Preoperative liver model non-rigid deformation correction method and device for intraoperative navigation

Abstract

The application discloses a preoperative liver model non-rigid deformation correction method and device for intraoperative navigation, and the method comprises the following steps: extracting a potential overlap area of an intraoperative liver reconstruction point cloud from a surface of a preoperative liver model after initial registration; predicting a liver local deformation field of the overlap area to the intraoperative liver reconstruction point cloud by using an implicit neural network model as a determined physical boundary condition; and determining a liver global deformation field by solving a mechanical equilibrium equation through iterative updating of node stress and displacement by using a corresponding relationship between the physical boundary condition and a preoperative liver model grid. The node stress and displacement solving mechanical equilibrium equation is a linear elastic finite element liver biomechanics model, and a diagonal loading strategy is introduced to assemble a global stiffness matrix to establish the equation in advance. By using a local guidance global coupling strategy, the application realizes high-precision, physically reasonable and rapid whole organ non-rigid registration without the time-consuming iterative corresponding relationship search in the traditional method.

Description

Technical Field

[0001] This invention relates to the field of medical image processing and application technology, and in particular to a method and device for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation. Background Technology

[0002] This section is intended to provide background or context for the embodiments of the invention set forth in the claims. The description herein is not an admission that it is prior art simply because it is included in this section.

[0003] The main problem in the existing technology is that in image-guided laparoscopic liver surgery (LLS), the preoperative three-dimensional model and the real-time liver soft tissue surface cannot be accurately registered due to non-rigid deformation.

[0004] Specifically, during laparoscopic surgery, pneumoperitoneum must be established to obtain surgical space, typically by injecting carbon dioxide gas at a pressure of approximately 12-15 mmHg into the abdominal cavity. This continuous pressure, combined with gravity and the traction of surgical instruments on tissues, causes significant non-rigid deformation of the soft-textured liver. However, most current clinical surgical navigation systems rely on preoperative static 3D models reconstructed from CT or MRI. If the preoperative model is simply superimposed onto the intraoperative laparoscopic video through rigid transformations (translation and rotation), the complex soft tissue deformations described above cannot be corrected. This results in a significant deviation (typically 10-20 mm or more) between the superimposed positions of internal structures such as blood vessels and tumors and their actual anatomical locations. This deviation can mislead surgeons, increasing the risk of ruptured blood vessels leading to massive bleeding or incomplete tumor resection.

[0005] Existing non-rigid registration techniques face a dilemma of balancing efficiency and physical reliability. On the one hand, traditional biomechanical model-based methods, while ensuring the physical plausibility of deformation, rely on searching for the correspondence between intraoperative point clouds and preoperative models. Due to the lack of initial correspondence, this process requires repeated iterations (finding correspondences, solving equations, and updating the model), resulting in huge computational costs and making it difficult to meet the real-time requirements of surgical navigation. Furthermore, it is prone to getting stuck in local optima when there is severe occlusion in the intraoperative field of view. On the other hand, while emerging deep learning-based methods have fast inference speeds, the lack of explicit physical constraints makes them prone to topological errors (such as volume collapse and mesh folding), leading to severe distortion in the prediction of internal vessel locations and poor generalization ability to scenes outside the training data domain.

[0006] Therefore, there is an urgent need for a non-rigid registration method that does not require explicit iterative search for correspondences, has a fast computation speed, and strictly conforms to the laws of biomechanics and physics. Summary of the Invention

[0007] This invention provides a method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation. This method achieves high-precision, physically reasonable, and rapid whole-organ non-rigid registration through a locally guided global coupling strategy, without requiring the time-consuming iterative correspondence search of traditional methods. The method includes: After initial rigid registration between the preoperative liver model and the intraoperative liver reconstruction point cloud, the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model. Using a pre-trained implicit neural network model, the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud is predicted as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of soft tissue surface above a preset frequency. By utilizing the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the global deformation field of the liver is determined by iteratively updating the mechanical equilibrium equations of nodal forces and displacements. The mechanical equilibrium equations of nodal forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0008] This invention also provides a preoperative liver model non-rigid deformation correction device for intraoperative navigation, which achieves high-precision, physically reasonable, and rapid whole-organ non-rigid registration through a local-guided global coupling strategy, without the time-consuming iterative correspondence search of traditional methods. The device includes: The extraction unit is used to extract the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud after the preoperative liver model and the intraoperative liver reconstruction point cloud have completed the initial rigid registration. The local deformation determination unit is used to predict the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud using a pre-trained implicit neural network model, as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit the discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of the soft tissue surface above a preset frequency. The global deformation determination unit is used to determine the global deformation field of the liver by using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, and solving the mechanical equilibrium equations by iteratively updating the nodal forces and displacements. The mechanical equilibrium equations for solving the nodal forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0009] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0010] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0011] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0012] In this embodiment of the invention, the preoperative liver model non-rigid deformation correction scheme for intraoperative navigation operates as follows: After the preoperative liver model and the intraoperative liver reconstruction point cloud are initially rigidly registered, the potential overlapping region between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model; using a pre-trained implicit neural network model, the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud is predicted as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformations into a continuous spatial mapping function to capture local geometric details of soft tissue surfaces above a preset frequency; using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the mechanical equilibrium equations are solved by iteratively updating the node forces and displacements to determine the global deformation field of the liver; the mechanical equilibrium equations for solving the node forces and displacements are based on a linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0013] The beneficial technical effects of the preoperative liver model non-rigid deformation correction scheme for intraoperative navigation provided in this invention embodiment are as follows: It adopts a local-guided global coupling strategy: First, it uses a noise-resistant implicit neural network model to quickly and robustly estimate the local surface deformation, and then uses the local deformation as a determined physical boundary condition to drive the biomechanical model, thereby achieving high-precision, physically reasonable and fast whole-organ non-rigid registration without the time-consuming iterative correspondence search in traditional methods. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart illustrating the non-rigid deformation correction method for preoperative liver model used for intraoperative navigation in an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the principle framework of non-rigid deformation correction of the preoperative liver model used for intraoperative navigation in an embodiment of the present invention. Figure 3 This is a schematic diagram of the qualitative results of registration of the in-Vitro dataset in an embodiment of the present invention; Figure 4 This is a schematic diagram of the qualitative results of OpenCAS dataset registration in an embodiment of the present invention; Figure 5 Box plots showing the numerical distribution of Jacobian determinants for different methods in embodiments of the present invention; Figure 6 This is a schematic diagram of the preoperative liver model non-rigid deformation correction device used for intraoperative navigation in an embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0016] The acquisition, storage, use, and processing of data in this application comply with relevant laws and regulations.

[0017] Before introducing the embodiments of the present invention, the problems existing in the prior art and the ideas of the embodiments of the present invention based on the technical problems existing in the prior art will be introduced first.

[0018] Laparoscopic liver resection, with its significant advantages such as smaller incisions, less bleeding, faster postoperative recovery, and shorter hospital stays, has gradually replaced traditional open surgery and become an important development direction in modern liver surgery for the treatment of primary liver cancer and liver metastases. However, while this procedure brings minimally invasive benefits to patients, it also presents surgeons with significant technical challenges. First, surgeons lose the opportunity to directly palpate the liver as in open surgery, making it impossible to perceive the texture and boundaries of tumors through tactile feedback. Second, laparoscopy only provides two-dimensional surface images, with a narrow field of view and a lack of depth perception, making it difficult for surgeons to accurately identify complex vascular variations (such as variant bile ducts and hepatic arteries) and deep, small tumors within the liver parenchyma through the opaque liver surface. This "black box" state of anatomical information can easily lead to insufficient surgical resection (positive resection margins) or accidental damage to important blood vessels, causing serious complications such as massive intraoperative hemorrhage or bile leakage.

[0019] To overcome this limitation, augmented reality (AR) surgical navigation systems have emerged. These systems utilize "virtual-real fusion" technology to render and precisely overlay a high-precision 3D model, reconstructed from high-resolution images (CT / MRI) and including internal anatomical structures such as tumors and blood vessels, onto the intraoperative laparoscopic video stream in real time. This gives surgeons "X-ray vision," allowing them to visually observe key structures hidden beneath the skin, thereby accurately planning the resection plane and achieving precise anatomical liver resection.

[0020] The clinical effectiveness of AR navigation systems fundamentally depends on the accuracy of registration, that is, achieving precise alignment between the virtual preoperative model and the actual intraoperative anatomical structures in the same spatiotemporal coordinate system. Currently, 3D-3D registration based on real-time intraoperative 3D reconstruction (using stereo vision, structured light, or SLAM technology) has become the mainstream technology in this field due to its rich depth information and high alignment accuracy. In such solutions, point clouds are typically used as a common information carrier for both the preoperative model and the intraoperative surface.

[0021] In clinical practice, rigid registration is typically performed first using rigid point cloud registration algorithms (such as ICP) or anatomical marker matching to address rotational and translational deviations in the coordinate system. However, the liver is an extremely soft, viscoelastic organ. During laparoscopic surgery, an artificial pneumoperitoneum must be established to create the surgical operating space, usually requiring the continuous injection of carbon dioxide gas at a pressure of approximately 12-14 mmHg into the abdominal cavity. This continuous pressure, combined with the patient's respiratory movements, gravity, and the traction and compression of tissues by surgical instruments, leads to significant, nonlinear, and anisotropic non-rigid deformation of the liver. Clinical studies have shown that surface displacement errors caused by this type of deformation often exceed 10-20 mm, with significant differences in the degree of deformation across different regions. In such cases, rigid registration alone cannot correct these complex local deformations, resulting in significant deviations between the superimposed vascular and tumor models and their actual positions. Therefore, after rigid registration is completed, a non-rigid registration step must be introduced to dynamically correct the preoperative model by calculating an accurate deformation field, so that it not only fits the intraoperative point cloud on the surface, but also reflects the real positional changes of the liver's internal structure in terms of volume.

[0022] In summary, the current navigation system approach in laparoscopic liver resection generally includes the following steps: a) Preoperative imaging and preoperative point cloud acquisition: The patient's abdomen is scanned using preoperative CT or MRI images, and 3D reconstruction technology is used to generate the 3D structure of the liver and its internal structure. Uniform sampling is performed on the surface of the liver model to obtain the preoperative point cloud, denoted as... .

[0023] b) Intraoperative point cloud acquisition: First, intraoperative video of the surgical area was acquired using laparoscopy, and the liver region was extracted from the video using image segmentation technology. Then, depth estimation methods were used to calculate the depth information of each pixel in the video. Combining the segmentation results with the depth information, the three-dimensional coordinates of the visible portion of the liver during surgery could be reconstructed, thus obtaining the intraoperative point cloud, denoted as . .

[0024] c) Initial rigid body registration: The preoperative point cloud and intraoperative point cloud are processed and calculated using a point cloud registration algorithm based on deep learning to obtain the transformation matrix from the preoperative medical image coordinate system to the intraoperative laparoscopic video reconstruction coordinate system.

[0025] d) Preoperative non-rigid registration of the liver model: Non-rigid registration algorithms (such as finite element method or deep learning method) are used to calculate the nonlinear mapping relationship between the surface of the preoperative model and the intraoperative point cloud. This process aims to solve for a dense displacement vector field so that the surface geometry of the preoperative model after deformation closely matches the intraoperative point cloud, while maintaining the topological integrity of the internal structure as much as possible.

[0026] e) Image Fusion: Based on the deformation field calculated in step d), the positions of all nodes in the preoperative liver model (including internally invisible deep blood vessels and tumors) are updated. Finally, combined with the intrinsic parameter matrix of the laparoscopic camera, the deformed 3D virtual model is reprojected and rendered onto the 2D laparoscopic video, achieving high-precision virtual-real fusion display to guide the surgeon.

[0027] The embodiments of this invention focus on non-rigid registration, a key step in correcting soft tissue deformation, and aim to provide a non-rigid registration method that does not require explicit iterative search for correspondences, has a fast computation speed, and strictly conforms to the laws of biomechanics and physics.

[0028] Current non-rigid registration techniques are mainly divided into two categories: (1) Data-driven method: This type of method is mainly based on deep learning technology. It directly fits the nonlinear mapping relationship between the input point cloud data and the output deformation field by constructing architectures such as Convolutional Neural Networks (CNN) or Graph Neural Networks (GNN). Its core advantage is that the inference efficiency is extremely high. Once the model is trained, the intraoperative inference process usually only takes milliseconds, which can easily meet the real-time requirements of surgical navigation. However, its limitations are also very significant: First, this type of method is essentially a geometric feature fitting and lacks an explicit physical constraint mechanism. When dealing with large deformations or complex boundary conditions, the deformation field predicted by the network is prone to violate the laws of biomechanics, producing topological errors such as volume collapse and mesh folding, which leads to serious distortion in the prediction of the location of blood vessels and tumors inside the liver. Second, high-quality real deformation data in the medical field is extremely scarce, and existing methods mostly rely on synthetic data for training. When encountering deformation patterns outside the training data domain during surgery (such as special instrument compression or large bending), the model often shows weak generalization ability and it is difficult to guarantee the reliability of registration.

[0029] (2) Model-driven method: This type of method is based on the principles of continuum mechanics, treating the liver as a physical entity for biomechanical modeling, and calculating deformation by solving partial differential equations (PDEs). The most mainstream implementation is based on the finite element method (FEM), which solves the mechanical equilibrium equations by minimizing the system's potential energy. Since this type of method strictly follows physical laws such as mass conservation and momentum conservation, the deformation field it generates inherently has topological preservation properties, enabling accurate prediction of the displacement of deep structures inside the liver. However, the bottleneck of this method lies in computational efficiency and the acquisition of correspondences. On the one hand, solving large-scale finite element equations is computationally expensive; on the other hand, the FEM solver is highly dependent on defined boundary conditions, i.e., the point correspondence between the preoperative model and the intraoperative point cloud. Since the intraoperative point cloud is often sparse, noisy, and subject to field-of-view occlusion, directly obtaining the correspondence is extremely difficult. Existing methods typically have to use the Iterative Closest Point (ICP) algorithm to repeatedly "match and solve" loops, which causes the overall computation time to increase exponentially, seriously hindering its application in real-time surgical navigation systems.

[0030] This invention proposes a preoperative liver model non-rigid deformation correction scheme for intraoperative navigation. This scheme is a novel local-to-global non-rigid registration method based on implicit neural representation and biomechanical models. This method utilizes implicit neural networks to rapidly and robustly estimate local surface deformation and uses it as a deterministic boundary condition to drive the global finite element model. This overcomes the challenges of low computational efficiency and heavy reliance on iterative correspondence search in traditional biomechanical methods, as well as the lack of physical constraints and susceptibility to topological errors in existing deep learning methods. Combined with an anti-occlusion overlapping region extraction strategy and a strict biomechanical constraint mechanism, the method provided by this invention achieves high-precision registration that balances real-time performance and physical plausibility without requiring explicit point correspondence, significantly improving the robustness of the algorithm in intraoperative partial occlusion and noisy environments. This technology not only provides reliable support for real-time intraoperative navigation with both speed and accuracy, helping surgeons accurately locate deep tumors and key blood vessels through the deformed liver surface, but also effectively reduces surgical risks caused by deformation errors, improving surgical efficiency and safety, and meeting the urgent clinical need for real-time, high-fidelity non-rigid registration. The following section provides a detailed introduction to the non-rigid deformation correction scheme for the preoperative liver model used for intraoperative navigation.

[0031] Figure 1 This is a flowchart illustrating the preoperative non-rigid deformation correction method for liver models used in intraoperative navigation in an embodiment of the present invention. Figure 1 As shown, the method includes the following steps: Step 101: After the initial rigid registration of the preoperative liver model and the intraoperative liver reconstruction point cloud is completed, the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model. Step 102: Using a pre-trained implicit neural network model, predict the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud as the determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of soft tissue surface above a preset frequency. Step 103: Using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the mechanical equilibrium equations are solved by iteratively updating the nodal forces and displacements to determine the global deformation field of the liver; the mechanical equilibrium equations for solving the nodal forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0032] In this embodiment of the invention, the non-rigid deformation correction method for preoperative liver model used for intraoperative navigation operates as follows: After initial rigid registration between the preoperative liver model and the intraoperative liver reconstruction point cloud, a potential overlapping region between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model; using a pre-trained implicit neural network model, the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud is predicted as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformations into a continuous spatial mapping function to capture local geometric details of soft tissue surfaces above a preset frequency; using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the mechanical equilibrium equations are solved by iteratively updating the node forces and displacements to determine the global deformation field of the liver; the mechanical equilibrium equations for solving the node forces and displacements are based on a linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0033] The beneficial technical effects of the preoperative liver model non-rigid deformation correction method for intraoperative navigation provided in this invention are as follows: It employs a local-guided-global coupling strategy: firstly, a noise-resistant implicit neural network model is used to quickly and robustly estimate local surface deformation; then, this local deformation is used as a defined physical boundary condition to drive the biomechanical model. This achieves high-precision, physically reasonable, and rapid whole-organ non-rigid registration without the time-consuming iterative correspondence search required by traditional methods. The following is a detailed description of this preoperative liver model non-rigid deformation correction method for intraoperative navigation.

[0034] The main contents of the preoperative liver model non-rigid deformation correction method for intraoperative navigation provided in this invention embodiment include: ① Robust extraction of overlapping regions: After the preoperative model and the intraoperative point cloud are initially rigidly aligned, the Top-k nearest neighbor strategy with an expanded search range is used to extract the set of points in the region that may overlap with the intraoperative point cloud from the preoperative mesh surface in order to deal with intraoperative field of view occlusion. ② Implicit Neural Network Construction: Construct a coordinate multilayer perceptron network based on sinusoidal activation function to fit discrete point cloud deformations into a continuous spatial mapping function in order to capture high-frequency local geometric details of soft tissue surfaces; ③ Local deformation estimation: The maximum correlation entropy criterion is used as the loss function to train the network in an unsupervised manner. Its noise resistance characteristics are used to automatically suppress the interference of the occluded area and quickly estimate the local deformation field from the overlapping area to the intraoperative surface. ④ High confidence boundary screening: Set a distance threshold for the local displacement results predicted by the network to perform secondary filtering, remove mismatch points with excessive deviation, and select a set of deformation points with high confidence as the determined physical boundary conditions. ⑤ Force-driven finite element modeling: A linear elastic finite element model is constructed based on patient-specific meshes, and a diagonal loading strategy is introduced to assemble the global stiffness matrix, establishing a mechanical equilibrium iterative solution framework based on nodal forces; ⑥ Global Deformation Calculation: Utilizing the topological correspondence between the point set selected in step ④ and the preoperative mesh, the mechanical equilibrium equations are solved by iteratively updating the forces and displacements of the nodes without updating the corresponding matrices, thereby calculating the global displacement field, including the internal structure.

[0035] The following section provides a detailed introduction to the main content of the non-rigid deformation correction method for preoperative liver models used for intraoperative navigation.

[0036] This invention proposes a non-rigid registration method for liver surgery navigation based on implicit neural representation and a biomechanical model. The overall framework of the method is shown in the figure below. Figure 2 As shown, Figure 2 This is a schematic diagram illustrating the principle framework of preoperative liver model non-rigid deformation correction for intraoperative navigation in this embodiment of the invention. The core of this scheme lies in employing a local-guided-global coupling strategy: firstly, a noise-resistant deep learning network is used to quickly and robustly estimate local surface deformation; then, this local deformation is used as a defined physical boundary condition to drive the biomechanical model, thereby achieving high-precision, physically reasonable, and rapid whole-organ non-rigid registration without the time-consuming iterative correspondence search required by traditional methods. The following section combines... Figure 2 This non-rigid registration method is described in detail.

[0037] In step 101 above, the overlapping region is robustly extracted.

[0038] After initial rigid registration between the preoperative model and the intraoperative point cloud, due to limited surgical field and instrument occlusion, there is only partial overlap between the complete preoperative liver model surface (Source) and the local point cloud (Target) reconstructed intraoperatively via laparoscopy. To prevent subsequent calculations from being misled by the geometric features of the non-overlapping regions, potential overlapping regions must first be extracted.

[0039] The specific technical implementation is as follows: Assume the preoperative tetrahedral mesh model of the liver is... Its surface node set is The point cloud reconstructed during the operation was This invention abandons the traditional "single nearest neighbor" strategy and proposes a Top-k nearest neighbor expansion strategy. In one embodiment, it extracts potential overlapping regions between the preoperative liver model surface and the intraoperative liver reconstruction point cloud. This includes using a Top-k nearest neighbor strategy with an expanded search range to extract these regions, addressing intraoperative field-of-view occlusion. Here, k is a positive integer greater than 1. For intraoperative points... Each point in Calculate its surface area before surgery Calculate the Euclidean distance between all nodes and select the nearest node in the previous node list. Points. In this embodiment, parameters Preferred settings All selected preoperative nodes constitute the overlapping region point set. :

[0040] By selecting A nearest neighbor point, rather than This effectively expands the search range of overlapping areas. Even if the intraoperative point cloud has significant noise or the initial registration has minor deviations, the actual anatomical corresponding points are highly likely to be included in the expanded point set. This significantly improves the robustness of the algorithm when facing partial occlusion.

[0041] In step 102 above, the implicit neural representation network is constructed in advance.

[0042] In the previous step, this embodiment of the invention obtained two point sets. (From preoperative model) and (From the intraoperative surface), among which The area covered is greater than Slightly larger. The goal of this step is to build a network model to estimate the size of the network. arrive The local deformation field. In this process, to ensure the flexibility of geometric fitting, explicit biomechanical constraints are omitted.

[0043] This invention models deformation field estimation as a non-rigid point cloud registration problem. To address noise and partial occlusion in the intraoperative point cloud, this invention uses implicit neural representations to characterize local deformation, modeling the deformation field as a continuous function on the surface domain. This modeling approach does not rely on a one-to-one explicit correspondence; instead, the network learns a smooth deformation mapping, naturally propagating reasonable motion from the visible region to the occluded region, thus producing robust and physically consistent local alignment. The specific technical implementation is as follows: a. Network definition: using a network defined by parameters Parameterized unsupervised neural networks implicitly define nonlinear mappings. It serves as a deformation network between two point clouds.

[0044] b. Network Architecture: This neural network is a fully connected Multilayer Perceptron (MLP), consisting of an input layer, three hidden layers, and an output layer. Each hidden layer contains 128 neurons.

[0045] c. Activation Function: To effectively capture high-frequency spatial details (such as minute anatomical textures and deformation folds) on the liver surface, embodiments of this invention employ a sinusoidal activation function. Its mathematical form includes a frequency factor. In this embodiment, the following settings are provided. In one embodiment, the frequency factor of the sinusoidal activation function can range from 25 to 35, preferably 30. This enables the network to fit high-frequency signals and avoids the oversmoothing problem caused by the traditional ReLU activation function.

[0046] In step 102 above, local deformation estimation is performed.

[0047] To train the aforementioned implicit neural network to accurately fit point clouds in the presence of occlusion and noise, this embodiment of the invention uses correlation entropy as a similarity measure. Correlation entropy is a statistic insensitive to outliers. Using it as a loss function ensures that points in occluded regions (outliers) contribute minimally to the objective function, thus achieving robust registration. Specifically, in one embodiment, the implicit neural network model is obtained through unsupervised training using the maximum correlation entropy criterion as the loss function. The specific technical implementation is as follows: a. Definition of correlation entropy: For any two scalar variables and Related entropy and its inductive measure The definition is as follows (where Represents the expectation operator. The Gaussian kernel function is represented by a specific Gaussian kernel function with translation invariant properties, which is preferred in this embodiment of the invention. ): (1) (2) b. Loss function construction: network parameters By minimizing the following bidirectional objective function Come and learn: (3) in, Let be the bidirectional objective function, be the network parameters of the implicit neural network model, and be the input point set. Corresponding overlapping areas target point set Corresponding intraoperative point cloud . For any two scalar variables and The induced measure of the relevant entropy, and These represent the nearest neighbors in the other's set after the transformation: (4) (5) c. Optimization Strategy: During training, the Adam optimizer is used. The optimization process is set to 200 iterations. To improve computational efficiency and increase randomness, each iteration starts from the source point cloud. and target point cloud Random sampling The loss is calculated using points. Once... Once optimization is complete, the network is defined from... arrive The optimal deformation mapping can be used to directly calculate the local deformation field.

[0048] The process between step 102 and step 103 may include the following high-confidence boundary filtering operation.

[0049] While implicit neural representations exhibit high accuracy in unoccluded regions, their lack of inherent physical constraints may lead the network to assign incorrect displacements to completely occluded areas (e.g., incorrectly stretching invisible regions to match the target). Therefore, the network's predictions must be filtered to obtain reliable boundary conditions. The specific technical implementation is as follows: a. Distance threshold filtering: using a trained network to filter distance thresholds. The deformed position is obtained by inferring the position of points in the matrix. A distance threshold is set. .

[0050] b. Construct set B: For each point after displacement, calculate its distance to the intraoperative point cloud. The Euclidean distance to the nearest point in the middle. If this distance is less than... If the match is found to be valid, the point is considered a valid match and is added to the set. If the match is correct, it is considered an occluded point or a mismatched point and is removed.

[0051] (6).

[0052] As can be seen from the above, in one embodiment, the preoperative liver model non-rigid deformation correction method for intraoperative navigation may further include: setting a distance threshold for the local deformation field and performing secondary filtering to remove mismatched points with deviations greater than a preset deviation value, thereby obtaining a set of deformation points with a confidence level higher than a preset confidence level as the determined physical boundary conditions.

[0053] In step 103 above, force-driven finite element modeling is performed in advance.

[0054] To ensure that localized surface deformation propagates physically into the liver, this invention establishes a finite element method (FEM) model based on continuum mechanics, specifically a linear elastic finite element liver biomechanical model. The specific technical implementation is as follows: a. Physical property definition: Preoperative tetrahedral mesh It is considered a linearly elastic material. Young's modulus is set. kPa, Poisson's ratio High Poisson's ratio is used to simulate the incompressibility of biological soft tissue.

[0055] b. Stiffness matrix assembly: Based on the principle of virtual work, the assembly... global stiffness matrix .

[0056] c. Diagonal loading regularization: To address the stiffness matrix under conditions without fixed displacement boundaries. Singularity can lead to unsolvable problems, while also restricting rigid body drift. This invention introduces a regularization term into the objective function. This is equivalent to diagonally loading the stiffness matrix to construct a regularized stiffness matrix. That is, assembling the global stiffness matrix using a diagonal loading strategy: (7) in, It is the identity matrix. This is a small regularization coefficient. This step ensures the stability of the numerical solution.

[0057] In step 103 above, the global deformation field is solved iteratively.

[0058] Step 103 above is the most crucial step that distinguishes this embodiment of the invention from the prior art. Traditional methods require repeated iterations of the "ICP search" at this step. This embodiment of the invention utilizes the high-confidence boundary determined in step four to achieve a fast solution without requiring a correspondence search. The specific technical implementation is as follows: a. Constructing Data Items: To measure the fit between the deformed preoperative model surface and the neural network prediction target, a data item target function is defined. This function measures the predicted deformed surface. Differences between the high-confidence target point set and the target point set: (8); in, The initial spatial position of the preoperative grid nodes; Let be the displacement vector of the node; The spatial location of the high-confidence point set predicted and selected by the neural network in step four; The correspondence (topological correspondence) matrix is ​​used because the selected high-confidence point set B is itself a preoperative liver tetrahedral mesh model. A subset of , therefore the correspondence matrix is ​​a constant matrix.

[0059] b. Introducing Biomechanical Model Constraints: To ensure the physical rationality of the deformation, a linear elastic finite element liver biomechanical model is incorporated into the data. This is achieved using the linear elastic mechanical equilibrium equations (linear elastic finite element liver biomechanical model). (in The stiffness matrix regularized by diagonal loading in step five (i.e., the global stiffness matrix assembled by the diagonal loading strategy) can be used to establish displacement. With driving force Linear relationship between them: (9); Substituting this relationship into the data term formula, the objective function is transformed into the force applied to the liver surface. Functions: (10) c. Optimization Solution: The optimal driving force can be solved through optimization. This makes the above data items Minimize. Solve for the optimal driving force. Then, substitute back into formula (9) to solve for the optimal displacement field.

[0060] As can be seen from the above, in one embodiment, the preoperative liver model non-rigid deformation correction method for intraoperative navigation may further include: pre-establishing the mechanical equilibrium equations for the force and displacement of the nodes according to the following method: Construct a data target function; the data target function is used to measure the degree of fit between the local deformation field of the liver and the preoperative liver model mesh, and the data target function includes the topological correspondence between the determined physical boundary conditions and the preoperative liver model mesh; A linear relationship between liver displacement and driving force is established using a linear elastic finite element liver biomechanical model. The linear relationship is then substituted into the data project metric function, which is transformed into a function of the force applied to the surface of the liver model. The linear relationship and the function of the force applied to the surface of the liver model constitute the mechanical equilibrium equation for solving the nodal force and displacement.

[0061] As can be seen from the above, in one embodiment, determining the global deformation field of the liver by iteratively updating the mechanical equilibrium equations based on the forces and displacements at the nodes can include: The optimal driving force is obtained by iteratively optimizing the function of the force applied to the surface of the liver model, thereby minimizing the function of the force applied to the surface of the liver model. Substituting the optimal driving force into the linear relationship between liver displacement and driving force, the optimal displacement field is solved as the global deformation field of the liver.

[0062] As can be seen from the above, in one embodiment, the mechanical equilibrium equations for solving the forces and displacements at the nodes can be: ; ; in, Based on the linear elastic finite element liver biomechanical model Establish, Assemble the global stiffness matrix for the diagonal loading strategy. As the driving force; Force applied to the surface of the liver model The function, The initial spatial positions of the mesh nodes in the preoperative liver model; This represents the displacement vector of the mesh nodes in the preoperative liver model; The spatial location of the point set of the local deformation field of the liver; This is the topological correspondence matrix between the physical boundary conditions and the preoperative liver model mesh.

[0063] In summary, the preoperative liver model non-rigid deformation correction method for intraoperative navigation provided by the embodiments of the present invention achieves the following: ① "Local guidance for global" coupled registration framework strategy: A phased registration architecture is proposed. First, the local deformation field is solved using implicit neural representation. Then, the prediction results are transformed into deterministic physical boundary conditions to drive the global finite element model, thus combining the inference speed of deep learning with the physical reliability of biomechanical models.

[0064] ② Finite element solution mechanism that does not require updating the correspondence: By utilizing the natural topological consistency between the point set after local deformation and the preoperative mesh, the corresponding matrix is ​​locked during the mechanical solution process without needing to be updated, completely eliminating the time-consuming iterative nearest point (ICP) search step in the traditional method, and greatly improving the computational efficiency of non-rigid registration.

[0065] The non-rigid deformation correction method for preoperative liver model used for intraoperative navigation provided in this embodiment of the invention has been validated using two publicly available datasets: the in-Vitro dataset [3] published by Yang et al. and the OpenCAS dataset [4]. This embodiment of the invention uses the target registration error (TRE) to evaluate the registration error and the Jacobi determinant (J) to evaluate the physical rationality of the deformation field. The specific calculation methods for the target registration error and the Jacobi determinant are as follows: (11) in and These represent the gold standard and the predicted 3D coordinates, respectively. For the registration error of a certain method on a certain sample, the result is calculated using all the marked points of that sample. The report is in the form of "mean ± standard deviation".

[0066] (12)

[0067] in Represents the displacement vector field. Represents the identity matrix. As an indicator of local volume change, the Jacobian determinant is used to verify whether the transformation preserves the topological structure and is physically consistent (i.e., avoids the occurrence of...). (folding artifacts)

[0068] To demonstrate the superiority of the method proposed in this embodiment, it is compared with references to [1] (Pfeiffer M, Riediger C, Leger S, et al. Non-rigid volume to surface registration using a data-driven biomechanical model[C] / / International Conference on Medical Image Computing and Computer-Assisted Intervention. Cham: Springer International Publishing, 2020: 724-734), [2] (Zhao M, Meng G, Yan D M. Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy[C] / / The Thirteenth International Conference on Learning Representations. 2025), and [3] (Yang Z, Simon R, Merrell K, et al. Boundaryconstraint-free biomechanical model-based surface matching for intraoperativeliver deformation correction[J]. IEEE Transactions on Medical Imaging, A comparative experiment was conducted on the three methods in (2025 Apr;44(4):1723-1734). The experimental results show that the registration methods proposed in the embodiments of the present invention can achieve the lowest registration error and a completely physically reasonable deformation field, and achieve three times the inference speedup compared with the literature [3] with similar error.

[0069] (1) Comparison of registration errors

[0070] In the in-Vitro dataset, non-rigid registration experiments were performed using partial and complete intraoperative surfaces in this embodiment of the invention to verify the robustness of the method under different intraoperative visibility conditions. Quantitative registration results are shown in Table 1 below, and qualitative visualization results are as follows: Figure 3 As shown, Figure 3This is a schematic diagram of the registration qualitative results of the in-Vitro dataset in this embodiment of the invention. The non-rigid deformation correction method for preoperative liver model used for intraoperative navigation in this embodiment of the invention maintains stable and accurate performance in both scenarios, achieving [success / achievement] on eight samples. The average TRE. Even with only partial surface input, the registration error is only slightly higher than the average TRE. This demonstrates its robust deformation estimation capability and its effective generalization capability beyond the visible region.

[0071] Table 1. Quantitative comparison of TRE on the in-Vitro dataset (unit: mm)

[0072] Table 2 summarizes the quantitative results on the OpenCAS dataset. The preoperative liver model non-rigid deformation correction method used for intraoperative navigation in this embodiment of the invention demonstrated robustness in all cases, slightly outperforming state-of-the-art baseline methods, and achieving the expected accuracy. Figure 4 shows the qualitative results on the OpenCAS dataset. Figure 4 This is a schematic diagram of the qualitative results of OpenCAS dataset registration in an embodiment of the present invention. The qualitative results show that the non-rigid deformation correction method of the preoperative liver model used for intraoperative navigation in this embodiment of the present invention can better maintain the real and physically reasonable deformation.

[0073] Table 2. Quantitative comparison of TRE on the OpenCAS dataset (unit: mm)

[0074] (2) Comparison of registration speeds

[0075] The method proposed in this embodiment of the invention has a significant improvement in solution efficiency compared with the traditional finite element model-based method. Therefore, a comparative experiment was conducted on the inference speed with the finite element model-based method proposed in reference [3]. The results are shown in Table 3 below. The local-global registration framework provided in this embodiment of the invention can achieve a speedup of 3.63 times. It can be seen from the results that when the preoperative model remains unchanged, the more points in the intraoperative point cloud, the more obvious the speedup effect of the local-global framework proposed in this embodiment of the invention. When the number of points reaches tens of thousands during the operation, it can even achieve a speedup effect of 4.46 times.

[0076] Table 3 Comparison of running time between the method of this invention and the method in reference [3] (unit: seconds); the last column shows the speedup of the non-rigid deformation correction method of the preoperative liver model used for intraoperative navigation in the embodiments of this invention compared with the method in reference [3].

[0077] (3) Comparison of physical registration rationality

[0078] To further verify the physical rationality of the estimated deformation, this embodiment of the invention analyzes the distribution of the Jacobian determinant values ​​calculated on tetrahedral mesh elements. This embodiment specifically selects video stereo reconstruction samples from the OpenCAS dataset for this evaluation because their high reconstruction noise and partial visibility best represent the real intraoperative scene.

[0079] Figure 5 Box plots comparing the numerical distributions of the Jacobian determinants of different methods in embodiments of the present invention. For example... Figure 5 As shown, the non-rigid deformation correction method for the preoperative liver model used for intraoperative navigation in this embodiment of the invention achieves a distribution that is tightly clustered in... Around, and maintain a strictly positive value on all grid cells. This demonstrates that the registration framework of the present invention maintains the topological integrity of the liver volume in the absence of singularities.

[0080] In summary, the beneficial technical effects of the preoperative liver model non-rigid deformation correction method for intraoperative navigation provided by the embodiments of the present invention are as follows: ① Significantly improved computational efficiency: Compared with existing biomechanical model-based methods (such as BCF-FEM), this invention utilizes neural networks to predict deterministic boundary conditions, eliminating the time-consuming ICP search in traditional methods. Registration can be completed quickly by solving the mechanical equilibrium equations without updating the corresponding matrix, reducing computation time by more than 60%, thus better meeting the real-time requirements of surgical navigation.

[0081] ② High physical reliability and avoidance of topological errors: Compared with existing purely data-driven (deep learning) methods, this invention does not rely entirely on deep networks to predict the full-field deformation, but introduces a linear elastic finite element biomechanical model as a global constraint. This ensures that the generated deformation field strictly follows the laws of continuum mechanics, eliminates non-physical phenomena such as volume collapse and mesh folding common in deep learning methods, and guarantees the accuracy of predicting the location of blood vessels and tumors inside the liver.

[0082] ③ Superior robustness to occlusion and noise: Existing technologies are prone to establishing incorrect correspondences and registration divergence when the intraoperative field of view is limited (partial occlusion) or when there is smoke noise. This invention introduces maximum correlation entropy as a loss function in the local deformation estimation stage, which can automatically suppress interference from occluded areas and outliers; combined with… The overlapping region extraction strategy enables the algorithm to maintain extremely high registration accuracy even in environments with low overlap rates and high noise levels.

[0083] This invention also provides a preoperative liver model non-rigid deformation correction device for intraoperative navigation, as described in the following embodiments. Since the principle by which this device solves the problem is similar to the preoperative liver model non-rigid deformation correction method for intraoperative navigation, the implementation of this device can refer to the implementation of the preoperative liver model non-rigid deformation correction method for intraoperative navigation; repeated details will not be elaborated further.

[0084] Figure 6 This is a schematic diagram of the preoperative liver model non-rigid deformation correction device used for intraoperative navigation in an embodiment of the present invention, as shown below. Figure 6 As shown, the device includes: Extraction unit 01 is used to extract the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud after the preoperative liver model and the intraoperative liver reconstruction point cloud have completed the initial rigid registration. The local deformation determination unit 02 is used to predict the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud using a pre-trained implicit neural network model, as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit the discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of the soft tissue surface above a preset frequency. The global deformation determination unit 03 is used to determine the global deformation field of the liver by using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, and solving the mechanical equilibrium equations by iteratively updating the node forces and displacements. The mechanical equilibrium equations for solving the node forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0085] In one embodiment, the implicit neural network model can be a model obtained by unsupervised training of the implicit neural network using the maximum correlation entropy criterion as the loss function.

[0086] In one embodiment, the loss function can be: ; in, It is a two-way objective function. The network parameters of the implicit neural network model are the input point set. Corresponding overlapping regions, target point set Corresponding to the intraoperative liver reconstruction point cloud, and Let each represent the nearest neighbor in the other's set after the transformation. For any two scalar variables and The inductive measure of the relevant entropy.

[0087] In one embodiment, the preoperative liver model non-rigid deformation correction device for intraoperative navigation further includes a high-confidence boundary screening unit, used to: set a distance threshold for the local deformation field for secondary filtering, remove mismatched points with deviations greater than a preset deviation value, and obtain a set of deformation points with confidence higher than a preset confidence value as the determined physical boundary conditions.

[0088] In one embodiment, the extraction unit is specifically used to: extract potential overlapping regions with the intraoperative liver reconstruction point cloud from the surface of the preoperative liver model using a Top-k nearest neighbor strategy that expands the search range, in order to address intraoperative field-of-view occlusion, where k is a positive integer greater than 1.

[0089] In one embodiment, the preoperative liver model non-rigid deformation correction device for intraoperative navigation further includes a unit for establishing the mechanical equilibrium equations for solving nodal forces and displacements, used to: pre-establish the mechanical equilibrium equations for solving nodal forces and displacements according to the following method: Construct a data target function; the data target function is used to measure the degree of fit between the local deformation field of the liver and the preoperative liver model mesh, and the data target function includes the topological correspondence between the determined physical boundary conditions and the preoperative liver model mesh; A linear relationship between liver displacement and driving force is established using a linear elastic finite element liver biomechanical model. The linear relationship is then substituted into the data project metric function, which is transformed into a function of the force applied to the surface of the liver model. The linear relationship and the function of the force applied to the surface of the liver model constitute the mechanical equilibrium equation for solving the nodal force and displacement.

[0090] In one embodiment, the global deformation determination unit is specifically used for: The optimal driving force is obtained by iteratively optimizing the function of the force applied to the surface of the liver model, thereby minimizing the function of the force applied to the surface of the liver model. Substituting the optimal driving force into the linear relationship between liver displacement and driving force, the optimal displacement field is solved as the global deformation field of the liver.

[0091] In one embodiment, the mechanical equilibrium equations for the forces and displacements at the nodes can be solved as follows: ; ; in, Based on the linear elastic finite element liver biomechanical model Establish, Assemble the global stiffness matrix for the diagonal loading strategy. As the driving force; Force applied to the surface of the liver model The function, The initial spatial positions of the mesh nodes in the preoperative liver model; This represents the displacement vector of the mesh nodes in the preoperative liver model; The spatial location of the point set of the local deformation field of the liver; This is the topological correspondence matrix between the physical boundary conditions and the preoperative liver model mesh.

[0092] In one embodiment, the frequency factor of the sinusoidal activation function can range from 25 to 35.

[0093] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0094] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0095] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation.

[0096] In this embodiment of the invention, the preoperative liver model non-rigid deformation correction scheme for intraoperative navigation operates as follows: After the preoperative liver model and the intraoperative liver reconstruction point cloud are initially rigidly registered, the potential overlapping region between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model; using a pre-trained implicit neural network model, the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud is predicted as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformations into a continuous spatial mapping function to capture local geometric details of soft tissue surfaces above a preset frequency; using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the mechanical equilibrium equations are solved by iteratively updating the node forces and displacements to determine the global deformation field of the liver; the mechanical equilibrium equations for solving the node forces and displacements are based on a linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

[0097] The beneficial technical effects of the preoperative liver model non-rigid deformation correction scheme for intraoperative navigation provided in this invention embodiment are as follows: It adopts a local-guided global coupling strategy: First, it uses a noise-resistant implicit neural network model to quickly and robustly estimate the local surface deformation, and then uses the local deformation as a determined physical boundary condition to drive the biomechanical model, thereby achieving high-precision, physically reasonable and fast whole-organ non-rigid registration without the time-consuming iterative correspondence search in traditional methods.

[0098] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] This invention is described with reference to flowchart illustrations and / or block diagrams of a preoperative liver model non-rigid deformation correction method, apparatus (system), and computer program product for intraoperative navigation according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0102] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting non-rigid deformation of a preoperative liver model for intraoperative navigation, characterized in that, include: After initial rigid registration between the preoperative liver model and the intraoperative liver reconstruction point cloud, the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud is extracted from the surface of the preoperative liver model. Using a pre-trained implicit neural network model, the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud is predicted as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of soft tissue surface above a preset frequency. By utilizing the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, the global deformation field of the liver is determined by iteratively updating the mechanical equilibrium equations of nodal forces and displacements. The mechanical equilibrium equations of nodal forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

2. The method as described in claim 1, characterized in that, The implicit neural network model is obtained by unsupervised training of the implicit neural network using the maximum correlation entropy criterion as the loss function.

3. The method as described in claim 2, characterized in that, The loss function is: ； in, It is a two-way objective function. The network parameters of the implicit neural network model are the input point set. Corresponding overlapping regions, target point set Corresponding to the intraoperative liver reconstruction point cloud, and Let each represent the nearest neighbor in the other's set after the transformation. For any two scalar variables and The inductive measure of the relevant entropy.

4. The method as described in claim 1, characterized in that, Also includes: The local deformation field is filtered a second time by setting a distance threshold to remove mismatched points with deviations greater than a preset deviation value, and the set of deformation points with confidence higher than the preset confidence value is obtained as the determined physical boundary condition.

5. The method as described in claim 1, characterized in that, Extracting potential overlapping regions between the preoperative liver model surface and the intraoperative liver reconstruction point cloud, including: using a Top-k nearest neighbor strategy with an expanded search range to extract potential overlapping regions between the preoperative liver model surface and the intraoperative liver reconstruction point cloud to address intraoperative field of view occlusion, where k is a positive integer greater than 1.

6. The method as described in claim 1, characterized in that, It also includes: pre-establishing the mechanical equilibrium equations for the forces and displacements of the nodes according to the following method: Construct a data target function; the data target function is used to measure the degree of fit between the local deformation field of the liver and the preoperative liver model mesh, and the data target function includes the correspondence between the determined physical boundary conditions and the preoperative liver model mesh; A linear relationship between liver displacement and driving force is established using a linear elastic finite element liver biomechanical model. The linear relationship is then substituted into the data project metric function, which is transformed into a function of the force applied to the surface of the liver model. The linear relationship and the function of the force applied to the surface of the liver model constitute the mechanical equilibrium equation for solving the nodal force and displacement.

7. The method as described in claim 6, characterized in that, By iteratively updating the forces and displacements at the nodes and solving the mechanical equilibrium equations, the global deformation field of the liver is determined, including: The optimal driving force is obtained by iteratively optimizing the function of the force applied to the surface of the liver model, thereby minimizing the function of the force applied to the surface of the liver model. Substituting the optimal driving force into the linear relationship between liver displacement and driving force, the optimal displacement field is solved as the global deformation field of the liver.

8. The method as described in claim 6, characterized in that, The mechanical equilibrium equations for the forces and displacements at the nodes are as follows: ； in, Based on the linear elastic finite element liver biomechanical model Establish, Assemble the global stiffness matrix for the diagonal loading strategy. As the driving force; Force applied to the surface of the liver model The function, The initial spatial positions of the mesh nodes in the preoperative liver model; This represents the displacement vector of the mesh nodes in the preoperative liver model; The spatial location of the point set of the local deformation field of the liver; This is the matrix showing the correspondence between the physical boundary conditions and the preoperative liver model mesh.

9. The method as described in claim 1, characterized in that, The frequency factor of the sinusoidal activation function ranges from 25 to 35.

10. A non-rigid deformation correction device for a preoperative liver model used for intraoperative navigation, characterized in that, include: The extraction unit is used to extract the potential overlapping area between the preoperative liver model and the intraoperative liver reconstruction point cloud after the preoperative liver model and the intraoperative liver reconstruction point cloud have completed the initial rigid registration. The local deformation determination unit is used to predict the local deformation field of the liver from the overlapping region to the intraoperative liver reconstruction point cloud using a pre-trained implicit neural network model, as a determined physical boundary condition; the implicit neural network model is a coordinate multilayer perceptron network model based on a sinusoidal activation function, which is used to fit the discrete point cloud deformation to a continuous spatial mapping function in order to capture local geometric details of the soft tissue surface above a preset frequency. The global deformation determination unit is used to determine the global deformation field of the liver by using the correspondence between the determined physical boundary conditions and the preoperative liver model mesh, and solving the mechanical equilibrium equations by iteratively updating the nodal forces and displacements. The mechanical equilibrium equations for solving the nodal forces and displacements are based on the linear elastic finite element liver biomechanical model, and a diagonal loading strategy is introduced to assemble the pre-established equations of the global stiffness matrix.

11. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 9.

12. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 9.

13. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 9.

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