CN110246562B - Method, device and computer system for determining sub-beam intensity in radiotherapy system - Google Patents

Method, device and computer system for determining sub-beam intensity in radiotherapy system Download PDF

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CN110246562B
CN110246562B CN201810185373.9A CN201810185373A CN110246562B CN 110246562 B CN110246562 B CN 110246562B CN 201810185373 A CN201810185373 A CN 201810185373A CN 110246562 B CN110246562 B CN 110246562B
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朱磊
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Hefei Yofo Medical Technology Co ltd
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Abstract

Methods, apparatus, and computer systems are provided for determining beamlet intensities in a radiotherapy system. The method according to the application is based on the compressive sensing theory to obtain the objective function by introducing the positions of the radiation field and the sub-beams into the traditional objective function. The objective function is then optimized to select a spare field from the plurality of fields. The beamlet intensities are derived by optimizing a conventional intensity modulated radiotherapy plan based on the spare field.

Description

Method, device and computer system for determining sub-beam intensity in radiotherapy system
Technical Field
The present application relates generally to methods and apparatus and computer systems for determining beamlet intensities in a radiotherapy system.
Background
Radiotherapy is one of the main technical means for treating malignant tumors, and aims to irradiate a tumor (tissue to be treated with radiotherapy or a target region) with radiation at a maximum concentration and to receive a minimum dose of surrounding normal tissues as much as possible. IMRT (intensity modulated radiation therapy), developed from three-dimensional conformal radiation therapy, is one type of radiation therapy. IMRT requires that the intensity of the sub-beams (also called beamlets) within the field be adjusted to certain requirements. The method is characterized in that the intensity of the sub-beams is adjusted according to the three-dimensional shape of the target area and the specific anatomical relationship between the vital organs and the target area under the condition that the fields are consistent with the shape of the target area, and the dose contribution in a single field is uneven but is more uniform in the whole volume of the target area than three-dimensional conformal treatment.
Each field is divided into a plurality of beamlets. In planning, these beamlets are assigned different weights according to the three-dimensional shape of the target and the anatomical relationship with the associated organs-at-risk to produce an optimized, non-uniform intensity contribution within the same field of view such that the beam flux through the organs-at-risk is reduced while the beam flux in other portions of the target is increased.
Currently, the inverse algorithm is adopted clinically to make an intensity modulated radiotherapy plan. The number, shape and weight (corresponding to the intensity of the sub-beams) of each field are obtained iteratively by an optimization algorithm according to the requirement of the user on the dose for uniform irradiation of the tumor and the requirement on the dose for protecting the surrounding normal tissue organs, and the requirement of the user on the position and number of the fields, the target dose on the tumor and the dose constraint on the organs at risk, which are specified empirically. However, since the positions and the number of the fields are empirically determined by the user, the intensity of the sub-beams in each field cannot be optimized. Therefore, it is particularly important to reduce the number of beamlets while ensuring compliance with the final dose distribution.
Disclosure of Invention
In view of the above, the present application provides a method, apparatus and computer system capable of selecting a spare field from a plurality of fields to more accurately determine beamlet intensities in a radiotherapy system.
According to an aspect of the application, a method of determining beamlet intensities in a radiotherapy system, the radiotherapy system comprising a plurality of fields, each field having a plurality of beamlets, the method comprising: 1) dividing tissue to be radiotreated and surrounding tissue around the tissue to be radiotreated into a plurality of voxels and determining a radiation dose for each of the plurality of voxels; 2) simulating a first unit dose contribution of each beamlet of the plurality of beamlets to each voxel at unit intensity based on the position of each field and beamlet relative to the tissue to be treated and surrounding tissue and the tissue information of the tissue to be treated and surrounding tissue; 3) establishing a first objective function based on the radiation dose and the first unit dose contribution; 4) selecting a spare field from the plurality of fields by optimizing a first objective function; 5) determining a second unit dose contribution of each beamlet in the spare field to each voxel at unit intensity from the selected spare field and the tissue information; 6) constructing a second objective function based on the second unit dose contribution and the radiation dose; 7) the intensity of the beamlets in the standby field is determined by optimizing a second objective function.
According to an embodiment of the present application, in step 2) and step 5), the first unit dose contribution and the second unit dose contribution may be modeled by a monte carlo method, respectively.
According to an embodiment of the present application, the first objective function may be constructed as:
Figure BDA0001590081650000021
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001590081650000022
corresponds to the radiation dose, A1The contribution of the first unit dose is expressed,
Figure BDA0001590081650000023
corresponds to a sub-beam intensity, x, in a plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure BDA0001590081650000024
represents the maximum beamlet intensity in the ith field of the plurality of fields, and β is a weight coefficient.
According to an embodiment of the present application, in the case where p ═ 1, the first objective function may be optimized by a newton method or a gradient descent method.
According to an embodiment of the present application, in step 4), in the case where p ═ 1, the first objective function may be converted into:
Figure BDA0001590081650000025
to optimize a first objective function, where yiSatisfy yi≥xijWith the proviso that T is
Figure BDA0001590081650000031
Quadratic form of the term.
In the transformed first objective function, p satisfies the constraint of 0. ltoreq. p.ltoreq.1,
Figure BDA0001590081650000032
corresponds to the radiation dose, A1The contribution of the first unit dose is expressed,
Figure BDA0001590081650000033
corresponds to a sub-beam intensity, x, in a plurality of fieldsijIntensity, y, of a jth sub-beam representing an ith field of the plurality of fieldsiRepresents the maximum beamlet intensity in the ith field of the plurality of fields, and β is a weight coefficient.
According to an embodiment of the present application, in step 4), the second objective function may be constructed as:
Figure BDA0001590081650000034
wherein A is2The contribution of the second unit dose is expressed,
Figure BDA0001590081650000035
each element in (a) corresponds to one sub-beam intensity in the spare field,
Figure BDA0001590081650000036
corresponds to the radiation dose.
According to an embodiment of the present application, in step 4), the first objective function may be further configured to:
Figure BDA0001590081650000037
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001590081650000038
is the radiation dose of one of the voxels corresponding to the tissue to be radiotreated, APTVRepresenting the unit dose contribution of each sub-beam at unit intensity to each voxel corresponding to the tissue to be radiotherapy treated, N representing the amount of said surrounding tissue, AOARkRepresenting the unit dose contribution of each beamlet at unit intensity to each voxel corresponding to the kth surrounding tissue，
Figure BDA0001590081650000039
Corresponds to a sub-beam intensity, x, in a plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure BDA00015900816500000310
represents the maximum beamlet intensity, β and λ, in the ith of the plurality of fieldskAre weight coefficients.
According to an embodiment of the present application, in step 4), the first objective function may be optimized by a global optimization algorithm.
According to another aspect of the present application, there is provided an apparatus for determining beamlet intensities in a radiotherapy system, the radiotherapy system comprising a plurality of fields, each field having a plurality of beamlets, the apparatus comprising a dose determination unit, a spare field selection unit and an intensity determination unit. The dose determination unit may be configured to divide the tissue to be radiotherapy and surrounding tissue surrounding the tissue to be radiotherapy into a plurality of voxels and to determine a radiation dose for each of the plurality of voxels. The spare field selection unit may be configured to: simulating a first unit dose contribution of each beamlet of the plurality of beamlets to each voxel at unit intensity based on the position of each field and beamlet relative to the tissue to be treated and surrounding tissue and the tissue information of the tissue to be treated and surrounding tissue; establishing a first objective function based on the radiation dose and the first unit dose contribution; and selecting a spare field from the plurality of fields by optimizing the first objective function. The intensity determination unit may be configured to: determining a second unit dose contribution of each beamlet in the spare field to each voxel at unit intensity from the selected spare field and the tissue information; constructing a second objective function based on the second unit dose contribution and the radiation dose; and determining the intensity of the beamlets in the standby field by optimizing the second objective function.
According to yet another aspect of the present application, there is provided a computer system for determining beamlet intensities in a radiotherapy system, the radiotherapy system comprising a plurality of fields, each field having a plurality of beamlets, the system for determining beamlet intensities in the radiotherapy system comprising: a memory storing computer instructions; a processor executing computer instructions stored by the memory to perform the following operations: dividing tissue to be radiotreated and surrounding tissue around the tissue to be radiotreated into a plurality of voxels and determining a radiation dose for each of the plurality of voxels; simulating a first unit dose contribution of each beamlet of the plurality of beamlets to each voxel at unit intensity based on the position of each field and beamlet relative to the tissue to be treated and surrounding tissue and the tissue information of the tissue to be treated and surrounding tissue; establishing a first objective function based on the radiation dose and the first unit dose contribution; selecting a spare field from the plurality of fields by optimizing a first objective function; determining a second unit dose contribution of each beamlet in the spare field to each voxel at unit intensity from the selected spare field and the tissue information; constructing a second objective function based on the second unit dose contribution and the radiation dose; the intensity of the beamlets in the standby field is determined by optimizing a second objective function.
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These and/or other aspects of the present application will become apparent and more readily appreciated from the following description of the exemplary embodiments, taken in conjunction with the accompanying drawings of which:
figure 1 is a flow chart of a method of determining beamlet intensities in a radiotherapy system according to an exemplary embodiment of the present application;
fig. 2 is a schematic plan view of a beam field including a plurality of beamlets according to an exemplary embodiment of the present application;
FIG. 3 is a schematic perspective view of irradiation of tissue to be radiotreated and surrounding tissue through multiple fields in accordance with an exemplary embodiment of the present application;
FIG. 4 is a graph of the dose contribution of a spare field selected by the method of determining beamlet intensities in a radiotherapy system of the present application to tissue to be treated and surrounding tissue in an intensity modulated radiotherapy method;
FIG. 5 is a schematic diagram of the dose contribution of a spare field empirically selected by a user to the tissue to be treated and surrounding tissue in an intensity modulated radiation therapy method;
figure 6 is a block diagram illustrating an apparatus for determining beamlet intensities in a radiotherapy system according to an embodiment of the present application; and
FIG. 7 is a block diagram illustrating a computer system suitable for implementing embodiments of the present application.
Detailed Description
While the disclosure is susceptible to various modifications and alternative embodiments, specific embodiments have been shown in the drawings and will be described in detail in this written description. Aspects and features of the present disclosure and methods or methods of accomplishing the same will become apparent when reference is made to the embodiments described with reference to the accompanying drawings. This disclosure may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.
As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. Furthermore, when describing embodiments of the present invention, the use of "may" refer to "one or more embodiments of the present invention. Expressions such as "at least one of" when following a column of elements modify the entire column of elements without modifying individual elements in the column. Additionally, the term "exemplary" is intended to mean exemplary or illustrative. The use of the singular forms "a", "an" and "the" encompass plural referents unless the context clearly dictates otherwise.
As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises," "comprising," "includes" and/or "including," when used herein, specify the presence of stated features or components, but do not preclude the presence or addition of one or more other features or components.
As used herein, "substantially," "about," "approximately," and similar terms are used as terms of approximation and not as terms of degree, and are intended to account for inherent deviations in measured or calculated values that would be recognized by one of ordinary skill in the art. Further, these terms, as used herein, include the set point and average value within an acceptable range of deviation for a particular value as determined by one of ordinary skill in the art in view of the measurement in question and the error associated with the measurement of the particular value (i.e., the limitations of the measurement system). For example, "about" can mean within one or more standard deviations, or within ± 30%, ± 20%, ± 10%, ± 5% of the stated values.
While certain embodiments may be implemented differently, the particular process sequence may be performed differently than described. For example, two consecutively described processes may be performed at approximately the same time, or in the reverse order to the described order.
The method and apparatus for determining the intensity of beamlets in a radiotherapy system of the present application will be described in detail with reference to fig. 1 to 6.
In a method of determining beamlet intensities in a radiotherapy system according to the present application, for example, the radiotherapy system may comprise a plurality of fields F (also referred to as fields) as shown in fig. 3, and each field has a plurality of beamlets B. The source F shown in fig. 2 comprises 9 beamlets B. For example, each field F is realized as a plurality of beamlets B by an MLC (Multi-Leaf collimator). The field F shown in FIG. 2 can be achieved by a radiation source and MCL included in the radiotherapy system. The source may emit X-rays or gamma-rays, i.e. the field F is a field of X-rays. As another example, the source may emit positively charged ions (i.e., protons). This is merely exemplary and the source according to the application is not limited thereto. In one example, the number of beamlets B in each field F may be the same or different, and each beamlet B may have a different shape.
Referring to fig. 1 and 3, in step S1, a tissue to be radiotherapy PTV and a surrounding tissue OAR around the tissue to be radiotherapy are divided into a plurality of voxels and a radiation dose of each of the plurality of voxels is determined. In the example shown in fig. 3, the tissue to be radiotherapy PTV is divided into a plurality of voxels, and the surrounding tissue OAR is divided into a plurality of voxels surrounding the tissue to be radiotherapy PTV. That is, the voxels divided by the tissue PTV to be treated with radiation and the surrounding tissue OAR may correspond to equal three-dimensional volumes. A voxel is the smallest unit of digital data on a three-dimensional partition. In fig. 3, 20 fields F are shown, but this is merely exemplary. The radiation dose for each of the plurality of voxels represents the radiation dose that each voxel needs to receive. For example, the radiation dose to be received by the tissue PTV to be treated is greater than a predetermined value, and the radiation dose to be received by the surrounding tissue OAR is less than a predetermined value. The radiation dose for each of the plurality of voxels may be determined from a CT image of the tissue PTV and surrounding tissue OAR to be radiotreated.
In step S2, the first unit dose contribution of each beamlet B in the plurality of fields F to each voxel is modeled based on the position of each field F and beamlet B relative to the tissue PTV and surrounding tissue OAR to be treated and the tissue information of the tissue PTV and surrounding tissue OAR to be treated.
The tissue information of the tissue PTV to be radiotherapy and the surrounding tissue OAR can be acquired by a computed tomography image (i.e., CT image) of the tissue PTV to be radiotherapy and the surrounding tissue OAR. For example, the tissue information may be acquired by a planning CT (computed tomography) device for inverse intensity modulated radiation therapy. The tissue information may include volume, shape, location and electron density information of the tissue to be treated for radiotherapy PTV and surrounding tissue OAR. The position of the plurality of fields F and beamlets B relative to the tissue PTV to be treated and the surrounding tissue OAR may typically be set manually. For example, the field F may be set so that the rays in the field F pass through the gaps between the voxels corresponding to the surrounding tissue OAR as much as possible and irradiate on the tissue PTV to be radiotreated. However, no matter how the position of the field F is set, the dose received by the OAR of the surrounding tissue cannot be zero.
The first unit dose contribution is the dose contribution of each beamlet B to each voxel at unit intensity.
In step S3, a first objective function is established based on the determined radiation dose and the first unit dose contribution. In step S4, a spare field P is selected from the plurality of fields F by optimizing the first objective function.
In inverse intensity modulated radiotherapy, with the radiation dose and first unit dose contribution determination, the main objective is to determine the intensities of all the beamlets B in the multiple fields F such that each voxel receives a dose that satisfies as much as possible the radiation dose it should receive.
Thus, the objective function used in the backprojection radiotherapy planning is:
Figure BDA0001590081650000071
wherein the content of the first and second substances,
Figure BDA0001590081650000072
corresponds to the radiation dose determined in step S1, a denotes the first unit dose contribution, vector, determined in step S2
Figure BDA0001590081650000073
Corresponds to the intensity, vector, of one beamlet B of the plurality of fields F in steps S1 and S2
Figure BDA0001590081650000074
It may be a vector in which the intensities of all the beamlets B are connected in series by a row. Solution of the conventional objective function
Figure BDA0001590081650000075
Is such that the vector
Figure BDA0001590081650000076
The second-order norm of (a) takes the vector of all beamlets B whose minimum value is connected in series by rows.
Thus, the first objective function according to the present application introduces the position of the field F and the beamlet B into the conventional objective function.
According to an embodiment of the present application, the field F and the position of the beamlet B may be introduced by introducing the intensity of the jth beamlet B of the ith field of the plurality of fields F in a conventional objective function. In other words, F is further determined based on the mapping relationship of the intensity of the jth sub-beam B of the ith field to the corresponding field F and sub-beam B, indirectly introducing the positions of field F and sub-beam B.
Further, unlike the conventional intensity modulated radiotherapy in which a doctor empirically determines a field to be used (hereinafter referred to as a spare field) from a plurality of fields F, the present application applies compressive sensing to inverse intensity modulated radiotherapy to select a more accurate spare field P from the plurality of fields F, thereby determining the position of the spare field P and the corresponding beamlets B included therein with respect to the tissue PTV to be radiotherapy and the surrounding tissue OAR.
Since the fundamental purpose of establishing the first objective function is to select several spare fields P from the plurality of fields F, i.e., to reduce the number of fields F while satisfying the radiation dose to be delivered.
Therefore, in the method of the present application, based on the objective function (i.e. equation 1) used in the inverse intensity modulated radiotherapy plan, based on the compressive sensing theory, the intensity set of the sub-beams is set such that the product of the sum of the intensity maxima of the sub-beams B in each field F and the weighting coefficient takes its minimum value (which may be a preset value) as a limiting condition, the intensity maxima of the sub-beams B in each field F are taken as sampling signals, and then the spare field P is selected from the field F by solving the sparse solution of the sampling signals through the compressive sensing, wherein the intensity set of the sub-beams in the spare field P simultaneously enables the radiation dose finally received by the tissue PTV to be irradiated and the surrounding tissue OAR to meet or most closely meet the intensity modulated radiotherapy target (i.e. the preset radiation dose). Therefore, the method according to an embodiment of the present application may also be considered as an application of the compressed sensing method in signal processing.
In one aspect, compressed sensing is a technique for reconstructing sparse or compressible signals. The mathematical manifestation of a sparse signal is that it contains many coefficients close to or equal to zero when expressed in some domains. That is, a signal is said to be sparse if it has only a finite non-zero sample point, while other sample points are zero (or close to zero). Efficient use of compressed sensing techniques (i.e., sparsity of the signal to be processed) can be used to reduce the number of measurement samples required. Mathematically, intensity modulated radiation therapy inverse planning is similar to the signal processing problem described above in the case where multiple fields F (i.e., all existing fields F) are the "signals" to be sought. As mentioned above, inverse planning is a pathological problem and there are usually a plurality of sets of spare fields P (i.e. a set of fields selected from the plurality of fields F, for example selected empirically by a physician) that can generate the radiation dose that the tissue PTV to be treated with radiation needs to receive, but in this case it is not necessarily possible to receive the minimum radiation dose to the surrounding tissue OAR. Therefore, in the present application, the spare field P is selected from the plurality of fields F by solving for sparseness of the sampling signals by using the maximum intensity value of the beamlet B in each field F as the sampling signal, and the set of the beamlet intensities in the spare field P enables the radiation dose finally received by the tissue PTV to be radiotherapy and the surrounding tissue OAR to satisfy or most approximate to the target of intensity modulated radiotherapy as the limiting condition (for example, equation (1) is satisfied). The number of non-zero values in the sparse solution found corresponds to the number of spare fields P.
On the other hand, when the maximum intensity value of the sub-beam B in each field F is used as the sampling signal, each term in the sparse solution obtained by the compressed sensing method may correspond to the maximum sub-beam intensity in one field F, so that a term of zero in the sparse solution indicates that the intensities of all the sub-beams B in the corresponding field F are all zero, that is, the field F corresponding to the term is not selected as the spare field P. In this way, a one-to-one mapping relationship of each item in the sparse solution with the position of the portal F can be realized.
Further, the number of candidate fields P can be set by setting the weight coefficient, and for example, the larger the weight coefficient, the smaller the number of candidate fields P.
According to one embodiment of the present application, the first objective function component may be:
Figure BDA0001590081650000091
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001590081650000092
each element in (1) corresponds to a plurality of volumesA radiation dose of one voxel in a voxel, a representing the first unit dose contribution described above,
Figure BDA0001590081650000093
each element in (a) corresponds to a beamlet intensity,
Figure BDA0001590081650000094
it may be a vector in which the intensities of all the beamlets B are connected in series by a row. x is the number ofijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000095
represents the maximum beamlet intensity in the ith field of the plurality of fields F, and β is a weight coefficient.
The number of candidate fields P selected from the plurality of fields F can be set by setting the value of the weight coefficient β. The larger the value of β, the smaller the number of candidate fields P. The value of β is greater than zero.
According to an embodiment of the present application, the first objective function (e.g., equation (2)) may be optimized by a global optimization algorithm to obtain a vector
Figure BDA0001590081650000096
(Vector)
Figure BDA0001590081650000097
Corresponds to the intensity of the respective beamlet B in the respective field F. That is, the intensity of each beamlet B corresponds to a unique beamlet B in a unique field F. Thus, the vector can be passed
Figure BDA0001590081650000101
The mapping relation between each element in (B) and the field F and the sub-beam B in the field F, and selects a spare field P from the plurality of fields F.
According to one embodiment of the present application, it is possible to determine whether the radiation dose to be finally achieved is closer to the radiation dose of the tissue to be treated PTV or the radiation dose of the surrounding tissue OAR by differentiating the voxels of the tissue to be treated PTV and the surrounding tissue OAR in the first objective function and setting the weighting coefficients.
Thus, according to another exemplary embodiment of the present application, the first objective function may be further structured as:
Figure BDA0001590081650000102
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001590081650000103
is the radiation dose, A, of one of the voxels corresponding to the tissue to be radiotherapy PTVPTVRepresenting the unit dose contribution of each beamlet B at unit intensity to each voxel corresponding to the tissue PTV to be irradiated, N representing the amount of said surrounding tissue, AOARkRepresenting the unit dose contribution of each beamlet B at unit intensity to each voxel corresponding to the k-th surrounding tissue OAR,
Figure BDA0001590081650000104
corresponds to the intensity of the beamlet B,
Figure BDA0001590081650000105
may be a vector, x, in which the intensities of all beamlets B are connected in series by a lineijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000106
represents the maximum beamlet intensity in the ith field of the plurality of fields F, beta is a weight coefficient, and lambda iskIs a weight coefficient
For example, in the examples shown in fig. 3 to 5, the number of N is 6, i.e., the number of the surrounding tissues OAR is 6. Can be set by setting lambdakDetermines whether the last selected spare field P is such that the radiation dose is more than that required for the tissue PTV to be treated or that required for the surrounding tissue OAR.
According to an embodiment of the present application, the first objective function (e.g., equation (3)) may be optimized by a global optimization algorithm to obtain a vector
Figure BDA0001590081650000107
Further, a plurality of spare fields P are selected from the plurality of fields F.
In the case where p in the first objective function (e.g., equation (2) or equation (3)) is equal to 1, the first objective function (e.g., equation (2) or equation (3)) may be optimized through a conventional iterative algorithm such as a newton method, a gradient descent method, a conjugate gradient method, or a quasi-newton method.
That is, in the case where 0 ≦ p ≦ 1, the first objective function (e.g., equation (2) or equation (3)) may be optimized by the global optimization algorithm to obtain a globally optimal solution for the objective function. The global optimization researches the characteristics and the construction of the global optimal solution of the multivariable nonlinear function in a certain constraint area to find the computing method of the global optimal solution, and the theoretical properties and the computing performance of the solving method. For example, the first objective function may be optimized using a global optimization algorithm such as simulated annealing algorithm, genetic algorithm, tabu search, particle swarm algorithm, ant colony algorithm. But the application is not limited thereto.
In the case where p is equal to 1 in the first objective function (e.g., equation (2) or equation (3)), the first objective function (e.g., equation (2) or equation (3)) may be optimized by an iterative algorithm such as a newton method, a gradient descent method, a conjugate gradient method, or a quasi-newton method.
In a method according to an embodiment of the present application, in a case where p in a first objective function (e.g., equation (2) or equation (3)) is equal to 1, within a norm of order 1 in equation (6) or equation (7), the p is set to be equal to 1
Figure BDA0001590081650000111
The term is used as a constraint to convert the non-linear problem into a linear problem to further reduce the amount of computation.
Taking equation (2) as an example, the first objective function is converted into:
Figure BDA0001590081650000112
wherein, yiSatisfy yi≥xijWith the proviso that T is
Figure BDA0001590081650000113
Quadratic form of the term.
In the formula (4), the reaction mixture is,
Figure BDA0001590081650000114
corresponds to the radiation dose of one of the plurality of voxels, a denotes the first unit dose contribution described above,
Figure BDA0001590081650000115
each element in (a) corresponds to a beamlet intensity,
Figure BDA0001590081650000116
may be a vector, x, in which the intensities of all beamlets B are connected in series by a lineijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000117
represents the maximum beamlet intensity in the ith field of the plurality of fields F, and β is a weight coefficient.
In this way, the objective function can be optimized by an iterative algorithm such as newton's method, gradient descent method, etc. with a reduced amount of computation to obtain a vector
Figure BDA0001590081650000118
Further, the vector may be passed
Figure BDA0001590081650000119
The mapping relation between each element in (B) and the field F and the sub-beam B in the field F, and selects a spare field P from the plurality of fields F.
Referring to fig. 3, through steps S3 and S4, a plurality of fields F (e.g., 3 fields F) can be selected as spare fields P from the 20 fields F shown in fig. 3.
In step S5, a second unit dose contribution of each beamlet B in the spare field P to each voxel at unit intensity is determined from the selected spare field P and the tissue information. For example, the second unit dose contribution is modeled based on the position of each field F and beamlet B relative to the tissue to be treated PTV and surrounding tissue OAR and tissue information of the tissue to be treated PTV and surrounding tissue OAR. The second unit dose contribution is simulated, for example, by the monte carlo method. Since the first objective function (step S3) is established by considering the set of beamlet intensities in the spare field P as the limiting condition, so that the radiation dose finally received by the tissue PTV to be treated and the surrounding tissue OAR meets or is closest to the intensity modulated radiation treatment target, the second unit dose contribution modeled by the spare field P can make the inverse planning result closer to the ideal, i.e. the finally obtained beamlet intensities can make the surrounding tissue OAR receive the minimum radiation dose while making the tissue PTV to be treated receive the preset radiation dose. In step S6, a second objective function is constructed from the second unit dose contribution and the radiation dose.
In an embodiment of the present application, the second objective function may correspond to a conventional objective function in an intensity modulated radiotherapy plan, that is:
Figure BDA0001590081650000121
wherein A is2Represents the contribution of the second unit dose,
Figure BDA0001590081650000122
corresponds to one sub-beam intensity in the alternative field P,
Figure BDA0001590081650000123
it may be a vector in which all the beamlet intensities in the candidate field P are connected in series by a row,
Figure BDA0001590081650000124
corresponds to the radiation dose.
In step S7, the intensity of the beamlet B in the spare field P is determined by optimizing the second objective function. In the case where the second objective function is equation (5), equation (5) can be optimized by newton's method or gradient descent method. As another example of the present application, equation (5) may be optimized using a global optimization algorithm. But the application is not limited thereto.
Fig. 4 shows a schematic diagram of the dose contribution of the spare field selected by the method of determining the intensity of the sub-beams in a radiotherapy system of the present application to the tissue to be radiotherapy PTV and the surrounding tissue OAR. Fig. 5 is a schematic diagram of the dose contribution of the spare field P empirically selected by the user to the tissue PTV to be treated and the surrounding tissue OAR in the intensity modulated radiation therapy method.
In fig. 4 and 5, the radiation dose received by the voxel is schematically represented by the number of lines in each tissue, i.e. a larger number of lines indicates a larger radiation dose received by the corresponding tissue. 3 from the 20 fields F shown in fig. 3 are selected as the spare fields P by steps S3 and S4 and the intensity of the sub-beam B is acquired based on the spare fields P again by steps S5 to S7. The radiation dose to the surrounding tissue OAR in fig. 4 is significantly reduced compared to the radiation dose to the surrounding tissue OAR in fig. 5.
In equations (2) to (9), the number of candidate fields P selected from the plurality of fields F can be set by setting the value of β. The larger the value of β, the smaller the number of candidate fields P. The value of β may be greater than zero.
The methods described with reference to fig. 1-5 may be implemented by a computer system. The computer system includes a memory storing executable instructions and a processor. The processor communicates with the memory to execute the executable instructions to implement the methods described with reference to fig. 1-5. Alternatively or additionally, the methods described with reference to fig. 1-5 may be implemented by a non-transitory computer storage medium. The medium stores computer readable instructions that, when executed, cause a processor to perform the method described with reference to fig. 1-5.
Figure 6 is a block diagram illustrating an apparatus 100 for determining beamlet intensities in a radiotherapy system according to an embodiment of the present application. An apparatus 100 for determining beamlet intensities in a radiotherapy system comprising: a dose determination unit 110 configured to divide a tissue to be radiotherapy PTV and a surrounding tissue OAR around the tissue to be radiotherapy into a plurality of voxels and determine a radiation dose of each of the plurality of voxels; a spare field selection unit 120 configured to: simulating a first unit dose contribution of each of the beamlets in a plurality of fields to each voxel at a unit intensity based on the position of each field F and beamlet B with respect to the tissue to be treated and the surrounding tissue and tissue information of the tissue to be treated PTV and surrounding tissue OAR; establishing a first objective function based on the radiation dose and the first unit dose contribution; selecting a standby radiation field P from the plurality of radiation fields F by optimizing the first objective function; an intensity determination unit configured to: determining a second unit dose contribution of each beamlet B in the spare field P to each voxel at a unit intensity from the selected spare field P and the tissue information; constructing a second objective function based on the second unit dose contribution and the radiation dose; the intensity of the sub-beam B in the backup field P is determined by means of the second objective function.
According to an embodiment of the present application, the spare field selection unit 120 and the intensity determination unit 130 may simulate the first unit dose contribution and the second unit dose contribution by the monte carlo method, respectively.
According to an embodiment of the present application, the spare field selection unit 120 constructs the first objective function as:
Figure BDA0001590081650000131
in the formula (6), p satisfies the constraint of 0. ltoreq. p.ltoreq.1,
Figure BDA0001590081650000132
corresponds to the radiation dose of one of the plurality of voxels, a denotes the first unit dose contribution described above,
Figure BDA0001590081650000133
each element in (a) corresponds to a beamlet intensity,
Figure BDA0001590081650000134
it may be a vector in which the intensities of all the beamlets B are connected in series by a row. x is the number ofijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000141
represents the maximum beamlet intensity in the ith field of the plurality of fields F, and β is a weight coefficient.
According to an embodiment of the present application, the first objective function (e.g., equation (6)) may be optimized by a global optimization algorithm to obtain a vector
Figure BDA0001590081650000142
(Vector)
Figure BDA0001590081650000143
Corresponds to the intensity of the respective beamlet B in the respective field F. That is, the intensity of each beamlet B corresponds to a unique beamlet B in a unique field F. Thus, the vector can be passed
Figure BDA0001590081650000144
The mapping relation between each element in (B) and the field F and the sub-beam B in the field F, and selects a spare field P from the plurality of fields F.
According to an embodiment of the present application, the spare field selection unit 120 may further configure the first objective function to:
Figure BDA0001590081650000145
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001590081650000146
in (1)Each element being the radiation dose, A, of one of the voxels corresponding to the tissue PTV to be treatedPTVRepresenting the unit dose contribution of each beamlet B at unit intensity to each voxel corresponding to the tissue PTV to be irradiated, N representing the amount of said surrounding tissue, AOARkRepresenting the unit dose contribution of each beamlet B at unit intensity to each voxel corresponding to the k-th surrounding tissue OAR,
Figure BDA0001590081650000147
corresponds to the intensity of the beamlet B,
Figure BDA0001590081650000148
may be a vector, x, in which the intensities of all beamlets B are connected in series by a lineijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000149
represents the maximum beamlet intensity in the ith field of the plurality of fields F, beta is a weight coefficient, and lambda iskAre weight coefficients.
According to an embodiment of the present application, the first objective function (e.g., equation (7)) may be optimized by a global optimization algorithm to obtain a vector
Figure BDA00015900816500001410
Further, a plurality of spare fields P are selected from the plurality of fields F.
That is, in the case where 0 ≦ p ≦ 1, the spare field selection unit 120 may optimize the first objective function (e.g., equation (6) or equation (7)) through a global optimization algorithm to obtain a global optimal solution for the objective function. The global optimization researches the characteristics and the construction of the global optimal solution of the multivariable nonlinear function in a certain constraint area to find the computing method of the global optimal solution, and the theoretical properties and the computing performance of the solving method. For example, the first objective function may be optimized using a global optimization algorithm such as simulated annealing algorithm, genetic algorithm, tabu search, particle swarm algorithm, ant colony algorithm. But the application is not limited thereto.
In the case where p in the first objective function (e.g., equation (6) or equation (7)) is equal to 1, the first objective function (e.g., equation (6) or equation (7)) may be optimized through an iterative algorithm such as a newton method, a gradient descent method, a conjugate gradient method, or a quasi-newton method. According to an embodiment of the present application, in the case where p is equal to 1 in the first objective function (e.g., equation (6) or equation (7)), the spare field selection unit 120 may optimize the first objective function (e.g., equation (6) or equation (7)) through a conventional iterative algorithm such as a newton method, a gradient descent method, a conjugate gradient method, or a quasi-newton method.
According to one embodiment of the present application, in case p is equal to 1, within a norm of order 1 in equation (6) or equation (7)
Figure BDA0001590081650000151
The term is used as a constraint to convert the non-linear problem into a linear problem to further reduce the amount of computation.
Taking equation (6) as an example, the spare field selection unit 120 converts the first objective function into:
Figure BDA0001590081650000152
in the transformed first objective function (i.e., equation (8)), T is
Figure BDA0001590081650000153
Quadratic form of the term, yiSatisfy yi≥xijThe limit conditions of (a), that is,
Figure BDA0001590081650000154
in the transformed first objective function,
Figure BDA0001590081650000155
corresponds to the radiation dose of one of the plurality of voxels, a denotes the first unit dose contribution described above,
Figure BDA0001590081650000156
each element in (a) corresponds to a beamlet intensity,
Figure BDA0001590081650000157
may be a vector, x, in which the intensities of all beamlets B are connected in series by a lineijAn intensity of a jth sub-beam representing an ith field of the plurality of fields F,
Figure BDA0001590081650000158
represents the maximum beamlet intensity in the ith field of the plurality of fields F, and β is a weight coefficient.
According to an embodiment of the present application, the intensity determination unit 130 may construct the second objective function as:
Figure BDA0001590081650000159
wherein A is2Represents the contribution of the second unit dose,
Figure BDA00015900816500001510
corresponds to one sub-beam intensity in the alternative field P,
Figure BDA00015900816500001511
it may be a vector in which all the beamlet intensities in the candidate field P are connected in series by a row,
Figure BDA00015900816500001512
corresponds to the radiation dose.
In one embodiment of the present application, the intensity determination unit 130 may determine the intensity of the beamlet B in the spare field P by optimizing the second objective function. In the case where the second objective function is equation (9), equation (9) can be optimized by newton's method or gradient descent method. As another example of the present application, equation (9) may be optimized using a global optimization algorithm. But the application is not limited thereto.
The apparatus for determining beamlet intensities in a radiotherapy system described with reference to figure 6 may be implemented by a computer system. The computer system may include a memory storing executable instructions and a processor. The processor communicates with the memory to execute executable instructions to implement the apparatus described with reference to fig. 6. Alternatively or additionally, the apparatus described with reference to fig. 6 may be embodied by a non-transitory computer storage medium. The medium stores computer readable instructions that, when executed by a computer, perform the functions of the apparatus described with reference to fig. 6.
Referring now to FIG. 7, FIG. 7 is a block diagram that illustrates a computer system 7000 that is suitable for implementing embodiments of the present application.
As shown in fig. 7, the computer system 7000 may include a processor (such as a Central Processing Unit (CPU)7001, a Graphic Processing Unit (GPU), or the like) that can perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM)7002 or a program loaded from a storage section 7008 into a Random Access Memory (RAM) 7003. In the RAM 7003, various programs and data required for the operation of the system 7000 are also stored. The CPU 7001, ROM 7002, and RAM 7003 are connected to one another through a bus 7004. An input/output I/O interface 7005 is also connected to the bus 7004.
The following are components that may be connected to the I/O interface 7005: an input portion 7006 including a keyboard, a mouse, and the like; an output portion 7007 including a cathode ray tube CRT, a liquid crystal display device LCD, a speaker, and the like; a storage portion 7008 including a hard disk and the like; and a communication portion 7009 including a network interface card (such as a LAN card and a modem). The communication portion 7009 can perform communication processing over a network such as the internet. The driver 7010 may also be connected to the I/O interface 7005 as necessary. A removable medium 7011 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like may be mounted on the drive 7010 so that a computer program read out therefrom is installed into the storage portion 7008 as needed.
In particular, according to embodiments of the present disclosure, the methods described above with reference to fig. 1 to 5 may be implemented as computer software programs. For example, embodiments of the disclosure may include a computer program product comprising a computer program tangibly embodied in a machine-readable medium. The computer program comprises program code for performing the method described with reference to fig. 1 to 5. In such an embodiment, the computer program can be downloaded from a network through the communication section 709 and installed, and/or can be installed from the removable medium 7011.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units or modules referred to in the embodiments of the present application may be implemented by software or hardware. The described units or modules may also be provided in a processor. The names of these units or modules should not be construed as limiting these units or modules.
According to the embodiments of the present application, the provided method, apparatus and computer system for determining the intensity of sub-beams in a radiotherapy system can be used in any kind of radiotherapy system. For example, a radiotherapy system that effects radiotherapy by X-rays, gamma-rays, or protons, but the application is not limited thereto.
The above description is only exemplary of the present application and illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features and the technical features having similar functions disclosed in the present application are mutually replaced to form the technical solution.

Claims (13)

1. A method of determining beamlet intensities in a radiotherapy system comprising a plurality of fields, each field having a plurality of said beamlets, the method comprising:
1) dividing tissue to be radiotreated and surrounding tissue surrounding the tissue to be radiotreated into a plurality of voxels and determining a radiation dose for each of the plurality of voxels;
2) modeling a first unit dose contribution of each of the beamlets in the plurality of fields to each of the voxels at a unit intensity as a function of the position of each of the fields and the beamlets relative to the tissue to be treated and the surrounding tissue and the tissue information for the tissue to be treated and the surrounding tissue;
3) establishing a first objective function based on the radiation dose and the first unit dose contribution;
4) selecting a spare field from the plurality of fields by optimizing the first objective function;
5) determining a second unit dose contribution of each of the beamlets in the back-up field to each of the voxels at a unit intensity from the selected back-up field and the tissue information;
6) constructing a second objective function from the second unit dose contribution and the radiation dose;
7) determining intensities of beamlets in the spare field by optimizing the second objective function, wherein,
the first objective function is constructed as:
Figure FDA0003120129030000011
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure FDA0003120129030000012
corresponds to the radiation dose, A1Represents the first unit dose contribution and the second unit dose contribution,
Figure FDA0003120129030000013
corresponds to a sub-beam intensity, x, of the plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure FDA0003120129030000014
represents the maximum beamlet intensity in the ith field of the plurality of fields, beta is a weight coefficient, the number of the spare fields is set by setting the value of the weight coefficient beta, beta is larger than zero as the beta value is larger, the number of the spare fields is smaller,
the second objective function is constructed as:
Figure FDA0003120129030000015
wherein A is2Represents the contribution of the second unit dose,
Figure FDA0003120129030000016
corresponds to one sub-beam intensity in the spare field,
Figure FDA0003120129030000021
corresponds to the radiation dose.
2. The method of claim 1, wherein in step 2) and step 5), the first unit dose contribution and the second unit dose contribution are modeled by a monte carlo method, respectively.
3. The method of claim 1, wherein the first objective function is optimized by newton's method or gradient descent method in case p ═ 1.
4. The method of claim 3, wherein in step 4), the first objective function is transformed into:
Figure FDA0003120129030000022
to optimize the first objective function,
wherein, yiSatisfy yi≥xijWith the proviso that T is
Figure FDA0003120129030000023
A quadratic form of the term, yi, represents a maximum beamlet intensity in an ith field of the plurality of fields.
5. The method of claim 1, wherein the first objective function is further constructed as:
Figure FDA0003120129030000024
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure FDA0003120129030000025
is the radiation dose of one of the plurality of voxels corresponding to the tissue to be radiotherapy-treated,
Figure FDA0003120129030000026
is the radiation dose of one of the voxels corresponding to the surrounding tissue, aPTVA unit representing the unit of each sub-beam under unit intensity for each voxel corresponding to the tissue to be radiotreatedDose contribution, N represents the amount of surrounding tissue, AOARkRepresenting a unit dose contribution of each of said sub-beams at a unit intensity to each voxel corresponding to a k-th of said surrounding tissue,
Figure FDA0003120129030000027
corresponds to a sub-beam intensity, x, of the plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure FDA0003120129030000028
represents the maximum beamlet intensity, β and λ, in the ith of the plurality of fieldskSetting the number of the spare fields by setting the value of the weight coefficient beta, wherein the larger the value of beta is, the smaller the number of the spare fields is, and lambda iskDetermines whether the last selected spare field is such that the radiation dose more satisfies the radiation dose required by the tissue to be treated or the radiation dose required by the surrounding tissue.
6. The method of claim 1, wherein in step 4), the first objective function is optimized by a global optimization algorithm.
7. An apparatus for determining beamlet intensities in a radiotherapy system comprising a plurality of fields, each field having a plurality of said beamlets, the apparatus comprising:
a dose determination unit configured to divide a tissue to be radiotherapy and a surrounding tissue around the tissue to be radiotherapy into a plurality of voxels and determine a radiation dose of each of the plurality of voxels;
a spare field selection unit configured to:
modeling a first unit dose contribution of each of the beamlets in the plurality of fields to each of the voxels at a unit intensity as a function of the position of each of the fields and the beamlets relative to the tissue to be treated and the surrounding tissue and the tissue information for the tissue to be treated and the surrounding tissue;
establishing a first objective function based on the radiation dose and the first unit dose contribution; and
selecting a spare field from the plurality of fields by optimizing the first objective function; and
an intensity determination unit configured to:
determining a second unit dose contribution of each of the beamlets in the back-up field to each of the voxels at a unit intensity from the selected back-up field and the tissue information;
constructing a second objective function from the second unit dose contribution and the radiation dose; and
determining intensities of beamlets in the spare field by optimizing the second objective function, wherein,
the spare field selection unit constructs the first objective function as:
Figure FDA0003120129030000031
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure FDA0003120129030000041
corresponds to the radiation dose, A1Represents the first unit dose contribution and the second unit dose contribution,
Figure FDA0003120129030000042
corresponds to a sub-beam intensity, x, of the plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure FDA0003120129030000043
represents the maximum beamlet intensity in the ith of the plurality of fields, β is a weight coefficient, β is greater than zero, andsetting the number of the spare fields by setting the value of a weight coefficient beta, wherein the larger the value of beta is, the smaller the number of the spare fields is; and
the intensity determination unit constructs the second objective function as:
Figure FDA0003120129030000044
wherein A is2Represents the contribution of the second unit dose,
Figure FDA0003120129030000045
corresponds to one sub-beam intensity in the spare field,
Figure FDA0003120129030000046
corresponds to the radiation dose.
8. The apparatus of claim 7, wherein the alternate field selection unit and the intensity determination unit simulate the first and second unit dose contributions, respectively, by a monte carlo method.
9. The apparatus of claim 7, wherein the alternate field selection unit optimizes the first objective function by newton's method or gradient descent method in case p ═ 1.
10. The apparatus of claim 9, wherein the alternate field selection unit converts the first objective function into:
Figure FDA0003120129030000047
to optimize the first objective function,
wherein, yiSatisfy yi≥xijWith the proviso that T is
Figure FDA0003120129030000048
A quadratic form of the term, yi, represents a maximum beamlet intensity in an ith field of the plurality of fields.
11. The apparatus of claim 7, wherein the alternate field selection unit further constructs the first objective function as:
Figure FDA0003120129030000049
wherein p satisfies the constraint condition that p is more than or equal to 0 and less than or equal to 1,
Figure FDA00031201290300000410
is the radiation dose of one of the plurality of voxels corresponding to the tissue to be radiotherapy-treated,
Figure FDA0003120129030000051
is the radiation dose of one of the voxels corresponding to the surrounding tissue, aPTVRepresenting the unit dose contribution of each of said sub-beams to each voxel corresponding to said tissue to be radiotherapy at a unit intensity, N representing the amount of said surrounding tissue, AOARkRepresenting a unit dose contribution of each of said sub-beams at a unit intensity to each voxel corresponding to a k-th of said surrounding tissue,
Figure FDA0003120129030000052
corresponds to a sub-beam intensity, x, of the plurality of fieldsijAn intensity of a jth sub-beam representing an ith field of the plurality of fields,
Figure FDA0003120129030000053
represents the maximum beamlet intensity, β and λ, in the ith of the plurality of fieldskBeta is greater than zero as a weight coefficientSetting the number of the spare fields by setting the value of the weight coefficient beta, wherein the larger the value of beta is, the smaller the number of the spare fields is, and lambda iskDetermines whether the radiation dose of the finally selected spare field is more satisfactory for the radiation dose required by the tissue to be treated or the radiation dose required by the surrounding tissue.
12. The apparatus of claim 7, wherein the alternate field selection unit optimizes the first objective function by a global optimization algorithm.
13. A computer system for determining beamlet intensities in a radiotherapy system, the radiotherapy system comprising a plurality of fields, each field having a plurality of beamlets, the system for determining beamlet intensities in the radiotherapy system comprising:
a memory storing computer instructions;
a processor executing computer instructions stored by the memory to perform the method of any of claims 1 to 6.
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调强放疗中的数学规划问题研究;闵志方;《中国博士学位论文全文数据库·基础科学辑》;中国学术期刊（光盘版）电子杂志社;20101115;全文 *

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