Tripod operation nail path mathematical model construction method, in-vitro guide frame construction method and operation navigation path planning method and system

Abstract

The invention discloses a Tripod surgical nail path mathematical model construction method, which comprises the following steps of: performing finite element analysis and topological structure analysis on pelvis at a large number of lesion positions to obtain nail paths of three nails, then obtaining the optimal nail path of the three nails by combining verification and correction of a SawBone model, and then constructing a geometric coordinate system of a three-dimensional pelvis model, acquiring a reference geometric shape having stable geometric limitation conditions with the optimal nail path of the three nails in the three-dimensional pelvis model, constructing an equation of the reference geometric shape and the geometric limitation conditions, and obtaining an equation of the optimal nail path of the three nails by utilizing the equation of the reference geometric shape and the geometric limitation conditions. When the method is applied to different patients, personalized optimal nail paths adaptive to different patients are obtained, and a guide tube of an in-vitro guide frame or a preoperative planning path of an operation navigation direction can be fitted; three stable Tripod screws can be placed according to the optimal screw path direction of a patient during a specific operation, and the optimal treatment effect is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of methods or devices for medical implantation or removal of internal or external fixators, and in particular to the technical field of methods for constructing mathematical models of guide nail paths related to Tripod surgery around the acetabulum. Specifically, the present invention provides a method for constructing a mathematical model of the nail paths for Tripod surgery, a method for constructing an in vitro guide frame, and a surgical navigation path planning method and system. Background Art

[0002] Bone tissue is a common site for the metastasis of malignant tumors. With the advancement of malignant tumor diagnosis and treatment technologies, the number of patients surviving with tumors has increased year by year, and the number of patients with bone metastasis has shown a significant annual increase. The pelvis and acetabulum are both important interconnected parts of the human locomotor system and high-incidence sites for bone metastasis. Traditional treatment methods such as radiotherapy and tumor resection surgery have many limitations: radiotherapy is slow to relieve symptoms and cannot treat pathological fractures; traditional surgical treatment is highly traumatic, has a high incidence of complications, and patients have a long postoperative recovery time and high medical costs. For this reason, for pelvic metastasis, the clinic urgently needs a treatment technology with less trauma, better results, and faster recovery to quickly relieve patients' symptoms, restore daily life functions, and connect with systemic tumor treatment.

[0003] The human pelvis supports body weight through the sacroiliac joints. The weight of the upper body is transferred to the top of the acetabulum via the ilium, particularly the greater sciatic notch. The weight is then transferred downward through the superior pubic ramus (anterior column) and ischium (posterior column), and then through the acetabulum via the femoral head and neck to the lower limbs. Based on a large amount of clinical data from normal patients and patients with pelvic metastatic cancer, and analyzing the different nature of lesions and pelvic structures, combined with surgical classification and biological characteristics, clinical researchers have innovatively proposed the concept of TRIPOD minimally invasive surgery.

[0004] TRIPOD minimally invasive surgery effectively reinforces the pelvis eroded by the tumor by forming a "tripod" support structure in the pelvis and acetabulum. The surgery uses a percutaneous approach to implant three intramedullary nails in the pelvis that interlock with each other in space, creating a "tripod" structure to support the acetabulum structure. These three intramedullary nails are connected to the anterior column, posterior column and top of the pelvis, namely the anterior column nail, posterior column nail and cross-column nail; they are designed to strengthen the key parts of pelvic mechanical conduction and achieve effective fixation and stabilization of the affected pelvis. This technology has the advantages of less trauma, fewer complications and low cost. It can quickly relieve patients' symptoms, allowing them to return to their daily lives as soon as possible and continue to receive systematic treatment.

[0005] The corresponding prior art discloses 202311786273.9 an extracorporeal guide frame for percutaneous internal fixation reinforcement nails around the acetabulum, which is anastomosed with the patient's pelvic skin through an arc-shaped guide plate. The three guide tubes are a cross-column nail catheter, a posterior column nail catheter, and anterior column nail catheter; they are respectively opposite to the anterior superior iliac spine and the anterior inferior iliac spine around the acetabulum on the affected side of the patient's pelvis, the ischial tuberosity of the buttocks, and the apex of the acetabulum in the direction of the pubic superior limb, and the cross-column nail, posterior column nail, and anterior column nail are respectively inserted to play a guiding role.

[0006] The above is the existing technology of the extracorporeal guide frame. Through the extracorporeal guide frame, a reference for the needle insertion point position and the nail insertion angle direction is provided for the patient's individualized percutaneous nail placement. However, because each patient has a different anatomical structure, it is necessary to quickly obtain a personalized optimal extracorporeal guide frame construction method based on each patient's unique anatomical characteristics; the key to solving the above problem is to obtain a personalized optimal needle insertion point position and nail insertion angle direction for the three internal fixation intramedullary nails (cross-column nails, posterior column nails and anterior column nails) that is effective for each patient's own anatomical structure characteristics.

[0007] In addition, surgical navigation equipment is also one of the current methods of precision surgical treatment. If the optimal personalized pin placement position based on the patient's individual anatomical structure can be constructed, an effective preoperative planning path can be constructed to serve the application of surgical navigation equipment in Tripod surgery.

[0008] In response to the above technical problems, the present invention proposes a Tripod surgery method, which is based on individual anatomical differences and a mathematical model construction method for the nail track position with optimal biomechanical properties. This model method is suitable for constructing an in vitro guide frame for Tripod surgery, as well as a path planning method and system for surgical navigation equipment. Summary of the Invention

[0009] Although the prior art 202311786273.9, an extracorporeal guide frame for percutaneous internal fixation and reinforcement of the acetabulum, discloses the direction of the catheter, there are large individual differences among different patients. When performing Tripod surgery on patients, the operator still needs to find a relatively suitable nail track position and direction based on experience. The determination of the nail track position and direction is highly dependent on the operator's experience and technical level. Everyone finds the position and direction of the nail track based on their own experience, and there are often deviations. If there is a deviation in nail placement, there is a risk that the implanted nail will pierce the pelvis into the abdominal cavity and damage various organs in the abdominal cavity. There is also a risk of penetrating the hip joint, causing greater harm to the patient.

[0010] Therefore, how to quickly identify the optimal nail track location with optimal biomechanical properties based on individual anatomical differences is a key factor in achieving the best possible outcome during tripod surgery. Using the determined optimal nail track location, the direction of the nail guide tube of an external guide frame is reverse-fitted. Then, combined with the method disclosed in prior art 202311786273.9, an external guide frame that guides the optimal nail track location can be produced using 3D printing technology, thereby quickly and accurately completing screw placement. Alternatively, when performing tripod surgery using surgical navigation technology, the calculated optimal designated position can be used for preoperative nail placement path planning. Under the guidance of the intraoperative navigation device, the three intramedullary nails of the tripod surgery are quickly placed in the optimal nail track location that conforms to individual anatomical differences and has optimal biomechanical properties. Therefore, how to obtain a standardized optimal nail track location that adapts to the individual anatomical differences of different patients is a key method for achieving the best surgical outcome. However, the current optimal nail track is determined through personalized biomechanical analysis, tailored to the specific patient. However, this construction process is cumbersome and cannot be effectively expressed, making it difficult to replicate on a large scale. Clinical application still relies on operator experience.

[0011] The present invention proposes a method for constructing a mathematical model of the position of a tripod surgical nail channel that is adapted to the individual anatomical differences of different patients and has optimal biomechanical properties. The mathematical model is used to obtain a standard expression of the optimal nail channel. The mathematical model can construct an optimal nail channel that is adapted to different patients and can be simply copied and operated. The nail channel can be effectively constructed by only constructing a coordinate system and combining the mathematical model. Specifically, the mathematical model is based on a large amount of preoperative pelvic CT scan data of patients. A three-dimensional reconstructed model of the patient's pelvis is constructed through three-dimensional reconstruction. After all or part of the three-dimensional model is subjected to finite element analysis, topological structure analysis, and Sawbone model analysis, the optimal nail channel is obtained, and a coordinate system of the three-dimensional pelvic model is constructed, and a reference geometric shape on the three-dimensional pelvic model that is in a stable geometric constraint condition with the optimal nail channel is found. By constructing equations of the reference geometric shape and the stable geometric constraint condition, the mathematical equations of three optimal nail channels that have a stable relationship with the three-dimensional model are constrained, and the construction of the mathematical models of the three optimal nail channels is completed. The mathematical model constructed by this method is related to the reference geometry and stable geometric constraints. When it is applied to different patients, because the patient's three-dimensional pelvic model is personalized, the mathematical model is constructed based on a stable relationship with the three-dimensional pelvic model. Therefore, the three optimal nail paths constructed using the mathematical model also meet the needs of individual differences. Once an effective mathematical model is constructed, the optimal nail path can be constructed according to the personalized coordinate system of each patient's own three-dimensional model, and finally an in vitro guide frame adapted to the optimal nail path or a preoperatively planned guide path can be constructed.

[0012] The present invention provides a method for constructing a mathematical model of the optimal nail path for Tripod surgery.

[0013] S110, constructing a three-dimensional pelvic model of different patients with different lesion locations using the patient's imaging images;

[0014] Step S120, performing biomechanical analysis using the three-dimensional pelvic model, and determining the nail track directions corresponding to the three nail tracks with the smallest stress and strain conditions of the pelvic model as the three optimal nail track directions;

[0015] Step S130, constructing a geometric coordinate system of the three-dimensional pelvic model, obtaining a reference geometric shape in the three-dimensional pelvic model that has stable geometric constraints on the optimal nail path of the three nails, and constructing a mathematical expression for the optimal nail path of the three nails using the stable geometric constraints and the reference geometric shape.

[0016] The mathematical expression constructed in the above manner is an expression related to the three-dimensional pelvic model of each patient. In this way, when subsequently searching for the optimal nail path, there is no need to resort to a complex biomechanical analysis process. After obtaining the patient's CT image, the patient's three-dimensional pelvic model is directly constructed. The three-dimensional pelvic model is then used to construct a geometric coordinate system in the same manner. Finally, the mathematical equations of the three optimal nail paths are applied to quickly obtain the patient's three optimal nail paths. The method of constructing the three optimal nail paths through mathematical equations is very fast and has good dissemination. The constructed optimal nail path is a personalized expression adapted to different patients.

[0017] Furthermore, in step S120, a first round of analysis is performed on the nail paths of the three nails using finite element analysis and topological structure analysis. The nail paths after the first round of analysis can be determined as the optimal nail paths, thus completing the construction of the mathematical model.

[0018] Furthermore, step S120 also includes using the simulated real three-dimensional pelvic model to perform a second round of analysis of the three nail tracks, performing an in vitro biomechanical analysis after inserting the three-dimensional pelvic model, verifying and correcting the three nail tracks of the first round of analysis, and obtaining the second round of three nail tracks. The second round of three nail tracks can be determined as the optimal three nail tracks, completing the construction of the mathematical model; by adding this step, the optimality of the optimal nail track can be further improved.

[0019] Furthermore, in step S120, finite element analysis and topological structure analysis are used to determine the three nail paths that most significantly alleviate stress concentration in the tumor bone defect, minimize stress on the internal fixation device, and best disperse stress concentration caused by the bone defect. By combining these significant effects, the optimal nail path is guaranteed to provide the best results in actual use.

[0020] Furthermore, in step S120, the real three-dimensional pelvic model is a SawBone model, which is an artificial bone model simulated according to the characteristics of human bones and has the same characteristics as real bones;

[0021] Furthermore, step S130 includes inserting three screws along the two rounds of three screw tracks in a clinical patient. Based on clinical results, the tracks of the three screws are further analyzed and modified to determine the optimal track for the three screws. The track of the three screws analyzed and modified in this step is determined as the optimal track for the three screws, and a corresponding mathematical equation is constructed. By further verifying clinical results and further improving the optimality of the optimal track, the three methods of analysis and modification are combined to obtain the optimal track for the three screws that suits most patients, ensuring the ultimate therapeutic effect.

[0022] Preferably, the situations of multiple different angles of a single nail path are analyzed separately, and / or the situations of different combinations of the optimal nail paths of three nails are analyzed, and the optimal nail paths of the three nails are obtained through comprehensive analysis.

[0023] Furthermore, equations referencing the geometric shape and geometric constraints are constructed using the coordinate system. The equations for the reference geometric shape and geometric constraints are then used to derive the equations for the optimal nail paths for the three nails. The equations for the optimal nail paths for the three nails serve as the constructed mathematical model for the optimal nail paths for the three nails. When performing a specific surgery on a patient, simply constructing a three-dimensional pelvic model of the patient and a geometric coordinate system allows the software to quickly determine the optimal nail paths for the three nails and present the directions of the nail paths on the three-dimensional pelvic model. Subsequently, reverse fitting can be performed to determine the optimal directions of the guide tubes on the in vitro guide frame, ultimately yielding a complete model of the in vitro guide frame. Alternatively, during surgical navigation, the nail path directions presented by the mathematical model can be used as the planned path for surgical navigation, allowing for direct guidance of nail placement during surgery.

[0024] Furthermore, the geometric coordinate system includes three planes: the sagittal, coronal, and transverse planes. The reference geometry of the 3D pelvic model is a circle or ellipse constructed by projecting multiple valid regions of the 3D pelvic model onto different planes. The geometric constraints are the tangent or auxiliary tangent relationships between the circle or ellipse and the projections of the three optimal nail paths onto different planes. By marking five points on the constructed circle or ellipse, the equation of the circle or ellipse is derived using these five points.

[0025] Furthermore, projections on the sagittal and coronal planes analyze the relationship between the tangents or auxiliary tangents of the circle or ellipse and the three optimal nail paths. Equations for the tangents and auxiliary tangents of the circle or ellipse are constructed. By combining the projections on the two planes with the geometric constraints of the reference geometry of the 3D pelvic model, the equations for the optimal nail paths for the three nails can be determined. This method of obtaining a mathematical model can meet the requirements for optimal nail paths and reduce the complexity of the software algorithm.

[0026] Furthermore, circles or ellipses of five valid areas on the three-dimensional pelvic model were determined on the sagittal and coronal planes, wherein circle A was the projection of a circle with the center of rotation of the femoral head as the center and the distance from the bony edge of the acetabulum on the affected side to the center of rotation of the femoral head as the radius on the coronal plane; ellipse B was the ellipse formed by the line connecting the iliac spine of the pelvis, the superior pubic ramus, the anterior edge of the S1 vertebra of the sacrum, and the S1 sacral foramen; ellipse C was the projection of the obturator foramen on the affected side of the pelvis on the coronal plane; circle D was the projection of the acetabulum on the sagittal plane; and ellipse E was the projection of a circle formed by the line connecting the bony edges of the ischial spine and the greater sciatic notch on the sagittal plane.

[0027] Furthermore, the tangent relationship between the projected circle or ellipse on the corresponding surface of the three-dimensional pelvic model and the straight line projected on the corresponding surface of the nail track is obtained, and the mathematical models of three mathematical nail tracks are obtained using the tangent relationship.

[0028] Furthermore, according to circle A, ellipse B, and circle D, a first nail path straight line is obtained, including:

[0029] According to circle A and ellipse B, obtain the first common tangent of circle A and ellipse B;

[0030] Draw a tangent from the pubic junction (0, y0) to the circle represented by circle D to obtain an auxiliary tangent;

[0031] According to the first common tangent and auxiliary tangent of circle A and ellipse B, the first nail track equation is obtained.

[0032] Furthermore, according to circle A, ellipse B, circle D, and ellipse E, a second nail path straight line is obtained, including:

[0033] According to circle A and ellipse B, the second common tangent of circle A and ellipse B is obtained;

[0034] According to the circle D and the ellipse E, the first common tangent of the circle D and the ellipse E is obtained;

[0035] According to the second common tangent line between circle A and ellipse B and the first common tangent line between circle D and ellipse E, a second nail path is obtained.

[0036] Furthermore, according to ellipse B, ellipse C, circle D, and ellipse E, the third nail track equation is obtained, including:

[0037] Connect the rightmost point of ellipse B and the rightmost point of ellipse C to obtain an auxiliary line;

[0038] According to the fourth equation and the ellipse E, the second common tangent of the circle D and the ellipse E is obtained;

[0039] According to the auxiliary connecting line and the second common tangent of circle D and ellipse E, the third nail track straight line is obtained.

[0040] The present invention also discloses a mathematical model of a Tripod surgical nail track, which is characterized in that the mathematical model is an equation for the optimal nail track of the three nails obtained by combining the optimal nail track of the three nails with the patient's three-dimensional pelvic model to construct a coordinate system. The optimal nail track of the three nails is obtained by using finite element analysis and topological structure analysis, combined with biomechanical analysis and correction of a real three-dimensional pelvic model, and analysis and correction of the nail placement effects of real clinical patients, to obtain the optimal nail track that meets the needs of most patients.

[0041] Furthermore, finite element analysis and topological structure analysis were used to obtain the three-nail nail path that most significantly alleviates the stress concentration problem in the tumor bone defect, minimizes the force on the internal fixation device, and best disperses the stress concentration problem caused by the bone defect; the SawBone model of the pelvis was used for biomechanical analysis and correction of the built-in nails to obtain two rounds of three-nail nail paths; three types of screws were inserted along the two rounds of three-nail nail paths in clinical patients to observe the clinical effects, and the nail paths of the inserted three nails were further analyzed and corrected to obtain the optimal three-nail nail path, corresponding to the optimal three-nail path.

[0042] The present invention also discloses a method for constructing an optimal nail path using a mathematical model. First, a CT image of the patient is obtained, and a three-dimensional pelvic model of the patient is constructed using the CT image. A geometric coordinate system of the three-dimensional pelvic model is constructed, and three optimal nail path directions are constructed in the three-dimensional pelvic model using the optimal nail path mathematical model of three nails.

[0043] The present invention also discloses a method for constructing an in vitro guide frame guide tube model, which obtains a three-dimensional pelvic model of the patient, constructs a coordinate system, uses a surgical nail track mathematical model to obtain the optimal nail tracks for three nails, and reversely fits to obtain three guide tube models of the in vitro guide frame.

[0044] The present invention also discloses a method for constructing an in vitro guide frame model, which obtains a three-dimensional pelvic model of the patient, constructs a coordinate system, uses a mathematical model of surgical nail paths to obtain the optimal nail paths of three nails, and reversely fits to obtain three guide tube models of the in vitro guide frame; then uses a three-dimensional model of the patient's skin to fit to obtain an in vitro arc guide plate model, and combines the guide tube model and the arc guide plate model to construct a complete in vitro guide frame model.

[0045] The present invention also discloses a method for constructing an in vitro guide frame, which obtains a three-dimensional pelvic model of the patient, uses the above-mentioned surgical nail track mathematical model to obtain the optimal nail tracks of three nails, and reversely fits to obtain three guide tube models of the in vitro guide frame; then uses the three-dimensional model of the patient's skin to fit to obtain an in vitro arc guide plate model, combines the guide tube model and the arc guide plate model together to construct a complete in vitro guide frame model; and uses the constructed in vitro guide frame model to 3D print an in vitro guide frame.

[0046] The present invention also discloses an in vitro guide frame, which is obtained by using the above in vitro guide frame construction method.

[0047] The present invention also discloses a method for planning nail paths during Tripod navigation surgery. The method obtains a three-dimensional pelvic model of the patient and uses the aforementioned mathematical model of surgical nail paths to determine the optimal nail paths for the three nails. The nail path is the optimal nail path for the three nails. Before surgical navigation, a three-dimensional pelvic model of the patient is obtained, and a geometric coordinate system is constructed according to the aforementioned method. The equations of the mathematical model for the optimal nail paths for the three nails are substituted into the system to determine the optimal nail paths for the three nails. This optimal path is then used as the navigation path for intraoperative navigation.

[0048] The present invention also discloses a Tripod navigation surgical navigation system, which includes using the above-mentioned surgical nail track mathematical model to obtain the nail body entry paths corresponding to the optimal nail tracks of the three nails.

[0049] The present invention also provides an electronic device comprising a processor and a memory storing a computer program, wherein when the processor executes the computer program, the processor implements any of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail approach in Tripod navigation surgery.

[0050] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it implements any of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail approach in Tripod navigation surgery.

[0051] The present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute any of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail approach in Tripod navigation surgery.

[0052] Beneficial effects

[0053] Through finite element analysis and topological structure analysis, combined with biomechanical analysis and correction of a real three-dimensional pelvic model, the optimal nail path for the three nails that meets the needs of most patients is obtained. The optimal nail path for the three nails is combined with the patient's three-dimensional pelvic model to construct a geometric coordinate system, and a mathematical model of the optimal nail path for the three nails is obtained. In this way, during specific surgery, as long as the patient's three-dimensional pelvic model is used and the corresponding spatial coordinate system is constructed, the optimal nail path for the three nails can be quickly obtained through the mathematical model of the optimal nail path for the three nails using the software, and the direction of the nail path can be presented on the three-dimensional pelvic model. Subsequently, the optimal direction of the guide tube on the in vitro guide frame can be obtained by reverse fitting, and an in vitro guide frame with a guide tube with the optimal nail path direction for the three nails can be effectively constructed; or during surgical navigation, the nail path direction presented by the mathematical model is used as the planning path for surgical navigation, and the nail placement can be directly guided during surgery.

[0054] By constructing a geometric coordinate system of a three-dimensional pelvic model, and constructing equations for the reference geometric shape of the three-dimensional pelvic model and equations for the optimal nail paths of the three nails and the geometric constraints of the reference geometric shape of the three-dimensional pelvic model, the equations for the optimal nail paths of the three nails can be derived, which becomes a simple and effective method to obtain a mathematical model of the optimal nail paths of the three nails.

[0055] By constructing a circle or ellipse as the projection of the effective area of the three-dimensional pelvic model on the sagittal and coronal planes in the three-dimensional pelvic model, and through the geometric constraints of a stable tangent relationship or auxiliary tangent relationship between the projection of the optimal nail path of the three nails on the corresponding plane and the circle or ellipse, this geometric constraint is simple and effective to construct, and it is an effective path for quickly obtaining the mathematical model of the optimal nail path of the three nails, and the software does not require too complex computing power when calculating. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A schematic flow chart of a method for constructing an optimal nail channel mathematical model provided by the present invention;

[0057] Figure 2 The present invention shows a schematic structural diagram of various analysis methods combined to obtain the best nail channel;

[0058] Figure 3 Schematic diagram of the coronal plane in the coordinate system of the three-dimensional pelvic model of the present invention. Lines 1, 2, and 3 represent the optimal nail paths for the three nails, respectively. This plane contains circle A, ellipse B, and ellipse C corresponding to the reference geometric shape of the three-dimensional pelvic model.

[0059] Figure 4 Schematic diagram of the sagittal plane in the coordinate system of the three-dimensional pelvic model of the present invention. Lines 1, 2, and 3 represent the optimal nail paths for the three nails, respectively. This plane contains the circle D and ellipse E corresponding to the reference geometric shape of the three-dimensional pelvic model.

[0060] Figure 5 The three screw channels at different viewing angles in the patient's three-dimensional pelvic model obtained by the present invention using the three screw channel mathematical models (the red, blue, and green channels simulate the three screws that need to be inserted);

[0061] Figure 6 Schematic diagram comparing the three screw paths obtained from different perspectives in a patient's three-dimensional pelvic model using the three screw path mathematical models (left side) and the images of the screws placed into the patient's pelvis from different perspectives using the optimal screw path (right side);

[0062] Figure 7 A schematic diagram of a process for constructing an in vitro guide frame for Tripod surgery around the acetabulum provided by the present invention;

[0063] Figure 8 A schematic diagram showing the comparison of pain symptoms and recovery of mobility in two groups of patients before and after percutaneous minimally invasive internal fixation surgery using the optimal nail track obtained; DETAILED DESCRIPTION

[0064] Example 1

[0065] refer to Figure 1 A method for constructing a mathematical model of the nail path in Tripod surgery.

[0066] Step S110, constructing a three-dimensional pelvic model of different patients with different lesion locations using the patient's imaging images;

[0067] Step S120: Using the three-dimensional pelvic model, perform finite element analysis and topological structural analysis to determine the nail paths for the three nails. This initial round of nail paths for the three nails is then determined. Through these analyses, the three nail paths are determined to most significantly alleviate stress concentration in the tumor bone defect, minimize stress on the internal fixation device, and best disperse stress concentration caused by the bone defect. This combination of significant effects ensures the optimal nail paths will be most effective in specific applications. Finite element analysis and topological structural analysis are used to simulate changes in pelvic biomechanical properties under different pathological conditions using a computer, and to test and determine the optimal nail placement for the Tripod procedure.

[0068] S121, using the simulated real three-dimensional pelvic model, an in vitro biomechanical analysis is performed after the three nail paths of the first round are placed in the three-dimensional pelvic model, the nail paths of the first round of three nails are verified and corrected, and the nail paths of the second round of three nails are obtained. The nail paths of the second round of three nails can be determined as the optimal three-nail paths, and the optimal three-nail paths are constructed in the three-dimensional model. In step S121, the real three-dimensional pelvic model is a SawBone model, which is an artificial bone model simulated according to the characteristics of human bones and has the same characteristics as real bones. The main purpose is to use the SawBone biomechanical physical model to perform biomechanical testing on the results of the computer simulation to further improve and confirm the optimal nail placement position.

[0069] Step S122, three types of screws are inserted into the body of a clinical patient along the nail channels of the two rounds of three nails. Based on the clinical effects, the nail channels of the three inserted nails are further analyzed and corrected to obtain the best nail channels of the three nails, corresponding to the best nail channels of the three nails; the nail channels of the three nails after this step of analysis and correction are determined as the best nail channels of the three nails. Through three methods of analysis and revision, the best nail channels of the three nails that meet the needs of most patients are obtained, which can ensure the final treatment effect. The clinical effect analysis mainly analyzes indicators such as pain conditions and the ability to recover mobility. In specific implementation, the mathematical model can be constructed based on the best nail channels of the three nails obtained in step 121;

[0070] Analysis reference of step S120 to step S112 Figure 2 , specifically the analysis of the application of SawBone model ( Figure 6 A, E, F) and finite element analysis technology of three-dimensional pelvic model ( Figure 6 BD); The pelvic biomechanics of real patients before and after Tripod surgery were analyzed, and it can be seen that the stress concentration problem in the affected area before surgery was effectively alleviated ( Figure 6 GH; blue line is before surgery, orange line is after surgery), the actual patients' osteolytic bone destruction caused by tumors before surgery ( Figure 6 Middle I), and 3 months after surgery, significant osteoblastic repair was observed in the area, which was a manifestation of pathological fracture healing ( Figure 6 (J) Postoperative results were significantly better than those before and after surgery. The optimal screw tract was constructed by combining the three aforementioned methods. The analysis of a single patient's 3D pelvic model included biomechanical simulations of the patient's standing, sitting, and walking postures, as well as analysis of stress concentration relief in the tumor bone defect, stress on the internal fixation device, and stress concentration and dispersion.

[0071] Step S130: Construct a geometric coordinate system for the 3D pelvic model. A reference geometric shape that has stable geometric constraints on the optimal nail paths for the three nails is obtained within the 3D pelvic model. Equations for the reference geometric shape and the geometric constraints are constructed using the coordinate system. The equations for the reference geometric shape and the geometric constraints are used to obtain the equations for the optimal nail paths for the three nails. The equations for the optimal nail paths for the three nails constitute the mathematical models of the constructed optimal nail paths for the three nails. The geometric coordinate system comprises three planes: the sagittal, coronal, and transverse planes. The reference geometric shape for the 3D pelvic model is a circle or ellipse constructed by projecting multiple valid regions of the 3D pelvic model onto different planes. The geometric constraints are the tangent or auxiliary tangent relationships between the circle or ellipse and the projections of the three optimal nail paths onto different planes. Five points are marked on the constructed circle or ellipse, and the equations of the circle or ellipse are obtained using these five points. Projections on the sagittal and coronal planes analyze the relationship between the tangents or auxiliary tangents of the circle or ellipse and the three optimal nail paths. Equations for the tangents and auxiliary tangents of the circle or ellipse are constructed. By combining the projections on the two planes with the geometric constraints of the reference geometry of the 3D pelvic model, the equations for the optimal nail paths for the three nails can be determined. This method of obtaining a mathematical model can meet the requirements for optimal nail paths and reduce the complexity of the software algorithm.

[0072] A more preferred embodiment is to determine five valid circles or ellipses on the three-dimensional pelvic model in the sagittal and coronal planes, wherein circle A is a circle with the center of rotation of the femoral head as the center and the distance from the bone edge of the affected acetabulum to the center of rotation of the femoral head as the radius projected on the coronal plane, ellipse B is an ellipse formed by the lines connecting the iliac spine of the pelvis, the superior pubic ramus, the anterior edge of the sacral S1 vertebra, and the S1 sacral foramen, ellipse C is a circle projected on the coronal plane by the obturator foramen of the affected side of the pelvis, circle D is a circle projected on the sagittal plane by the acetabulum, and ellipse E is an ellipse projected on the sagittal plane by the circle formed by the lines connecting the ischial spine and the bone edge of the greater sciatic notch.

[0073] Specifically, according to circle A, ellipse B, and circle D, the first nail path straight line is obtained, including:

[0074] According to circle A and ellipse B, obtain the first common tangent of circle A and ellipse B;

[0075] Draw a tangent from the pubic junction (0, y0) to the circle represented by circle D to obtain an auxiliary tangent;

[0076] According to the first common tangent and auxiliary tangent of circle A and ellipse B, the first nail track equation is obtained.

[0077] Furthermore, according to circle A, ellipse B, circle D, and ellipse E, a second nail path straight line is obtained, including:

[0078] According to circle A and ellipse B, the second common tangent of circle A and ellipse B is obtained;

[0079] According to the circle D and the ellipse E, the first common tangent of the circle D and the ellipse E is obtained;

[0080] According to the second common tangent line between circle A and ellipse B and the first common tangent line between circle D and ellipse E, a second nail path is obtained.

[0081] Furthermore, according to ellipse B, ellipse C, circle D, and ellipse E, the third nail track equation is obtained, including:

[0082] Connect the rightmost point of ellipse B and the rightmost point of ellipse C to obtain an auxiliary line;

[0083] According to the fourth equation and the ellipse E, the second common tangent of the circle D and the ellipse E is obtained;

[0084] According to the auxiliary connecting line and the second common tangent of circle D and ellipse E, the third nail track straight line is obtained.

[0085] refer to Figure 3-4 ; More specifically, based on the patient's three-dimensional pelvic model, a spatial coordinate system of the patient's three-dimensional pelvic model is established. In the coronal view, the pubic symphysis is used as the origin, the longitudinal midline axis of the patient's body is used as the y-axis, the head end is the positive direction of the y-axis, and the left coronal plane of the patient is used as the positive direction of the x-axis to establish an xy coordinate system; in the sagittal view, the pubic symphysis level is used as the y-axis, the head end is the positive direction of the y-axis, the ischial tuberosity level is used as the z-axis, and the dorsal side is the positive direction of the z-axis to establish a yz coordinate system. In the axial view-upward view, the pubic symphysis level is used as the x-axis, the left coronal plane of the patient is used as the positive direction of the y-axis. The first xz coordinate system is established with the lateral side as the positive x-axis, the ischial tuberosity level as the z-axis, and the dorsal side as the positive z-axis. In the axial view - top view, the second xz coordinate system is established with the pubic symphysis level as the x-axis, the patient's left side as the positive x-axis, the ischial tuberosity level as the z-axis, and the dorsal side as the positive z-axis. The xy coordinate system, the yz coordinate system, the first xz coordinate system, and the second xz coordinate system form a spatial coordinate system. The equations of circle A, ellipse B, and ellipse C on the xoy plane, and the equations of circle D and ellipse E on the yoz plane are obtained. The xoy plane is the coronal plane, and the yoz plane is the sagittal plane.

[0086] According to the equation of circle A, the equation of ellipse B, and the equation of circle D, we get the equation of the first nail track;

[0087] According to the equations of circle A, ellipse B, circle D and ellipse E, we can get the equation of the second nail track.

[0088] According to the equation of ellipse B, the equation of ellipse C, the equation of circle D and the equation of ellipse E, we get the equation of the third nail track.

[0089] The specific process is as follows: 1. The process of obtaining the straight line equation 1 corresponding to the first nail track

[0090] On the xoy plane,

[0091] Equation of ellipse A: (x-x1) 2 +(y-y1) 2 -r 2 =0 (1) Ellipse B:

[0092] Tangent line between circle A and ellipse B: y = Kx + T (3)

[0093] (3) Substitute into (1)

[0094] (x-x1) 2 +(Kx+T-y1) 2 -r 2 =0

[0095]

[0096] Discriminant

[0097]

[0098] Get the equation

[0099]

[0100] (3) Substitute into (2)

[0101]

[0102] Discriminant

[0103]

[0104] Get the equation

[0105]

[0106] simultaneous equations

[0107]

[0108] The equations can be solved using MATLAB to obtain K + ,T + (Theoretically, there are four solutions, take the one with a positive slope and leaning towards the horizontal), so we have the tangent equation

[0109] y=K + x+T + (6)

[0110] In the yoz plane, the equation of circle D is (z-z1′)2 +(y-y1′) 2 -r ′2 =0.

[0111] Draw a tangent line from the pubic junction (0, y0) to circle D and find the equation of the tangent line

[0112] y=K′z+T′ (7)

[0113] Substituting (0, y0) into y = K′z + T′, we get T′ = y0, and the tangent equation is written as

[0114] y=K′z+y0(7*)

[0115] The tangent line through the pubic symphysis is set as

[0116] y=Kx(3*)

[0117] Applying the implicit function derivation rule, the derivative of (2) is Let the point of intersection of (2) and (3*) be (x 03 ,y 03 ), the slope of the tangent is The tangent line equation is

[0118] Tangent point (x 03 ,y 03 ) on the tangent line, we get Arranged

[0119] (x 03 ,y 03 ) is also on the ellipse (2), satisfying the equation The two equations can be solved together to obtain

[0120] So the tangent is

[0121]

[0122] Combining (3**) and (7*), we get the equation of the straight line Due to the problem of consistency in coordinate system selection, the correction should be Then equation (8*) is the spatial straight line equation 1 corresponding to the first nail path.

[0123] 2. The process of obtaining the equation 2 of the line corresponding to the second nail track (I) Common tangent of circle A and ellipse B

[0124] In the xoy plane, find the common tangent of circle A and ellipse B. Solve equations (4) and (5) to obtain K - ,T +(Theoretically, there are four solutions. Take the one with negative slope, positive intercept, and the one that is steeper.) Thus, we have the tangent equation

[0125] y=K - x+T + (9)

[0126] (2) Common tangent of circle D and ellipse E

[0127] In the yoz plane, the equation of circle D is

[0128] (z-z1′) 2 +(y-y1′) 2 -r′ 2 =0 (10)Assume that the standard equation of the ellipse E is

[0129]

[0130] Let the common tangent of circle D and ellipse E be

[0131] y=K de z+T de (12)(12)Substitute into (10)

[0132]

[0133] Discriminant Δ de1 =0 to get the equation

[0134]

[0135] (12) Substitute into (11) tidy

[0136]

[0137] Discriminant

[0138]

[0139] Get the equation

[0140]

[0141] simultaneous equations

[0142]

[0143] The system of equations can be solved using MATLAB to obtain (Theoretically, there are four solutions, take the solution with positive slope and positive intercept above circle D and ellipse E), so we have the tangent equation

[0144]

[0145] (3) Combine the equations to obtain the linear equation in space

[0146] Combining two planes (9) and (12*), we get a space straight line equation

[0147]

[0148] Then equation (15) is the spatial straight line equation 2 corresponding to the second nail track.

[0149] 3. The process of obtaining the equation 3 of the line corresponding to the third nail track (I) Common tangent of ellipse B and ellipse C

[0150] In the xoy plane, the equation of the ellipse B is

[0151] Ellipse B: Let the equation of the ellipse C be

[0152] oval The common tangent of ellipse B and ellipse C is set to

[0153] y=K bc x+T bc (17) Substitute (17) into (2), Arranged

[0154] Discriminant

[0155]

[0156] Get the equation

[0157]

[0158] Substituting (17) into (16), Arranged

[0159] Discriminant Get the equation

[0160] simultaneous equations

[0161]

[0162] Theoretically, there are four sets of solutions. Take the one with the largest absolute value of slope and the largest intercept.

[0163] (2) Common tangents of circle D, ellipse E, and ellipse F

[0164] In the yoz plane, line 3 is tangent to circle D, ellipse E, and ellipse F respectively.

[0165] Ellipse F is the image of ellipse C at another angle. The common tangent of ellipse B and ellipse C (17) ensures that it is a plane in space (17) and will not intersect with ellipse C or F. Therefore, only the common tangent of circle D and ellipse E are considered here.

[0166] As mentioned above, the equation of circle D in the yoz plane is (z-z1′) 2 +(y-y1′) 2 -r′ 2 =0(10)The standard equation of the ellipse E is The common tangent of circle D and ellipse E is y = K de z+T de (12) Substitute (12) into (10), and (12) into (11). The discriminant is zero, and we get the system of equations:

[0167] Theoretically, there are four groups of solutions. The group with the largest absolute value of slope, which is between circle D and ellipse E, is recorded as

[0168] (3) Combine the equations to obtain the linear equation in space

[0169] Combining the two planes (17) and (20), we get a space straight line equation

[0170]

[0171] Then equation (21) is the spatial straight line equation 3 corresponding to the third nail path.

[0172] refer to Figure 5 、 Figure 6 These are the results obtained after applying the optimal nail tract mathematical model to a specific patient.

[0173] See also Figure 5 The three nail paths at different viewing angles in the patient's three-dimensional pelvic model obtained using the three nail path mathematical models are shown.

[0174] Figure 6Figures A, B, and C show the three screw paths (Figures A, C, and E) obtained from different perspectives in a three-dimensional pelvic model of a patient using three mathematical models of screw paths. The optimal screw paths for each of the three screws are shown, along with images of the screws placed into the patient's pelvis from different perspectives (Figures B, D, and F). Figures A and B correspond, Figure C corresponds to Figure D, and Figure E corresponds to Figure F. The patient was a 78-year-old man who was admitted to the hospital with three months of left hip pain, which worsened and led to two weeks of inability to walk. He had a history of multiple metastatic hepatocellular carcinoma. The clinical diagnosis was right pelvic hepatocellular carcinoma bone metastasis. X-rays, CT scans, and MRI scans revealed osteolytic bone destruction around the acetabulum with a soft tissue mass.

[0175] Example 2

[0176] A mathematical model for tripod surgical nail paths is provided. The mathematical model uses the optimal nail paths of three nails combined with the patient's three-dimensional pelvic model to construct a coordinate system. The equations for the optimal nail paths of the three nails are obtained by combining the projection lines of the three optimal nail paths obtained on the sagittal and coronal planes with the stable tangent or auxiliary tangent relationship between the circle or ellipse of the projection of the effective area of the three-dimensional model on the sagittal and coronal planes. The optimal nail paths of the three nails are obtained by finite element analysis and topological structure analysis, combined with biomechanical analysis and correction of a real three-dimensional pelvic model, and analysis and correction of the actual clinical patient nail placement effects to obtain the optimal nail path that suits the patient. The mathematical model is constructed using the method of Example 1, specifically:

[0177] The first nail track equation is:

[0178]

[0179] The second channel equation is:

[0180]

[0181] The third nail track equation is:

[0182]

[0183] Example 3

[0184] refer to Figure 7 , a method for constructing an in vitro guide frame for tripod surgery around the acetabulum,

[0185] S210, reconstructing a three-dimensional pelvic model of the patient based on the medical imaging image of the patient's pelvic position;

[0186] S220, establishing a geometric coordinate system in the patient's three-dimensional pelvic model. The method for constructing the geometric coordinate system is the same as the method for constructing the mathematical model of the optimal nail path in step 1. Then, using the mathematical model of the optimal nail paths for the three nails, three nail paths suitable for the patient are presented in the three-dimensional pelvic model. The presented optimal nail path is the personalized optimal nail path that meets the patient's own pelvic characteristics.

[0187] S230, performing reverse fitting based on the three screw track directions presented in the three-dimensional pelvic model to obtain three-dimensional models of three guide tubes of the external fixation guide frame used in Tripod surgery around the acetabulum;

[0188] S240, obtain a three-dimensional surface image of the outside of the patient's pelvis and construct a three-dimensional model of the surface skin. Use the three-dimensional model of the patient's pelvic surface skin and the position of the arc guide plate involved in the extracorporeal fixed guide frame to fit the extracorporeal arc guide plate model, and combine the guide tube model and the arc guide plate model to construct an extracorporeal guide frame model.

[0189] S250 uses an in vitro guide frame model to 3D print an in vitro guide frame. When the in vitro guide frame obtained in this way is used in surgery, the screw will be quickly inserted into the optimal nail channel position through the guide tube.

[0190] More specifically, a system suitable for treating patients in remote areas includes using a first platform to obtain image data for constructing a three-dimensional pelvic model of the patient; transmitting the image data to a second hospital, and the second platform constructing an extracorporeal guide frame using the above-mentioned extracorporeal guide frame construction method; and mailing the extracorporeal guide frame to the first platform.

[0191] The method of obtaining an in vitro guide frame in this way can be applied to the treatment of patients in remote areas. Local doctors only need to use local CT technology to obtain the image data for constructing a three-dimensional pelvic model, and remotely transmit the image data to a hospital in a central city with technical strength to form a cooperation. The central city hospital uses the above method to construct an in vitro guide frame model, prints the guide frame, and mails it to a hospital in a remote area again. Because it is used in vitro, the doctor only needs to simply disinfect it when using it, and then place the guide frame on the outer surface of the pelvis. Because the guide plate is also matched to the patient, the setting is very simple. After setting it up, the screws can be directly set under the guidance of the guide tube. It is very simple. Therefore, the guide frame is constructed by a hospital or company with technology in this way; it can reduce the difficulty of operation for hospitals with poor technical strength.

[0192] See also Figure 8A retrospective analysis was conducted on patients who underwent Tripod surgery using the in vitro guide frame printed according to the above method. The patients were divided into two groups, and the pain level and the level of recovery of mobility in each group were analyzed separately. The patients' pain was greatly relieved the day after surgery. The upper left is the result of the first group, and the lower left is the result of the second group. It can be seen that the pain scores of both groups were significantly reduced; the quality of life was significantly improved after surgery, and the recovery of mobility scores were significantly improved. Figure 8 The upper right middle image shows the results of the first group, and the lower right image shows the results of the second group. Both groups showed that pain was significantly reduced, and the quality of life and ability to resume mobility were greatly improved. The pain scores and the ability to resume mobility were scored according to the commonly used clinical scoring methods.

[0193] Example 4

[0194] The method for planning nail body approaches in tripod navigation surgery obtains a three-dimensional pelvic model of the patient based on medical imaging reconstruction of the patient's pelvic position; a geometric coordinate system is established in the patient's three-dimensional pelvic model, and the method of constructing the geometric coordinate system is the same as the geometric coordinate system for constructing the optimal nail track mathematical model in Example 1. Through the mathematical expression of the optimal nail tracks of the three nails, three nail tracks suitable for the patient are presented in the three-dimensional pelvic model, and the nail body approach path is the optimal nail track path of the three nails on the three-dimensional pelvic model.

[0195] The above clearly and completely describes the technical solutions in the embodiments of the present invention through specific specific embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation methods. In the absence of conflict, the above embodiments and features in the embodiments can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

Claims

1. A method for constructing a mathematical model of the nail path in Tripod surgery. S110, constructing a three-dimensional pelvic model of different patients with different lesion locations using the patient's imaging images; S120, performing a biomechanical analysis using a three-dimensional pelvic model, and determining the nail track directions corresponding to the three nail tracks with the smallest stress and strain conditions of the pelvic model as three optimal nail track directions; S130, constructing a geometric coordinate system of the three-dimensional pelvic model, obtaining a reference geometric shape in the three-dimensional pelvic model that has stable geometric constraints on the optimal nail path of the three nails, and constructing a mathematical expression for the optimal nail path of the three nails using the stable geometric constraints and the reference geometric shape.

2. The construction method according to claim 1, characterized in that Using step S110, the nail path of the first round of 3 nails is obtained; Adding step S111: using the simulated real three-dimensional pelvic model, analyzing the in vitro biomechanical analysis after the three nail paths of the first round are placed in the three-dimensional pelvic model, verifying and correcting the three nail paths of the first round, obtaining the three nail paths of the second round, determining the three nail paths of the second round as the optimal three nail paths, and constructing the optimal three nail paths in the three-dimensional model; Preferably, in step S110, finite element analysis and topological structure analysis are used to analyze and obtain the three nail tracks that most significantly alleviate the stress concentration problem in the tumor bone defect, minimize the force on the internal fixation device, and best disperse the stress concentration problem caused by the bone defect; Preferably, in step S111, the real three-dimensional pelvic model is a SawBone model, which is an artificial bone model simulated according to the characteristics of human bones and has the same characteristics as real bones.

3. The construction method according to claim 2, characterized in that An equation referencing the geometric shape and the geometric constraints is constructed through a coordinate system. The equation for the optimal nail path of the three nails is obtained using the equation for the reference geometric shape and the equation for the geometric constraints. The equation for the optimal nail path of the three nails is the constructed mathematical model of the optimal nail path of the three nails. Preferably, the geometric coordinate system includes three planes, namely the sagittal plane, the coronal plane, and the horizontal plane. The reference geometric shape of the three-dimensional pelvic model is a circle or an ellipse constructed by projecting multiple valid areas of the three-dimensional pelvic model on different planes. The geometric constraint condition is the relationship between the tangent or auxiliary tangent of the circle or ellipse and the projections of the three optimal nail paths on different planes. Preferably, the relationship between the tangent line or the auxiliary tangent line of the circle or ellipse and the three optimal nail paths is analyzed by projection on the sagittal and coronal planes, and equations of the tangent line and the auxiliary tangent line of the circle or ellipse are constructed. The equations of the optimal nail paths for the three effective nails can be determined by the projection on the two planes and the geometric constraints of the reference geometry of the three-dimensional pelvic model. Preferably, circles or ellipses of five valid areas on the three-dimensional pelvic model are determined on the sagittal and coronal planes, wherein circle A is a circle with the center of rotation of the femoral head as the center and the distance from the bone edge of the affected acetabulum to the center of rotation of the femoral head as the radius projected on the coronal plane, ellipse B is an ellipse formed by the lines connecting the iliac spine of the pelvis, the superior pubic ramus, the anterior edge of the S1 vertebra of the sacrum, and the S1 sacral foramen, ellipse C is a circle projected on the coronal plane by the obturator foramen of the affected side of the pelvis, circle D is a circle projected on the sagittal plane by the acetabulum, and ellipse E is an ellipse projected on the sagittal plane by the circle formed by the lines connecting the bone edges of the ischial spine and the greater sciatic notch.

4. The construction method according to claim 3, characterized in that According to circle A, ellipse B, and circle D, the first nail path straight line is obtained, including: According to circle A and ellipse B, obtain the first common tangent of circle A and ellipse B; Draw a tangent from the pubic junction (0, y0) to the circle represented by circle D to obtain an auxiliary tangent; According to the first common tangent and auxiliary tangent of circle A and ellipse B, the first nail track equation is obtained; Preferably, the second nail path straight line is obtained according to the circle A, the ellipse B, the circle D, and the ellipse E, including: According to circle A and ellipse B, the second common tangent of circle A and ellipse B is obtained; According to the circle D and the ellipse E, the first common tangent of the circle D and the ellipse E is obtained; According to the second common tangent line between circle A and ellipse B and the first common tangent line between circle D and ellipse E, the second nail path is obtained; Preferably, the third nail track equation is obtained according to ellipse B, ellipse C, circle D, and ellipse E, including: Connect the rightmost point of ellipse B and the rightmost point of ellipse C to obtain an auxiliary line; According to the fourth equation and the ellipse E, the second common tangent of the circle D and the ellipse E is obtained; According to the auxiliary connecting line and the second common tangent of circle D and ellipse E, the third nail track straight line is obtained.

5. The construction method according to claim 3, characterized in that Based on the patient's three-dimensional pelvic model, the spatial coordinate system of the patient's three-dimensional pelvic model was established. In the coronal view, the pubic symphysis was used as the origin, the longitudinal midline of the patient's body was used as the y-axis, the head end was used as the positive direction of the y-axis, and the left coronal plane of the patient was used as the positive direction of the x-axis to establish the xy coordinate system; in the sagittal view, the pubic symphysis level was used as the y-axis, the head end was used as the positive direction of the y-axis, the ischial tuberosity level was used as the z-axis, and the dorsal side was used as the positive direction of the z-axis to establish the yz coordinate system. In the axial view-supine view, the pubic symphysis level was used as the x-axis, the left side of the patient was used as the x-axis. In the positive direction of the axis, the z-axis is taken as the level of the ischial tuberosity and the positive direction of the z-axis is taken as the dorsal side to establish the first xz coordinate system; in the axial view-top view, the x-axis is taken as the level of the pubic symphysis and the positive direction of the x-axis is taken as the left side of the patient, the z-axis is taken as the level of the ischial tuberosity and the positive direction of the z-axis is taken as the dorsal side to establish the second xz coordinate system. The xy coordinate system, the yz coordinate system, the first xz coordinate system and the second xz coordinate system form a spatial coordinate system; the equations of circle A, ellipse B and ellipse C on the xoy plane and the equations of circle D and ellipse E on the yoz plane are obtained; According to the equation of circle A, the equation of ellipse B, and the equation of circle D, we get the equation of the first nail track; According to the equations of circle A, ellipse B, circle D and ellipse E, we can get the equation of the second nail track. According to the equations of ellipse B, ellipse C, circle D and ellipse E, we get the equation of the third nail track; Preferably, the equation of circle A is: (x-x1) 2 +(y-y1) 2 -r 2 =0; The equation of ellipse B is: The equation of ellipse C is: The equation of circle D is: (z-z1′) 2 +(y-y1′) 2 -r′ 2 =0; The equation of the ellipse E is: Preferably, obtaining the first nail track equation according to the equation of circle A, the equation of ellipse B, and the equation of circle D includes: According to the equation of circle A and the equation of ellipse B, the equation of the first common tangent of the equation of circle A and the equation of ellipse B is obtained; Draw a tangent line from the pubic junction (0, y0) to the circle represented by the equation of circle D to obtain the auxiliary tangent line equation; According to the first common tangent and auxiliary tangent of the circle A equation and the ellipse B equation, the first nail track equation is obtained. Preferably, the first common tangent line of the equation of circle A and the equation of ellipse B is: y=K′z+T′; The auxiliary tangents are: The first nail track equation is: Preferably, obtaining the second nail track equation according to the equation of circle A, the equation of ellipse B, the equation of circle D, and the equation of ellipse E includes: According to the equation of circle A and the equation of ellipse B, the second common tangent of the equation of circle A and the equation of ellipse B is obtained; According to the equation of circle D and the equation of ellipse E, the first common tangent line of the equation of circle D and the equation of ellipse E is obtained; According to the second common tangent line between the equation of circle A and the equation of ellipse B and the first common tangent line between the equation of circle D and the equation of ellipse E, we can get the equation of the second nail track. Preferably, the second common tangent of the equation of circle A and the equation of ellipse B is: y=K - x+T + ; The first common tangent of the equation of circle D and the equation of ellipse E is: The second nail track equation is: Preferably, obtaining the third nail track equation according to the equation of ellipse B, the equation of ellipse C, the equation of circle D, and the equation of ellipse E includes: Connect the rightmost point of the circle represented by the equation of ellipse B with the rightmost point of the circle represented by the equation of ellipse C to obtain an auxiliary connecting line; According to the equation of circle D and the equation of ellipse E, the second common tangent of the equation of circle D and the equation of ellipse E is obtained; According to the auxiliary connecting line and the second common tangent of the equation of circle D and the equation of ellipse E, the equation of the third nail track is obtained. Preferably, the auxiliary connection line is: y=K bc x+T bc ; The second common tangent of the equation of circle D and the equation of ellipse E is: The third nail track equation is:

6. A method for constructing an optimal nail path using a mathematical model, comprising: first obtaining a CT image of a patient, constructing a three-dimensional pelvic model of the patient using the CT image, constructing a geometric coordinate system of the three-dimensional pelvic model, and constructing three optimal nail path directions in the three-dimensional pelvic model using the optimal nail path mathematical model of three nails constructed by any one of claims 2-5.

7. A mathematical model of the nail path for Tripod surgery, characterized in that: The mathematical model is constructed by the method according to claims 2-5.

8. A method for constructing an in vitro guide frame guide tube model, which obtains a patient's three-dimensional pelvic model, constructs a coordinate system, uses the surgical nail track mathematical model constructed according to any one of claims 1-5 to obtain the optimal nail tracks for three nails, and reversely fits to obtain three guide tube models of the in vitro guide frame.

9. A method for constructing an in vitro guide frame model, characterized in that: A three-dimensional pelvic model of the patient is obtained, a coordinate system is constructed, and the optimal nail paths of the three nails are obtained using the mathematical model of the surgical nail path constructed according to any one of claims 1 to 5. Three guide tube models of the in vitro guide frame are obtained by reverse fitting. Then, an in vitro arc guide plate model is obtained by fitting using the three-dimensional model of the patient's skin surface. The guide tube model and the arc guide plate model are combined to construct a complete in vitro guide frame model.

10. A method for constructing an in vitro guide frame, characterized in that: A three-dimensional pelvic model of the patient is obtained, and the optimal nail paths of the three nails are obtained using the mathematical model of the surgical nail path constructed according to any one of claims 1 to 5. Three guide tube models of the in vitro guide frame are obtained by reverse fitting. An in vitro arc guide plate model is then obtained by fitting the three-dimensional model of the patient's skin surface. The guide tube model and the arc guide plate model are combined to construct a complete in vitro guide frame model. The constructed in vitro guide frame model is 3D printed into an in vitro guide frame.

11. An in vitro guide frame, characterized in that: An in vitro guide frame obtained by the in vitro guide frame construction method according to claim 10.

12. A method for planning nail path in Tripod navigation surgery, characterized in that: A three-dimensional pelvic model of the patient is obtained, and the optimal nail tracks of the three nails are obtained using the surgical nail track mathematical model constructed according to any one of claims 1 to 5, and the nail body entry path is the optimal nail track path of the three nails.

13. A Tripod navigation surgical navigation system, comprising a surgical nail track mathematical model constructed using any one of claims 1-5 to obtain nail body access paths corresponding to optimal nail tracks for three nails.

14. An electronic device comprising a processor and a memory storing a computer program, wherein when the processor executes the computer program, it implements any one of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail path in Tripod navigation surgery.

15. A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail path in Tripod navigation surgery.

16. A computer program product, comprising a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute any of the above-mentioned methods for constructing an in vitro guide frame model for Tripod surgery or a method for planning a nail approach in Tripod navigation surgery.

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