CN102262699B - Soft tissue deformation simulation method based on coupling of mesh-free Galerkin and mass spring - Google Patents

Abstract

The invention relates to an object deformation real-time simulation graphic processing technique, particularly a soft tissue deformation simulation method based on coupling of mesh-free Galerkin and mass spring, which comprises the following steps: in the pretreatment process, establishing a linear viscoelasticity biomechanical model for soft tissues; in the deformation computation process, dynamically partitioning a mesh-free region and a mass spring region according to the load carried by the soft tissues, establishing a transitional unit of the connection region between the mesh-free region and mass spring region, and constructing a transitional unit approximation displacement function, thereby implementing self-adapting coupling of a mesh-free Galerkin method and a mass spring method; and in the after-treatment process, outputting the state of the mass or node of each time step in the deformation process onto a screen, carrying out illumination rendering, and finally displaying the real-time deformation process of the soft tissue organ under stressed conditions on the screen, thereby implementing visualization effect of dynamic deformation. By utilizing the advantage of high efficiency in the mass spring method and the advantages of high precision and no need of mesh reconstruction in the mesh-free Galerkin method, the invention overcomes the defect that the Galerkin method is not suitable for solving a large-scale problem, thereby effectively lowering the complexity of computation in the soft tissue deformation simulation and enhancing the operation efficiency.

Description

Soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring

Technical field

The present invention relates to a kind of object deformation real time modelling graph processing technique, particularly relate to a kind of soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring.

Background technology

Human body soft tissue deformation Study of calculation model can be traced back to the eighties in last century; Early stage deformation model comes from Computer-aided Geometric Design (CAGD) field; Be some non-physical models that use pure geometric techniques; This model is not considered the physics law of true deformation, and after 1 year, the deformation model based on physical features that is proposed by Terzopoulos substitutes.At present; Deformation computation model based on physical characteristics mainly is divided into particle spring model (Mass-Spring), finite element model (Finite-Element Model; Be abbreviated as FEM) and boundary element model (Boundary Element Model is abbreviated as BEM) three major types.The particle spring model is separated into some spots with object, and using has the point of quality to come representation physique amount, influencing each other between the spring of the no quality of usefulness and damper are expressed a little.This modular concept is simple, calculated amount is little, and real-time is good, is widely used in the virtual operation emulation such as distortion, cutting, stitching of soft tissue by the scholar.But itself also has the shortcoming that himself can't overcome this model; Owing to connect with spring between the supposition soft tissue; And the setting of the elastic coefficient does not have theoretical foundation, can only derive from laboratory technician's experience and debugging constantly, and when the soft tissue large deformation, problem of dtmf distortion DTMF can occur; The finite element model that therefore, can overcome this shortcoming becomes the focus of research gradually.

Finite element method is the classical way of finding the solution Elasticity Problems, and its basic thought is to find the solution the assembly that discrete region is a group limited and the unit that is connected with each other by certain way with continuous.Approximate function with being supposed in each unit comes burst ground to represent to find the solution dependent variable undetermined in the territory, utilizes variational principle to set up the Algebraic Equation set of finding the solution dependent variable, thereby calculates deformation.Its advantage is to have higher precision, and adaptability is stronger, can be applicable to the emulation of various geometries and material behavior.Its shortcoming is: the pre-treatment for the 3 D complex structure is that 3D grid makes up difficulty, and is consuming time longer; The common displacement of its result of calculation is continuous, and stress, strain are discontinuous, need the aftertreatment smooth; " volume self-locking " phenomenon appears when structured material is incompressible; The mesh distortion problem can appear when large deformation.Because soft tissue organs has incompressibility, so when using finite element model, " volume self-locking " phenomenon can occur; In virtual operation, large deformation situation or cutting, sew application often take place, at this moment the topological structure of organ can change, and utilizes finite element method constantly to carry out grid reconstruction, not only takes time and effort, and occurs the mesh distortion problem easily; Because stress, the strain result of FEM calculation are discontinuous, need the aftertreatment smooth, can influence the accuracy and the real-time of force feedback in the virtual operation.This shows that finite element method is not the preferred plan that soft tissue deformation is calculated, need to explore other computing method that are more suitable for.

Boundary element method is meant that the elementary solution with governing equation is the basis, and the boundary problem in zone is turned to the equation on the boundary surface, and division unit on boundary surface is found the solution with Galerkin method or other numerical computation method more then.It can become two-dimensional problems to three-dimensional problem, and two-dimensional problems become one-dimensional problem, and the degree of freedom of finding the solution is descended, but because boundary element method also is based on the numerical method of grid, so also mesh distortion and distortion possibly occur.

Commonly used have the grid physical model need expend very big energy to construct grid model, and follow-up computation process mostly closely depends on this network structure; Mesh distortion might take place when the soft tissue large deformation; Cutting, during topology change such as stitching, need construct grid again; Therefore there is grid method to be difficult to large deformation of accurate description soft tissue and topology change situation.For addressing these problems, produced the idea of in the numerical value processing procedure, breaking away from grid naturally, no gridding method is arisen at the historic moment.No gridding method is removed the network in the finite element method; Replacing a series of node fully arranges; Need not utilize predefined grid that field variable is carried out interpolation with approximate; And be based on a little approximate, adopt weight function to characterize nodal information, and the node on certain territory can influence the mechanical characteristic of any point on the research object.Like this, broken away from uncontinuity, guaranteed the precision found the solution to be particularly suitable for the topology change that cutting, sew application cause in the virtual operation the constraint of problem (like grid reconstruction etc.).In no grid method; Galerkin method only needs nodal information to describe with the border just can become one group of algebra system equation with formula formal transformation a little less than it; And adopt a kind of smooth mobile least squqre approximation function that can reach optimal approximation as the displacement approximate function with the value of each sampling spot; Characterize nodal information with this, so computational accuracy is highly stable far above the strong formula method of no grid.

But; The golden shortcoming of no grid gal the Liao Dynasty is that calculated amount is bigger; The large-scale golden method of gal the Liao Dynasty of using can increase computing time greatly; Therefore design the deformation emulating that a better model of performance is realized soft tissue, and satisfy requirement as much as possible, become the matter of utmost importance that the soft tissue deformation emulating faces about real-time, robustness, accuracy.In fact, in virtual operation, only just can produce topology changes such as big distortion and cutting and stitching at the contact area of operating theater instruments and organ, less at other regional deformation, therefore there is no need to use the distant golden method of no grid gal in whole zone.Therefore, we adopt the method for no grid gal the Liao Dynasty's gold and the coupling of particle spring, in the golden method of contact area employing no grid gal the Liao Dynasty of operating theater instruments and organ, in other zone employing particle spring method.

Summary of the invention

The present invention is directed to the prior art deficiency; A kind of soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring is proposed; To not have grid gal the Liao Dynasty gold and solve soft tissue deformation emulating problem in the virtual operation with the coupling of particle spring; Purpose is to utilize the advantage that the high and no grid Galerkin method precision of particle SPRING METHOD OF STONE efficient is high, need not reconstructed mesh, remedies the unsuitable defective of finding the solution extensive problem of Galerkin method, thereby effectively reduces the computation complexity in the soft tissue deformation emulating; Improve operation efficiency, better solve the contradiction of accuracy and real-time in the soft tissue deformation emulating.

The technical scheme that the present invention adopted:

A kind of soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring comprises the pre-treatment process, calculates deformation process, three steps of last handling process, in the pre-treatment process, for soft tissue is set up the linear viscoelasticity biomechanical model; In calculating deformation process; Dynamically divide no net region and particle spring zone according to the load that soft tissue carried; And the join domain between no net region and particle spring zone is set up transition element; The approximate displacement function of structure transition element is realized the self-adaptation coupling of no grid gal golden method of the Liao Dynasty and particle spring method; In last handling process; According to deformation result of calculation, the particle of each time step of deformation process or the state of node are outputed on the screen, and carry out illumination and play up; Finally, realize dynamic deformation effect of visualization showing the real-time deformation process of soft tissue organs under stressing conditions on the screen; The process of said calculating deformation specifically comprises following four steps:

1) function between design load and the distance, as the foundation of dividing no net region, and make no net region enough greatly with the assurance noncoherent boundary all in no net region, other zone is that the particle spring is regional;

2) for no net region and particle spring zone, set up effective data structure respectively, the Classification Management data;

3) join domain between no net region and particle spring zone is set up transition element:

(1) the no net region that will divide and particle spring zone are as two entities; Two entities contact part as transition boundary; On the basis of background grid; The background grid at segmentation transition boundary place and as subelement, making has a node or particle to exist at most in each subelement, with the unit that do not comprise node or particle as the gap unit;

(2) with the gap unit as object search; Respectively to left-right and front-back six direction search subelement up and down; Through iteration, progressively will not have the gap unit that inside, net region meets switch condition and be converted into no grid cell, the gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit; No longer change until the gap unit, and with remaining gap unit as transition element;

4) in transition element, set up transition node, confirm the approximate displacement function of transition node, realize the smooth transition between no net region and the particle spring zone; Two conditions are satisfied in the foundation of transition node:

(1) transition node receives the acting force in no net region and particle spring zone respectively, and it is made a concerted effort is zero;

(2) transition node receives the acting force in no net region and particle spring zone respectively, and its displacement equates;

According to above-mentioned condition; Make up linear viscoelasticity dynamic motion equation respectively, find the solution the differential equation, draw the approximate displacement of two differences of same transition node based on no grid gal the Liao Dynasty's gold and particle spring; Travel through all transition nodes; Obtain the approximate displacement function that two kinds of model constructions go out, set up the funtcional relationship between the two, as the approximate displacement function of transition node.

Described soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring, the switch condition that inner gap unit, no net region is converted into no grid cell is:

1) top to bottom, left and right, front and rear three prescriptions are no grid cell to the subelement of middle existence direction more than two groups and two groups;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3) for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are no grid cell;

4) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are no grid cell;

5) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are no grid cell.

Described soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring, the gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit, and its switch condition is:

1) top to bottom, left and right, front and rear three prescriptions are the particle spring unit to the subelement of middle existence direction more than two groups and two groups;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3) for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are the particle spring unit;

4) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are the particle spring unit;

5) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are the particle spring unit.

Described soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring, remaining gap unit is meant as transition element:

1) do not meet no grid cell switch condition, do not meet the gap unit of particle spring unit switch condition yet;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear comprise no grid cell and particle spring unit simultaneously, perhaps comprise no grid cell, particle spring unit and gap unit simultaneously.

Described soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring; In the pre-treatment process; Suppose that soft tissue is even, isotropic material; Have accurate incompressibility, linear viscoelasticity characteristic, and definite initialization data, definition starting condition, displacement boundary conditions and stress boundary condition; With the elasticity of spring simulation viscoelastic body, damper is simulated its viscosity then, and the distortion and the load of hypothesis spring are proportional, and the speed of the distortion of damper and distortion is proportional; Secondly the distortion of isotropic material can separate into stereomutation and isopyknic shape distortion two parts; So resolve into its spherical tensor sum deviator to the stress and strain tensor; And then the constitutive equation of structure Kelvin model, simulation soft tissue stress relaxation and creep properties; Set up geometric equation, balance equation at last, and apply boundary condition and starting condition, for soft tissue is set up the linear viscoelasticity biomechanical model.

Described soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring in calculating deformation process, at first generates initial background grid; Divide no net region and particle spring zone according to external load; Foundation to the data structure the particle spring data, to reduce the frequency that the data reusing phenomenon takes place in the adaptive process, is secondly set up transition element at join domain from no grid; In transition element, set up the approximate displacement function of transition node and transition node; Realize the smooth transition between no net region and the particle spring zone, apply boundary condition then, in conjunction with Kelvin normal linearity Viscous Elastic Mechanics model; Adopt method of addition to find the solution displacement, ask stress, strain according to displacement.

Useful good effect of the present invention:

1, uses the golden method of no grid gal the Liao Dynasty in large deformation and topology change zone; The link information that does not need node; Effectively avoid finite element and mesh distortion in the Element BEM and reconstruct commonly used at present, be fit to very much often take place in the operation emulation situation of large deformation and topology change; The golden method of no grid gal the Liao Dynasty has good continuity and form field function flexibly, has advantages of higher stability and computational accuracy; The ess-strain result of the golden method of no grid gal the Liao Dynasty has slickness preferably, can fine holding power feedback device.

2, adopt based on no grid gal the Liao Dynasty's gold and particle spring coupling process; Adopt the golden method of high-precision no grid gal the Liao Dynasty in large deformation and topology change zone; Adopt high efficiency particle spring method in other deformation than the zonule; Not only can bring into play the plurality of advantages of the golden method of above-mentioned no grid gal the Liao Dynasty, and improve deformation emulating efficient.

3, use can effectively be simulated creep and the relaxation property that soft tissue is shown based on Kelvin normal linearity viscoelastic model in deformation process.This Elasticity model that generally uses at present based on viscoelastic model for coupling meets the biomechanics characteristic of human body soft tissue more.

Description of drawings

Fig. 1 is the soft tissue deformation emulating manner of execution process flow diagram that the present invention is based on no grid gal the Liao Dynasty's gold and the coupling of particle spring;

Fig. 2 dynamically divides the sectional view in no net region and particle spring zone for the present invention; Among the figure; 1 is the operating theater instruments range of influence, and the distant golden Model Calculation soft tissue deformation of no grid gal is used in this zone, and 2 is transitional region; 3 is particle spring zone, and this zone uses the particle spring model to calculate soft tissue deformation;

Fig. 3 dynamically divides the stereographic map in no net region and particle spring zone for the present invention;

Fig. 4 is the sectional view of no grid gal the Liao Dynasty's gold of the present invention and particle spring coupling model;

Fig. 5 is that liver organ is respectively at the deformation design sketch that receives under pulling force and the pressure condition.

Embodiment

Embodiment one: referring to Fig. 1, the present invention is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty's gold and the coupling of particle spring, comprise the pre-treatment process, calculate deformation process, three parts of last handling process:

In the pre-treatment process, for soft tissue is set up the linear viscoelasticity biomechanical model.Suppose that soft tissue is even, isotropic material, have accurate incompressibility, linear viscoelasticity characteristic, structure constitutive equation, geometric equation and balance equation apply boundary condition and starting condition;

In calculating deformation process; Dynamically divide no net region and particle spring zone according to the load that soft tissue carried; And the join domain between no net region and particle spring zone is set up transition element; The approximate displacement function of structure transition element is realized the self-adaptation coupling of no grid gal golden method of the Liao Dynasty and particle spring method;

In last handling process; According to deformation result of calculation, the particle of each time step of deformation process or the state of node are outputed on the screen, and carry out illumination and play up; Finally, realize dynamic deformation effect of visualization showing the real-time deformation process of soft tissue organs under stressing conditions on the screen.

Embodiment two: present embodiment is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty gold with the coupling of particle spring, and different with embodiment one is: the process of calculating deformation specifically comprises following four steps:

1) function between design load and the distance, as the foundation of dividing no net region, and make no net region enough greatly with the assurance noncoherent boundary all in no net region, other zone is that the particle spring is regional;

2) for no net region and particle spring zone, set up effective data structure respectively, the Classification Management data;

3) join domain between no net region and particle spring zone is set up transition element;

4) in transition element, set up the approximate displacement function of transition node and transition node, realize the smooth transition between no net region and the particle spring zone.

Embodiment three: present embodiment is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty's gold and the coupling of particle spring; Different with embodiment two is: the join domain between no net region and particle spring zone is set up transition element; Comprise following two steps: the no net region that 1) will divide and particle spring zone are as two entities; Two entities contact part as transition boundary, on the basis of background grid, and the background grid at segmentation transition boundary place and as subelement; Making has a node or particle to exist at most in each subelement, with the unit that do not comprise node or particle as the gap unit;

2) with the gap unit as object search; Respectively to left-right and front-back six direction search subelement up and down; Through iteration, progressively will not have the gap unit that inside, net region meets switch condition and be converted into no grid cell, the gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit; No longer change until the gap unit, and with remaining gap unit as transition element.

The present invention is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty's gold and the coupling of particle spring, in calculating deformation process, at first confirm no net region and particle spring zone, node in two zones or particle information are stored respectively; Join domain segmentation background grid between no net region and particle spring zone guarantees at most only to comprise in each subelement a node or particle; Then, as object search, the application searches algorithm is no grid cell or particle spring unit with part gap cell translation with the gap unit, and with remaining gap unit as transition element.

Embodiment four: present embodiment is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty gold with the coupling of particle spring, and different with embodiment three is: in transition element, set up transition node, confirm the approximate displacement function of transition node according to following method.Transition node satisfies two conditions:

1) transition node receives the acting force in no net region and particle spring zone respectively, and it is made a concerted effort is zero;

2) transition node receives the acting force in no net region and particle spring zone respectively, and its displacement equates;

According to above-mentioned condition; Make up linear viscoelasticity dynamic motion equation respectively, find the solution the differential equation, draw the approximate displacement of two differences of same transition node based on no grid gal the Liao Dynasty's gold and particle spring; Travel through all transition nodes; Obtain the approximate displacement function that two kinds of model constructions go out, set up the funtcional relationship between the two, and as the approximate displacement function of transition node.

Embodiment five: referring to Fig. 1, present embodiment is based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty gold with the coupling of particle spring, the pre-treatment process, calculates deformation process, last handling process respectively as follows:

Pre-treatment process: at first set up the linear viscoelasticity biomechanical model for soft tissue.Suppose that soft tissue is even, isotropic material; Have accurate incompressibility, linear viscoelasticity characteristic, with the elasticity of spring simulation viscoelastic body, its viscosity of damper simulation; And the distortion and the load of hypothesis spring are proportional, and the speed of the distortion of damper and distortion is proportional; Secondly the distortion of isotropic material can separate into stereomutation and isopyknic shape distortion two parts; So resolve into its spherical tensor sum deviator to the stress and strain tensor; And then the constitutive equation of structure Kelvin model, simulate soft tissue stress relaxation and creep properties preferably; Set up geometric equation, balance equation at last, and apply boundary condition and starting condition.

Calculate deformation process: during operating theater instruments contact soft tissue; No matter push or lift or cut, all based on the suffered load of organ local surfaces of operating theater instruments contact, design load and apart between functional relation; Thereby dynamically divide no net region and particle spring zone; Make no net region and particle spring zone satisfy predetermined scope, and noncoherent boundary is finally still in no net region, continuum boundary is all in particle spring zone; Secondly establish the data structure of effect respectively in no net region and particle spring zone, and the Classification Management data; The no net region that to divide then and particle spring zone are as two entities; Two entities contact part as transition boundary; The background grid at segmentation transition boundary place; And the background grid after will segmenting is as subelement, and subelement satisfies the condition that has a node or particle at the most, obtains the border of two entities like this; Because the background grid after the segmentation exists and does not comprise the unit of node or particle, is defined as the gap unit so will not comprise the unit of node or particle; With the gap unit as object search; Select for use and go up afterwards earlier, from left to right, vertical order is progressively searched for subelement; Pass through iteration; The gap unit that progressively will meet switch condition is converted into no grid cell or particle spring unit, no longer change until the gap unit, and with remaining gap unit as the transition element between no grid and the particle spring; In transition element, set up transition node at last,, set up the approximate displacement function of transition node based on displacement and the dynamic balance condition that transition node satisfies.

The golden model of described no grid gal the Liao Dynasty is used for calculating the big zone of deformation that operating theater instruments contacts with soft tissue, adopts Pascal figure to set up three-dimensional basis function p (x), confirms the number m of basis function; The background grid of the weak formula method of the structure overall situation is set point x _QBe the calculation level x in the domain of influence, calculate the size d of the domain of influence _s, definite field node number n of participating in the MFree shape function of structure calculation level guarantees m=n; Utilize selected node of the domain of influence, set up weight function W and derivative thereof; Adopt the node shape function φ (x) and the partial derivative thereof that move all nodes in the least square method structure influence territory

Obtain the golden weak variation form of gal the Liao Dynasty by Viscous Elastic Mechanics governing equation corresponding energy functional; And carry out totally dispersing, get and stay value, get the overall discrete governing equation of EFG method; Apply essential boundary condition, utilize the Gauss of the two-dimentional equiband storage elimination method that circulates to obtain discrete nodal displacement.

Described particle spring model is used for calculating deformation than the zonule, according to Hooke's law, sets up the lagrange equation of motion of single particle movement:

$m\frac{{\&PartialD;}^2{u}^{\mathrm{MS}}}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="110727084305.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}+\mathrm{\&gamma;}\frac{\&PartialD;u^{\mathrm{MS}}}{\&PartialD;t}+f_{\mathrm{int}}^i=f_{\mathrm{ext}}^i$

In the formula, u ^MSThe position vector of expression particle i, m representes the quality of particle i, γ representes the stickiness density between adjacent particle, The internal force that the expression spring is applied particle i,

The suffered external force of expression particle i according to the suffered external force of particle, is separated the differential equation and is got particle displacement.

Described no grid gal the Liao Dynasty's gold and particle spring coupling model are used for realizing not having the natural transition between net region and the particle spring zone.The transition node of in transition element, setting up satisfies two conditions: 1) transition node receives the acting force in no net region and particle spring zone respectively, and it is made a concerted effort is zero; 2) transition node receives the acting force in no net region and particle spring zone respectively, and its displacement equates.Existing according to above-mentioned condition; Make up the linear viscoelasticity dynamic simulation equation of motion respectively based on no grid and particle spring; Find the solution the approximate displacement of two differences that the differential equation gets same transition node, travel through all transition nodes, obtain the approximate displacement function that uses two kinds of model constructions to go out; Set up the funtcional relationship between the two, and as the approximate displacement function of transition node.

Suppose that t=0 displacement, speed and acceleration constantly is known; To find the solution the time territory 0～T be divided into n time interval Δ t (=T/n); Utilize central difference method or Newmark method to calculate the useful load and the displacement of each time step, ask strain, and calculate new bulk strain and shape distortion by strain according to displacement; According to rheological equations, volume calculated stress, deviatoric stress and particle stress;

Last handling process: carry out playing up of illumination according to the deformation result calculated, finally real-time rendering goes out the particle of each time step or the state of node on screen, like this, just can realize dynamic deformation effect of visualization.

Embodiment six: present embodiment combines Fig. 1～Fig. 5, and technical scheme of the present invention is elaborated:

As shown in Figure 1, when the deformation of simulation soft tissue, mainly be divided into three big modules and implement:

1, pre-treatment process

At first, set up the linear viscoelasticity biomechanical model for soft tissue.Suppose that soft tissue is even, isotropic material; Have accurate incompressibility, linear viscoelasticity characteristic; This model combines by the Maxwell model is parallelly connected with Hookean spring; And the supposition Hookean spring produces the distortion that is directly proportional with load at once, and damper can produce the speed that is directly proportional with load in arbitrary moment, so constitutive equation is:

$\mathrm{\&sigma;}+\frac{\mathrm{\&eta;}}{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="110727084305.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}={\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="110727084305.png"\; state="\{\{state\}\}">E</figure-callout>}}_1\mathrm{\&epsiv;}+\mathrm{\&eta;}(1+\frac{E_1}{E_2})\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}$

σ representes stress in the formula, and ε representes strain, and E representes the elasticity coefficient of Hookean spring, E ₁The elasticity coefficient of representing the Hookean spring parallelly connected with the Maxwell model, E ₂The elasticity coefficient of expression Maxwell model neutral line spring, η representes the coefficient of viscosity of damper,

With Represent the derivative of stress and strain respectively about the time.

The material parameter of Kelvin standard lines viscoelastic model is obtained more or less freely, and can realize somatometry, the lax and creep properties that is had in the time of therefore can describing soft tissue generation deformation through the adjustment parameter, and wherein creep function is:

$C\left(t\right)=\frac{1}{E_1}[1-(1-\frac{{\mathrm{\&tau;}}_{\mathrm{\&epsiv;}}}{{\mathrm{\&tau;}}_{\mathrm{\&sigma;}}}{e}^{-t/{\mathrm{\&tau;}}_{\mathrm{\&sigma;}}})]I\left(t\right)$

Relaxation function is:

$K\left(t\right)=E_1[1-(1-\frac{{\mathrm{\&tau;}}_{\mathrm{\&sigma;}}}{{\mathrm{\&tau;}}_{\mathrm{\&epsiv;}}}{e}^{-t/{\mathrm{\&tau;}}_{\mathrm{\&epsiv;}}})]I\left(t\right)$

In the formula ${\mathrm{\&tau;}}_{\mathrm{\&epsiv;}}=\frac{\mathrm{\&eta;}}{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="110727084305.png"\; state="\{\{state\}\}">E</figure-callout>}}_2},$ ${\mathrm{\&tau;}}_{\mathrm{\&sigma;}}=\frac{\mathrm{\&eta;}}{E_1}(1+\frac{E_1}{E_2}),$

Generally speaking; The distortion of isotropic material can separate into stereomutation and isopyknic shape distortion two parts, and promptly volumetric stress only changes volume, and the deviator of stress causes isopyknic shape distortion; So resolve into its spherical tensor sum deviator part to the stress and strain tensor, promptly

${\mathrm{\&sigma;}}_{\mathrm{mn}}=s_{\mathrm{mn}}+\frac{1}{3}{\mathrm{\&delta;}}_{\mathrm{mn}}{\mathrm{\&sigma;}}_{\mathrm{ii}},$ ${\mathrm{\&epsiv;}}_{\mathrm{mn}}=e_{\mathrm{mn}}+\frac{1}{3}{\mathrm{\&delta;}}_{\mathrm{mn}}{\mathrm{\&epsiv;}}_{\mathrm{ii}},$ m，n＝1，2，3

Wherein, δ _MnBe the Kronecker symbol; ε _IiAnd σ _IiBe respectively bulk strain and volumetric stress; e _MnAnd s _MnBe respectively the component of the strain deviation and the deviator of stress; e _Mm=0 and s _Mn=0.

Because viscous-elastic behaviour and effect under two kinds of situations can consider respectively, so based on Kelvin normal linearity Viscous Elastic Mechanics model, the three-dimensional viscoelastic constitutive equation between deviatoric stress tensor and the inclined to one side strain tensor, between volumetric stress and the bulk strain is:

$s_{\mathrm{mn}}+\frac{\mathrm{\&eta;}}{E_2}{\stackrel{\&CenterDot;}{s}}_{\mathrm{mn}}=E_1{e}_{\mathrm{mn}}+\mathrm{\&eta;}(1+\frac{E_1}{E_2}){\stackrel{\&CenterDot;}{e}}_{\mathrm{mn}},$ m，n＝1，2，3

${\mathrm{\&sigma;}}_{\mathrm{ii}}+\frac{\mathrm{\&eta;}}{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="110727084305.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}{\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_{\mathrm{ii}}={\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="110727084305.png"\; state="\{\{state\}\}">E</figure-callout>}}_1{\mathrm{\&epsiv;}}_{\mathrm{ii}}+\mathrm{\&eta;}(1+\frac{E_1}{E_2}){\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_{\mathrm{ii}}$

Wherein

is respectively inclined to one side rate of strain and volumetric strain.

2, calculate deformation process

1) sets up the golden model of no grid gal the Liao Dynasty

The golden model of described no grid gal the Liao Dynasty is used for calculating the big zone of deformation that operating theater instruments contacts with soft tissue, adopts Pascal figure to set up three-dimensional basis function p (x), and the number m of definite basis function,

p ^T(x)=[1 x y z] ^TM=4, p=1 is linear basis function;

p ^T(x)=[1 x y z x ²Xy y ²Yz z ²Zx] ^TM=10, p=2 is the secondary base function;

p ^T(x)=[1 x y z x ²Xy y ²Yz z ²Zx x ³x ²Y xy ²y ³y ²Z yz ²z ³z ²X zx ²Xyz] ^TM=20, p=3 is three basis functions;

The background grid of the weak formula method of the structure overall situation is set point x _QBe the calculation level x in the domain of influence, through setting the size d of the domain of influence _s

$d_s=a_s{d}_c,d_c=\frac{\sqrt[3]{V_s}}{\sqrt[3]{n_{v_s}}-1}$

Confirm the field node n of the MFree shape function of participation structure calculation level, guarantee m=n.A in the formula _sBe the dimensionless size of this domain of influence, d _cFor being positioned at an x _QNear nodal pitch, V _sVolume for the pre-estimation domain of influence;

For being included in volume V _sIn the pre-estimation domain of influence in the node number.

Utilize selected node of the domain of influence, set up weight function W and derivative thereof, existing is example with cubic spline function as weight function:

$W_i\left(x\right)=\left\{\begin{array}{cc}2/3-4{\mathrm{<figure-callout\; id="2"\; label="r\; i"\; filenames="110727084305.png"\; state="\{\{state\}\}">r</figure-callout>}}_i^{}+4r_i^3& r_i\&le;0.5\\ 4/3-4r_i+4r_i^2-4/3{\mathrm{<figure-callout\; id="3"\; label="r\; i"\; filenames="110727084305.png"\; state="\{\{state\}\}">r</figure-callout>}}_i^{}& 0.5<r_i\&le;1\\ 0& r_i>1\end{array}\right.$

In the formula

d _i=| x-x _i| be node x _iAnd the distance between the calculation level x, r _wBe weight function support region size.

In all directions differentiate, the first order derivative that gets weight function is to weight function:

$W_i\left(x\right)=\left\{\begin{array}{cc}-8r_i+12r_i^2& r_i\&le;0.5\\ -4+8r_i-4{\mathrm{<figure-callout\; id="2"\; label="r\; i"\; filenames="110727084305.png"\; state="\{\{state\}\}">r</figure-callout>}}_i^{}& 0.5<r_i\&le;1\\ 0& r_i>1\end{array}\right.$

Adopt the node shape function φ (x) and the partial derivative

thereof that move all nodes in the least square method structure influence territory to obtain the golden weak variation form of gal the Liao Dynasty by Viscous Elastic Mechanics governing equation corresponding energy functional

$\underset{\mathrm{\&Omega;}}{\&Integral;}\mathrm{\&delta;}{\left(\mathrm{Lu}\right)}^{T}D\left(\mathrm{Lu}\right)\mathrm{d\&Omega;}-\underset{\mathrm{\&Omega;}}{\&Integral;}\mathrm{\&delta;}{u}^T\mathrm{bd\&Omega;}-\underset{{\mathrm{\&Gamma;}}_t}{\&Integral;}\mathrm{\&delta;}{u}^T\stackrel{\&OverBar;}{t}\mathrm{d\&Gamma;}-\mathrm{\&delta;}\underset{{\mathrm{\&Gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="110727084305.png"\; state="\{\{state\}\}">u</figure-callout>}}}{\&Integral;}\frac{1}{2}{(u-\stackrel{\&OverBar;}{u})}^T\mathrm{\&alpha;}(u-\stackrel{\&OverBar;}{u})\mathrm{d\&Gamma;}=0$

Above-mentioned equation is carried out totally dispersing, gets and stay value, get the overall discrete governing equation of EFG method,

[K+K ^α]U＝F+F ^α

In the formula, U is the nodal displacement parameter of all nodes in the whole Problem Areas, the global stiffness matrix of K for being assembled by the node stiffness matrix, the overall outer force vector of F for being assembled by the nodal force vector, K ^αThe added martix that the overall punishment stiffness matrix of serving as reasons causes, F ^αFor vectorial by the caused additional force of essential boundary condition, K, K ^α, F and F ^αDo three-dimensional Gauss integration or the Irons integration obtains through the point of the Gauss integration in the background grid; Apply essential boundary condition, utilize the Gauss of the two-dimentional equiband storage elimination method that circulates to obtain discrete nodal displacement.

2) set up the particle spring model

Described particle spring model is used for calculating deformation than the zonule, according to Hooke's law, sets up the lagrange equation of motion of single quality point motion

$m\frac{{\&PartialD;}^2{u}^{\mathrm{MS}}}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="110727084305.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}+\mathrm{\&gamma;}\frac{\&PartialD;u^{\mathrm{MS}}}{\&PartialD;t}+f_{\mathrm{int}}^i=f_{\mathrm{ext}}^i$

Wherein: u ^MSThe position vector of expression particle i; M representes the quality of particle i, and γ representes the stickiness density between adjacent particle,

The internal force that the expression spring is applied particle i,

The suffered external force of expression particle i according to the suffered external force of particle, is separated PDE and is got particle displacement.

3) set up no grid gal the Liao Dynasty's gold and particle spring coupling model

For a soft tissue, stressed when a certain position, the deformation that then takes place with the point of stress point close together is more violent, and more small away from the histogenetic deformation ratio of stress point.In order to guarantee computational accuracy, improve counting yield, the golden model of no grid gal the Liao Dynasty is adopted in the big zone of deformation, and deformation is adopted the particle spring model than the zonule.Existing load of being born according to the organ local surfaces that operating theater instruments contacted; Function between design load and the distance; And with its foundation as no net region of division and particle spring zone; Wherein do not have the net region and predetermined scope will be satisfied in particle spring zone, to guarantee noncoherent boundary in no net region, continuum boundary is in particle spring zone; Secondly in no net region and particle spring zone, set up effective data structure respectively, and the Classification Management data; The no net region that to divide then and particle spring zone are as two entities; Two entities contact part as transition boundary; On the basis of background grid; The background grid at segmentation transition boundary place, and the background grid after will segment is as subelement, the condition that subelement satisfies are node or particle existence at the most in the unit; The unit that definition does not comprise node or particle is the gap unit; Existing with the gap unit as object search, according to the sequential search subelement before and after up and down, through iteration; Progressively will not have the gap unit that inside, net region meets switch condition and be converted into no grid cell; The gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit, and with remaining gap unit as transition element, wherein

(1) inner gap unit, no net region is converted into the switch condition of no grid cell and is:

1. top to bottom, left and right, front and rear three prescriptions are no grid cell to the subelement of middle existence direction more than two groups and two groups;

2. six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3. for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are no grid cell;

4. for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are no grid cell;

5. for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are no grid cell;

(2) the gap unit of particle spring intra-zone is converted into the switch condition of particle spring unit and is:

1. top to bottom, left and right, front and rear three prescriptions are the particle spring unit to the subelement of middle existence direction more than two groups and two groups;

2. six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3. for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are the particle spring unit;

4. for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are the particle spring unit;

5. for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are the particle spring unit.

(3) being characterized as of remaining gap unit:

1. do not meet no grid cell switch condition, do not meet the gap unit of particle spring unit switch condition yet;

2. six sub-cells on the six direction of top to bottom, left and right, front and rear comprise no grid cell and particle spring unit simultaneously, perhaps comprise no grid cell, particle spring unit and gap unit simultaneously.

After confirming transition element, in transition element, set up transition node, and transition node satisfies two equilibrium conditions:

(1) transition node receives the acting force in no net region and particle spring zone respectively, and it is made a concerted effort is zero;

(2) transition node receives the acting force in no net region and particle spring zone respectively, and its displacement equates;

According to above-mentioned condition, make up the linear viscoelasticity dynamic simulation equation of motion respectively based on no grid gal the Liao Dynasty's gold and particle spring, find the solution the differential equation; Draw the approximate displacement of two differences of same transition node; Travel through all transition nodes, obtain the approximate displacement function that two kinds of model constructions go out, set up the funtcional relationship between the two; And, realize the smooth transition between no net region and the particle spring zone as the approximate displacement function of transition node.

Suppose that at last t=0 displacement, speed and acceleration constantly is known; To find the solution the time territory 0～T be divided into n time interval Δ t (=T/n); Utilize central difference method or Newmark method to calculate the useful load and the displacement of each time step, ask strain, and calculate new bulk strain and shape distortion by strain according to displacement; According to the constitutive equation of Kelvin standard lines viscoelasticity biomechanical model, volume calculated stress, deviatoric stress and particle stress.

3, last handling process

Carry out illumination according to the deformation result calculated and play up, finally real-time rendering goes out the particle of each time step or the state of node on screen, realizes dynamic deformation effect of visualization.

Like Fig. 2,3, shown in 4; The load of at first being born according to the organ local surfaces that operating theater instruments contacted; Function between design load and the distance is dynamically divided no net region and particle spring zone, between no net region and particle spring zone, sets up a series of transition element then; Construct corresponding displacement approximate function at last, be coupled to two kinds of methods together.When the load that liver applied up or down, through based on the soft tissue deformation computation model of no grid gal the Liao Dynasty gold with the coupling of particle spring, simulation true to nature operative region soft tissue deformation effect, as shown in Figure 5.With respect to the finite element model that generally adopts at present, this model has reduced overall complexity, has accelerated computing velocity.In addition, this model is convenient to realize operation technique emulation such as cutting, stitching, can provide powerful support for force feedback equipment, can be used as soft tissue physical model in the virtual operation.

Claims (5)

1. one kind based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty gold with the coupling of particle spring; Comprise the pre-treatment process, calculate deformation process, three steps of last handling process; In the pre-treatment process, suppose that soft tissue is even, isotropic material, has accurate incompressibility, linear viscoelasticity characteristic; And definite initialization data, definition starting condition, displacement boundary conditions and stress boundary condition; With the elasticity of spring simulation viscoelastic body, damper is simulated its viscosity then, and the distortion and the load of hypothesis spring are proportional, and the speed of the distortion of damper and distortion is proportional; Secondly the distortion of isotropic material can separate into stereomutation and isopyknic shape distortion two parts; So resolve into its spherical tensor sum deviator to the stress and strain tensor; And then the constitutive equation of structure Kelvin model, simulation soft tissue stress relaxation and creep properties; Set up geometric equation, balance equation at last, and apply boundary condition and starting condition, for soft tissue is set up the linear viscoelasticity biomechanical model; In last handling process; According to deformation result of calculation, the particle of each time step of deformation process or the state of node are outputed on the screen, and carry out illumination and play up; Finally, realize dynamic deformation effect of visualization showing the real-time deformation process of soft tissue organs under stressing conditions on the screen; It is characterized in that: the process of said calculating deformation specifically comprises following four steps:

1) function between design load and the distance, as the foundation of dividing no net region, and make no net region enough greatly with the assurance noncoherent boundary all in no net region, other zone is that the particle spring is regional;

2) for no net region and particle spring zone, set up effective data structure respectively, the Classification Management data;

3) join domain between no net region and particle spring zone is set up transition element:

(1) the no net region that will divide and particle spring zone are as two entities; Two entities contact part as transition boundary; On the basis of background grid; The background grid at segmentation transition boundary place and as subelement, making has a node or particle to exist at most in each subelement, with the unit that do not comprise node or particle as the gap unit;

(2) with the gap unit as object search; Respectively to left-right and front-back six direction search subelement up and down; Through iteration, progressively will not have the gap unit that inside, net region meets switch condition and be converted into no grid cell, the gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit; No longer change until the gap unit, and with remaining gap unit as transition element;

4) in transition element, set up transition node, confirm the approximate displacement function of transition node, realize the smooth transition between no net region and the particle spring zone; Two conditions are satisfied in the foundation of transition node:

(1) transition node receives the acting force in no net region and particle spring zone respectively, and it is made a concerted effort is zero;

(2) transition node receives the acting force in no net region and particle spring zone respectively, and its displacement equates;

According to above-mentioned condition, make up linear viscoelasticity dynamic motion equation respectively based on no grid gal the Liao Dynasty's gold and particle spring, find the solution the differential equation; Draw the approximate displacement of two differences of same transition node; Travel through all transition nodes, obtain the approximate displacement function that two kinds of model constructions go out, set up the funtcional relationship between the two; As the approximate displacement function of transition node, realize the self-adaptation coupling of no grid gal golden method of the Liao Dynasty and particle spring method.

2. according to claim 1 based on the soft tissue deformation emulating method of no grid gal the Liao Dynasty gold with the coupling of particle spring, it is characterized in that: inner gap unit, no net region is converted into no grid cell, need satisfied switch condition be following each,

1) top to bottom, left and right, front and rear three prescriptions are no grid cell to the subelement of middle existence direction more than two groups and two groups;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3) for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are no grid cell;

4) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are no grid cell;

5) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are no grid cell.

3. the soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring according to claim 1; It is characterized in that: the gap unit that particle spring intra-zone is met switch condition is converted into the particle spring unit; Said switch condition be following each

1) top to bottom, left and right, front and rear three prescriptions are the particle spring unit to the subelement of middle existence direction more than two groups and two groups;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear all are the gap unit;

3) for borderline unit, every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situations that all exist, and every prescription is to getting a sub-cells, and three sub-cells on totally three directions are the particle spring unit;

4) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of a prescription is all got; In addition two prescriptions in every group of subelement of getting on one of them direction, four sub-cells that amount on the four direction are the particle spring unit;

5) for borderline unit; Every group of subelement that top to bottom, left and right, front and rear three prescriptions make progress is not the situation that all exists; Wherein the subelement that makes progress of two prescriptions is all got; Another prescription is upwards got the subelement on one of them direction, and five sub-cells that amount on five directions are the particle spring unit.

4. the soft tissue deformation emulating method based on no grid gal the Liao Dynasty's gold and the coupling of particle spring according to claim 1, it is characterized in that: said transition element promptly satisfies the remaining gap unit of one of following condition:

1) do not meet no grid cell switch condition, do not meet the gap unit of particle spring unit switch condition yet;

2) six sub-cells on the six direction of top to bottom, left and right, front and rear comprise no grid cell and particle spring unit simultaneously, perhaps comprise no grid cell, particle spring unit and gap unit simultaneously.

5. according to each described soft tissue deformation emulating method of claim 1～4, it is characterized in that: in calculating deformation process, at first generate initial background grid based on no grid gal the Liao Dynasty's gold and the coupling of particle spring; Divide no net region and particle spring zone according to external load; Foundation to the data structure the particle spring data, to reduce the frequency that the data reusing phenomenon takes place in the adaptive process, is secondly set up transition element at join domain from no grid; In transition element, set up the approximate displacement function of transition node and transition node; Realize the smooth transition between no net region and the particle spring zone, apply boundary condition then, in conjunction with Kelvin normal linearity Viscous Elastic Mechanics model; Adopt method of addition to find the solution displacement, ask stress, strain according to displacement.

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