Radiation treatment plan

Abstract

1. A method and apparatus for generating radiation treatment plans for a volume, comprising: receiving a first treatment plan on which a second treatment plan is based, the first treatment plan indicating a dose distribution; receiving at least one dose distribution derivative configured to provide a value based at least in part on the dose distribution; receiving a probability distribution, each of which includes a target value for each dose distribution derivative; determining an optimization problem, the or each objective function being a function of the dose distribution derivative, the respective probability distribution, and a respective loss function; performing an optimization process based on the optimization problem; and determining the second treatment plan.

Description

Technical Field

[0001] The present disclosure relates to an apparatus and method for radiation treatment planning. In particular, the present disclosure relates to an apparatus and method for radiation treatment planning that uses an optimization process to derive a treatment plan. The present disclosure also relates to related methods and computer programs.

Background Art

[0002] Radiation treatment planning may be performed for different types of radiation therapy, such as external beam radiation therapy or brachytherapy based on photons, light ions, or electrons.

[0003] A major challenge in the field of radiation therapy is devising a high-quality plan. A treatment plan can define the amount of radiation to be delivered to a target volume for a treatment method and, for example, the amount of radiation that can be delivered to one or more organs at risk (OARs) or other body tissues during said treatment method. There is a process for creating, and in particular improving, a treatment plan to minimize damage to healthy tissue and preferably ensure the desired radiation dose is delivered to a target volume, such as a tumor, without any damage to OARs such as the heart or spinal cord.

[0004] One approach for creating or improving a treatment plan involves an optimization process that uses mathematical optimization techniques. This optimization process is typically based on an optimization problem that includes a set of functions, where each function can represent an objective (i.e., an objective function) or a constraint (i.e., a constraint function). The functions used in the optimization problem may be at least somewhat incompatible in the sense that the output from one function may require the degradation of the output from one or more of the other functions. From the perspective of starting with an idealized radiation dose distribution and optimizing until a set of parameters that define a deliverable treatment plan is reached, an optimization process can be used to create a treatment plan.

[0005] The objective function and the constraint function used in the optimization problem may be regarded as quality metrics for treatment planning. The objective function may typically measure the deviation of a parameter from a desired value regarding the dose distribution. The desired value of the parameter may indicate, for example, the minimum or maximum dose to a specific organ or volume. The constraint function may include quality metrics and / or may define a set of feasible values that the parameter can take. Thus, in one or more examples, the feasible values may be configured to take into account the technical limitations of the radiation therapy delivery device. The quality metrics used as functions must have mathematical properties that make them suitable for optimization, such as continuity and differentiability.

[0006] The most common way to reach a treatment plan after defining the optimization problem is to find the parameters representing the treatment plan in such a way that the weighted sum of the objective function is minimized or maximized while satisfying the constraints. When there are conflicting incentives among the component objectives in the total weighted sum objective, the weights are typically adjusted to ensure that the resulting plan has characteristics that match the planner's preferences, and re-optimization is performed in an iterative process until a plan of satisfactory quality is found. Since the functions used as objectives and constraints are not usually directly related to the criteria used for evaluating the plan quality, this iterative process can be significantly time-consuming. Thus, more specifically, there is a need for tools aimed at fine-tuning an existing treatment plan, particularly for more accurately measuring the deviation between the current level and the desired level of the plan quality metrics and for more accurately capturing the complexity in the planner's preferences. SUMMARY OF THE INVENTION

[0007] According to a first aspect of the present disclosure, the inventors have receiving a first treatment plan that serves as a basis for a second treatment plan, the first treatment plan showing a dose distribution across a patient's volume, and Receiving at least one dose distribution derivative function, wherein the or each dose distribution derivative function is configured to provide, for at least a part of the volume for which it is defined, a value as an output based on at least a part of the dose distribution as an input. Receiving a target for each value of each dose distribution derivative function, including receiving a probability distribution for each or a group of at least one dose distribution derivative function, wherein the probability distribution represents the desirability of the range of values output from the dose distribution derivative function for the input dose distribution. Determining an optimization problem including an overall objective function, wherein the overall objective function includes the sum of one or more objective functions, and wherein the or each objective function includes one or more of at least one dose distribution derivative function, respective probability distributions, and respective loss functions. Performing an optimization process based on the optimization problem. Determining the second treatment plan from the optimization process. Provided is a computer-implemented method for generating a radiation treatment plan for a volume of a patient, including the above.

[0008] In one or more examples, the step of receiving at least one dose distribution derivative function includes receiving at least two dose distribution derivative functions.

[0009] In one or more examples, the probability distribution for each or a group of dose distribution derivative functions represents the preference or attainability for the range of values output from the dose distribution derivative function for the input dose distribution before and after each target value. In one or more examples, the most preferred target value may be located at one or more peaks of the probability distribution.

[0010] In one or more examples, the step of receiving a probability distribution includes receiving user input defining the probability distribution, and the user selecting the probability distribution from a plurality of predefined candidate probability distributions including one or more of the above.

[0011] In one or more examples, the first treatment plan is a treatment plan defined with respect to the operating parameters of the radiation therapy delivery device and where the dose distribution over the volume can be derived, a treatment plan defined with respect to the dose distribution, and a treatment plan defined with respect to the irradiation intensity integrated over time from each direction in space and where the dose distribution over the volume can be derived including one of.

[0012] In one or more examples, the step of receiving a dose distribution derivative function includes receiving user input to define one or more of the dose distribution derivative functions, and selecting one or more dose distribution derivative functions from a set of candidate dose distribution derivative functions, the candidate dose distribution derivative functions being determined based on a part of the patient's body in which the volume is defined including one or more of.

[0013] In one or more examples, the at least one dose distribution derivative function includes, for the whole or a part of the volume, one or more of a dose / volume, volume / dose, average dose, uniformity including a measure of dose uniformity in the whole or a part of the volume, a concordance index (CI), and a penalty function including a minimum dose, a maximum dose, or a dose-volume histogram function.

[0014] In one or more examples, the at least one dose distribution derivative function includes at least a first dose distribution derivative function and a second dose distribution derivative function, where the first dose distribution derivative function is configured to provide a value indicative of an improvement for a desired change in the dose distribution for the selected partial volume of the volume in a second treatment plan relative to a first treatment plan in response to the optimization process, in that the first dose distribution derivative function is associated with that goal, and The second dose distribution derivative function is configured to provide a value indicating the worsening of any deviation in the dose distribution for one or more selected partial volumes of the volume, along with its associated target, such that the dose distribution of one or more partial volumes defined in the first treatment plan is substantially maintained in the second treatment plan after the optimization process. It includes a function for use in maintaining substantially the dose distribution of one or more partial volumes defined in the first treatment plan in the second treatment plan after the optimization process.

[0015] In one or more examples, the loss function is a log loss function, and a cross-entropy loss function selected from one or more of these.

[0016] In one or more examples, the objective function or each objective function includes one or more functions of a dose distribution derivative function, each target represented by a normal probability distribution concentrated on that target, and each loss function. In other examples, a probability distribution having a form different from the normal distribution is used.

[0017] Thus, in one or more examples, the method can be advantageous in that it can convert a dose distribution derivative function into an objective function for forming at least part of an optimization problem by a process of receiving a dose distribution derivative function and a probability distribution (which may include, for example, a normal distribution) defining a target and using it as an input to a loss function. In one or more examples, the overall objective function may include only the objective function transformed from the dose distribution derivative function by the method.

[0018] In one or more examples, the method includes the step of representing the probability distribution for each dose distribution derivative function as a cumulative distribution function or a probability density function in the optimization problem.

[0019] In one or more examples, the step of performing the optimization process includes minimizing an overall objective function, where the overall objective function includes a weighted sum of one or more objective functions.

[0020] In one or more examples, the method includes receiving an image of the volume, and the dose distribution derived from the first and / or second treatment plan may be determined based on a plurality of voxels of the image. In one or more examples, the image includes a plurality of voxels that define distinct partial volumes of the image.

[0021] In one or more examples, the computer-implemented method is a method performed by a computing device. In one or more examples, the method is performed by a computing device having an input device for receiving user input, a memory call device for retrieving predetermined data from a memory, and a processing device. In one or more examples, the step of receiving the first treatment plan and / or the step of receiving at least one dose distribution derivative function and / or the step of receiving a goal may be performed by the input device or the memory call device. In one or more examples, the step of determining an optimization problem and / or the step of performing an optimization process and / or the step of determining the second treatment plan may be performed by the processing device. In one or more examples, the computing device comprises an output device capable of outputting the determined second treatment plan to a further device or user.

[0022] In one or more examples, the second treatment plan includes data output from a device that can be used to program a radiation therapy delivery device. In other examples, the second treatment plan may include data representing the irradiation intensity integrated over time from each direction in space.

[0023] In one or more examples, the volume includes a three-dimensional image, and the dose distribution derived from the first and / or second treatment plan may be determined based on a plurality of voxels of the image, and the voxels define a three-dimensional region of the image.

[0024] According to a third aspect of the present disclosure, the inventors provide an apparatus for generating a radiotherapy plan, the apparatus comprising a processor, a memory, and computer program code stored in the memory, the computer program code being configured to cause the apparatus to perform the method of the first aspect when executed by the processor.

[0025] In one or more examples, the apparatus comprises an input device configured to receive an input drawn by a user representing a probability distribution.

[0026] According to a further aspect, the inventors receive a first treatment plan that is the basis for a second treatment plan, the first treatment plan showing a dose distribution over a volume, receive at least one dose distribution derivative, the dose distribution derivative or each dose distribution derivative being configured to provide a value as an output based on at least a part of the dose distribution as an input for at least a part of the volume for which it is defined, receiving a target for each value of each dose distribution derivative, including receiving a probability distribution for each or a group of the at least one dose distribution derivative, the probability distribution representing the desirability of the range of values output from the dose distribution derivative for the input dose distribution, determining an optimization problem including an overall objective function, the overall objective function including the sum of one or more objective functions, where the objective function or each objective function includes one or more functions of a dose distribution derivative, each probability distribution and each loss function, performing an optimization process based on the optimization problem, and determining the second treatment plan from the optimization process provide an apparatus for generating a radiotherapy plan, comprising means for or at least one processing module configured to perform them.

[0027] In one or more examples, a plurality of means or processing modules may be provided to each perform one or more of the respective operations for receiving a first treatment plan, receiving at least one dose distribution derivative function, receiving a goal, determining an optimization problem, performing an optimization process, and determining the second treatment plan.

[0028] According to a further aspect, the inventors provide an apparatus or method for generating a plan defining the delivery of radiation to a volume represented by an image including a plurality of voxels, the method providing an apparatus or method defined by the steps of the first aspect using the image of the volume.

[0029] According to a third aspect of the present disclosure, the inventors provide a computer program including instructions configured to perform the method of the first aspect when executed by an apparatus having at least one processor.

[0030] In one or more examples, the computer program is stored on a computer-readable medium such as a non-transitory computer-readable medium.

[0031] Next, a detailed description of embodiments of the present invention will be given as a mere example with reference to the following figures.

Brief Description of the Drawings

[0032]

Figure 1

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Mode for Carrying Out the Invention

[0033] Radiation treatment planning is a complex task involving many different factors that play a part. The size and location of tumors in the body, the location and sensitivity of organs around the tumor (so-called risk organs), the technical capabilities of the radiation therapy delivery device, and the clinical results of past radiation treatments can all contribute to the determination of the treatment plan.

[0034] The example of FIG. 1 shows an example of a treatment planning device 100. The device 100 may comprise a computer system 101 having a processor 102 and a memory 103 configured to perform a method defined by computer program code, which code may be stored in the memory or otherwise provided to the computer system 101. Naturally, the computer system 101 may comprise a terminal connected to a network such as the Internet, and the processor and memory performing the present method may be located on one or more remote servers (not shown) with the terminal providing an interface to the user.

[0035] The treatment planning device 100 may comprise an input device 104 to enable a user to input information for performing a treatment plan. In one or more examples, the input device 104 may enable a preference or other input to be input via a graphical user interface. In one or more examples, the input device 104 may enable a user to draw an input as a picture. Accordingly, the input device 104 may particularly include a stylus, a mouse, or a touch screen interface. The treatment planning device 100 may comprise a display device 105 connected to the computer system 101 for display of information and / or presentation of a graphical user interface.

[0036] In one or more examples, the treatment planning device 100 may be connected to or connectable to a radiation therapy delivery device 106 for delivering radiation to a patient. Thus, a treatment plan determined using the treatment planning device 100 may be provided to the radiation therapy delivery device 106 for subsequent delivery thereby. In one or more examples, the treatment plan may be converted into operation parameters of the radiation therapy delivery device 106, or the treatment plan may already be defined with respect to the operation parameters of the radiation therapy delivery device 106.

[0037] When performing treatment planning using optimization techniques, it is common to start with a first treatment plan and make adjustments in an attempt to improve it. Such a process is known in the art as treatment plan optimization. However, of course, the term "optimization" is used in the sense of obtaining an improvement based on a defined measure, rather than finding an absolute optimum solution. Generally, treatment plan optimization is the search for treatment plan parameters that minimize as well as possible several overall objective functions that evaluate the treatment plan under several constraints. For example, the parameters of the treatment plan may include operation parameters of the radiation therapy delivery device 106 (such as multi-leaf collimator position, gantry rotation speed over time, radiation beam power over time, and any other operation parameters), the overall objective function may be defined with respect to the calculated radiation dose distribution delivered to the volume based on those operation parameters, and the constraints may include the technical limits of the device 106. In other examples, the parameters of the treatment plan may be a fluence map, where the parameters define the irradiation intensity integrated over time from each direction in space. Thus, of course, the treatment plan may be defined with respect to many different types of parameters that define or indicate the radiation dose distribution in the volume of the patient being treated. The dose distribution includes a definition of how the dose is distributed over the volume. The dose distribution may be defined with respect to the dose delivered to each of a plurality of voxels, where the plurality of voxels includes a separate volume derived from an image of the volume being treated. Generally, the treatment plan may define the delivery of radiation and derive the dose distribution over the volume therefrom.

[0038] In one or more examples, the starting point of the optimization process includes a treatment plan having parameters corresponding to an existing treatment plan, such as a treatment plan previously delivered for the current patient, which may be determined by the optimization process itself (known in the art as a warm start). In one or more other examples, the starting point for optimization may include a treatment plan having parameters for which assumptions have been made, such as assumptions meeting clinician experience for their appropriate values (known in the art as a cold start). For example, a cold start treatment plan may be defined with respect to one or more of the planning parameters corresponding to the delivery of an average dose at a target volume (or a target approximating the target volume) equal to a randomly selected planning parameter or an associated prescribed dose level. The optimization process described herein is not concerned with whether the treatment plan is achievable in terms of representing a plan that the planning device 106 can technically deliver, or whether the treatment plan is idealized in terms of being deliverable or not by the radiation therapy delivery device 106.

[0039] Thus, in summary, the first treatment plan may of course include a realistic treatment plan including what is achievable, for example, under the constraints of the operating parameters of the radiation therapy delivery device or other constraints. In other examples, the first treatment plan may be an idealized treatment plan in that it may not have been determined whether it is achievable.

[0040] According to an example of the present disclosure, it may be desirable to adjust the parameters of a treatment plan in an optimization process with respect to a value obtained from a dose distribution derivative for a given dose distribution, where the dose distribution is derivable from the parameters of the treatment plan. The inventors mean by a dose distribution derivative any function that receives as input a dose distribution (or a part thereof) and returns a number as output. Thus, the number output by the dose distribution derivative represents a measure related to the dose that can be used as a score for a rating scale, where a further function may define the rating scale. The input to the dose distribution derivative may include a dose distribution over a plurality of voxels representing the volume to be treated or a part thereof.

[0041] Thus, the optimization process described in the examples herein may be configured to adjust the parameters of a first treatment plan, determine a modified dose distribution for the volume based on the adjusted parameters, and then evaluate the modified dose distribution, for example, by using the output of a dose distribution derivative. Thus, by (partially) solving the optimization, adjusted parameters that define a second treatment plan may be obtained. The second treatment plan may be considered an improvement over the first treatment plan in view of a dose distribution derivative value that is closer to each dose scale target. In fact, the second treatment plan may be such that its dose distribution is not relatively different from the original dose distribution of the first treatment plan with respect to some distance measures based on either a three-dimensional dose distribution or some aggregate of dose distribution derivatives. However, the optimization process may still obtain a second treatment plan that is considered an improvement.

[0042] In other examples, the first treatment plan may be defined with respect to a dose distribution, and determining one or more objective functions may include determining the parameters of a second treatment plan, and the optimization process may be configured to adjust the determined parameters of the second treatment plan and determine a modified dose distribution for the volume based on the adjusted parameters. The method may further include evaluating the modified dose distribution, for example, by using the output of a dose distribution derivative.

[0043] Referring to the examples of FIGS. 2, 3 and 4, the inventors describe an example of a method 400 performed by the treatment planning device 100.

[0044] This method relates to the generation of a radiation treatment plan, hereinafter referred to as a second treatment plan, in the following example. The second treatment plan may include parameters that define how radiation should be delivered to the patient's volume.

[0045] Referring to FIG. 4, step 401 includes receiving a first treatment plan that serves as a basis for the second treatment plan. Thus, in the examples herein, the parameters of the first treatment plan are optimized to generate the second treatment plan.

[0046] The first treatment plan and the second treatment plan also show the dose distribution over the volume. Thus, the dose distribution over the volume can be calculated from the parameters of the first treatment plan (and / or the parameters of the second treatment plan). In one or more examples, the parameters of the first treatment plan are "complete" in that they uniquely determine the corresponding dose distribution. The first treatment plan may be defined in various ways. In one or more examples, the first treatment plan has parameters that define the operating parameters of the radiation therapy delivery device 106, and the dose distribution over the volume is calculated therefrom. In one or more other examples, the first treatment plan has parameters that define the dose distribution. In one or more other examples, the first treatment plan has parameters that define the irradiation intensity integrated over time from each direction in space, including a so-called fluence map, and the dose distribution over the volume is determined therefrom. Algorithms used to derive the dose distribution obtained from the parameters of the first treatment plan or the parameters of the second treatment plan are known to those skilled in the art.

[0047] The dose distribution may be determined based on a three-dimensional image of the patient's volume discretized into a set of voxels, where each voxel or group of voxels is assigned a value representing the dose that the voxel or group of voxels receives based on a first treatment plan (and subsequently, a second treatment plan described below). The image typically includes the output from a computed tomography (CT) scanner or a magnetic resonance imaging (MRI) scanner, such as an X-ray or positron emission tomography-based scanner, but other medical imaging techniques may be used.

[0048] The example of FIG. 2 shows a dose-volume histogram 200. The x-axis 201 represents dose, and the y-axis 202 represents the amount of the target volume. Lines 203 and 204 represent the dose in the tumor and thus represent the first partial volume of the patient's volume. Lines 205 and 206 represent the dose in the risk organ and thus represent the second partial volume of the patient's volume. The dashed line 203 represents the dose delivered by the first treatment plan. The solid line 204 represents the dose that the clinician desires to be delivered to the tumor by the second treatment plan (i.e., a more uniform dose) after this method. The dashed line 205 represents the dose delivered by the first treatment plan. The solid line 206 represents the dose that the clinician desires to be delivered to the risk organ by the second treatment plan (i.e., a lower dose) after this method.

[0049] Thus, naturally, in this example, the clinician may desire to vary the uniformity of the dose to the tumor in the treatment plan, as indicated by arrow 207. Also naturally, in this example, the clinician may desire to reduce the dose to the OAR in the treatment plan, as indicated by arrow 208. As described below, one or more dose distribution derivatives may be defined to achieve changes 207 and 208.

[0050] Step 402 includes receiving one or more dose distribution derivative functions. Such functions may be known in the art as statistical or clinical goals of the dose. A clinician / user (or AI) may specify or input a dose distribution derivative function to control the optimization process in a way that achieves an effective treatment plan for a patient. The input may include one or more of the regions of the volume, dose requirements, or the function itself, as described below. Each dose distribution derivative function includes a function that provides a numerical value as an output based at least in part on at least a portion of the dose distribution as an input, for at least a portion of the volume for which it is defined. Thus, the dose distribution derivative function may receive as input the dose distribution over a partial volume of the voxels or over the entire volume. This numerical value is referred to as a dose scale value for ease of reference.

[0051] The dose scale value output by the or each dose distribution derivative function is used in part to drive the optimization. Thus, the dose distribution derivative function is configured to output a dose scale value that can be used to derive a score. The score may take a high or low value when the dose distribution provided to the associated dose distribution derivative function is desirable for the target. The dose distribution derivative function may be determined by a user such as a clinician and / or selected from a set of candidate dose distribution derivative functions.

[0052] Thus, in one or more examples, step 402 of receiving a dose distribution derivative function includes receiving user input via an input device 204 or the like to define one or more of the dose distribution derivative functions. The user input may include selecting a region in one or more images of the volume and associating the selected region with a dose requirement. The dose distribution derivative function may be determined based on this user input. Thus, in one or more examples, the user may define a partial volume of the volume and input dose-related goals such as a minimum dose, a maximum dose, or other target requirements, and the dose distribution derivative function may be at least partially based on the user definition.

[0053] In one or more other examples, step 402 includes selecting one or more dose distribution derivative functions from a set of candidate dose distribution derivative functions. In one or more examples, the candidate dose distribution derivative functions are determined based on a part of the patient's body where the volume is located. Accordingly, predetermined dose distribution derivative functions may be associated with different parts of the body and then selected as candidates based on the part of the body of interest. In one or more examples, the method includes the user identifying internal organs in the volume, or the computer system 201 identifying internal organs in the volume based on a predetermined organ identifier or the like, and presenting a plurality of predetermined "candidate" dose distribution derivative functions pre-associated with the identified organs for selection.

[0054] The dose distribution derivative function or each dose distribution derivative function may be a function that determines one or more of dose / volume (such as a ratio of the volume), volume / dose with respect to a predetermined dose level, or average dose for a predetermined part or all of the volume, for the entire volume or a part thereof. The dose distribution derivative function or each dose distribution derivative function may be a function that determines a uniformity index (such as a ratio of the volume) for a predetermined part or all of the volume that represents the dose uniformity in the target volume or a partial volume thereof, for the entire volume or a part thereof. The dose distribution derivative function or each dose distribution derivative function may be a function that determines a concordance index for a predetermined isodose level, for the entire volume or a part thereof. The concordance index of the treatment plan may be defined as the ratio of the volume covered by the reference isodose level to the target volume. Of course, there are multiple definitions of the uniformity index and the concordance index and algorithms for calculating them, but for the purposes of the present disclosure, it does not matter which one is used.

[0055] The dose distribution derivative function or each dose distribution derivative function may be a penalty function such as a quadratic penalty function, for the entire volume or a part thereof. Examples of the type of quadratic penalty function include a minimum dose function, a maximum dose function, or a dose-volume histogram function.

[0056] The dose distribution derivative function may be a so-called single voxel function for the voxels that outputs the dose delivered to several voxels throughout the volume or a part thereof. In one or more examples, the set of candidate dose distribution derivative functions includes a corresponding single voxel function for each of the voxels in the volume. Thus, in the above example of the dose distribution derivative function, the reference to a part of the volume may include one or more single voxels in one or more examples.

[0057] Generally, the dose distribution derivative function may be any function that receives a dose distribution as input for several regions of interest (i.e., single voxels or groups of voxels) of the volume and gives a single number as output. That number, i.e., the dose metric value, includes statistics regarding the dose that can be compared to a dose-related target.

[0058] Step 403 described below includes receiving a dose-related target for each dose metric value of each dose distribution derivative function. Thus, a target for moving towards it may be assigned to the dose metric value output by the dose distribution derivative function in the optimization process. Thus, the clinician may specify a target dose metric to be achieved by the optimization process.

[0059] In one or more examples, at least two dose distribution derivative functions may be received. The at least two dose distribution derivative functions may be of different "types" for either improving a part of the dose distribution of the treatment plan or maintaining a part of the dose distribution of the treatment plan. Thus, in one or more examples, the dose distribution derivative function includes at least a first dose distribution derivative function and a second dose distribution derivative function.

[0060] The first dose distribution derivative function may be a function for improving the dose distribution for a selected sub-volume in a second treatment plan with respect to the dose distribution for a selected sub-volume of said volume in a first treatment plan. Of course, said improvement is achieved by an optimization process as described below. Thus, the first dose distribution derivative function, together with its associated goal, is configured in such a way that the agreement of the dose scale value with said associated goal (evaluated against the dose distribution derived from the second treatment plan) indicates an improvement in the desired change in the dose distribution for the selected sub-volume of said volume.

[0061] The second dose distribution derivative function may be a function for substantially maintaining the dose distribution of one or more sub-volumes defined in the first treatment plan in the second treatment plan. Thus, the second dose distribution derivative function has the effect of maintaining the dose distribution for the sub-volume during said optimization. Thus, the second dose distribution derivative function, together with its associated goal, is configured in such a way that the disagreement of its dose scale value with respect to said associated target (evaluated against the dose distribution of the second treatment plan) indicates a worsening of any deviation in the dose distribution from the dose distribution of the first treatment plan for the selected sub-volume.

[0062] This combination of types of dose distribution derivative functions may provide effective control of optimization that was not previously possible. Thus, the optimization variables may include treatment plan parameters, and the dose distribution derivative functions may include any criteria used for the evaluation of the second treatment plan, which in one or more examples can provide a more precisely targeted optimization than was previously possible, and thus also reduce the need for potentially time-consuming repeated optimizations in the process of reaching an improved second treatment plan. The use of the dose distribution derivative functions and their subsequent incorporation into the optimization process is more effectively adapted to the optimization problem to be solved according to the wishes of the clinician as described below.

[0063] As an example, a user (e.g., a clinician) may wish to meet a specific clinical goal by making the dose scale value of the dose distribution derivative evaluated against the dose distribution of the second treatment plan smaller or larger than some associated threshold or target value. Accordingly, a corresponding dose distribution derivative is defined for inclusion in the optimization process.

[0064] In other aspects, the user may wish to preserve the quality of the second treatment plan as well as possible with respect to the first treatment plan. To achieve this, one or more second dose distribution derivatives may be generated to summarize the current state of the plan. The one or more second dose distribution derivatives may be designed such that the degradation of their dose scale values with respect to the goals based on the dose distribution of the second treatment plan implies the degradation of the quality of the second treatment plan with respect to the first treatment plan.

[0065] In one or more examples, one or more second dose distribution derivatives may be generated by determining dose / volume goals at (e.g., equally) spaced volume positions for one or more regions of interest selected by the user. In one or more examples, one or more second dose distribution derivatives may be generated by determining a corresponding single voxel function that associates the dose distribution with the dose at said voxel for each voxel of the region of interest. The single voxel function for the voxel with subscript i associates the dose distribution d = (d_1, …, d_n) with d_i.

[0066] In one or more examples, the step 403 of receiving a target includes receiving a probability distribution in at least one dose distribution derivative function. In one or more examples, the target or the probability distribution may be specific to a particular one of the at least one dose distribution derivative function. However, in the examples described herein, the probability distribution for each dose distribution derivative function is represented as a target for a set (e.g., a plurality) of dose distribution derivative functions. In such a case, the method may assume independence between the separate dose distribution derivative functions and derive a probability distribution for the set. Alternatively, the method may use predefined correlation data to derive a probability distribution for a set of dose distribution derivative functions from the probability distributions for each of the component dose distribution derivative functions, and the correlation data may indicate how different dose distribution derivative functions can be correlated with each other.

[0067] From the probability distribution, a preference or an attainability for a dose scale value can be determined for a range of the dose distribution derivative function around some associated target values. Naturally, the preference may represent the preference of a clinician and thus can also be understood as the degree of acceptance of the dose scale value for the target.

[0068] Thus, in one or more examples, by using a probability distribution instead of a single target value for the dose distribution derivative function, one may obtain the ability to better represent the goals and preferences of a clinician user when performing treatment planning, and / or the clinical relevance / satisfaction levels associated with different dose metrics output from the dose distribution derivative function can be more effectively characterized by the probability distribution, so that more effective and efficient optimization may be obtained. Thus, in one or more examples, the different nuances in clinical (dis)satisfaction associated with different outcomes of a second treatment plan are captured in the specification of the probability distribution. Thus, using a probability distribution instead of a single target value can be regarded as a "fuzzy" target value, and thus may be advantageous in that more information can be obtained than when using a single target value for the optimization process. Also, the use of a probability distribution compared to the use of weights for the respective dose distribution derivative functions may be advantageous as the probability distribution provides more information for the optimization process. Thus, with more information for the optimization process, a more efficient and effective optimization process is obtained, and thus a more effective second treatment plan is obtained.

[0069] The step of receiving a probability distribution may include receiving user input that defines the probability distribution via an input device 204 or the like. Thus, in one or more examples, the user input may represent a probability distribution drawn by the user and thus may indicate the degree of preference for the range of values of the one or more dose distribution derivative functions. In other examples, the method may include generating a probability distribution based on one or more parameters input by a user indicating one or more of an average vector, a covariance, and any other defining features of the characteristics of the probability distribution specified for at least the range of dose metric values.

[0070] In one or more examples, the step of receiving a probability distribution may include receiving a user selection of a probability distribution from a plurality of predefined candidate probability distributions. The candidate probability distributions may have various shapes, widths, mean vectors or covariances, and any other defining characteristics. The candidate probability distributions may be presented by system 201 for selection by the user. The candidate probability distributions displayed to the user for selection may be subjected to a filtering process based on a selected region of the volume, such as a selection of a particular internal organ, to obtain one or more candidate probability distributions most appropriate for that region selected based on predefined filtering information.

[0071] In one or more examples, the predefined candidate probability distributions may be based on past data from other treatment plans, and thus may indicate the probability of achieving a desired goal for a range of dose scale values of the dose distribution derivative based on what has been achieved in the past.

[0072] In one or more examples, the probability distribution is represented as a composition of several probability distributions. Thus, for example, the probability distribution regarding the dose scale values of a set of dose distribution derivatives may be represented by the respective associated probability distributions of said dose distribution derivatives. Naturally, the associated probability distributions of the dose scale values of the dose distribution derivatives of each component can be determined from the joint probability distribution regarding all of said dose distribution derivatives.

[0073] The probability distribution may include a continuous function regarding a predefined range of dose scale values. For example, the predefined range of dose scale values may include a non-zero range specified by the user and may include the default settings of the method performed by system 101.

[0074] The example of FIG. 3 shows a dose - volume histogram 300 with annotations representing the dose distributions 203, 205 of the first treatment plan shown in the example of FIG. 2, where two dose - distribution derivatives are defined for two different regions of volume (tumor and OAR) indicated by arrows 301 and 302. Probability distributions 303 and 304 are also defined for each dose - distribution derivative 301, 302.

[0075] In one or more examples, the probability distributions 303, 304 for each dose - distribution derivative 301, 302 effectively assign the corresponding probabilities of dose - scale values (output from a dose - distribution derivative given an input dose distribution) that are achieved / acceptable / satisfactory in a treatment plan (i.e., the second treatment plan). One probability distribution 303 is wide and symmetric, which may indicate that the clinician accepts a wider range of dose - scale values around the target dose - scale value. The other probability distribution 304 is narrower and skewed, which may indicate that the clinician accepts dose - scale values on one side rather than the other side of the target dose - scale value less readily.

[0076] Thereby, the probability distributions 303, 304 for each dose - distribution derivative 301, 302 are designed in such a way that the tolerances at the dose - scale values of each dose - distribution derivative for the second treatment plan are reflected. This provides flexibility in defining what is achievable based on the user / clinician's preference or past data. Thus, a clinician may input a probability distribution with a small standard deviation and a peak concentrated at the desired dose - scale target if the associated dose - scale dose - distribution derivative has to be met exactly. Alternatively, if the dose - scale target associated with the dose - distribution derivative does not have to be met as strictly, a probability distribution with a larger standard deviation and a peak concentrated at the desired target may be used. Also, different - shaped probability distributions, symmetric or asymmetric as needed, may be used to represent the clinician's preference. Similarly, past data may show how accurately the dose - scale target can be met, and the shape / defining characteristics of the probability distribution may reflect this.

[0077] For example, the tolerance in the dose scale value of the dose / volume function at the treatment target is likely to be smaller than that for the dose scale value of the dose / volume function in the risk organ, and they can be measured in different units such as cGy (e.g., for dose / volume) or dimensionless quantities (e.g., for the uniformity index). The use of the probability distributions 303, 304 can account for these differences.

[0078] More specifically, once a set of dose distribution derivatives is defined, a probability distribution of a multi-dimensional real random variable having a dimension equal to the number n of the dose distribution derivatives may be specified. Such a probability distribution may be derived from the probability distributions of the respective dose distribution derivatives. The probability distribution of the n-dimensional random variable x = (x1, x2, …, x n ) is for all i = 1, 2, …, n, x i ≤ y i such that for all pairs of realized values of x and y (x1, x2, …, x n ), (y1, y2, …, y n ), F x (x1, x2, …, x n ) ≤ F x (y1, y2, …, y n ), and for all i = 1, 2, …, n

Number

Number

Number

[0079] Thus, in one or more examples, the probability distribution for the set of dose distribution derivatives is represented as a cumulative distribution function. However, the probability distribution may be specified in different ways, and the cumulative distribution function is just one way.

[0080] For each component x i the marginal cumulative distribution function F xi is the following integral:

Equation

[0081] Thus, in one or more examples, the probability distribution is represented by the marginal cumulative distribution function F xi (i = 1, 2, …, n). Of course, in one or more examples, to fully define the corresponding optimization problem, it is sufficient to simply specify the marginal cumulative distribution function associated with each of the component dose distribution derivatives. In one or more examples, with additional assumptions about the distribution characteristics of x, the cumulative distribution function F i for all x xi can be recovered from the marginal cumulative distribution function F x for x. Thus, in one or more examples, assume that x follows a multivariate normal distribution and the correlation between each pair of x i ,x j is given (e.g., by user input or as a predefined value), and then the cumulative distribution function F x can be determined by a process known to those skilled in the art.

[0082] As described above, the first dose distribution derivative function may include a function for improving the dose distribution for the selected sub-volume in the second treatment plan with respect to the dose distribution for the selected sub-volume of the volume in the first treatment plan. As an example, two first dose distribution derivative functions having corresponding target values may be defined, for example, as "at least 5900 cGy in 95% volume of the target" and "at most 6100 cGy in 5% volume of the target".

[0083] Therefore, the inventors assume that x = (x1, x2) is a multivariate normal random variable having a mean of 5900, 6100 and a covariance matrix:

Equation

[0084] Therefore, the marginal cumulative distribution functions of x1 and x2 are functions of univariate normal distributions having means of 5900, 6100 and standard deviations of 50, respectively. In this example, the value 50 (cGy) is used as the default parameter value, but other standard deviation values may be used. Therefore, the cumulative distribution function F x can be expressed as the product of the cumulative distribution functions of the univariate normal distributions.

[0085] As described above, one or more second dose distribution derivative functions are designed to maintain the quality of the first treatment plan in the second treatment plan.

[0086] Thus, as an example, in the case of some partial volumes of the volume (covering the risk organs), it may have a first treatment plan where the dose / volume values at 10, 20, …, 90% of the volume are 900, 800, …, 100 cGy, respectively. In order to preserve the current situation of the risk organ dose as well as possible, the inventors may construct a multivariate normal distribution in the same way as described above such that the peripheral distribution is a univariate normal distribution having an average of 900, 800, …, 100 and a standard deviation of 200 (default parameter values). In this example, the value 200 (cGy) is used as the default parameter value, but other standard deviation values may be used.

[0087] In one or more other examples, the first treatment plan may be defined only with respect to one or more dose distributions of a set of clinical plans delivered in the past (this is an example in the case of a so-called cold start). Thus, the method may be configured to evaluate a dose distribution derivative with respect to a past dose distribution and generate an evaluated Gaussian mixture model (i.e., a combination of several normal distributions) calculated from its peripheral distribution. The mathematical process for calculating the peripheral distribution from the Gaussian mixture model is known to those skilled in the art.

[0088] Step 404 includes determining the optimization problem to be solved. Generally, step 404 may include determining an overall objective function including the contribution from the said or each dose distribution derivative and its corresponding target / probability distribution and any constraints that exist, where a loss function is applied to each dose distribution derivative or the objective function derived therefrom. The overall objective function may include a weighted contribution from the objective function.

[0089] Process 404 may include determining a set of objective functions for performing an optimization process thereon, i.e., (partially) solving an optimization problem, each objective function of the set of objective functions being at least one variable including parameters defining a second treatment plan, wherein a modification of at least one variable is configured to affect at least one of the dose metric values output by a dose distribution derivative function, and wherein the determination of the set of objective functions is based on the dose distribution derivative functions as well as their respective targets (and optionally probability distributions).

[0090] Accordingly, the first treatment plan may be defined with respect to a first set of parameters, and the optimization process described below may provide a second set of parameters defining a second treatment plan by determining a change with respect to the first set of parameters. The objective functions may be defined with respect to one or more of those parameters. Alternatively, the first treatment plan may provide a dose distribution based on which a dose distribution derivative function is determined, and process 404 may include defining an objective function that is a parameter defining a second treatment plan.

[0091] Process 404 may include converting one or more dose distribution derivative functions into objective functions, which may define an optimization problem by applying respective loss functions to each dose distribution derivative function and its associated probability distribution. In other examples, including where process 403 receives dose metric targets and does not receive probability distributions, process 404 may include converting one or more dose distribution derivative functions into objective functions that can define an optimization problem by applying respective loss functions to each dose distribution derivative function and a default distribution (e.g., a normal distribution) concentrated on the dose metric targets.

[0092] Examples of how to derive one or more objective functions and thus all objective functions from dose distribution derivative functions are as follows.

[0093] Processes 402 and 403 are n dose distribution derivative functions Ψ1, Ψ2,..., Ψ of dose distribution d nProvide a set (e.g., one or more) and, for example, an associated probability distribution for the set.

[0094] The overall objective function Ψ tot To determine, η shall mean the planning parameters that the inventors use to represent the second treatment plan. The planning parameters may include, for example, the operating parameters of the device 106 from which the dose distribution can be derived, but in principle the planning parameters can be any parameters that uniquely determine the dose distribution. Naturally, the corresponding dose distribution d = d(η) is completely determined by the planning parameters. The function d(η) that converts the planning parameters into the dose distribution may be pre-determined or known to those skilled in the art.

[0095] In step 405, the optimization problem to be solved determined in step 404 is Minimize: Ψ tot (η) Condition: η satisfies any constraints that can be provided by the user or the technical constraints of the radiation therapy delivery device 106 is.

[0096] In one or more examples, the method is in weighted sum form:

Number

[0097] Naturally, the M objective functions that form the overall objective function may be equal to or smaller than the number n of dose distribution derivatives. Thus, in one or more examples, two or more of the plurality of dose distribution derivatives may be combined into one objective function.

[0098] The setup may include the following steps. 1. The number of functions M and the weights w iDetermine. System 101 may receive user input to specify these values or may have default values. For example, M may be equal to 2, and the dose distribution derivative function may be divided into two groups, namely a single voxel function and a non-single voxel function. Therefore, the functions of each of these two groups may be combined into two objective functions. 2. For each of i = 1, 2, …, M, a. Determine a set of indices S that is a subset of all indices {1, 2, …, n}. i Determine. System 101 may receive user input to specify the S i value or may use a default value. b. In the set of indices, the dose distribution derivative function: [Number] For example, the cumulative distribution function F x or the probability density function ∫ x (where x = (x1, x2, …, x n ) is a vector-valued random variable) to determine the parameter representation of the probability distribution regarding the value. This can be determined by user input or a predefined algorithm. One exemplary method is to use the probability density function for the function defined by the single voxel type of dose distribution and the cumulative distribution function for the rest. c. Receive as input the output of the parameter representation in 2b, and determine a loss function L that gives a number representing the loss contribution as output when observing the said output of the parameter representation. For example, L can be the log loss L(t) = -log t or the cross-entropy loss L(t) = -a log t - (1 - a) log(1 - t) (where a ∈ {0, 1}). Here too, the selection of the loss function may be received by user input or a predefined loss function may be selected. In one or more examples, the selection of the loss function may be based on the type of function defined by the dose distribution, for example, the single voxel type or the non-single voxel type. d. We, the inventors, have F x or ∫ xDepending on whether it is used (assuming the former), [Number] as Ψ i is obtained.

[0099] As an example, the inventors assume that they want to group the dose distribution derivative function into searches for lower / higher peaks (as low / high as possible) and searches for tails (as close to the mode as possible). The inventors then use the cumulative distribution function and the cross-entropy loss with 0 / 1 in the former case and the probability density function and the log loss in the latter case. Here, the subscript set represents the relevant subscripts of the function.

[0100] Thus, in summary, in one or more examples, the overall objective function is the sum of all objective functions, and each objective function is determined using one or more of the dose distribution derivative function and the associated probability distribution or target and loss function. Thus, the overall objective function Ψ tot essentially incorporates the dose distribution derivative function and any probability distribution. As described herein, the formulation of the optimization problem is thus advantageous with respect to the flexibility to select the dose scale to guide the optimization process.

[0101] As a more specific example, the method (i) receives a set of dose distribution derivative functions divided into a subscript set S1 of single-voxel functions of all components and a subscript set S2 of functions of all components that are not single-voxel functions, (ii) for each function in S1 and S2, receives the associated probability distribution represented as a marginal cumulative distribution function, (iii) assumes the independence of the dose scale values of all functions in S1 and S2, and obtains two cumulative distribution functions, i.e., one of them in S1 and one of them in S2 (the method of deriving the cumulative distribution from the marginal distribution and the assumption of independence are known to those skilled in the art), (iv) For S2, apply a cross-entropy loss function to the corresponding cumulative distribution function that defines one objective function Ψ2. (v) For S1, identify from the cumulative distribution function the corresponding probability density function and apply a log-loss function that defines another objective Ψ1. (vi) Using equal weights w1 = w2 = 1, obtain the total objective function as Ψ tot = Ψ1 + Ψ2. Thereby, it may be configured to determine a total objective function including at least one objective function based on each of at least one dose distribution defining function.

[0102] In one or more examples, the method is advantageous for providing greater flexibility in defining the optimization problem. In prior art methods, the objective function is typically a quadratic penalty. However, in prior art methods, it may be desirable to perform the optimization process using one or more dose distribution derivative functions (usually called clinical objectives) that are not easily optimized or cannot be directly optimized, and thus there has been a compromise of performing optimization with respect to the quadratic penalty instead of the dose distribution derivative functions.

[0103] Rather than using the dose distribution derivative functions to evaluate each iteration of the optimization process, the method can provide additional flexibility by directly deriving the objective functions and their targets and any probability distributions from the dose distribution derivative functions. The method described herein of transforming the dose distribution derivative functions into objective functions that define the optimization problem using either a probability distribution combined with a normal distribution or a dose scale target together with a loss function can provide improved flexibility and effectiveness.

[0104] Step 405 includes (partially) solving the optimization problem determined in step 404. Thus, step 405 includes finding variables (parameters of the second treatment plan) that minimize the total objective function subject to satisfying the constraints. Solving the optimization problem defined in step 404 is conventional.

[0105] Step 406 may include determining the second treatment plan from the treatment plan parameters obtained from step 405.

[0106] Step 407 includes any step of configuring or programming the radiation therapy delivery device 106 using the second treatment plan for delivery of radiation therapy according to the second treatment plan.

[0107] The exemplary method of the present disclosure may enable capturing specific goals regarding clinical objectives when attempting to fine-tune a treatment plan. By using a novel all-purpose function, it reduces the need to find specific weights of conventional penalty functions that correspond to a clinician's preferences (which can be a time-consuming process). Also, since the formulation of the optimization problem may not include non-linear constraints, in one or more examples, it may enable the optimization to be performed significantly faster.

[0108] The method described herein may be advantageous in one or more examples in providing the ability to select any dose distribution definition function to generate an all-purpose function. For example, evaluation criteria such as clinical objectives can be directly incorporated. This enables a natural way to fine-tune an existing treatment plan by using the first and second dose distribution definition functions described above. Further, in one or more examples, the probability distribution can capture nuances of more complex user preferences than when using only quadratic penalties. Instead, by receiving user input in the form of a probability distribution and using an appropriate loss function, the all-purpose function is a function that becomes very large when its value is considered such that the plan is not valid, which is similar to the way a clinician can think when planning manually. In one or more examples, the method can also more effectively handle trade-offs between different goals by using probability distributions.

[0109] Of course, in one or more examples, the method includes receiving one or more constraints, where a first treatment plan is defined with respect to a first set of parameters, and the one or more constraints define values for which the parameters of a second treatment plan can or cannot accept the optimization. For example, the first treatment plan may be defined with respect to parameters associated with the radiation therapy delivery device 106, and thus the constraints may relate to the technical limits of the radiation therapy delivery device with respect to, for example, a maximum gantry rotation speed or a maximum power output. In other examples, the constraints may represent limits on the dose distribution for the volume or a sub-volume thereof.

[0110] The example of FIG. 5 shows a computer-readable medium 500 as an example of a computer program product. The computer-readable medium may include a non-transitory computer-readable medium. The computer-readable medium 500 includes a computer program including computer program code configured to perform the methods described herein when executed by an apparatus such as a computer system 201 having a processor 202 and a memory 203.

[0111] The instructions and / or flowchart steps in the figures above can be executed in any order unless a specific order is specified. Also, those skilled in the art will recognize that, although one exemplary set of instructions / methods has been considered, the materials herein can be combined in various ways to obtain other examples, and that they are within the scope of the context provided by this detailed description.

[0112] In some exemplary embodiments, the steps of the methods described above are implemented as functions and software instructions embodied as a set of executable instructions programmed by and controlled by the executable instructions and performed on a computer or machine. Such instructions are loaded for execution on a processor (such as one or more CPUs). The term processor includes microprocessors, microcontrollers, processor modules or subsystems (including one or more microprocessors or microcontrollers), or other control or computing devices. A processor can refer to a single component or multiple components.

[0113] In other examples, the methods described herein and the data and instructions associated therewith are stored in respective storage devices, which are implemented as one or more non-transitory machines or one or more computer-readable media or computer-usable storage media. Such one or more computer-readable or computer-usable storage media are considered part of an article (or product). The article or product can be referred to as any manufactured single component or multiple components. One or more non-transitory machines or computer-usable media as defined herein exclude signals, but such one or more media can be capable of receiving and processing information from signals and / or other transitory media.

[0114] Exemplary embodiments of the materials discussed herein can be implemented in whole or in part via a network in computer or database devices and / or services. These include clouds, the Internet, intranets, mobile, desktop, processors, lookup tables, microcontrollers, consumer devices, infrastructure, or other enabling devices and services. The following non-exclusive definitions are provided as may be used in this specification and the claims.

[0115] In one example, one or more of the instructions or processes discussed herein are automated. The terms automated or automatic (and similar variations thereof) mean the controlled operation of a device, system, and / or process using a computer and / or a machine / electrical device without the need for human intervention, observation, effort, and / or decision-making that requires user input, unless otherwise specified.

[0116] Exemplary embodiments are provided herein with respect to a selected set of details. However, one of ordinary skill in the art will understand that many other exemplary embodiments can be implemented that include these details for different selected sets. The following claims are intended to encompass all possible exemplary embodiments.

Claims

1. A computer-implemented method for generating a radiation treatment plan for a patient's volume, the method comprising: Receiving a first treatment plan that serves as a basis for a second treatment plan, the first treatment plan showing a dose distribution across the patient's volume; Receiving at least one dose distribution derivative function, the at least one dose distribution derivative function being configured to provide a dose scale value as an output based on at least a portion of the dose distribution as an input; Receiving a target for each of the dose scale values output from each dose distribution derivative function, the target including a probability distribution for each or a group of the at least one dose distribution derivative function, the probability distribution representing the desirability of the dose scale value that can be output from the at least one dose distribution derivative function for the input dose distribution; Determining an optimization problem including an overall objective function, the overall objective function including the sum of one or more objective functions, the one or more objective functions including one or more of the at least one dose distribution derivative function, each probability distribution, and each loss function; Performing an optimization process based on the optimization problem; Determining the second treatment plan from the optimization process; A computer-implemented method comprising.

2. The probability distribution for each or a group of the at least one dose distribution derivative function represents the preference or attainability for each target of the dose scale value output from the at least one dose distribution derivative function for the input dose distribution. The computer-implemented method according to Claim 1.

3. The step of receiving the probability distribution includes: Receiving user input that defines the probability distribution, and The user selecting a probability distribution from a plurality of predefined candidate probability distributions The computer-implemented method according to Claim 1 or Claim 2, including one or more of.

4. The first treatment plan is: The operating parameters of a radiation therapy delivery device capable of deriving a dose distribution across the volume, The dose distribution across the volume, and The irradiation intensity integrated over time from each direction in space capable of deriving the dose distribution across the volume The computer-implemented method according to any one of Claims 1 to 3, determined by one of.

5. The step of receiving the at least one dose distribution derivative function comprises: receiving user input to define one or more of the dose distribution derivative functions, and selecting one or more dose distribution derivative functions from a set of candidate dose distribution derivative functions, wherein the candidate dose distribution derivative functions are determined based on a part of the body of the patient for which the volume is defined The computer-implemented method according to any one of claims 1 to 4, comprising one or more of the above.

6. The dose distribution derivative function includes, for the whole or a part of the volume, one or more of dose / volume, volume / dose, average dose, uniformity including a measure of dose uniformity in the whole or a part of the volume, a concordance index, and a penalty function including a minimum dose, a maximum dose, or a dose-volume histogram function. The computer-implemented method according to any one of claims 1 to 5.

7. The at least one dose distribution derivative function includes at least a first dose distribution derivative function and a second dose distribution derivative function, The first dose distribution derivative function includes a function for use in improving the dose distribution for a selected partial volume of the volume in the second treatment plan as compared to the first treatment plan in response to the optimization process. The first dose distribution derivative function is configured to provide a value indicating an improvement in the dose distribution for the selected partial volume of the volume, together with its associated goal, and The second dose distribution derivative function includes a function for use in substantially maintaining the dose distribution of one or more partial volumes defined in the first treatment plan in the second treatment plan after the optimization process. The second dose distribution derivative function is configured to provide a value indicating a worsening of any deviation in the dose distribution for one or more selected partial volumes of the volume, together with its associated goal. The computer-implemented method according to any one of claims 1 to 6.

8. The loss function is a log loss function, and a cross-entropy loss function The computer-implemented method according to any one of claims 1 to 7, selected from one or more of the above.

9. The one or more objective functions include one or more functions of the at least one dose distribution derivative function, the respective goals represented by a normal distribution having a target mean value, and the respective loss functions. The computer-implemented method according to claim 1.

10. The computer-implemented method according to any one of claims 1 to 9, comprising, for each line dose distribution derivative, representing the probability distribution as a cumulative distribution function or a probability density function in the optimization problem.

11. The step of performing the optimization process is to minimize the overall objective function, where the overall objective function includes a weighted sum of the one or more objective functions The computer-implemented method according to any one of claims 1 to 10.

12. An apparatus for generating a radiotherapy plan, the apparatus comprising a processor, a memory, and computer program code stored in the memory, the computer program code being configured to cause the apparatus to perform the method according to any one of claims 1 to 11 when executed by the processor.

13. The apparatus according to claim 12, comprising an input device configured to receive user input representing a probability distribution.

14. A computer program comprising computer program code configured to perform the method according to any one of claims 1 to 11 when executed by a processor.

15. The computer program according to claim 14, stored on a computer-readable medium such as a non-transitory computer-readable medium.

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