CN105167849B - A kind of blood vessel three-dimensional path planning method based on ant group algorithm - Google Patents

A kind of blood vessel three-dimensional path planning method based on ant group algorithm Download PDF

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CN105167849B
CN105167849B CN201510255090.3A CN201510255090A CN105167849B CN 105167849 B CN105167849 B CN 105167849B CN 201510255090 A CN201510255090 A CN 201510255090A CN 105167849 B CN105167849 B CN 105167849B
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ant
pheromones
blood vessel
path
maximum
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CN105167849A (en
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陈民
陈一民
高明柯
黄晨
李泽宇
张云华
许丽娟
张典华
邹波
邹一波
刘权
邹国志
高雅平
吕圣卿
陆佳辉
赵林林
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University of Shanghai for Science and Technology
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Abstract

The invention discloses a kind of blood vessel three-dimensional path planning method based on ant group algorithm, the operating procedure of this method is as follows:Vessel centerline network topology structure, 5 ant reconnaissance algorithms, 6 parameter initializations, the calculating of 7 heuristic informations, the volatilization of 8 probability selections, 9 pheromones dynamic, 10 pheromones incremental computations, 11 Pheromone updates, 12 planning end judgements, the output of 13 results are set up in the importing of 1 data, the modeling of 2 blood vessels, 3 blood vessel center line drawings, 4.This method uses ant reconnaissance algorithms on the basis of heart line drawing in the blood vessel, by improving ant group algorithm, and considers conduit diameter, length of vessel, minimum diameter, maximum curvature and the optimal path of maximum torsion assisted surgery doctor planning operation.This method puies forward the reliability of the preoperative path planning of blood vessel intervention operation, it is ensured that conduit by property, a kind of new operation pathway normative reference can be provided for surgeon.

Description

A kind of blood vessel three-dimensional path planning method based on ant group algorithm
Technical field
The present invention relates to a kind of blood vessel three-dimensional path planning method based on ant group algorithm, belong to blood vessel three-dimensional path Planning technology field.
Background technology
Blood vessel intervention operation has bleeding few, and wound is small, recovers fast advantage, therefore obtained in the treatment of vascular diseases Extensive use.The blood vessel intervention operation of the most of hospital in the whole nation still by surgeon's hand operation catheter guide wire and is borrowed at present The computer aided techniques such as the medical imaging technologies such as X-ray and virtual reality are helped to complete operation.Under limited technical conditions, from The factors such as the operation level of doctor, danger, the postoperative complications performed the operation consider, thicker sustainer conduct is generally selected in art Operation pathway, other possible optimal paths are not considered.
Blood vessel three-dimensional path planning is in three-dimensional geometry space, to find one from operative incision to lesions position Optimal path, is a kind of Global motion planning problem, is the important means of preoperative planning.The key technology of intravascular three-dimensional path planning It is the extraction of vessel centerline and the planning of guidance path.Extracting the method for center line has topological thinning method, range conversion method, gesture Can field method, method based on level set method and based on segmentation etc..In terms of navigation path planning, with the rise of intelligent algorithm, have Scholar searches the shortest path between 2 points using dijkstra's algorithm and A star algorithms in the vessel centerline of extraction.But Other characteristics of these methods in planning process not in view of blood vessel.
Ant group algorithm is one of Swarm Intelligence Algorithm in bionics, and it is 1991 by Italian scholar M.Dorigo et al. Proposed by after the inspiration of the behavior of Food Recruiment In Ants in real world.It is residual that algorithm core is that ant can be chosen with higher probability Pheromone concentration highest path is stayed, increasing ant can be attracted on this paths, form a kind of positive feedback principle To find one from food source most short path.The three-dimensional path planning based on ant group algorithm is concentrated mainly on nothing both at home and abroad at present In terms of man-machine, submersible, three-dimensional tube, robot, temporary no document applies ant group algorithm in blood vessel three-dimensional path planning Aspect.
The content of the invention
The problem of it is an object of the invention to exist for existing blood flow paths planning technology and deficiency are based on there is provided one kind The three-dimensional path planning method of ant group algorithm, this method uses ant reconnaissance algorithms on the basis of heart line drawing in the blood vessel, leads to Improvement ant group algorithm is crossed, and considers conduit diameter, length of vessel, diameter, curvature and torsion assisted surgery doctor planning hand The optimal path of art.
To reach above-mentioned purpose, idea of the invention is that:Blood vessel modeling is carried out to CTA medical image datas and center is extracted Line, ant reconnaissance algorithms are used in the vessel centerline network of given starting point on this basis, by improving ant group algorithm, Composite catheter diameter and blood vessel other characteristics, such as length of vessel, minimum diameter, maximum curvature and maximum torsion factor carry out global Path planning.
According to the design of the present invention, the present invention is realized using following technical scheme:
A kind of blood vessel three-dimensional path planning method based on ant group algorithm, it is characterised in that operating procedure is as follows:1 data are led Enter, the modeling of 2 blood vessels, 3 blood vessel center line drawings, 4 set up vessel centerline network topology structure, 5 ant reconnaissance algorithms, 6 parameters Initialization, the calculating of 7 heuristic informations, the volatilization of 8 probability selections, 9 pheromones dynamic, 10 pheromones incremental computations, 11 pheromones are more Newly, 12 planning terminate judgement, the output of 13 results.
Step 1 data are imported:Import one group of complete medicine CT A view data (DICOM);
The step 2 blood vessel modeling:The CTA view data of importing is carried out into blood vessel using the method based on 3D level sets to build Mould;
The step 3 blood vessel center line drawing:The vascular pattern of foundation is used and is based on Voronoi diagram and Eikonal side The method of journey extracts vessel centerline, and tries to achieve maximum inscribe radius of a ball R;
The step 4 sets up vessel centerline network topology structure:Network topology knot is set up according to central line pick-up result Structure, determines the quantity on node and side, and calculates distance, maximum curvature, maximum torsion and the minimum diameter in each section of path;
4-1 distances are calculated, and the length of space curve is calculated using first form curve integral.Assuming that the sky of parameterized form Half interval contour equation is
Therefore the range formula of space curve can be obtained is:
4-2 maximum curvatures are calculated, and curvature (curvature) is aiming at the tangent directional angle that some is put on curve to arc length Rotation rate calculate the curvature of each point curve on center line, center curvature of a curve reflects the degree of vascular bending, and curvature More big then vascular bending degree is bigger, will increase the difficulty that conduit passes through, and reduces the passability of blood vessel.For parametrization shape The curvature estimation of formula space curve equation is:
The curvature each put on the path is calculated according to this formula and the maximum curvature C in the path is tried to achievemax
4-3 maximum torsions are calculated, on the absolute value measure of torsion (torsion) curve neighbouring 2 points secondary normal vector it Between angle to the rate of change of arc length, the torsion on center line can reflect the degree of buckling of vessel, for basin endoluminal vascular Degreeof tortuosity be that than larger, and the bigger buckling of vessel degree of torsion is bigger, will also increase the difficulty that conduit passes through, and reduces blood Pipe passability, reduces safety coefficient.Torsion for parameterized form space curve equation is calculated as:
The torsion each put on the path is calculated according to this formula and the maximum torsion T in the path is tried to achievemax
4-4 minimum diameters are calculated, and the diameter D each put on center line can be calculated according to maximum inscribe radius of a ball R, is thus counted Calculate the minimum diameter D on each pathmin, it is assumed that a diameter of D of surgical cathetersc, it is desirable to the minimum diameter D of this section of blood flow pathsmin > DcTo ensure that conduit can pass through blood vessel;
The step 5 ant reconnaissance algorithms:Starting point is determined, the ant reconnaissance algorithms with self-replacation function are performed.
Because blood vessel network topological structure is not that loop is not present between a complete graph, some nodes, one is certainly existed A little leafs.If ant is in search process, when having gone to a leaf and not terminal, otherwise pathfinding is just directly exited, The upper node for just returning to leaf continues pathfinding.If selecting the former, although can accelerate convergence, but the shortcoming overall situation is examined Consider, exit too early;If selecting the latter, although from overall situation consideration, but efficiency of algorithm can be reduced.Therefore, the present invention is it is determined that starting After point, allow ant first to be scouted to whole network topological structure, distinguish and perform ant again after removing this kind of non-terminal leaf Group's algorithm.This kind of scouting ant possesses self-replacation function, during scouting can according to summit V number of degrees N, i.e. side number, Corresponding self-replacation (in addition to the side accessed), then respectively toward the continuation scouting of other summits.
5-1 places the ant Mv=Nv, Mu=Nu of respective amount according to starting point v and terminal the u number of degrees respectively;
Every ant of 5-2 scouts summit ViWhen be first saved to respective routing table TaiIn, do scouting mark;
Every ant of 5-3 judges the summit V scoutediNumber of degrees Ni,
If 5-3-1 n ≠ 1, n-2 ant copy is replicated, continues to scout;
If 5-3-2 n=1, summit V is reportediFor abnormity point, the point is rejected, a summit V thereon is changedi-1The number of degrees Ni-1, overall network topology structure is updated, into step 5-4;
5-4 is according to routing table TaiA summit V is returned to along former roadi-1If n=1 performs step 5-3-2;If n ≠ 1, then into step 5-5;
If 5-5 has been scouted on all summits, terminate and scout, into parameter initialization 6;Otherwise step 5-3 is entered;
Step 6 parameter initialization:Each parameter is initialized, ant quantity M, pheromones intensity constant Q, iteration are such as set Sum, conduit diameter Dc, ant is placed in initial position;
Step 7 heuristic information is calculated:Heuristic function has important shadow to convergence and stability Ring, in ant group algorithm, heuristic information η is usually the inverse ratio of distance between two points, i.e. 1/LI, J, path planning of the present invention Standard is that operation safety and path are optimal, therefore the length L of blood vessel is not only considered in path planningI, J, maximum curvature Cmax With maximum torsion Tmax, it is contemplated that the minimum diameter D of blood vesselmin, heuristic information is defined as
ηI, J(t) represent that t node I (x, y, z) arrives node J (x ', y ', z ') heuristic information;X, y, z and x ', y ', Z ' is the three-dimensional coordinate of point;DminRepresent the minimum diameter of this paths, DcRepresent conduit diameter, it is desirable to Dmin> Dc;LI, JRepresent This path length;CmaxRepresent the maximum curvature in this section of path, Tmax, represent the maximum torsion in this section of path.
Step 8 probability selection:Provided with M ant, n node, ai(t) represent that t is located at certain node I ant Quantity, thenIn each step Path selection of ant group algorithm, ant m according to probability determine next step toward which Bar is moved on road.
Represent that t ant m is moved to point J probability, allowed by point Im={ 1,2 ..., n }-tmTable Show the node that ant next step can be selected, tmRepresent the node that ant once accessed;α represents pheromones heuristic factor, table Show residual risk element amount the role of when ant move, value is bigger to illustrate that ant is more likely to select other ants processes Collaboration capabilities between path, ant are stronger;β represents desired value heuristic factor, shows heuristic information when ant selects path By attention degree, be worth bigger, state metastatic rule is closer to greedy rule.τI, J(t) represent t point I to point J paths Pheromones.
Step 9 pheromones are dynamically volatilized:Pheromones evaporation rate can be over time by temperature, humidity etc. Factor and change, be a process dynamically changed, more complicated path, heuristic information is smaller, evaporation rate is faster, information Element residual it is fewer, therefore pheromones volatility coefficient ρ with heuristic information ηI, J(t) change and dynamic is volatilized, all ants After reaching home, calculated by following relation,
ρI, J(t) volatility coefficient of the t on I to J paths, η are representedI, J(t) information on t I to J paths is represented Element,The heuristic information on all paths of t is represented, k represents certain ant in t paths traversed number.
The step 10 pheromones incremental computations:Pheromone update model be Basic Ant Group of Algorithm random search with it is quick Restrain important step.The optimum of overall situation requirement of the present invention for problem in itself, using all models of ant;It is minimum straight in view of blood vessel The influence of footpath and conduit diameter in operation, all models of modification ant are as follows:
Q is pheromones intensity constant, is the total of the pheromones that ant discharges in paths traversed in a cycle Amount, affects convergence of algorithm speed to a certain extent;It is required that the minimum diameter D of blood flow pathsmin> Dc, LmRepresent m only Ant paths traversed length in this circulation, according to every ant in its routing table TamIn result calculate.
Step 11 Pheromone update:Pheromones amount on each path of initial time is equal, when ant completes one After secondary circulation, pheromones can gradually volatilize over time, therefore pheromone concentration will be updated, and enter in ant Following renewal is done to the pheromones in respective paths before entering next circulation:
τI, J(t+1)=(1- ρ) τI, J(t)+ΔτI, J(t, t+1)
ρ (O < ρ < 1) is the dynamic volatility coefficient of pheromones, and 1- ρ are the pheromones dynamically residual factors,Table Show the pheromones amount that the m ant leaves in this circulation on path (I, J), Δ τI, J(t, t+1) represents that this circulation is worked as In the pheromones increment that leaves of all ants by path (I, J).
Step 12 planning terminates to judge:When reaching that maximum iteration then exits circulation, otherwise enter heuristic letter Breath calculates 7, continues cycling through;
The step 13 result output:Arrange routing table output result.
The present invention compared with prior art, substantive distinguishing features and remarkable advantage is obviously protruded with following:
(1) ant group algorithm is applied to blood vessel three-dimensional path planning technical field by the present invention.
(2) present invention improves over the heuristic information model in ant group algorithm, conduit diameter, blood vessel have been considered long Degree, minimum diameter, maximum curvature and maximum torsion, improve the reliability of preoperative path planning, it is ensured that conduit passes through property.
(3) present invention improves over the pheromones incremental model in ant group algorithm, combine blood vessel minimum diameter and conduit is straight Influence of the footpath in planning, accelerates convergence of algorithm.
Brief description of the drawings
Fig. 1 is a kind of flow chart of the blood vessel three-dimensional path planning method based on ant group algorithm of the present invention.
Embodiment
Embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings.
Embodiment one:
Referring to Fig. 1, a kind of blood vessel three-dimensional path planning method based on ant group algorithm, it is characterised in that operating procedure is such as Under, the importing of 1 data, the modeling of 2 blood vessels, 3 blood vessel center line drawings, 4 are set up vessel centerline network topology structure, 5 ants and scouted Algorithm, 6 parameter initializations, the calculating of 7 heuristic informations, 8 probability selections, 9 pheromones dynamic volatilization, 10 pheromones incremental computations, 11 Pheromone updates, 12 planning terminate judgement, the output of 13 results.
Step 1 data are imported:Import one group of complete medicine CT A view data (DICOM);
The step 2 blood vessel modeling:The CTA view data of importing is carried out into blood vessel using the method based on 3D level sets to build Mould;
The step 3 blood vessel center line drawing:The vascular pattern of foundation is used and is based on Voronoi diagram and Eikonal side The method of journey extracts vessel centerline, and tries to achieve maximum inscribe radius of a ball R;
The step 4 sets up vessel centerline network topology structure:Network topology knot is set up according to central line pick-up result Structure, determines the quantity on node and side, and calculates distance, maximum curvature, maximum torsion and the minimum diameter in each section of path;
4-1 distances are calculated, and the length of space curve is calculated using first form curve integral;
4-2 maximum curvatures are calculated, and are calculated according to the curvature estimation formula of parameterized form space curve equation on the path The curvature each put and the maximum curvature C for trying to achieve the pathmax
4-3 maximum torsions are calculated, and are calculated according to the torsion calculation formula of parameterized form space curve equation on the path The torsion each put and the maximum torsion T for trying to achieve the pathmax
4-4 minimum diameters are calculated, and the diameter D each put on center line is calculated according to maximum inscribe radius of a ball R, is thus calculated Minimum diameter D on each pathmin, it is assumed that a diameter of D of surgical cathetersc, then the minimum diameter D of this section of blood flow paths is requiredmin > DcTo ensure that conduit can pass through blood vessel.
The step 5 ant reconnaissance algorithms:It is determined that after starting point, allowing ant first to be detectd to whole network topological structure Examine, distinguish and perform ant group algorithm again after removing this kind of non-terminal leaf.This kind of scouting ant possesses self-replacation function, Can be according to summit V number of degrees N, i.e. side number, corresponding self-replacation (in addition to the side accessed), then distinguish during scouting Continue to scout toward other summits;
5-1 places the ant Mv=Nv, Mu=Nu of respective amount according to starting point v and terminal the u number of degrees respectively;
5-2 selects a summit V from vertex set Vi, judge summit ViWhether scout;
If 5-2-1 ViDo not scout, then every ant scouts summit ViWhen be first saved to respective routing table TajIn, Do scouting mark;
If 5-2-2 ViIt has been scouted that, then return to 5-2;
Every ant of 5-3 judges the summit V scoutediNumber of degrees Ni,
If 5-3-1 n ≠ 1, n-2 ant copy is replicated, continues to scout;
If 5-3-2 n=1, summit V is reportediFor abnormity point, the point is rejected, a summit V thereon is changedi-1The number of degrees Ni-1, overall network topology structure is updated, into step 5-4;
5-4 is according to routing table TaiA summit V is returned to along former roadi-1If n=1 performs step 5-3-2;If n ≠ 1, then into step 5-5;
If 5-5 has been scouted on all summits, terminate and scout, into parameter initialization 6;Otherwise step 5-3 is entered;
Step 6 parameter initialization:Each parameter is initialized, ant quantity M, pheromones intensity constant Q, iteration are such as set Sum, conduit diameter Dc, ant is placed in initial position.
Embodiment two:The present embodiment and embodiment one are essentially identical, and special feature is as follows:
Step 7 heuristic information is calculated:The standard of path planning of the present invention is that operation safety and path are optimal, therefore The length L of blood vessel is not only considered in path planningI, J, maximum curvature CmaxWith maximum torsion Tmax, it is contemplated that blood vessel Minimum diameter Dmin
Step 8 probability selection:In each step Path selection of ant group algorithm, ant m according to new probability formula ratio Rate determines next step toward moving on which bar road;
Step 9 pheromones are dynamically volatilized:Pheromones evaporation rate can be over time by temperature, humidity etc. Factor and change, be a process dynamically changed, more complicated path, heuristic information is smaller, evaporation rate is faster, information Element residual it is fewer, therefore pheromones volatility coefficient ρ with heuristic information ηI, J(t) change and dynamic is volatilized.
Embodiment three:The present embodiment and embodiment two are essentially identical, and special feature is as follows:
The step 10 pheromones incremental computations:Pheromone update model be Basic Ant Group of Algorithm random search with it is quick Restrain important step.The optimum of overall situation requirement of the present invention for problem in itself, using all models of ant;It is minimum straight in view of blood vessel The influence of footpath and conduit diameter in operation, is calculated according to pheromones incremental model after improvement;
Step 11 Pheromone update:Pheromones amount on each path of initial time is equal, when ant completes one After secondary circulation, pheromones can gradually volatilize over time, therefore pheromone concentration will be updated, and enter in ant Corresponding renewal is done to the pheromones in respective paths before entering next circulation;
Step 12 planning terminates to judge:When reaching that maximum iteration then exits circulation, otherwise enter heuristic letter Breath calculates 7, continues cycling through;
The step 13 result output:Arrange routing table output result.

Claims (4)

1. a kind of blood vessel three-dimensional path planning method based on ant group algorithm, it is characterised in that operating procedure is as follows:1 data are led Enter, the modeling of 2 blood vessels, 3 blood vessel center line drawings, 4 set up vessel centerline network topology structure, 5 ant reconnaissance algorithms, 6 parameters Initialization, the calculating of 7 heuristic informations, the volatilization of 8 probability selections, 9 pheromones dynamic, 10 pheromones incremental computations, 11 pheromones are more Newly, 12 planning terminate judgement, the output of 13 results;
Step 1 data are imported:Import one group of complete medicine CT A view data;
The step 2 blood vessel modeling:The CTA view data of importing is subjected to blood vessel modeling using the method based on 3D level sets;
The step 3 blood vessel center line drawing:The vascular pattern of foundation is used based on Voronoi diagram and Eikonal equations Method extracts vessel centerline, and tries to achieve maximum inscribe radius of a ball R;
The step 4 sets up vessel centerline network topology structure:Network topology structure is set up according to central line pick-up result, really Determine the quantity on node and side, and calculate distance, maximum curvature, maximum torsion and the minimum diameter in each section of path;
4-1 distances are calculated, and the length of space curve is calculated using first form curve integral;
4-2 maximum curvatures are calculated, and calculate each on the path according to the curvature estimation formula of parameterized form space curve equation The curvature of point and the maximum curvature C for trying to achieve the pathmax
4-3 maximum torsions are calculated, and calculate each on the path according to the torsion calculation formula of parameterized form space curve equation The torsion of point and the maximum torsion T for trying to achieve the pathmax
4-4 minimum diameters are calculated, and the diameter D each put on center line is calculated according to maximum inscribe radius of a ball R, each road is thus calculated Minimum diameter D on footpathmin, it is assumed that a diameter of D of surgical cathetersc, then the minimum diameter D of this section of blood flow paths is requiredmin> DcWith Ensure that conduit can pass through blood vessel;
The step 5 ant reconnaissance algorithms:It is determined that after starting point, allow ant first to be scouted to whole network topological structure, Distinguish and perform ant group algorithm again after removing this kind of non-terminal leaf;This kind of scouting ant possesses self-replacation function, is detecing Can be according to summit V number of degrees N, i.e. side number, corresponding self-replacation during examining, then continue toward other summits to scout respectively;
5-1 places the ant Mv=Nv, Mu=Nu of respective amount according to starting point v and terminal the u number of degrees respectively;
5-2 selects a summit V from vertex set Vi, judge summit ViWhether scout;
If 5-2-1 ViDo not scout, then every ant scouts summit ViWhen be first saved to respective routing table TaiIn, detect Examine mark;
If 5-2-2 ViIt has been scouted that, then return to 5-2;
Every ant of 5-3 judges the summit V scoutediNumber of degrees Ni,
If 5-3-1 n ≠ 1, n-2 ant copy is replicated, continues to scout;
If 5-3-2 n=1, summit V is reportediFor abnormity point, the point is rejected, a summit V thereon is changedi-1Number of degrees Ni-1, more New overall network topology structure, into step 5-4;
5-4 is according to routing table TaiA summit V is returned to along former roadi-1If n=1 performs step 5-3-2;If n ≠ 1, enter Enter step 5-5;
If 5-5 has been scouted on all summits, terminate and scout, into parameter initialization 6;Otherwise step 5-3 is entered;
Step 6 parameter initialization:Each parameter is initialized, ant quantity M is such as set, pheromones intensity constant Q, iteration is total Number, conduit diameter Dc, ant is placed in initial position;
Step 7 heuristic information is calculated:The standard of this path planning is that operation safety and path are optimal, therefore path planning In not only will consider blood vessel length LI, J, maximum curvature CmaxWith maximum torsion Tmax, it is contemplated that the minimum diameter of blood vessel Dmin
The step 10 pheromones incremental computations:Pheromone update model is the random search and Fast Convergent of Basic Ant Group of Algorithm Important step;For the optimum of overall situation requirement of problem in itself, using all models of ant;It is straight in view of blood vessel minimum diameter and conduit Influence of the footpath in operation, is calculated according to pheromones incremental model after improvement, and all models of modification ant are as follows:
Q is pheromones intensity constant, is the total amount for the pheromones that ant discharges in paths traversed in a cycle, Convergence of algorithm speed is affected to a certain extent;It is required that the minimum diameter D of blood flow pathsmin> Dc, LmRepresent that the m ant exists Paths traversed length in this time circulating, according to every ant in its routing table TamIn result calculate.
2. the blood vessel three-dimensional path planning method according to claim 1 based on ant group algorithm, it is characterised in that the step Rapid 8 probability selection:In each step Path selection of ant group algorithm, ant m determines that next step is past according to the ratio of new probability formula Any moved on bar road.
3. the blood vessel three-dimensional path planning method according to claim 1 based on ant group algorithm, it is characterised in that the step Rapid 9 pheromones are dynamically volatilized:Pheromones evaporation rate can over time by temperature, humidity factor and change, be one The individual process dynamically changed, more complicated path, heuristic information is smaller, and evaporation rate is faster, and pheromones residual is fewer, therefore The volatility coefficient ρ of pheromones is with heuristic information ηI, J(t) change and dynamic is volatilized.
4. the blood vessel three-dimensional path planning method according to claim 1 based on ant group algorithm, it is characterised in that the step Rapid 11 Pheromone update:Pheromones amount on each path of initial time is equal, after ant completes one cycle, pheromones It can gradually volatilize, therefore pheromone concentration will be updated over time, enter next circulation in ant The preceding pheromones in respective paths do corresponding renewal;
Step 12 planning terminates to judge:When reaching that maximum iteration then exits circulation, otherwise into heuristic information meter 7 are calculated, is continued cycling through;
The step 13 result output:Arrange routing table output result.
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