A method for planning non-coplanar circular arc delivery trajectories that incorporates tumor respiratory motion

Abstract

This invention proposes a non-coplanar circular arc delivery trajectory planning method that integrates tumor respiratory motion, comprising the following steps: Step 1, selecting delivery nodes on a radiating spherical surface using a beam angle optimization algorithm; Step 2, transforming the angle representation of the delivery nodes on the radiating spherical surface according to spatial geometric relationships; Step 3, planning the delivery path and delivery posture of the shortest circular arc between two delivery nodes on the radiating spherical surface; Step 4, integrating tumor respiratory motion with the circular arc delivery trajectory to plan a dynamic non-coplanar circular arc delivery trajectory; Step 5, building a simulated delivery verification platform to verify the effectiveness of the delivery trajectory planning method. This invention plans a continuous delivery beam path and incident posture for tumors containing respiratory motion, which is beneficial for shortening the delivery time of radiotherapy and improving the treatment accuracy of radiotherapy robots.

Description

Technical Field

[0001] This invention relates to the field of radiotherapy robot technology, and in particular to a non-coplanar circular arc delivery trajectory planning method that integrates tumor respiratory motion, which can solve the problem of trajectory planning for continuous beam delivery in stereotactic radiotherapy robots. Background Technology

[0002] The incidence and mortality rates of cancer are rising year by year, seriously affecting people's lives and health. In cancer treatment, radiotherapy is a crucial method, offering advantages such as being painless, non-invasive, having a short treatment cycle, and providing good therapeutic effects. Beam delivery trajectory planning is a vital part of radiotherapy robot treatment planning, determining the duration of a single radiotherapy session and the final delivery location of the beam dose to the tumor.

[0003] Beam dose delivery first selects delivery nodes on the radiation sphere surrounding the patient using a beam angle optimization (BAO) algorithm. Traditional radiotherapy robots then use a gantry-driven beam to traverse these delivery nodes to deliver the dose. However, for non-coplanar delivery nodes on the radiation sphere, a combination of gantry and medical bed movement is required to reach the delivery node position relative to the patient. This method is highly effective for static tumors, but for treatment scenarios requiring compensation for tumor respiratory motion, such as lung tumors, this beam delivery method lacks mobility and flexibility, significantly reducing radiotherapy accuracy. To address the issue of beam flexibility, precision radiotherapy robots often use a 6-DOF (DoF) spatial robotic arm to drive the beam for dose delivery. This ensures that the beam reaches the predetermined delivery node while compensating for tumor respiratory motion, thereby improving radiotherapy accuracy.

[0004] Radiotherapy delivery methods include intermittent spot delivery and continuous delivery. Spot delivery involves activating the linear accelerator to release the beam dose after it reaches a predetermined delivery node, and then shutting off the linear accelerator as the beam moves between nodes. This method requires a relatively long delivery time. Continuous delivery, on the other hand, achieves uninterrupted dose delivery between nodes. The delivery trajectory is planned during treatment planning, and the linear accelerator maintains a continuous dose output throughout the treatment process, thus shortening the overall treatment duration. Currently, continuous delivery is typically used for treating static tumors. However, for tumors involving respiratory motion, real-time compensation for tumor movement is required during treatment, making it difficult to plan the delivery trajectory. Therefore, intermittent spot delivery is usually used for dynamic tumor scenarios.

[0005] While many effective solutions have been proposed for delivery trajectory planning, most continuous delivery trajectory planning methods only address static tumors, and the planned trajectories are typically only applicable to traditional gantry and medical bed drive systems. Research on trajectory planning methods for delivery scenarios involving robotic arms driving beams to compensate for tumor respiratory motion is scarce. Therefore, considering tumor respiratory motion, it is necessary to explore a non-coplanar continuous delivery trajectory planning method that incorporates tumor respiratory motion to shorten treatment delivery time. This is of great significance for improving the accuracy of radiotherapy robots and reducing patient exposure time under radiation. Summary of the Invention

[0006] The purpose of this invention is to provide a non-coplanar circular arc delivery trajectory planning method that integrates tumor respiratory motion, in order to solve the trajectory planning problem of continuous beam delivery in stereotactic radiotherapy robots.

[0007] The technical solution of this invention is: a method for planning non-coplanar circular arc delivery trajectories that integrates tumor respiratory motion, comprising the following steps:

[0008] Step 1: Select the radiating spherical delivery node using the beam angle optimization algorithm;

[0009] Step 2: Considering the limitations of traditional delivery node angle representation in mathematical operations, transform the angle representation of radial spherical delivery nodes according to spatial geometric relationships;

[0010] Step 3: Plan the delivery path and delivery posture of the shortest circular arc between the two delivery nodes of the radial sphere;

[0011] Step 4: Integrate tumor respiratory motion with circular arc delivery trajectory to plan a dynamic non-coplanar circular arc delivery trajectory;

[0012] Step 5: Build a simulated delivery verification platform to verify the effectiveness of the delivery trajectory planning method.

[0013] In the above technical solution, step 1 involves first selecting the beam angle, and then using a beam angle optimization algorithm to select the treatment delivery node within the radiation sphere above the patient.

[0014] In the above technical solution, the position of the spherical delivery node selected by the beam angle optimization algorithm in step 2 is represented by the gantry angle of the radiotherapy robot and the medical bed angle. This representation of the spherical node position differs from the commonly used polar coordinate representation of spherical nodes in mathematics. Transforming the nodes represented by the traditional gantry angle and medical bed angle to the spherical polar coordinate system through geometric analysis facilitates the mathematical derivation and calculation of the delivery trajectory planning between nodes. For a node p on the spherical radiotherapy surface, if the horizontal plane of the medical bed is taken as the xoy plane, the direction in which the patient's head points on the medical bed is the x-axis, and the direction perpendicular to the horizontal plane of the medical bed is the z-axis, let the points projected onto the yoz, xoz, and xoy planes be p1, p2, and p3, respectively. Then, the gantry angle Θ of the traditional radiotherapy robot represents the angle between op1 and the z-axis, with op1 having an initial angle of 0° when it is on the xoz plane; the medical bed angle Φ represents the angle between op2 and the z-axis, with op2 having an initial angle of 0° when it is on the xoy plane. However, the commonly used polar coordinate representation of a point on a spherical surface is represented by angles... And θ represents, Let θ be the angle between op3 and the x-axis, and θ be the angle between op and the z-axis. This traditional method of representing the spherical node positions in radiotherapy robots differs from the mathematically common polar coordinate representation of spherical nodes. To facilitate the mathematical derivation of delivery trajectories between nodes, the nodes represented by traditional gantry angles and medical bed angles are geometrically transformed to a spherical polar coordinate system. When considering tumor respiratory motion, to facilitate flexible beam compensation for tumor positional changes, a robotic arm-driven linear accelerator is used for dose delivery, while the medical bed angle remains fixed. To avoid the medical bed's influence on the beam and robotic arm movement, the upper hemisphere of the patient is taken as the radiation area, i.e. Based on spatial geometric relationships, we can obtain:

[0015]

[0016]

[0017] Some of the singularity cases:

[0018]

[0019] In the above technical solution, in step 3, the shortest arc between the two delivery nodes on the radial sphere is the intersection line of the plane formed by the two delivery nodes and the center of the sphere with the sphere, where the shortest arc in the intersection line is the shortest arc. The equation of the trajectory of this intersection line is then solved. Let the equation of the surface formed by the three points p1(x1, y1, z1), p2(x2, y2, z2), and the center of the sphere p0(x0, y0, z0) be:

[0020] ax + by + cz + d = 0 (3)

[0021] By solving for the normal vector of the plane, the equation of the plane formed by the three points can be determined using the point normal form. The normal vector is perpendicular to any vector on the plane, and can be calculated by taking the product of any two of the direction vectors formed by the three points.

[0022]

[0023] Based on formulas (3) and (4), the parameters of the plane equation can be obtained as follows:

[0024]

[0025] The polar coordinates of any point on a sphere can be represented as:

[0026]

[0027] Where r represents the radius of the radiating sphere.

[0028] Combining the polar coordinate formula (6) for any point on the sphere and the plane equation (3), we can obtain the equation of the intersection line of the sphere and the plane:

[0029]

[0030] Where a, b, and c are obtained from the coordinates of the center p0 and p1, p2 of the sphere using formula (5), and further simplification yields the equation of the shortest arc between two nodes on the sphere:

[0031]

[0032] θ is positive when the node on the trajectory is in the upper hemisphere, and negative when the node on the trajectory is in the lower hemisphere.

[0033] In the above technical solution, step 3 involves planning the beam delivery posture between the delivery nodes of the radiative spherical surface to ensure precise delivery of the beam dose to the tumor. The z-axis of the fixed linear accelerator coordinate system coincides with the beam. To ensure precise beam irradiation of the tumor, the beam direction of the linear accelerator is the same as the beam direction at each delivery path point p of the radiative spherical surface. i With real-time tumor location T i The vector formed Using quaternions This represents the attitude of the end effector linear accelerator relative to the base coordinate system of the radiotherapy robotic arm, based on the z-axis of the linear accelerator coordinate system and... Solve for the beam delivery attitude at each path point using overlapping constraints. Let the unit vector of the z-axis in the radiotherapy robot's base coordinate system be... Define a vector Angle α i , making Around Rotation αi After angled, it was obtained The quaternion representing the beam delivery attitude is:

[0034]

[0035] vector pass and Solving for the cross product, angle α i Solve using the formula for the angle between two vectors:

[0036]

[0037]

[0038] in

[0039] In the above technical solution, step 4 considers the tumor position movement caused by the patient's breathing. The tumor position within the body is predicted in real time using external measurement signals. The real-time tumor position is used as the center of the radiating sphere, thereby integrating tumor respiratory motion with the circular arc delivery trajectory to plan a dynamic non-coplanar circular arc delivery trajectory. The center p0(t) changes with time, and the coordinates p of any point on the radiating sphere at this time... i (t) can be represented as:

[0040]

[0041] According to formula (8), the formula for the arc trajectory points between two nodes on the upper hemisphere can be obtained as follows:

[0042]

[0043] Where a(t), b(t), and c(t) are obtained according to formula (5), when it is known that the projection of the radiotherapy robot arm end beam during the treatment delivery process is in angular velocity in the direction is If the time taken to reach the i-th point from the starting node is t, then we can calculate... θ at this moment can be calculated using formula (13). i The delivery posture at the current moment is obtained by formula (9), thus obtaining the spatial position and delivery posture of the delivery node on the circular trajectory between the two nodes. Therefore, a dynamic delivery trajectory for the fusion of tumor respiratory motion between the two nodes is planned.

[0044] For all nodes selected by the BAO algorithm, any two nodes p j p j+1 When the delivery trajectory p between two nodes ji =p j+1 When, it indicates that at this moment, the two nodes p are currently... j and pj+1 The treatment delivery between stages has been completed; proceed to the next arc trajectory p. j+1 to p j+2 Delivery until p j+n =p end This indicates that delivery has reached the last node p. end Delivery has ceased.

[0045] In the above technical solution, step 5 establishes a verification platform for simulating radiotherapy delivery. This platform uses a triaxial sliding stage to reproduce the respiratory motion of the tumor, effectively simulating the movement of the tumor in the body.

[0046] In the above technical solution, step 5 establishes a verification platform for simulated radiotherapy delivery. This platform uses a six-degree-of-freedom robotic arm to drive a simulated beam to perform delivery experiments on a planned delivery trajectory. The beam and tumor posture are detected by an electromagnetic probe, and the beam irradiation trajectory is detected by a laser test strip, thereby verifying the effectiveness and accuracy of the delivery trajectory planning algorithm.

[0047] Beneficial Effects: This invention provides a non-coplanar circular arc delivery trajectory planning method that incorporates tumor respiratory motion, solving the trajectory planning problem for continuous beam delivery in stereotactic radiotherapy robots. Compared to traditional point-to-point delivery methods, the proposed method improves treatment delivery time and reduces patient exposure time under radiation. By incorporating tumor respiratory motion and adjusting the position of the radiation sphere based on real-time tumor location prediction, this invention plans a non-coplanar circular arc delivery trajectory that incorporates tumor respiratory motion, improving delivery accuracy and reducing beam impact on surrounding healthy tissues. To verify the effectiveness and accuracy of the delivery trajectory, this invention proposes a simulated radiotherapy delivery verification platform, providing a testing platform for preoperative radiotherapy plan evaluation, thereby ensuring the reliability of the planned beam delivery trajectory and incident posture in the radiotherapy plan. Attached Figure Description

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0049] Figure 1 This is a flowchart of the method according to Embodiment 1 of the present invention.

[0050] Figure 2 This is the set of treatment delivery nodes selected in Embodiment 1 of the present invention.

[0051] Figure 3 This is a schematic diagram of the angle of a node on a radial sphere according to Embodiment 1 of the present invention.

[0052] Figure 4 This refers to the shortest circular arc delivery path between nodes planned based on the method proposed in this invention.

[0053] Figure 5 This is a non-coplanar dynamic circular arc delivery trajectory planned based on the method proposed in this invention. Detailed Implementation

[0054] In order to achieve the purpose of this invention, such as Figure 1 As shown, in one embodiment of the present invention, a non-coplanar circular arc delivery trajectory planning method incorporating tumor respiratory motion includes the following steps:

[0055] Step 1: Beam angle selection is a necessary prerequisite for delivery trajectory planning. Using a BAO algorithm, 20 treatment delivery nodes are selected within the upper hemisphere of a publicly available dataset. The selected set of delivery nodes is as follows: Figure 2 As shown.

[0056] Step 2: The location of the delivery node, selected using the BAO algorithm, is represented by the gantry angle of the radiotherapy robot and the angle of the medical bed. For example... Figure 3 Consider a node p on a spherical surface. If the horizontal plane of the medical bed is taken as the xoy plane, the direction the patient's head points on the medical bed is the x-axis, and the vertical direction upwards from the horizontal plane of the medical bed is the z-axis, let p1, p2, and p3 be the points projected onto the yoz, xoz, and xoy planes, respectively. Then, the gantry angle Θ of a traditional radiotherapy robot represents the angle between op1 and the z-axis, with op1 having an initial angle of 0° when it is on the xoz plane; the medical bed angle Φ represents the angle between op2 and the z-axis, with op2 having an initial angle of 0° when it is on the xoy plane. The polar coordinates of a point on a sphere, commonly used mathematically, are determined by angles... And θ represents, Let θ be the angle between op3 and the x-axis, and θ be the angle between op and the z-axis. This traditional method of representing the spherical node positions in radiotherapy robots differs from the mathematically common polar coordinate representation of spherical nodes. To facilitate the mathematical derivation of delivery trajectories between nodes, the nodes represented by the traditional gantry angle and medical bed angle are geometrically transformed to a spherical polar coordinate system. When considering tumor respiratory motion, to facilitate flexible beam compensation for tumor positional changes, a robotic arm-driven linear accelerator is used for dose delivery, while the medical bed angle remains fixed. To avoid the medical bed's influence on the beam and robotic arm movement, the upper hemisphere of the patient is taken as the radiation area. Based on spatial geometric relationships, we can obtain:

[0057]

[0058]

[0059] Some of the singularity cases:

[0060]

[0061] Step 3: Plan the shortest circular arc path between two nodes on the sphere. The shortest circular arc between two nodes on the sphere is the intersection of the plane formed by the two nodes and the center of the sphere with the sphere itself. The shortest arc in the intersection is the shortest arc. Let the equation of the surface formed by the three points p1(x1, y1, z1), p2(x2, y2, z2), and the center of the sphere p0(x0, y0, z0) be:

[0062] ax + by + cz + d = 0 (3)

[0063] By solving for the normal vector of the plane, the equation of the plane formed by the three points can be determined using the point normal form. The normal vector is perpendicular to any vector on the plane, and can be calculated by taking the product of any two of the direction vectors formed by the three points.

[0064]

[0065] Based on formulas (3) and (4), the parameters of the plane equation can be obtained as follows:

[0066]

[0067] The polar coordinates of any point on a sphere can be represented as:

[0068]

[0069] Where r represents the radius of the radiating sphere.

[0070] Combining the polar coordinate formula (6) for any point on the sphere and the plane equation (3), we can obtain the equation of the intersection line of the sphere and the plane:

[0071]

[0072] Where a, b, and c are obtained from the coordinates of the center p0 and p1, p2 of the sphere using formula (5), and further simplification yields the equation of the shortest arc between two nodes on the sphere:

[0073]

[0074] θ is positive when a node on the trajectory is in the upper hemisphere and negative when a node is in the lower hemisphere. Based on the derived shortest circular arc trajectory equation, the delivery path between the 20 nodes described in step 1 is planned, and the result is as follows: Figure 4 As shown.

[0075] Step 3 involves planning the beam delivery orientation between spherical nodes to ensure precise beam dose delivery to the tumor. The z-axis of the fixed linear accelerator coordinate system is aligned with the beam. To guarantee precise beam irradiation of the tumor, the beam direction of the linear accelerator is the direction of each delivery path point p on the radiating sphere. i With real-time tumor location Ti The vector formed Using quaternions This represents the attitude of the end effector linear accelerator relative to the base coordinate system of the radiotherapy robotic arm, based on the z-axis of the linear accelerator coordinate system and... Solve for the beam delivery attitude at each path point using overlapping constraints. Let the unit vector of the z-axis in the radiotherapy robot's base coordinate system be... Define a vector Angle α i , making Around Rotation α i After angled, it was obtained The quaternion representing the beam delivery attitude is:

[0076]

[0077] vector pass and Solving for the cross product, angle α i Solve using the formula for the angle between two vectors:

[0078]

[0079]

[0080] in

[0081] Step 4: Considering tumor movement caused by the patient's breathing, predict the tumor location in real time using external measurement signals. The real-time tumor location is used as the center of the radiation sphere. The center p0(t) changes with time, and the coordinates p of any point on the radiation sphere at this time are... i (t) can be represented as:

[0082]

[0083] According to formula (8), the formula for the arc trajectory points between two nodes on the upper hemisphere can be obtained as follows:

[0084]

[0085] Where a(t), b(t), and c(t) are obtained according to formula (5), when it is known that the projection of the radiotherapy robot arm end beam during the treatment delivery process is in angular velocity in the direction is If the time taken to reach the i-th point from the starting node is t, then we can calculate... θ at this moment can be calculated using formula (13). iThe delivery posture at the current moment is obtained by formula (9), thus obtaining the spatial position and delivery posture of the delivery node on the circular trajectory between the two nodes. Therefore, a dynamic delivery trajectory for the fusion of tumor respiratory motion between the two nodes is planned.

[0086] For all nodes selected by the BAO algorithm, any two nodes p j p j+1 When the delivery trajectory p between two nodes ji =p j+1 When, it indicates that at this moment, the two nodes p are currently... j and p j+1 The treatment delivery between stages has been completed; proceed to the next arc trajectory p. j+1 to p j+2 Delivery until p j+n =p end This indicates that delivery has reached the last node p. end Delivery stops. For the delivery trajectory described in step 2, a dynamic trajectory is planned after adding respiratory motion to the tumor location, as shown below. Figure 5 As shown.

[0087] Step 5: A verification platform for simulating radiotherapy delivery was built. This platform uses a triaxial sliding stage to reproduce the respiratory motion of the tumor, effectively simulating the movement of the tumor in the body.

[0088] Step 5 also established a verification platform for simulated radiotherapy delivery. This platform uses a six-degree-of-freedom robotic arm to drive a simulated beam to conduct delivery experiments on a planned delivery trajectory. The beam and tumor posture are detected by an electromagnetic probe, and the beam irradiation trajectory is detected by a laser test strip, thereby verifying the effectiveness and accuracy of the delivery trajectory planning algorithm.

[0089] Of course, the above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be used to limit the scope of protection of the present invention. All modifications made according to the spirit and essence of the main technical solution of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for planning non-coplanar circular arc delivery trajectories that integrates tumor respiratory motion, characterized in that, Includes the following steps: Step 1: Select the radiating spherical delivery node using the beam angle optimization algorithm; Step 2: Transform the angular representation of the spherical delivery node based on spatial geometric relationships. The position of the spherical delivery node is selected by the beam angle optimization algorithm, which is represented by the gantry angle and medical bed angle of the radiotherapy robot. The node represented by the traditional gantry angle and medical bed angle is transformed to the spherical polar coordinate system through geometric analysis. Step 3: Plan the delivery path and delivery posture of the shortest circular arc between the two delivery nodes on the radial sphere. The shortest circular arc between the two delivery nodes on the radial sphere is the intersection line of the plane formed by the two delivery nodes and the center of the sphere with the sphere. The shortest circular arc in the intersection line is the shortest arc. Solve for the trajectory equation of the intersection line. Step 4: Integrate tumor respiratory motion with circular arc delivery trajectory to plan a dynamic non-coplanar circular arc delivery trajectory; Step 5: Build a simulated delivery verification platform to verify the effectiveness of the delivery trajectory planning method.

2. The method for planning non-coplanar circular arc delivery trajectories incorporating tumor respiratory motion according to claim 1, characterized in that, In step 1, the beam angle is first selected, and then the treatment delivery node is selected within the radiation sphere above the patient using a beam angle optimization algorithm.

3. The method for planning non-coplanar circular arc delivery trajectories incorporating tumor respiratory motion according to claim 1, characterized in that, In step 3, the beam delivery posture between the radiation spherical delivery nodes is planned to ensure that the beam dose is accurately delivered to the tumor.

4. The method for planning non-coplanar circular arc delivery trajectories incorporating tumor respiratory motion according to claim 1, characterized in that, In step 4, the location of the tumor in the body is predicted in real time by external measurement signals. The real-time tumor location is used as the center of the radiating sphere, thereby integrating the tumor respiratory motion with the circular arc delivery trajectory to plan a dynamic non-coplanar circular arc delivery trajectory.

5. The method for planning non-coplanar circular arc delivery trajectories that integrates tumor respiratory motion according to claim 1, characterized in that, In step 5, a verification platform for simulating radiotherapy delivery was built. This platform uses a triaxial sliding stage to reproduce the respiratory motion of the tumor, effectively simulating the movement of the tumor in the body.

6. The method for planning non-coplanar circular arc delivery trajectories incorporating tumor respiratory motion according to claim 1, characterized in that, In step 5, a verification platform for simulated radiotherapy delivery was built. The platform uses a six-degree-of-freedom robotic arm to drive a simulated beam to perform delivery experiments on a planned delivery trajectory. The beam and tumor posture are detected by an electromagnetic probe, and the beam irradiation trajectory is detected by a laser test strip, thereby verifying the effectiveness and accuracy of the delivery trajectory planning algorithm.

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