CN109616211B - Mixed suture line model based on mass point springs and knotting method thereof - Google Patents
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Abstract
A mixed suture model based on mass point springs and a knotting method thereof are provided, wherein the model is added with a torsion spring and a method for calculating suture tension in a segmented manner on the basis of the mass point spring model, and a primitive collision detection method and a collision cluster method are combined, and limitation of the maximum movement distance of the suture peak in a unit time step is also added. The mixed suture line model and the knotting method thereof can truly simulate the internal tension of the suture line, effectively avoid the phenomena of false detection and missed detection collision, and improve the accuracy of collision feedback force calculation. Experiments show that compared with the traditional FTL suture modeling method, the model and the knotting method thereof have more authenticity in visual rendering and have more stability in the treatment of complex knot simulation such as 'called human knots'.
Description
Technical Field
The invention relates to construction of a suture model in a virtual operation simulation system, which is used for realizing simulation of a wound suturing and knotting process in a virtual operation.
Background
A suture is a deformable object (Deformable Linear Objects, DLO) of very small mass, very resistant to tensile deformation, but hardly resistant to bending deformation, typically simulated using spline curves, and in some simulation systems the suture is rendered directly into one-dimensional line segments for simplicity of calculation. A good suture model is the basis of a virtual surgical simulation system. The simulation of the suture line not only requires a proper physical model, but also requires a real three-dimensional rendering effect; meanwhile, accurate calculation of the tension in the suture is also the basis of interaction with soft tissues. In addition, knotting simulation of suture lines requires a fine self-collision detection and feedback method to prevent missed detection and false detection collisions.
With the continuous development of computer hardware level, more and more sutures of three-dimensional models are present in the current simulation system, and common suture simulation methods are as follows: FTL (Follow The Leader) Mass Spring Model (MSM) and discrete elastic rod Model represented by "curve-angle" built on the Cosseat theory. Early Phillips et al simulated a rope by using a series of spheres that overlap each other, adding new spheres as it was stretched to ensure rope integrity, and removing previously filled spheres as it contracted. Later, brown et al proposed a suture model based on FTL method, which consisted of a limited number of rigid rods of equal length end to end (and unchanged during the experiment), the joints of the rods being free to rotate. During the self-collision process of the suture line, when two rigid rods are intersected, the corresponding vertexes are fixed in the current time step, and the next time step is pushed away to simulate the friction effect. Since this algorithm is a geometric model-based modeling method, it does not simulate changes in the internal tension of the suture.
Unlike the suture constructed by the FTL method, in the suture constructed using the mass spring model, the length of each suture is a variable linear spring, and the tension inside the suture is simulated by the variation of the length of the linear spring. In order to realize a more realistic suture model, payandeh et al have added a torsion spring to the suture model while also taking into account the force of air resistance on the suture, and have proposed using a replacement algorithm to determine whether a certain suture apex is inside or outside the soft tissue during the process of treating the interaction of the suture with the soft tissue. In calculating the tension of the suture, lenoir et al also considered a segmented treatment after the suture passed through the soft tissue, while friction between the suture and the soft tissue at each puncture point could also be added when calculating the tension of each segment of suture separately, to obtain a more accurate force feedback effect. This method of sectionally manipulating suture tension is also a common method of suture simulation. 2013 Lv Mengya et al constructed a suture using a mass-spring model, which references the updating method of FTL algorithm in the position updating of the suture vertex, thereby realizing the rapid implementation of the mechanical interaction process between suture and soft tissue. But does not provide a corresponding self-collision detection process and implementation of knots.
The first application of cosseat elastic rod theory to virtual surgery was suture simulation by Pai et al. However, the implicit approach to the elastic rod centerline greatly increases its computational complexity in the collision process. The Spillmann et al have improved on this basis by using a display method to treat the centerline of the spring rod and an implicit method to treat the cross-sectional direction of the spring rod. Punak et al optimize performance by omitting kinetic effects, internal friction and other dissipative effects. The simplicity in calculation ensures the relative accuracy of the model, improves the calculation speed, realizes good compromise between precision and calculation cost of the Cosseat elastic rod model, but the excessively high calculation complexity still makes the method difficult to meet the real-time interactive operation of virtual operation suture simulation, and particularly the calculation complexity is obviously increased when the knotting simulation is processed. The Bergou et al establishes a discrete elastic rod model represented by a curve-angle on the basis of the Cosseat theory, and decomposes the model to be simulated into a torsion-free Bishop rod and a rotation angle tangential to the center of the elastic rod. However, this model may suffer from some energy leakage when dealing with constraints, resulting in inaccuracies in calculating the minimum energy.
In summary, although the conventional FTL (follow the leader) -based method is simple and easy to implement and can meet the real-time requirement in suture simulation, the tension change inside the suture cannot be simulated, and the internal tension of the suture is the basis for calculating the friction force between the suture and the soft tissue, and the authenticity requirement of the suture simulation process cannot be met only by manually adding some fixed tension. The coserat elastic rod model has the problem that the real-time performance of suture simulation is reduced due to the excessive computational complexity. Compared with the prior art, the suture line formed by connecting a plurality of sections of linear springs with variable lengths can be constructed by adopting the mass point spring model, the tension in the suture line is simulated through the change of the lengths of the linear springs, and the accurate calculation of the tension not only improves the authenticity of the suture line model, but also is beneficial to simulating the friction force between the suture line and soft tissues.
Disclosure of Invention
Based on the background, the invention provides a suture line mixed model based on mass point springs and a knotting method thereof. On the construction of a model, the method for calculating the tension of the suture thread by adding a torsion spring and a segmentation on the basis of a mass spring model combines the method for detecting the collision of the graphic element and the method for clustering the collision on the basis of the treatment of the knotting process of the suture thread, and adds the limitation on the maximum moving distance of the vertex of the suture thread in a unit time step.
The invention is realized by the following technical scheme.
The invention relates to a hybrid suture line model based on mass point springs and a knotting method thereof, which comprises the following steps:
in the virtual operation suture simulation system, a suture line with the length of L and the radius of R is arranged, according to the mass point spring modeling principle, the suture line is regarded as formed by connecting N sections of linear springs with the original length of L end to end, the common end point of two adjacent springs is the top point of the suture line, and N top points are marked as P i ，i＝1,2,3……N,N＝n+1。
Step 1: first, constructing any vertex P according to Newton's second law of motion i And solving the equation by using Euler finite difference method to obtain the position vector r of N vertexes of the suture line i Updating the position information of all vertexes in each time step to obtain the motion state of the whole suture line;
step 2: calculating the tension of the suture line in a segmented manner: as shown in FIG. 1, each segment is first separated from the suture headDetecting length of suture, detecting suture segment p i+1 p i+2 No stretching occurs, the length of suture has a tension of
And suture apex p i+1 、p i+2 The acting force of the suture is 0, thereby knowing the suture segment p i p i+1 The tension on is f i The magnitude of the component force in the direction of the suture, i.e.:>
suture segment p i-1 p i The tension of (2) is f i-1 、f i The magnitude of the resultant force in the direction of the length of suture, namely:
By this method, the first length of suture p is deduced 1 p 2 Is the same as the tension of the apex p i+3 The direction of the last section of suture p is calculated by the same method n p n+1 Is a tension of (2);
recalculate the torsion spring force f i-1 ,f i Direction vector n of (2) i-1 ,n i The method comprises the following steps:
finally calculate point P i-1 、P i+1 The torsion spring force f i-1 、f i-1 The method comprises the following steps of:
wherein v is i-1 ,v i ,v i+1 Respectively point P i-1 ,P i ,P i+1 Velocity at k td Is the torsion spring force coefficient, point P i Torsion spring force f at i The calculation formula of (f) is i ＝-(f i-1 +f i+1 ) In addition, the air resistance is recorded as f air The size of the air resistance coefficient is multiplied by the corresponding air resistance coefficient k according to the speed of each suture peak air In a direction opposite to the direction of movement of the suture apex.
Step 4: three-dimensional rendering of suture: as shown in figure 3, with suture p i p i+1 As axes, i=1, 2, … …, N, n=n+1, a cylinder with a height L and a radius R is constructed. Then with each suture vertex p i A sphere with the same radius is constructed for the sphere center to connect two sections of adjacent cylinders so as to fill the gap which is visually generated at the joint of two sections of suture lines when the suture lines are bent,smoothing the line by using a Catmull-Rom spline curve interpolation method;
step 5: self-collision detection and feedback of suture: the present invention treats collision detection of two sections of suture as collision detection between two cylinders, as shown in fig. 4. For two cylindrical sutures p of radius r in time step dt i p i+1 ,p j p j+1 First, the distance d between the two column-shaped suture lines needs to be calculated, if d<2r, the suture thread is considered to have self-collision, otherwise no collision occurs. With suture section p i p i+1 ,p j p j+1 In the event of a collision, p is first calculated i p i+1 ,p j p j+1 To point c of shortest distance to each other i ,c j Then calculate the slave point c i To point c j The positions of vertices i, i+1, j, j+1 are adjusted as follows:
wherein D is the displacement distance, and the calculation formula is: d= 2*r-d+α, where α is a friction substitution coefficient, and is an adjustable non-negative number to eliminate some errors due to interpolation operation, while α is equivalent to existence of friction, and the larger α is, the smaller the equivalent friction, if a segment of suture collides with multiple segments of suture simultaneously in one time step, the final position is the average value of the feedback position results of multiple collisions, namely d= (D) 1 +D 2 +......+D n )/n；
Step 6: the improved penetration depth algorithm aims at solving the problem that the calculation of repulsive force is inaccurate because the penetration depth method does not have too great depth when processing thin objects such as suture lines, and the maximum distance D of the movement of the suture line peak point in unit time step is calculated max The value of r/4 is set to be less than or equal to the value of r/4, so that the accurate calculation of repulsive force in self-collision feedback can be ensured, and D is taken in the invention max ≤0.5mm；
Step 7: in the collision detection traversal process, four vertexes corresponding to two sections of suture lines which have detected collision are classified into one collision cluster, if one suture line belongs to two collision clusters, the two collision clusters are combined, the number of vertexes of each collision cluster is counted after the collision detection traversal is finished each time, if the number of vertexes reaches a certain threshold value, the collision cluster is regarded as one suture knot, and collision detection processing is not carried out on the vertexes.
The invention can truly simulate the internal tension of the suture line, effectively avoid the phenomena of false detection and missing detection of collision, and improve the accuracy of collision feedback force calculation. Experiments show that compared with the traditional FTL suture modeling method, the model is more realistic in visual rendering and more stable in processing complex junction simulation such as 'called knots'.
Drawings
Fig. 1 is a graph of tension analysis of a suture.
Fig. 2 is a diagram of torsion spring stress analysis.
FIG. 3 is a perspective view of a simulated suture thread of a mass spring model.
FIG. 4 is a schematic view of a suture self-collision.
Fig. 5 is a comparison of "8-junction" reality, FTL model, and hybrid model knots. Wherein, (a) is an actual knotting diagram of an 8-shaped knot, (b) is a knotting diagram based on an FTL model, and (c) is a knotting diagram of a mixed model.
FIG. 6 is a comparison of "man-knot" reality and mixed model knots. Wherein, (a) is a true knot map and (b) is a mixed model knot map. The FTL model cannot complete the processing of complex junctions such as 'called knots', so that an effect diagram of the FTL model is not available.
Detailed Description
The invention will be further illustrated by the following examples.
In the virtual operation suture simulation system, a suture line with the length of 0.4m and the radius of 2mm is arranged, according to the mass point spring modeling principle, the suture line is regarded as being formed by connecting 80 sections of linear springs with the original length of 5mm end to end, the common end point of two adjacent springs is set as the top point of the suture line, and N top points are marked as P i ，i＝1,2,3……N,N＝81。
Step 1: first, constructing any vertex P according to Newton's second law of motion i And solving the equation by using Euler finite difference method to obtain the position vector r of N vertexes of the suture line i Updating the position information of all vertexes in each time step to obtain the motion state of the whole suture line;
step 2: the tension of the suture is calculated in segments, as shown in fig. 1, by first detecting the length of each length of suture from the head of the suture, and detecting the suture segment p i+1 p i+2 No stretching occurs, the length of suture has a tension of
And suture apex p i+1 、p i+2 The acting force of the suture is 0, thereby knowing the suture segment p i p i+1 The tension on is f i The magnitude of the component force in the direction of the suture, i.e.:>
suture segment p i-1 p i The tension of (2) is f i-1 、f i The magnitude of the resultant force in the direction of the length of suture, namely:
By this method, the first length of suture p is deduced 1 p 2 Is the same as the tension of the apex p i+3 The direction of the last section of suture p is calculated by the same method n p n+1 Is a tension of (a).
recalculate the torsion spring force f i-1 ,f i Direction vector n of (2) i-1 ,n i The method comprises the following steps:
finally calculate point P i-1 、P i+1 The torsion spring force f i-1 、f i-1 The method comprises the following steps of:
wherein v is i-1 ,v i ,v i+1 Respectively point P i-1 ,P i ,P i+1 Velocity at k td Is the torsion spring force coefficient, point P i Torsion spring force f at i The calculation formula of (f) is i ＝-(f i-1 +f i+1 ) In addition, the air resistance is recorded as f air The size of which is based on the velocity of each suture apex multiplied byCorresponding air resistance coefficient k air In a direction opposite to the direction of movement of the suture apex, k in the present invention air The value is 0.2Ns/m.
Step 4: three-dimensional rendering of the suture, as shown in figure 3, with suture p i p i+1 As axes, i=1, 2, … …, N, n=n+1, a cylinder with a height L and a radius R is constructed. Then with each suture vertex p i And constructing a sphere with the same radius for the sphere center to connect two sections of adjacent cylinders so as to fill up a gap visually generated at the joint of the two sections of suture lines when the suture lines are bent, and smoothing lines by using a Catmull-Rom spline curve interpolation method.
Step 5: self-collision detection and feedback of suture, the invention regards collision detection of two sections of suture as collision detection between two cylinders, as shown in fig. 4. For two cylindrical sutures p of radius r in time step dt i p i+1 ,p j p j+1 First, the distance d between the two column-shaped suture lines needs to be calculated, if d<2r, the suture thread is considered to have self-collision, otherwise no collision occurs. With suture section p i p i+1 ,p j p j+1 In the event of a collision, p is first calculated i p i+1 ,p j p j+1 To point c of shortest distance to each other i ,c j Then calculate the slave point c i To point c j The positions of vertices i, i+1, j, j+1 are adjusted as follows:
wherein D is the displacement distance, and the calculation formula is: d= 2*r-d+α, where α is a friction substitution coefficient, and is an adjustable non-negative number to eliminate some errors due to interpolation operation, while α is equivalent to existence of friction, and the larger α is, the smaller the equivalent friction, if a segment of suture collides with multiple segments of suture simultaneously in one time step, the final position is the average value of the feedback position results of multiple collisions,i.e. d= (D 1 +D 2 +......+D n )/n。
Step 6: the improved penetration depth algorithm aims at solving the problem that the calculation of repulsive force is inaccurate because the penetration depth method does not have too great depth when processing thin objects such as suture lines, and the maximum distance D of the movement of the suture line peak point in unit time step is calculated max Setting the value to be less than or equal to r/4 ensures accurate calculation of the repulsive force in the self-collision feedback, D is taken in the invention max ≤0.5mm。
Step 7: in the collision detection traversal process, four vertexes corresponding to two sections of suture lines which have detected collision are classified into one collision cluster, if one suture line belongs to two collision clusters, the two collision clusters are combined, the number of vertexes of each collision cluster is counted after the collision detection traversal is finished each time, if the number of vertexes reaches a certain threshold value, the collision cluster is regarded as one suture knot, and collision detection processing is not carried out on the vertexes.
Claims (1)
1. A mixed suture line model based on mass point springs and a knotting method thereof are characterized by comprising the following steps:
in the virtual operation suture simulation system, a suture line with the length of L and the radius of R is regarded as being formed by connecting N sections of linear springs with the original length of L end to end according to the mass point spring modeling principle, the common end point of two adjacent springs is the top point of the suture line, and N top points are marked as P i ，i＝1,2,3……N,N＝n+1；
Step 1: first, constructing any vertex P according to Newton's second law of motion i And solving the equation by using Euler finite difference method to obtain the position vector r of N vertexes of the suture line i Updating the position information of all vertexes in each time step to obtain the motion state of the whole suture line;
step 2: calculating the tension of the suture line in a segmented manner: first, the length of each suture is detected from the head of the suture, and the suture segment p is detected i+1 p i+2 No occurrence ofStretching, the length of suture tension is of the magnitude of
And suture apex p i+1 、p i+2 The acting force of the suture is 0, thereby knowing the suture segment p i p i+1 The tension on is f i The magnitude of the force component in the suture direction is:
Suture segment p i-1 p i The tension of (2) is f i-1 、f i The magnitude of the resultant force in the direction of the length of suture, namely:
By this method, the first length of suture p is deduced 1 p 2 Is the same as the tension of the apex p i+3 The direction of the last section of suture p is calculated by the same method n p n+1 Is a tension of (2);
step 3: calculating the elasticity and air resistance of the torsion spring: in addition to the suture p 1 、p n+1 Considering each of the remaining vertices, except for two vertices, as the vertex of an included angle, forming a curved spring model under both sides of the included angle, the component of force normal to the spring segment will be used at the vertex of each included angle to calculate the angle
The formula of (2) is as follows:
recalculate the torsion spring force f i-1 ,f i Direction vector n of (2) i-1 ,n i The method comprises the following steps:
finally calculate point P i-1 、P i+1 The torsion spring force f i-1 、f i-1 The method comprises the following steps of:
wherein v is i-1 ,v i ,v i+1 Respectively point P i-1 ,P i ,P i+1 Velocity at k td Is the torsion spring force coefficient, point P i Torsion spring force f at i The calculation formula of (f) is i ＝-(f i-1 +f i+1 ) In addition, the air resistance is recorded as f air The size of the air resistance coefficient is multiplied by the corresponding air resistance coefficient k according to the speed of each suture peak air In a direction opposite to the direction of movement of the suture thread apex;
step 4: three-dimensional rendering of suture: with suture p i p i+1 As the axis, i=1, 2, … …, N, n=n+1, a cylinder with a height of L and a radius of R is constructed, and each suture line vertex p is used i Constructing a sphere with the same radius for connecting two sections of adjacent cylinders so as to fill up a gap visually generated at the joint of two sections of suture lines when the suture lines are bent, and smoothing lines by using a Catmull-Rom spline curve interpolation method;
step 5: self-collision detection and feedback of suture: regarding collision detection of two pieces of suture as collision detection between two cylinders within a time step dt for two cylindrical slits with radius rLine p i p i+1 ，p j p j+1 First, the distance d between the two column-shaped suture lines needs to be calculated, if d<2r, if the suture thread is considered to have self-collision, otherwise, no collision occurs, a suture segment p is arranged i p i+1 ,p j p j+1 In the event of a collision, p is first calculated i p i+1 ，p j p j+1 To point c of shortest distance to each other i ，c j Then calculate the slave point c i To point c j The positions of vertices i, i+1, j, j+1 are adjusted as follows:
wherein D is the displacement distance, and the calculation formula is: d= 2*r-d+α, where α is a friction substitution coefficient, and is an adjustable non-negative number to eliminate some errors due to interpolation operation, while α is equivalent to existence of friction, and the larger α is, the smaller the equivalent friction, if a segment of suture collides with multiple segments of suture simultaneously in one time step, the final position is the average value of the feedback position results of multiple collisions, namely d= (D) 1 +D 2 +......+D n )/n；
Step 6: improved penetration depth algorithm: aiming at the problem that the repulsive force calculation is inaccurate because the depth is not too large when the penetration depth method is used for processing thin objects such as sutures, the maximum distance D of the movement of the suture peak in the unit time step is obtained max The value less than or equal to r/4 can ensure accurate calculation of the repulsive force in the self-collision feedback;
step 7: collision cluster method: in the collision detection traversal process, classifying four vertexes corresponding to two sections of suture lines which have detected collision into one collision cluster, merging the two collision clusters if one suture line belongs to the two collision clusters, counting the number of vertexes of each collision cluster after each collision detection traversal is completed, and regarding the collision cluster as a suture knot if the number of vertexes reaches a certain threshold value, wherein collision detection processing is not carried out on the vertexes.
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