CN111597720B - Interventional operation guide wire modeling method considering large spatial deformation and application thereof - Google Patents

Interventional operation guide wire modeling method considering large spatial deformation and application thereof Download PDF

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CN111597720B
CN111597720B CN202010424821.3A CN202010424821A CN111597720B CN 111597720 B CN111597720 B CN 111597720B CN 202010424821 A CN202010424821 A CN 202010424821A CN 111597720 B CN111597720 B CN 111597720B
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guide wire
beam unit
unit
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CN111597720A (en
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胡陟
虞磊
戴贤萍
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Anzhi Shanghai Technology Co ltd
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Shanghai University of Engineering Science
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
    • A61B2034/101—Computer-aided simulation of surgical operations
    • A61B2034/102—Modelling of surgical devices, implants or prosthesis
    • A61B2034/104—Modelling the effect of the tool, e.g. the effect of an implanted prosthesis or for predicting the effect of ablation or burring
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses an interventional operation guide wire modeling method considering large space deformation and application thereof, wherein the method comprises the following steps: discretizing the guidewire into a finite number of beam elements; the single beam unit takes the node displacement vector and the slope vector of the displacement field as generalized coordinates, the guide wire deformation and the guide wire section rotation are described through the node displacement vector and the node slope vector, and the expression of the total kinetic energy and the total potential energy of the single beam unit is obtained through derivation; combining the total kinetic energy, the total potential energy and the elastic force of the single beam unit by utilizing a Lagrange equation to obtain a kinetic equation of the single beam unit; obtaining the kinetic equation of the whole guide wire by assembling the kinetic equations of all the units; combining the following formula with a dynamic equation of the whole guide wire to obtain the stress and position information of all beam units of the whole guide wire through the position information of one end of the guide wire;
Figure DDA0002498264200000011
δ＝‖r‑R‖+rb‑rt. The method has the advantages of small data processing amount, high modeling speed, capability of truly simulating the guide wire and good application prospect.

Description

Interventional operation guide wire modeling method considering large spatial deformation and application thereof
Technical Field
The invention belongs to the technical field of guide wire modeling, and relates to an interventional operation guide wire modeling method considering large spatial deformation and application thereof.
Background
Minimally invasive cardiovascular interventional surgery is widely used due to the advantages of reducing postoperative pain, shortening recovery time, causing small trauma and the like, wherein a guide wire is used as a key interventional instrument and needs to go deep to the position of stenosis or obstruction of the wall of a coronary artery cavity of the heart. The virtual reality technology is applied to interventional surgery as a key technology for improving the telepresence, a virtual reality environment which is completely consistent with the real surgery system environment is reconstructed through the virtual reality technology, and an operator directly interacts with the virtual reality environment through the human-computer interaction equipment to immediately generate sense feelings such as vision, hearing, touch, force sense and the like.
The flexible cable model expression is the basis for interventional operation simulation in a virtual environment, the model not only needs to support the geometric characteristics of the guide wire, but also needs to support the physical characteristic expression, and the specific real-time requirement of a virtual reality system is met. Guidewires are characterized by a length that is much greater than their diameter. Because the shape of the guide wire is not fixed as a rigid body, but changes along with different external conditions, the modeling difficulty is high.
In the interventional operation process, the guide wire is in moving contact with the vessel wall, so that large-scale friction stress exists, and the real-time simulation of the physical deformation characteristics of the main end by using a virtual reality technology is challenging work. The detection of the collision of the surgical instrument with the vessel wall is time-consuming, and the quality of the collision detection algorithm determines the overall performance of the system to a large extent.
The guide wire performs a large range of motion during operation in interventional procedures, which must be described and calculated using kinetic methods. The parts which must take into account the influence of elastic deformation are treated as flexible bodies, finite element discretization is carried out, and limited freedom degrees are reserved. For the real-time simulation of the physical deformation of a slender object such as a guide wire, the guide wire is generally discretized along the length direction, and the deformation and stress of each infinitesimal element are analyzed.
The existing interventional guide wire modeling technology has the following defects:
1. the lack of an efficient physical model;
the method is represented by a series of mass points and a linear spring connecting the mass points, has stronger real-time performance, but has low accuracy due to high simplification of the model.
A discrete elastic rod model established by using a Kirchhoff theory and a cosstrat theory can also be used for simulating the motion of a guide wire in an interventional instrument, the cosstrat elastic rod model utilizes the Cosserat theory, the cross section of an elastic rod is regarded as a rigid body by the theory, physical parameters such as axial line strain, bending shear strain and the like of the elastic rod are considered, a continuous energy expression of the rod is derived on the basis of the theory, the energy of each unit of the rod is calculated by the dispersion of the rod, a dynamic differential equation of the rod is further obtained by a Lagrange equation, the differential equation is numerically solved to obtain the dynamic change of the guide wire, the cosstrat elastic rod model can simulate any extra-large bending deformation of a one-dimensional elastic body, but the bending rigidity of the guide wire cannot be considered by the rod model, and simultaneously, because the deformation between connected nodes is small deformation, the large deformation of the flexibility of the body needs to be divided into a denser grid to obtain a high-precision solution, but the center line of the guide wire after the dispersion is a broken line. The Kirchhoff elastic rod is a special case of a Cosserat elastic rod model neglecting central line expansion and section truncation deformation, and is suitable for the quasi-statics problem of a one-dimensional slender elastomer.
Compared with a rod model, the beam model can consider the bending stiffness of the guide wire, and for different simplified conditions, dynamic models with different approximation degrees such as a Bernoulli beam or a Timoshenko beam are established, but the two beam models are applied on the premise of being based on a small deformation hypothesis, and have obvious errors on large deformation movement of the guide wire.
2. Detecting a collision;
the blood vessels not only play a role in restricting the motion of the guide wires, but also have moving contact when the guide wires move along the blood vessels, and in order to accurately describe the mechanical behavior of the contact between the guide wires and the blood vessels, the guide wires are usually required to be scattered into a dense grid to ensure the convergence of calculation. The common practice of rod/beam-vessel contact detection is to arrange a contact detection point in the rod/beam unit to see if it collides with the pipe, and AABB (axial-aligned bounding box) is a typical method. The AABB bounding box is actually a cuboid detection box, a series of AABB bounding boxes are constructed through adjacent pipeline nodes, and the method is simple in construction. By cycling through the bounding boxes, determining which bounding box the touch detection point is located in, and calculating its projected point on the axis of the vessel, this step is very time consuming, as all bounding boxes must be examined in sequence from the top to the bottom of the vessel. And finally, calculating the contact force applied to the rod/beam unit by calculating the relative embedding depth and speed of the detection point and the contact surface.
Therefore, the development of the guide wire modeling method which has small data processing amount and high modeling speed and can truly simulate the large deformation motion of the guide wire is of great practical significance.
Disclosure of Invention
The invention aims to overcome the defects that the prior art cannot really simulate large deformation movement of a guide wire, and has large data processing capacity and low modeling speed, and provides a guide wire modeling method which has small data processing capacity and high modeling speed and can really simulate the large deformation movement of the guide wire.
In order to achieve the purpose, the invention provides the following technical scheme:
an interventional operation guide wire modeling method considering large space deformation is used for electronic equipment and comprises the following steps:
(1) discretizing the guidewire into a finite number of beam elements;
(2) the single beam unit takes the node displacement vector and the slope vector of the displacement field as generalized coordinates, the guide wire deformation and the guide wire section rotation are described through the node displacement vector and the node slope vector, and an expression of the total kinetic energy and the total potential energy of the single beam unit is obtained through derivation;
(3) combining the total kinetic energy, the total potential energy and the elastic force of the single beam unit by utilizing a Lagrange equation to obtain a kinetic equation of the single beam unit;
(4) obtaining a dynamic equation of the whole guide wire by grouping the dynamic equations of all the units, wherein the dynamic equation of the whole guide wire reflects the mutual relation of the forces borne by all the action points of the whole guide wire;
(5) combining the following formula with the dynamic equation of the whole guide wire obtained in the step (4), namely acquiring the stress and position information of all beam units of the whole guide wire through the position information of one end of the guide wire;
Figure BDA0002498264180000031
δ＝‖r-R‖+rb-rt；
wherein f isnIs the normal contact force between the guide wire-beam unit and the tube wall, and has the unit of N, delta,
Figure BDA0002498264180000041
k. e and c are a collision invasion depth, a relative invasion speed, a collision rigidity coefficient and a collision damping coefficient of the beam unit in units of mm, mm/s, N/m and N/(mm/s), respectively, e is a collision invasion index of the beam unit, which is a constant, R, R, RtAnd rbThe unit of the distance from the corresponding detection point of the beam unit to the origin, the distance from the corresponding projection point of the detection point to the origin, the radius of the pipeline and the radius of the beam unit are respectively mm, mm and mm.
The method comprises the steps of firstly dispersing a research object into a limited number of units by adopting an absolute node coordinate method to model a guide wire flexible body, specifically, establishing a kinetic equation of the units by deducing a kinetic energy expression and a potential energy expression of the units and combining a Lagrange equation, and then obtaining the kinetic equation of the whole flexible body by assembling all the unit kinetic equations. The invention models the guide wire based on the absolute node coordinate beam unit theory and Lagrange multiplier method, because the absolute node coordinate beam unit modeling method adopts nonlinear Green strain to represent geometric nonlinearity in the relation of strain and deformation gradient, for the application scene that the deformation of the guide wire is large enough to cause the displacement of the structure to generate large change (namely, the force-displacement relation is not linear any more), the geometric nonlinearity description of the absolute node coordinate beam unit theory is accurate, is suitable for describing large displacement and large deformation movement, and can be directly used for truly simulating the curve movement and the caused bending deformation of the guide wire of the slender elastic body in the operation process. In addition, the invention adopts the bounding boxes arranged along the pipeline axis to replace AABB bounding boxes to carry out guide wire-blood vessel contact detection, can ensure all contact points to be detected, simplifies the contact detection from a three-dimensional problem to a one-dimensional problem, improves the contact detection efficiency, obtains the mutual relation between the stress and the position of all beam units of the whole guide wire by combining the dynamic equation of the guide wire and the guide wire-blood vessel collision detection equation, and obtains the stress and the position information of all beam units of the whole guide wire by obtaining the position or the stress of any point of the guide wire.
As a preferred technical scheme:
according to the interventional operation guide wire modeling method considering the large spatial deformation, the position vector r of any point in the single beam unit can be represented by the beam unit generalized coordinate e and the beam unit shape function N, and the beam unit based on the absolute node coordinate is specifically shown in FIG. 1;
r(X,t)＝N(X)e(t)；
wherein X is the coordinates of the material at the unit point in mm, and t is time in s;
the absolute displacement u of any point within a single beam element can be expressed as;
Figure BDA0002498264180000051
wherein beam unit nodal displacement
Figure BDA0002498264180000052
In units of mm, e0The generalized coordinates of the nodes in the initial configuration of the beam unit.
The interventional operation guide wire modeling method considering the large spatial deformation is characterized in that the generalized coordinate e of the beam unit is as follows:
e＝[(e1)T (e2)T]T；
the generalized coordinates of the beam unit nodes comprise space absolute position vectors and material derivatives thereof, and each node comprises 6 generalized coordinates;
Figure BDA0002498264180000053
Figure BDA0002498264180000054
Figure BDA0002498264180000055
wherein L is the length of the beam unit in the initial configuration and is in mm, x is the substance coordinate of the beam unit and is in mm,
Figure BDA0002498264180000056
is a dimensionless unit.
The interventional surgical guide wire modeling method considering the large spatial deformation is characterized in that the beam element shape function N is:
N＝[N1I N2I N3I N4I]；
wherein N is1、N2、N3And N4The definition is as follows:
Figure BDA0002498264180000061
Figure BDA0002498264180000062
wherein L is the length of the beam element in the initial configuration, and has a unit ofmm, beam unit parameters
Figure BDA0002498264180000063
And x epsilon (0, L) is the substance coordinate of the beam unit, and the unit is mm.
The interventional operation guide wire modeling method considering the large space deformation has the advantages that the kinetic energy T of the beam uniteThe expression is as follows:
Figure BDA0002498264180000064
where ρ is the density of the material in kg/mm3，MeIs a unit mass array, V0、
Figure BDA0002498264180000065
And
Figure BDA0002498264180000066
the units of (A) are mm/s, mm/s and mm/s respectively;
the strain energy U expression of the beam unit is as follows:
Figure BDA0002498264180000067
EA and EJ are respectively axial unit stiffness and transverse unit stiffness, the units of EA and EJ are respectively N/mm and N/mm, epsilon and kappa are respectively axial strain and transverse curvature, and the epsilon and kappa are dimensionless units;
Figure BDA0002498264180000068
Figure BDA0002498264180000069
wherein the content of the first and second substances,
Figure BDA00024982641800000610
and
Figure BDA00024982641800000611
the slope of the beam curve and the slope of the beam curve, respectively, are dimensionless units.
According to the interventional operation guide wire modeling method considering the large spatial deformation, the total kinetic energy and the total potential energy of a single beam unit are respectively formed by accumulating the kinetic energy and the potential energy of the beam unit;
total kinetic energy T of beam unitANCAnd total potential energy UANCThe expression of (c) is:
Figure BDA0002498264180000071
Figure BDA0002498264180000072
wherein e isiIs the generalized coordinate vector of the ith node;
elastic force Q corresponding to the elastic energyKThe expression is as follows:
Figure BDA0002498264180000073
using Lagrange's equation in combination with TANC、UANCAnd QkAnd (3) obtaining a dynamic equation of a single beam unit:
Figure BDA0002498264180000074
wherein M is a system mass array, e is a system generalized coordinate vector, sigma is a Laplace multiplier vector, C (e, t) is a constraint equation, and CeFor derivation of the constraint equation to generalized coordinates, QeFor external force acting on the beam unit, the system motion differential equation and algebraic constraint equation set are a group, and the differential equation of the group is solved by a backward difference method, namely backward differential equation for mullasNumerical equations.
According to the interventional operation guide wire modeling method considering the large spatial deformation, the blood vessel is divided into intervals along the generatrix thereof, the arc length coordinates of each interval pipeline node are obtained, meanwhile, the contact detection point is arranged in the center line of the beam unit, whether the contact detection point collides with the pipeline is judged, and as the guide wire moves in the pipeline, which pipe section the detection point is located in is determined according to the arc length coordinate s corresponding to the contact detection point in the beam unit, the condition required to be met is that s1 is not less than s2, wherein s, s1 and s2 are respectively the arc length coordinates of the contact point and two adjacent pipeline nodes, and are particularly shown in FIG. 2;
the method for calculating the projection points of the contact detection points on the pipeline axis is shown in fig. 3, beam nodes P1 and P2 are respectively located in pipeline sections s1 and s2, the corresponding projection points are A1 and A2, the detection point C1 is located in units P1 and P2, the corresponding projection point is B1, and as B1C1 is perpendicular to the pipeline central axis, the arc length coordinate s of B1 meets the requirement that the arc length coordinate s of B1 is equal to the central axis of the pipeline
f(s)＝(R-r(s))·r′(s)＝0；
Wherein R and R are the distances from the detection point C1 and the projection point B1 to the origin respectively, R' is the tangent vector of the point B1, the above formula is a nonlinear equation, and the Newton-Raphson method can be used for iterative solution.
According to the interventional operation guide wire modeling method considering the large spatial deformation, when delta is less than or equal to 0, fn＝0。
The present invention also provides an electronic device comprising one or more processors, one or more memories, and one or more programs;
the one or more programs are stored in the memory and when executed by the processor cause the electronic device to perform a method of interventional surgical guidewire modeling that accounts for spatially large deformations as described above.
The specific structure of the electronic device can be designed by referring to the following description: an integrated circuit board for realizing electrical control is arranged in the electronic equipment, four encoders, four motors and corresponding drivers are combined to form 4 sets of direct current servo drive units, all servo units are in communication connection by adopting a CAN bus and are converted into USB bus communication through a CAN card, and finally are connected with a computer, and the other 3 encoders are connected with a data acquisition card and transmit data to the computer by the data acquisition card;
the computer is provided with graphic rendering software, when processing is carried out, a Central Processing Unit (CPU) of the computer loads data (including some geometric data (vertex coordinates, normal vectors, texture coordinates, textures and the like)) into a graphics card (GPU), then rendering information is set through the GPU (graphics processing unit), and the GPU starts rendering, wherein vertex coordinate transformation, illumination, clipping, projection and screen mapping are carried out in the GPU. The scope of the invention is not limited thereto, but only by one possible solution.
Furthermore, the present invention also provides a computer storage medium comprising computer instructions which, when run on an electronic device, cause the electronic device to perform an interventional surgical guidewire modeling method considering spatially large deformations as described above. When the computer storage medium runs computer instructions through electronic equipment, collision detection, collision response, physical modeling of the guide wire, rendering of the guide wire and the blood vessel and reading in of data can be carried out, and real-time motion simulation of the guide wire in the blood vessel is completed.
Has the advantages that:
(1) the interventional operation guide wire modeling method considering the large spatial deformation adopts the absolute node coordinate beam unit theory to participate in modeling, adopts nonlinear Green strain to represent geometric nonlinearity in a relation between strain and deformation gradient, is suitable for describing large displacement and large deformation movement, and can be directly used for truly simulating the curve movement and the caused bending deformation of the guide wire of a slender elastic body in the operation process;
(2) according to the interventional operation guide wire modeling method considering the large spatial deformation, the bounding boxes arranged along the pipeline axis are adopted to replace AABB bounding boxes to carry out beam-pipeline contact detection, all contact points can be detected, the contact detection is simplified from a three-dimensional problem to a one-dimensional problem, the data processing amount is greatly reduced, and the contact detection efficiency is improved;
(3) the electronic equipment disclosed by the invention is simple in structure, low in cost, capable of rapidly and accurately carrying out interventional operation guide wire modeling and good in application prospect.
Drawings
FIG. 1 is a schematic view of a single beam unit of the present invention;
FIG. 2 is a schematic diagram of a beam contact detection algorithm of the present invention;
FIG. 3 is a schematic view of the projected point of the computed contact detection point of the present invention on the pipeline axis;
FIG. 4 is a flow chart of an interventional surgical guidewire modeling method of the present invention that accounts for spatially large deformations;
FIG. 5 is a schematic structural diagram of an electronic device according to the present invention;
FIG. 6 is a logic diagram of an electronic device according to the present invention.
Detailed Description
The following further describes the embodiments of the present invention with reference to the attached drawings.
Example 1
An interventional operation guide wire modeling method considering large spatial deformation is used for an electronic device, and the steps are shown in fig. 4, and specifically include:
(1) discretizing the guide wire into a limited number of beam elements, a single beam element as shown in fig. 1;
(2) the single beam unit takes the node displacement vector and the slope vector of the displacement field as generalized coordinates, the guide wire deformation and the guide wire section rotation are described through the node displacement vector and the node slope vector, and the expressions of the total kinetic energy and the total potential energy of the single beam unit are obtained through derivation, and the expressions are specifically as follows:
the position vector r of any point in a single beam unit can be represented by a beam unit generalized coordinate e and a beam unit shape function N;
r(X,t)＝N(X)e(t)；
wherein X is the material coordinate at the unit point in mm, t is time in s;
the absolute displacement u of any point within a single beam element can be expressed as;
Figure BDA0002498264180000101
wherein the beam unit node displacement
Figure BDA0002498264180000102
In units of mm, e0The node generalized coordinate is the node generalized coordinate when the beam unit is initially configured;
the beam element generalized coordinates e are:
e＝[(e1)T (e2)T]T；
the generalized coordinates of the beam unit nodes comprise space absolute position vectors and material derivatives thereof, and each node comprises 6 generalized coordinates;
Figure BDA0002498264180000103
Figure BDA0002498264180000104
Figure BDA0002498264180000105
wherein, L is the length of the beam unit in the initial configuration and has a unit of mm, x belongs to (0, L) and is the substance coordinate of the beam unit and has a unit of mm,
Figure BDA0002498264180000111
is a dimensionless unit;
the beam element shape function N is:
N＝[N1I N2I N3I N4I]；
wherein N is1、N2、N3And N4The definition is as follows:
Figure BDA0002498264180000112
Figure BDA0002498264180000113
wherein L is the length of the beam unit in the initial configuration, and the unit is mm, and the beam unit parameter
Figure BDA0002498264180000114
x is an element (0, L) of the beam unit, and the unit of x is mm;
kinetic energy T of beam uniteThe expression is as follows:
Figure BDA0002498264180000115
where ρ is the density of the material in kg/mm3，MeIs a unit mass array, V0、
Figure BDA0002498264180000116
And
Figure BDA0002498264180000117
the units of (A) are mm/s, mm/s and mm/s respectively;
the strain energy U expression of the beam unit is as follows:
Figure BDA0002498264180000118
EA and EJ are respectively axial unit stiffness and transverse unit stiffness, the units of EA and EJ are respectively N/mm and N/mm, epsilon and kappa are respectively axial strain and transverse curvature, and the epsilon and kappa are dimensionless units;
Figure BDA0002498264180000119
Figure BDA0002498264180000121
wherein the content of the first and second substances,
Figure BDA0002498264180000122
and
Figure BDA0002498264180000123
the slope of the beam curve and the slope of the beam curve are respectively, and are dimensionless units;
total kinetic energy T of beam unitANCAnd total potential energy UANCThe expression of (a) is:
Figure BDA0002498264180000124
Figure BDA0002498264180000125
wherein e isiIs the ith node generalized coordinate vector;
elastic force Q corresponding to elastic energyKThe expression is as follows:
Figure BDA0002498264180000126
(3) the lagrangian equation is utilized to combine the total kinetic energy, the total potential energy and the elastic force of a single beam unit to obtain a kinetic equation of the single beam unit, and the kinetic equation specifically comprises the following steps:
using Lagrange's equation in combination with TANC、UANCAnd QkAnd (3) obtaining a dynamic equation of a single beam unit:
Figure BDA0002498264180000127
wherein M is a system mass array, e is a system generalized coordinate vector, sigma is a Laplace multiplier vector, C (e, t) is a constraint equation,Cefor derivation of the constraint equation to generalized coordinates, QeSolving can be completed by a backward difference method for the external force acting on the beam unit;
(4) obtaining the kinetic equation of the whole guide wire by assembling the kinetic equations of all the units;
(5) to the collision detection of seal wire and blood vessel, adopt the bounding box that arranges along the pipeline axis to replace the AABB bounding box and carry out seal wire-blood vessel contact detection, simplify contact detection from the three-dimensional problem to one-dimensional problem, improved contact detection's efficiency, specifically do: the method comprises the steps of performing interval division on a blood vessel along a generatrix of the blood vessel, obtaining arc length coordinates of pipeline nodes of each interval, meanwhile, arranging a contact detection point in the center line of a beam unit, and judging whether the contact detection point collides with a pipeline or not, wherein a guide wire moves in the pipeline, and determining which pipe section the detection point is located in according to an arc length coordinate s corresponding to the contact detection point in the beam unit, wherein a condition required to be met is that s1 is not less than s2, wherein s, s1 and s2 are respectively a contact point and arc length coordinates of two adjacent pipeline nodes, and are specifically shown in FIG. 2;
the method for calculating the projection points of the contact detection points on the pipeline axis is shown in fig. 3, beam nodes P1 and P2 are respectively located in pipeline sections s1 and s2, the corresponding projection points are A1 and A2, the detection point C1 is located in units P1 and P2, the corresponding projection point is B1, and as B1C1 is perpendicular to the pipeline central axis, the arc length coordinate s of B1 meets the requirement that the arc length coordinate s of B1 is equal to the central axis of the pipeline
f(s)＝(R-r(s))·r′(s)＝0；
Wherein R and R are respectively the distance from a detection point C1 and a projection point B1 thereof to the origin, R' is a tangent vector of a point B1, and a Newton-Raphson method is used for iterative solution;
combining the following formula with the dynamic equation of the whole guide wire obtained in the step (4), namely acquiring the stress and position information of all beam units of the whole guide wire through the position information of one end of the guide wire;
Figure BDA0002498264180000131
δ＝‖r-R‖+rb-rt；
wherein f isnIs the normal contact force between the guide wire-beam unit and the tube wall, and has the unit of N, delta,
Figure BDA0002498264180000132
k. e and c are a collision invasion depth, a relative invasion speed, a collision rigidity coefficient and a collision damping coefficient of the beam unit in units of mm, mm/s, N/m and N/(mm/s), respectively, e is a collision invasion index of the beam unit, which is a constant, R, R, RtAnd rbRespectively the distance from the corresponding detection point of the beam unit to the origin, the distance from the corresponding projection point of the detection point to the origin, the radius of the pipeline and the radius of the beam unit, wherein the units are mm, mm and mm, and when delta is less than or equal to 0, fn＝0。
The interventional operation guide wire modeling method considering the large space deformation adopts the absolute node coordinate beam unit theory to participate in modeling, adopts nonlinear Green strain to represent geometric nonlinearity in the relation between strain and deformation gradient, is suitable for describing large displacement and large deformation movement, and can be directly used for truly simulating the curve movement and the caused bending deformation of the guide wire of a slender elastic body in the operation process; the bounding box arranged along the axis of the pipeline is adopted to replace an AABB bounding box for beam-pipeline contact detection, so that all contact points can be detected, the contact detection is simplified from a three-dimensional problem to a one-dimensional problem, the data processing amount is greatly reduced, and the contact detection efficiency is improved.
Example 2
An electronic device, as shown in fig. 5, includes one or more processors, one or more memories, and one or more programs;
one or more programs are stored in the memory which, when executed by the processor, cause the electronic device to perform the same interventional surgical guidewire modeling method considering spatially large deformations as in example 1, the processing logic of the electronic device being as shown in fig. 6;
the electronic equipment has the following specific structure: an integrated circuit board for realizing electrical control is arranged in the electronic equipment, four encoders, four motors and corresponding drivers are combined to form 4 sets of direct current servo drive units, all servo units are in communication connection by adopting a CAN bus and are converted into USB bus communication through a CAN card, and finally are connected with a computer, and the other 3 encoders are connected with a data acquisition card and transmit data to the computer by the data acquisition card;
the computer is provided with graphic rendering software, when processing is carried out, a Central Processing Unit (CPU) of the computer loads data (comprising some geometric data (vertex coordinates, normal vectors, texture coordinates, textures and the like)) into a graphics card (GPU), then rendering information is set through the GPU (graphic processor), and the GPU starts rendering, wherein vertex coordinate transformation, illumination, clipping, projection and screen mapping are carried out in the GPU.
The electronic equipment disclosed by the invention is simple in structure, low in cost, capable of rapidly and accurately carrying out interventional operation guide wire modeling and good in application prospect.
Example 3
A computer storage medium comprising computer instructions which, when run on an electronic device, cause the electronic device to perform the same method of interventional surgical guidewire modeling that accounts for spatially large deformations as in embodiment 1.
Although specific embodiments of the present invention have been described above, it will be appreciated by those skilled in the art that these embodiments are merely illustrative and various changes or modifications may be made without departing from the principles and spirit of the invention.

Claims (5)

1. An interventional operation guide wire modeling method considering large space deformation is used for electronic equipment, and is characterized by comprising the following steps:
(1) discretizing the guidewire into a finite number of beam elements;
(2) the single beam unit takes the node displacement vector and the slope vector of the displacement field as generalized coordinates, the guide wire deformation and the guide wire section rotation are described through the node displacement vector and the node slope vector, and an expression of the total kinetic energy and the total potential energy of the single beam unit is obtained through derivation;
(3) combining the total kinetic energy, the total potential energy and the elastic force of the single beam unit by utilizing a Lagrange equation to obtain a kinetic equation of the single beam unit;
(4) obtaining the kinetic equation of the whole guide wire by assembling the kinetic equations of all the units;
(5) combining the following formula with the dynamic equation of the whole guide wire obtained in the step (4), namely acquiring the stress and position information of all beam units of the whole guide wire through the position information of one end of the guide wire;
Figure FDA0003508102730000011
δ＝||r-R||+rb-rt；
wherein f isnIs the normal contact force between the guide wire-beam unit and the tube wall, and has the unit of N, delta,
Figure FDA0003508102730000012
k and c are a collision invasion depth, a relative invasion speed, a collision rigidity coefficient and a collision damping coefficient of the beam unit in units of mm, mm/s, N/m and N/(mm/s), respectively, e is a collision invasion index of the beam unit, which is a constant, R, R, RtAnd rbThe distance from a corresponding detection point of the beam unit to the origin, the distance from a corresponding projection point of the detection point to the origin, the radius of the pipeline and the radius of the beam unit are respectively in units of mm, mm and mm;
the position vector r of any point in the single beam unit can be represented by a beam unit generalized coordinate e and a beam unit shape function N;
r(X,t)＝N(X)e(t)；
wherein X is the coordinates of the material at the unit point in mm, and t is time in s;
the absolute displacement u of any point within a single beam element can be expressed as;
Figure FDA0003508102730000021
wherein beam unit nodal displacement
Figure FDA0003508102730000022
In units of mm, e0The node generalized coordinate is the node generalized coordinate when the beam unit is initially configured;
the generalized coordinates e of the beam unit are as follows:
e＝[(e1)T (e2)T]T；
the generalized coordinates of the beam unit nodes comprise space absolute position vectors and material derivatives thereof, and each node comprises 6 generalized coordinates;
Figure FDA0003508102730000023
r1＝r(0,t),
Figure FDA0003508102730000024
r2＝r(L,t),
Figure FDA0003508102730000025
wherein L is the length of the beam unit in the initial configuration and is in mm, x is the substance coordinate of the beam unit and is in mm,
Figure FDA0003508102730000026
is a dimensionless unit;
the beam element shape function N is:
N＝[N1I N2I N3I N4I]；
wherein N is1、N2、N3And N4The definition is as follows:
Figure FDA0003508102730000027
Figure FDA0003508102730000028
wherein L is the length of the beam unit in the initial configuration, and the unit is mm, and the beam unit parameter
Figure FDA0003508102730000029
Is the beam element material coordinate, which is in mm;
kinetic energy T of beam uniteThe expression is as follows:
Figure FDA0003508102730000031
where ρ is the density of the material in kg/mm3，MeIs a unit mass array, V0、
Figure FDA0003508102730000032
And
Figure FDA0003508102730000033
the units of (A) are mm/s, mm/s and mm/s respectively;
the strain energy U expression of the beam unit is as follows:
Figure FDA0003508102730000034
EA and EJ are respectively axial unit stiffness and transverse unit stiffness, the units of EA and EJ are respectively N/mm and N/mm, epsilon and kappa are respectively axial strain and transverse curvature, and the epsilon and kappa are dimensionless units;
Figure FDA0003508102730000035
Figure FDA0003508102730000036
wherein the content of the first and second substances,
Figure FDA0003508102730000037
and
Figure FDA0003508102730000038
the slope of the beam curve and the slope of the beam curve are respectively, and are dimensionless units;
the guide wire moves in the pipeline, and the pipe section in which the detection point is located is determined according to an arc length coordinate s corresponding to the contact detection point in the beam unit, wherein the condition required to be met is that s is greater than or equal to s1 and is less than or equal to s2, and s, s1 and s2 are respectively arc length coordinates of the contact point and two adjacent pipeline nodes;
the beam nodes P1 and P2 are respectively located in the pipeline sections s1 and s2, corresponding projection points are A1 and A2, the detection point C1 is located in the units P1 and P2, the corresponding projection point is B1, and due to the fact that B1C1 is perpendicular to the central axis of the pipeline, the arc length coordinate s of B1 meets the requirement that the arc length coordinate s of the B1 is equal to the central axis of the pipeline
f(s)＝(R-r(s))·r′(s)＝0；
Wherein R and R are the distances from the detection point C1 and the projection point B1 to the origin point, respectively, and R' is the tangent vector of the point B1.
2. The interventional procedure guide wire modeling method considering spatial large deformation according to claim 1, wherein a total kinetic energy T of the beam unitANCAnd total potential energy UANCThe expression of (c) is:
Figure FDA0003508102730000041
Figure FDA0003508102730000042
wherein e isiIs the generalized coordinate vector of the ith node;
elastic force Q corresponding to the elastic energyKThe expression is as follows:
Figure FDA0003508102730000043
using Lagrange's equation in combination with TANC、UANCAnd QkAnd (3) obtaining a dynamic equation of a single beam unit:
Figure FDA0003508102730000044
wherein M is a system mass array, e is a system generalized coordinate vector, sigma is a Laplace multiplier vector, C (e, t) is a constraint equation, and CeFor derivation of the constraint equation to generalized coordinates, QeIs an external force acting on the beam unit.
3. The interventional procedure guide wire modeling method considering spatial large deformation according to claim 1, wherein f is when δ ≦ 0n＝0。
4. An electronic device comprising one or more processors, one or more memories, and one or more programs;
the one or more programs stored in the memory, when executed by the processor, cause the electronic device to perform a method of interventional surgical guidewire modeling with consideration of spatially large deformations as set forth in any one of claims 1-3.
5. A computer storage medium comprising computer instructions which, when run on an electronic device, cause the electronic device to perform a method of interventional surgical guidewire modeling with consideration of spatially large deformations as set forth in any one of claims 1-3.
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