CN108765543B - Cardiovascular image reconstruction method and system based on implicit deformable model - Google Patents
Cardiovascular image reconstruction method and system based on implicit deformable model Download PDFInfo
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Abstract
The invention provides a cardiovascular image reconstruction method and a system based on an implicit deformable model, wherein the method comprises the following steps: acquiring a three-dimensional image of a human heart, and constructing a partial differential equation of a embedding function by using parameters of the three-dimensional image of the heart; respectively initializing a cardiovascular aorta image and a coronary artery image by adopting a mode of combining a rapid propulsion method and a collision forward method, performing expansion, smoothing and convection treatment, and solving the partial differential equation of the embedding function to obtain a reconstructed cardiovascular three-dimensional image; and processing the reconstructed cardiovascular three-dimensional image by using a block advancing method to obtain a cardiovascular three-dimensional model. The method and the system solve the problem of poor calculation stability commonly existing in the conventional cardiovascular image reconstruction method, realize fast and accurate segmentation of the required area on the premise of ensuring the stability of the calculation result, are simple to operate, and are convenient for subsequent computational fluid mechanics analysis and the like.
Description
Technical Field
The invention relates to the technical field of medical image processing, in particular to a cardiovascular image reconstruction method and system based on an implicit deformable model.
Background
With the continuous development of computational hemodynamics (CFD), it has been found that hemodynamics are closely linked to the development, development and treatment of cardiovascular diseases. In recent years, hemodynamic research into the cardiovascular system has been a focus of biomechanical and biomedical engineering research. Many researchers have attempted to apply computational hemodynamic techniques to the cardiovascular field to aid in the diagnosis of cardiovascular disease by obtaining some of the blood flow characteristics. Computational hemodynamics, however, require calculations based on cardiovascular three-dimensional models, which require the extraction or reconstruction of cardiovascular three-dimensional models from cardiovascular images.
Cardiac three-dimensional medical images include, but are not limited to, cardiac computed tomography (CT/CTA), magnetic resonance imaging (MRI/MRA), Single Photon Emission Computed Tomography (SPECT), and the like. The existing cardiovascular image reconstruction method mainly comprises a threshold value method, a clustering method or a region growing method, wherein the threshold value method is to divide a gray image into binary images based on gray values so as to divide the original images, but is not suitable for complicated image division. The clustering method divides the image into k clusters for iteration, and the quality of the reconstructed result depends on an initial group of clusters and k value, which leads the reconstructed result to be very sensitive to parameters. The region growing method is a method in which pixels with similar properties are collected to form a region, and is also based on iteration, so that space and time costs are high. In summary, the above methods cannot ensure the stability of the result of the cardiovascular image reconstruction model, so how to design a cardiovascular image reconstruction method capable of ensuring the stability of the calculation result becomes a major problem at present.
Disclosure of Invention
The invention aims to provide a cardiovascular image reconstruction method and system based on an implicit deformable model, which solve the problem of poor calculation stability of the conventional cardiovascular image reconstruction method and realize rapid and accurate segmentation of a required area on the premise of ensuring the stability of a calculation result.
In order to achieve the above object, the present invention provides a cardiovascular image reconstruction method based on an implicit deformable model, comprising the following steps:
acquiring a three-dimensional image of a human heart, and constructing a partial differential equation of a embedding function by using parameters of the three-dimensional image of the heart;
solving the partial differential equation of the embedding function by using a finite difference method to obtain a reconstructed cardiovascular three-dimensional image;
and processing the reconstructed cardiovascular three-dimensional image by using a block advancing method to obtain a cardiovascular three-dimensional model.
Preferably, the partial differential equation of the embedding function constructed by using the parameters of the heart three-dimensional image is shown as equation (1):
wherein the content of the first and second substances,
representing a mosaic function
Partial differentiation of the iteration time term t, w1Represents the coefficient of expansion, G (x) represents the expansion rate function; w is a2It is shown that the coefficient of smoothness,
h (x) represents the mean curvature of the three-dimensional image of the heart; w is a3The coefficient of convection is expressed as a function of,
where I represents the intensity of the three-dimensional image of the heart.
Preferably, the solving of the partial differential equation of the embedding function by using a finite difference method to obtain the reconstructed cardiovascular three-dimensional image specifically includes the following steps:
initializing a coronary artery image in the three-dimensional image of the heart by using a collision forward method, and initializing an aorta image in the three-dimensional image of the heart by using a fast propulsion method to obtain initial conditions of the partial differential equation of the embedding function
Based on the initial conditions
And (3) performing expansion, smoothing and convection treatment on the curved surface part in the heart three-dimensional image to obtain a reconstructed heart blood vessel three-dimensional image.
Preferably, the coronary artery image in the cardiac three-dimensional image is initialized by using a collision forward method, and the specific process is that two seed points, namely a source point and a target point, which are positioned at two ends of a blood vessel branch are selected firstly, and then image reconstruction is performed based on two mutually independent wavefronts emitted by the two seed points; the propagation velocity of the wavefront is proportional to the intensity of the image, as shown in equation (2):
t represents the time when the wave front reaches any other point in the image area, and the reciprocal of the image intensity I represents the slowness of the wave front; solving equation (2) by windward finite difference method to obtain action components T of two seed points to any point in the image region1And T2Initial condition of the partial differential equation of the embedding function
Preferably, the aortic image in the cardiac three-dimensional image is initialized by using the fast propulsion method, and the specific process is that a series of source points and target points are selected, image reconstruction is performed based on mutually independent wavefronts emitted by the source points and the target points, and then the equation (2) is solved by the windward finite difference method to obtain the solution of the equation (2), and the initial condition of the embedding function
T represents the solution of equation (2), TtargetRepresents the minimum value of the solution of equation (2).
The invention also provides a cardiovascular image reconstruction system based on the implicit deformable model, which comprises the following components:
the function equation constructing module is used for acquiring a three-dimensional image of a human heart and constructing an embedded function partial differential equation by using parameters of the three-dimensional image of the heart;
the cardiovascular three-dimensional image reconstruction module is used for solving the partial differential equation of the embedding function through a finite difference method to obtain a reconstructed cardiovascular three-dimensional image;
and the cardiovascular three-dimensional model acquisition module is used for processing the reconstructed cardiovascular three-dimensional image by utilizing a moving block method to obtain a cardiovascular three-dimensional model.
Preferably, the cardiovascular three-dimensional image reconstruction module comprises:
an initialization unit, configured to initialize a coronary artery image in the three-dimensional cardiac image by using a collision-forward method, and initialize an aorta image in the three-dimensional cardiac image by using a fast-marching method, so as to obtain an initial condition of the partial differential equation of the embedding function
And the processing unit is used for performing expansion, smoothing and convection processing on the curved surface part in the cardiovascular three-dimensional image to obtain a reconstructed cardiovascular three-dimensional image.
Preferably, the initialization unit initializes the coronary artery image in the three-dimensional image of the heart by using a collision-forward method, and specifically, the initialization unit first selects two seed points, namely a source point and a target point, located at two ends of a blood vessel branch, and then performs image reconstruction based on two mutually independent wavefronts emitted by the two seed points; the propagation velocity of the wavefront is proportional to the intensity of the image, as shown in equation (2):
t represents the time when the wave front reaches any other point in the image area, and the reciprocal of the image intensity I represents the slowness of the wave front; solving equation (2) by windward finite difference method to obtain action components T of two seed points to any point in the image region1And T2Initial condition of the partial differential equation of the embedding function
Preferably, the initialization unit first selects a series of source points and target points, performs image reconstruction based on mutually independent wavefronts emitted by the source points and the target points, and then solves equation (2) by a windward finite difference method to obtain a solution of equation (2), an initial condition of an embedding function
T represents the solution of equation (2), TtargetRepresents the minimum value of the solution of equation (2).
The invention also provides a cardiovascular image reconstruction system based on the implicit deformable model, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the steps of any one of the methods when executing the computer program.
Compared with the prior art, the invention has the following advantages and prominent effects:
according to the method and the system for reconstructing the cardiovascular image based on the implicit deformable model, the partial differential equation of the embedding function is constructed by utilizing the parameters of the three-dimensional image of the heart, the cardiovascular aorta image and the coronary artery image are respectively initialized by adopting a mode of combining a fast propulsion method and a collision forward method, the partial differential equation is solved by combining expansion, smoothing and convection operation, the reconstructed cardiovascular three-dimensional image is obtained, and then the cardiovascular three-dimensional model is obtained by combining a travelling block method.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a cardiovascular image reconstruction method based on an implicit deformable model according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a cardiovascular image reconstruction system based on an implicit deformable model according to an embodiment of the present invention;
FIG. 3 is a three-dimensional image of a human heart for constructing a partial differential equation of a embedding function according to an embodiment of the present disclosure;
4a, 4b and 4c are schematic diagrams illustrating the initialization by the collision-forward method according to the embodiment of the present invention;
FIG. 5 is a diagram illustrating the result of initializing a coronary artery image in a three-dimensional cardiac image by a collision-forward method according to an embodiment of the present invention;
FIGS. 6a and 6b are schematic diagrams illustrating the result of initializing a portion of an aorta image in a three-dimensional cardiac image by fast marching according to an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating the result of a reconstructed cardiovascular three-dimensional image according to an embodiment of the disclosure;
FIG. 8 is a diagram illustrating the results of a cardiovascular three-dimensional model obtained by the marching squares method according to an embodiment of the present invention;
fig. 9 is a schematic diagram of the result of the cardiovascular three-dimensional model obtained after geometric processing such as cutting and smoothing, which is disclosed in the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, an embodiment of the present invention discloses a cardiovascular image reconstruction method based on an implicit deformable model, where the implicit deformable model is essentially a partial differential equation, and the cardiovascular image reconstruction method includes the following steps:
step S101, obtaining a human heart three-dimensional image, and constructing a partial differential equation of a embedding function by using parameters of the heart three-dimensional image. The three-dimensional image of the heart in this embodiment is shown in fig. 3, and the partial differential equation of the embedding function after construction is expressed as equation (1):
wherein the content of the first and second substances,
representing a mosaic function
Partial differentiation of the iteration time term t, the first term on the right of the partial differential equation representing the expansion term, w1Is the coefficient of expansion, G (x) represents the expansion rate function, in this example
That is, the value of the expansion term in the cardiovascular image is larger, and the value at the boundary of the cardiovascular image is smaller; the second term represents the smoothing term, w2Representing the smoothing factor, H (x) representing the mean curvature of the three-dimensional image of the heart,
the third term represents a convection term, where w3The coefficient of convection is expressed as a function of,
representing a vector field associated with a convection current, wherein,
i represents the intensity of the three-dimensional image of the heart. Representing the cardiovascular three-dimensional image to be acquired as S (t), wherein S (t) is a mosaic function
Is determined by a zero level of (i.e. is)
And S102, solving the partial differential equation of the embedding function by using a finite difference method to obtain a reconstructed cardiovascular three-dimensional image. The specific process is as follows: initializing a coronary artery image in the three-dimensional image of the heart by using a collision forward method, and initializing an aorta image in the three-dimensional image of the heart by using a fast propulsion method to obtain initial conditions of a partial differential equation of a embedding function
Then based on the initial conditions
And (3) performing expansion, smoothing and convection treatment on the curved surface part in the heart three-dimensional image to obtain a reconstructed heart blood vessel three-dimensional image.
The collision forward method comprises the specific steps of firstly selecting two seed points, namely a source point and a target point, which are positioned at two ends of a blood vessel branch, as shown in fig. 4a, and then reconstructing an image based on two mutually independent wavefronts emitted by the two seed points; the propagation velocity of the wavefront is proportional to the intensity of the image, as shown in equation (2):
t represents the time when the wave front reaches any other point in the image area, and the reciprocal of the image intensity I represents the slowness of the wave front; solving equation (2) by windward finite difference method to obtain action components T of two seed points to any point in the image region1And T2Initial condition of the partial differential equation of the embedding function
And
the field image of (2) is shown in fig. 4 b. The time of the wave front emitted by the seed point propagating outward to reach itself is defined as 0, that is, the starting time is defined as 0, and the principle of the collision forward method for initializing based on two seed points is shown in fig. 4 c.
When the directions of propagation of the two wavefronts are opposite,
negative, the region between two seed points can be identified as the initial level set. When the two wave fronts are transmitted to the branch blood vessels, the included angle between the two vectors is less than 90 degrees, and at the moment
Positive, so the side branches can be automatically excluded from the initial level set. The initial volume of the cardiovascular three-dimensional image is defined as two seed points s1And s2In between and
a region that is always negative.
In this embodiment, fig. 5 shows the result of initializing the coronary artery image in the three-dimensional image of the heart in fig. 3 by the collision forward method.
The fast propulsion method is realized based on a collision forward method, and comprises the specific steps of firstly selecting a series of source points and target points, as shown in fig. 6a, reconstructing an image based on mutually independent wavefronts emitted by the source points and the target points, and then solving an equation (2) by a windward finite difference method to obtain a solution of the equation (2), and initial conditions of an embedding function
T represents the solution of equation (2), TtargetRepresents the minimum value of the solution of equation (2).
In this embodiment, the result of initializing a partial aorta image in the three-dimensional image of the heart in fig. 3 by using the fast marching method is shown in fig. 6 b.
The effect of carrying out expansion processing on the curved surface part in the cardiovascular three-dimensional image is to enable the cardiovascular three-dimensional image to extend from a central line to a vessel wall direction in a radius range of capturing a flow item, so as to obtain an initial value of the cardiovascular three-dimensional image; the smoothing is used for denoising the initialized cardiovascular three-dimensional image, is particularly suitable for a data set with poor signal-to-noise ratio, and is beneficial to smoothing the reconstructed image. The effect of the convection processing is to draw the initialized cardiovascular three-dimensional image close to the ridge line of the gradient field of the image parameters, that is, close to the place where the gradient field of the intensity I changes most, so as to obtain the finally reconstructed cardiovascular three-dimensional image, where the cardiovascular three-dimensional image obtained in this embodiment is shown in fig. 7.
Step S103, processing the reconstructed cardiovascular three-dimensional image by using a marching block method to obtain a cardiovascular three-dimensional model, where the cardiovascular three-dimensional model obtained by using the marching block method is shown in fig. 8. Then, the cardiovascular three-dimensional model in fig. 8 is subjected to geometric processing such as cutting and smoothing, so as to obtain a final cardiovascular three-dimensional model, as shown in fig. 9. The marching block method is a computer vision algorithm, and can extract a polygon mesh from a 3D discrete scalar field.
As shown in fig. 2, an embodiment of the present invention further discloses a cardiovascular image reconstruction system based on an implicit deformable model, including:
and a function equation constructing module 201, configured to acquire a three-dimensional image of a human heart, and construct a partial differential equation of a embedding function by using parameters of the three-dimensional image of the heart. The partial differential equation of the embedding function after construction is expressed as equation (1):
wherein the content of the first and second substances,
representing a mosaic function
Partial differentiation of the iteration time term t, the first term on the right of the partial differential equation representing the expansion term, w1Is the coefficient of expansion, G (x) represents the expansion rate function, in this example
That is, the value of the expansion term in the cardiovascular image is larger, and the value at the boundary of the cardiovascular image is smaller; the second term represents the smoothing term, w2Representing the smoothing factor, H (x) representing the mean curvature of the three-dimensional image of the heart,
the third term represents a convection term, where w3The coefficient of convection is expressed as a function of,
representing a vector field associated with a convection current, wherein,
i represents the intensity of the three-dimensional image of the heart. Representing the cardiovascular three-dimensional image to be acquired as S (t), wherein S (t) is a mosaic function
Is determined by a zero level of (i.e. is)
And the cardiovascular three-dimensional image reconstruction module 202 is configured to solve the partial differential equation (1) of the embedding function through a finite difference method to obtain a reconstructed cardiovascular three-dimensional image. The specific process is as follows: initializing a coronary artery image in the three-dimensional image of the heart by using a collision forward method, and initializing an aorta image in the three-dimensional image of the heart by using a fast propulsion method to obtain initial conditions of the partial differential equation of the embedding function
Based on the initial conditions
And (3) performing expansion, smoothing and convection treatment on the curved surface part in the heart three-dimensional image to obtain a reconstructed heart blood vessel three-dimensional image.
And the cardiovascular three-dimensional model obtaining module 203 is configured to process the reconstructed cardiovascular three-dimensional image by using a marching block method to obtain a cardiovascular three-dimensional model. The marching block method is a computer vision algorithm, and can extract a polygon mesh from a 3D discrete scalar field.
The embodiment of the invention also discloses a cardiovascular image reconstruction system based on the implicit deformable model, which comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the steps of the cardiovascular image reconstruction method based on the implicit deformable model when executing the computer program.
According to the cardiovascular image reconstruction method and system based on the implicit deformable model, the parameters of the heart three-dimensional image are used for constructing the partial differential equation of the embedding function, then the partial differential equation is solved by using the finite difference method, the cardiovascular three-dimensional image is obtained, and then the cardiovascular three-dimensional image is processed by using the block-advancing method, so that the cardiovascular three-dimensional model is obtained, the required area is rapidly and accurately segmented, the calculation result is stable, and the subsequent CFD analysis and the like are facilitated.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A cardiovascular image reconstruction method based on an implicit deformable model is characterized by comprising the following steps:
acquiring a three-dimensional image of a human heart, and constructing a partial differential equation of a embedding function by using parameters of the three-dimensional image of the heart; the partial differential equation of the embedding function constructed by using the parameters of the heart three-dimensional image is shown as equation (1):
wherein the content of the first and second substances,
representing a mosaic function
Partial differentiation of the iteration time term t, w1Represents the coefficient of expansion, G (x) represents the expansion rate function; w is a2It is shown that the coefficient of smoothness,
h (x) represents the mean curvature of the three-dimensional image of the heart; w is a3The coefficient of convection is expressed as a function of,
wherein I represents the intensity of a three-dimensional image of the heart; solving the partial differential equation of the embedding function by using a finite difference method to obtain a reconstructed cardiovascular three-dimensional image;
and processing the reconstructed cardiovascular three-dimensional image by using a block advancing method to obtain a cardiovascular three-dimensional model.
2. The method for reconstructing the cardiovascular image based on the implicit deformable model according to claim 1, wherein the finite difference method is used for solving the partial differential equation of the embedding function to obtain the reconstructed cardiovascular three-dimensional image, and the method specifically comprises the following steps:
initializing a coronary artery image in the three-dimensional image of the heart by using a collision forward method, and initializing an aorta image in the three-dimensional image of the heart by using a fast propulsion method to obtain initial conditions of the partial differential equation of the embedding function
Based on the initial conditions
And (3) performing expansion, smoothing and convection treatment on the curved surface part in the heart three-dimensional image to obtain a reconstructed heart blood vessel three-dimensional image.
3. The method for reconstructing cardiovascular image based on implicit deformable model as claimed in claim 2, wherein the initialization of coronary artery image in three-dimensional image of heart by using collision forward method is carried out by:
firstly, selecting two seed points, namely a source point and a target point, which are positioned at two ends of a blood vessel branch, and then reconstructing an image based on two mutually independent wavefronts emitted by the two seed points; the propagation velocity of the wavefront is proportional to the intensity of the image, as shown in equation (2):
t represents the time when the wave front reaches any other point in the image area, and the reciprocal of the image intensity I represents the slowness of the wave front; solving equation (2) by windward finite difference method to obtain action components T of two seed points to any point in the image region1And T2Initial condition of the partial differential equation of the embedding function
4. The method of claim 3, wherein the fast marching method is used to initialize the aorta image in the three-dimensional cardiac image by selecting a series of source points and target points, reconstructing the image based on the independent wavefronts from the source points and the target points, and solving equation (2) by the windward finite difference method to obtain the solution of equation (2), and the initial conditions of the embedding function
T represents the solution of equation (2), TtargetRepresents the minimum in the solution of equation (2).
5. A cardiovascular image reconstruction system based on an implicit deformable model, comprising:
the function equation constructing module is used for acquiring a three-dimensional image of a human heart and constructing an embedded function partial differential equation by using parameters of the three-dimensional image of the heart; the partial differential equation of the embedding function constructed by using the parameters of the heart three-dimensional image is shown as equation (1):
wherein the content of the first and second substances,
representing a mosaic function
Partial differentiation of the iteration time term t, w1Represents the coefficient of expansion, G (x) represents the expansion rate function; w is a2It is shown that the coefficient of smoothness,
h (x) represents the mean curvature of the three-dimensional image of the heart; w is a3The coefficient of convection is expressed as a function of,
wherein I represents the intensity of a three-dimensional image of the heart;
the cardiovascular three-dimensional image reconstruction module is used for solving the partial differential equation of the embedding function through a finite difference method to obtain a reconstructed cardiovascular three-dimensional image;
and the cardiovascular three-dimensional model acquisition module is used for processing the reconstructed cardiovascular three-dimensional image by utilizing a moving block method to obtain a cardiovascular three-dimensional model.
6. The system of claim 5, wherein the cardiovascular three-dimensional image reconstruction module comprises:
an initialization unit, configured to initialize a coronary artery image in the three-dimensional cardiac image by using a collision-forward method, and initialize an aorta image in the three-dimensional cardiac image by using a fast-marching method, so as to obtain an initial condition of the partial differential equation of the embedding function
And the processing unit is used for performing expansion, smoothing and convection processing on the curved surface part in the cardiovascular three-dimensional image to obtain a reconstructed cardiovascular three-dimensional image.
7. The system of claim 6, wherein the initialization unit initializes the coronary artery image in the three-dimensional cardiac image by a collision-forward method, and the initialization unit first selects two seed points, namely a source point and a target point, at two ends of a blood vessel branch, and then reconstructs the image based on two mutually independent wavefronts emitted by the two seed points; the propagation velocity of the wavefront is proportional to the intensity of the image, as shown in equation (2):
t represents the time when the wave front reaches any other point in the image area, and the reciprocal of the image intensity I represents the slowness of the wave front; solving equation (2) by windward finite difference method to obtain action components T of two seed points to any point in the image region1And T2Initial condition of the partial differential equation of the embedding function
8. The system of claim 7, wherein the initialization unit first selects a series of source points and target points, performs image reconstruction based on mutually independent wavefronts emitted by the source points and the target points, and then solves equation (2) by windward finite difference method to obtain a solution of equation (2), and initial conditions of the embedding function
T represents the solution of equation (2), TtargetRepresents the minimum in the solution of equation (2).
9. A cardiovascular image reconstruction system based on an implicit deformable model, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the method according to any one of claims 1 to 4.
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