CN111242965B - Genetic algorithm-based breast tumor contour dynamic extraction method - Google Patents
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Abstract
The invention discloses a method for extracting a dynamic contour of a breast tumor based on a genetic algorithm, which mainly solves the problems of low resolution and optimization efficiency of the existing microwave imaging technology. The scheme is as follows: 1) Constructing an initial tumor model; 2) Constructing a fitness function; 3) Obtaining the central position of the tumor in the initial tumor model and the rectangular outline thereof by utilizing confocal imaging; 4) Acquiring a distance compensation fitness function; 5) Obtaining an initial contour model sequence according to the optimal tumor rectangular contour, and iteratively training the sequence to obtain an evolution contour model sequence; 6) And performing iterative training on the evolution contour model sequence, calculating the sequence by using a distance compensation fitness function to obtain a fitness value, comparing the fitness value with a preset threshold value, and outputting a tumor contour map of the optimal model. The invention focuses on extracting the contour shape of the tumor, reduces the chromosome length of a genetic algorithm, improves the imaging resolution and the optimization efficiency, and can be used for high-precision imaging of the breast tumor.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image contour extraction method which can be used for extracting a two-dimensional contour shape of a breast tumor.
Background
Microwave imaging uses microwaves to irradiate a measured object, and electromagnetic parameter distribution of the object is reconstructed through measured data of a scattered field outside the object. The permittivity and conductivity of tumor tissue are clearly distinguished from those of adjacent normal tissue in a particular electromagnetic wave frequency range. For example, at a frequency of 6GHz, the relative permittivity of normal tissue is 9.8, the electrical conductivity is 0.4S/m, and the corresponding parameters of tumor tissue are 50.74 and 4.82S/m, respectively. Therefore, the electromagnetic parameter distribution of the object tissue can be inverted by using the microwave irradiation and the measured data of the scattered field, and tumor imaging is realized.
The current common approach is to optimize the results of microwave imaging using genetic algorithms. For example, in 2000, R.Olmi et al realized the reconstruction of electromagnetic parameters of an imaged region using genetic algorithms in the literature "Olmi R, bini M, priority S.A. genetic algorithm to image retrieval in electronic image biology (J. Kiee International Transactions on electronics & Applications,2000,4-c (3): 309-320". The method is characterized in that a circular imaging area is divided into 96 triangular lattices, and the genetic iteration times are 1000. The method has a high calculation cost, and the pixels of the tumor contour are larger than 1cm.
In 2007, abas Sabouri et al, sabouria, xu M, noghaian S, et al, effective microwave branching imaging technique using parallel algorithm optimized microwave imaging results and parallel computing accelerated genetic algorithm iteration speed, achieved 7.5mm pixel tumor imaging in a 12cm diameter circular imaging region.
The methods of microwave imaging by using genetic algorithm are all used for imaging the whole tumor region, and all have the defect of low imaging resolution, and the resolution is not enough for further observing the specific contour of the tumor. If the method is used for directly carrying out high-resolution imaging, the chromosome length of a genetic algorithm is obviously lengthened, the data size and the iteration times are obviously increased, and the result cannot be output in a reasonable time by using the conventional computing equipment.
Disclosure of Invention
The invention aims to provide a breast tumor contour dynamic extraction method based on a genetic algorithm aiming at the defects of the prior art, so that the chromosome length of the genetic algorithm is reduced, the iteration efficiency is improved, and the imaging resolution of a tumor is improved.
The technical scheme of the invention is as follows: by combining a genetic algorithm and an integrated algorithm, the cross section area of the pair of the sensors is 100mm 2 Extracting the edge contour of the left and right two-dimensional breast tumors to obtain a two-dimensional breast tumor image with 1mm pixels, which comprises the following steps:
1. a breast tumor contour dynamic extraction method based on genetic algorithm is characterized in that:
(1) Construction of initial tumor model
1a) Acquiring an existing breast tumor ultrasonic image;
1b) Distinguishing the tumor tissue and the normal tissue according to the gray value difference in the image, converting the image into a binary image, and respectively marking the tumor tissue and the normal tissue;
1c) The binary map in 1 b) is gridded according to a set resolution ratio to generate a grid image, and a tissue matrix A is obtained:
wherein, a ij Indicating the organization information at position (i, j) in the grid image, if a ij =0, indicating that the site is normal tissue, if a ij =1, indicating that this location is tumor tissue;
1d) Establishing an initial tumor model X in XFDTD electromagnetic simulation software according to the tissue matrix A obtained in 1 c) a N antennas are arranged around the model, each antenna emits electromagnetic waves in turn to radiate the tumor, all the antennas receive and record electromagnetic echoes at the same time, and N is more than or equal to 8;
1e) Copying original tumor model X a Replacing the tumor tissue with normal tissue to obtain tumor-free model X b ；
(2) Constructing an initial evaluation function F:
wherein N represents the total number of antennas, M is the total number of current samples per antenna,
representing the initial tumor model X a The ith antenna receives the current value of the echo at the time t, and then>
Representing a tumor-free model X b The ith antenna receives the current value of the echo at the time t;
(3) The central position of the tumor and the optimal rectangular outline of the tumor are obtained by confocal imaging:
3a) Initial tumor model X established in 1 d) a Determining the basic area of the tumor by confocal imaging;
3b) Tumor-free model X established in 1 e) b In the method, a tumor tissue cell with the side length of 8mm is used for traversing a tumor basic region to obtain a model X with the tumor tissue cell o Calculating the fitness value of the model through an initial fitness function F, and selecting the model X o The position of the cell with the highest medium fitness value is used as the central position of the tumor;
3c) Adjusting the length and width of the small grid at the central position to obtain a rectangular tumor model X s Iteratively calculating the fitness value of the model by means of an initial evaluation function F until the fitness value no longer increases, at which point the model X s The rectangular contour in (1) is the optimal tumor rectangular contour;
(4) Modifying the initial fitness function F to obtain a distance compensation fitness function F';
(5) Adjusting the position of the rectangular tumor obtained in the step (3) to obtain an initial contour model sequence, calculating the fitness value of the initial contour model sequence by using a distance compensation fitness function F', encoding the initial contour model sequence, training the encoded initial contour model sequence sequentially by using a genetic algorithm and an integration algorithm, and continuously evolving the shape of the tumor contour by using a variable quantity of 1mm to obtain an evolved contour model sequence;
(6) Distance compensation fitness value sequence f of evolution contour model sequence 1 ′，f 2 ′...，f l 'maximum value f' max And (3) comparing with a preset fitness threshold value f:
if 'f' max F is larger than or equal to f, the optimal model exists in the evolution contour model sequence obtained in the step (5), the training is finished, and a tumor contour image of the model is output;
if' max If f, the optimal model is not obtained, and the pair is neededAnd (5) coding the evolution contour model sequence again, continuously and sequentially performing iterative training through a genetic algorithm and an integration algorithm, and if the optimal model is not obtained when the set maximum iteration times are reached, outputting a tumor contour image with the highest adaptability value.
Compared with the prior art, the invention has the following advantages:
firstly, when the genetic algorithm is used for high-resolution imaging, the factors of data magnitude and antenna position are fully considered, a new evaluation function is constructed, the calculated fitness value can better evaluate the quality of an iteration result, and the iteration efficiency is improved.
Secondly, the invention focuses on extracting the outline of the tumor without concerning the internal tissue structure of the tumor, so that when the genetic algorithm is used, the tissue is coded, the coding length can be reduced by about 50 percent, the iteration speed of the genetic algorithm can be greatly improved, and the resolution of tumor imaging can be improved.
Thirdly, the invention combines the integration algorithm, utilizes the uncertainty of the genetic algorithm result, and adopts the integrated result as the final result of each iteration, thereby greatly improving the imaging accuracy.
Drawings
FIG. 1 is a flow chart of an implementation of the invention;
FIG. 2 is an ultrasound image of a breast tumor used in an embodiment of the present invention;
FIG. 3 is a contour map of the breast tumor image of FIG. 2 binarized using the present invention;
FIG. 4 is a 1mm gridded profile of the binarized profile of FIG. 3 using the present invention;
FIG. 5 is a diagram of an initial tumor model modeled in XFDTD according to the gridded profile of FIG. 4;
FIG. 6 is a tumor contour progression graph obtained by iterative training according to the present invention;
FIG. 7 is a grid plot of the initial tumor model gridded using XFDTD software.
Detailed Description
Embodiments and effects of the present invention will be described in detail with reference to the accompanying drawings.
Referring to fig. 1, the implementation of this embodiment is as follows:
step 1, constructing an initial tumor model.
1.1 Obtaining an existing breast tumor sonogram, as shown in fig. 2;
1.2 Tumor tissue and normal tissue are distinguished according to the gray value difference in fig. 2 and converted into a binary image, which is marked respectively, i.e. black represents normal tissue and white represents tumor tissue, as shown in fig. 3;
1.3 Set the resolution of the divided mesh to 1mm, and perform gridding to generate a mesh image in accordance with the set resolution in fig. 3, as shown in fig. 4, and generate a tissue matrix a:
wherein a is ij Indicating the organization information at position (i, j) in the grid image, if a ij =0, indicating that the site is normal tissue, if a ij =1, this location is tumor tissue;
1.4 Based on the tissue matrix A obtained in 1.3, an initial tumor model X was established in XFDTD electromagnetic simulation software a As shown in fig. 5, in which,
the center of the normal tissue is at the origin of coordinates, the radius of the normal tissue is 50mm, the tumor tissue is arranged in the normal tissue, and the area of the tumor tissue is 104mm 2 8 antennas are uniformly distributed around the tissue, each antenna emits electromagnetic waves in turn to radiate the tumor, and all the antennas receive and record electromagnetic echoes at the same time; selecting a single-frequency sine wave as a transmitting signal of an antenna, wherein the transmitting frequency is 6GHz, the phase is 0 degree, at the frequency, the relative dielectric constant of a normal tissue is 9.8, the conductivity is 0.4S/m, and the corresponding parameters of a tumor tissue are 50.74S/m and 4.82S/m respectively;
1.5 ) copy of initial tumor model X a Replacing the tumor tissue with normal tissue to obtain tumor-free model X b 。
And 2, constructing an initial fitness function.
2.1 By XFDTD simulation software for initial tumor model X a And tumor-free model X b Carrying out simulation to obtain X a The current value of the echo received by the ith antenna at the time point t is
And X b The ith antenna receives the echo at the time t, and the current value is ^>
And calculates the square error of the two currents>
2.2 Time-by-time, antenna-by-antenna accumulation X a And X b Current square error of
Obtaining a total current error E:
in the formula, N is the total number of the antennas, and M is the total current sampling number of each antenna;
2.3 Inverse E) to obtain a fitness function F:
after the tumor is added into the tumor-free model, the value of F is larger as the model is similar to the initial tumor model.
And 3, obtaining the central position of the tumor and the optimal rectangular outline of the tumor by utilizing confocal imaging.
3.1 In 1.4) initial tumor model X a Determining a basic tumor area by using confocal imaging, wherein the basic tumor area is a rectangular area, the central coordinate of the area is (-2mm, 15mm), the length of the area is 14mm, and the width of the area is 10mm;
3.2 In 1.5) established tumor-free model X b In the method, a tumor cell with the side length of 8mm is used for traversing the whole confocal imaging area to obtain a model X with the tumor cell o Calculating the fitness value of the model through an initial evaluation function F, and selecting the model X o The position of the small lattice with the highest medium fitness value is taken as the central position of the tumor, and the central position of the small lattice is (-3mm, 15mm);
3.3 Adjusting the length and width of the small grid at the center position to obtain a rectangular tumor model X s The fitness value of the model is iteratively calculated by means of an initial evaluation function F until the fitness value no longer increases, at which point the model X s The rectangular outline in (1) is the optimal tumor rectangular outline, and the obtained optimal rectangular outline has the center coordinates of (-3 mm,15.5 mm), the length of 12mm and the width of 9mm.
And 4, modifying the initial fitness value function F to obtain a distance compensation fitness function F'.
4.1 Computing an adjustment coefficient a for each antenna i ：
a i ＝l i -2 /max(l 1 -2 ，l 2 -2 ，...，l i -2 ...，l N -2 )，
In the formula I i The distance between the ith antenna and the center position of the tumor is expressed, and N is the total number of the antennas;
4.2 ) calculate the total current error E for each antenna i ：
In the formula (I), the compound is shown in the specification,
representing the initial tumor model X a The ith antenna receives the current value of the echo at the time t, and then>
Representing a rectangular tumor model X s At tThe current value of the echo is received at any moment, and M is the total current sampling number of each antenna;
4.3 Based on the total current error E for each antenna i And its adjustment coefficient a i And obtaining a distance compensation fitness function F':
and 5, obtaining an initial contour model sequence, and training the model sequence sequentially through a genetic algorithm and an integrated algorithm to obtain an evolution contour model sequence.
5.1 Moving a rectangular tumor model X within a range of 1mm s The position of the tumor in the model, and the sequence of the generated initial contour model is x 1 ，x 2 ，...，x i ，...，x k ；
5.2 ) extract an initial contour model sequence x 1 ，x 2 ，...，x i ，...，x k Any of the models x i The edge of the medium tumor is gridded for the areas inside and outside the edge to obtain an inner and outer double-layer grid S with the side length of 1mm and tangent with the edge, and any small grid in the grid S is expressed as S i ；
5.3 Code the lattice S on a chromosome G, each gene of the chromosome and the small lattice S i Corresponds to, is represented as g i For each gene g i ：
If g is i If =0, the cell s i Is a normal tissue;
if g is i 1, then small lattice s i Is tumor tissue;
5.4 To the initial contour model sequence x 1 ，x 2 ，...，x i ，...，x k Continuously coding the models which are not coded to obtain a coded initial contour model sequence X 1 ，X 2 ，…，X i ，…，X k ；
5.5 Setting the crossover probability of the genetic algorithm to be 0.9, the mutation probability of the genetic algorithm to be 0.01, the population number of the genetic algorithm to be 100, and the genetic algorithmThe maximum number of iterations of (a) is 100; training encoded model sequence X using genetic algorithm 1 ，X 2 ，…，X i ，…，X k Obtaining a tissue matrix sequence as follows: a. The 1 ，A 2 ，…，A i ，…，A k ；
5.6 Computing the encoded initial contour tumor model sequence X by using a distance compensation fitness function F 1 ，X 2 ，…，X i ，…，X k The fitness value sequence of the coded initial contour tumor model is obtained as follows: f. of 1 ，f 2 ，…，f i ，…，f k ；
5.7 Will organize matrix sequence A 1 ，A 2 ，…，A i ，…，A k Sequence of fitness values f with encoded initial contour tumor model 1 ，f 2 ，…，f i ，…，f k Respectively multiplying to obtain the coded initial contour model sequence X 1 ，X 2 ，…，X i ，…，X k Corresponding weighted reorganization matrix sequence B 1 ，B 2 ，…，B i ，…，B k Any matrix B of the sequence i Expressed as:
B i ＝f i ×A i (i＝1，2，...，k)，
in the formula, f i Sequence of fitness values f representing a sequence of encoded initial models 1 ，f 2 ，…，f i ，…，f k Any one value of (A) i Representing a sequence of organization matrices A 1 ，A 2 ，…，A i ，…，A k Any of the matrices of (a);
5.8 Will weighted organization matrix sequence B 1 ，B 2 ，…，B i ，…，B k Accumulating and normalizing to obtain an integrated weight matrix
In the formula, the function max takes the maximum element of the matrix;
5.9 The integrated weight matrix
Is ordered to obtain a value sequence>
And the values of the sequence are individually compared with a matrix->
The integrated tissue matrix sequence is obtained>
Wherein the matrix +>
Element in position (i, j)>
Comprises the following steps:
in the formula
Represents a matrix->
Element at position (i, j), based on the number of pixels in the image sensor>
Represents a numerical sequence->
Any value of (a);
5.10 Based on the integrated organization matrix sequence
Establishing evolution contour model sequence X of tumor in XFDTD software 1 ′，X 2 ′，...，X k ′，...，X l ′。
Step 6, for the evolution contour model sequence X 1 ′，X 2 ′，...，X k ′，...，X l And performing iterative training and outputting a tumor contour map of the optimal model.
For the evolving contour model sequence X 1 ′，X 2 ′，...，X k ′，...，X l ' iterative training may use static contour iteration and dynamic contour iteration;
static contour iteration refers to the iteration of the contour model sequence X 1 ′，X 2 ′，...，X k ′，...，X l When training is carried out, the sequence is not coded, and the tumor contour region of iteration does not change relative to the step 5, so the method is called static contour iteration;
the dynamic contour iteration refers to the sequence X of an evolution contour model 1 ′，X 2 ′，...，X k ′，...，X l When training, the sequence is encoded, and the tumor contour region of the iteration changes relative to the step 5, so the method is called dynamic contour iteration;
the example uses dynamic profile iteration, the implementation process is as follows:
6.1 A sequence f) of fitness values to evolve a sequence of contour models 1 ′，f 2 ′，...，f l Maximum value of f m ′ ax Comparing with a preset fitness threshold value f = 32:
if' max If the value is more than or equal to f, the optimal model exists in the evolution contour model sequence obtained in the step (5), the training is finished, and a tumor contour image of the model is output;
if 'f' max If f is less than f, it means that the optimum is not obtainedAnd the model needs to encode the evolution contour model sequence again, and continues to carry out iterative training sequentially through a genetic algorithm and an integration algorithm. If the optimal model is not obtained when the set maximum iteration number D =8 is reached, outputting a tumor contour image with the highest fitness value, wherein a tumor contour evolution diagram in the iterative training process is shown in FIG. 6;
6.2 Using XFDTD software for initial tumor model X a Gridding is performed to obtain a tumor grid map of the initial tumor model, as shown in fig. 7;
6.3 Comparing the optimal tumor profile in fig. 6 with that of fig. 7, the tumor profile was found to match completely, demonstrating that this example has a cross-sectional area of 104mm 2 The two-dimensional breast tumor has good imaging results.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (5)
1. A breast tumor contour dynamic extraction method based on genetic algorithm is characterized in that:
(1) Construction of initial tumor model
1a) Acquiring an existing breast tumor ultrasonic image;
1b) Distinguishing the tumor tissue and the normal tissue according to the gray value difference in the image, converting the image into a binary image, and respectively marking the tumor tissue and the normal tissue;
1c) The binary map in 1 b) is gridded according to a set resolution ratio to generate a grid image, and a tissue matrix A is obtained:
wherein, a ij Indicating position in grid image(i, j) organization information if a ij =0, indicating that the site is normal tissue, if a ij =1, indicating that this location is tumor tissue;
1d) Establishing an initial tumor model X in XFDTD electromagnetic simulation software according to the tissue matrix A obtained in 1 c) a N antennas are arranged around the model, each antenna emits electromagnetic waves in turn to radiate the tumor, all the antennas receive and record electromagnetic echoes at the same time, and N is more than or equal to 8;
1e) Copy original tumor model X a Replacing the tumor tissue with normal tissue to obtain tumor-free model X b ；
(2) Constructing an initial evaluation function F:
wherein N represents the total number of antennas, M is the total number of current samples per antenna,
representing the initial tumor model X a The ith antenna receives the current value of the echo at the time t, and then>
Representing a tumor-free model X b The ith antenna receives the current value of the echo at the time t;
(3) The central position of the tumor and the optimal rectangular outline of the tumor are obtained by confocal imaging:
3a) Initial tumor model X established in 1 d) a Determining the basic area of the tumor by confocal imaging;
3b) Tumor-free model X established in 1 e) b In the method, a tumor tissue cell with the side length of 8mm is used for traversing a tumor basic region to obtain a model X with the tumor tissue cell o Calculating the fitness value of the model through an initial fitness function F, and selecting the model X o The position of the cell with the highest medium fitness value is used as the central position of the tumor;
3c) Adjusting the length and width of the small grid at the central position to obtain a rectangular tumor model X s Iteratively calculating the fitness value of the model by means of an initial evaluation function F until the fitness value no longer increases, at which point the model X s The rectangular contour in (1) is the optimal tumor rectangular contour;
(4) Modifying the initial fitness function F to obtain a distance compensation fitness function F';
(5) Adjusting the position of the rectangular tumor obtained in the step (3) to obtain an initial contour model sequence, calculating the fitness value of the initial contour model sequence by using a distance compensation fitness function F', encoding the initial contour model sequence, training the encoded initial contour model sequence sequentially through a genetic algorithm and an integrated algorithm, and continuously evolving the shape of the tumor contour by using a variable quantity of 1mm to obtain an evolved contour model sequence;
(6) Distance compensation fitness value sequence f of evolution contour model sequence 1 ′，f 2 ′...，f l 'maximum value f' max And (3) comparing with a preset fitness threshold value f:
if 'f' max If the value is more than or equal to f, the optimal model exists in the evolution contour model sequence obtained in the step (5), the training is finished, and a tumor contour image of the model is output;
if' max If the number of the iteration times reaches the set maximum iteration number, the optimal model is still not obtained, the evolution contour model sequence needs to be encoded again, iterative training is continuously carried out through the genetic algorithm and the integration algorithm, and if the optimal model is not obtained yet, the tumor contour image with the highest adaptability value is output.
2. The method of claim 1, wherein: constructing an initial fitness function F in the step (2), and realizing the following steps:
2a) Respectively aligning the initial tumor model X by XFDTD simulation software a And tumor-free model X b Carrying out simulation to obtain X a The ith antenna receives the current value of the echo at the time t
And X b The ith antenna receives the current value of the echo at the time t>
Calculating the square error of both currents->
2b) Time-by-time, antenna-by-antenna accumulation of X a And X b Current squared error of
Obtaining a total current error E:
in the formula, N is the total number of the antennas, and M is the total current sampling number of each antenna;
2c) Taking the reciprocal of E to obtain a fitness function F:
after the tumor is added into the tumor-free model, the value of F is larger as the model is similar to the initial tumor model.
3. The method of claim 1, wherein: obtaining a distance compensation fitness function F 'in the step (4), wherein the distance compensation fitness function F' is realized as follows:
4a) Calculating the adjustment coefficient a of each antenna i ：
a i ＝l i -2 /max(l 1 -2 ，l 2 -2 ，...，l i -2 ...，l N -2 )，
In the formula I i Is shown asThe distance between the ith antenna and the center of the tumor, wherein N is the total number of the antennas;
4b) Calculating the total current error E of each antenna i ：
In the formula (I), the compound is shown in the specification,
representing the initial tumor model X a The ith antenna receives the current value of the echo at the time t, and then>
Representing a rectangular tumor model X s The ith antenna receives the current value of the echo at the time t, and M is the total current sampling number of each antenna;
4c) According to the total current error E of each antenna i And the adjustment coefficient a i And obtaining a distance compensation fitness function F':
4. the method of claim 1, wherein: the initial contour model sequence is coded in the step (5) and is realized as follows:
5a) Extracting the edge of the tumor in any model in the initial contour model sequence, gridding the region inside and outside the edge to obtain an inner and outer double-layer grid S with the side length of 1mm and tangent to the edge, wherein any small grid in the grid S is represented as S i ；
5b) Encoding lattice S on a chromosome G, each gene and cell of the chromosome i Corresponds to, is represented as g i For each gene g i ：
If g is i If =0, the cell s i Is a normal tissue;
if g is i =1, then cell s i Is tumor tissue.
5. The method of claim 1, wherein: the initial contour model sequence is trained sequentially through a genetic algorithm and an integrated algorithm in the step (5), and the following steps are realized:
5c) Training coded initial contour model sequence X by genetic algorithm 1 ，X 2 ，…，X i ，…，X k And obtaining a tissue matrix sequence as follows: a. The 1 ，A 2 ，…，A i ，…，A k Calculating a sequence of models X 1 ，X 2 ，…，X i ，…，X k Is used for compensating the value sequence f of the fitness function 1 ，f 2 ，…，f i ，…，f k Obtaining a model sequence X 1 ，X 2 ，…，X i ，…，X k Corresponding weighted organization matrix sequence B 1 ，B 2 ，…，B i ，…，B k Any matrix B of the sequence i Expressed as:
B i ＝f i ×A i (i＝1，2，...，k)，
in the formula (f) i Sequence of fitness values f representing a sequence of encoded initial models 1 ，f 2 ，…，f i ，…，f k Any one value of (A) i Representing a sequence of organization matrices A 1 ，A 2 ，…，A i ，…，A k Any of the matrices of (a);
5d) Organizing matrix sequence B with weight 1 ，B 2 ，…，B i ，…，B k Accumulating and normalizing to obtain an integrated weight matrix
In the formula, the function max takes the maximum element of the matrix;
5e) The integrated weight matrix
Is ordered to obtain a value sequence>
And the values of the sequence are individually compared with a matrix->
The integrated tissue matrix sequence is obtained>
Wherein the matrix->
Element in position (i, j)>
Comprises the following steps:
in the formula
Representing a matrix +>
Element in position (i, j), based on the status of the cell>
Representing a sequence of values>
Any value of (a);
5f) According to the integrated organization matrix sequence
Establishing evolution outline model sequence X of tumor in XFDTD software 1 ′，X 2 ′，...，X k ′，...，X l ′。/>
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