which may be particular to the current level;   successive iterations not yielding optimization results that approach optimization goals  61 ; and   operator termination of the optimization process.
 
Additionally or alternatively, the block  174  termination conditions may include reaching a maximum number of iterations of blocks  166  through  174  within a particular level of method  150  regardless of the resultant optimization quality. For example, the maximum number of iterations for level 1 may be 10 4 . The maximum number iterations may vary for each level. For example, the maximum number of iterations may increase for each level in conjunction with a corresponding increase in the number of control points  32  or may decrease for each level in conjunction with a corresponding increase in the number of control points  32 .
       

     Additionally or alternatively, the block  174  termination conditions may include reaching a maximum number of successful iterations of blocks  166  through  174  within a particular level of method  150  (i.e. iterations where method  150  proceeds through the block  172  YES output and the block  166  variation is kept in block  173 ). Again, the maximum number of successful iterations may vary (increase or decrease) for each level. In some embodiments, the maximum number of successful iterations within a particular level decreases as the level (i.e. the number of control points  32 ) increases. In one particular embodiment, the maximum number of successful iterations decreases exponentially as the level increases. 
     If the termination criteria have not been met (block  174  NO output), method  150  loops back to perform another iteration of blocks  166  through  174  at the current level. If the termination criteria have been met (block  174  YES output), method  150  proceeds to block  178 , where method  150  inquires into the general termination conditions for optimization process  154 . The general termination conditions of block  178  may be similar to the termination conditions in block  174 , except the block  178  termination conditions pertain to optimization process  154  as a whole rather than to a particular level of optimization process  154 . By way of non-limiting example, the termination conditions for block  178  may comprise any one or more of:
         successful achievement of optimization goals  61  to within a tolerance level particular to optimization process  154  as a whole;   successive iterations not yielding optimization results that approach optimization goals  61 ; and   operator termination of the optimization process.
 
Additionally or alternatively, the block  178  termination conditions may include reaching a suitable minimum number of control points  32 . This minimum number of control points may depend on the number of control points  32  required to ensure that dose simulation calculations have sufficient accuracy (see  FIG.  6   ).
       

     The block  178  termination conditions may additionally or alternatively comprise having minimum threshold level(s) of control points  32  for corresponding changes in the motion axes parameters, the beam shape parameters and/or the beam intensity parameter. In one particular example, the block  178  termination conditions may comprise minimum threshold level(s) of at least one control point  32  for:
         each intensity change greater than 10%;   each MLC leaf position change greater than 5 mm;   each MLC orientation change greater than 5°;   each gantry angle change greater than 1°; and/or   each couch position change greater than −3 mm.       

     If the block  178  termination criteria have been met (block  178  YES output), method  150  proceeds to block  175 , where the current beam shapes and intensities are saved as an optimization result. After block  175 , method  150  terminates. On the other hand, if the block  178  termination criteria have not been met (block  178  NO output), method  150  proceeds to block  180 , where the number of control points  32  is increased. 
     The addition of new control points  32  in block  180  may occur using a wide variety of techniques. In one particular embodiment, new control points  32  are added between pairs of existing control points  32 . In addition to adding new control points  32 , block  180  comprises initializing the parameter values associated with the newly added control points  32 . For each newly added control point  32 , such initialized parameter values may include: motion axes parameters which specify the position of source  12  and the orientation of beam  14  (i.e. the set of motion axis positions corresponding to the newly added control point  32 ); an initial beam shape parameter (e.g. the configuration of the leaves  36  and/or orientation φ of a MLC  35 ); and an initial beam intensity parameter. 
     The motion axes parameters corresponding to each newly added control point  32  may be determined by the previously specified trajectory  30  (e.g. by desired trajectory data  62 ). The initial beam shape parameters and the initial beam intensity parameters corresponding to each newly added control point  32  may be determined by interpolating between the current beam shape parameters and current beam intensity parameters for previously existing control points  32  on either side of the newly added control point  32 . Such interpolation may comprise linear or non-linear interpolation for example. 
     The initial parameter values for the newly added control points  32  and the subsequent permissible variations of the parameter values for the newly added control points  32  may be subject to the same types of constraints discussed above for the original control points  32 . For example, the constraints on the parameter values for newly added control points  32  may include:
         constraints on the amount that radiation source  12  (or any one or more motion axes) can move between control points  32 ;   constraints on the amount that the beam shape can change between successive control points  32  (e.g. constraints on the maximum rotation MLC orientation φ or movement of the leaves  36  of MLC  35 ); or   constraints on the amount that the intensity of source  12  may change between successive control points  32 .
 
Those skilled in the art will appreciate that the magnitude of these optimization constraints will vary with the number of control points  32  and/or the separation of adjacent control points  32 . For example, if the constraint on a maximum movement of a leaf  36  of MLC  35  is 2 cm between successive control points  32  when there are 100 control points  32  and the number of control points  32  is doubled to 200, the constraint may be halved, so that the constraint on the maximum movement of a leaf  36  of MLC  35  is 1 cm between control points  32  (assuming that the newly added control points  32  are located halfway between the existing control points  32 ).
       

     After adding and initializing the new control points  32  in block  180 , method  180  proceeds to block  182  where the level counter  182  is incremented. Method  150  then returns to block  164 , where the iteration process of blocks  164  through  174  is repeated for the next level. 
     An example of the method  150  results are shown in  FIG.  9   , which graphically depicts the dose distribution quality versus the number of iterations on a linear scale.  FIG.  9    also shows that the number of control points  32  increases as the dose distribution gets closer to the optimization goals  61 . It can be seen that by starting the optimization process with a relatively low number of control points  32  and then adding additional control points  32  as the optimization process approaches the optimization goals  61 , the number of iterations required to achieve an acceptable solution has been dramatically reduced.  FIG.  9    also shows that:
         the use of a small number of control points  32  at the beginning of the optimization process allows the optimization to get close to optimization goals  61  after a relatively small number of iterations;   the introduction of additional control points  32  during the course of the optimization allows the flexibility to derive a dose distribution that meets optimization goals  61 ; and   before the overall optimization process is terminated, a large number of control points  32  have been added and the parameters associated with these additional control points obey the associated optimization constraints, thereby preserving the dose calculation accuracy.       

     As with method  50  discussed above, method  150  describes a simple optimization process  154 . In other embodiments, the block  154  optimization process may additionally or alternatively include other known optimization techniques such as: simulated annealing, gradient-based techniques, genetic algorithms, applying neural networks or the like. 
     In method  150 , additional control points  32  are added when the level is incremented. In a different embodiment, the addition of one or more new control points may be treated as an alteration in block  66  of method  50 . In such an embodiment, the procedures of block  180  associated with the addition of control points  32  may be performed as a part of block  66 . In such an embodiment, the termination conditions of block  74  may also comprise an inquiry into whether the optimization has achieved a minimum number of control points  32 . In other respects, such an embodiment is similar to method  50 . 
     The result of optimization method  50  or optimization method  150  is a set of control points  32  and, for each control point  32 , a corresponding set of parameters which includes: motion axes parameters (e.g. a set of motion axis positions for a particular radiation delivery apparatus that specify a corresponding beam position and beam orientation); beam shape parameters (e.g. a configuration of an MLC  35  including a set of positions for leaves  36  and, optionally, an orientation angle φ of MLC  35  about axis  37 ); and a beam intensity parameter. The set of control points  32  and their associated parameters form the basis of a radiation treatment plan which may then be transferred to a radiation delivery apparatus to effect the dose delivery. 
     The radiation intensity at a control point  32  is typically not delivered instantaneously to the subject but is delivered continuously throughout the portion of the trajectory  30  defined by that control point  32 . The radiation output rate of the source  12  may be adjusted by the radiation delivery apparatus  10  and control system  23  so that the total radiation output for that control point  32  is the same as the intensity determined from the radiation plan. The radiation output rate will normally be determined by the amount of time required for the position of the radiation source  12  and the shape of the radiation beam to change between the previous, current and following control points  32 . 
     A control system of the radiation delivery apparatus (e.g. control system  23  of radiation delivery apparatus  10 ) uses the set of control points  32  and their associated parameters to move radiation source  12  over a trajectory  30  while delivering radiation dose to a subject S. While the radiation delivery apparatus is moving over trajectory  30 , the control system controls the speed and/or position of the motion axes, the shape of the beam and the beam intensity to reflect the motion axis parameters, beam shape parameters and the beam intensity parameters generated by the optimization methods  50 ,  150 . It will be appreciated by those skilled in the art that the output of the optimization methods  50 ,  150  described above may be used on a wide variety of radiation delivery apparatus. 
     Pseudocode for Exemplary Embodiment of Optimization Process 
     Pre-Optimization 
     
         
         
           
             Define 3-dimensional target and healthy tissue structures. 
             Set optimization goals for all structures based on one or more of:
           Histograms of cumulative dose;   Prescribed dose required to the target;   Uniformity of dose to the target;   Minimal dose to healthy tissue structures.   
         
             Combine all optimization goals into a single quality factor (i.e. an optimization function). 
             Define the trajectory for the radiation source:
           Select a finite number of control points; and   Set the axis position for each axis at each control point.
 
Initialization
   
         
             Configure MLC characteristics (e.g. leaf width, transmission). 
             Initialize level counter and initial number of control points. 
             Initialize MLC leaf positions to shape the beam to the outline of the target. 
             Perform dose simulation calculation to simulate dose distribution for all targets and healthy tissue structures:
           Generate a random distribution of points in each target/structure;   Calculate the dose contribution from each initial control point; and   Add the contribution from each initial control point.   
         
             Rescale the beam intensity and corresponding dose so that the mean dose to the target is the prescription dose. 
             Set constraints for:
           maximum change in beam shape parameters (i.e. movement of MLC leaves and/or rotations of MLC); and   maximum change in beam intensity;   
         
             for corresponding variations the relevant motor axes, including, where relevant:
           Gantry angle;   Couch angle;   Couch position; and   MLC orientation.   
         
             Set maximum intensity constraint. 
             Set maximum treatment time constraint. 
             Set optimization parameters:
           Probability of adding control points;   At each iteration:
               Probability of changing beam shape parameter (e.g. MLC leaf position or MLC orientation) taking into account constraints on range of changes in MLC leaf position; and   Probability of changing a radiation intensity taking into account constraints on range of intensity changes.
 
Optimization
   
               
         
           
         
         While the optimization goals have not been attained: 
         1. Select a control point. 
         2. Select a beam shape alteration, intensity alteration, or add control points.
       If a beam shape alteration (e.g. a change in position of an MLC leaf) is selected:
           Randomly select an MLC leaf to change;   Randomly select a new MLC leaf position;   Ensure that the new MLC leaf position does not violate any positional constraints:
               Leaf does not overlap with opposing leaf;   Leaf does not move outside of the initialized aperture; and   Leaf does not violate the maximum movement constraints.   
               Perform dose distribution simulation to calculate the new dose distribution for all structures.   Calculate quality factor (i.e. optimization function) for new dose distribution.   If the quality factor (i.e. optimization function) indicates an improvement, then accept the new leaf position.   
           If an intensity alteration is selected:
           Randomly select a new intensity;   Ensure that the new intensity does not violate any constraints:
               Intensity cannot be negative;   Intensity cannot violate the maximum intensity constraint; and   Intensity cannot violate the maximum intensity variation constraints.   
               Perform dose distribution simulation to calculate the new dose distribution for all structures.   Calculate quality factor (i.e. optimization function) for new dose distribution.   If the quality factor (i.e. optimization function) indicates an improvement, then accept the new intensity.   
           If adding control points is selected:
           Insert one or more control points within the existing trajectory.   Adjust optimization constraints (e.g. beam shape constraints and intensity constraints) based on addition of new control points.   Initialize beam shape parameters, intensity parameters and motion axes parameters of new control point(s).   Perform dose distribution simulation (incorporating the new control points) to calculate the new dose distribution for all structures.   Rescale all intensities so that the new intensities provide a mean dose to the target equal to the prescription dose.   Continue optimization with the added control points.   
           If the termination criteria have been attained:
           Terminate the optimization; and   Record all optimized parameters (e.g. beam shape parameters, motion axes parameters and beam intensity parameters) and transfer optimized parameters to the radiation device.   
           If the termination criteria has not be attained:
           Go to step (1) and select another beam shape alteration, intensity alteration, or add control points.
 
Example Implementation of a Particular Embodiment
   
           
     
       
    
     The following represents an illustrative example implementation of a particular embodiment of the invention.  FIG.  10    shows a three-dimensional example of target tissue  200  and healthy tissue  202  located within the body of a subject S. This example simulates a radiation delivery apparatus similar to radiation delivery apparatus  10  ( FIG.  1   ). 
     In this example, a trajectory  30  is defined as a 360° rotation of gantry  16  about axis  18  and a movement of couch  15  in the −Z direction (as shown in the coordinate system of  FIG.  10   ). While this particular example uses a trajectory  30  involving two motion axes, it will be appreciated that trajectory  30  may involve movement of fewer motion axes or a greater number of motion axes.  FIGS.  11 A and  11 B  respectively depict the initial control point  32  positions of the relevant motion axes corresponding to the selected trajectory  30  (i.e. the angular positions of gantry  16  about axis  18  and the position of couch  15  in the Z dimension). 
     For this example, the optimization goals  61  included a desired dose distribution  60  having a uniform level of 70 Gy for target  200  and a maximum dose of 35 Gy for healthy tissue  202 . At each initial control point  32 , the beam shape parameters were initialized such that the leaves  36  of a MLC  35  shaped the beam into a beam&#39;s eye view outline of target  200 . In this example, the orientation φ of MLC  35  was maintained constant at 45° and the orientation φ of MLC  35  was not specifically optimized. At each initial control point  32 , the beam intensity was initialized so that the mean dose delivered to the target  200  was 70 Gy. 
       FIGS.  12 A-F  graphically depict the simulated dose distribution calculation at various stages of the optimization process by way of a dose volume histogram (DVH). In  FIGS.  12 A-F , dashed line  204  represents the percentage of the volume of healthy tissue  202  that receives a certain quantity of dose and the solid line  206  represents the percentage of the volume of target  200  that receives a certain quantity of dose. A DVH is a convenient graphical tool for evaluating dose distribution quality. It will be appreciated that movement of dashed line  204  downwardly and leftwardly represents a minimization of dose delivered to healthy tissue  202  and that movement of solid line  206  upwardly (as far as 100%) and rightwardly (as far as the dose distribution target (70 Gy in this example)) represents effective delivery of dose to target  200 . 
     In this example, the optimization process starts at zero iterations with the 12 control points depicted in  FIGS.  11 A and  11 B . The result at zero iterations is shown in  FIG.  12 A . In this example, the number of iterations and the number of control points are increased during the optimization process as shown in  FIG.  12 B- 12 F . After 900 iterations and an increase to 23 control points ( FIG.  12 B ), a dramatic improvement in dose quality can be observed by the leftwardly and downwardly movement of dashed line  204 . Further improvement is seen at 1800 iterations and 45 control points ( FIG.  12 C ) and at 3200 iterations and 89 control points ( FIG.  12 D ). The magnitude of the improvement in dose distribution quality per iteration decreases as the optimization progresses.  FIGS.  12 D- 12 F  show that there is little improvement in the dose distribution quality between 3200 iterations and 89 control points ( FIG.  12 D ), 5800 iterations and 177 control points ( FIG.  12 E ) and 8500 iterations and 353 control points. As discussed above, notwithstanding the minimal improvement in dose distribution quality between  FIGS.  12 D and  12 F , it can be useful to continue to increase the number of control points in the optimization to improve the accuracy of the dose simulation calculations. 
       FIG.  13    is another graphical representation of this example which shows how the optimization goals  61  are achieved (to within an acceptable tolerance level) after 5800 iterations (177 control points). 
     The optimization of this example was terminated after 11,000 iterations because the optimization goals had been attained (to within acceptable tolerances) and there was no further improvement in the dose distribution quality or accuracy with further iterations. The results of this example are shown in  FIGS.  14 A- 14 D , which respectively depict the motion axes parameters at each of the final control points (in this case, the orientation of gantry  16  about axis  18  ( FIG.  14 A ) and the Z position of couch  15  ( FIG.  14 B )), the radiation intensity at each of the final control points ( FIG.  14 C ) and the beam shaping parameters at each of the final control points (in this case, positions of two leaves  36  of an MLC  35  ( FIG.  14 D )).  FIG.  14 D  shows that there are no dramatic changes in position of the illustrated leaves  36  of MLC  3 , as constraints were applied to the allowable rate of change of the leaves  36  of MLC  35 . 
       FIG.  15    shows a two-dimensional cross-section of the optimized dose distribution.  FIG.  15    shows plots contour lines of constant dose (isodose lines) indicating the regions of high and low dose. The amount of dose associated with each isodose line is enumerated on the line itself. Recalling the shape and relative position of the target  200  and healthy tissue  202  from  FIG.  10   ,  FIG.  15    shows that the high dose region is confined to the c-shape target area  200  while inside the concavity (i.e. the region of healthy tissue  202 ), the dose is significantly reduced. 
     In this example, the optimization time was 15.3 minutes. The treatment time required to deliver this dose distribution is approximately 1.7 minutes (assuming a dose rate of 600 MU/min). 
     In some embodiments, the methods described herein for delivering radiation dose to a subject S are used in conjunction with one or more imaging techniques and corresponding imaging apparatus. A suitable imaging technique is cone-beam computed tomography (cone-beam CT), which obtains a three-dimensional image of a subject. Cone-beam CT involves a radiation source and a corresponding sensor which can be suitably mounted on a radiation delivery apparatus. For example, a cone-beam CT radiation source may be mounted on gantry  16  of radiation delivery apparatus  10  and a corresponding sensor may be mounted on the opposing side of subject S to detect radiation transmitted through subject S. In some embodiments, the cone-beam CT source is the same as the treatment radiation source  12 . In other embodiments, the cone-beam CT source is different than the treatment radiation source  12 . The radiation delivery apparatus may move the cone-beam CT source and the CT sensor relative to subject S using the same motion axes (or substantially similar motion axes) used to move the treatment radiation source  12 . At any point in which the cone-beam CT source is activated, a 2-dimensional projection image is formed from the transmission of radiation emanating from the cone-beam CT source, passing through subject S and impinging onto the corresponding sensor (which typically comprises a 2-dimensional array of radiation sensors). In some embodiments, the cone-beam CT radiation source and the treatment radiation source are time division multiplexed, such that the cone-beam CT sensor can distinguish between imaging radiation and treatment radiation. 
     In the acquisition of a 3-dimensional cone-beam CT image, the cone-beam CT source and sensor array move through a trajectory to acquire a plurality of 2-dimensional projection images of subject S. The plurality of 2-dimensional projection images are combined using methods known to those skilled in the art in order to reconstruct the 3-dimensional image of subject S. The 3-dimensional image may contain spatial information of the target and healthy tissue. 
     In some embodiments, a cone-beam CT image of subject S is acquired while delivering radiation to the subject. The 2-dimensional images may be taken from around the same trajectory  30  and in the same time interval that the radiation is delivered to subject S. In such embodiments, the resultant cone-beam CT image will be representative of the subject position, including the 3-dimensional spatial distribution of target and healthy tissue, at the time the subject was treated. The spatial distribution of target and healthy tissue can be referenced to the particular radiation delivery apparatus, allowing an observer to accurately assess what radiation dose distribution was actually delivered to the target and healthy tissue structures. 
     Subject S, and more particularly, the locations of target and healthy tissue, can move during radiation delivery. While some movement can be reduced or eliminated, one difficult movement to stop is respiration. For example, when subject S breathes, a target located inside the lung may shift as a function of the breathing cycle. In most dose simulation calculations, subject S is assumed to be stationary throughout the delivery. Accordingly, ordinary breathing by subject S can result in incorrect delivery of dose to the target and healthy tissue. In some embodiments, radiation source  12  is activated only when a position or configuration of subject S is within a specified range. 
     In some embodiments, one or more sensors are used to monitor the position of subject S. By way of non-limiting example, such sensors may include respirometer, infrared position sensors, electromyogram (EMG) sensors or the like. When the sensor(s) indicate that subject S is in an acceptable position range, radiation source  12  is activated, the configuration of beam-shaping mechanism  33  changes and the motion axes move as described in the radiation treatment plan. When the sensor(s) indicate that subject S is not in the acceptable position range, the radiation is deactivated, the configuration of beam-shaping mechanism  33  is fixed and the motion axes are stationary. An acceptable position range may be defined as a particular portion of the respiratory cycle of subject S. In such embodiments, the radiation treatment plan is delivered intermittently, with intervals where the radiation apparatus and radiation output are paused (i.e. when the subject is out of the acceptable position range) and intervals where the radiation apparatus and radiation output are resumed (i.e. when the subject is in the acceptable position range). Treatment delivery proceeds in this way until the treatment plan has been completely delivered. The process of position dependent delivery of radiation may be referred to as “position gating” of radiation delivery. 
     In one particular embodiment of the invention, cone-beam CT images are acquired while position gated treatment is being delivered to subject S. The acquisition of 2-dimensional projection images may also gated to the patient position, so that the cone-beam CT images will represent the position of subject S at the time of treatment delivery. Such embodiments have the additional benefit that the 2-dimensional cone-beam CT images are obtained with subject S in a consistent spatial position, thereby providing a 3-dimensional cone-beam CT with fewer motion artifacts. 
     As discussed above, in some embodiments where beam-shaping mechanism  33  comprises a MLC  35 , it is possible to optimize beam-shape parameters including, without limitation: the positions of MLC leaves  36  and the corresponding shape of the MLC apertures  38 ; and the MLC orientation angle φ about beam axis  37 . In other embodiments where beam-shaping mechanism  33  comprises a MLC  35 , it may be desired to maintain a constant MLC orientation angle φ about beam axis  37 —e.g. where a particular radiation delivery apparatus  10  does not permit adjustment of MLC orientation angle φ during delivery and/or where processing power used in the optimization process is at a premium. 
     Where MLC orientation angle φ is maintained constant, MLC  35  may have certain limitations in its ability to approximate arbitrary beam shapes. In such instances, the selection of the particular constant MLC orientation angle φ may impact treatment plan quality and ultimately the radiation dose that is delivered to subject S. An example of this scenario is illustrated schematically in  FIGS.  16 A and  16 B , where it is desired to provide a beam shape  301 . In the  FIG.  16 A  example, leaf-translation directions  41  are oriented substantially parallel with the motion of beam  14  along source trajectory direction  43  (i.e. MLC orientation angle φ=0°). In the  FIG.  16 B  example, leaf-translation directions  41  are oriented substantially orthogonally to the motion of beam  14  along source trajectory direction  43  (i.e. MLC orientation angle φ=90°). It can be seen by comparing  FIGS.  16 A and  16 B  that when φ=0° ( FIG.  16 A ), the beam shape of MLC  35  does a relatively good job of approximating desired beam shape  301 , whereas when φ=90° ( FIG.  16 B ), there are regions  303  where MLC does a relatively poor job of approximating desired beam shape  301 . 
     While not explicitly shown in  FIGS.  16 A and  16 B , it will be understood that if desired beam shape  301  was rotated 90° from the orientation shown in  FIGS.  16 A and  16 B , then the MLC orientation angle φ=90° would produce a relatively accurate beam shape relative to the MLC orientation of φ=0°. Accordingly, selection of a constant MLC orientation φ may impact treatment plan quality and ultimately the radiation dose that is delivered to subject S. It is therefore important to consider which MLC orientation angle φ to select when using a constant MLC orientation angle φ to plan and deliver radiation to a subject S. 
     One aspect of the invention provides for radiation planning and delivery systems which provide a constant MLC orientation angle φ having a generally preferred value. Consider a trajectory  30  where radiation is delivered to a subject where there are substantially opposing radiation beams throughout the trajectory—i.e. beams that are parallel but have opposing directions. By way of non-limiting example, such a trajectory  30  may comprise rotation of gantry  16  through one full rotation of 180° or more.  FIG.  17    shows the projections  305 A,  305 B of target  307  and healthy tissue  309  for opposing beam directions (e.g. a gantry angle of 0° ( 305 A) and a gantry angle of 180° ( 305 B). The projection of target  307  and healthy tissue  309  is approximately mirrored for the parallel and opposing beam directions. 
     It follows that a desirable beam shape from parallel and opposing beam directions will also be approximately mirrored. This observed symmetry may be exploited by selecting MLC orientation angles φ that result in a superior radiation plan. Consider the examples shown in  FIGS.  16 A and  16 B  with respect to the shaping capabilities of MLC  35 . For the two orientations shown in  FIG.  16 A  (φ=0°) and in  FIG.  16 B  (φ=90°), mirroring the desired beam shape will not change the ability of MLC  35  to create desired beam shape  301  because of the mirror symmetry already inherent in MLC  35 . In particular embodiments, MLC orientation angle φ is selected to exploit the mirroring of opposing beam projections by choosing an MLC orientation φ that is not 0° or 90° such that the MLC orientations φ with respect to the subject S will be different for opposing beam directions. 
     For example, choosing MLC orientation angle φ such that |φ|=45° (where |●| represents an absolute value operator) will result in MLC orientations that are orthogonal to one another (i.e. with respect to the projection of subject S) when the beam is oriented in opposing beam directions. This is shown in  FIGS.  18 A and  18 B  which show MLC  35  and the projections of target  307  and healthy tissue  309  for opposing beam directions corresponding to opposing gantry angles of 0° ( FIG.  18 A ) and 180° ( FIG.  18 B ) and in  FIGS.  18 C and  18 D  which show MLC  35  and the projections of desired beam shape  301  for opposing beam directions corresponding to opposing gantry angles of 0° ( FIG.  18 C ) and 180° ( FIG.  18 D ). With this MLC orientation angle |φ|=45°, the beam shaping limitations associated with constant MLC orientation angle φ are thereby reduced because effectively two different MLC orientation angles φ are available for opposing beam directions and may be used to provide a desired beam shape. 
     Other MLC orientation angles φ that are not φ=0° or φ=90° may also provide this advantage. Currently preferred embodiments incorporate MLC orientation angles φ such that |φ| is in a range 15°-75° and particularly preferred embodiments incorporate MLC angles φ where |φ| is in a range of 30°-60°. The benefit of selecting MLC orientation angles φ within these ranges may be realized for all substantially opposed beam orientations throughout the delivery of radiation and may be provided by any trajectories which comprise one or more substantially opposed beam directions. Non-limiting examples of such trajectories  30  include: trajectories  30  which comprise rotations of gantry  16  about axis  18  by any amount greater than 180° (e.g. 360° rotations of gantry  16  about axis  18 ) and trajectories  30  which comprise multiple planar arcs wherein at least one of the arcs comprises opposing beam directions. Selection of MLC orientation angles φ within these ranges is not limited to trajectories  30  comprising opposing beams and may be used for any trajectories. These advantages of increased MLC shaping flexibility may be manifested as increased plan quality, reduced delivery time, reduced radiation beam output requirements or any combination of the above. 
     A further desirable aspect of providing MLC orientation angles φ that are not φ=0° or φ=90° relates to physical properties of typical MLCs  35 . Although individual MLC leaves  36  block most of radiation from radiation source  12 , there is often some undesirable radiation leakage that permeates MLC  35  and there is a relatively large amount of radiation leakage at the edges of MLC leaves  36  where they translate independently relative to each other. Choosing a MLC orientation angle φ=0° with respect to the motion of beam  14  along source trajectory direction  43  may result in interleaf radiation leakage that is compounded in planes defined by the edges of MLC leaves  36  and the beam axis  37  for particular trajectories  30 . MLC orientation angles φ other than φ=0° may cause the orientation of the interleaf leakage planes to change along the trajectory  30 , thereby reducing any systematic accumulation of unwanted radiation leakage and corresponding unwanted dose within subject S. 
     The edges of MLC leaves  36  may be constructed with a tongue-and-groove shape on each side for reduction of interleaf leakage. For some beam shapes, such tongue-and-groove MLC leaf edges may cause an unwanted reduction in radiation dose delivered to subject S. Similar to the effect on inter-leaf leakage, the tongue-and-groove underdosage effect will be compounded along the leaf edges. Selecting MLC orientation angles φ other than φ=0° may reduce systematic underdosing of the subject S caused by these tongue-and-groove leaf edges. 
     Additional considerations that affect the selection of MLC orientation angle φ include the maximum speed of MLC leaves  36  as well as the ability of MLC  35  to create shapes that continuously block areas of important healthy tissue  309  while maintaining a relatively high dose to target  307 . 
     When it is desirable to block a central portion of radiation beam  14 , it can be more efficient to choose a MLC orientation angle φ other than φ=0°. In particular circumstances, blocking a central portion of radiation beam  14  may be achieved more efficiently when the MLC orientation angle φ is approximately φ=90°. In contrast, when there are dramatic changes in desired beam shape as source  12  moves along its trajectory  30 , it may be difficult for MLC leaves  36  to move into position with sufficient speed. Generally, the desired projection shape  301  will change more rapidly in the direction  43  of source motion along trajectory  30 . It may therefore be desirable to have leaf-translation axis  41  oriented to approximately the same direction  43  as the source motion along trajectory  30 . Such a selection would result in a MLC orientation angle φ of approximately φ=0°. 
     The competing benefits/disadvantages of a MLC orientation angle φ of 0° versus 90° may be mitigated by using a MLC orientation angle φ that is substantially in between these two angles (i.e. approximately |φ|=45°. It will be appreciated that a MLC orientation angle φ of exactly |φ|=45° is not essential and other factors specific to the given subject S to be irradiated may need to be considered when selecting a MLC orientation angle φ. 
     Certain implementations of the invention comprise computer processors which execute software instructions which cause the processors to perform a method of the invention. For example, one or more data processors may implement the methods of  FIG.  4 A  and/or  FIG.  8    by executing software instructions in a program memory accessible to the data processors. The invention may also be provided in the form of a program product. The program product may comprise any medium which carries a set of computer-readable signals comprising instructions which, when executed by a data processor, cause the data processor to execute a method of the invention. Program products according to the invention may be in any of a wide variety of forms. The program product may comprise, for example: physical media such as magnetic data storage media including floppy diskettes, hard disk drives, optical data storage media including CD ROMs, DVDs, electronic data storage media including ROMs, flash RAM, or the like. The computer-readable signals on the program product may optionally be compressed or encrypted. 
     Where a component (e.g. a software module, processor, assembly, device, circuit, etc.) is referred to above, unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention. 
     While a number of exemplary aspects and embodiments have been discussed above, those of skill in the art will recognize certain modifications, permutations, additions and subcombinations thereof. For example:
         In the embodiments described above, control points  32  used to define a trajectory  30  are the same as the control points used to perform the block  54  optimization process. This is not necessary. For example, a simple trajectory  30 , such as an arc of gantry  16  about axis  18  ( FIG.  1   ), may be defined by two control points at its ends. While such control points may define the trajectory, more control points will generally be required to achieve an acceptable treatment plan. Accordingly, the block  54 ,  154  optimization processes may involve using different (e.g. more) control points than those used to define the trajectory.   In the embodiments described above, constraints (e.g. constraints on the changes in beam position/orientation parameters between control points  32 , constraints on the changes in beam shape parameters between control points  32  and constraints on the changes in the beam intensity between control points  32 ) are used throughout the optimization processes  54 ,  154 . In other embodiments, the optimization constraints may be imposed later in the optimization process. In this manner, more flexibility is available in meeting the optimization goals  61  in an initial number of iterations. After the initial number of iterations is performed, the constraints may be introduced. The introduction of constraints may require that some beam position/orientation parameters, beam shape parameters and/or intensity parameters be changed, which may result in a need for further optimization to meet the optimization goals  61 .   In the embodiments described above, the beam position and beam orientation at each control point  32  are determined prior to commencing the optimization process  54 ,  154  (e.g. in blocks  52 ,  152 ) and are maintained constant throughout the optimization process  54 ,  154  (i.e. optimization processes  54 ,  154  involve varying and optimizing beam shape parameters and beam intensity parameters, while trajectory  30  remains constant). In other embodiments, the beam position and beam orientation parameters (i.e. the set of motion axis positions at each control point  32 ) are additionally or alternatively varied and optimized as a part of optimization processes  54 ,  154 , such that optimization processes  54 ,  154  optimize the trajectory  30  of the radiation delivery apparatus. In such embodiments, optimization processes  54 ,  154  may involve placing constraints on the available motion axis positions and/or the rate of change of motion axis positions between control points  32  and such constraints may be related to the physical limitations of the particular radiation delivery apparatus being used to deliver the dose to the subject S.   In some embodiments, the radiation intensity may be held constant and the optimization processes  54 ,  154  optimize the beam shape parameters and/or the motion axis parameters. Such embodiments are suitable for use in conjunction with radiation delivery apparatus which do not have the ability to controllably vary the radiation intensity. In some embodiments, the beam shape parameters may be held constant and the optimization processes  54 ,  154  optimize the intensity and/or the motion axis parameters.   There are an infinite number of possible trajectories that can be used to describe the position and orientation of a radiation beam. Selection of such trajectories are limited only by the constraints of particular radiation delivery apparatus. It is possible to implement the invention using any trajectory capable of being provided by any suitable radiation delivery apparatus.       

     It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and subcombinations as are within their true spirit and scope.