CN105205867A - A Collision Detection Method in Minimally Invasive Virtual Abdominal Aortic Vascular Surgery - Google Patents

Abstract

The invention relates to the technical field of simulation control and graphic processing, in particular to a collision detection method in a virtual minimally invasive abdominal aorta vascular surgery, which comprises the following steps: 1. three-dimensional modeling of an abdominal aorta blood vessel, 2, model construction of abdominal aorta blood vessel deformation, 3, coarse collision detection and 4, accurate collision detection. The invention solves the problems of complex intersection test and low efficiency in the classic bounding box method by utilizing the rapid collision detection of the outer AABB bounding box, and improves the real-time property of the system. The characteristics of the tightness of the inner K-DOPs bounding box are utilized to carry out accurate collision detection, so that the high accuracy of a detection result is ensured.

Description

A Collision Detection Method in Minimally Invasive Virtual Abdominal Aortic Vascular Surgery

technical field

The invention relates to a collision detection method in minimally invasive virtual abdominal aortic vascular surgery, and belongs to the technical field of simulation control and graphics processing.

Background technique

The minimally invasive surgery simulation system based on virtual reality technology, that is, the minimally invasive virtual surgery simulation system, is a technology that replaces traditional medical training methods. It is conducive to improving surgical skills and reducing surgical errors, and has great development prospects. A basic minimally invasive virtual vascular surgery simulation system can be composed of functional modules such as vascular model, collision detection, vision and force feedback, among which collision detection runs through the whole process of vascular surgery simulation, and realizes the immersion and Interactivity and other aspects play an important role.

The basic task of collision detection in minimally invasive virtual vascular surgery system is to determine whether there is contact or penetration between surgical instruments and blood vessels. An efficient collision detection algorithm is beneficial to ensure that blood vessels and surgical equipment collide to produce real and real-time deformation results, and improve the immersion of the virtual surgery system. Therefore, improving the speed and accuracy of the collision detection process is the premise to ensure the authenticity and real-time performance of the surgical simulation system. Soft tissue collision detection methods commonly used in virtual surgery simulation systems include space method, image space based collision detection method and collision bounding box method. The space method is mainly suitable for uniformly distributed objects in a sparse environment, while the collision detection method based on the image space is difficult to guarantee the accuracy of the detection due to the discreteness of the image hardware itself. The hierarchical bounding box method can quickly remove the geometric elements that are unlikely to be in contact, find out the geometric sets that may collide, and reduce the calculation amount of the intersection test, so it is suitable for the intersection test of soft tissues. However, due to the characteristics of plasticity, viscoelasticity, anisotropy, inhomogeneity, and nonlinearity of the blood vessel itself, its deformation model is very complicated, and the calculation amount of the collision detection process is very large. The classic hierarchical bounding box method has disadvantages such as difficult construction, poor compactness, complex intersection test, and low efficiency, and it is difficult to meet the real-time and accuracy requirements of virtual surgery at the same time.

Contents of the invention

In order to overcome the deficiencies in the prior art, the object of the present invention is to provide a collision detection method in minimally invasive virtual abdominal aortic vascular surgery. In order to improve the accuracy and real-time performance of the minimally invasive virtual vascular surgery system, the present invention aims at the characteristics of abdominal aortic vessels, and proposes a method based on AlignedAxisBoundingBox (AABB) and discrete oriented polyhedrons (DiscreteOrientationPolytope, K-DOPs). ) bounding box hybrid double-layer bounding box collision detection method, using a top-down method for bounding box construction of abdominal aortic vessels and scalpels. This method uses the fast collision detection of the outer AABB bounding box to solve the problem of complex intersection test and low efficiency existing in the classic bounding box method, and improves the real-time performance of the system. Using the tightness of the inner K-DOPs bounding box to perform accurate collision detection ensures high accuracy of detection results.

In order to achieve the above-mentioned purpose of the invention and solve the problems existing in the prior art, the technical solution adopted by the present invention is: a collision detection method in a virtual minimally invasive abdominal aortic vascular surgery, comprising the following steps:

Step 1, three-dimensional modeling of the abdominal aorta blood vessel: the collision detection of the present invention is based on the geometric model of the abdominal aorta blood vessel, and at first the CT of the abdominal aorta blood vessel is performed using medical image software in the model preparation stage before the collision detection Perform 3D reconstruction of the data to obtain a 3D geometric model, and then perform overlay repair, smoothing, and mesh optimization operations on the reconstructed 3D geometric model to obtain a more accurate 3D geometric model, specifically including the following sub-steps:

(a), window width and level adjustment and pseudo-color enhancement are performed on the CT image of the abdominal aorta to increase the contrast of the abdominal aortic tissue;

(b), using a hybrid segmentation method combining threshold segmentation and region growth to segment most of the abdominal aorta vascular tissue;

(c), cavity filling is performed on the mask of the segmented abdominal aorta vascular tissue to reduce noise introduced by region growth;

(d), continue to edit the mask of the abdominal aorta vascular tissue to reduce boundary loss and obtain complete abdominal aortic vascular tissue information;

(e), carrying out three-dimensional reconstruction of the complete abdominal aorta vascular tissue after segmentation;

(f), using coverage and smoothing operations to reduce the burrs on the surface of the abdominal aorta vessel model, and optimize the reconstruction of the abdominal aorta vessel model;

Step 2. Model construction of abdominal aortic vessel deformation: use finite element analysis software to construct a viscoelastic finite element model of abdominal aortic vessel based on tetrahedral mesh, and simulate vessel cutting by assigning material properties, applying load and force However, the deformation characteristics when not cut, specifically include the following sub-steps:

(a), import the abdominal aortic vessel geometric model reconstructed by the medical image software into the finite element analysis software;

(b) Set the parameters of the geometric model of the abdominal aorta, select the unit type of the finite element model of the abdominal aorta, and combine the tissue characteristics of the abdominal aorta to construct the physical deformation model of the abdominal aorta; the tissue of the abdominal aorta The main components are elastic fibers and collagen fibers, in which the elastic fibers are a network structure, and the collagen fibers are a folded corrugated structure; when the stress is small, only the elastic fibers work, and the elastic modulus of the abdominal aorta at this time is The elastic modulus of elastic fibers; as the stress increases, the folded part of the collagen fibers is gradually stretched. At this time, it is not only the elastic fibers but also the collagen fibers that determine the deformation of the abdominal aortic blood vessels. Therefore, the elasticity of the abdominal aortic blood vessels The modulus includes the elastic modulus of elastic fibers and collagen fibers. According to this characteristic, the following mechanical property formula (1) of blood vessels is obtained:

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: σ is the stress, ε is the strain, E ₁ is the elastic modulus of elastic fibers, E ₂ is the elastic modulus of collagen fibers, λ is the critical point of deformation; combined with a large number of tensile and compression experimental data, the vascular elastic fibers and the elastic modulus values of collagen fibers are respectively E ₁ =2.208×10 ⁵ N/m ² and E ₂ =8.112×10 ⁵ N/m ² , and the deformation critical point value is λ=0.130, so that

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0.221</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.130</span>}\\ \mathrm{<span\; class="notranslate">\; 1.032</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.105</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0.130</span>}\end{array}\right.<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

(c), carry out tetrahedron grid division, adopt the free grid division mode to carry out tetrahedron grid division to abdominal aorta vascular geometric model;

(d), establish a finite element model, add a degree of freedom constraint to the finite element model and apply a load, solve the analysis, and display the deformation result of the abdominal aorta blood vessel with the applied external force;

Step 3. Rough collision detection: Rough collision detection is mainly to establish AABB bounding boxes for blood vessels and scalpels and perform fast collision detection, quickly remove the set of elements that cannot collide, and determine possible collisions, specifically including the following sub-steps:

(a), import abdominal aorta vessel model and scalpel model and determine all root nodes and leaf nodes;

(b) Calculate the maximum value (X _max , Y _max , Z _max ) and minimum value (X _min , Y _min , Z _min ) of all root nodes of the abdominal aorta on the three coordinate axes, and determine the abdominal aorta For the AABB bounding box of blood vessels, calculate the maximum value (x _max , y _max , z _max ) and minimum value (x _min , y _min , z _min ) of all the root nodes of the scalpel on the three coordinate axes in the same way, and construct the operation The AABB bounding box of the knife;

(c) Determine the collision situation through the AABB bounding box. The intersection test method of the bounding box is to compare the overlapping of the projections of the two AABB bounding boxes on the three coordinate axes. When the projections on the three coordinate axes overlap The bounding boxes intersect, and the projection area is obtained by the maximum and minimum values on each coordinate axis, and no more than 6 comparison operations are required; suppose the space occupied by the abdominal aortic vessel V and the scalpel S is F _V and F _S respectively, and its AABB The space occupied by the bounding box is C _V and C _S , and If V and S collide, the set of geometric primitives that collide is the intersection of abdominal aorta blood vessels and scalpel geometric elements, that is, E=F _V ∩ F _S and Then the AABB bounding box corresponding to both should be

Step 4. Accurate collision detection: In the rough collision detection stage, use the AABB bounding box to remove the collection that cannot collide and obtain a collidable object object set, quickly narrowing the range that needs to be detected, thereby improving the speed of collision detection; precise collision The detection is mainly to establish a K-Dops bounding box for the collection of objects that may collide in the blood vessel and the scalpel, and then sequentially perform an overlapping test on the projections of the two K-DOPs bounding boxes on the K/2 direction axis of their fixed direction set, In this way, it is judged whether the two intersect each other, and if so, the collision point is determined, which specifically includes the following sub-steps:

(a), the selected direction set is 26-DOPs, 6-DOPs are determined by the positive and negative directions of the three coordinate axes, and (1,1,1), (1,-1,1) are added on the basis of 6-DOPs ), (1,1,-1) and (1,-1,-1) The positive and negative directions of the four vectors determine the 14-DOPs, and then add (1,1,0), (1 ,0,1), (0,1,1), (1,-1,0), (1,0,-1) and (0,1,-1) the positive and negative directions of six vectors determine DOPs;

(b), obtain the K-DOPs bounding box by calculating the maximum and minimum inner product of the leaf node vector and each direction vector, set the set of leaf node vector and direction vector as P and D respectively, is the ith leaf node vector, is the jth direction vector, T _j is the set of the inner product of each vector in P and d _j , where the inner product value of p _i and d _j is t _ij =<p _i ,d _j >, and then the minimum value in T _j is set The leaf node corresponding to the value t _jmin is p _jmin , the leaf node corresponding to the maximum value t _jmax is p _jmax , then the plane d jmin passing through the leaf node p _jmin and the direction is d _j is the same as the plane d _jmin passing through the leaf node p _jmax and the direction The plane d _jmax of d _j constitutes the plane pair of the K-DOPs bounding box in the direction of d _j , and the other plane pairs of the K-DOPs bounding box can be obtained through similar calculations;

(c), judging whether the projections of the two K-DOPs bounding boxes on the 13 direction axes all overlap, if the projections of the two bounding boxes on a certain direction axis do not overlap, it means that the two bounding boxes do not collide; Conversely, the overlapping geometric element sets can be obtained, and then the collision occurrence point can be determined according to the overlapping geometric element sets, and the deformed part of the abdominal aorta after being cut by the scalpel can be found.

The beneficial effect of the present invention is: a collision detection method in virtual minimally invasive abdominal aortic vessel surgery, comprising the following steps: 1. Three-dimensional modeling of abdominal aortic vessel, 2. Model construction of abdominal aortic vessel deformation, 3. Rough collision detection, 4. Accurate collision detection. Compared with the prior art, the present invention solves the problem of complicated intersection test and low efficiency in the classic bounding box method by using the fast collision detection of the outer AABB bounding box, and improves the real-time performance of the system. The precise collision detection is performed by using the tightness of the inner K-DOPs bounding box, which ensures the high accuracy of the detection results.

Description of drawings

Fig. 1 is a flowchart of the method steps of the present invention.

Fig. 2 is a three-dimensional geometric model diagram of the abdominal aorta reconstructed in the present invention.

Fig. 3 is a schematic diagram of the deformed part after the blood vessel collides with the scalpel in the present invention.

Fig. 4 is a comparison result diagram of collision detection time in the present invention.

Fig. 5 is a result diagram of the variation of the collision detection time with the number of node triangles in the present invention.

Fig. 6 is a histogram of the correct rate of three collision detection algorithms in the present invention.

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing.

As shown in Figure 1, a collision detection method in virtual minimally invasive abdominal aortic vascular surgery includes the following steps:

Step 1, three-dimensional modeling of the abdominal aorta blood vessel: the collision detection of the present invention is based on the geometric model of the abdominal aorta blood vessel, and at first the CT of the abdominal aorta blood vessel is performed using medical image software in the model preparation stage before the collision detection Perform 3D reconstruction of the data to obtain a 3D geometric model, and then perform overlay repair, smoothing, and mesh optimization operations on the reconstructed 3D geometric model to obtain a more accurate 3D geometric model, specifically including the following sub-steps:

(a), window width and level adjustment and pseudo-color enhancement are performed on the CT image of the abdominal aorta to increase the contrast of the abdominal aortic tissue;

(b), using a hybrid segmentation method combining threshold segmentation and region growth to segment most of the abdominal aorta vascular tissue;

(c), cavity filling is performed on the mask of the segmented abdominal aorta vascular tissue to reduce noise introduced by region growth;

(d), continue to edit the mask of the abdominal aorta vascular tissue to reduce boundary loss and obtain complete abdominal aortic vascular tissue information;

(e), carrying out three-dimensional reconstruction of the complete abdominal aorta vascular tissue after segmentation;

(f) Using covering and smoothing operations to reduce burrs on the surface of the abdominal aorta vessel model, and optimize and reconstruct the abdominal aorta vessel model, as shown in FIG. 2 .

Step 2. Model construction of abdominal aortic vessel deformation: use finite element analysis software to construct a viscoelastic finite element model of abdominal aortic vessel based on tetrahedral mesh, and simulate vessel cutting by assigning material properties, applying load and force However, the deformation characteristics when not cut, specifically include the following sub-steps:

(a), import the abdominal aortic vessel geometric model reconstructed by the medical image software into the finite element analysis software;

(b) Set the parameters of the geometric model of the abdominal aorta, select the unit type of the finite element model of the abdominal aorta, and combine the tissue characteristics of the abdominal aorta to construct the physical deformation model of the abdominal aorta; the tissue of the abdominal aorta The main components are elastic fibers and collagen fibers, in which the elastic fibers are a network structure, and the collagen fibers are a folded corrugated structure; when the stress is small, only the elastic fibers work, and the elastic modulus of the abdominal aorta at this time is The elastic modulus of elastic fibers; as the stress increases, the folded part of the collagen fibers is gradually stretched. At this time, it is not only the elastic fibers but also the collagen fibers that determine the deformation of the abdominal aortic blood vessels. Therefore, the elasticity of the abdominal aortic blood vessels The modulus includes the elastic modulus of elastic fibers and collagen fibers. According to this characteristic, the following mechanical property formula (1) of blood vessels is obtained:

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: σ is the stress, ε is the strain, E ₁ is the elastic modulus of elastic fibers, E ₂ is the elastic modulus of collagen fibers, λ is the critical point of deformation; combined with a large number of tensile and compression experimental data, the vascular elastic fibers and the elastic modulus values of collagen fibers are respectively E ₁ =2.208×10 ⁵ N/m ² and E ₂ =8.112×10 ⁵ N/m ² , and the deformation critical point value is λ=0.130, so that

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0.221</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.130</span>}\\ \mathrm{<span\; class="notranslate">\; 1.032</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.105</span>}& \mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0.130</span>}\end{array}\right.<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

(c), carry out tetrahedron grid division, adopt the free grid division mode to carry out tetrahedron grid division to abdominal aorta vascular geometric model;

(d), establish a finite element model, add a degree of freedom constraint to the finite element model and apply a load, solve the analysis, and display the deformation result of the abdominal aorta blood vessel with the applied external force;

Step 3. Rough collision detection: Rough collision detection is mainly to establish AABB bounding boxes for blood vessels and scalpels and perform fast collision detection, quickly remove the set of elements that cannot collide, and determine possible collisions, specifically including the following sub-steps:

(a), import abdominal aorta vessel model and scalpel model and determine all root nodes and leaf nodes;

(b) Calculate the maximum value (X _max , Y _max , Z _max ) and minimum value (X _min , Y _min , Z _min ) of all the root nodes of the abdominal aorta on the three coordinate axes, and determine the abdominal aorta For the AABB bounding box of blood vessels, calculate the maximum value (x _max , y _max , z _max ) and minimum value (x _min , y _min , z _min ) of all the root nodes of the scalpel on the three coordinate axes in the same way, and construct the operation The AABB bounding box of the knife;

(c) Determine the collision situation through the AABB bounding box. The intersection test method of the bounding box is to compare the overlapping of the projections of the two AABB bounding boxes on the three coordinate axes. When the projections on the three coordinate axes overlap The bounding boxes intersect, and the projection area is obtained by the maximum and minimum values on each coordinate axis, and no more than 6 comparison operations are required; suppose the space occupied by the abdominal aortic vessel V and the scalpel S is F _V and F _S respectively, and its AABB The space occupied by the bounding box is C _V and C _S , and If V and S collide, the set of geometric primitives that collide is the intersection of abdominal aorta blood vessels and scalpel geometric elements, that is, E=F _V ∩ F _S and Then the AABB bounding box corresponding to both should be

Step 4. Accurate collision detection: In the rough collision detection stage, use the AABB bounding box to remove the collection that cannot collide and obtain a collidable object object set, quickly narrowing the range that needs to be detected, thereby improving the speed of collision detection; precise collision The detection is mainly to establish a K-Dops bounding box for the collection of objects that may collide in the blood vessel and the scalpel, and then sequentially perform an overlapping test on the projections of the two K-DOPs bounding boxes on the K/2 direction axis of their fixed direction set, In this way, it is judged whether the two intersect each other, and if so, the collision point is determined, which specifically includes the following sub-steps:

(a), the selected direction set is 26-DOPs, 6-DOPs are determined by the positive and negative directions of the three coordinate axes, and (1,1,1), (1,-1,1) are added on the basis of 6-DOPs ), (1,1,-1) and (1,-1,-1) The positive and negative directions of the four vectors determine the 14-DOPs, and then add (1,1,0), (1 ,0,1), (0,1,1), (1,-1,0), (1,0,-1) and (0,1,-1) the positive and negative directions of six vectors determine DOPs;

(b), obtain the K-DOPs bounding box by calculating the maximum and minimum inner product of the leaf node vector and each direction vector, set the set of leaf node vector and direction vector as P and D respectively, is the ith leaf node vector, is the jth direction vector, T _j is the set of the inner product of each vector in P and d _j , where the inner product value of p _i and d _j is t _ij =<p _i ,d _j >, and then the minimum value in T _j is set The leaf node corresponding to the value t _jmin is p _jmin , and the leaf node corresponding to the maximum value t _jmax is p _jmax , then the plane d jmin passing through the leaf node p _jmin and the direction of d _j is the same as the plane d _jmin passing through the leaf node p _jmax and the direction The plane d _jmax of d _j constitutes the plane pair of the K-DOPs bounding box in the direction of d _j , and the other plane pairs of the K-DOPs bounding box can be obtained through similar calculations;

(c), judging whether the projections of the two K-DOPs bounding boxes on the 13 direction axes all overlap, if the projections of the two bounding boxes on a certain direction axis do not overlap, it means that the two bounding boxes do not collide; On the contrary, the set of overlapping geometric elements can be obtained, and then the collision occurrence point can be determined according to the overlapping set of geometric elements, and the deformation part of the abdominal aorta after being cut by the scalpel can be found, as shown in Fig. 3 .

Table 1 shows the analysis results of the AABB-K-DOPs mixed hierarchical bounding box collision detection method for the abdominal aorta vessels of the 5 groups of subjects. It can be seen that the AABB-K-DOPs mixed hierarchical bounding box removed a large number of different Geometric primitives (node triangles) that may collide, thus greatly reducing the calculation amount of collision detection, reducing the time of collision detection, and greatly improving the speed of collision detection.

Table 1

Fig. 4 is a time comparison diagram of the collision detection methods of AABB, K-DOPs and AABB-K-DOPs, and Fig. 5 is a comparison diagram of the collision detection time of the three methods with the number of node triangles. It can be clearly seen from Figure 4 and Figure 5 that the time required by K-DOPs is about 8 times that of AABB-K-DOPs method, and the detection time required by AABB-K-DOPs is slightly longer than that of AABB. During the 20 collision detection experiments, the fluctuation of the time spent by AABB-K-DOPs is relatively more stable than that of K-DOPs. Therefore, the detection speed, execution performance and stability of the mixed hierarchical bounding box based on AABB-K-DOPs are much improved compared with the K-DOPs bounding box.

Figure 6 is a comparison of the accuracy rates of the three collision detection methods for 5 subjects after 20 collision detection experiments. It can be seen from Figure 6 that the accuracy rate of the AABB-K-DOPs hybrid hierarchical bounding box collision detection method is basically the same as that of the K-DOPs bounding box collision detection method, while the AABB-K-DOPs hybrid hierarchical bounding box collision detection method The correct rate is significantly higher than the AABB bounding box collision detection method. Therefore, the accuracy rate of the AABB-K-DOPs hybrid bounding box collision detection method is much higher than that of the AABB bounding box collision detection method.

Experimental results show that the hybrid hierarchical bounding box collision detection method based on AABB-K-DOPs meets the real-time requirements while meeting the accuracy of virtual vascular surgery.

The invention has the advantages of: a collision detection method in virtual minimally invasive abdominal aortic vascular surgery, using the fast collision detection of the outer AABB bounding box to solve the problems of complex intersection testing and low efficiency in the classic bounding box method, and improve the System real-time. The precise collision detection is performed by using the tightness of the inner K-DOPs bounding box, which ensures the high accuracy of the detection results.

Claims (1)

1. the collision checking method in the abdominal aorta vascular surgery of virtual Wicresoft, is characterized in that comprising the following steps:

The three-dimensional modeling of step 1, abdominal aorta blood vessel: collision detection of the present invention is based upon on the basis of abdominal aorta blood vessel geometric model, first the model preparation stage before collision detection utilizes medical image software to carry out three-dimensional reconstruction to abdominal aorta blood vessel CT data and obtains 3-D geometric model, then obtain more accurate 3-D geometric model after covering reparation, level and smooth fairing and grid optimization operation being carried out to the 3-D geometric model rebuild, specifically comprise following sub-step:

(a), abdominal aorta blood vessel CT image carried out to window width and window level adjustment and puppet coloured silk strengthens, increase the contrast of abdominal aorta vascular tissue;

B (), employing Threshold segmentation increase with region the mixing partitioning scheme combined and are partitioned into most of abdominal aorta vascular tissue;

(c), cavity filling is carried out to the masking-out of abdominal aorta vascular tissue after segmentation, for reducing the noise introduced because region increases;

(d), continue to edit the masking-out of abdominal aorta vascular tissue, for reducing marginal loss, obtain complete abdominal aorta vascular tissue information;

(e), the complete abdominal aorta vascular tissue after dividing processing is carried out three-dimensional reconstruction;

F (), utilization covering and smooth operation reduce the burr on abdominal aorta vascular pattern surface, optimized reconstruction abdominal aorta vascular pattern;

The model construction of step 2, the deformation of abdominal aorta blood vessel: utilize finite element analysis software to construct the viscoelasticity finite meta-model based on tetrahedral grid of abdominal aorta blood vessel, and by composing material properties, imposed load and power, the cutting of emulation blood vessel but deformation behavior when not cutting, specifically comprise following sub-step:

(a), the abdominal aorta blood vessel geometric model of medical image software rebuild is imported in finite element analysis software;

(b), setting parameter is carried out to abdominal aorta blood vessel geometric model, select abdominal aorta finite element model cell type, and build the physical deformation model of abdominal aorta blood vessel in conjunction with the tissue characteristics of abdominal aorta blood vessel; The chief component of abdominal aorta vascular tissue is snapback fibre and collagenous fibres, and wherein snapback fibre is reticulate texture, and collagenous fibres are folding wave structures; When stress is less, only have snapback fibre to work, now the elastic modulus of abdominal aorta blood vessel is the elastic modulus of snapback fibre; Along with stress increases, the folded part of collagenous fibres is stretched gradually and is opened, what at this moment determine the deformation of abdominal aorta blood vessel is not only snapback fibre, also have collagenous fibres, thus the elastic modulus of abdominal aorta blood vessel comprises the elastic modulus of snapback fibre and collagenous fibres, draws the mechanical characteristic formula (1) of following blood vessel according to this characteristic:

$\mathrm{\&sigma;}=\left\{\begin{array}{cc}{E}_1\&CenterDot;\mathrm{\&epsiv;}& 0\&le;\mathrm{\&epsiv;}\&le;\mathrm{\&lambda;}\\ E_1\&CenterDot;\mathrm{\&epsiv;}+E_2\&CenterDot;(\mathrm{\&epsiv;}-\mathrm{\&lambda;})=(E_1+E_2)\&CenterDot;\mathrm{\&epsiv;}-E_2\&CenterDot;\mathrm{\&lambda;}& \mathrm{\&epsiv;}>\mathrm{\&lambda;}\end{array}\right.---\left(1\right)$

In formula: σ is stress, ε is strain, E ₁for the elastic modulus of snapback fibre, E ₂for the elastic modulus of collagenous fibres, λ is deformation critical point; In conjunction with a large amount of stretching, compression experiment data, the elastic mould value obtaining blood vessel elasticity fiber and collagenous fibres is respectively E ₁=2.208 × 10 ⁵n/m ²and E ₂=8.112 × 10 ⁵n/m ², deformation critical point is λ=0.130, thus obtains

$\mathrm{\&sigma;}=\left\{\begin{array}{cc}0.221\mathrm{\&epsiv;}& 0\&le;\mathrm{\&epsiv;}\&le;0.130\\ 1.032\mathrm{\&epsiv;}-0.105& \mathrm{\&epsiv;}>0.130\end{array}\right.,\left(MPa\right)---\left(2\right)$

(c), carry out tetrahedral grid division, adopt free mesh mode to carry out tetrahedral grid division to abdominal aorta blood vessel geometric model;

(d), set up finite element model, add degree of freedom constraint and imposed load to finite element model, solve analysis, display abdominal aorta blood vessel is with the deformation results applying external force;

Step 3, coarse collision detection: coarse collision detection is mainly set up AABB bounding box to blood vessel and scalpel and carried out collision detection fast, the element set that quick removal can not collide, and determine to collide, specifically comprise following sub-step:

(a), import abdominal aorta vascular pattern and scalpel model and determine all root nodes and leafy node;

(b), obtain the maximal value (X of all root nodes of abdominal aorta blood vessel in three coordinate axis _max, Y _max, Z _max) and minimum value (X _min, Y _min, Z _min), determine the AABB bounding box of abdominal aorta blood vessel, in like manner obtain the maximal value (x of all root nodes of scalpel in three coordinate axis _max, y _max, z _max) and minimum value (x _min, y _min, z _min), the AABB bounding box of structure scalpel;

(c), determined situation about colliding by AABB bounding box, the test for intersection method of bounding box is compare the overlapping cases that two AABB bounding boxs project in three coordinate axis, when the projection in three coordinate axis all has overlap, bounding box intersects, view field is drawn by the maximin in each coordinate axis, needs comparison operation to be no more than 6 times; If abdominal aorta blood vessel V and the space shared by scalpel S are respectively F _vand F _s, its space shared by AABB bounding box is C _vand C _s, and if V and S collides, the geometric primitive set collided is the common factor of abdominal aorta blood vessel and scalpel geometric element, i.e. E=F _v∩ F _sand the AABB bounding box then corresponding to both should be

Step 4, collision detection of high precision: after the coarse collision detection stage utilizes AABB bounding box to get rid of the set that can not collide, obtain a subject collection that can collide, reduce rapidly the scope needing to detect, thus improve the speed of collision detection; Collision detection of high precision mainly sets up K-Dops bounding box to the object set that may collide in blood vessel and scalpel, then overlap test is carried out in the projection on the K/2 axis of orientation concentrated at its fixed-direction two K-DOPs bounding boxs successively, judge whether intersect between the two with this, if intersected, determine the point of impingement, specifically comprise following sub-step:

A (), the direction set selected are 26-DOPs, determine 6-DOPs by the positive negative direction of three coordinate axis, and the basis of 6-DOPs increases (1,1,1), (1,-1,1), (1,1 ,-1) and (1 ,-1,-1) four vectorial positive negative directions determine 14-DOPs, then increase (1,1 on 14-DOPs basis, 0), (1,0,1), (0,1,1), (1 ,-1,0), (1,0,-1) and the vectorial positive negative direction in (0,1 ,-1) six determine 26-DOPs;

(b), obtain K-DOPs bounding box by calculating leafy node vector with the minimax inner product of all directions vector, if the set of leafy node vector sum direction vector is respectively P and D, i-th leafy node vector, for a jth direction vector, T _jfor vector each in P and d _jthe set of inner product, wherein p _iwith d _jinner product value be t _ij=<p _i, d _j>, then establish T _jmiddle minimum value t _jmincorresponding leafy node is p _jmin, maximal value t _jmaxcorresponding leafy node is p _jmax, then through leafy node p _jminand direction is d _jplane d _jminwith through leafy node p _jmaxand direction is d _jplane d _jmaxconstitute at d _jk-DOPs bounding box plane pair on direction, in like manner calculates and can obtain other planes pair of K-DOPs bounding box;

(c), judge that the projection of two K-DOPs bounding boxs on 13 axis of orientations be whether all overlapping, if two projections of bounding box on a direction axle are not overlapping, then illustrate that two bounding boxs do not collide; Otherwise, overlapping geometric element set can be obtained, and then determine to collide origination point according to the geometry set of overlap, and the deformation position after finding abdominal aorta blood vessel to be cut by scalpel.