Patent Publication Number: US-9901749-B2

Title: Radiation system with rotating patient support

Description:
RELATED APPLICATION DATA 
     This application is a continuation of U.S. patent application Ser. No. 14/081,866, filed Nov. 15, 2013, which is a continuation of U.S. patent application Ser. No. 12/830,310, filed on Jul. 3, 2010, now issued as U.S. Pat. No. 8,588,369, which is a continuation-in-part of U.S. patent application Ser. No. 12/201,271, filed on Aug. 29, 2008, now issued as U.S. Pat. No. 7,773,723, which is a continuation of U.S. patent application Ser. No. 12/200,639 filed on Aug. 28, 2008, now issued as U.S. Pat. No. 7,835,494, the entire disclosures of all of the above applications are expressly incorporated by reference herein. 
    
    
     FIELD 
     This application relates generally to treatment and diagnostic systems, and more specifically, to treatment systems and diagnostic systems that involve a rotating beam source. 
     BACKGROUND 
     Radiation therapy has been employed to treat tumorous tissue. In radiation therapy, a high energy beam is applied from an external source towards the patient. The external source, which may be rotating (as in the case for arc therapy), produces a collimated beam of radiation that is directed into the patient to the target site. The dose and placement of the dose must be accurately controlled to ensure that the tumor receives sufficient radiation, and that damage to the surrounding healthy tissue is minimized. 
     Existing radiation machines for providing treatment radiation beam may include a bore, into which the patient is placed during a treatment procedure. Other radiation machines may include an arm that carries the radiation source, wherein the patient is placed at an operative position relative to the source during a procedure. Similarly, existing imaging machines, such as CT machines, for obtaining images of the patient also include a bore, into which the patient is placed during an imaging procedure. 
     Applicants of the subject application determines that the bores of existing treatment and imaging machines may be too small, and that a patient may not feel comfortable when confined within the limited space of the bore of the treatment or imaging machine. Also, for treatment and imaging machines that do not include a bore, but include an arm for carrying the radiation source, the configuration of the arm may be limiting in some situations. This is especially the case when the patient is overweight, and/or when a treatment or imaging session takes a while to complete. If the distance between the patient and the source is too small, the patient may not feel comfortable. Thus, applicants of the subject application determine that it would be desirable to provide a new patient support system for addressing the above problems. 
     SUMMARY 
     In accordance with some embodiments, a radiation system includes a radiation source, and a patient support for supporting a patient, the patient support located at an operative position relative to the radiation source such that the radiation source can deliver radiation towards the patient while the patient is supported on the patient support, wherein the patient support and the radiation source are positionable at least partially around a same spatial region. 
     In accordance with other embodiments, a radiation method includes placing a radiation source at a first gantry angle, delivering a first beam using the radiation source towards a target supported on a support, the first beam is delivered when the radiation source is at the first gantry angle and when the support is located at a first position, placing the radiation source at a second gantry angle, positioning the support at least partially around a spatial region to move the support from the first position to a second position, and delivering a second beam using the radiation source towards the target when the radiation source is at the second gantry angle and when the support is at the second position. 
     In accordance with other embodiments, a patient support system includes a patient support having a surface for supporting a patient, the patient support having a longitudinal axis, and a positioner coupled to the patient support for positioning the patient support, the positioner configured to rotate the patient support about an axis that is parallel to, and spaced away from, the longitudinal axis. 
     In accordance with other embodiments, a patient support system includes a patient support having a surface for supporting a patient and a longitudinal axis, and a positioner coupled to the patient support for positioning the patient support, wherein the positioner is configured to move the patient support along a path that has an arc, circular, or zig-zag shape, and wherein the path lies within a plane that forms an angle with the surface of the patient support. 
     Other and further aspects and features will be evident from reading the following detailed description of the embodiments, which are intended to illustrate, not limit, the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings illustrate the design and utility of embodiments, in which similar elements are referred to by common reference numerals. These drawings are not necessarily drawn to scale. In order to better appreciate how the above-recited and other advantages and objects are obtained, a more particular description of the embodiments will be rendered, which are illustrated in the accompanying drawings. These drawings depict only typical embodiments and are not therefore to be considered limiting of its scope. 
         FIG. 1  illustrates a system for delivering radiation in accordance with a treatment plan determined in accordance with embodiments described herein; 
         FIGS. 2 and 3  illustrate a method of determining a treatment plan in accordance with some embodiments; 
         FIG. 4  illustrates an example of a target region and three dose calculation points; 
         FIG. 5  illustrates an example of a fluence map representing fluence generated using a collimator; 
         FIG. 6  illustrates an example of converting fluence map into leaf sequencing; 
         FIG. 7  illustrates an example of converting fluence map into radiation source positioning; 
         FIG. 8  illustrates a radiation system in accordance with other embodiments; 
         FIG. 9  illustrates another radiation system in accordance with other embodiments; 
         FIG. 10A  illustrates a patient support system in accordance with some embodiments; 
         FIG. 10B  illustrates another patient support system in accordance with other embodiments; 
         FIGS. 11A-11C  illustrate examples of trajectories of a treatment plan; and 
         FIG. 12  is a block diagram of a computer system architecture, with which embodiments described herein may be implemented. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Various embodiments are described hereinafter with reference to the figures. It should be noted that the figures are not drawn to scale and that elements of similar structures or functions are represented by like reference numerals throughout the figures. It should also be noted that the figures are only intended to facilitate the description of the embodiments. They are not intended as an exhaustive description of the invention or as a limitation on the scope of the invention. In addition, an illustrated embodiment needs not have all the aspects or advantages shown. An aspect or an advantage described in conjunction with a particular embodiment is not necessarily limited to that embodiment and can be practiced in any other embodiments even if not so illustrated. 
       FIG. 1  illustrates a radiation treatment system  10  for delivering radiation in accordance with a treatment plan that is determined using techniques described herein. The system  10  includes a gantry  12  (in the form of an arm), a patient support  14  for supporting a patient, and a control system  18  for controlling an operation of the gantry  12 . The system  10  also includes a radiation source  20  that projects a beam  26  of radiation towards a patient  28  while the patient  28  is supported on support  14 , and a collimator system  22  for controlling a delivery of the radiation beam  26 . The radiation source  20  can be configured to generate a cone beam, a fan beam, or other types of radiation beams in different embodiments. 
     In the illustrated embodiments, the radiation source  20  is a treatment radiation source for providing treatment energy. In other embodiments, in addition to being a treatment radiation source, the radiation source  20  can also be a diagnostic radiation source for providing diagnostic energy. In such cases, the system  10  will include an imager, such as the imager  100 , located at an operative position relative to the source  20  (e.g., under the support  14 ). In some embodiments, the treatment energy is generally those energies of 160 kilo-electron-volts (keV) or greater, and more typically 1 mega-electron-volts (MeV) or greater, and diagnostic energy is generally those energies below the high energy range, and more typically below 160 keV. In other embodiments, the treatment energy and the diagnostic energy can have other energy levels, and refer to energies that are used for treatment and diagnostic purposes, respectively. In some embodiments, the radiation source  20  is able to generate X-ray radiation at a plurality of photon energy levels within a range anywhere between approximately 10 keV and approximately 20 MeV. Radiation sources capable of generating X-ray radiation at different energy levels are described in U.S. patent application Ser. No. 10/033,327, entitled “RADIOTHERAPY APPARATUS EQUIPPED WITH AN ARTICULABLE GANTRY FOR POSITIONING AN IMAGING UNIT,” filed on Nov. 2, 2001, and U.S. patent application Ser. No. 10/687,573, entitled “MULTI-ENERGY X-RAY SOURCE,” filed on Oct. 15, 2003. In further embodiments, the radiation source  20  can be a diagnostic radiation source. In the illustrated embodiments, the radiation source  20  is coupled to the arm gantry  12 . Alternatively, the radiation source  20  may be located within a bore. 
     In the illustrated embodiments, the control system  18  includes a processor  54 , such as a computer processor, coupled to a control  40 . The control system  18  may also include a monitor  56  for displaying data and an input device  58 , such as a keyboard or a mouse, for inputting data. In the illustrated embodiments, the gantry  12  is rotatable about the patient  16 , and during a treatment procedure, the gantry  12  rotates about the patient  16  (as in an arch-therapy). In other embodiments, the gantry  12  does not rote about the patient  16  during a treatment procedure. In such case, the gantry  12  may be fixed, and the patient support  14  is rotatable. The operation of the radiation source  20 , the collimator system  22 , and the gantry  12  (if the gantry  12  is rotatable), are controlled by the control  40 , which provides power and timing signals to the radiation source  20  and the collimator system  22 , and controls a rotational speed and position of the gantry  12 , based on signals received from the processor  54 . Although the control  40  is shown as a separate component from the gantry  12  and the processor  54 , in alternative embodiments, the control  40  can be a part of the gantry  12  or the processor  54 . 
     It should be noted that the system  10  is not limited to the configuration described above, and that the system  10  may have other configurations in other embodiments. For example, in other embodiments, the system  10  may have a different shape. In other embodiments, the radiation source  20  of the system  10  may have different ranges of motions and/or degrees of freedom. For example, in other embodiments, the radiation source  20  may be rotatable about the patient  28  completely through a 360° range, or partially through a range that is less than 360°. Also, in other embodiments, the radiation source  20  is translatable relative to the patient  28 . Further, the radiation source  20  is not limited to delivering treatment energy in the form of x-ray, and may deliver other types of radiation energy. For example, in other embodiments, the radiation source  20  may be a proton source for delivering protons to treat patient, or other types of particle source for delivering other types of particles for treating patient. 
       FIGS. 2 and 3  illustrate a method  200  of determining a radiation treatment plan that may be used by the system  10  in accordance with some embodiments. The method  200  will be described with reference to treating a target region TR using a radiation source  20  that rotates about the target region TR (e.g., 360° about the target region TR), as in an arc therapy ( FIG. 4 ). However, it should be understood that the method  200  is not limited to the example illustrated in  FIG. 4 , and that the method  200  may be used to determine other treatment plans with a different setup. For example, in other embodiments, the method  200  may be used to determine a treatment plan in which the radiation source  20  does not rotate completely about the TR, but only partially (e.g., less than 360° about the patient  28 ). 
     First, a number of dose calculation points are defined (step  202 ). A dose calculation point is used to represent a component that is a part of a divided treatment. In particular, the total dose of a treatment may be divided into components. A broadly defined dose calculation point contains the dose delivered during some part of the treatment. The sum of doses from all dose calculation points is the total dose of the treatment. The division of the treatment into components may be done with respect to various parameters in different embodiments. In the illustrated example, the treatment is initially divided into three components represented by dose calculation points DC 1 , DC 2 , DC 3 , wherein the division is done with respect to the gantry angles such that DC 1 , DC 2 , DC 3  represent respective 120° gantry ranges ( FIG. 4 ). Division of a treatment based on gantry angles may be useful in determining treatment plans for arc treatments. In other embodiments, the number of dose calculation points may be different from three. For example a 360° treatment can be divided into 10° components, in which case, the number of dose calculation points would be 36. Each component would cover the dose delivered in different 10° gantry angle intervals. In further embodiments, instead of having each dose calculation point representing an interval with a same range, the dose calculation points may represent respective intervals with different ranges (e.g., DC 1  may represent gantry angles from 0°-180°, DC 2  may represent gantry angles from 180°-300°, and DC 3  may represent gantry angles from 300°-360°). 
     In the illustrated embodiments, for each of the dose calculation points, the radiation can be modeled by assuming radiation coming from one fixed gantry angle. For example, for the dose calculation point covering dose from 0° to 120°, the dose can be calculated by assuming that all radiation in this 0° to 120° interval is coming from 60° angle. It is easier and faster to calculate the dose from a single fixed ganty angle than from a curved path from 0° to 120°. 
     For each of the dose calculation points, the radiation that is desired to be delivered is modeled by considering fluence. Fluence is the amount of radiation passing through a spatial region, and may be represented by a fluence map. A fluence map is a matrix that covers a spatial region (e.g., a plane). For each point in the plane, the fluence map defines the amount of radiation passing through that element.  FIG. 5  illustrates an example of a fluence map. In the example, the radiation source sends radiation with strength  2 . There is a block  502  (which may be, for example, a leaf of a collimator) in the middle of radiation beam blocking half of the radiation passing through that block. For example, the  502  block may be extended half way to allow radiation to pass through half of a prescribed region. Alternatively, the block  502  may be retracted to let radiation pass through the region half the time, and may be dosed completely to prevent radiation from passing through the region the other half the time. The fluence in the fluence plane is 0 in parts where the collimator leaves  504  block the radiation to prevent the radiation from passing through. The fluence is 2 where all the radiation from source reaches (and passes through) fluence plane. The fluence is 1 where half of the radiation was blocked by the  502  block. The matrix of fluence elements form a fluence map 00002120000. 
     In some cases, a computer user interface, such as a screen and an input device, may be provided for allowing a user to input data for defining dose calculation points. For example, the screen may display one or more input fields for allowing the user to input the data, such as number of dose calculation points, and treatment division parameters. The screen may also display input fields for allowing user to input target region size, target region shape, maximum allowable dose, minimum required dose, etc. The displaying of the input fields may be done in response to a processor (which may be the same processor  54 , or a separate processor) and/or software executing a set of instruction. In such cases, the processor and/or the software determines the dose calculation points by receiving input by the user. 
     Returning to  FIG. 2 , next, the processor and/or the software performs optimization using the three defined dose calculation points DC 1 , DC 2 , DC 3  (Step  204 ). As discussed, the regions represented by respective dose calculation points DC 1 , DC 2 , DC 3  are modeled with respective fluence maps. In step  204 , the processor and/or software runs the fluence optimization for some number of iterations (e.g., 100). The objective of the optimization is to get fluence maps that produce best dose in patient  28  by optimizing the individual components in the fluence maps. In some cases, the optimization objective may be defined using DVH (dose volume histogram) constraints in patient dose. Dose volume histogram is a graph (function) DVH(x) that tells which fraction of a defined volume receives less than x dose, and DVH constraint is a constraint that describes which shapes of DVH are preferred. For example, a user may specify (e.g., using a user interface) not to put more than 30 Gy dose to spine, but to keep the dose in target between 60 and 70 Gy. The objective is to find out the best fluence map configuration at the various dose points that will give the desired dose at the target, while minimizing dose to healthy tissue outside the target DVH function and constraints am well known in the art. 
     Next, the method moves to dose calculation point level  2 , in which the interval for each dose calculation point is halved such that the treatment is modeled in six intervals (Step  206 ). The division can be done by assuming that two adjacent dose calculation points at level  2  have the same fluence as the parent fluence map at level  1 . So the dose calculation points DC 1  and DC 2  at level  2  would have a fluence map that is equal to the fluence map of dose calculation point DC 1  at level  1  times 0.5. As a result of Step  206 , six dose calculation points are modeled with six fluence maps. 
     Next, the processor and/or the software runs a number (e.g., 100) of iterations of fluence optimization again, this time using the dose calculation points DC 1 -DC 6  at level  2  (Step  208 ). The objective of the optimization is to get fluence maps that produce best dose in patient  28  by optimizing the individual components in the fluence maps for the six dose calculation points DC 1 -DC 6 . The technique for performing the optimization in step  208  may be the same as that described with reference to step  204 . 
     The complexity of all fluences at level  2  is then evaluated (Step  210 ). Various techniques may be used to evaluate the complexity of a fluence at any given level. In some embodiments, the complexity of a fluence is represented by the complexity of its corresponding fluence map. In such cases, the complexity of the fluence map is calculated by converting the fluence map to machine parameters, and calculating the time required to move the leaves based on the machine parameters. The more the time that is required to move the leaves to achieve a fluence profile, the more complex is the fluence. In other embodiments, instead of, or in addition to, using the time required to move the leaves to determine a complexity of a fluence, other parameters may also be used. For example, in other embodiments, the number of leaves that need to be moved in order to achieve a fluence may also be used to determine the complexity of the fluence. In such cases, the more the number of leaves that need to be moved, the more the complex the fluence. In further embodiments, the distance that the leaf(s) need to travel may also be used to determine the complexity of the fluence. In such cases, the more the distance, the more the complex the fluence. In other embodiments, any combination of the above parameters and/or other parameters not described herein may be used to determine a complexity of a fluence. 
     Next, the processor and/or the software converts all but the most complex fluence to machine parameters by using a leaf sequencing algorithm (Step  212 ).  FIG. 6  illustrates an example of converting a fluence map  600  to machine parameters using a leaf sequencing technique. As shown in the figure, the fluence represented by the fluence map  600  can be converted to leaf sequence (an example of machine parameter), which in the example, has four leaf positions  602   a - 402   d  at respective four time points t=1, 2, 3, 4. In particular, the leaves would first be dosed  602   a  at time step  1 . Then the leaves would be open in the regions shown in the leaf configuration  602   b  at time step  2 . Then the leaves would be open in the regions shown in the leaf configuration  602   c  at time step  3 . Then the leaves would be closed again  602   d  (time step  6 ). The fluence components  604   a - 604   d  for the respective leaf positions  602   a - 602   d  are also shown. As shown in the figure, the sum of the fluence components  604   a - 604   d  equals the fluence map  600 . In the illustrated example, the most complex region is in the dose calculation point  5  at level  2  ( FIG. 3 ). Thus, the processor and/or software converts all of the fluence to machine parameters, except that for dose calculation point  5 . In some cases, the processor and/or software determines whether a level of complexity of a fluence is below a prescribed threshold, and converts the corresponding fluence map to one or more machine parameters for the dose calculation point when it determines that the level of complexity is below the prescribed threshold. In other embodiments, the processor and/or software determines whether a level of complexity of a fluence is above a prescribed threshold, and converts the corresponding fluence map to one or more machine parameters for the dose calculation point when it determines that the level of complexity is above the prescribed threshold. 
     In the above example, each of the leaf positions  602   a - 602   d  is a machine parameter that corresponds with a machine control point. As used in this application, the term “machine control point” or “control point” refers to a component of a treatment plan that includes one or more machine parameters for prescribing a part of the treatment plan. For example, a treatment plan may be prescribed using N number of machine control points, each of which contains machine parameter(s) (such as any or a combination of: gantry speed, gantry angle, beam-on/activation signal, beam-off/deactivation signal, collimator position, leaves&#39; positions, couch position, beam energy, beam type, dose (or monitor units), and dose rate (or beam intensity)) for defining a part of the treatment plan. The number of machine control points that correspond with a fluence map may vary. For example, a complex fluence map may be converted into a higher number of leaves&#39; positions (machine control points), while a simpler fluence map may only require fewer machine control points to achieve the desired fluence. In some cases, the total number of machine control points in a complete treatment plan may be in the range of hundreds or even thousands. In the illustrated embodiments, the number of machine control points are higher than the number of dose calculation points. However, the dose at the dose calculation point is used to evaluate the machine parameters, thereby obviating the need to calculate dose for each of the machine control points, which in some cases, may take up a significant amount of computation time and resources. It has been discovered that determining dose at dose calculation points without doing the same at all of the machine control points can achieve a treatment plan that is sufficiently accurate. 
     It should be noted that a machine control point may be modeled with other parameters instead of, or in addition to, leaf sequencing.  FIG. 7  illustrates an example of converting a fluence map  700  to machine parameters using a leaf sequencing technique. As shown in the figure, the fluence represented by the fluence map  700  can be converted to radiation source positions (another example of machine parameters), which in the example, has four radiation source positions  702   a - 702   d  at respective four time points. In particular, the radiation source would first be placed at positions  702   a - 702   b  at respective time steps  1 - 4 . The fluence components  704   a - 704   d  for the respective radiation source positions  702   a - 702   d  are also shown. As shown in the figure, the sum of the fluence components  704   a - 704   d  equals the fluence map  700 . In the illustrated example, each of the radiation source positions  702   a - 702   d  corresponds with a machine control point. Thus, in the example, there are four machine control points that correspond with the fluence map at the corresponding dose calculation point. The number of machine control points that correspond with a fluence map may vary. For example, a complex fluence map may be converted into a higher number of radiation source positions (machine control points), while a simpler fluence map may only require fewer machine control points to achieve the desired fluence. In the above example, the radiation source is illustrated as translating. However, the same principle can be used with a radiation source  20  that rotates, with each time step corresponding to one machine control point. 
     In the above embodiments, the number of machine control points for each dose calculation point is constant. In other embodiment, the number of machine control points may be different for different dose calculation points, depending on the complexity of the fluence for the particular dose calculation point. Regardless of the number of machine control points, the dose calculation is always performed at the dose calculation points. There will be some error because the angle changes during rotation, but the error could be acceptable if the separation of final dose calculation points is small enough. For example there could be one dose calculation points every 1 or 2 degrees, but within that 1 or 2 degree range, there could be 1, 2, 3, 10, or 100 machine control points. It would be a waste of computation time to calculate the dose with 1/100 degree interval, because that level of accuracy is not required. The change in fluence may be significant due to leaf movement, but the change due to angular rotation may be too small to justify calculating dose at every machine control point. 
     Returning to  FIG. 2 , the optimization is continued (Step  214 ). In particular, gradient back projection technique is used in the optimization for fluence maps, and direct aperture method is used in the optimization for regions modeled with machine control points. In gradient back projection method, the derivatives of the objective function with respect to change in fluence are calculated in gradient map. It is called gradient back projection because the gradients are calculated in some volume elements, and the derivatives of the objective function at those volume elements are projected back and summed to fluence plane to form a gradient plane. Then the fluence is modified by adding the gradient plane to fluence plane (first the gradient plane values are multiplied by some scalar, because the scale is different). Direct aperture methods refer to directly modeling the treatment in machine parameters, wherein the gradient of objective function is calculated with respect to machine parameters and the machine parameters are changed according to the gradients. Thus, in gradient back projection technique, the objective function gradient is calculated with respect to the fluence sum elements, and in direct aperture technique, the objective function gradient is calculated with respect to leaf positions ( FIG. 6 ). In the illustrated embodiments, the dose is still calculated at dose calculation points. The average fluence from machine control points is accumulated at dose calculation point, and the dose is assumed to come from the dose calculation point. The optimization objective of the optimization in step  214  is the same as that described previously. In particular, the machine control points are modified so that they produce a desired fluence in the corresponding dose calculation point (which may represents a range of gantry angles for positions of the radiation source). The goal is to produce an optimal radiation fluence. 
     In some embodiments, the optimization in step  214  utilizes an iterative technique in which more and more dose calculation points are progressively converted into machine parameters as the number of iterations increases. Alternatively, the process  200  may repeat the step of converting fluence to machine parameters (Step  212 ) and the step of optimization (Step  214 ) until all of the dose calculation points (except the ones with the most complex fluence) modeled with fluence maps are converted to machine parameters at machine control points. The determined machine parameters are based on the complexity of fluence from other directions. Therefore the more demanding leaf movements have been considered, except for the range  240 - 300  corresponding with dose calculation point  5  at level  2  ( FIG. 3 ). For this range, because there is limited time to move leaves to achieve a complex fluence, the resulting fluence may only be partially accomplished. In order to address this, for this range which has been determined to have the most complex fluence, the processor and/or software uses a slower gantry rotation to determine the portion of the treatment that corresponds with this gantry range. With slower gantry rotation, there is more time to move the leaves and the more complex fluence can be converted to machine parameters more accurately (Step  216 ). In other embodiments, in addition to prescribing a slower gantry speed, the processor and/or software can also use more control points (e.g., more machine control points and/or more dose calculation points) for the complex region(s). Such technique will also allow the more complex fluence to be accomplished more accurately. Also, in other embodiments, different maximum speeds of gantry rotation may be prescribed for different gantry ranges/intervals. In such cases, the machine parameters are determined for the corresponding control points based on the prescribed maximum speed for the corresponding gantry range/interval. 
     After all of the fluence has been converted to machine parameters at machine control points, the processor and/or software performs optimization again using the machine parameters for all of the dose calculation points (Step  218 ). The objective of this optimization is to fine tune the previously determined machine parameters such that they produce the desired fluence at the various dose calculation points. The resulting machine parameters for the machine control points are then stored as a treatment plan in a medium for later use (Step  220 ). 
     In some embodiments, the method  200  may go one level further, e.g., to level  3 , where dose calculation points are increased such that the dose calculation points and machine control points could coincide, but this is not always necessary. This is because the treatment is modeled using final accuracy of machine control points inside the dose calculation point and keeping the machine control points valid (so that the machine would be able to deliver the treatment as presented in machine control points). However, the dose is not calculated from the direction of all machine control points. The total radiation fluence from all of the machine control points belonging to one dose calculation points is first calculated (this is a fast step). Then the dose in patient is calculated from the fluence map in control point. Therefore the part of the treatment modeled as machine control points is a valid treatment. The division to even more dose calculation points is done to decrease another source of error in dose calculation. Large angular separation between dose calculation points may also produce error in dose calculation. Thus, it is desirable that there be enough dose calculation points at final level to have good enough angular dose calculation accuracy, but that number can be smaller that the required number of machine control points. In other embodiments, it could also be same. 
     So even when the treatment in dose calculation point is modeled as machine parameters, the fluence of a treatment resulting from those machine control points is first calculated and the dose in patient is calculated from that fluence. Maintaining the delivery information in machine control points accounts for machine limitation, such as leaf speed and geometry. On the other hand, when the delivery in dose calculation point is modeled as a fluence only, it ignores most of the machine limitations. The unconstrainted optimization is faster and less sensitive to local minima. 
     In the above embodiments, the processor and/or software evaluates the complexity of fluence in order to determine which control points to change in an iteration, and the conversion starts from most simple interval. Such technique allows the simpler parts of the treatment plan to be determined early on. In other embodiments, the conversion may be based on a different technique. For example, in other embodiments, the conversion may start from most complex interval. Such technique would allow the optimizer to determine the most difficult conversion problems early on in the optimization process. In other embodiments, instead of determining control points to convert based on complexity, all of the control points may be converted regardless of the fluence complexity. In further embodiments, the processor and/or software may use spatial order. For example, control points in first range of angles 0°-10° may be converted, then control points for angles 10°-20° are converted, and then the control points for angles 20°-30° are converted. This technique removes the connectivity problem of machine parameters. 
     In the above embodiments, the initial number of dose calculation points is small, and is then increased progressively (e.g., from dose calculation level  1  to dose calculation level  2 ) as the treatment plan is refined. There are two benefits in having small number of dose calculation points initially. First, the optimization may be accomplished faster because the total dose can be evaluated more quickly using fewer number of dose calculation points. Second, the leaf sequencing may be accomplished easier because there is more time (the treatment time modeled in a dose calculation interval is longer) for the leaves to move to produce the desired fluence. As illustrated above, at some point during the treatment planning phase, the fluence maps are desired to be converted to machine parameters. The conversion is not perfect—i.e., because of machine limitation, some parts of the resulting fluence may be different from that calculated at the dose calculation points. This means that the resulting dose may be different from the optimized one. After the conversion has been done, the optimization can be continued in that interval using direct machine parameter optimization methods. This way the treatment planning can first benefit from quick convergence to a good solution (with less consideration of machine limits), and then can decrease the err resulting from the conversion of fluence maps to machine parameters using direct machine parameter optimization (applying machine limits). As illustrated above, the process could first model all intervals of the treatment using fluence maps. Then one or more of the fluence maps are converted to machine parameters. Optimization is continued, in which fluence optimization is used for intervals modeled by fluence maps, and direct machine parameter optimization is used for intervals that are modeled by machine parameters. The errors resulting from the conversion are decreased very efficiently by other intervals modeled by fluence maps. In such technique, more and more intervals are converted to machine parameters as the optimization progresses. Finally the treatment is modeled by machine parameters. 
     In some cases, practical solution would be to start with only a few dose calculation points, all modeled by unconstrained fluences. Just before the number of dose calculation points is increased, the fluences are converted to machine control points. Because of the small number of dose calculation points, the time they model is longer and the leaf sequencing is easier. Then, to decrease the dose calculation error produced by angular separation, the number of dose calculation points is increased. However, it may be desirable to perform the transition from unconstrained fluences to machine control points in early phase due to easier leaf sequencing. 
     In other embodiments, instead of having two dose calculation point levels before step  212 , the method  200  may include additional dose calculation point level(s). Also, in other embodiments, the dose calculation points may increase at any part of the method  200 . For example, the method  200  can repeat steps  206 ,  208  to increase dose calculation points and perform optimization at any time during the method  200  (See arrows  230 ,  240 ,  250  in  FIG. 2 ). In further embodiments, the method  200  may include only one dose calculation point level. In such cases, steps  206 ,  208  may be omitted. Also, in other embodiments, instead of increasing dose calculation points by subdividing the intervals for all of the dose calculation points, only the intervals for a subset of all the dose calculation points are subdivided to increase the number of dose calculation points. In any of the embodiments described herein, the optimization used by the method  200  is an iterative technique, in which cases, the number of dose calculation points may be increased at any one of the iterations. 
     In the above embodiments, the process  200  initially models parts of a treatment (e.g., an arc treatment) in 120° intervals of gantry angles with fluence maps. In other embodiments, the treatment may be modeled in other intervals (e.g., 1°, 5°, 10°, etc.) of gantry angles. Also, in other embodiments, the treatment may be modeled initially using fluence maps for some intervals, and machine parameters (e.g., leaf positions) for other intervals. For example, in other embodiments, the treatment may be divided into components, for example in 10 degree intervals in gantry angle, in which the first three intervals may be modeled by fluence maps and the rest of 33 intervals with direct machine parameters. Both modeling techniques to present part(s) of treatment have their advantages. A fluence map can very efficiently represent radiation from some direction and there are very efficient optimization methods to find good fluence maps. However, in some cases, it may be difficult to model machine limitations with fluence map optimization. On the other hand, if a part of the treatment in an interval is modeled using machine parameters, it is easier to apply machine limitations in optimization. However, these optimization methods may be slower, more constrained, and may be more easily trapping into a local minima. 
     In the above embodiments, the division of the treatment into components is done with respect to the gantry angles. In other embodiments, the division of the treatment into components may be done with respect to other parameters. For example, in other embodiments, the dose calculation points may be defined so that they correspond with respective time. For example a 60 second treatment can be divided into 6 dose calculation points. First dose calculation point would cover the dose delivered from 0 second to 10 second, second dose calculation point from 10 second to 20 second, and so on. 
     In other embodiments, the dose calculation points may be defined so that they correspond with monitor units. Monitor units is the amount of radiation units produced by the machine  10 . For example a 600 MU treatment may be divided into 3 dose calculation points. First dose calculation point would cover the dose delivered from 0 to 200 MU, second dose calculation point would cover the dose delivered from 200 to 400 MU, and third dose calculation point would cover the dose delivered from 400 to 600 MU. 
     In other embodiments, the dose calculation points may be defined so that they correspond with respective regions of the patient  28  (e.g., different parts of a target region). 
     In other embodiments, the dose calculation points may be defined such that they correspond to some other geometric parameters. For example, the dose calculation points may be defined such that they correspond with respective positions of the support  14  (e.g., couch) along its longitudinal axis, with respective angles of the support  14 , or respective collimator angles. 
     In the above embodiments, the treatment is described as involving rotating the radiation source  20  at least partially around the patient  28 . However, in other embodiments, the treatment may also involve translating the patient  28  relative to the radiation source  20 .  FIG. 8  illustrates another embodiment of a radiation system  10  in which the patient support  14  is translatable. The system  10  includes a gantry  12  having an arm  800 , a support structure  802  to which the gantry is rotatably coupled, and a radiation source  20 . In the illustrated embodiments, the patient support  14  is coupled to a positioner  804 , which is for translating the patient support  14  in a back and forth manner. During use, the radiation source  20  rotates at least partially around the patient  28  so that radiation can be delivered to target region from a plurality of gantry angles. Also, during use, the positioner  804  moves the patient support  14  along the longitudinal axis  806  (the Z-axis) forward  808  and backward  810 , so that different parts of the target region along the axis  806  may receive radiation from a plurality of gantry angles. Thus, by coupling the rotation of the radiation source  20  with the translation of the patient support  14 , any part of the target region along the axis  806  may be treated by radiation delivered from a plurality of gantry angles. The system  10  of  FIG. 8  is advantageous for treating target that cannot be irradiated with one gantry rotation using existing systems. For example, the system  10  may be used to perform whole body irradiation or irradiation of long tumor near spine with one continuous radiation trajectory. Also, providing back and forth trajectories is desirable in that it results in control points that represent independent degrees of freedom in the optimization that have independent constraints. In addition, translating the patient support  14  in a back and forth manner during a treatment saves time. The trajectory is simple and easy to understand spatially, and saves treatment planning time. This allows the trajectory to be evaluated easily, and used for many purposes. In some cases, the radiation source  20  may be stationary while the patient support  14  is translated back and forth. This allows radiation to be modulated along the axis  806  such that different parts of the target region along the axis  808  receives different amount of radiation (i.e., for a given gantry angle). 
     The above described trajectory also allows collision between radiation device and patient  28 /support  14  to prevented more easily. This is because in the above described trajectory, the radiation source moves relative to the patient  28  and support  14  in paths that form a cylinder. Cylinder is relatively easy to understand spatially, and therefore, a user may more easily evaluate a risk of collision for such trajectory than for a more complex trajectory. In some embodiments, the system  10  uses a collision prevention mechanism that involves comparing an image of the patient  28  and the support  14  with a cylinder/ring with a specific radius, and checking to see if the cylinder/ring collides with the patient  28  or support  14 . Because the support  14  moves back and forth along the same route, the collision detection cylinder will be the same for all passes. This simplifies the collision detection. 
     In other embodiments, instead of moving the patient support  14 , the radiation source  20  may be translatable in the Z-axis direction. In either case, the patient support  14  and the radiation source  20  may be considered as moveable or translatable relative to each other. In further embodiments, the radiation source  20  may be configured to tilt about an axis (e.g., axis  812 ) that forms an angle (e.g., 90°) relative to the longitudinal axis  806 . During use, the radiation source  20  tilts about the axis  812  so that radiation may be delivered to different parts of the target region along the axis  806 . The radiation source  20  also rotates at least partially around the patient  28  so that it can deliver radiation to the target region from a plurality of gantry angles. 
     In other embodiments, the patient support  14  may be configured to rotate during the treatment.  FIG. 9  illustrates another embodiment of a radiation system  10  in which the patient support  14  is configured to rotate in correspondence with the rotation of the radiation source  20 . In the illustrated embodiments, the patient  28  with the support  14  is shifted away from the isocenter  900 . During use, the radiation source  20  rotates at least partially along path  902  to deliver radiation to the patient  28  from a plurality of gantry angles. In correspondence with the position of the radiation source  20 , the patient support  14  is configured (e.g., using a positioner) to rotate at least partially along path  904 . As shown in the figure, at another point in time during a treatment procedure, the radiation source is moved to another gantry position (represented by reference numeral  20 ′), and accordingly, the support and the patient are moved dynamically around spatial region  908  such that the support and the patient is at operative positions (represented by reference numerals  14 ′,  28 ′) opposite from the radiation source. Such configuration is beneficial in that it provides relatively more room between the patient  28  and the radiation source  20 , thereby allowing bigger and heavier patient (which may otherwise be impossible if the support  14  is closer to the isocenter) to be treated. Such feature is also advantageous in that it allows the patient  28  who is being treated to feel more comfortable (especially if the patient  28  is claustrophobic), and reduces the risk of having the patient  28 /support  14  collide with the radiation source  20 . Such feature is also advantageous in that it provides more room between the patient and the radiation source  20  without changing a size of a bore (or a configuration of an arm if an arm is used instead of a bore) of an existing machine. Another advantage of such feature is that it allows a wider target area to be treated. This is because as the distance between the patient and the radiation source is increased, the fan shape of the radiation beam will “fan-out” or diverge more before it reaches the patient. In the illustrated embodiments, the radiation source  20  and the patient support  14  (with the patient  28 ) both rotate at least partially around a spatial region  908 , and about an axis (which may coincide with, or locate next to, isocenter  900 ). It should be noted that the term “around” (e.g., as in “around a spatial region”) is not limited to movement by the support  14  or source  20  that is in an arc or circular path, and that the term “around” may refer to movement by the support  14  or source  20  that is in other path shapes in different embodiments, as long as the trajectory of the support  14  or source  20  forms a loop that surrounds the spatial region, or a partial loop (e.g., an arc that is less than 360°) that partially surrounds a part of the spatial region. In other embodiments, the radiation source  20  and the patient support  14  (with the patient  28 ) may rotate about different respective axes that are parallel to, and spaced apart from, each other. 
       FIG. 10A  illustrates a patient support system  1000  that may be used to move the patient support  14  in the manner described in the embodiment of  FIG. 9 . The patient support system  1000  includes a base  1002 , an arm  1004 , and the patient support  14 . The arm  1004  has a first end  1006  that is rotatably coupled to the base  1002 , and a second end  1008  that is rotatably coupled to the support  14 . In particular, the arm  1004  is rotatable about an axis  1010  relative to the base  1002 , and is also rotatable about another axis  1012  relative to the support  14 . During use, a positioning device (e.g., a motor) in the base  1002  rotates the arm  1004 . As the arm  1004  rotates about the axis  1010 , the support  14  is rotated relative to the arm  1004  about the axis  1012  such that the support surface of the support  14  always faces upward while the support  14  is rotated about the axis  1010 . In other embodiments, the patient support system  1000  may further include a positioning device coupled between the support  14  and the arm  1004  for translating the support  14  back and forth along axis  1014 . This allows the patient support system  1000  to be used in a similar manner as that described with reference to  FIG. 8 . It should be noted that the patient support system  1000  is not limited to the configuration described previously, and that the patient support system  1000  may have other configurations (e.g., may have different degrees of freedom) in other embodiments, as long as the patient support  14  can move at least partially around the patient  16 . 
       FIG. 10B  illustrates another patient support system  1040  that may be used to move the patient support  14  in the manner described in the embodiment of  FIG. 9 . The patient support system  1040  includes a base  1002 , a first positioner  1050 , a second positioner  1052 , and the patient support  14 . The first positioner  1050  is configured to move the patient support  14  vertically, e.g., in an upward or downward direction along a vertical axis, as illustrated by the arrow  1054 . The second positioner  1052  is configured to move the patient support  14  in a lateral direction, e.g., in a left or right direction along a horizontal axis, as illustrated by the arrow  1056 . The patient support  14  is translatable relative to the second positioner  1052  along its longitudinal axis, as illustrated by the arrow  1058 . In other embodiments, the patient support  14  may be fixedly secured to the second positioner  1052 . In such cases, the second positioner  1052  may be configured to translate relative to the first positioner  1050  in both the lateral direction  1056  and the longitudinal direction  1058 . Also, in further embodiments, the first and second positioners  1050 ,  1052  may be parts of a positioner system. It should be noted that the patient support system  1040  is not limited to the examples described, and that the patient support system  1040  may have other configurations. For example, in other embodiments, the patient support system  1040  may have additional degree(s) of freedom in the positioning of the patient support  14 . Also, in other embodiments, instead of having two positioners  1050 ,  1052  that translate in different respective directions, the patient support system  1040  may have one positioner for moving the patient support  14  in both the vertical direction  1054 , and the lateral direction  1056 . In such cases, the positioner may include a first component for translating the patient support  14  along a first axis (e.g., a vertical axis), and a second component for translating the patient support  14  along a second axis (e.g., a horizontal axis). 
     During use of the patient support system  1040 , the patient support system  1040  is aligned with the radiation source  12 , like that shown in  FIG. 9 . The positioners  1050 ,  1052  are then operated to move the patient support  14  along path  904  in one direction, while the radiation source  12  is moved along path  902  in the same direction but on the opposite side of the spatial region  908  facing towards the patient support  14 . In the illustrated embodiments, the movement of the patient support  14  along the path  904  may be accomplished by simultaneously translating the patient support  14  in both the vertical direction  1054  and the lateral direction  1056 , and synchronizing the sliding motions in these two directions in the manner shown in graph  1060 . In the graph  1060 , the x-axis represents time, and the y-axis represents the position for each of the vertical and lateral movements. As shown in the graph  1060 , the sliding of the patient support  14  in the lateral direction  1056  (represented by the solid line) is performed in a sinusoidal manner, and the sliding of the patient support  14  in the vertical direction  1054  (represented by the dashed line) is also performed in a sinusoidal manner. Synchronizing the sliding motions in the lateral and vertical directions  1056 ,  1054  (along the horizontal and vertical axes, respectively) to a common time base like that shown in graph  1060  will cause rotation of the patient support  14  in trajectory  904 . In some embodiments, the motions in the lateral and vertical directions occur simultaneously so that the resulting path has an arc or circular shape. In other embodiments, the motions in the lateral and vertical directions may occur in an alternating manner such that the resulting path has a zig-zag configuration. Also, in further embodiments, the zig-zag motion may be implemented using translation along other axes (e.g., translation along direction  1054  and along the longitudinal direction  1058 , or translation along direction  1056  and along the longitudinal direction  1058 ). In any of the embodiments described herein, the movement of the patient support  14  may involve accelerating and/or decelerating the patient support  14  smoothly to avoid moving the patient in an abrupt manner. 
     It should be noted that the trajectory technique described with reference to  FIGS. 9-10  may be implemented for a treatment system (e.g., a radiation treatment system configured to deliver treatment radiation beam), or a diagnostic system (e.g., a radiation diagnostic system for delivering radiation beam for imaging purpose). Also, in any of the embodiments described herein, the patient support  14  may be configured to tilt about one or more axes. In such cases, the patient support  14  may further include a device (e.g., a belt, a harness, etc.) for securing the patient relative to the patient support  14 . 
     It should be noted that any of the trajectories described herein (including the trajectory described with reference to  FIGS. 8 and 9 ) may be used in the treatment planning method  200  described with reference to  FIG. 2 . For example, with respect to the embodiments of  FIG. 9 , the method  200  may involve defining a parameter that corresponds with rotation of the patient support  14 . In such cases, the rotation parameter may be optimized during the method  200  (e.g., in step  204 ,  208 ,  214 , and/or  218 ). Similarly, with respect to the embodiment of  FIG. 8 , the method  200  may involve defining a parameter that corresponds with a translation of the patient support  14 . In such cases, the translation parameter may be optimized during the method  200  (e.g., in step  204 ,  208 ,  214 , and/or  218 ). As discussed, providing back and forth trajectories is desirable in that it results in control points that represent independent degrees of freedom in the optimization that have independent constraints. As used in this specification, the term “optimization” (or variation thereof—e.g., optimizes, optimizing, etc.) refers to the act of making something better, which may involve changing a value of a parameter, wherein the changing of the value may be performed manually by a user, or automatically using an optimization software. 
       FIG. 11A  illustrates an example of a user interface  1100  that may allow a user to determine a treatment plan in accordance with some embodiments. As used in this specification, the term “user” may refer to a single person, or a plurality of persons. In some cases, the user interface  1100  may be used in the method  200  to determine a treatment plan. The user interface  1100  includes a screen  1102  displaying an input interface  1104 . The input interface  1104  may be generated by a processor that executes a set of instruction programmed to provide the image of the input interface  1104 . In the illustrated embodiments, the input interface  1104  includes a table  1106  having fields that allow the user to input parameters and/or values. In the illustrated example, the user has defined in table  1106  control points  1108 , parameter  1110  for the allowable starting point of support  14 , parameter  1112  for allowable ending point of support  14 , parameter  1114  for allowable gantry starting angle, and parameter  1116  for allowable gantry ending angle. As shown in the example, a control point may represent a single point (e.g., “0,” “1,” “2”), or an interval between two points (e.g., “0-1 interval,” “1-2 interval”). The table  1106  includes various input fields for allowing the user to input values for the parameters at different control points. As shown in the example, a value may be a numerical value, or an instruction (e.g., “interpolate”—which specifies that values for the corresponding control point are to be calculated in accordance with a prescribed scheme). In some embodiments, the user needs not enter all or any value for the input fields. In such cases, the processor/software for determining the treatment plan is configured to determine the values for the various fields in the table  1106 . 
     In the illustrated example, the trajectory is defined by the control points  1108 , wherein each control point  108  defines a region in parameter space. The optimized trajectory has to pass through the defined region before proceeding to the next control point  108 . The allowed region (range of parameters) between the control points is also defined. Thus, the control points define the region where the machine control points must be placed. In some cases, the processor/software for determining the treatment plan is configured to generate machine control points based on these rules and the defined parameters. For example, as similarly discussed with reference to  FIG. 2 , the processor/software may perform optimization based on geometric properties of target region(s) and healthy region(s). The processor/software may then continue with the optimization using dose based method(s), e.g., direct aperture method, or fluence based method. In some embodiments, the user interface  1100  allows the user to input initial values for some or all of the parameters. During the optimization process, the processor/software optimizes the values based on certain user-defined constraints (e.g., size, shape, and location of target, path of source, etc.). In other embodiments, the processor/software may be configured to determine the values for the parameters without any initial input values from the user. 
     In the illustrated example of  FIG. 11A , the trajectory would move the support  14  from 0 cm to 40 cm in the Z direction (from control point 0 to control point  1 ), and back to 0 cm (from control point  1  to control point  2 ). The gantry  12  would rotate from somewhere between 0° and 45° to between 315° and 360°, and back to between 0° and 45°. The Z-positions of the support  14  would be interpolated (e.g., linearly, or using some other interpolation scheme) between the control points. In some embodiments, the optimizer of the processor/software that is used to perform method  200  is configured to determine the route between the control points for gantry angles in the 0° to 360° interval. 
     In some cases, the user interface  1100  also allows the user to perform simple operations on defined trajectory. For example, in some embodiments, the trajectory of  FIG. 11A  may be stretched in the Z-direction by applying a multiplication of 2 in the Z-direction of the support  14 . After the multiplication operation, the trajectory would be that shown in  FIG. 11B . In other embodiments, at least part of the trajectory may be shifted. For example, the support  14  may be translated in the Z-direction by −20 can from the trajectory of  FIG. 11B , which will result in the trajectory of  FIG. 11C . 
     In any of the embodiments described herein, the range of relative motion between the support  14  and the radiation source (or a reference location) can be a value that is between 5 cm and 50 cm. This range is adequate if the target is one connected region. In other embodiments, if the target includes multiple regions (e.g., which may be separated from each other) desired to be treated, then the range of relative motion between the patient support  14  and the radiation source could be anywhere between 5 cm and 2 m. 
     In some embodiments, the user interface  1100  allows the user to save the designed trajectory in a medium. The trajectory may be saved as a part of a treatment plan, which will be used later in a treatment procedure. Alternatively, or additionally, the trajectory may be saved as a trajectory class. In some cases, the trajectory classes may be organized based on specific machines (e.g., different machines may have different classes of trajectories), patient anatomy, location of target regions, sizes of target regions, shapes of target regions, and/or other disease specific factors. In such cases, a user may retrieve a trajectory from one of the available trajectory classes, based on the specific machine, target region&#39;s shape, size, and location, and type of disease. The user may then revise the retrieved trajectory to fine-tune it so that is can be better used for a specific treatment for a specific patient. For example, the user may perform a multiplication and/or an adding procedure for any part (e.g., a parameter type) of the trajectory, such as those discussed with reference to  FIGS. 11B and 11C , to thereby fit the dimensions and/or positions of a target in a specific patient. 
     It should be noted that the type of parameters that may be defined using the user interface  1100  is not limited to the example discussed, and that the user interface  1100  may allow the user to define other parameters, such as gantry angle, positions (e.g., x, y, z) of support  14 , orientations (O x , O y , O z ) of support  14 , dose (e.g., user may specify whether dose is to be delivered for a control point), dose rate, leaves&#39; positions, and speed limits (e.g., of gantry rotation, leaves movements, support  14  movements, etc.). 
     As illustrated in the above embodiments, the user interface  1100  provides a flexible method for a planner to communicate to the optimizer which class of trajectories is considered for a specific case. The trajectory is defined as a set of control points, in which some parameters are to be optimized, and other parameters are to be interpolated. In some embodiments, parameters that are not optimized are interpolated using an interpolation scheme. The user interface  1100  also allows ranges to be defined, and provides tools for a user to manipulate the trajectory class. In some cases, the parameters to be optimized may be different for different intervals of the treatment. Thus, the user interface  1100  provides a tool for allowing a user to define a trajectory that is flexible enough for different applications, and is easy to converge to a good solution (because not all of the parameters need to be optimized—some of the parameters may be interpolated). 
     Although the above embodiments have been described with reference to delivering treatment radiation that is in the form of x-rays, in other embodiments, the system and technique described herein may be used for other types of treatment energy. For examples, in other embodiments, in other embodiments, the radiation source  20  may be a proton source for delivering protons to treat a patient, or an electron source for delivering electrons. Accordingly, embodiments of the treatment planning technique described herein may be used to determine treatment plan for other types of treatment, such as proton treatment. Also, it should be noted that the term “collimator” is not limited to a device having leaves for blocking radiation, and may refer to a device having one or more jaws or jaw blocks. Thus, a position of a collimator may refer to position of leaves of a collimator, position of collimator jaws, or a global position of the collimator itself relative to some coordinate system (e.g., a position of the collimator relative to a gantry or relative to a radiation machine, etc.). 
     Computer System Architecture 
       FIG. 12  is a block diagram that illustrates an embodiment of a computer system  1200  upon which an embodiment of the invention may be implemented. Computer system  1200  includes a bus  1202  or other communication mechanism for communicating information, and a processor  1204  coupled with the bus  1202  for processing information. The processor  1204  may be an example of the processor  54  of  FIG. 1 , or another processor that is used to perform various functions described herein. In some cases, the computer system  1200  may be used to implement the processor  54 . The computer system  1200  also includes a main memory  1206 , such as a random access memory (RAM) or other dynamic storage device, coupled to the bus  1202  for storing information and instructions to be executed by the processor  1204 . The main memory  1206  also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by the processor  1204 . The computer system  1200  further includes a read only memory (ROM)  1208  or other static storage device coupled to the bus  1202  for storing static information and instructions for the processor  1204 . A data storage device  1210 , such as a magnetic disk or optical disk, is provided and coupled to the bus  1202  for storing information and instructions. 
     The computer system  1200  may be coupled via the bus  1202  to a display  1212 , such as a cathode ray tube (CRT), for displaying information to a user. An input device  1214 , including alphanumeric and other keys, is coupled to the bus  1202  for communicating information and command selections to processor  1204 . Another type of user input device is cursor control  1216 , such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor  1204  and for controlling cursor movement on display  1212 . This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. 
     The computer system  1200  may be used for performing various functions (e.g., calculation) in accordance with the embodiments described herein. According to one embodiment, such use is provided by computer system  1200  in response to processor  1204  executing one or more sequences of one or more instructions contained in the main memory  1206 . Such instructions may be read into the main memory  1206  from another computer-readable medium, such as storage device  1210 . Execution of the sequences of instructions contained in the main memory  1206  causes the processor  1204  to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in the main memory  1206 . In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions to implement the invention. Thus, embodiments of the invention are not limited to any specific combination of hardware circuitry and software. 
     The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to the processor  1204  for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as the storage device  1210 . A non-volatile medium is an example of a non-transitory medium. Volatile media includes dynamic memory, such as the main memory  1206 . A volatile medium is another example of a non-transitory medium. Transmission media includes coaxial cables, copper wire and fiber optics, including the wires that comprise the bus  1202 . Transmission media can also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications. 
     Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read. 
     Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor  1204  for execution. For example, the instructions may initially be carried on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system  1200  can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to the bus  1202  can receive the data carried in the infrared signal and place the data on the bus  1202 . The bus  1202  carries the data to the main memory  1206 , from which the processor  1204  retrieves and executes the instructions. The instructions received by the main memory  1206  may optionally be stored on the storage device  1210  either before or after execution by the processor  1204 . 
     The computer system  1200  also includes a communication interface  1218  coupled to the bus  1202 . The communication interface  1218  provides a two-way data communication coupling to a network link  1220  that is connected to a local network  1222 . For example, the communication interface  1218  may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface  1218  may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, the communication interface  1218  sends and receives electrical, electromagnetic or optical signals that carry data streams representing various types of information. 
     The network link  1220  typically provides data communication through one or more networks to other devices. For example, the network link  1220  may provide a connection through local network  1222  to a host computer  1224  or to equipment  1226  such as a radiation beam source or a switch operatively coupled to a radiation beam source. The data streams transported over the network link  1220  can comprise electrical, electromagnetic or optical signals. The signals through the various networks and the signals on the network link  1220  and through the communication interface  1218 , which carry data to and from the computer system  1200 , are exemplary forms of carrier waves transporting the information. The computer system  1200  can send messages and receive data, including program code, through the network(s), the network link  1220 , and the communication interface  1218 . 
     Although particular embodiments have been shown and described, it will be understood that they are not intended to limit the present inventions, and it will be obvious to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the present inventions. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense. The present inventions are intended to cover alternatives, modifications, and equivalents, which may be included within the spirit and scope of the present inventions as defined by the claims.