CN106844994B - Choroidal neovascularization growth prediction method combining constitutive model and finite element - Google Patents

Choroidal neovascularization growth prediction method combining constitutive model and finite element Download PDF

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CN106844994B
CN106844994B CN201710071557.8A CN201710071557A CN106844994B CN 106844994 B CN106844994 B CN 106844994B CN 201710071557 A CN201710071557 A CN 201710071557A CN 106844994 B CN106844994 B CN 106844994B
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陈新建
左畅
朱伟芳
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Suzhou were Medical Technology Co. Ltd.
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Abstract

The invention discloses a choroidal neovascularization growth prediction method combining a constitutive model and finite elements, which comprises the steps of image preprocessing; region extraction and division: dividing the image into 4 regions of CNV region, outer retina layer, inner retina layer and choroid layer; gridding: generating tetrahedral meshes for the 4 regions; modeling: modeling by using a hyperelastic biomechanics model and a reaction diffusion equation, and adding the mass change of the grown choroidal neovascularization into the equation as a source term to enable the deformation gradient tensor to continuously change according to the growth of the neovascularization; optimizing the model, calculating the optimal accuracy rate, and performing parameter inspection; and fitting a parameter curve according to the predicted parameters of each time point, and predicting the growth parameters of the last time point to obtain a prediction result. The method can be used for a more flexible and personalized mode biomechanical model, the assumed tissue of the model is orthogonal anisotropy, the model also has a good prediction result on a nonlinear large-deformation area, and the accuracy is high.

Description

Choroidal neovascularization growth prediction method combining constitutive model and finite element
Technical Field
The invention relates to the technical field of computer vision, image processing and analysis, belongs to a modeling method for growth prediction, and particularly relates to a modeling method for Choroidal Neovascularization (CNV) growth prediction applied to SD-OCT (frequency domain optical coherence tomography).
Background
The choroid is located between the retina and sclera and is composed of fibrous tissue, small blood vessels and capillaries. The choroid blood circulation nourishes the outer retina, crystalline lens, vitreous body and the like, and due to the characteristics of large blood flow, slow flow rate and soft and thin choroid, the choroid blood circulation can not resist external influence or impact, so that pathogens are easy to stay at the position to cause choroid diseases and various fundus diseases, and therefore, a plurality of important data can be obtained by researching the growth of Choroid Neovascularization (CNV), and basic support data is provided for subsequent medical research.
The method has certain defects and limitations that ① is based on isotropic assumption, ② does not consider different biological characteristics of different tissue structures, ③ can only predict linear change, ④ can only predict change of small deformation, prediction of large deformation change is inaccurate, and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a comprehensive method for the first time, namely a method for predicting and analyzing the growth of choroidal neovascularization by combining a biomechanical model based on a super-elastic material and a reaction diffusion equation, and has high accuracy.
In order to solve the technical problem, the invention provides a three-dimensional generation prediction method of choroidal neovascularization.
The method mainly comprises 6 steps:
step 1, image preprocessing: down-sampling processing is carried out on the three-dimensional retina frequency domain optical coherence tomography SD-OCT image;
step 2, region extraction and division: dividing the image into 4 areas of choroidal neovascularization CNV area, outer retina layer, inner retina layer and choroid layer;
step 3, gridding: performing multi-scale, adaptive tetrahedral mesh generation for the CNV region, the inner retinal layer, the outer retinal layer and the choroid layer;
and 4, modeling by using a hyperelastic biomechanics model and a reaction diffusion equation: in the structure of the hyperelastic biomechanics model, integrating different volume moduli and shear moduli of all regions and corresponding volume elastic responses and equal-volume elastic responses of all regions, and adding mass changes of the grown choroidal neovascularization as source terms into an equation to enable the deformation gradient tensor to continuously change according to the growth of the neovascularization;
step 5, optimizing the model, calculating the optimal accuracy rate, and performing parameter inspection;
and 6, fitting a parameter curve according to the predicted parameters of each time point, predicting the growth increment rate parameter of the last time point, and obtaining a prediction result.
The image preprocessing in step 1 comprises the following steps:
(1a) and (3) downsampling processing:
(1b) OCT image registration was performed using CAVASS software.
And 3, performing multi-scale and self-adaptive tetrahedral mesh generation on the CNV region, the inner retina layer, the outer retina layer and the choroid layer by adopting a three-dimensional curved surface and volume mesh generator.
Step 4 comprises the following steps:
(4a) invasion and diffusion of reactive diffusion equations
The logistic regression-type growing reaction diffusion equation is expressed as:
where t is time and D is the anisotropic diffusion tensor, comprising three components D x，D y，D zThe three components are components of an x axis, a y axis and a z axis respectively; ρ represents the growth proliferation rate, N is the number of cells per unit volume, K maxRepresents the maximum cell volume of the cell,
when the anisotropic concentration of vascular endothelial growth factor When, the following formula is given:
Figure BDA0001222945770000023
(4b) mass effect and superelastic biomechanical model
The strain energy density function of the nonlinear stress-strain behavior of a material is:
Figure BDA0001222945770000031
wherein the content of the first and second substances,
Figure BDA0001222945770000032
representing the Green-Lagrange strain tensor, F TA transposed tensor representing the deformed gradient tensor F, I being an identity matrix; j represents the determinant of the deformation gradient tensor F, i.e., J ═ det (F); κ and μ represent the bulk modulus and shear modulus, respectively; tr represents a trace of the matrix; i is 1Is the first principal invariant of the cauchy-green deformation tensor;
the cauchy stress tensor σ is J by the gradient force f in equation 4 -1FSF TAnd the anisotropic concentration c of vascular endothelial growth factor:
Figure BDA0001222945770000033
where f represents the gradient force generated by c, i.e., the density gradient force, ξ represents a constant that needs to be estimated, which depends on the biological properties of the material, and S represents the PK 2-second Piola-Kirchoff stress tensor.
In step 5, optimizing the growth increment rate rho parameter by using a first-order Markov sequence: the data of the first n time points, each time point being associated with a previous time point, the value of p is calculated.
Estimates of growth increment rate parameters were made from all previous time points, and then the accuracy of the predictions was calculated using the following formula:
Figure BDA0001222945770000034
Figure BDA0001222945770000035
is based on all previous time points I i,c(I ═ 1, 2.., 10) predicted results, I i+1,cIs the gold standard for the current time point;
finally, estimating parameters: v is i＝{D x,D y,D z,ρ；c}。
Defining the coincidence pixel point of the prediction result and the gold standard
Figure BDA0001222945770000036
Calculating various indexes reflecting the accuracy of the prediction result:
(1) recall rate
Figure BDA0001222945770000041
(2) Error rate
Figure BDA0001222945770000042
(3) Similarity DICE coefficient
In the step 6, a fitting curve is drawn by using the obtained growth increment rate rho values of the previous n time points, so that the growth increment rate rho of the (n + 1) th time point is predicted; and substituting the predicted growth increment rate rho of the (n + 1) th time point into the nth time point, overlapping the obtained predicted image with the real (n + 1) th image, and calculating the prediction accuracy.
The invention achieves the following beneficial effects:
the invention provides a comprehensive growth prediction method for the first time, namely a method for predicting and analyzing the growth of choroidal neovascularization by combining a biomechanics model based on a super-elastic material and a reaction diffusion equation.
The method of the invention combines the superelasticity material and the reaction diffusion equation, and can be used for a more flexible and personalized mode biomechanical model. Unlike previous materials which are isotropic, the model assumes an organization that is orthotropic. Different biological characteristics of different tissue structures are simulated at a disease part (choroid neovascularization area) and surrounding tissues (including outer retina, choroid, inner retina layer and the like), and based on the assumption of orthogonal anisotropy, a nonlinear large deformation area is well predicted, and the accuracy is high.
Drawings
FIG. 1 is an overall block diagram of choroidal neovascularization prediction;
FIG. 2a is the result of gridding the original image (512X 1024X 128) of OCT;
FIG. 2b is the result of the down-sampled image (64 × 64 × 64) after meshing;
FIG. 2c shows node information and cell information of an original image;
FIG. 2d illustrates node information and cell information of a down-sampled image;
FIG. 3a is a trellis division reconstructed from downsampled data;
FIG. 3b is the intracellular volume (ICV) of choroidal neovascularization;
FIG. 3c is an iso-surface image of an ICV;
fig. 3d is a display of stress distribution: on each slice, the thick line circle and the thin line ellipse of the CNV region respectively represent the positions of strong stress (generally distributed at the edge of the CNV) and weak stress (generally distributed in the CNV);
fig. 4 is a graphical representation of CNV volume differences for different patients.
Detailed Description
The following further details the embodiments of the present invention:
the basic block diagram of the method is shown in fig. 1, and mainly comprises the following steps:
1) image pre-processing
(a) And (3) downsampling processing: to improve processing efficiency and optimize memory usage, the three-dimensional retinal SD-OCT image of each pixel 512 × 1024 × 128 is down-sampled to pixel 64 × 64 in this embodiment.
(b) OCT image registration was performed using CAVASS software (software developed by MIPG).
2) Region extraction and partitioning
Manually marking gold standard, and extracting a retina interested region (CNV region) and dividing peripheral tissues (inner retina layer, outer retina layer and choroid layer);
3) gridding, namely performing multi-scale and self-adaptive tetrahedral grid generation on the CNV region, the inner retina layer, the outer retina layer and the choroid layer by using a three-dimensional curved surface and volume grid generator, which is shown in fig. 2a, 2b, 2c and 2 d;
4) modeling 4 areas, namely a CNV area, an inner retina layer, an outer retina layer and a choroid layer, wherein each area is subjected to parameter training by different superelastic biomechanics models and reaction diffusion equation models, so that the CNV area grows according to different physiological characteristics:
(a) invasion and diffusion of reactive diffusion equations
The Logistic regression (Logistic) growing reaction diffusion equation can be expressed as:
Figure BDA0001222945770000051
where t is time and D is the anisotropic diffusion tensor, comprising three components D x，D y，D zThe three components are x-axis, y-axis, and z-axis components, respectively. ρ represents the growth proliferation rate, N is the number of cells per unit volume, K maxRepresents the maximum cell volume when the anisotropic concentration of Vascular Endothelial Growth Factor (VEGF)
Figure BDA0001222945770000061
When, the following formula is given:
(b) mass effect and superelastic biomechanical model
In the model structure, different volume moduli and shear moduli of each region and the corresponding volume elastic response part and isovolumetric elastic response part in the constitutive equation are relatively and comprehensively integrated through equation (3), and the mass change after the growth of the CNV is taken as a source term to be added into the constitutive equation of the superelasticity biomechanics, so that the deformation gradient tensor continuously changes according to the growth of the new blood vessel:
the superelastic biomechanical model can be used for predicting large deformation, and the strain energy density function of the nonlinear stress-strain behavior of the material is as follows:
wherein the content of the first and second substances,
Figure BDA0001222945770000064
representing the Green-Lagrange strain tensor, F TA transposed tensor representing the deformed gradient tensor F whose component relationship is (F) T) ij＝F jiI is an identity matrix; j represents the determinant of the deformation gradient tensor F, i.e., J ═ det (F); κ and μ represent the bulk modulus and shear modulus, respectively; tr represents a trace of the matrix; i is 1Is the first principal invariant of the Cauchy-Green deformation tensor.
The meshing of the data reconstruction and the stress distribution on the individual slices are shown in fig. 3a, 3b, 3c, 3 d.
Meanwhile, the process is simulated using the static equilibrium equation:
Figure BDA0001222945770000065
the equation sets the cauchy stress tensor σ to J by the gradient force f -1FSF T(where S stands for PK 2-second Piola-Kirchoff stress tensor), and the anisotropic concentration c of vascular endothelial growth factor:
where f represents the gradient force (i.e., density gradient force) generated by c and ξ represents a constant that needs to be estimated, which depends on the biological properties of the material.
5) Optimizing the model, calculating the optimal accuracy and carrying out parameter inspection.
Optimizing the parameter rho (growth increment rate) by a first-order Markov sequence: data of the first n time points (in this embodiment, n is 10) each of which is associated with one of the previous time points, and the value ρ is calculated.
Estimates of the model parameters (growth proliferation rate) were made from all previous time points, and then the accuracy of the predictions was calculated using the following formula:
Figure BDA0001222945770000071
Figure BDA0001222945770000072
is based on all previous time points I i,c(I ═ 1, 2.., n) predicted results, I i+1,cIs the gold standard at the current point in time, w 1、w 2Respectively represent weights.
The parameters κ and μ for CNV, choroid (choroid) and other moieties, respectively, are set according to the physiological properties of choroidal neovascularization: kappa CNV＝5kPa,κ choroid＝6kPa,κ others＝3kPa,μ CNV＝μ choroid＝5*10 3N/m 2,μ others＝1*10 3N/m 2. Finally, the parameters we want to estimate are: v is i＝{D x,D y,D zρ; c }. Defining the coincidence pixel point of the prediction result and the gold standard
Figure BDA0001222945770000073
And calculating various indexes reflecting the accuracy of the prediction result, wherein the indexes are used as the standard of the evaluation and inspection model: (1) recall rate
Figure BDA0001222945770000074
(2) Error rate (3) Similarity DICE coefficient
Figure BDA0001222945770000076
6) And fitting a parameter curve according to the predicted parameters of each time point, and predicting the growth parameters of the last time point to obtain a prediction result.
Using the obtained growth increment rate ρ values of the first n time points (in this embodiment, n is 10), a fitting curve is drawn, so as to predict the growth increment rate ρ of the (n + 1) th time point. And substituting the predicted growth increment rate rho of the (n + 1) th time point into the nth time point, overlapping the obtained predicted image with the real (n + 1) th image, and calculating the prediction accuracy.
7) The experimental results are as follows:
as shown in FIG. 4, CNV volumes were obtained for six patients at 10 time points, and it can be seen that CNV specificity was evident with varying fluctuations. In fact, the CNVs at different time points vary widely from patient to patient, both in size and morphology.
The sensitivity of the retina to light also increases the display of stress distribution in the results (see figure 3d below), helping to more intuitively display the mechanical impact on the CNV region.
Predicting a second time point parameter based on the deformation at the first time point; and predicting the deformation parameters of the third time point according to the deformation of the first two time points. By analogy, a curve fitted by the growth increment rate rho of the first n (n equals to 10) time points is substituted into the nth time point to obtain a prediction result
Figure BDA0001222945770000081
This was compared to the true value (gold standard at time point n + 1) to give the predicted results, as in table 1.
Figure BDA0001222945770000082
Table 1 shows the prediction results of the method, and it can be found that the other prediction results have better accuracy except for patients with great difference in time point change before and after the individual CNV.
To this end, a three-dimensional CNV growth prediction model has been implemented and validated. The invention provides a technical scheme of fusing a superelasticity biomechanics model, a reaction diffusion equation and a mass source, combining automatic detection of optimization parameters of an objective function and displaying stress distribution of the whole region in a result, and experimental results show that the growth prediction method can better solve the growth prediction problem of Choroidal Neovascularization (CNV) and has higher prediction accuracy.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (7)

1. A choroidal neovascularization growth prediction method combining constitutive models and finite elements is characterized by comprising the following steps:
step 1, image preprocessing: down-sampling processing is carried out on the three-dimensional retina frequency domain optical coherence tomography SD-OCT image;
step 2, region extraction and division: dividing the image into 4 areas of choroidal neovascularization CNV area, outer retina layer, inner retina layer and choroid layer;
step 3, gridding: performing multi-scale, adaptive tetrahedral mesh generation for the CNV region, the inner retinal layer, the outer retinal layer and the choroid layer;
and 4, modeling by using a hyperelastic biomechanics model and a reaction diffusion equation: in the structure of the hyperelastic biomechanics model, integrating different volume moduli and shear moduli of all regions and corresponding volume elastic responses and equal-volume elastic responses of all regions, and adding mass changes of the grown choroidal neovascularization as source terms into an equation to enable the deformation gradient tensor to continuously change according to the growth of the neovascularization;
step 5, optimizing the model, calculating the optimal accuracy rate, and performing parameter inspection;
step 6, fitting a parameter curve according to the predicted parameters of each time point, predicting the growth increment rate parameters of the last time point, and obtaining a prediction result;
step 4 comprises the following steps:
(4a) invasion and diffusion of reactive diffusion equations
The logistic regression-type growing reaction diffusion equation is expressed as:
where t is time and D is the anisotropic diffusion tensor, comprising three components D x，D y，D zThe three components are components of an x axis, a y axis and a z axis respectively; ρ represents the growth proliferation rate, N is the number of cells per unit volume, K maxRepresents the maximum cell volume of the cell,
when the anisotropic concentration of vascular endothelial growth factor
Figure FDA0002189190490000012
When, the following formula is given:
Figure FDA0002189190490000013
(4b) mass effect and superelastic biomechanical model
The strain energy density function of the nonlinear stress-strain behavior of a material is:
Figure FDA0002189190490000021
wherein the content of the first and second substances, representing the Green-Lagrange strain tensor, F TA transposed tensor representing the deformed gradient tensor F, I being an identity matrix; j represents the determinant of the deformation gradient tensor F, i.e., J ═ det (F); κ and μ represent the bulk modulus and shear modulus, respectively; tr represents a trace of the matrix; i is 1Is the first principal invariant of the cauchy-green deformation tensor;
the cauchy stress tensor σ is J by the gradient force f in equation 4 -1FSF TAnd the anisotropic concentration c of vascular endothelial growth factor:
div(σ)+f＝0；f＝-ξ▽c (4)
where f represents the gradient force generated by c, i.e., the density gradient force, ξ represents a constant that needs to be estimated, which depends on the biological properties of the material, and S represents the PK 2-second Piola-Kirchoff stress tensor.
2. The method for predicting choroidal neovascularization by constitutive model combined with finite element analysis as claimed in claim 1, wherein the image preprocessing in step 1 comprises the steps of:
(1a) and (3) downsampling processing:
(1b) OCT image registration was performed using CAVASS software.
3. The method as claimed in claim 1, wherein step 3 is performed by using a mesh generator with three-dimensional curved surface and volume to generate multi-scale and adaptive tetrahedral mesh for CNV region, inner retina layer, outer retina layer and choroid layer.
4. The method for predicting choroidal neovascularization by constitutive model in combination with finite element as claimed in claim 1, wherein in step 5, the growth increment rate ρ parameter is optimized by first order Markov sequence: the data of the first n time points, each time point being associated with a previous time point, the value of p is calculated.
5. The method of claim 4, wherein the estimation of growth proliferation rate parameters is performed from all previous time points, and then the accuracy of the prediction is calculated using the following formula:
Figure FDA0002189190490000031
Figure FDA0002189190490000032
is based on all previous time points I i,c(I ═ 1, 2.., 10) predicted results, I i+1,cIs the gold standard for the current time point;
finally, estimating parameters: v is i＝{D x,D y,D z,ρ；c}。
6. The method as claimed in claim 5, wherein the constitutive model and finite element combined choroidal neovascularization prediction method is characterized by defining coincidence pixel points of prediction results and gold standard
Figure FDA0002189190490000033
Calculating various indexes reflecting the accuracy of the prediction result:
(1) recall rate
Figure FDA0002189190490000034
(2) Error rate
Figure FDA0002189190490000035
(3) Similarity DICE coefficient
7. The method for predicting choroidal neovascularization growth according to claim 4, 5 or 6, wherein in step 6, the growth increment rate p at the n +1 th time point is predicted by drawing a fitting curve using the obtained growth increment rate p at the first n time points; and substituting the predicted growth increment rate rho of the (n + 1) th time point into the nth time point, overlapping the obtained predicted image with the real (n + 1) th image, and calculating the prediction accuracy.
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Denomination of invention: Prediction method of choroidal neovascularization based on constitutive model and finite element method

Effective date of registration: 20220520

Granted publication date: 20200211

Pledgee: Suzhou high tech Industrial Development Zone sub branch of Bank of Communications Co.,Ltd.

Pledgor: SUZHOU BIGVISION MEDICAL TECHNOLOGY Co.,Ltd.

Registration number: Y2022320010152

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