Urinary system blood vessel modeling method based on 3D Gaussian splashing and surgical robot navigation method

Abstract

The invention belongs to the technical field of medical image modeling, and particularly relates to a urinary system blood vessel modeling method based on 3D Gaussian splashing and a surgical robot navigation method.The blood vessel modeling method comprises the steps that a data source is preprocessed, and a urinary system blood vessel model is constructed; describing the center line and the section shape of the blood vessel based on a Bezier curve and an NURBS curve, and realizing dynamic 3DGS modeling of the blood vessel; dynamic 3DGS modeling, finite element analysis and computational fluid mechanics are combined, and hemodynamics simulation is achieved through a two-way mapping algorithm of Gaussian parameters and finite element grids. Compared with the prior art, the method solves the problem that in the prior art, due to the fact that a high-precision model for the dynamic characteristics of the blood vessels of the urinary system is lacked, accurate navigation and operation of urinary system interventional operation are difficult. According to the scheme, a high-precision model is constructed for urinary system blood vessels (such as renal arteries and bladder blood vessels) based on the three-dimensional Gaussian sputtering technology, and precise navigation and operation of urinary system interventional operations are effectively assisted.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image modeling, and in particular relates to a urinary system blood vessel modeling method and a surgical robot navigation method based on 3D Gaussian splashing. Background Art

[0002] Interventional treatment of urinary system diseases (such as renal artery stenosis, bladder tumor blood supply abnormalities, etc.) relies on high-precision vascular models and real-time navigation technology. At present, vascular modeling methods based on CT / MRI mainly generate static three-dimensional models through voxelization or surface mesh reconstruction. For example, CN112182994A discloses a vascular modeling method and device based on the hemodynamics of Nutcracker syndrome, which realizes modeling based on CT medical images and combined with mesh division; CN119068107A discloses a coronary vascular modeling method, device, electronic device and storage medium, which performs static modeling based on computed tomography angiography images; However, these methods face the following challenges:

[0003] 1. Poor dynamic adaptability: Traditional methods have difficulty capturing the dynamic changes of urinary system blood vessels (such as the displacement of the renal artery with respiratory movement), resulting in a mismatch between the model and real-time intraoperative images.

[0004] 2. Low computational efficiency: Simulations based on finite element analysis (FEA) or computational fluid dynamics (CFD) require high computing resources and are difficult to meet real-time interaction requirements.

[0005] 3. Loss of details: Voxelization or mesh simplification will lose the geometric details of tiny blood vessels, affecting the accuracy of surgical planning.

[0006] 3D Gaussian Splatting (3DGS) technology uses Gaussian functions to represent the continuous three-dimensional distribution of a scene, which has the following advantages:

[0007] 1. Efficient rendering: Tile-based splattering technology can generate high-resolution images in real time (≥30fps).

[0008] 2. Dynamic modeling: Adaptive density control algorithm supports real-time updating of dynamic structures (such as blood vessel deformation).

[0009] 3. High-precision expression: The covariance matrix of the Gaussian function can accurately describe the local geometric characteristics of blood vessels (such as curvature and thickness).

[0010] For example, CN119206038A discloses a method for reconstructing cardiac interventional surgery scenes based on 3D ultrasound imaging rendering. However, in this solution, the pre-processed image is voxelized, and the continuous image information is discretized into a regular grid. However, for organs such as the urinary system with extremely high microvascular density (the total number of microvessels can reach billions), if the voxelized grid resolution cannot match the microvascular diameter (usually 5-50μm), the geometric details of the tiny blood vessels will be lost. Even if a 3D Gaussian function is subsequently used to simulate each voxel to form a continuous three-dimensional scene, the details of the constructed model will still be missing and omitted to a certain extent: microvessels smaller than the voxel size (such as renal capillaries) are merged or ignored, and fine structures such as vascular bifurcations and curvatures are distorted due to grid simplification. The urinary system's microvascular network is key to maintaining its functions (such as glomerular filtration and bladder blood supply). Loss of detail can lead to the omission of tiny blood supply vessels during surgical planning, increasing the risk of intraoperative bleeding and failing to accurately simulate blood flow distribution, affecting postoperative functional assessment. Therefore, models constructed during urinary system interventional surgery must account for the presence of these microvessels and their dynamic characteristics. Summary of the Invention

[0011] The purpose of the present invention is to provide a urinary system blood vessel modeling method and a surgical robot navigation method based on 3D Gaussian sputtering in order to solve at least one of the above problems, so as to solve the problem that the existing technology lacks a high-precision model of the dynamic characteristics of urinary system blood vessels, which makes it difficult to achieve precise navigation and operation of urinary system interventional surgery. This solution is based on three-dimensional Gaussian sputtering technology, combined with Bezier curve and NURBS curve parametric modeling, and introduces ECG-gated respiratory motion compensation technology. It can construct a model with high-precision geometric details (microvascular reconstruction rate > 98%) and dynamic adaptability (respiratory motion compensation accuracy < 0.5mm) for urinary system blood vessels (such as renal arteries, bladder blood vessels, etc.), which effectively assists in the precise navigation and operation of urinary system interventional surgery.

[0012] The purpose of the present invention is achieved through the following technical solutions:

[0013] The first aspect of the present invention discloses a urinary system blood vessel modeling method based on 3D Gaussian splashing, comprising the following steps:

[0014] S1: Preprocess the data source and construct the urinary system vascular model;

[0015] S2: Describe the centerline and cross-sectional shape of blood vessels based on Bezier curves and NURBS curves to achieve dynamic 3DGS modeling of blood vessels;

[0016] S3: Combining dynamic 3DGS modeling with finite element analysis and computational fluid dynamics, efficient simulation of hemodynamics is achieved through a bidirectional mapping algorithm between Gaussian parameters and finite element meshes.

[0017] Preferably, in step S1, the data sources include DICOM sequences, real-time three-dimensional ultrasound images and ECG signals.

[0018] Preferably, the slice thickness of the DICOM sequence is ≤0.5 mm.

[0019] Preferably, in step S1, the pretreatment includes one or more of the following:

[0020] i) Image registration: The image registration adopts a method combining affine transformation and B-spline deformation, and the transformation formula is:

[0021]

[0022] Where A is the affine matrix, b is the translation vector, φ i (x) is the B-spline basis function, c i are the coefficients of the B-spline basis function;

[0023] ii) Vessel segmentation: The vessel segmentation is based on the U-Net network to extract the vessel mask and use the Dice loss function to measure the difference between the predicted result and the true label. The Dice loss function is:

[0024]

[0025] Where Y represents the true blood vessel mask, represents the predicted vessel mask, |Y| and denote the number of pixels in the true mask and the predicted mask, respectively, Indicates the number of pixels where the real mask and the predicted mask overlap;

[0026] iii) Noise reduction and enhancement: the noise reduction and enhancement use anisotropic diffusion filtering, and its partial differential equation is:

[0027]

[0028] Where I represents the image, t represents the time, is the diffusion coefficient.

[0029] Preferably, in step S2, a NURBS curve is used to describe the centerline of the blood vessel, and a Gaussian function distribution along the centerline is initialized by a covariance matrix;

[0030] The parametric equation of the NURBS curve is as follows:

[0031]

[0032] Where N i,p (u) is the B-spline basis function, w i is the weight, P i is the control point;

[0033] The covariance matrix is:

[0034]

[0035] Where, κ is the local curvature of the blood vessel centerline, τ is the torsion rate of the blood vessel centerline, R(θ) is the rotation matrix, σ r , σ θ , σ z Represents the variance in the radial, circumferential and axial directions, respectively, and is used to describe the distribution characteristics of blood vessels in the circumferential direction. Its value is related to the local geometric characteristics of the blood vessels, such as the cross-sectional shape of the blood vessels, local expansion or contraction, etc. By adjusting σ r , the Gaussian function can better fit the morphological changes of blood vessels in the circumferential direction, thereby improving the accuracy of blood vessel modeling.

[0036] More preferably, the NURBS curve is also combined with ECG gating technology to dynamically adjust the density and distribution parameters of the Gaussian function according to the respiratory cycle to achieve real-time compensation of vascular respiratory movement; specifically, the respiratory phase is determined by the ECG signal, and when the blood vessels are displaced due to breathing, the σ in the covariance matrix is ​​dynamically updated. r and σ z Parameters are set to match the Gaussian function distribution with the real-time vascular morphology, avoiding model distortion caused by motion.

[0037] Preferably, in step S3, in the finite element analysis, the stress-strain relationship of the blood vessel wall is described by a hyperelastic model, and the strain energy function is:

[0038] Ψ=C 10 (I1-3)+C 01 (I2-3);

[0039] Where I1 and I2 are functions of the deformation gradient tensor, C 10 ,、C 01 is the material parameter.

[0040] Preferably, in step S3, in the computational fluid dynamics, the blood flow velocity field is solved by the Navier-Stokes equation:

[0041]

[0042] Where ρ is the density of blood, v is the blood flow velocity vector, is the convection term, p is the pressure, and μ is the dynamic viscosity of blood;

[0043] The dynamic 3DGS model provides the boundary conditions for vessel wall motion.

[0044] Specifically, step S3: based on the Gaussian function covariance matrix generated by the NURBS curve (such as ) drives the adaptive division of the finite element mesh, automatically encrypting the mesh in areas with large vascular curvature and many bifurcations; at the same time, the vascular wall stress distribution obtained by finite element analysis (such as the strain energy Ψ calculated by the hyperelastic model) is fed back to the Gaussian parameters through the density feedback algorithm, dynamically adjusting the distribution and density of the local Gaussian function to form

[0045] Closed-loop process of '3DGS modeling → finite element simulation → model optimization'.

[0046] A second aspect of the present invention discloses a surgical robot navigation method, comprising the following steps: adjusting the deviation Δx between the robot end position and the blood vessel model through PID control;

[0047] The control law of the PID control is:

[0048]

[0049] Where K p is the proportionality coefficient, K i is the integration coefficient, K d is the differential coefficient; the deviation Δx of the vascular model is obtained by any of the urinary system vascular modeling methods described above.

[0050] Preferably, the method further includes the following steps: performing path planning and operation adjustment of the surgical robot based on a model predictive control algorithm;

[0051] The optimization objective function of the model predictive control algorithm is:

[0052]

[0053] Where x k is the predicted system state, is the reference state, u k is the control input, and λ is the weight coefficient.

[0054] Preferably, the model predictive control algorithm is optimized by a reinforcement learning algorithm, and the reinforcement learning algorithm is PPO or TRPO.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. For the first time, NURBS and 3DGS are combined to optimize Gaussian distribution through parameterized curves to improve the accuracy of urinary system vascular centerline modeling.

[0057] 2. A dynamic Gaussian density control algorithm is proposed, combined with respiratory gating technology to compensate for the respiratory movement of blood vessels such as the renal artery in real time.

[0058] 3. Design a lightweight coupled simulation framework to map Gaussian parameters to the finite element mesh to achieve efficient mechanical simulation.

[0059] 4. Introduce the reinforcement learning PPO / TRPO algorithm to optimize the surgical robot's path planning and dynamic adjustment, and improve navigation robustness and accuracy. DETAILED DESCRIPTION

[0060] The present invention will be described in detail below with reference to specific embodiments, but the present invention is by no means limited thereto.

[0061] For the following matters not covered, existing technologies can be used.

[0062] Example

[0063] This paper proposes a urinary system vascular modeling and surgical robot navigation method based on 3DGS. The core scheme is as follows:

[0064] 1. Multimodal data fusion: Integrate preoperative CT / MRI and intraoperative ultrasound images to generate a high-precision urinary vascular model through registration and segmentation.

[0065] 2. Dynamic 3DGS modeling: Utilizing the parametric characteristics of the Gaussian function, combined with Bezier curves and NURBS (non-uniform rational B-splines) to describe the centerline and cross-sectional shape of blood vessels, dynamic blood vessel modeling is achieved.

[0066] 3. Coupled simulation optimization: Combine the 3DGS model with finite element analysis (FEA) and computational fluid dynamics (CFD) to simulate vascular mechanical behavior and hemodynamics.

[0067] 4. Real-time robot interaction: Based on the model predictive control (MPC) algorithm and combined with the reinforcement learning PPO (Proximal Policy Optimization) or TRPO (Trust Region Policy Optimization) algorithm, the surgical robot optimizes the real-time tracking and operation adjustment of the vascular model.

[0068] Specifically:

[0069] Data collection and preprocessing

[0070] Data source:

[0071] Preoperative: CT / MRI DICOM sequence (slice thickness ≤ 0.5 mm).

[0072] Intraoperative: Real-time three-dimensional ultrasound (RT3D-US) and ECG signals.

[0073] Preprocessing steps:

[0074] 1. Image registration:

[0075] In the process of urinary system vascular modeling, it is necessary to register the preoperative CT / MRI images with the intraoperative ultrasound images to obtain a unified coordinate system for subsequent analysis and processing. The registration method used is a combination of affine transformation and B-spline deformation. The transformation formula is:

[0076]

[0077] Here, A is an affine matrix, which describes linear transformations, including scaling, rotation, translation, and shear. Its introduction is based on the fact that affine transformations can effectively adjust the geometric shape of an image in image processing, enabling preliminary alignment of images of different modalities. In practical applications, the elements of the affine matrix A can be solved by calculating the correspondence between feature points in the image and using methods such as least squares. b is the translation vector, which determines the amount of spatial translation of the image and ensures proper alignment of the image in the translation direction.

[0078] φ i (x) is the B-spline basis function, which has good local control characteristics and can perform more precise local deformation on the image. By adjusting the coefficient c of the B-spline basis function i , which can realize local shape adjustment of the image and adjust the image deformation through local control, is particularly suitable for the precise registration of complex structures such as the renal artery.

[0079] Aligning images of different modalities in space enables subsequent segmentation and analysis of blood vessels to be performed in a unified coordinate system, laying the foundation for building a high-precision blood vessel model. In actual operation, SIFT (Scale Invariant Feature Transform) technology is used to detect extreme points (such as edges and corners) in the image to generate descriptors with scale and rotation invariance, perform feature extraction on CT and ultrasound images, find the corresponding feature points, and then use these feature points to solve the affine matrix A and translation vector b, and then adjust the coefficient c of the B-spline basis function through the stochastic gradient descent algorithm. i , and iterate continuously until a satisfactory registration effect is achieved.

[0080] 2. Blood vessel segmentation:

[0081] When extracting blood vessel masks based on the U-Net network, the Dice loss function is used to measure the difference between the predicted results and the true labels. The formula is:

[0082]

[0083] Among them, Y represents the true blood vessel mask, Represents the predicted blood vessel mask. The Dice coefficient was originally used to calculate the similarity between two sample sets. In the field of image segmentation, it can well reflect the degree of overlap between the segmentation result and the true target.

[0084] In the denominator, |Y| and Denote the number of pixels in the true mask and the predicted mask respectively, and their sum reflects the overall size of the two masks. This is twice the number of pixels in the overlapping part between the real mask and the predicted mask. This design is to amplify the weight of the overlapping part, making the loss function more sensitive to the accuracy of the segmentation result. When the predicted mask completely overlaps with the real mask, At this time L Dice = 0, indicating a perfect segmentation effect; and when the two do not overlap at all, L Dice =1, the segmentation effect is the worst.

[0085] This provides a quantitative error metric for training the U-Net network for vessel segmentation. The network continuously adjusts its parameters through the backpropagation algorithm to minimize this loss function, thereby improving vessel segmentation accuracy. During training, a large number of images with true vessel mask labels are fed into the U-Net network. The Dice loss between the predicted results and the true labels is calculated, and the network weights are adjusted based on the loss value. After multiple rounds of training, the network learns the characteristics of blood vessels and achieves accurate vessel segmentation.

[0086] 3. Noise reduction and enhancement:

[0087] Anisotropic diffusion filtering is used to reduce noise and enhance the image. Its partial differential equation is:

[0088]

[0089] Where I represents the image, t represents the time, Represents the gradient of an image, which reflects the rate of change of pixel intensity in the image. div represents the vector field divergence operation, which is used to describe the intensity of the flux source or sink of a vector field.

[0090] is the diffusion coefficient, which is adaptively adjusted according to the size of the image gradient. When it is small, that is, the area where the pixel intensity changes smoothly in the image, Close to 1, the diffusion effect is strong and the noise can be effectively removed; When it is larger, that is, in the area where there are edges or textures in the image, When it is close to 0, the diffusion effect is suppressed, thus protecting the edge and detail information of the image. K is a threshold parameter used to control the sensitivity of the diffusion coefficient to the gradient.

[0091] In noisy smooth areas, the diffusion force is increased to smooth the image; in edge and textured areas, the diffusion force is reduced to preserve image details. In practical applications, by iteratively solving this partial differential equation, the image pixel values ​​are gradually updated to achieve image noise reduction and enhancement. For example, for speckle noise present in ultrasound images, anisotropic diffusion filtering can remove the noise while preserving the edges and internal structure of the blood vessels, providing clear image data for subsequent modeling of blood vessels such as the renal artery.

[0092] 3DGS modeling method

[0093] 1. Vascular centerline modeling:

[0094] The center line is described by NURBS curve, and the parametric equation is as follows:

[0095]

[0096] Among them, w i is the weight, which can adjust the control point P i The degree of influence on the shape of the curve. i As it increases, the curve moves toward the control point P i Otherwise, the curve will move away from the control point. i These control points determine the general shape of the NURBS curve.

[0097] N i,p (u) is the B-spline basis function, which is obtained by recursive definition.

[0098] For p = 0, N i,0 (u) in u i ≤u≤u i+1 1 when p>0, 0 otherwise.

[0099]

[0100] NURBS curves are used to describe the centerline of blood vessels because they are highly flexible and accurate. They can accurately represent shapes such as conic sections, and by adjusting weights and control points, they can fit complex blood vessel paths well. In practical applications, a series of control points P are first determined based on the general direction of the blood vessels. i Then choose the appropriate weight w i By calculating this parametric equation, we can obtain a smooth vascular centerline. For example, in coronary artery modeling, by selecting key locations on the vascular wall, such as the renal artery, as control points, we can use NURBS curves to accurately depict the winding path of the renal artery, providing an accurate centerline foundation for subsequent vascular modeling.

[0101] 2. Gaussian distribution initialization:

[0102] A Gaussian function is generated along the center line, and the covariance matrix ∑ is determined by the local curvature κ and the torsion τ:

[0103]

[0104] in, R(θ) is the rotation matrix, σ r , σ θ , σ z Representing the variance in the radial, circumferential, and axial directions, respectively, they describe the circumferential distribution of blood vessels. In three-dimensional space, the Gaussian function is used to describe the local geometry of blood vessels. The covariance matrix ∑ determines the distribution of the Gaussian function in each direction.

[0105] The local curvature κ reflects the degree of curvature of the blood vessel centerline at a certain point. When κ is large, it means that the blood vessel is more curved. r When κ is small, the distribution range of the Gaussian function in the direction perpendicular to the center line is narrower, which can better fit the curved shape of the blood vessel. On the contrary, when κ is small, σ r The larger the value, the wider the distribution range of the Gaussian function. The torsion rate τ describes the torsion of the blood vessel centerline, σ z Inversely proportional to τ, the larger τ is, the greater σ z The smaller it is, the more concentrated the distribution of the Gaussian function in the center line direction.

[0106] The rotation matrix R(θ) is used to adjust the direction of the Gaussian function so that it is consistent with the local direction of the blood vessel. The Gaussian distribution initialized in this way can be adaptively adjusted according to the local geometric characteristics of the blood vessel, providing a more accurate basis for building a high-precision blood vessel model. In actual operation, the curvature κ and torsion τ of the blood vessel centerline are first calculated, and then σ is determined based on the proportional relationship. r and σ zThe value of , combined with the rotation matrix R(θ), can obtain the appropriate covariance matrix ∑, and then initialize the Gaussian function distribution along the center line.

[0107] Model optimization and simulation

[0108] 1. Finite element analysis:

[0109] The stress-strain relationship of the vascular wall is described by the hyperelastic model, and the strain energy function is:

[0110] Ψ=C 10 (I1-3)+C 01 (I2-3)

[0111] Among them, I1 and I2 are invariants, which are functions of the deformation gradient tensor.

[0112] Here F is the deformation gradient tensor, which describes the local deformation of the object during the deformation process. 10 , C 01 These are material parameters, which are determined based on the specific material properties of the blood vessel wall. Different types of blood vessels have different material parameters, and these parameters are usually obtained through experimental measurements or reference to relevant literature.

[0113] The strain energy function Ψ reflects the energy stored in the blood vessel wall during deformation. In finite element analysis, the stress and strain distribution of the blood vessel wall is determined by minimizing the strain energy function. When a blood vessel is subjected to external forces, stress and strain are generated within it. Using this strain energy function and the associated finite element algorithm, stress and strain values ​​at different locations can be calculated, thereby understanding the mechanical behavior of the blood vessel wall.

[0114] In the finite element analysis, the stress-strain relationship of the vascular wall is described by the hyperelastic model, and its strain energy function is coupled with the Gaussian parameters of the 3DGS model:

[0115] The covariance matrix parameter of the Gaussian function (σ r , σ z ) determines the spatial resolution of the finite element mesh, in σ r In the area below 0.5 mm, the grid cell size is automatically set to σ r ×0.8;

[0116] The vascular wall deformation (such as radial expansion Δr) obtained by finite element calculation is mapped to the spatial transformation of the Gaussian function through the rotation matrix R(θ), and the 3DGS representation of the vascular morphology is updated in real time.

[0117] The rotation matrix R(θ) is constructed based on the Frenet-Serret framework, and the local coordinate system matrix is ​​constructed by the tangent vector T, normal vector N, and binormal vector B of the blood vessel centerline as follows:

[0118]

[0119] The rotation angle θ is determined by the cumulative effect of the centerline torsion τ, that is, The matrix orientation is dynamically aligned with the torsional morphology of the vessel. This matrix aligns the eigendirection of the covariance matrix with the local geometric orientation of the vessel, enabling adaptive finite element meshing and dynamic optimization of the Gaussian distribution.

[0120] 2. Fluid mechanics simulation:

[0121] The blood flow velocity field is solved by the Navier-Stokes equation:

[0122]

[0123] Where ρ is the blood density, a physical quantity that depends on factors such as blood composition and temperature and can generally be considered a constant. v is the blood velocity vector, which describes the speed and direction of blood flow within the blood vessels. It represents the rate of change of velocity over time, reflecting the non-steady-state characteristics of blood flow. Under special circumstances, the blood flow velocity will change significantly over time, and this item plays an important role. It is the convection term, which reflects the momentum transfer caused by the uneven velocity of blood during flow. For example, at the bifurcation of blood vessels, the velocity distribution of blood is uneven, and the convection term will have an important impact on the blood flow velocity field.

[0124] p is pressure, represents the pressure gradient, one of the primary driving forces of blood flow. Pressure distribution within blood vessels is uneven, causing blood to flow from areas of high pressure to areas of low pressure. μ represents the dynamic viscosity of blood, which reflects the internal friction characteristics of blood. The dynamic viscosity of blood varies depending on blood composition and physiological state. It is the Laplace operator acting on the velocity vector that describes the diffusion and viscous dissipation effects of the velocity.

[0125] The boundary conditions are driven by the vascular wall motion provided by the 3DGS model, as vascular wall motion affects the blood flow velocity field. By combining the 3DGS model with the Navier-Stokes equations, hemodynamics can be simulated more accurately. In practical applications, the Navier-Stokes equations are discretely solved using numerical methods (such as the finite volume method and the finite element method). Combined with the vascular wall motion boundary conditions provided by the 3DGS model, the intravascular blood flow velocity field distribution can be determined, providing an important basis for studying the pathological mechanisms of renal artery blood flow and evaluating surgical plans.

[0126] Surgical robot interaction

[0127] 1. Real-time feedback strategy:

[0128] The deviation Δx between the robot end position q and the blood vessel model is adjusted by PID control, and its control law is:

[0129]

[0130] Among them, K p Is the proportional coefficient, which directly produces a control effect according to the size of the deviation Δx. When the deviation is large, K p The value of Δx is also large, which can quickly push the robot to move in the direction of reducing the deviation; when the deviation is small, K p The value of Δx is reduced accordingly to avoid over-adjustment of the robot. i is the integration coefficient, This term integrates the deviation to eliminate the system's steady-state error. For example, during surgery, if there are constant disturbances causing the robot to consistently deviate, the integral term will accumulate, eventually generating enough control to eliminate this steady-state error.

[0131] K d is the differential coefficient, The control variable is adjusted based on the rate of change of the deviation. When the deviation changes rapidly, the differential term exerts a greater control effect, suppressing the rapid change of the deviation and making the robot's movement smoother. During the interaction between the surgical robot and the vascular model, the deviation Δx between the robot's end-position and the vascular model is continuously measured. The control variable u(t) is calculated based on this PID control law, and the robot's movement is then adjusted to achieve real-time tracking of the vascular model, ensuring the accuracy and stability of the surgical operation.

[0132] 2. Adaptive path planning:

[0133] Based on model predictive control (MPC), the optimization objective function is:

[0134]

[0135] Among them, x k It is the predicted system state. In the application of surgical robots, it can represent the robot's position and posture at a certain moment in the future. is the reference state, which is the desired pose of the robot. It measures the difference between the predicted state and the reference state. By minimizing this term, the robot’s actual motion can be made as close as possible to the desired trajectory.

[0136] u k The control input, or control command for the robot, is used to measure the magnitude of the control input. The weight coefficient λ is introduced to balance the system state tracking error and the magnitude of the control input. A larger λ places greater emphasis on the magnitude of the control input, limiting the robot's range of motion and ensuring smoother control, but potentially resulting in larger tracking errors. A smaller λ places greater emphasis on state tracking accuracy, allowing the robot to quickly track the reference trajectory with larger control inputs, but potentially resulting in less smooth motion.

[0137] In actual adaptive path planning, the MPC algorithm predicts the system state and control input at multiple future moments at each sampling moment. By solving this optimization objective function, the optimal control input u at the current moment is obtained. k , thereby realizing the path planning and operation adjustment of the surgical robot, enabling it to better adapt to the dynamic changes of the vascular model and improve the accuracy and safety of the operation.

[0138] Application Example 1

[0139] The modeling method proposed in the embodiment is used to implement static renal artery modeling, wherein the data source is preoperative CT images (resolution 0.3 mm).

[0140] Steps: Registration → NURBS centerline fitting → 3DGS initialization → finite element simulation.

[0141] Application Example 2

[0142] The modeling method proposed in the embodiment is used to implement dynamic bladder vascular modeling, wherein the data source is an ECG-gated ultrasound sequence (25 fps).

[0143] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A urinary system vascular modeling method based on 3D Gaussian splashing, characterized in that: The steps include: S1: Preprocess the data source and construct the urinary system vascular model; S2: Describe the centerline and cross-sectional shape of blood vessels based on Bezier curves and NURBS curves to achieve dynamic 3DGS modeling of blood vessels; S3: Combining dynamic 3DGS modeling with finite element analysis and computational fluid dynamics, the simulation of hemodynamics is achieved through a bidirectional mapping algorithm between Gaussian parameters and finite element meshes.

2. The urinary system vascular modeling method based on 3D Gaussian splashing according to claim 1, characterized in that: In step S1, the data sources include DICOM sequences, real-time three-dimensional ultrasound images, and ECG signals.

3. The urinary system vascular modeling method based on 3D Gaussian splashing according to claim 2, characterized in that: The slice thickness of the DICOM sequence is ≤0.5 mm.

4. The method for modeling urinary system blood vessels based on 3D Gaussian splashing according to claim 1, characterized in that: In step S1, the pre-processing includes one or more of the following: i) Image registration: The image registration adopts a method combining affine transformation and B-spline deformation, and the transformation formula is: Where A is the affine matrix, b is the translation vector, φ i (x) is the B-spline basis function, c i are the coefficients of the B-spline basis function; ii) Vessel segmentation: The vessel segmentation is based on the U-Net network to extract the vessel mask and use the Dice loss function to measure the difference between the predicted result and the true label. The Dice loss function is: Where Y represents the true blood vessel mask, represents the predicted vessel mask, |Y| and denote the number of pixels in the true mask and the predicted mask, respectively, Indicates the number of pixels where the real mask and the predicted mask overlap; iii) Noise reduction and enhancement: the noise reduction and enhancement use anisotropic diffusion filtering, and its partial differential equation is: Where I represents the image, t represents the time, is the diffusion coefficient.

5. The method for modeling urinary system blood vessels based on 3D Gaussian splashing according to claim 1, characterized in that: In step S2, a NURBS curve is used to describe the centerline of the blood vessel, and the Gaussian function distribution along the centerline is initialized by the covariance matrix; The parametric equation of the NURBS curve is as follows: Where N i,p (u) is the B-spline basis function, w i is the weight, P i is the control point; The covariance matrix is: Where, σ r , σ θ , σ z represent the variance in the radial, circumferential and axial directions respectively, is the local curvature of the blood vessel centerline, τ is the torsion rate of the blood vessel centerline, and R(θ) is the rotation matrix.

6. The urinary system vascular modeling method based on 3D Gaussian splashing according to claim 1, characterized in that: In step S3, in the finite element analysis, the stress-strain relationship of the blood vessel wall is described by a hyperelastic model, and the strain energy function is: Ψ=C 10 (I1-3)+C 01 (I2-3); Where I1 and I2 are functions of the deformation gradient tensor, C 10 ,、C 01 is the material parameter.

7. The method for modeling urinary system blood vessels based on 3D Gaussian splashing according to claim 1, characterized in that: In step S3, in the computational fluid dynamics, the blood flow velocity field is solved by the Navier-Stokes equation: Where ρ is the density of blood, v is the blood flow velocity vector, is the convection term, p is the pressure, and μ is the dynamic viscosity of blood; The dynamic 3DGS model provides the boundary conditions for vessel wall motion.

8. A surgical robot navigation method, characterized in that: The method comprises the following steps: adjusting the deviation Δx between the robot end position and the blood vessel model through PID control; The control law of the PID control is: Where K p is the proportionality coefficient, K i is the integration coefficient, K d is the differential coefficient; the deviation Δx of the vascular model is obtained by the urinary system vascular modeling method according to any one of claims 1-7.

9. A surgical robot navigation method according to claim 9, characterized in that: The method further includes the following steps: performing path planning and operation adjustment of the surgical robot based on a model predictive control algorithm; The optimization objective function of the model predictive control algorithm is: Where x k is the predicted system state, is the reference state, u k is the control input, and λ is the weight coefficient.

10. A surgical robot navigation method according to claim 9, characterized in that: The model predictive control algorithm is optimized by a reinforcement learning algorithm, and the reinforcement learning algorithm is PPO or TRPO.

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