CN105167849B - A three-dimensional path planning method for blood vessels based on ant colony algorithm - Google Patents

Abstract

The invention discloses a three-dimensional path planning method for blood vessels based on the ant colony algorithm. The operation steps of the method are as follows: 1. data import, 2. blood vessel modeling, 3. blood vessel centerline extraction, 4. establishment of the network topology structure of the blood vessel centerline, 5. ants Reconnaissance algorithm, 6 parameter initialization, 7 heuristic information calculation, 8 probability selection, 9 pheromone dynamic volatilization, 10 pheromone incremental calculation, 11 pheromone update, 12 planning end judgment, 13 result output. The method uses ant scouting algorithm based on the extraction of vascular centerline, improves the ant colony algorithm, and comprehensively considers catheter diameter, vessel length, minimum diameter, maximum curvature, and maximum torsion to assist the surgeon in planning the optimal path for surgery. This method improves the reliability of preoperative path planning for vascular interventional surgery, ensures the passability of catheters, and can provide surgeons with a new surgical path reference standard.

Description

A three-dimensional path planning method for blood vessels based on ant colony algorithm

technical field

The invention relates to a blood vessel three-dimensional path planning method based on an ant colony algorithm, and belongs to the technical field of blood vessel three-dimensional path planning.

Background technique

Vascular interventional surgery has the advantages of less bleeding, less trauma, and faster recovery, so it is widely used in the treatment of vascular diseases. At present, vascular interventional operations in most hospitals across the country still rely on surgeons to operate catheter guide wires with bare hands and use medical imaging technologies such as X-rays and computer-aided technologies such as virtual reality to complete the operation. Under limited technical conditions, considering factors such as the doctor's operating level, the risk of surgery, and postoperative complications, the thicker aorta is usually used as the surgical path during surgery, regardless of other possible optimal paths.

Vascular three-dimensional path planning is to find an optimal path from the surgical incision to the lesion in three-dimensional geometric space, which is a global planning problem and an important means of preoperative planning. The key technology of intravascular 3D path planning is the extraction of vascular centerline and the planning of navigation path. The methods for extracting the centerline include topological refinement method, distance transformation method, potential energy field method, level set based method and segmentation based method, etc. In terms of navigation path planning, with the rise of intelligent algorithms, some scholars use Dijkstra algorithm and A-star algorithm to search for the shortest path between two points on the extracted blood vessel center line. However, these methods do not take into account other properties of vessels during the planning process.

Ant colony algorithm is one of the swarm intelligence algorithms in bionics. It was proposed in 1991 by Italian scholar M.Dorigo et al. after being inspired by the behavior of ants foraging in the real world. The core of the algorithm is that ants can choose the path with the highest residual pheromone concentration with a higher probability, and more and more ants will be attracted to this path, forming a positive feedback principle to find a path with the shortest distance from the food source. At present, the 3D path planning based on the ant colony algorithm at home and abroad is mainly concentrated in the aspects of unmanned aerial vehicles, submersibles, 3D pipelines, robots, etc. There is no literature that applies the ant colony algorithm to the 3D path planning of blood vessels.

Contents of the invention

The purpose of the present invention is to provide a three-dimensional path planning method based on the ant colony algorithm for the existing problems and deficiencies in the existing vascular path planning technology. Algorithm, and comprehensively consider catheter diameter, vessel length, diameter, curvature and torsion to assist surgeons in planning the optimal path for surgery.

In order to achieve the above object, the idea of the present invention is: carry out blood vessel modeling on CTA medical image data and extract the centerline, and use ant scouting algorithm on this basis in the blood vessel centerline network of a given starting point, and improve the ant colony algorithm , which integrates the diameter of the catheter and other characteristics of the vessel, such as vessel length, minimum diameter, maximum curvature and maximum torsion, for global path planning.

According to design of the present invention, the present invention adopts following technical scheme to realize:

A vascular three-dimensional path planning method based on ant colony algorithm, characterized in that the operation steps are as follows: 1 data import, 2 vessel modeling, 3 vessel centerline extraction, 4 establishment of vessel centerline network topology, 5 ant reconnaissance algorithm, 6 Parameter initialization, 7 heuristic information calculation, 8 probability selection, 9 pheromone dynamic volatilization, 10 pheromone incremental calculation, 11 pheromone update, 12 planning end judgment, 13 result output.

The step 1 data import: import a group of complete medical CTA image data (DICOM);

The step 2 vascular modeling: the imported CTA image data is used for vascular modeling based on a 3D level set method;

Said step 3 blood vessel center line extraction: the established blood vessel model is extracted based on the Voronoi diagram and the Eikonal equation to extract the blood vessel center line, and obtain the maximum radius R of the inscribed sphere;

The step 4 establishes the network topology of the blood vessel centerline: establishes the network topology according to the centerline extraction result, determines the number of nodes and edges, and calculates the distance, maximum curvature, maximum torsion and minimum diameter of each path;

4-1 Distance calculation, using the first kind of curve integral to calculate the length of the space curve. Suppose the space curve equation in parametric form is

Therefore, the distance formula of the available space curve is:

4-2 Maximum curvature calculation, curvature (curvature) is to calculate the curvature of the curve at each point on the center line based on the rotation rate of the tangent direction angle of a certain point on the curve to the arc length, and the curvature of the center line reflects the degree of bending of the blood vessel. The greater the curvature, the greater the curvature of the blood vessel, which will increase the difficulty of passing the catheter and reduce the passability of the blood vessel. The curvature calculation for the parametric form space curve equation is:

Calculate the curvature of each point on the path according to this formula and obtain the maximum curvature C _max of the path;

4-3 Calculation of the maximum torsion, the absolute value of the torsion measures the change rate of the angle between the subnormal vectors of two adjacent points on the curve to the arc length, and the torsion on the center line can reflect the distortion of the blood vessel The degree of twisting of the blood vessels in the pelvic cavity is relatively large, and the greater the torsion, the greater the degree of twisting of the blood vessels, which will also increase the difficulty of passing the catheter, reduce the passability of the blood vessels, and reduce the safety factor. For the parametric form space curve equation, the torsion is calculated as:

Calculate the torsion of each point on the path according to this formula and obtain the maximum torsion T _max of the path;

4-4 Calculation of the minimum diameter, the diameter D of each point on the center line can be calculated according to the maximum radius R of the inscribed sphere, and the minimum diameter D _min on each path can be calculated. Assuming that the diameter of the surgical catheter is D _c , this section is required The minimum diameter of the vascular path D _min > D _c to ensure that the catheter can pass through the blood vessel;

The step 5 ant reconnaissance algorithm: determine the starting point, and execute the ant reconnaissance algorithm with self-replication function.

Since the topology of the vascular network is not a complete graph, there are no loops between some nodes, and there must be some end nodes. If the ant reaches an end node instead of the end point during the search process, it either directly exits the pathfinding, or returns to the previous node of the end node to continue pathfinding. If you choose the former, although it will speed up the convergence, it lacks overall consideration and exits prematurely; if you choose the latter, although you consider the overall situation, it will reduce the efficiency of the algorithm. Therefore, after the starting point is determined, the present invention allows the ants to scout the entire network topology, distinguish and remove such non-terminal nodes, and then execute the ant colony algorithm. This kind of reconnaissance ants have the function of self-replication. During the reconnaissance process, they can copy themselves according to the degree N of the vertex V, that is, the number of edges (except the visited edges), and then continue reconnaissance to other vertices respectively.

5-1 Place the corresponding number of ants Mv=Nv, Mu=Nu respectively according to the degrees of the starting point v and the ending point u;

5-2 When each ant scouts the vertex V _i , it first saves it in its own routing table Ta _i , and marks it as a scout;

5-3 Each ant judges the degree N _i of the reconnaissance vertex V _i ,

5-3-1 If n≠1, copy n-2 copies of ants and continue reconnaissance;

5-3-2 If n=1, report the vertex V _i as an abnormal point, remove this point, modify the degree N _i-1 of the previous vertex V _i- 1, update the overall network topology, and proceed to step 5- 4;

5-4 Return to the previous vertex V _i-1 along the original route according to the routing table Ta _i , if n=1, execute step 5-3-2; if n≠1, enter step 5-5;

5-5 If all the vertices have been scouted, stop the scouting and go to parameter initialization 6; otherwise go to step 5-3;

Parameter initialization in step 6: initializing various parameters, such as setting the number of ants M, the pheromone intensity constant Q, the total number of iterations, and the diameter of the conduit D _c , and placing the ants at the initial position;

Said step 7 heuristic information calculation: the heuristic function has an important impact on the convergence and stability of the algorithm. In the ant colony algorithm, the heuristic information η is generally the inverse ratio of the distance between two points, i.e. 1/L _{1 , J} , the path planning criteria of the present invention are surgical safety and optimal path, so not only the length L _{I, J} of the blood vessel, the maximum curvature C _max and the maximum torsion T _max should be considered in path planning, but also the length of the blood vessel The minimum diameter D _min , the heuristic information is defined as

η _{I, J} (t) represents the heuristic information from node I (x, y, z) to node J (x', y', z') at time t; x, y, z and x', y', z' is the three-dimensional coordinates of the point; D _min represents the minimum diameter of this path, D _c represents the diameter of the catheter, and D _min > D _c is required; L _{I, J} represent the length of this path; C _max represents the maximum diameter of this path Curvature, T _max , represents the maximum torsion of this path.

Said step 8 probability selection: set M ants, n nodes, a _i (t) represents the number of ants at a certain node I at time t, then In each path selection step of the ant colony algorithm, the ant m decides which path to move to next according to the probability.

Indicates the probability that ant m moves from point I to point J at the tth moment, allowed _m = {1, 2, ..., n}-t _m represents the node that the ant can choose in the next step, and t _m represents the node that the ant has visited Node; α indicates the pheromone inspiration factor, indicating the role of the amount of residual pheromone in the movement of ants. The larger the value, the more inclined the ants are to choose the path passed by other ants, and the stronger the cooperation ability between ants; β indicates the expected value The heuristic factor indicates the importance of heuristic information when ants choose a path. The larger the value, the closer the state transition rule is to the greedy rule. τ _{I, J} (t) represents the pheromone on the path from point I to point J at time t.

The step 9 is dynamic volatilization of pheromone: the volatilization speed of pheromone will change with the passage of time due to factors such as temperature and humidity, and it is a dynamic process. The more complicated the path, the smaller the heuristic information and the faster the volatilization speed , the less pheromone remains, so the volatilization coefficient ρ of pheromone dynamically volatilizes with the change of heuristic information η _{I, J} (t). After all ants reach the end point, it is calculated according to the following relationship,

ρ _{I, J} (t) represents the volatilization coefficient on the path from I to J at time t, and η _{I, J} (t) represents the pheromone on the path from I to J at time t, Represents the heuristic information on all paths at time t, and k represents the number of paths an ant passes through at time t.

The step 10 pheromone incremental calculation: the pheromone update model is an important part of the random search and fast convergence of the basic ant colony algorithm. The present invention aims at the overall optimal requirement of the problem itself, and adopts the ant-circumference model; considering the influence of the minimum diameter of the blood vessel and the diameter of the catheter in the operation, the ant-circumference model is modified as follows:

Q is the pheromone intensity constant, which is the total amount of pheromone released by ants on the path they pass in a cycle, which affects the convergence speed of the algorithm to a certain extent; it is required that the minimum diameter of the blood vessel path D _min > D _c , L _m represents the path length that the m-th ant passes through in this cycle, and it is calculated according to the result of each ant in its routing table Ta _m .

The step 11 pheromone update: the amount of pheromone on each path at the initial moment is equal. After the ant completes a cycle, the pheromone will gradually volatilize over time, so the pheromone concentration needs to be updated. Before the ant enters the next cycle, the pheromone on the corresponding path is updated as follows:

τ _{I, J} (t+1) = (1-ρ)τ _{I, J} (t) + Δτ _{I, J} (t, t+1)

ρ(O<ρ<1) is the dynamic volatilization coefficient of pheromone, 1-ρ is the dynamic residual factor of pheromone, Indicates the amount of pheromone left by the mth ant on the path (I, J) in this cycle, Δτ _{I, J} (t, t+1) represents all the pheromones that pass through the path (I, J) in this cycle Pheromone increments left by ants.

The step 12 planning end judgment: when the maximum number of iterations is reached, then exit the loop, otherwise enter the heuristic information calculation 7 and continue the loop;

Result output of the step 13: arrange the output result of the routing table.

Compared with the prior art, the present invention has the following obvious outstanding substantive features and significant advantages:

(1) The present invention applies the ant colony algorithm to the technical field of three-dimensional path planning of blood vessels.

(2) The present invention improves the heuristic information model in the ant colony algorithm, comprehensively considers the catheter diameter, blood vessel length, minimum diameter, maximum curvature and maximum torsion rate, improves the reliability of the preoperative planning path, and ensures the safety of the catheter. Passability.

(3) The present invention improves the pheromone increment model in the ant colony algorithm, combines the influence of the minimum diameter of the blood vessel and the diameter of the catheter in planning, and accelerates the convergence of the algorithm.

Description of drawings

FIG. 1 is a flowchart of a three-dimensional path planning method for blood vessels based on ant colony algorithm in the present invention.

detailed description

Embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

Embodiment one:

Referring to Figure 1, a three-dimensional path planning method for blood vessels based on ant colony algorithm is characterized in that the operation steps are as follows, 1 data import, 2 vessel modeling, 3 vessel centerline extraction, 4 establishment of vessel centerline network topology, 5 ant Reconnaissance algorithm, 6 parameter initialization, 7 heuristic information calculation, 8 probability selection, 9 pheromone dynamic volatilization, 10 pheromone incremental calculation, 11 pheromone update, 12 planning end judgment, 13 result output.

The step 1 data import: import a group of complete medical CTA image data (DICOM);

The step 2 vascular modeling: the imported CTA image data is used for vascular modeling based on a 3D level set method;

Said step 3 blood vessel center line extraction: the established blood vessel model is extracted based on the Voronoi diagram and the Eikonal equation to extract the blood vessel center line, and obtain the maximum radius R of the inscribed sphere;

The step 4 establishes the network topology of the blood vessel centerline: establishes the network topology according to the centerline extraction result, determines the number of nodes and edges, and calculates the distance, maximum curvature, maximum torsion and minimum diameter of each path;

4-1 Distance calculation, using the first type of curve integral to calculate the length of the space curve;

4-2 Calculate the maximum curvature, calculate the curvature of each point on the path according to the curvature calculation formula of the parametric form space curve equation and obtain the maximum curvature C _max of the path;

4-3 Calculate the maximum torsion, calculate the torsion of each point on the path according to the torsion calculation formula of the parametric form space curve equation and obtain the maximum torsion T _max of the path;

4-4 Calculate the minimum diameter, calculate the diameter D of each point on the center line according to the maximum radius R of the inscribed sphere, and then calculate the minimum diameter D _min on each path, assuming that the diameter of the surgical catheter is D _c , then this section is required The minimum diameter of the blood vessel path D _min >D _c ensures that the catheter can pass through the blood vessel.

The step 5 ant reconnaissance algorithm: After determining the starting point, let the ants conduct reconnaissance on the entire network topology first, and then execute the ant colony algorithm after distinguishing and removing such non-terminal nodes. This kind of reconnaissance ants have the function of self-replication. During the reconnaissance process, they can copy themselves according to the degree N of the vertex V, that is, the number of edges (except the visited edges), and then continue reconnaissance to other vertices respectively;

5-1 Place the corresponding number of ants Mv=Nv, Mu=Nu respectively according to the degrees of the starting point v and the ending point u;

5-2 Select a vertex V _i from the vertex set V, and judge whether the vertex V _i has been reconnaissance;

5-2-1 If V _i has no reconnaissance, when each ant reconnaissance vertex V _i , first save it in its respective routing table Ta _j , and make a reconnaissance mark;

5-2-2 If V _i has been reconnaissance, return to 5-2;

5-3 Each ant judges the degree N _i of the reconnaissance vertex V _i ,

5-3-1 If n≠1, copy n-2 copies of ants and continue reconnaissance;

5-3-2 If n=1, report the vertex V _i as an abnormal point, remove this point, modify the degree N _i-1 of the previous vertex V _i- 1, update the overall network topology, and proceed to step 5- 4;

5-4 Return to the previous vertex V _i-1 along the original route according to the routing table Ta _i , if n=1, execute step 5-3-2; if n≠1, enter step 5-5;

5-5 If all the vertices have been scouted, stop the scouting and go to parameter initialization 6; otherwise go to step 5-3;

Parameter initialization in step 6: Initialize various parameters, such as setting the number of ants M, the pheromone intensity constant Q, the total number of iterations, the diameter of the conduit D _c , and placing the ants at the initial position.

Embodiment 2: This embodiment is basically the same as Embodiment 1, and the special features are as follows:

Heuristic information calculation in step 7: The criteria for path planning in the present invention are surgical safety and optimal path, so not only the length L _{I, J} of the blood vessel, the maximum curvature C _max and the maximum torsion T _max must be considered in path planning, Also take into account the minimum diameter D _min of the vessel;

The step 8 probability selection: in each step path selection of the ant colony algorithm, the ant m decides which road to move next according to the ratio of the probability formula;

The step 9 is dynamic volatilization of pheromone: the volatilization speed of pheromone will change with the passage of time due to factors such as temperature and humidity, and it is a dynamic process. The more complicated the path, the smaller the heuristic information and the faster the volatilization speed , the less pheromone remains, so the volatilization coefficient ρ of pheromone dynamically volatilizes with the change of heuristic information η _{I, J} (t).

Embodiment three: this embodiment is basically the same as embodiment two, and the special features are as follows:

The step 10 pheromone incremental calculation: the pheromone update model is an important part of the random search and fast convergence of the basic ant colony algorithm. According to the overall optimal requirement of the problem itself, the present invention adopts the ant circle model; considering the influence of the minimum diameter of the blood vessel and the diameter of the catheter in the operation, the calculation is performed according to the improved pheromone increment model;

The step 11 pheromone update: the amount of pheromone on each path at the initial moment is equal. After the ant completes a cycle, the pheromone will gradually volatilize over time, so the pheromone concentration needs to be updated. The pheromone on the corresponding path is updated accordingly before the ant enters the next cycle;

The step 12 planning end judgment: when the maximum number of iterations is reached, then exit the loop, otherwise enter the heuristic information calculation 7 and continue the loop;

Result output of the step 13: arrange the output result of the routing table.

Claims (4)

1. A blood vessel three-dimensional path planning method based on ant colony algorithm, characterized in that the operation steps are as follows: 1 data import, 2 blood vessel modeling, 3 blood vessel centerline extraction, 4 establishment of blood vessel centerline network topology, 5 ant reconnaissance algorithm , 6 parameter initialization, 7 heuristic information calculation, 8 probability selection, 9 pheromone dynamic volatilization, 10 pheromone incremental calculation, 11 pheromone update, 12 planning end judgment, 13 result output; The step 1 data import: import a set of complete medical CTA image data; The step 2 vascular modeling: the imported CTA image data is used for vascular modeling based on a 3D level set method; Said step 3 blood vessel center line extraction: the established blood vessel model is extracted based on the Voronoi diagram and the Eikonal equation to extract the blood vessel center line, and obtain the maximum radius R of the inscribed sphere; The step 4 establishes the network topology of the blood vessel centerline: establishes the network topology according to the centerline extraction result, determines the number of nodes and edges, and calculates the distance, maximum curvature, maximum torsion and minimum diameter of each path; 4-1 Distance calculation, using the first type of curve integral to calculate the length of the space curve; 4-2 Calculate the maximum curvature, calculate the curvature of each point on the path according to the curvature calculation formula of the parametric form space curve equation and obtain the maximum curvature C _max of the path; 4-3 Calculate the maximum torsion, calculate the torsion of each point on the path according to the torsion calculation formula of the parametric form space curve equation and obtain the maximum torsion T _max of the path; 4-4 Calculate the minimum diameter, calculate the diameter D of each point on the center line according to the maximum radius R of the inscribed sphere, and then calculate the minimum diameter D _min on each path, assuming that the diameter of the surgical catheter is D _c , then this section is required The minimum diameter of the vascular path D _min > D _c to ensure that the catheter can pass through the blood vessel; The step 5 ant reconnaissance algorithm: After determining the starting point, let the ants conduct reconnaissance on the entire network topology, distinguish and remove such non-terminal nodes and then execute the ant colony algorithm; this type of reconnaissance ants have self-replication function , in the reconnaissance process, it can copy itself according to the degree N of the vertex V, that is, the number of edges, and then continue reconnaissance to other vertices respectively; 5-1 Place the corresponding number of ants Mv=Nv, Mu=Nu respectively according to the degrees of the starting point v and the ending point u; 5-2 Select a vertex V _i from the vertex set V, and judge whether the vertex V _i has been reconnaissance; 5-2-1 If V _i has no reconnaissance, when each ant detects vertex V _i , first save it in its respective routing table Ta _i , and make a reconnaissance mark; 5-2-2 If V _i has been reconnaissance, return to 5-2; 5-3 Each ant judges the degree N _i of the reconnaissance vertex V _i , 5-3-1 If n≠1, copy n-2 copies of ants and continue reconnaissance; 5-3-2 If n=1, report the vertex V _i as an abnormal point, remove this point, modify the degree N _i-1 of the previous vertex V _i- 1, update the overall network topology, and proceed to step 5- 4; 5-4 Return to the previous vertex V _i-1 along the original route according to the routing table Ta _i , if n=1, execute step 5-3-2; if n≠1, enter step 5-5; 5-5 If all the vertices have been scouted, stop the scouting and go to parameter initialization 6; otherwise go to step 5-3; Parameter initialization in step 6: initializing various parameters, such as setting the number of ants M, the pheromone intensity constant Q, the total number of iterations, and the diameter of the conduit D _c , and placing the ants at the initial position; Heuristic information calculation in Step 7: The criteria for planning the path are surgical safety and optimal path, so not only the length L _{I, J} of the blood vessel, the maximum curvature C _max and the maximum torsion T _max must be considered in path planning, but also To take into account the minimum diameter _Dmin of the vessel; The step 10 pheromone increment calculation: the pheromone update model is an important part of the random search and fast convergence of the basic ant colony algorithm; for the global optimal requirements of the problem itself, the ant circle model is adopted; considering the minimum diameter of the blood vessel and the catheter The influence of diameter in surgery is calculated according to the improved pheromone incremental model, and the ant-circumference model is modified as follows: Q is the pheromone intensity constant, which is the total amount of pheromone released by ants on the path they pass in a cycle, which affects the convergence speed of the algorithm to a certain extent; it is required that the minimum diameter of the blood vessel path D _min > D _c , L _m represents the path length that the m-th ant passes through in this cycle, and it is calculated according to the result of each ant in its routing table Ta _m . 2. the blood vessel three-dimensional path planning method based on ant colony algorithm according to claim 1, is characterized in that said step 8 probability selection: in each step path selection of ant colony algorithm, the ant m determines the following according to the ratio of the probability formula Which way to move one step at a time. 3. The blood vessel three-dimensional path planning method based on ant colony algorithm according to claim 1, characterized in that said step 9 pheromones are dynamically volatilized: the pheromone volatilization speed can be changed by temperature and humidity factors as time goes on, It is a dynamic process, the more complicated the path, the smaller the heuristic information, the faster the volatilization speed, and the less pheromone residue, so the volatilization coefficient ρ of pheromone changes with the heuristic information η _{I, J} (t) And dynamic volatility. 4. The blood vessel three-dimensional path planning method based on ant colony algorithm according to claim 1, characterized in that said step 11 pheromone update: the amount of pheromone on each path at the initial moment is equal, when the ant completes a cycle , the pheromone will gradually volatilize over time, so the pheromone concentration should be updated, and the pheromone on the corresponding path should be updated accordingly before the ant enters the next cycle; The step 12 planning end judgment: when the maximum number of iterations is reached, then exit the loop, otherwise enter the heuristic information calculation 7 and continue the loop; Result output of the step 13: arrange the output result of the routing table.