Non-equidistant lattice distribution optimization method based on local dose constraint

Abstract

The invention provides a non-equidistant lattice distribution optimization method based on local dose constraint. The method comprises the following steps: generating an initial lattice based on a patient image and a delineated target region; calculating and storing a dose kernel in advance based on a Monte Carlo algorithm; calling a dose core to carry out rapid dose optimization and calculation; establishing an independent peripheral subspace dose evaluation region and a local dose constraint condition for each lattice target region; establishing a multi-objective function for lattice target region position optimization; dynamically adjusting lattice positions and intervals by using a rapid simulated annealing method or a gradient descent method until target region position distribution and dose distribution meeting a dose multi-objective function and constraint conditions are generated; according to the invention, through dynamic adjustment of the lattice spacing and position and combination of the patient specific anatomical structure, accurate control of the valley dose around each lattice is realized, so that the problems of non-uniform target dose distribution and insufficient valley dose control in traditional equal spacing lattice radiotherapy are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of radiotherapy, and in particular to an optimization method for non-uniform lattice distribution based on local dose constraints. Background Art

[0002] Spatial fractionated radiotherapy is considered an innovative treatment technique for large-volume or advanced tumors. It mainly forms a highly non-uniform dose distribution within the tumor GTV through a single large-dose irradiation, achieving effective control of the progression of malignant tumors while reducing the radiotherapy damage to normal tissues. Its safety and effectiveness have been proven.

[0003] The research on the immunological mechanism of spatial fractionated radiotherapy believes that the distribution pattern of high-dose and low-dose regular intervals may synergistically enhance the anti-tumor immune effect. Based on this theory, it is usually required that the peak dose within the lattice target area be high enough to induce tumor-specific immune responses, while the valley dose in the gap between lattice target areas be low enough to protect the function of tumor microvessels, allowing the circulation of cytokines / chemokines / or immunogenic factors, thereby synergistically inducing anti-tumor immunity. This dose distribution characteristic is usually quantified and characterized by the peak-to-valley dose ratio (PVDR). Based on this, the current spatial fractionated radiotherapy plans usually use the peak-to-valley dose ratio as the main dosimetric optimization parameter to achieve this characteristic dose distribution.

[0004] Currently, there are mainly two ways to achieve this distribution pattern of peak dose and valley dose intervals:

[0005] (1) Based on the volume of the tumor GTV, determine the size and uniform spacing of the lattice target area, manually / automatically delineate the equally spaced lattice target area, and use the peak-to-valley dose ratio as the optimization target parameter to achieve the design of the target dose and treatment plan.

[0006] (2) Optimize the spatial fractionated radiotherapy plan with the size, uniform spacing, and peak-to-valley dose ratio of the lattice target area as the main parameters.

[0007] However, based on a pre-determined equidistant distributed lattice target area, the focus is usually on the planned dosimetric optimization. However, since the size and interval of the lattice have been determined, the final achievable optimized dose target is also limited. As a result, the peak-valley dose ratio cannot reach the most ideal state, thereby reducing the tumor control rate. Even if the size and spacing parameters of the lattice are introduced during the planning optimization process to achieve further dose optimization, when there are many lattices, due to the dose superposition effect, the valley dose in the central region of the PTV in this layout of equidistant lattice target areas is still higher than the valley dose level in the edge region, which may increase the probability of damaging the microvascular circulation function around the lattice target area and then reduce the immune effect. In addition, although the peak-valley dose ratio is a currently good quantitative evaluation index, it is the ratio of the dosimetric statistical values of two relatively large regions (lattice target area and lattice target area), lacking the ability to reflect the dose distribution characteristics of the sub-space around each lattice target area. Therefore, it cannot ensure that sufficient valley dose is obtained around each lattice target area to enhance the immune effect synergy of each sub-space. Summary of the Invention

[0008] Aiming at the deficiencies of the prior art, the present invention provides a non-equidistant lattice distribution optimization method based on local dose constraints. By dynamically adjusting the spacing and position of each lattice and combining with the patient-specific anatomical structure, precise control of the valley dose around each lattice is achieved.

[0009] The technical solution of the present invention is as follows: A non-equidistant lattice distribution optimization method based on local dose constraints, comprising the following steps:

[0010] S1) Generate an initial lattice based on patient images and the contoured target area;

[0011] S2) Pre-calculate and store the dose kernel based on the Monte Carlo algorithm;

[0012] S3) Call the dose kernel for fast dose optimization and calculation;

[0013] S4) Establish an independent peripheral sub-space dose evaluation area and local dose constraint conditions for each lattice target area;

[0014] S5) Establish and calculate the multi-objective function for optimizing the lattice target area position;

[0015] S6) Dynamically adjust the lattice position and spacing by using the fast simulated annealing method or the gradient descent method until the target area position distribution and dose distribution that meet the dose multi-objective function in step S5) and the constraint conditions in step S4) are generated;

[0016] Preferably, in step S1), the generation of the initial lattice includes the following steps:

[0017] S11), establish a tumor volume and morphology model based on the patient's image and the delineated target area, and calculate the tumor volume and morphological parameters;

[0018] S12), construct an initial lattice position distribution based on the tumor volume and morphology model and the tumor volume and morphological parameters.

[0019] Preferably, in step S11), from the patient's CT / MRI image and the delineated anatomical structure set, extract the tumor three-dimensional surface mesh as the tumor volume and morphology model, and define the tumor spatial domain as Ω.

[0020] Preferably, in step S11), the tumor volume and morphological parameters include the local curvature of the target area, the distance between the target area and the adjacent sensitive organs, and the volume density distribution:

[0021] Among them, the local curvature of the target area quantifies the surface concavity and convexity through the Gaussian curvature K. Among them, K>0.2 is the high-curvature area;

[0022] The distance d between the target area and the adjacent sensitive organs is the Euclidean distance from each point on the tumor surface to the nearest sensitive organ;

[0023] The volume density distribution ρ∈(0,1) divides the tumor into 1mm 3 voxels, and statistically calculates the proportion of tumor tissue in the voxels.

[0024] Preferably, in step S12), the rules for the initial lattice arrangement are:

[0025] a), for the high-curvature area, increase the lattice density linearly according to the curvature K, and the spacing s satisfies:

[0026] s = s base -λ K ·K;

[0027] In the formula, s base is the system default lattice spacing; λ K represents the spacing adjustment constant;

[0028] b), on the side of the adjacent sensitive organ, if d < d safe , the spacing s is expanded to:

[0029] s = s base +μ·(d safe -d);

[0030] In the formula, d safe is the safety distance; μ represents the safety distance adjustment constant;

[0031] c), in the tumor core area, lattice points are evenly distributed, and the volume density distribution ρ>0.8; the spacing

[0032] s core = s base 。

[0033] Preferably, in step S2), the dose kernel K is pre-calculated and simulated by the Monte Carlo algorithm to generate a dose kernel matrix corresponding to each beam angle and store it for subsequent rapid dose calculation.

[0034] Preferably, in step S3, the dose kernel is called for rapid dose optimization and calculation, specifically:

[0035] For the total dose D of a given voxel i , it is equal to the product of all dose kernels K ij contributing to it and the corresponding weight W j , that is:

[0036] D i = ∑ j K ij W j ;

[0037] In the formula, j represents the beam number; K ij is a sparse matrix, and the dose convolution kernel is non-zero only on the beamlet path, and the dose at each point comes from the cumulative dose contribution of each beamlet within a limited range around it.

[0038] Preferably, in step S4), an independent peripheral sub-space dose evaluation region is established for each lattice target area depending on the three-dimensional Voronoi diagram, and the segmentation rule of the three-dimensional Voronoi diagram is:

[0039] a), Taking the initial lattice point set as the seed points, generate a Voronoi diagram, and divide the tumor spatial domain Ω into N non-overlapping Voronoi diagram cells satisfying:

[0040]

[0041] In the formula, x represents the Voronoi diagram boundary coordinate;

[0042] b), The center point c i of each Voronoi diagram cell V i is used as the optimized lattice target point.

[0043] Preferably, in step S4), the lattice target area T i is a spherical region centered on each lattice target point c i with a radius of r peak , and the dose of the lattice target area needs to reach the prescribed dose D target ;

[0044] T i = {x ∈ Ω | |||x - c i || ≤ r peak}.

[0045] Preferably, in step S4), the lattice target region T i and the region between it and the adjacent lattices around it are used as the sub - space S around the lattice target region ij , that is, for any two adjacent lattice target points c i and c j , the intersection of their Voronoi cells is defined as the sub - space S ij , and the expression of the sub - space S ij is:

[0046] S ij = {x ∈ Ω | |||x - c i || = ||x - c j ||} ∩ B((c i + c j ) / 2, R);

[0047] In the formula, B((c i + c j ) / 2, R) represents a sphere centered at (c i + c j ) / 2 with a radius of R.

[0048] Preferably, in step S4), if the sub - space S ij is close to the sensitive organ, its shape is changed to a cube with a side length of 2R to limit the dose evaluation range; if the sub - space S ij is located in the tumor core, it remains spherical to enhance uniformity.

[0049] Preferably, in step S4), the local dose constraint condition is: the maximum dose ij in each sub - space S satisfies:

[0050]

[0051] Peak - to - valley dose ratio PVDR ≤ 0.3;

[0052] where η represents the desired valley dose coefficient;

[0053] The peak - to - valley dose ratio PVDR is the ratio of the global peak dose to the global valley dose; the global peak dose is the dose covering 95% of the volume of all lattice target regions; the global valley dose is the dose covering 95% of the volume of the valley dose region; the valley dose region is the region remaining after subtracting 3 mm of the outer expansion of the lattice target region from the tumor volume.

[0054] Preferably, in step S5), the multi-objective function for optimizing the lattice target area is as follows:

[0055]

[0056] In the formula, is the peak dose compliance term;

[0057] is the valley dose constraint term; γ·HI is the uniformity penalty term; is the sensitive organ protection term; ε·(PVDR - 0.3) is the overall peak-to-valley ratio constraint term; N represents the total number of lattice target areas; α, β, γ, δ, ε are the weight systems; represents the peak dose of the i-th lattice target area; D target represents the target prescription dose; represents the maximum dose in the subspace S ij within; η represents the desired valley dose coefficient; HI represents the global dose uniformity index; M represents the number of sensitive organs; represents the average dose of the k-th sensitive organ; represents the maximum allowable dose of the k-th sensitive organ; PVDR is the peak-to-valley dose ratio.

[0058] Preferably, in step S6), if the fast simulated annealing method is adopted, the lattice position direction sampling strategy is as follows: After each dose optimization subroutine is completed, calculate the dose D i in the middle region between each lattice target area T ij and its surrounding adjacent lattice target areas;

[0059] If the dose D ij is less than the target valley dose, mark this position as 0 in the lattice position direction sampling matrix, otherwise, mark it as 1. In subsequent lattice position size sampling, only the positions marked as 1 in the lattice position direction sampling matrix participate in resampling and subsequent optimization;

[0060] And the position sampling size selects the long-range Cauchy-Lorentz distribution:

[0061] p(Δx) ∝ [(Δx) 2 + W(T) 2 -(n+1) / 2

[0062] In the formula, Δx is the change step size of the lattice position; n is the number of optional lattice positions; W(T) is the temperature-related width of the sampling distribution; p(Δx) represents the probability corresponding to the change step size of Δx.

[0063] ​Preferably, in step S6), if the gradient descent method is used, the gradient of the objective function with respect to the lattice position c is calculated by the adjoint field method. i Gradient For the update direction:

[0064]

[0065] In the formula, ∈ is the step size, t represents the number of iterations; J represents the objective function, and the gradient is the partial derivative of the objective function J with respect to the lattice position c i and is used to guide the direction of parameter update;

[0066] Record the lattice movement directions in the last k times, prohibit repeated search in the same direction, and if the result of the objective function does not improve after more than T iterations, trigger a random perturbation to jump out of the local optimum.

[0067] The beneficial effects of the present invention are as follows:

[0068] 1. By dynamically adjusting the lattice spacing and position and combining with the patient-specific anatomical structure, the present invention realizes precise control of the valley dose around each lattice, thus solving the problems of uneven target dose distribution and insufficient valley dose control in traditional equal-spacing lattice radiotherapy.

[0069] 2. The present invention can obtain a better lattice target position distribution and dose distribution. It not only considers the limiting factors of the surrounding OARs, but also ensures the dose limit of the valley dose in the sub-space region around each lattice target, and also solves the problem of high dose in the central region of the tumor caused by conventional equal-spacing distribution, while taking into account the influence of the tumor boundary curvature change on the dose. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a schematic flow chart of the method of the present invention;

[0071] Figure 2 is a schematic diagram of the non-uniform lattice distribution in the tumor space domain of the present invention;

[0072] Figure 3 is a schematic diagram of the sub-space shape dynamic adjustment strategy of the present invention;

[0073] Figure 4 is a schematic diagram of the optimal result of the non-equal-spacing distribution of the lattice target of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0074] The following further describes the specific embodiments of the present invention with reference to the drawings:

[0075] As Figure 1 shown, this embodiment provides a non-equal-spacing lattice distribution optimization method based on local dose constraints, including the following steps:

[0076] S1), generating an initial lattice based on the patient's image and the contoured target area; including the following steps:

[0077] S11), establishing a tumor volume morphology model based on the patient's image and the contoured target area, and calculating tumor volume morphology parameters;

[0078] In this implementation, through the patient's CT / MRI image and the contoured anatomical structure set, the three-dimensional surface mesh of the tumor is extracted as the tumor volume morphology model, and the tumor space domain is defined as Ω.

[0079] And calculating the tumor volume morphology parameters according to the tumor volume morphology model. In this implementation, the tumor volume morphology parameters include the local curvature of the target area, the distance between the target area and adjacent sensitive organs (such as the bladder, rectum), and the volume density distribution:

[0080] Among them, the local curvature of the target area quantifies the surface concavity and convexity through the Gaussian curvature K. Among them, K>0.2 is the high curvature area;

[0081] The distance d between the target area and the adjacent sensitive organ is the Euclidean distance from each point on the tumor surface to the nearest sensitive organ;

[0082] The volume density distribution ρ∈(0,1) divides the tumor into 1mm 3 voxels, and statistically calculates the proportion of tumor tissue in the voxels.

[0083] S12), constructing an initial lattice position distribution based on the tumor volume morphology model and the tumor volume morphology parameters;

[0084] In this embodiment, the rules for arranging the initial lattice are as follows:

[0085] a), in the high curvature area, the lattice density is increased linearly according to the curvature K, and the spacing s satisfies:

[0086] s = s base -λ K ·K;

[0087] In the formula, s base is the system default lattice spacing; λ K represents the spacing adjustment constant; in this embodiment, s base = 30mm, λ K = 10mm;

[0088] b), on the side of the adjacent sensitive organ, if d < d safe , the spacing s is expanded to:

[0089] s = s base +μ·(d safe -d);

[0090] In the formula, d safe is the safety distance; μ represents the safety distance adjustment constant; in this embodiment, d safe = 20 mm, μ = 0.25;

[0091] c), Tumor core area, lattice points are evenly distributed, and the volume density distribution ρ > 0.8; the center spacing s of the lattice target area core = s base .

[0092] S2), Pre-calculate and store the dose kernel based on the Monte Carlo algorithm;

[0093] In this embodiment, calculation simulation is performed through the Monte Carlo algorithm to generate and store the dose kernel matrix corresponding to each beam angle for subsequent rapid dose calculation.

[0094] S3), Call the dose kernel for rapid dose optimization and calculation;

[0095] In this embodiment, dose optimization can be performed using the commonly used optimization algorithm engine in the current treatment planning system;

[0096] The dose calculation method shown is: for the total dose D of a given voxel i , it is equal to the product of all dose kernels K ij contributing to it and the corresponding weight W j , that is:

[0097] D i = ∑ j K ij W j ;

[0098] In the formula, j represents the beam number; K ij is a sparse matrix, and only the dose convolution kernel on the beam sub-beam path is non-zero, and the dose at each location comes from the cumulative dose contribution of each beam sub-beam within a limited range around it.

[0099] S4), Establish an independent peripheral sub-space dose evaluation area and local dose constraint conditions for each lattice target area;

[0100] The three-dimensional Voronoi diagram is created based on the initial lattice position distribution, as shown in Figure 2 ;

[0101] In this embodiment, the segmentation rule of the three-dimensional Voronoi diagram is:

[0102] a), Using the initial lattice point set as the seed points, generate the Voronoi diagram, and divide the tumor spatial domain Ω into N non-overlapping Voronoi diagram units satisfying:

[0103]

[0104] Wherein, x represents the Voronoi diagram boundary coordinates;

[0105] b), the center point c i of each Voronoi diagram cell V i is used as the optimized lattice target point.

[0106] The lattice target area T i is a spherical region centered on each lattice target point c i with a radius of r peak ,

[0107] The dose of the lattice target area needs to reach the prescribed dose D target ;

[0108] T i = {x ∈ Ω | ||x - c i || ≤ r peak}.

[0109] The region between the lattice target area T i and its adjacent surrounding lattices is used as the sub - space S ij around the lattice target area, that is, for any two adjacent lattice target points c i and c j , the intersection of their Voronoi cells is defined as the sub - space S ij , and the expression of the sub - space S ij is:

[0110] S ij = {x ∈ Ω | ||x - c i || = ||x - c j ||} ∩ B((c i + c j ) / 2, R);

[0111] Wherein, B((c i + c j ) / 2, R) represents a sphere centered on (c i + c j ) / 2 with a radius of R.

[0112] As Figure 3 shown, wherein, if the sub - space S ij is close to the sensitive organ, its shape is changed to a cube with a side length of 2R to limit the dose evaluation range, as Figure 3 (a) shown; if the sub - space S ij is located in the tumor core, it remains spherical to enhance uniformity, as Figure 3 (b) shown.

[0113] In this embodiment, the local dose constraint condition is: the maximum dose in each subspace S ij within

[0114] satisfies:

[0115]

[0116] Peak-to-valley dose ratio PVDR ≤ 0.3;

[0117] where η represents the expected valley dose coefficient;

[0118] The peak-to-valley dose ratio PVDR is the ratio of the global peak dose to the global valley dose; the global peak dose is the dose covering 95% of the volume of all lattice target regions; the global valley dose is the dose covering 95% of the volume of the valley dose region; the valley dose region is the remaining region after subtracting 3 mm of the outer expansion of the lattice target region from the tumor volume.

[0119] S5), establish and calculate the multi-objective function for optimizing the lattice target region position; quantify the difference between the current dose distribution and the expected dose distribution; the multi-objective function for optimizing the lattice target region is:

[0120]

[0121] In the formula, is the peak dose compliance term;

[0122] is the valley dose constraint term; γ·HI is the uniformity penalty term; is the sensitive organ protection term; ε·(PVDR - 0.3) is the overall peak-to-valley ratio constraint term; α, β, γ, δ, ε are the weight systems; represents the peak dose of the i-th lattice target region; D target represents the target prescription dose; η represents the expected valley dose coefficient; M represents the number of sensitive organs; N represents the total number of lattice target regions; represents the maximum dose within the subspace S ij within; HI represents the global dose uniformity index; represents the average dose of the k-th sensitive organ; represents the maximum allowable dose of the k-th sensitive organ; PVDR is the peak-to-valley dose ratio.

[0123] S6), dynamically adjust the lattice position and spacing by using the fast simulated annealing method or the gradient descent method until the target region position distribution and dose distribution that satisfy the dose objective function described in step S5) and the constraint conditions described in step S4) are generated;

[0124] In this embodiment, if the fast simulated annealing method is adopted, the sampling strategy for the lattice position direction is as follows: after each dose optimization subroutine shown in step S3) is completed, the maximum dose D of each lattice target region T i in the intermediate subspace region adjacent to the surrounding lattice target regions is calculated ij = max(D ij (k), k ∈ [1, N]), where k represents the k-th pixel point in the subspace and N represents the total number of pixel points in the subspace;

[0125] If the dose D ij is less than the target valley dose η·D target , this position in the lattice position direction sampling matrix is marked as 0; otherwise, it is marked as 1. During subsequent lattice position size sampling, only the positions marked as 1 in the lattice position direction sampling matrix participate in resampling and subsequent optimization;

[0126] The position sampling size selects a long-range Cauchy-Lorentz distribution:

[0127] p(Δx) ∝ [(Δx) 2 + W(T) 2 -(n+1) / 2

[0128] In the formula, Δx is the change step size of the lattice position; n is the number of optional lattice positions; W(T) is the temperature-related width of the sampling distribution; p(Δx) represents the probability corresponding to the change step size of Δx.

[0129] In this embodiment, if the gradient descent method is adopted, the gradient of the objective function with respect to the lattice position c i is calculated by the adjoint field method for updating the direction:

[0130]

[0131] In the formula, ∈ is the step size, t represents the number of iterations; J represents the objective function, and the gradient is the partial derivative of the objective function J with respect to the lattice position c i and is used to guide the direction of parameter update;

[0132] Record the directions of the last k lattice movements, and prohibit repeated search in the same direction. If the result of the objective function does not improve after more than T iterations, trigger a random perturbation to jump out of the local optimum.

[0133] ​In each iteration of the above optimization process in this embodiment, a position optimization result of the lattice target area is generated. Each time, the corresponding parameters are saved, and the dose target is optimized for rapid convergence until the target dose meets the requirements, that is, not only satisfying the constraint of the peak-to-valley ratio statistically, but also optimizing the dose of each subspace by constructing a multi-objective function, so as to meet the requirement of the valley dose at each sub-detail and obtain the optimal result of the non-uniform spacing distribution of the final lattice target area, as Figure 4 shown, where Fig. 4(a) is a schematic diagram of the uniform distribution of the lattice target area of the existing method; while Figure 4 (b) is a schematic diagram of the non-uniform distribution of the lattice target area of this embodiment.

[0134] The above embodiments and the descriptions in the specification only illustrate the principles and the best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the claimed present invention.

Claims

1. A non-uniform lattice distribution optimization method based on local dose constraints, characterized in that It includes the following steps: S1), generating an initial lattice based on the patient's image and the contoured target area; S2), pre-calculating and storing the dose kernel based on the Monte Carlo algorithm; S3), calling the dose kernel for fast dose optimization and calculation; S4), establishing an independent peripheral sub-space dose evaluation area and local dose constraint conditions for each lattice target area; S5), establishing and calculating a multi-objective function for optimizing the lattice target area position; S6), dynamically adjusting the lattice position and spacing by using the fast simulated annealing method or the gradient descent method until a target area position distribution and dose distribution that meet the dose multi-objective function in step S5) and the constraint conditions in step S4) are generated.

2. The non-uniform lattice distribution optimization method based on local dose constraint according to claim 1, wherein: In step S1), the generation of the initial lattice includes the following steps: S11), establishing a tumor volume morphology model based on the patient's image and the contoured target area, and calculating tumor volume morphology parameters; S12), constructing an initial lattice position distribution based on the tumor volume morphology model and the tumor volume morphology parameters.

3. The non-uniform lattice distribution optimization method based on local dose constraint according to claim 2, wherein: In step S11), through the patient's CT / MRI image and the contoured anatomical structure set, the tumor three-dimensional surface grid is extracted as the tumor volume morphology model, and the tumor space domain is defined as Ω; The tumor volume morphology parameters include the local curvature of the target area, the distance between the target area and adjacent sensitive organs, and the volume density distribution: Among them, the local curvature of the target area quantifies the surface concavity and convexity through the Gaussian curvature K, where K>0.2 is the high curvature area; The distance d between the target area and adjacent sensitive organs is the Euclidean distance from each point on the tumor surface to the nearest sensitive organ; The volume density distribution ρ ∈ (0, 1) divides the tumor into 1 mm 3 voxels, and the proportion of tumor tissue within the voxels is statistically analyzed.

4. A non-uniform lattice distribution optimization method based on local dose constraints according to claim 3, characterized in that: In step S12), the rules for arranging the initial lattice are as follows: a), in the high curvature area, the lattice density is increased linearly according to the curvature K, and the spacing s satisfies: s = s base -λ K ·K; where s base is the system default lattice spacing; λ K represents the spacing adjustment constant; b), on the side adjacent to the sensitive organ, if d < d safe , the spacing s is enlarged to: s = s base + μ·(d safe - d); where d safe is the safety distance; μ represents the safety distance adjustment constant; c), in the tumor core area, lattice points are evenly distributed, and the volume density distribution ρ>0.8; the spacing s core = s base 。 5. A non-uniform lattice distribution optimization method based on local dose constraints according to claim 1, characterized in that: In step S4), for each lattice target area T i Establishing an independent peripheral sub-space dose evaluation area depends on a three-dimensional Voronoi diagram; the segmentation rule of the three-dimensional Voronoi diagram is as follows: a), with the initial lattice point set as the seed points, generate a Voronoi diagram and divide the tumor spatial domain Ω into N non-overlapping Voronoi diagram cells Satisfy: In the formula, x represents the boundary coordinates of the Voronoi diagram; b), the center point c of each Voronoi diagram cell V i is used as the optimized lattice target point. i ​ 6. The non-uniform lattice distribution optimization method based on local dose constraint according to claim 5, characterized in that: In step S4), the lattice target area T i is a spherical region centered on each lattice target point C i with a radius of r peak The dose in the lattice target area needs to reach the prescribed dose D target ； T i = {x ∈ Ω | ||x - c i || ≤ r peak}; Take the lattice target area T i The area between the lattice target area T and the adjacent lattices around it is used as the sub-space S around the lattice target area ij , that is, for any two adjacent lattice target points c i and c j , the intersection of their Voronoi cells is defined as the sub-space S ij , the expression of the sub-space S ij is as follows: S ij = {x ∈ Ω | |||x - c i || = ||x - c j ||} ∩ B((c i + c j ) / 2, R); In the formula, B((c i +c j ) / 2, R) represents a sphere centered at (c i +c j ) / 2 with a radius of R; If the sub-space S ij is close to the sensitive organ, change its shape to a cube with side length 2R to limit the dose evaluation range; if the sub-space S ij is located at the tumor core, maintain the spherical shape to enhance uniformity.

7. A non-uniform lattice distribution optimization method based on local dose constraints according to claim 6, characterized in that: In step S4), the local dose constraint condition is that the maximum dose within each subspace S ij satisfies: within is The peak-valley dose ratio PVDR≤0.3; Among them, η represents the expected valley dose coefficient; The peak-valley dose ratio PVDR is the ratio of the global peak dose to the global valley dose; the global peak dose is the dose covering 95% of the volume of all lattice target areas; the global valley dose is the dose covering 95% of the volume of the valley dose area; the valley dose area is the area remaining after subtracting 3 mm of the outer expansion of the lattice target area from the tumor volume.

8. A non-uniform lattice distribution optimization method based on local dose constraints according to claim 7, characterized in that: In step S5), the multi-objective function for optimizing the lattice target area position is: In the formula, is the peak dose compliance item; is the trough dose constraint item; γ·HI is the uniformity penalty item; is the sensitive organ protection item; ε·(PVDR - 0.3) is the overall peak-to-trough ratio constraint item; N represents the total number of lattice target regions; α, β, γ, δ, ε are the weight systems; represents the peak dose of the i-th lattice target region; D target represents the target prescription dose; represents the maximum dose within the subspace S ij inside; η represents the expected valley dose coefficient; HI represents the global dose uniformity index; M represents the number of sensitive organs; represents the average dose of the k-th sensitive organ; represents the maximum allowable dose of the k-th sensitive organ; PVDR is the peak-to-valley dose ratio.

9. The non-uniform lattice distribution optimization method based on local dose constraint according to claim 8, wherein: In step S6), if the fast simulated annealing method is adopted, the sampling strategy for the lattice position direction is as follows: after each dose optimization subroutine in step S3) is completed, calculate the dose D of the intermediate region between each lattice target area T i and the surrounding adjacent lattice target areas ij ; If the dose D ij is less than the target trough dose, this position in the lattice position direction sampling matrix is marked as 0; otherwise, it is marked as 1. During subsequent lattice position size sampling, only the positions marked as 1 in the lattice position direction sampling matrix participate in resampling and subsequent optimization; And the position sampling size selects the long-range Cauchy-Lorentz distribution: p(Δx) ∝ [(Δx) 2 + W(T) 2 -(n+1) / 2 ​ In the formula, Δx is the change step of the lattice position; n is the number of optional lattice positions; W(T) is the temperature-related width of the sampling distribution; p(Δx) represents the probability corresponding to the change step of Δx.

10. A method for optimizing non-uniform lattice distribution based on local dose constraint according to claim 9, characterized in that: In step S6), if the gradient descent method is adopted, the gradient of the objective function with respect to the lattice position c is calculated by the adjoint field method i for the update direction: ​ where ∈ is the step size, t represents the number of iterations; J represents the objective function, and the gradient is the partial derivative of the objective function J with respect to the lattice position c i and is used to guide the direction of parameter update.

Images