CN106570335A - Colorless transformation based on correlation model between tumor and marker point in stereoscopic radiotherapy - Google Patents

Abstract

The invention provides colorless transformation based on a correlation model between a tumor and a marker point in stereoscopic radiotherapy. The colorless transformation comprises traditional linear correlation model modeling, improved linear correlation model modeling, UT transformation-based correlation model modeling and an effectiveness experiment of UT transformation-based correlation model modeling. The modeling method of the traditional linear correlation model modeling is a linear fitting model built on the basis of the least square method, the improved linear correlation model modeling is a novel linear correlation model built by considering a measurement error of marker point data, UT transformation-based correlation model modeling is a probability correlation model built by considering sensor noise and the uncertainty of the model and the model is taken as a basis of a respiratory movement tracking algorithm, and the experiment is mainly used for verifying the effectiveness of colorless transformation-based modeling.

Description

Colourless conversion in three-dimensional radiotherapy based on correlation model between tumor and mark point

Technical field

The invention belongs to field of medical technology, and in particular to be based on correlation model between tumor and mark point in three-dimensional radiotherapy Colourless conversion.

Background technology

In recent years, image guiding stereotactic radiotherapy is developed rapidly as a kind of important method for treating tumor, is put Penetrate treatment and experienced the different differentiation of several generations, the radiotherapy of early stage needs to be mainly used in treating intracranial by stereotactic frame Tumor, with the development of technology, radiotherapy starts that in-vivo tumour, such as pulmonary carcinoma, hepatocarcinoma, cancer of pancreas etc. can be treated.But control During treatment, in-vivo tumour can change with respiratory movement, and in order to reduce respirometric impact, simplest method is to expand Therapy area, but so can inevitably hurt perilesional and normally organize, and another kind of method is respiratory control skill Art, but the weak patient of meeting donor brings pain, and respiratory gating technology precision is higher, but treatment cycle is long, and does not examine The time delay of worry system.Most efficient method is the synchronous breathing tracking technique in ejected wave knife breathing tracking system, and the technology passes through The correlation model set up between patient body-surface mark point and in-vivo tumour motion, it is possible to calculated by the exercise data of mark point To the position of in-vivo tumour, so as to adjust treatment beam real-time tracking tumor, to reach the purpose of accurate treatment.Traditional association mould The modeling method of type is the linear or multinomial model set up based on method of least square, but traditional method does not account for passing The randomness of sensor noise and model.And in actual therapeutic, in-vivo tumour and skin-marker all can be with respiratory movements It is continually changing, then correlation model between the two is also what is be continually changing, therefore should be by sensor when respiratory movement is modeled The uncertainty of error of measured data and model is all taken into account, to improve the accuracy of model.

The content of the invention

It is an object of the invention to provide the colourless conversion in three-dimensional radiotherapy based on correlation model between tumor and mark point, solution Certainly above-mentioned problem.

The present invention provides the colourless conversion in three-dimensional radiotherapy based on correlation model between tumor and mark point, including：

(1) conventional linear correlation model modeling：Based on the linear correlation that method of least square is set up between tumor and mark point Model；

(2) linear correlation model modeling is improved：Mark point is designed in the conventional linear correlation model modeling method DATA REASONING error；

(3) based on UT conversion correlation model modelings：Be designed into sensing in linear correlation model modelling approach in described improvement The conversion of device noise and model.

Further technical scheme, in step (), the conventional linear correlation model modeling is following by minimizing Second-order equation obtains linear model y=ax+b：

Wherein, x_i(i=1 ... n) be the mark tally evidence for measuring pivot variable, y_i(i=1 ... n) it is in-vivo tumour X, Y or Z-direction measurement data,It is the optimal value of yi, a and b is the parameter of linear model.

Further technical scheme, in step (two), the linear correlation model modeling that improves is by below optimization Object function is obtained：

Wherein,For x_iOptimal value, with above formulaIt is updated in equation and obtains equation below：

The equation is non-recessed second order function, using this equation of numerical method solution, for equation (3), provides the near-optimization of a ValueThenBe one with regard to b andRecessed second order function：

Object functionMinima can be obtained by least mean square algorithm,

Assume X=[b, x₁,...x_n]^T, then equation (4) form of matrix can be written as：

Wherein

ThenMinima be calculated as by least mean square algorithm

The then optimal estimation of a and b can be obtained by following steps：

First, obtain the near-optimization value of a using equation (1)

Second, interval [a is set₁ a₂] conductThe optimal estimation value region closed on；

3rd, it is evenly dividing interval [a₁ a₂], for the value of each possible a in interval, obtain b's using equation (9) Optimal estimation value, substitutes into equation (5) calculating target functionWillValue be stored in form；Minima in finding out, phase The a and b of pass is in equation (3)Optimal estimation value.

Further technical scheme, it is described to be obtained by following calculating based on UT conversion correlation model modelings in step (three) ：

The correlation model for assuming equation (3) is written as following form：

Wherein, S is an augmented matrix being made up of measurement data, and its covariance matrix is P：

S=[x₁,...x_n,y₁,...y_n]^T (11)

First, 2L+1 Sigma point is constructed, their weight is W, wherein, L is the dimension of vectorial S：

χ₀=S (12)

Wherein, λ=α²(L+ κ)-L is scale parameter, and α is scale factor, and β is kurtosis function, and κ is second scale parameter It is usually arranged as 0,For the i-th row of matrix (L+ λ) P roots.After calculating Sigma points, by equation (10) Non-linear conversion propagates to obtain following formula：

y_i=f (χ_i), i=0 ..., 2L (18)

Then the best estimate and covariance of Y is respectively：

Further technical scheme, also includes after step (three)：Step (four) converts having for correlation model modeling based on UT The experiment of effect property：By conventional linear correlation model modeling with described based on UT conversion correlation model modeling contrast verifications.

Further technical scheme, in step (four), the effectiveness experiment for converting correlation model modeling based on UT is adopted Verified with chi square test, it is assumed that correlation model is y=h (Y, x)=ax+b (Y=[a b]^T), for each measurement point, geneva away from Can be calculated as follows from D：

V=y_i-h(a,b,x_i) (21)

D=v^TC^-1v (23)

Wherein, Q be the calculated covariance matrix of equation (19), q_xAnd q_yIt is respectively x_iAnd y_iCovariance,

Chi square test judges the compatibility of measured value and correlation model using mahalanobis distance：

Wherein,The inverse cumulative distribution function in card side is represented, d is the dimension of y, and 1- α are confidence level, are usually arranged as 95%.

It is an advantage of the invention that：The uncertainty of measurement error and model is taken into account, the accuracy of modeling is improve. More accurate correlation model is applied to breathe in track algorithm by the method, for the survival rate and China for improving patient Medical skill development tool has very important significance.

Description of the drawings

Fig. 1 is to be based on to be adopted in the colourless conversion of correlation model between tumor and mark point in three-dimensional radiotherapy of the present invention With the respiratory movement time phase dividing figure of modeling data；

Fig. 2 be in three-dimensional radiotherapy of the present invention based between tumor and mark point the colourless conversion of correlation model it is many The fitting of item formula and the modeling error relative analyses figure of improved linear fit model；

Fig. 3 is the chi square test result figure that correlation model modeling is converted based on UT of the present invention；

Fig. 4 is the chi square test result figure of the modeling method for not considering model error of the present invention.

Specific embodiment

The present invention is provided to be included in three-dimensional radiotherapy based on the colourless conversion of correlation model between tumor and mark point：First, Conventional linear correlation model is modeled；Then, linear correlation model modeling is improved, then, based on UT conversion correlation model modelings.

It is understandable to enable the above objects, features and advantages of the present invention to become apparent from, with reference to the accompanying drawings and examples Further illustrate technical scheme.But the invention is not restricted to listed embodiment, should also be included in institute of the present invention Other any known changes in the interest field of requirement.

" one embodiment " or " embodiment " referred to herein is referred to and may be included at least one implementation of the invention Special characteristic, structure or characteristic." in one embodiment " that in this manual different places occur not refers both to same Individual embodiment, nor single or selectively mutually exclusive with other embodiment embodiment.

In robot stereotactic radiotherapy, in order to avoid human body long-time is irradiated by X-ray, in-vivo tumour Data interval collect, the exercise data of skin-marker can be measured in real time.Set up between tumor and mark point Correlation model the movement position of tumor can be in real time obtained by the exercise data of mark point, and using this correlation model as prediction The measurement model look-ahead of algorithm goes out the position that tumor will reach, with the time delay of compensation system.Traditional correlation model is Based on the linear correlation model that method of least square is set up, the data of modeling are provided by the public database of Lubeck universities.Due to It is two different motor processs to exhale with air-breathing, therefore needs first to divide the data into expiration and air-breathing two parts before modeling, Then this two parts data is modeled respectively.Fig. 1 is referred to, Fig. 1 is based on tumor and mark in three-dimensional radiotherapy of the present invention Respiratory movement time phase dividing figure between note point in the colourless conversion of correlation model using modeling data.As shown in figure 1, breathing fortune The division result of dynamic phase place, using the peak value and valley of respiratory movement curve as the cut-point exhaled with air-breathing, whole breathing Motor process is divided into expiration and air-breathing two parts, and correlation model is set up respectively.

The first step, the modeling of conventional linear correlation model：Linear model y=ax is obtained by the second-order equation for minimizing following +b：

Wherein, x_i(i=1 ... n) be the mark tally evidence for measuring pivot variable, y_i(i=1 ... n) it is in-vivo tumour X, Y or Z-direction measurement data,It is y_iOptimal value, a and b is the parameter of linear model.This modeling method It is widely used in the stereotactic radiotherapy with ejected wave knife as representative, but the method thinks that measurement data is accurate , in fact, noise error is exist during sensor measurement data, so measurement error should be taken into account during modeling.

Second step, improves linear correlation model modeling：The exercise data error of external label point is taken into account, it is linear to close Gang mould type is obtained by the object function below optimization：

Wherein,For x_iOptimal value, with above formulaIt is updated in equation and obtains equation below：

The equation is non-recessed second order function, using this equation of numerical method solution, for equation (3), provides the near-optimization of a ValueThenBe one with regard to b andRecessed second order function：

Object functionMinima can be obtained by least mean square algorithm.

Assume X=[b, x₁,...x_n]^T, then equation (4) form of matrix can be written as：

Wherein

ThenMinima be calculated as by least mean square algorithm

The then optimal estimation of a and b can be obtained by following steps：

The near-optimization value of a is obtained using equation (1)

First, interval [a is set₁ a₂] conductThe optimal estimation value region closed on；

Secondly, it is evenly dividing interval [a₁ a₂], for the value of each possible a in interval, obtain b's using equation (9) Optimal estimation value, substitutes into equation (5) calculating target functionWillValue be stored in form；

Then, the minima in finding out, related a and b is in equation (3)Optimal estimation value.

Fig. 2 is referred to, Fig. 2 is the nothing in three-dimensional radiotherapy of the present invention based on correlation model between tumor and mark point Fitting of a polynomial and the modeling error relative analyses figure of improved linear fit model that complexion changed is changed.As shown in Fig. 2 bent in error The apex of line, the algorithm of improved linear fit model compares the algorithm of fitting of a polynomial and somewhat reduces error of fitting.

In the modeling of conventional linear correlation model, correlation model is considered as accurate and deterministic model, and in tracking During keep constant, but correlation model is obtained by measure data fitting, and measurement data can be subject to noise jamming, institute Should be uncertain with correlation model, therefore also the randomness of model should be taken into account in state estimation.Become using UT The method changed can obtain the randomness of correlation model, and without using analytic equation transfer problem can be just solved.So carry out 3rd step, based on UT conversion correlation model modelings：The correlation model for assuming equation (3) is written as following form：

Wherein, S is an augmented matrix being made up of measurement data, and its covariance matrix is P：

S=[x₁,...x_n,y₁,...y_n]^T (11)

First, construct 2L+1 Sigma point, their weight is W (L is the dimension of vectorial S)：

χ₀=S (12)

Wherein, λ=α²(L+ κ)-L is scale parameter, and α is scale factor, and β is kurtosis function, and κ is second scale parameter It is usually arranged as 0,For the i-th row of matrix (L+ λ) P roots.After calculating Sigma points, by equation (10) Non-linear conversion propagates to obtain following formula：

y_i=f (χ_i), i=0 ..., 2L (18)

Then the best estimate and covariance of Y is respectively：

After the 3rd step, for the result, the effectiveness that can carry out converting correlation model modeling based on UT is tested Card：Conventional linear correlation model modeling is verified based on UT conversion correlation model modelings with described using chi square test, it is false If correlation model is, for each measurement point, mahalanobis distance D can be calculated as follows：

V=y_i-h(a,b,x_i) (21)

D=v^TC^-1v (23)

Wherein, Q be the calculated covariance matrix of equation (19), q_xAnd q_yIt is respectively x_iAnd y_iCovariance.Card side surveys Examination judges whether measured value and correlation model are compatible using mahalanobis distance：

Wherein,The inverse cumulative distribution function in card side is represented, d is the dimension of y, and 1- α are confidence level, are usually arranged as 95%.

Inverse cumulative distribution function is a kind of dialect in probability, cumulative distribution letter corresponding with cumulative distribution function Number represents the probability sums less than or equal to the value all for the particular value of system, and inverse cumulative distribution function is then represented for one The corresponding system value of probit, herein,The corresponding mahalanobis distance value of chi-square value when confidence level is 95% is represented, if horse Family name's distance is less than the value, illustrates to have passed through compatibility test.

It is the chi square test result that correlation model modeling is converted based on UT of the present invention to refer to Fig. 3 and Fig. 4, Fig. 3 Figure；Fig. 4 is the chi square test result figure of the modeling method for not considering model error of the present invention.As shown in Figure 3 and Figure 4, Fig. 4 is than there is more data to pass through consistency check in Fig. 3, because the modeling of conventional linear correlation model does not account for model The error of itself, cause estimated result over-confident.In the prediction work of tumor tracking, data can not be examined by concordance Testing will cause prediction algorithm singular point occur, and these singular points can reduce the accuracy of tumor tracking.

In sum, the present invention provide three-dimensional radiotherapy in based between tumor and mark point correlation model without complexion changed Change.The uncertainty of measurement error and model is taken into account, the accuracy of modeling is improve.

It should be noted that above example is only unrestricted to illustrate technical scheme, although with reference to preferably Embodiment has been described in detail to the present invention, it will be understood by those within the art that, can be to the technology of the present invention Scheme is modified or equivalent, and without deviating from the spirit and scope of technical solution of the present invention, it all should cover at this In the middle of bright right.

Claims (6)

1. the colourless conversion in three-dimensional radiotherapy based on correlation model between tumor and mark point, it is characterised in that include：

(1) conventional linear correlation model modeling：The linear correlation mould set up between tumor and mark point based on method of least square Type；

(2) linear correlation model modeling is improved：Mark tally evidence is designed in the conventional linear correlation model modeling method Measurement error；

(3) based on UT conversion correlation model modelings：Be designed into sensor in linear correlation model modelling approach and make an uproar in described improvement The conversion of sound and model.

2. the colourless conversion in three-dimensional radiotherapy according to claim 1 based on correlation model between tumor and mark point, its It is characterised by：In step (), the conventional linear correlation model is modeled and obtained linearly by minimizing following second-order equation Model y=ax+b：

$\begin{array}{c}\left\{\begin{array}{c}{\mathrm{\&chi;}}_1^2(a,b,\stackrel{-}{y_1},\mathrm{...}\stackrel{-}{y_n})=\underset{i=1}{\overset{n}{\&Sigma;}}{(\stackrel{-}{y_i}-y_i)}^2\\ s.t.\stackrel{\&OverBar;}{y}={\mathrm{ax}}_i+b\end{array}\right.\\ <\hat{a},\hat{b}>=\underset{\&ForAll;{\stackrel{\&OverBar;}{y}}_1,\mathrm{...}{\stackrel{\&OverBar;}{y}}_n}{\arg \min }{\mathrm{\&chi;}}_1^2(a,b,\stackrel{-}{y_1},\mathrm{...}\stackrel{-}{y_n})\end{array}---\left(1\right)$

Wherein, x_i(i=1 ... n) be the mark tally evidence for measuring pivot variable, y_i(i=1 ... n) it is in-vivo tumour X, Y Or Z-direction measurement data,It is y_iOptimal value, a and b is the parameter of linear model.

3. the colourless conversion in three-dimensional radiotherapy according to claim 1 based on correlation model between tumor and mark point, its It is characterised by：In step (two), the linear correlation model modeling that improves is obtained by the object function below optimization：

$\begin{array}{c}\left\{\begin{array}{c}{\mathrm{\&chi;}}_2^2(a,b,\stackrel{-}{x_1},\mathrm{...}\stackrel{-}{x_n},\stackrel{-}{y_1},\mathrm{...}\stackrel{-}{y_n})=\underset{i=1}{\overset{n}{\&Sigma;}}({\left(\stackrel{\&OverBar;}{x}-x_i\right)}^2+{\left(\stackrel{\&OverBar;}{y}-y_i\right)}^2)\\ s.t.\stackrel{\&OverBar;}{y}=a\stackrel{-}{x_i}+b\end{array}\right.\\ <\hat{a},\hat{b}>=\underset{\&ForAll;\stackrel{-}{x_1},\mathrm{...}\stackrel{-}{x_n},\stackrel{-}{y_1},\mathrm{...}\stackrel{\&OverBar;}{y}}{\arg \min }{\mathrm{\&chi;}}_2^2(a,b,\stackrel{-}{x_1},\mathrm{...}\stackrel{-}{x_n},\stackrel{-}{y_1},\mathrm{...}\stackrel{-}{y_n})\end{array}---\left(2\right)$

Wherein,For x_iOptimal value, with above formulaIt is updated in equation and obtains equation below：

$\left\{\begin{array}{c}{\mathrm{\&chi;}}_3^2(a,b,\stackrel{-}{x_1},\mathrm{...}\stackrel{-}{x_n})=\underset{i=1}{\overset{n}{\&Sigma;}}({\left(\stackrel{-}{x_i}-x_i\right)}^2+{\left(a\stackrel{-}{x_i}+b-y_i\right)}^2)\\ <\hat{a},\hat{b}>=\underset{\&ForAll;{\stackrel{\&OverBar;}{x}}_1,\mathrm{...}{\stackrel{\&OverBar;}{x}}_n}{\arg \min }{\mathrm{\&chi;}}_3^2(a,b,\stackrel{-}{x_1},\mathrm{...}\stackrel{-}{x_n})\end{array}\right.---\left(3\right)$

The equation is non-recessed second order function, using this equation of numerical method solution, for equation (3), provides the near-optimization value of aThenBe one with regard to b andRecessed second order function：

Object functionMinima can be obtained by least mean square algorithm,

Assume X=[b, x₁,...x_n]^T, then equation (4) form of matrix can be written as：

${\mathrm{\&chi;}}_4^2\left(X\right)={\mathrm{\&chi;}}_4^2(b,\stackrel{-}{x_1},...\stackrel{-}{x_n})=X^{T}AX+X^{T}B+C---\left(5\right)$

Wherein

$B=\left[\begin{array}{c}-2x_1-2{\mathrm{ay}}_1\\ .\\ .\\ .\\ -2x_n-2{\mathrm{ay}}_n\\ -2(y_1+...+y_n)\end{array}\right]---\left(7\right)$

$C={\mathrm{\&Sigma;}}_{i=1}^n{x}_i^2+y_i^2---\left(8\right)$

ThenMinima be calculated as by least mean square algorithm

The then optimal estimation of a and b can be obtained by following steps：

First, obtain the near-optimization value of a using equation (1)

Second, interval [a is set₁ a₂] conductThe optimal estimation value region closed on；

3rd, it is evenly dividing interval [a₁ a₂], for the value of each possible a in interval, using equation (9) optimum of b is obtained Estimated value, substitutes into equation (5) calculating target functionWillValue be stored in form；Minima in finding out is related A and b are in equation (3)Optimal estimation value.

4. the colourless conversion in three-dimensional radiotherapy according to claim 1 based on correlation model between tumor and mark point, its It is characterised by：It is described to be obtained by following calculating based on UT conversion correlation model modelings in step (three)：

The correlation model for assuming equation (3) is written as following form：

$Y=\left[\begin{array}{c}a\\ b\end{array}\right]=f\left(S\right)---\left(10\right)$

Wherein, S is an augmented matrix being made up of measurement data, and its covariance matrix is P：

S=[x₁,...x_n,y₁,...y_n]^T (11)

First, 2L+1 Sigma point is constructed, their weight is W, wherein, L is the dimension of vectorial S：

χ₀=S (12)

${\mathrm{\&chi;}}_i=S+{\left(\sqrt{\left(L+\mathrm{\&lambda;}\right)P}\right)}_i,i=1,...,L---\left(13\right)$

${\mathrm{\&chi;}}_i=S-{\left(\sqrt{\left(L+\mathrm{\&lambda;}\right)P}\right)}_{i-L},i=L+1,...,2L---\left(14\right)$

$W_0^{\left(m\right)}=\mathrm{\&lambda;}/(L+\mathrm{\&lambda;})---\left(15\right)$

$W_0^{\left(c\right)}=\frac{\mathrm{\&lambda;}}{L+\mathrm{\&lambda;}}+(1-{\mathrm{\&alpha;}}^2+\mathrm{\&beta;})---\left(16\right)$

$W_i^{\left(m\right)}=W_i^{\left(c\right)}=\frac{1}{2L+2\mathrm{\&lambda;}},i=1,...,2L---\left(17\right)$

Wherein, λ=α²(L+ κ)-L is scale parameter, and α is scale factor, and β is kurtosis function, and κ is that second scale parameter is usual It is set to 0,For the i-th row of matrix (L+ λ) P roots.After calculating Sigma points, by equation (10) non-thread Property conversion propagate to obtain following formula：

y_i=f (χ_i), i=0 ..., 2L (18)

Then the best estimate and covariance of Y is respectively：

$\hat{Y}={\&Sigma;}_{i=0}^{2L}{W}_i^{\left(m\right)}{y}_i---\left(19\right)$

$P_y={\&Sigma;}_{i=0}^{2L}{W}_i^{\left(c\right)}(y_i-\hat{Y}){(y_i-\hat{Y})}^T---\left(20\right).$

5. the colourless conversion in three-dimensional radiotherapy according to claim 1 based on correlation model between tumor and mark point, its It is characterised by, also includes after step (three)：Step (four) converts the effectiveness experiment of correlation model modeling based on UT：By the biography System linear correlation model modeling is with described based on UT conversion correlation model modeling contrast verifications.

6. the colourless conversion in three-dimensional radiotherapy according to claim 5 based on correlation model between tumor and mark point, its It is characterised by：In step (four), the effectiveness experiment for converting correlation model modeling based on UT is verified using chi square test, false If correlation model is y=h (Y, x)=ax+b (Y=[a b]^T), for each measurement point, mahalanobis distance D can be calculated as follows：

V=y_i-h(a,b,x_i) (21)

$C=\frac{\&part;h}{\&part;Y}Q{\left(\frac{\&part;h}{\&part;Y}\right)}^T+\frac{\&part;h}{\&part;x_i}{q}_x{\left(\frac{\&part;h}{\&part;x_i}\right)}^T+q_y---\left(22\right)$

D=v^TC^-1v (23)

Wherein, Q be the calculated covariance matrix of equation (19), q_xAnd q_yIt is respectively x_iAnd y_iCovariance.Chi square test profit Judge the compatibility of measured value and correlation model with mahalanobis distance：

$D<{\mathrm{\&chi;}}_{d,1-\mathrm{\&alpha;}}^2---\left(24\right)$

Wherein,The inverse cumulative distribution function in card side is represented, d is the dimension of y, and 1- α are confidence level, are usually arranged as 95%.