CN1452946A - Fully automatic femur reference axis determining method - Google Patents

Abstract

The fully automatic femur reference axis determining method includes pre-treatment of slices obtained through CT scanning of femur to eliminate noise, edge extraction to obtain the pixel coordinates of marrow controlled center position and converting the pixel coordinates into image coordinates; least mid value square process to minimize the mid value of squared data point residual error, find out the optimal estimated parameter of fitting straight line and obtain the fitting straight line of specific femur section; binary coding of the data point of whole marrow controlled center positions and optimizing the fitting straight line via genetic algorithm to find out the optimal reference axis position of the whole femur section. The present invention is used in robot-aided whole knee joint replacement based on CT, and has reduced cost, high precision and short design period.

Description

Full-automatic femur standard shaft line is determined method

Technical field:

The present invention relates to a kind of full-automatic femur standard shaft line and determine method, be used for auxiliary total knee arthroplasty based on the robot of CT modeling.Belonging to advanced makes and technical field of automation.

Background technology:

Since the nineties, because robotics and correlation theory is progressively ripe, for the accurate installation that realizes knee-joint prosthesis and save various relevant costs, the auxiliary total knee arthroplasty of robot is being developed and progressively application in recent years rapidly.In total knee arthroplasty, realize that the displacement of femoral prosthesis mainly relies on five planar clean cut of femur.Wherein important with first cutting planes.Other four planes all with first plane as benchmark, and determine corresponding normal direction and position according to patient's femur size and corresponding prosthese model.Determine that first cutting planes just must at first determine the direction of the anatomical axis of femur.Femur base axis determination has crucial effects in total knee arthroplasty, at first other four planes is had the effect of a benchmark, the more important thing is that the recovery of lower limb mechanics axis all depends on the accurate pointing of femur standard shaft line basically.In traditional TKA, this standard shaft line mainly relies on the interior interior bar of marrow that inserts of femoral bone cavitas medullaris and obtains, and this is actually the process of a fitting a straight line.

In based on the auxiliary total knee arthroplasty of the robot of CT modeling, just must at first carry out femur base axis determination in the model before art.But because the length of the femur fragment that obtains is different, except that being subjected to the noise spot interference, the epimere section and the section of hypomere condyle portion of femur itself also have very big influence to basic axis determination in preoperative cast.In robot knee surgery in the past, mainly take method of least square to carry out the match of standard shaft line, as document " a kind of practical describe of femur design standard shaft line one femoral axis line in artificial hip joint CAD " (Yao Zhenqiang, Wang Chengtao.The medical bio mechanics.1996; 11 (2), June:103-106) introduce.Method of least square is simple, is convenient to calculate, but directly uses method of least square, will be easy to be subjected to the interference of noise spot, and a very little noise spot just is enough to regression straight line is pulled away from correct position.Therefore trunk portion must consideration in practical operation how to choose femur, the influence that whole femur standard shaft line is brought with the section of avoiding femoral head top and condyle portion.Select the CT cross section of different femur fragment will produce different effects, inappropriate selection may produce bigger error.This method poor anti jamming capability, precision is low and it is loaded down with trivial details to operate, anthropic factor is excessive, can not search out best femur standard shaft line position automatically.Mainly rely on doctor's experience to carry out choosing of femur fragment in practice.Therefore the result of operation will depend on the environment of operation and doctor's experience fully, and this will bring very big error to operation.

Summary of the invention:

The objective of the invention is to deficiency and actual needs at conventional art, for providing high accuracy, full automatic femur standard shaft line to determine method based on the auxiliary total knee arthroplasty of the robot of CT, reduce the standard shaft line and determine additional cost, to improve precision, shorten the design cycle that the standard shaft line is determined.

For realizing such purpose, full-automatic femur standard shaft line in the auxiliary total knee arthroplasty of robot proposed by the invention is determined method, noise is removed in the section pretreatment that femur is carried out obtaining after the CT scan earlier, extract the pixel coordinates of pulp cavity center, and pixel coordinates is converted to image coordinate; The intermediate value that re-uses minimum intermediate value square law minimization data point residual error square is obtained the best estimate parameter of fitting a straight line, thereby obtains the fitting a straight line of specific femur fragment; Then the data point of whole section femoral bone cavitas medullaris center is carried out binary coding, use genetic algorithm that fitting a straight line is carried out optimizing, find the best base axial location of whole femur fragment, realized a full automatic process.

Method of the present invention mainly comprises following step:

1. the extraction of pulp cavity center

Carry out edge extracting after at first noise being removed in the section pretreatment, then image is carried out the part that binary conversion treatment obtains femur profile intramedullary cavity.For bianry image, the center of object is identical with the barycenter of object, tries to achieve the pixel coordinates of the center of femur section according to the barycenter formula of plane picture, and pixel coordinates is converted to image coordinate.

2. minimum intermediate value square law carries out the match of femur standard shaft line

The present invention uses minimum intermediate value square law to come femur standard shaft line is carried out match.Minimum intermediate value square law belongs to the robust regression method, has very strong capacity of resisting disturbance.In theory, the noise spot that minimum intermediate value square law can fault-tolerant 50% that is to say that the data that half is arranged are interfered and can not influence the result of match in data point set.In the center of all femur sections, select the point of p relatively close femur standard shaft line.These points are carried out minimum intermediate value two take advantage of match.If the coordinate of these central points is (x _i, y _i), at first set up a straight line equation ${\hat{y}}_i={\widehat{\mathrm{\β}}}_1{x}_i+{\widehat{\mathrm{\β}}}_0,$ Here With Be not the actual parameter of linear equation, but the estimated value that the center location point is carried out match, promptly by center point estimation the best

With

Secondly, ask for the residual error of each data point $r_i=y_i-{\hat{y}}_i,$ And ask for square r of residual error _i ²Intermediate value by minimization residual error square obtains at last

With Best estimated value, thus this p the fitting a straight line that point is best obtained.

3. use genetic algorithm to seek best femur standard shaft line position

Though minimum intermediate value square law has very strong capacity of resisting disturbance in the process of calculating p point, but how to choose this p point and select the numerical value of p that what remain a problem for, we wish to find automatically by certain mode the optimum of fitting a straight line.The present invention here adopts genetic algorithm to carry out the search of fitting a straight line.

For whole section femur section, adopt the chromosome binary coding among the present invention, each is corresponding to a section.Wherein represent this section selected for " 1 ", it is selected that " 0 " represents that this section does not have.Should guarantee that herein selected number p is greater than p _Th, p _ThBe a threshold value, in practice should according to the length of femur and the number and the spacing of the CT that gets section decide p _ThThe excessive time that will increase search, but p _ThCan not be too small, p _ThToo smallly will mean the positional information of losing the section of too much femur, also not have a practical meaning even the straight line error that match is at this moment come out is very little.To the section of promising " 1 " carry out minimum intermediate value two and take advantage of match, obtain the error e rror of minimum intermediate value square law.And with F=C _Max-error is as this individual object function, C _MaxIt is a bigger constant.Carry out individual selection according to object function, the ideal adaptation degree that F is big more is high more.Chromosome is intersected mutation operation.If the number that " 1 " wherein occurs is less than p _ThSituation, then with its fitness zero setting, prevent the little but insignificant situation of error.The individuality of getting the fitness maximum is as final fitting result.The individuality of fitness maximum is represented position and the numerical value of best p, and Dui Ying fitting a straight line is best femur standard shaft line with it.

The present invention is fully automatically in femur standard shaft line deterministic process, has reduced and has used complicated anchor clamps to carry out the definite fringe cost that is brought of standard shaft line in the artificial knee joint operation.With use traditional method of least square to carry out the match of standard shaft line to compare and have very strong capacity of resisting disturbance, reduced the error that anthropic factor brings, improved the precision of standard shaft line design greatly, shortened the design cycle that the standard shaft line is determined.

Description of drawings:

Fig. 1 is femoral cut floor map in the robot complete knee joint operation.

Fig. 2 is femur standard shaft line sketch map in the robot complete knee joint operation.

Fig. 3 is the centre of form of femur section.

Fig. 4 (a)-(f) is the result that minimum intermediate value square law carries out the match of femur standard shaft line.

Fig. 5 (a)-(b) is to use genetic algorithm to seek best femur standard shaft line position.

The specific embodiment:

Technical scheme for a better understanding of the present invention is described in further detail below in conjunction with drawings and Examples.

In total knee arthroplasty, realize that the displacement of femoral prosthesis mainly relies on five planar clean cut of femur as Fig. 1.Wherein important with first cutting planes.Other four planes all with first plane as benchmark, and determine corresponding normal direction and position according to patient's femur size and corresponding prosthese model.Determine that first cutting planes just must at first determine the direction of the anatomical axis of femur, shown in arrow among the figure.

As Fig. 2 when human body is stood, femoral head center B, the knee joint center O, should be in same straight line with the ankle joint center C, this straight line is the mechanics axis of lower limb or claims mechanical axis (mechanical axis), and then should in ground parallel through the planar trunnion axis of knee joint (transverse axis) this moment.Femur anatomical axis and above-mentioned lower limb mechanical axis through femoral shaft intersect the valgus angle that forms θ (5 °～9 °) at knee joint center O place.In total knee arthroplasty, osteotomy just can make the lower limb line of force obtain correct reconstruction by calculating and measure accurately.The reconstruction of the lower limb line of force is to guarantee the successful key of performing the operation, and also is to avoid the postoperative stress uneven and cause loosening important step.Owing to directly determine comparatively difficulty of BO, in knee surgery,, at first determine femur standard shaft line AO usually in order to recover this line of force as much as possible.In traditional TKA, this standard shaft line mainly relies on the interior interior bar of marrow that inserts of femoral bone cavitas medullaris and obtains.And in based on the auxiliary total knee arthroplasty of the robot of CT modeling, just must at first carry out femur base axis determination in the model before art.

At first edge extracting is carried out in section as Fig. 3, then image is carried out binary conversion treatment, obtain the part of femur profile intramedullary cavity.For bianry image, the center of object is identical with the barycenter of object, at first tries to achieve the center of femur section according to the barycenter formula (1) of plane picture.

If bianry image is B[i, j] therefore can use following formula to try to achieve the center of femur section. $\stackrel{-}{x}=\frac{\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}\mathrm{jB}[i,j]}{A},\stackrel{-}{y}=\frac{\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}\mathrm{iB}[i,j]}{A}---\left(1\right)$ Wherein: $A=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-1}{\mathrm{\Σ}}}B[i,j]$

What obtain is the pixel coordinates of femur central point herein.Pixel coordinates should be converted to image coordinate.Image plane coordinate centre coordinate is: $c_x=\frac{m-1}{2},c_y=\frac{n-1}{2}---\left(2\right)$ Then pixel coordinates (x, y) transformation for mula to image coordinate (x ', y ') is: $x^{\′}=s_x(\stackrel{-}{x}-c_x)=s_x(\stackrel{-}{x}-\frac{m-1}{2}),y^{\′}=s_y(\stackrel{-}{y}-c_y)=s_y(\stackrel{-}{y}-\frac{n-1}{2})---\left(3\right)$ S wherein _x, s _yBe respectively the ranks spacing of image array.

As Fig. 4 (a)-(f), in whole section femur section, select slice numbers p=74 respectively, 64,59,54,40,30.These points are carried out minimum intermediate value two take advantage of match.If the coordinate of these central points is (x _i, y _i), at first set up a straight line equation ${\hat{y}}_i={\widehat{\mathrm{\β}}}_1{x}_i+{\widehat{\mathrm{\β}}}_0,$ Here

With

Be not the actual parameter of linear equation, but the estimated value of the center location point being carried out match.Secondly, ask for the residual error of each data point $r_i=y_i-{\hat{y}}_i,$ And ask for square r of residual error _i ²Intermediate value by minimization residual error square obtains at last

With Best estimated value, thus the best-fitting straight line of corresponding selected femur fragment obtained.Can see that from whole fit procedure carrying out match with the intermediate value method of least square is subjected to the influence of femur upper segment very little, even also obtained effect preferably when getting p=74, can demonstrate fully the capacity of resisting disturbance of minimum intermediate value square law.Along with the minimizing gradually of choosing slice numbers (Fig. 4 a-Fig. 4 e), the error of match also reduces gradually, but when p=30, it is big that error becomes suddenly, and this explanation can not rely on the number that reduces section simply and improve the precision of match.Seek out higher fitting precision, must select suitable section.

As Fig. 5 (a)-(b), though minimum intermediate value square law has very strong capacity of resisting disturbance in the process of calculating p point, but how to choose this p point and select the numerical value of p that what remain a problem for, we wish to find automatically by certain mode the optimum of fitting a straight line.The present invention here adopts genetic algorithm to carry out the search of fitting a straight line.For whole section femur section, the present invention adopts the chromosome binary coding, and each is corresponding to a section.Wherein then represent this section selected for " 1 ", it is selected that " 0 " represents that then this section does not have.Should guarantee that herein selected number p is greater than p _Th, p _ThBe a threshold value, in practice should according to the length of femur and the number and the spacing of the CT that gets section decide p _ThThe excessive time that will increase search, but p _ThCan not be too small, p _ThToo smallly will mean the positional information of losing the section of too much femur, also not have a practical meaning even the straight line error that match is at this moment come out is very little.To the section of promising " 1 " carry out minimum intermediate value two and take advantage of match, obtain the error e rror of minimum intermediate value square law.And with F=C _Max-error is as this individual object function, C _MaxIt is a bigger constant.Carry out individual selection according to object function, the ideal adaptation degree that F is big more is high more.Chromosome is intersected mutation operation.If the number that " 1 " wherein occurs is less than p _ThSituation, then with its fitness zero setting, prevent the little but insignificant situation of error.The individuality of fitness maximum is represented position and the numerical value of best p, and Dui Ying fitting a straight line is best femur standard shaft line with it.Fig. 5 a is the fitting result when running to for 50 generations, and " * " expression participates in the slice position of match.The interference effect of femur upper segment just greatly reduces when proceeding to for 50 generations as can be seen from Fig. 5 a, and this time error is also very little.Fig. 5 b is the fitting result when proceeding to for 70 generations, and this moment, femur upper segment and middle part effect of noise were eliminated fully, at this moment thinks to have reached best fitting result, and this time error is minimum.

Claims (1)

1, a kind of full-automatic femur standard shaft line is determined method, it is characterized in that comprising following concrete steps:

1) extraction of the center of pulp cavity: carry out edge extracting after at first noise being removed in the section pretreatment, then image is carried out the part that binary conversion treatment obtains femur profile intramedullary cavity, for bianry image, the center of object is identical with the barycenter of object, try to achieve the pixel coordinates of femur section center according to the barycenter formula of plane picture, and pixel coordinates is converted to image coordinate;

2) minimum intermediate value square law carries out the match of femur standard shaft line: select p these points to be carried out minimum intermediate value two take advantage of match relatively near the point of femur standard shaft line in the center of all femur sections, the coordinate of establishing these central points is (x _i, y _i), at first set up linear equation ${\hat{y}}_i={\widehat{\mathrm{\β}}}_1{x}_i+{\widehat{\mathrm{\β}}}_0,$

With

Be the estimated value of the center location point being carried out match, ask for the residual error of each data point $r_i=y_i-{\hat{y}}_i,$ And ask for square r of residual error _i ², obtain by the intermediate value of minimization residual error square

With

Best estimated value, thus this p the fitting a straight line that point is best obtained;

3) seek best femur standard shaft line position automatically with genetic algorithm: for whole section femur section, adopt the chromosome binary coding, each is corresponding to a section, it is selected that wherein " 1 " represents this section, it is selected that " 0 " represents that this section does not have, then to the section of promising " 1 " carry out minimum intermediate value two and take advantage of match, obtain the error e rror of minimum intermediate value square law, and with F=C _Max-error is as this individual object function, C _MaxBe a bigger constant, carry out individual selection according to object function, chromosome is intersected, mutation operation is if wherein the number of appearance " 1 " is less than p _ThSituation, then with its fitness zero setting, the individuality of fitness maximum is represented position and the numerical value of best p, Dui Ying fitting a straight line is best femur standard shaft line with it, wherein, p _ThFor according to the length of femur and the number of the CT that gets section and the threshold value that spacing is determined.

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