CN108122616B - Method for generating individual-specific cardiovascular models and use thereof - Google Patents
Method for generating individual-specific cardiovascular models and use thereof Download PDFInfo
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Abstract
The invention provides a generation method and application of an individual-specific cardiovascular model, wherein the cardiovascular model is a one-dimensional (1D) model and is characterized in that: the cardiovascular model is a model of a micro-vessel that is not available via image reconstruction, the generation method comprising: performing acquisition of medical image data on an organ of interest; analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree; calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest including the target vessel tree therein; generating a 1D model of the microvessels starting with an exit of the 3D model of the target vessel tree and the organ region of interest as a bounding region.
Description
The application is a divisional application of Chinese invention application with the application date of 2016, 12 and 28, and the application number of 201611236767.X, and the name of the invention is 'generation method of individual specificity cardiovascular model and application thereof'.
Technical Field
The invention relates to the field of modeling of blood vessels of a human circulatory system, in particular to a method for generating an individual-specific cardiovascular model and a method for generating boundary conditions based on the individual-specific cardiovascular model.
Background
With the development of image acquisition and high-end computing technologies, biomedical engineering has become one of the important means for further understanding blood circulation. For example, a vessel dynamics simulation for a cardiovascular coronary artery can accurately calculate the pressure distribution in the vessel and, in turn, the Fractional Flow Reserve (FFR). This emerging numerical simulation computed FFR (virtual FFR) technique utilizes high-definition image acquisition data (e.g., CT, MRI, etc.) to reconstruct a model of a patient's blood vessel, and incorporates Computational Fluid Dynamics (CFD) to simulate the flow of blood in the blood vessel. Compared with the traditional invasive FFR measurement technology (namely invasive measurement), the virtual FFR is noninvasive, can effectively reduce the risk of the operation to the patient, and can reduce the pain of the patient and save the treatment cost. In contrast to clinical trials, virtual FFR is very effective in diagnosing myocardial ischemia and is also superior to existing imaging evaluation methods. In addition to the cardiovascular aspect, hemodynamic simulation is also used for various other body organs (e.g., cerebral vessels, liver, etc.) and the body's entire circulatory system.
As a leading-edge technique, the vascular dynamics simulation also faces technical challenges and challenges. Due to the limitations of current image acquisition techniques and the multi-scale nature of blood vessels, it has not been possible to fully reconstruct the entire vessel model from the major vessels on the centimeter scale up to the capillaries on the micrometer scale. The individual model obtained from image reconstruction typically includes, at a minimum, only vessel branches in the millimeter scale (hereinafter referred to as the general 3D model), so that very small vessels smaller than this scale are ignored. This results in that we have to build a suitable model in the numerical simulation to simulate the influence of the neglected part of the blood vessel on the flow (e.g. using suitable boundary conditions). Currently, the mainstream leading edge blood vessel simulation calculation technology generally assumes boundary conditions according to the statistical general data, such as flow distribution of each branch of the human blood vessel tree, and mathematical model (0D model for short) of analog circuit. Furthermore, a (1D) tree model of ideal vessel branches is further used, such as the lengths of two sub-branches of any parent branch always satisfy a fixed ratio, to describe the omitted vessel parts and extract the appropriate boundary condition setting based on the description. However, these models and attempts neglect individual characteristics of the patient, inevitably affect the suitability of the boundary conditions set for the individual simulation, and further affect the accuracy of the simulation result, which becomes a bottleneck for further improving the accuracy of the numerical simulation of the physiological characteristics.
It is necessary to create an individual-specific vascular tree model to describe the part of the micro vessels that is omitted due to insufficient image accuracy, thereby creating a 1D model of the individual-specific micro vessels (hereinafter referred to as a micro 1D model) and further creating an individual-specific complete cardiovascular model (hereinafter referred to as a complete 1D model) that integrates the micro 1D model. By CFD calculation of the fine 1D model and/or the complete 1D model, entry and exit boundary conditions with individual specificity can be obtained more accurately for the 3D CFD model. The established micro 1D model can be regarded as a bridge for connecting the 3D model outlet obtained by image reconstruction to local organ tissues, so that the method can help us to determine the proper 3D model outlet boundary condition. In addition, the CFD calculation of the complete 1D model is quick and effective, and can help the doctor to confirm the general distribution of the fluid parameters in the whole blood vessel tree and further decide which branch needs to be focused on, so that the doctor can use the complete 1D CFD calculation result to set the targeted inlet and outlet boundary conditions for the selected branch, and the accurate distribution of the fluid parameters in the selected branch can be accurately obtained by using the 3D CFD calculation of the selected branch.
Disclosure of Invention
According to a first aspect, the present invention provides a method for generating an individual-specific cardiovascular model, said cardiovascular model being a one-dimensional (1D) model, characterized by: the cardiovascular model is a model of a micro-vessel that is not available via image reconstruction, the generation method comprising:
performing acquisition of medical image data on an organ of interest;
analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree;
calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on the results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest in which the target vessel tree is located;
and generating a 1D model of the capillary vessel by taking an outlet of the 3D model of the target vessel tree as a starting point and the interested organ region as a defined region.
According to a second aspect, the present invention provides a method of setting an exit boundary condition for a 3D CFD model of the target vessel tree using a generated 1D model of a fine vessel, characterized in that the exit boundary condition is a tree-based resistance-related boundary condition or a mass-conservation-based flow distribution boundary condition.
Preferably, the method of setting exit boundary conditions for a 3D CFD model of a target vessel tree comprises the steps of: generating a computational grid for the 1D model of the capillary vessel, setting the inlet boundary condition of the 1D model of the capillary vessel as flow and the outlet boundary condition thereof as corresponding pressure or venous pressure, calculating the pressure of each inlet of the 1D model of the capillary vessel, calculating the capillary resistance of each inlet according to the calculated pressure and flow of each inlet, and calculating the equivalent capillary resistance at the outlet of the target vessel tree as the outlet boundary condition of the 3D CFD model of the target vessel tree by utilizing the tree-shaped connection relation of each inlet based on the calculated equivalent capillary resistance.
Preferably, the method for setting the exit boundary condition by the 3D CFD model of the target vessel tree comprises the following steps: generating a computational grid for the 1D model of the fine blood vessel, setting the inlet boundary condition of the 1D model of the fine blood vessel as pressure and the outlet boundary condition thereof as corresponding flow, calculating the flow of each inlet of the 1D model of the fine blood vessel, and calculating the equivalent flow at the outlet of the target blood vessel tree by utilizing the tree-shaped connection relation of each inlet according to the calculated flow of each inlet to serve as the outlet boundary condition of the 3D CFD model of the target blood vessel tree. Wherein the flow of the 1D model outlet of the microvessels may be obtained based on a specified flow distribution, an area of influence of the outlet vessels, or a blood perfusion related medical image. The specified outlet flow distribution may be the simplest uniform flow field distribution, or a flow field distribution that is correlated to the outlet location (e.g., flow varies gradually from apex to end of the heart with outlet location, end to base flow distribution), etc. The size of the area of influence of the exit vessel may define the flow distribution, and the area of influence of the exit vessel may be obtained by voronoi regions, fuzzy distance variations, or the like. Furthermore, the flow of the outlet vessel can be measured or derived from relevant medical images (e.g. perfusion scan image methods) (modeling yields the correlation between the flow of the outlet vessel and the thickness of the myocardium, local image pixels, etc.).
According to a third aspect, the present invention provides a method for generating an individual-specific cardiovascular model, said cardiovascular model being a one-dimensional (1D) model, characterized by: the cardiovascular model is a complete model of a target vessel tree containing fine vessels that are not available via image reconstruction, the generation method comprising:
performing acquisition of medical image data on an organ of interest;
analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree;
calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on the results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest in which the target vessel tree is located;
generating a 1D model of the microvessels starting with an exit of the 3D model of the target vessel tree and the region of the organ of interest as a bounding region;
obtaining a complete 1D model of the target vessel tree by converting the 3D model back to a 1D model and integrating with the 1D model of the microvessels.
According to a fourth aspect, the present invention provides a method for setting entry boundary conditions for a 3D CFD model of a target vessel tree using a complete 1D model of the target vessel tree generated by the generation method, the method comprising: and performing CFD calculation on the complete 1D model, calculating the flow at each position in the complete target blood vessel tree, and setting the flow at each position in the complete 1D model obtained by calculation, which corresponds to the inlet of the 3D CFD model of the target blood vessel tree, as the inlet boundary condition of the 3D CFD model of the target blood vessel tree.
According to a fifth aspect, the invention provides a method of setting exit boundary conditions for a 3D CFD model of a target vessel tree generated according to the generation method using a complete 1D model of the target vessel tree, the method comprising: and performing CFD calculation on the complete 1D model, calculating the flow and pressure at each position in the complete target blood vessel tree, and calculating the micro-vessel resistance at the outlet of the 3D CFD model of the target blood vessel tree based on the flow and pressure at each position in the complete 1D model corresponding to the outlet of the 3D CFD model of the target blood vessel tree, wherein the micro-vessel resistance is used as the outlet boundary condition.
According to a sixth aspect, the present invention provides a method for setting exit boundary conditions for a 3D CFD model of a target vessel tree using a complete 1D model of the target vessel tree generated by the generation method, the method comprising: and performing CFD calculation on the complete 1D model, calculating fluid parameters at each position in the complete target blood vessel tree, and setting the fluid parameters at each position in the complete 1D model corresponding to the outlet of the 3D CFD model of the target blood vessel tree as outlet boundary conditions of the fluid parameters.
According to a seventh aspect, the present invention provides a method of performing a 3D-1D coupling calculation on a target vessel tree, the method comprising the steps of:
generating a complete 1D model of the target vessel tree and a 3D model of the target vessel tree according to the following generation methods:
performing acquisition of medical image data on an organ of interest;
analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree;
calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on the results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest in which the target vessel tree is located;
generating a 1D model of the microvessels starting with an exit of the 3D model of the target vessel tree and the organ region of interest as a bounding region;
obtaining a complete 1D model of the target vessel tree by converting the 3D model back to a 1D model and integrating with the 1D model of the microvessels, the 1D model being generated based on a fractal calculation method;
generating a computational grid for the complete 1D model of the target vessel tree and setting corresponding boundary conditions to calculate fluid parameters at various positions in the complete target vessel tree;
selecting whether to perform CFD calculation for part or whole of the 3D model of the target blood vessel tree, generating a calculation grid for the selected part or whole of the target blood vessel tree and setting corresponding boundary conditions to calculate the fluid parameters of corresponding parts in the target blood vessel tree, wherein
If the CFD calculation is carried out on the whole of the 3D model of the target blood vessel tree, the inlet boundary condition of the CFD calculation is set as the blood flow of the target blood vessel tree in the applied congestion state, and the outlet boundary condition of the CFD calculation is set as the fluid parameters of the whole 1D model, which correspond to the local outlet of the 3D model of the target blood vessel tree;
if the CFD calculation is selected to be carried out on the part of the 3D model of the target blood vessel tree, the inlet boundary condition and the outlet boundary condition of the CFD calculation are set as the fluid parameters of the whole 1D model corresponding to the inlet and the outlet of the part of the 3D model of the target blood vessel tree.
Drawings
Various embodiments of the present invention are described in detail below with reference to the attached drawing figures, wherein
FIG. 1 illustrates a 3D geometric model of a region of the heart (including the left atrium, left ventricle, right atrium, right ventricle) and the aorta, left and right arteries in accordance with one embodiment of the present invention;
FIG. 2 shows a 3D left ventricle and corresponding 2D bull's eye plot;
FIG. 3 shows a schematic diagram of an individual-specific cardiovascular 1D model generated in accordance with one embodiment of the present invention;
fig. 4(a) -4 (c) show examples of a 3D CFD model and boundary conditions according to an embodiment of the present invention, wherein fig. 4(a) shows a relationship between a cross-sectional view of a medical image and a geometric model of a segmentation reconstruction, fig. 4(b) shows a three-dimensional geometric model of a vessel tree including an aorta, left and right arteries, and vessel branches resulting from the segmentation reconstruction, and fig. 4(c) shows a CFD model of a vessel tree of a left artery and corresponding boundary conditions including a vessel wall and entrance and exit boundary conditions.
FIG. 5 shows a schematic diagram of a 3D-1D coupling network of a left artery and its branches resulting from a method of performing 3D-1D coupling calculations according to another embodiment of the invention.
Detailed Description
Embodiments of the method of generation of an individual-specific cardiovascular model and its uses of the present invention will now be described in detail with reference to the drawings, in which like reference numerals designate identical or corresponding elements in each of the several views.
Fig. 4(a) -4 (c) show examples of steps of establishing a 3D CFD model for a coronary artery of a patient according to an embodiment of the present invention, wherein fig. 4(a) shows a cross-sectional view of a medical image, a geometric model of a segmentation reconstruction and a relationship therebetween, fig. 4(b) shows a three-dimensional geometric model of a vessel tree resulting from the segmentation reconstruction and including an aorta, left and right aorta and major vessel branches, and fig. 4(c) shows a CFD model of a vessel tree of a left aorta and corresponding boundary conditions including a vessel wall and inlet and outlet boundary conditions.
The acquisition of medical image data is first performed on an organ of interest, in this embodiment exemplified by a heart containing coronary arteries. Acquisition may be performed using various medical imaging modalities, including but not limited to high definition Computed Tomography (CT), Magnetic Resonance Imaging (MRI), ultrasound imaging, and the like. To improve the sharpness and resolution of the objects in the image, a suitable blood vessel-lightening agent or contrast agent may be injected prior to image acquisition. Although the heart including coronary arteries is taken as an example in the present embodiment, the organ of interest may be, but is not limited to, the heart, the brain, the liver, the kidney, and the like.
The acquired medical image data is analyzed and segmented to segment an organ region of interest (in this embodiment, a heart region), a target blood vessel (in this embodiment, a coronary artery). The analysis may include image pre-processing, such as noise reduction, calibration, etc. The segmentation may be performed by using a conventional segmentation method, such as a fast stepping algorithm (fast marching) or a deep learning method. In this step, the vessel is optionally brightened (e.g., by computing a vesselness measure, etc.) using suitable image processing methods. Based on the results of the image analysis and segmentation, it may be possible to compute and reconstruct the vessel centerline and the vessel wall of the resulting vessel tree, e.g. using various open-source software including vmtk (the Vascular Modeling toolkit), to construct a 3D geometric model of the vessel tree, as shown in fig. 1 and 4 (b). The 3D model of the vessel tree thus generated is reconstructed to cover at most vessel branches of millimeter scale (hereinafter referred to as a general 3D model), so that very small vessels smaller than that scale are ignored.
By analyzing and segmenting the series of medical images, it is also possible to extract regions of the heart, including the coronary arteries, and a 3D model of the heart (including the left atrium, left ventricle, right atrium, right ventricle) is shown in fig. 1. In addition, fig. 1 also shows a 3D model of the aorta and the left and right coronary arteries. In particular, the boundaries of the 3D model of the vessel tree of the coronary arteries itself are shown in fig. 4(b), these boundaries comprising an entrance and an exit (the exit comprising exits 1-8, as shown in fig. 4 (c)). Starting with the exit of the 3D model of the coronary artery as a boundary region, a certain range of the surface of the heart where the coronary artery is located (where the fine branches of the coronary artery are distributed) is set as a bridge from the exit of the 3D model to the boundary region, thereby generating a 1D model (referred to simply as a fine 1D model) representing the fine blood vessels. Note that the organ area as the delimited area may be selected by the physician based on anatomical knowledge of the micro-vessels, which in particular should be the boundary of the whole or local area of the organ where the micro-vessels grow from the exit of the 3D model to the furthest away. By "organ region of interest in which the target vessel tree is located", it is meant a region of a certain range of the organ of interest in which the fine branches of the target vessel tree are distributed, to which the fine branches of the target vessel tree may grow. A number of different methods may be employed to generate a 1D model of a microvessel, exemplified below by a fractal-based calculation method. Specifically, a series of uniformly or randomly distributed dot matrixes are placed in a defined area, points corresponding to the nearest distance of each blood vessel outlet (N blood vessel outlets) are found and form a point set (N point sets in total), the mass center of the point set and the center line of the terminal blood vessel form a plane, the point set is divided into two molecular point sets (2N sub-point sets in total) by adopting the plane, and the straight line from the blood vessel outlet to the mass center of the sub-point set is defined as a new 1D blood vessel branch (2N new blood vessel outlets in total) and is used as the starting point of the subsequent 1D blood vessel generation. The process is repeated until the new blood vessel branch is smaller than the preset shortest blood vessel length, or the point set corresponding to the new blood vessel branch only contains one point. By the method, a network structure of the capillary can be obtained, and the branch structure is analyzed (including a blood vessel series, a Strahler series). The blood vessel grade is started by a main branch and is increased by each branch grade, and usually, the branch grade of the tail end of the blood vessel is different because the branch frequency of each path of the blood vessel is different; the strathler series starts from the end of the blood vessel, the series of all blood vessels at the end is defined as 1, counting towards the main branch, and the series of the parent branch (parent branch) is equal to the series of the child branches +1 every time the branch passes, so that the main branch always corresponds to the maximum strathler series. The stratler series better describes the asymmetric vessel geometry and can be used to estimate the diameter of a vessel, see the expression:
log Dn＝(n-N)logRd+logDN
where n is the Strahler series of the current vessel, corresponding to a diameter DnN is the maximum strathler series of the vessel tree, and the corresponding diameter is DN,RdIs a constant.
The process can be directly implemented in a 3D space, or the 3D space can be converted into a 2D space, and then converted back into the 3D space after the 1D model is generated. For example, for coronary artery, a 3D left ventricular wall can be converted into a 2D bull's eye map, which is shown in fig. 2, and the generated 1D model of a blood capillary can be converted into a 3D space after the generation of the model in the 2D space. Specifically, the initial and defined regions in the 3D space may be mapped to the 2D bull's eye map according to the mapping relationship shown in fig. 2, and accordingly the 1D model of the blood capillary may be calculated in the 2D space, and then the calculated 1D model of the blood capillary may be inversely mapped to the 3D space by using the mapping relationship shown in fig. 2, so as to obtain the 1D model of the blood capillary in the 3D space.
It should be noted that, starting from the exit of the 3D model and taking the region of the organ of interest where the target vessel tree is located as the defined region, other calculation methods besides fractal may be adopted to generate the 1D model of the microvessels, such as establishing a topological model of microvessels specific to various organs according to anatomical experience, and generating the 1D model based on the topological model of the microvessels, which are not described herein in detail.
The thus generated minute 1D model is based on medical imaging information and anatomical structure of the patient itself, and is therefore individual-specific, and can accurately reproduce the structure of the minute blood vessels of the patient. Compared with the prior art that boundary conditions are assumed according to statistical data or a (1D) tree model of ideal vessel branches is adopted to describe omitted vessel parts, individual differences of the micro vessels of the patient can be reflected, so that the corresponding 1D CFD calculation accuracy is higher, the boundary conditions of the 3D CFD calculation set based on the calculation results are more accurate and more suitable, and the corresponding 3D CFD calculation accuracy is higher.
Although the 1D CFD model of the blood vessel tree has small calculation amount and high calculation speed, the main characteristics of a flow field, such as pressure drop, flow distribution, blood flow speed and the like along the blood vessel can be quickly simulated by neglecting the slight flow field change. The blood flow parameter accuracy obtained by simulation is not enough to be directly used for clinical diagnosis of vascular symptoms, but the boundary conditions of the corresponding inlet and outlet of the 3D CFD model serving as the vascular tree are enough, the individual specificity is fully embodied, and the accuracy of simulation calculation of the 3D CFD model can be greatly improved.
The fine 1D model is in 3D
Application of CFD model in establishing outlet boundary condition
The above-described fine 1D model may be used to set outlet boundary conditions with individual specificity, such as tree-based resistance-related boundary conditions, mass-conservation-based flow distribution boundary conditions, and the like, for the 3D CFD model. Specifically, a computational mesh may be generated for the above-mentioned fine 1D model, and the inlet boundary conditions of the fine 1D model are set as flow rates Q in the cardiac output of the patient theoretically allocated to the respective inlets i of the fine 1D model (i.e., the outlets of the respective 3D CFD models)in,iSetting its outlet boundary condition to the corresponding pressure poutOr more simply set to venous pressure (typically 0), the predicted pressure P at each inlet boundary is computed by solving the 1D CFD model under inlet and outlet boundary conditions as abovei,in(i is the number of each entry), using the relation Pi,in＝Qi,inRiCalculating the microvascular resistance R at each inlet ii. Wherein the corresponding pressure poutCan be obtained using existing vessel simulation calculation techniques, such as derivation from statistically derived generic data, such as simulation calculations using the OD models described above, and so forth. Assume that the exit j of the 3D CFD model is opposite to the ith of the fine 1D model1…ijAn inlet, then use the ith1…ijThe tree-shaped connection relation (series-parallel connection relation) of the inlets is used for calculating the equivalent total capillary resistance of the tree shape based on the capillary resistance of each inlet, and the equivalent total capillary resistance is used as the capillary resistance of the outlet j, namely the outlet boundary condition of the 3D CFD model.
It is also possible to calculate by solving the 1D CFD model under the inlet and outlet boundary conditions as described above by setting the inlet boundary condition of the fine 1D model to the corresponding pressure and the outlet boundary condition thereof to the flow ratePredicting actual flow Q at various entry boundariesi,in(i is the number of each entry). Wherein the flow of the 1D model outlet of the microvessels may be obtained based on a specified flow distribution, an area of influence of the outlet vessels, or a blood perfusion related medical image. The specified outlet flow distribution may be the simplest uniform flow field distribution, or a flow field distribution that is correlated to the outlet location (e.g., flow varies gradually from apex to end of the heart with outlet location, end to base flow distribution), etc. The size of the area of influence of the exit vessel may define the flow distribution, and the area of influence of the exit vessel may be obtained by voronoi regions, fuzzy distance variations, or the like. Furthermore, the flow of the outlet vessel can be measured or derived from relevant medical images (e.g. perfusion scan image methods) (modeling yields the correlation between the flow of the outlet vessel and the thickness of the myocardium, local image pixels, etc.). Assume that the exit j of the 3D CFD model is opposite to the ith of the fine 1D model1…ijAn inlet, then use the ith1…ijTree connection relation (series-parallel relation) of the entries to base actual flow Q of each entryi,inThe tree-shaped equivalent total flow is calculated, and the mass conservation, namely the actual flow of the outlet j is taken as the outlet boundary condition of the 3D CFD model.
The complete 1D model is in 3D
Application of CFD model in establishing inlet and outlet boundary conditions
The accuracy of the simulation results of the cardiovascular 3D CFD model depends on the appropriate setting of the entry and exit boundary conditions, and by establishing a specific and complete (including those micro-vessels that can be missed by the medical image reconstruction) 1D CFD model for the individual, by solving it, can be used to set the appropriate individual-specific entry and exit boundary conditions.
The complete 1D CFD model can be obtained by: obtaining a complete 1D model by converting the established 3D model back to a 1D model and integrating it with a fine 1D model, or generating a 1D model in parallel with the 3D model and integrating it with a fine 1D model to obtain a complete 1D model; a computational mesh is generated for the complete 1D model, thereby building a complete 1D CFD model of the vessel tree. Corresponding inlet and outlet boundary conditions can be set for the complete 1D CFD model of the vessel tree, and the physical properties and flow equations of blood are set; then, based on the inlet and outlet boundary conditions, the set physical properties and the flow equations, the complete 1D CFD model of the vessel tree is solved to obtain the fluid parameters throughout the vessel tree.
Entry boundary condition
The entry boundary condition for the 3D CFD model may be set by building a complete 1D CFD model of the vessel tree (e.g., using the complete individual-specific 1D model generation method described above), solving it to calculate the flow rates everywhere in the complete vessel tree, and applying the calculated flow rates everywhere in the complete vessel tree to the entry boundary of the 3D CFD model of the vessel tree. Although flow is used as an example, any one or both of the flow, pressure and velocity of the blood may be used as the inlet and outlet boundary conditions. It is also possible to use the same fluid parameters for the inlet and outlet boundary conditions, as long as it is ensured that the convergence of the 3D CFD model meets the clinical requirements. Even if individual-specific inlet and outlet boundary conditions are not set for the complete 1D CFD model, considering that the complete 1D CFD model itself reflects the complete blood vessel characteristics of an individual, through CFD iterative solution, the individual specificity is also completely and well reflected by the flow at each location corresponding to the inlet boundary of the 3D CFD model in the complete blood vessel tree obtained during convergence, thereby also setting the individual-specific inlet boundary conditions for the 3D CFD model. The 1D CFD calculation only needs a very small number of grids, and the calculation speed is very quick (can be considered as real-time calculation), so that the entrance boundary condition of the 3D CFD model obtained by the 1D CFD calculation can promote the accuracy of the calculation result without influencing the calculation speed of the complete calculation process of the 3D CFD model.
Outlet boundary condition
There are two setting methods for the exit boundary conditions of the 3D CFD model that can be combined with the calculation of the individual-specific complete 1D CFD model, the first being to set the exit boundary conditions as the microvascular resistance throughout the vascular tree of the coronary arteries of the individual patient; in a second way, similar to the above setting of the entrance boundary conditions, the 1D CFD calculation result is applied to the exit of the 3D CFD model, and the exit boundary conditions of the 3D CFD model are set as the pressures at the corresponding places in the blood vessel obtained by the solution of the 1D CFD model of the blood vessel tree.
The 1D CFD calculation only needs a very small number of grids, the calculation speed is very fast (can be considered as real-time calculation), and by utilizing the advantages, a 1D CFD model of a complete coronary artery tree is established, and initial entrance boundary conditions are set, wherein the entrance boundary conditions can be obtained by various methods in the prior art, such as a method of obtaining total entrance blood flow and an assumed branch flow ratio, a method of setting by utilizing statistics of a large number of samples of a crowd, and a method combining the solution of the 1D CFD; the outlet boundary conditions may then all be set to the respective pressure (how the respective pressure is obtained is described above) or the venous pressure (typically 0). Calculating the 1D CFD model under the set inlet boundary condition and outlet boundary condition to obtain the flow and pressure of each outlet corresponding to the 3D CFD model in the 1D CFD model, and using the relation Pi,out＝Qi,outRiCalculating microvascular resistance R of each exit boundary of the 3D CFD modeli. The application can greatly simplify the solving of the microvascular resistance of the outlet boundary condition in the 3D CFD calculation, the 1D CFD model covers the peripheral microvascular of an individual and is individual-specific, and the accuracy of the calculated microvascular resistance of each outlet is enough to serve as the outlet boundary condition of the 3D CFD model, although the flow and pressure of each corresponding part obtained by setting the inlet and outlet boundary conditions as above cannot be directly used for medical diagnosis.
The second approach uses the calculation of the complete 1D CFD model to derive the pressure everywhere in the vessel tree of the complete coronary artery and applies the corresponding pressure to the corresponding exit boundary of the 3D CFD model. Of course, instead of pressure, other kinds of fluid parameters, including flow, velocity, etc. may be used as outlet boundary conditions for the 3D CFD model.
As described above, the fluid parameters everywhere, which are directly obtained from the calculation of the microvascular resistance of the coronary artery based on the simulation result of the complete 1D CFD model or the simulation of the complete 1D CFD model, are taken as outlet boundary conditions, and finally the fluid parameters everywhere in the vessel tree are obtained by 3D CFD modeling and calculation of substantially the entire vessel tree.
3D-1D coupling simulation
3D CFD simulation can capture slight flow field changes, but the calculation amount is large and the time consumption is long; the corresponding 1D CFD simulation ignores subtle flow field variations but can quickly simulate flow field key features such as pressure drop along the vessel. Due to the limitation of the current computing technology, the computation amount of 3D CFD simulation of the complete blood vessel tree structure is very large, and the method cannot be used for clinical auxiliary treatment; conversely, if only 1D CFD simulation is used, the influence of large-scale fine flow field features on the entire flow field is ignored, and a relatively large calculation error is caused. In practice, it is necessary to further simplify and speed up the setting of boundary conditions and further speed up the overall calculation speed of fluid parameters while ensuring the calculation accuracy.
Furthermore, physicians require that CFD modeling not only be able to accurately simulate and compute the complete coronary artery, but also to separately simulate and compute a specific vessel branch (such as a suspected lesion segment), and that the accuracy of the simulated computation is different from one coronary artery to another. For example, a physician may wish to quickly obtain the general distribution of blood flow characteristics, such as Fractional Flow Reserve (FFR), of an intact coronary artery by real-time 1D CFD modeling calculations, so that a particular vessel branch that requires more clinical attention can be manually or automatically selected therefrom, and a relatively time-consuming but more accurate 3D CFD modeling calculation can be performed on that particular vessel branch.
Accordingly, the present invention also provides a method for performing 3D-1D coupled calculations (which we refer to as virtual digital subtraction angiography) to meet the above upgrade requirements, which combines the features and respective advantages of using 3D-1D CFD to greatly simplify the requirements for boundary conditions. The method can relatively accurately simulate and calculate the complete coronary artery including the tiny blood vessels, and can more accurately and specifically simulate and calculate the specific blood vessel branch (such as a suspected lesion segment) independently, thereby further greatly shortening the time required by calculation and preferentially ensuring the accuracy of the simulated calculation of the specific blood vessel branch with more clinical attention.
The method sets the blood in the blood vessel to be Newtonian fluid and laminar flow, sets the blood density and the blood flow viscosity which accord with the physiological characteristics of the human body, and sets the flow equation to be unsteady flow so as to ensure that the calculation result is convergent. Depending on the specific requirements for solving the fluid parameters, the 3D CFD mesh and model for the specific requirements may be generated for the vessel tree of the entire left and right aorta, or for a specific vessel branch of a certain segment; the 1D CFD mesh and model is then generated for the vessel tree of the complete coronary artery (including the microvessels).
Corresponding boundary conditions are set for the 1D CFD model and the 3D CFD model of the vessel tree. Wherein the inlet boundary conditions of the 1D CFD model are set to the left and right aortic blood flow in a hyperemic state, and the outlet boundary conditions of the 1D CFD model are set to the corresponding pressure or venous pressure (typically 0).
Different entry boundary conditions are set for whether the vessel trees of the entire left and right aorta or only for a specific vessel branch are simulated by the 3D CFD model. Specifically, if the vessel tree of the whole left and right aorta is simulated, the inlet boundary condition is set as the blood flow of the left and right aorta in the hyperemia state; if a specific blood vessel branch is simulated, the inlet boundary condition is set as the calculated flow rate at the corresponding position under the inlet boundary condition and the outlet boundary condition (corresponding pressure or venous pressure) set as above by using the 1D CFD model, and other fluid parameters besides the flow rate can also be used.
The outlet boundary condition of the 3D CFD model is set to a pressure value calculated at the corresponding position using the 1D CFD model under the inlet boundary condition and the outlet boundary condition (the respective pressure or the venous pressure) set as above, and fluid parameters other than the pressure may be used here.
Thus, the coupling calculation of 3D-1D CFD is realized.
In the 3D and 1D CFD calculation, a Navier-Stokes (N-S) equation set (mass and momentum conservation equation) of the non-pressure flow is set:
u is the fluid velocity vector, p is the pressure, ρ is the fluid density, and ρ is the fluid' S kinematic viscosity, so that both 1D CFD and 3D CFD solutions are based on the non-compressible flow N-S equation system.
Taking the example of the intention to model the left aorta in coronary arteries alone, fig. 5 shows a 1D CFD mesh generated for the complete coronary arteries including the distal microvessels and a 3D CFD mesh generated for the left aorta of clinical interest only, with the blood flow characteristics distribution everywhere in the left aorta obtained by the above-described 3D-1D coupling calculation, which 3D-1D coupling calculation results proved to provide sufficient accuracy and clinically acceptable time consumption.
Therefore, the above description should not be taken as limiting, but merely as exemplifications of particular embodiments. Those skilled in the art will envision other modifications within the scope and spirit of the claims appended hereto.
Claims (10)
1. A method of generating an individual-specific cardiovascular model, said cardiovascular model being a one-dimensional (1D) model, characterized by: the cardiovascular model is a model of a micro-vessel that is not available via image reconstruction, the generation method comprising:
performing acquisition of medical image data on an organ of interest;
analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree;
calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on the results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest in which the target vessel tree is located;
and generating a 1D model of the capillary vessel by taking an outlet of the 3D model of the target vessel tree as a starting point and the interested organ region as a defined region, wherein the 1D model is generated based on a fractal calculation method.
2. A method of setting exit boundary conditions for a 3D CFD model of the target vessel tree using a 1D model of a microvessel generated by the generation method of claim 1, characterized in that the exit boundary conditions are tree-based resistance-related boundary conditions or mass-conservation-based flow distribution boundary conditions, the 1D model being generated using a Strahler series.
3. The method according to claim 2, wherein the method of setting exit boundary conditions for the 3D CFD model of the target vessel tree comprises the steps of: generating a computational grid for the 1D model of the capillary vessel, setting the inlet boundary condition of the 1D model of the capillary vessel as flow and the outlet boundary condition thereof as corresponding pressure or venous pressure, calculating the pressure of each inlet of the 1D model of the capillary vessel, calculating the capillary resistance of each inlet according to the calculated pressure of each inlet and the set flow, and calculating the equivalent capillary resistance at the outlet of the target vessel tree as the outlet boundary condition of the 3D CFD model of the target vessel tree based on the equivalent capillary resistance by utilizing the tree-shaped connection relation of each inlet.
4. The method according to claim 2, wherein the method of setting exit boundary conditions for the 3D CFD model of the target vessel tree comprises the steps of: generating a computational grid for the 1D model of the fine blood vessel, setting the inlet boundary condition of the 1D model of the fine blood vessel as pressure and the outlet boundary condition thereof as corresponding flow, calculating the flow of each inlet of the 1D model of the fine blood vessel, and calculating the equivalent flow at the outlet of the target blood vessel tree by utilizing the tree-shaped connection relation of each inlet according to the calculated flow of each inlet to serve as the outlet boundary condition of the 3D CFD model of the target blood vessel tree.
5. The method according to claim 4, wherein the respective flow rates of the 1D model outlets of the microvessels are obtainable based on a specified flow distribution, an area of influence of the outlet vessels, or a blood perfusion related medical image.
6. A method of generating an individual-specific cardiovascular model, said cardiovascular model being a one-dimensional (1D) model, characterized by: the cardiovascular model is a complete model of a target vessel tree containing fine vessels that are not available via image reconstruction, the generation method comprising:
performing acquisition of medical image data on an organ of interest;
analyzing and segmenting acquired medical image data to segment out an interested organ and a target blood vessel tree;
calculating and reconstructing a vessel centerline and a vessel wall generating a target vessel tree based on the results of the analysis and segmentation of the medical image data, thereby constructing a three-dimensional (3D) model of the target vessel tree, and calculating and reconstructing an organ region of interest in which the target vessel tree is located;
generating a 1D model of the microvessels starting with an exit of the 3D model of the target vessel tree and the organ region of interest as a bounding region;
obtaining a complete 1D model of the target vessel tree by converting the 3D model back to a 1D model and integrating with the 1D model of the microvessels, the 1D model being generated based on a fractal calculation method.
7. A method of setting entry boundary conditions for a 3D CFD model of a target vessel tree generated using the complete 1D model of the target vessel tree generated by the generation method of claim 6, the method comprising: and performing CFD calculation on the complete 1D model, calculating the flow at each position in the complete target blood vessel tree, and setting the flow at each position in the complete 1D model obtained by calculation, which corresponds to the inlet of the 3D CFD model of the target blood vessel tree, as the inlet boundary condition of the 3D CFD model of the target blood vessel tree.
8. A method of setting exit boundary conditions for a 3D CFD model of a target vessel tree generated using the complete 1D model of the target vessel tree generated by the generation method of claim 6, the method comprising: and performing CFD calculation on the complete 1D model, calculating the flow and pressure at each position in the complete target blood vessel tree, and calculating the micro-vessel resistance at the outlet of the 3D CFD model of the target blood vessel tree based on the flow and pressure at each position in the complete 1D model corresponding to the outlet of the 3D CFD model of the target blood vessel tree, wherein the micro-vessel resistance is used as the outlet boundary condition.
9. A method of setting exit boundary conditions for a 3D CFD model of a target vessel tree generated using the complete 1D model of the target vessel tree generated by the generation method of claim 6, the method comprising: and performing CFD calculation on the complete 1D model, calculating fluid parameters at each position in the complete target blood vessel tree, and setting the fluid parameters at each position in the complete 1D model corresponding to the outlet of the 3D CFD model of the target blood vessel tree as outlet boundary conditions of the fluid parameters.
10. A method of performing a 3D-1D coupling calculation on a target vessel tree, the method comprising the steps of:
generating a complete 1D model of a target vessel tree and a 3D model of the target vessel tree according to the generation method of claim 6;
generating a computational grid for the complete 1D model of the target vessel tree and setting corresponding boundary conditions to calculate fluid parameters at various positions in the complete target vessel tree;
selecting whether to perform CFD calculation for part or whole of the 3D model of the target blood vessel tree, generating a calculation grid for the selected part or whole of the target blood vessel tree and setting corresponding boundary conditions to calculate the fluid parameters of corresponding parts in the target blood vessel tree, wherein
If the CFD calculation is carried out on the whole of the 3D model of the target blood vessel tree, the inlet boundary condition of the CFD calculation is set as the blood flow of the target blood vessel tree in the applied congestion state, and the outlet boundary condition of the CFD calculation is set as the fluid parameters of the whole 1D model, which correspond to the local outlet of the 3D model of the target blood vessel tree;
if the CFD calculation is selected to be carried out on the part of the 3D model of the target blood vessel tree, the inlet boundary condition and the outlet boundary condition of the CFD calculation are set as the fluid parameters of the whole 1D model corresponding to the inlet and the outlet of the part of the 3D model of the target blood vessel tree.
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