Blood vessel coordinate system construction method and device, computer device, and storage medium

Abstract

The application relates to a blood vessel coordinate system construction method and device, computer equipment, a storage medium and a computer program product. The method comprises the following steps: calculating the radial direction of a reference point in a blood vessel wall body grid according to a first normal vector and a second normal vector associated with the reference point; selecting a companion point of the reference point from a blood vessel center line based on the relative distance between the reference point and the blood vessel center line; setting a temporary axial direction along the companion point and the same-group discrete points of the companion point; the same-group discrete points and the companion point belong to the same blood vessel center line; converting the temporary axial direction into a coordinate system circumferential direction through coordinate system radial direction conversion, and calculating the final coordinate system axial direction through the coordinate system radial direction and the coordinate system circumferential direction. The method can accurately construct the coordinate system radial direction, the coordinate system circumferential direction and the coordinate system axial direction of the blood vessel coordinate system, provides a data basis for generating a physiological real blood vessel wall mechanical model, and the blood vessel wall mechanical model comprises but is not limited to a constitutive model, a material model and the like.

Description

Technical Field

[0001] This application relates to the field of image processing, and in particular to a method, apparatus, computer device, storage medium, and computer program product for constructing a vascular coordinate system. Background Technology

[0002] Blood vessel walls possess extremely complex mechanical properties, primarily derived from their microscopic components such as smooth muscle cells, elastin networks, and collagen fibers. However, these mechanical properties cannot be directly obtained and set during medical image segmentation and CAD modeling. Therefore, when generating the finite element analysis mesh of the blood vessel wall, it is necessary to define a coordinate system (i.e., a local coordinate system) point-by-point to impart anisotropic material properties (i.e., mechanical properties).

[0003] Morphologically based methods are suitable for analyzing complex, personalized vascular geometries. This approach primarily analyzes the morphological structure of blood vessels, directly using image data to construct a three-dimensional model and generating a local coordinate system based on it, without considering parameters such as material properties and residual stress. However, the accuracy of the coordinate system obtained by this method needs improvement. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, computer device, computer-readable storage medium, and computer program product for constructing a vascular coordinate system that can improve accuracy in addressing the aforementioned technical problems.

[0005] Firstly, this application provides a method for constructing a vascular coordinate system. The method includes:

[0006] The radial direction of the reference point is calculated based on the first and second normal vectors associated with the reference point in the vessel wall mesh; the first normal vector points from the outer wall surface of the vessel wall to the outside of the vessel wall mesh, and the second normal vector points from the inner wall surface of the vessel wall to the outside of the vessel wall mesh.

[0007] Based on the relative distance between the reference point and the vessel centerline, the accompanying points of the reference point are selected from the vessel centerline.

[0008] A temporary axis is defined along the accompanying point and the discrete points in the same group as the accompanying point; the discrete points in the same group and the accompanying point belong to the same vascular centerline.

[0009] The temporary axial direction is transformed into the circumferential direction of the coordinate system by radial transformation of the coordinate system, and the axial direction of the coordinate system is calculated by the radial and circumferential directions of the coordinate system.

[0010] In one embodiment, calculating the radial direction of the reference point based on a first normal vector and a second normal vector associated with the reference point in the vessel wall mesh includes:

[0011] Based on the distances from the reference points in the vessel wall mesh to the inner and outer surfaces of the vessel wall, the weighting factors of the distance negative correlation are calculated.

[0012] The first normal vector and the second normal vector are weighted according to the respective weighting factors to obtain the radial direction of the reference point.

[0013] In one embodiment, the step of filtering out the companion points of the reference points from each of the discrete points based on the relative distances between the reference points in the blood vessel wall mesh and each of the discrete points includes:

[0014] Obtain the radius of the blood vessel to which each of the discrete points belongs;

[0015] Calculate the distance between the reference point in the blood vessel wall mesh and each of the discrete points to obtain the distance between each discrete point;

[0016] The relative distance between each discrete point is calculated based on the radius of the blood vessel to which each discrete point belongs and the distance between each discrete point.

[0017] Based on the relative distance that satisfies the companion condition of the reference point, the companion point of the reference point is selected from multiple discrete points.

[0018] In one embodiment, calculating the relative distance between the discrete points based on the radius of the blood vessel to which each discrete point belongs and the distance between the discrete points includes:

[0019] Based on the distance between each discrete point and the length of the blood vessel to which each discrete point belongs, the relative distance between each discrete point is obtained.

[0020] The step of selecting the companion point of the reference point from multiple discrete points based on the relative distance that satisfies the companion condition of the reference point includes:

[0021] Based on the minimum relative distance among the relative distances of the discrete points, the discrete point with the minimum relative distance is selected from the plurality of discrete points as the companion point of the reference point.

[0022] In one embodiment, defining a temporary axis along the accompanying point and the set of discrete points of the same group as the accompanying point includes:

[0023] Based on the order of discrete points corresponding to the blood vessel centerline to which the accompanying point belongs, the neighboring points of the accompanying point are selected from the same group of discrete points of the accompanying point.

[0024] A temporary axis is defined along the line connecting the accompanying point and the adjacent point.

[0025] In one embodiment, the step of selecting neighboring points of the accompanying point from the same group of discrete points of the accompanying point according to the discrete point order corresponding to the blood vessel centerline to which the accompanying point belongs includes:

[0026] Based on the blood flow direction indicated by the discrete point sequence of the vessel centerline to which the accompanying point belongs, the nearest neighboring point is selected from the same group of discrete points of the accompanying point;

[0027] The step of setting a temporary axis along the line connecting the accompanying point and the neighboring point includes:

[0028] The direction of the line connecting the accompanying point and the neighboring point is determined according to the order of the discrete points;

[0029] A temporary axial direction is set according to the direction of the connection.

[0030] In one embodiment, the step of transforming the temporary axial direction to the circumferential direction of the coordinate system radially and calculating the coordinate system axial direction using the coordinate system radial and circumferential directions includes:

[0031] The circumferential direction of the coordinate system is obtained by performing a cross product operation on the radial direction of the coordinate system and the temporary axial direction.

[0032] The coordinate system axial direction is obtained by performing a cross product between the radial direction and the circumferential direction of the coordinate system.

[0033] Secondly, this application also provides a device for constructing a vascular coordinate system. The device includes:

[0034] The discrete point radial calculation module is used to calculate the radial direction of the reference point based on the first and second normal vectors associated with the reference point in the blood vessel wall mesh.

[0035] The accompanying point filtering module is used to filter out the accompanying points of the reference point from the blood vessel centerline based on the relative distance between the reference point and the blood vessel centerline.

[0036] A temporary axis construction module is used to set a temporary axis along the accompanying point and a set of discrete points in the same group as the accompanying point; the set of discrete points in the same group and the accompanying point belong to the same vascular centerline;

[0037] The coordinate system integration and construction module is used to transform the temporary axis to the coordinate system circumferential direction through the coordinate system radial direction, and to calculate the coordinate system axis through the coordinate system radial direction and the coordinate system circumferential direction.

[0038] Thirdly, this application also provides a computer device. The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of constructing the vascular coordinate system in any of the above embodiments.

[0039] Fourthly, this application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps of constructing the blood vessel coordinate system in any of the above embodiments.

[0040] Fifthly, this application also provides a computer program product. The computer program product includes a computer program that, when executed by a processor, implements the steps of constructing the vascular coordinate system in any of the above embodiments.

[0041] The aforementioned method, apparatus, computer equipment, storage medium, and computer program product for constructing a vascular coordinate system, since the first normal vector points from the outer wall surface of the vascular wall to the outer side of the vascular wall mesh, and the second normal vector points from the inner wall surface of the vascular wall to the outer side of the vascular wall mesh, calculates the radial direction of the reference point based on the first and second normal vectors associated with the reference point in the vascular wall mesh, so that the radial direction can accurately reflect the shape information such as the thickness of the vascular wall where the reference point is located; and based on the relative distance between the reference point and the vascular centerline, accurately and efficiently selects the accompanying points of the reference point from the vascular centerline; then, along the accompanying points and discrete points in the vascular centerline to which the accompanying points belong, a temporary axis is set, which initially reflects the blood flow direction; then, the temporary axis is transformed into the circumferential direction of the coordinate system through the radial direction, so that the shape information accurately reflected by the radial direction of the coordinate system is used to transform the temporary axis, making the circumferential direction of the coordinate system more accurate; finally, the coordinate system axis is calculated through the radial and circumferential directions of the coordinate system, so that the coordinate system axis is also adjusted based on the shape information. Therefore, for any reference point in the vessel wall mesh, the radial, circumferential, and axial coordinate systems of the vessel can be accurately constructed. This accuracy is particularly evident when blood vessels have complex structures. This provides a data foundation for generating physiologically realistic vascular wall mechanical models, including but not limited to constitutive models and material models. Attached Figure Description

[0042] Figure 1 This is an application environment diagram of a method for constructing a blood vessel coordinate system in one embodiment;

[0043] Figure 2 This is a flowchart illustrating the method for constructing a blood vessel coordinate system in one embodiment;

[0044] Figure 3Here is a mesh diagram of the blood vessel wall in one embodiment;

[0045] Figure 4 This is a rendering of the blood vessel centerline and blood vessel wall in one embodiment;

[0046] Figure 5 This is a rendering of the blood vessel wall in another embodiment;

[0047] Figure 6 This is a diagram illustrating the application environment for calculating relative distances in one embodiment.

[0048] Figure 7 This is a structural block diagram of a device for constructing a blood vessel coordinate system in one embodiment;

[0049] Figure 8 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0051] The method for constructing a vascular coordinate system provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on another network server.

[0052] The terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle systems. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers. This solution can be implemented based on the terminal 102, the server 104, or a combination of both.

[0053] In one embodiment, such as Figure 2 As shown, a method for constructing a blood vessel coordinate system is provided, which can be applied to... Figure 1 Taking terminal 102 as an example, the explanation includes the following steps:

[0054] Step 202: Calculate the radial direction of the reference point based on the first and second normal vectors associated with the reference point in the vessel wall mesh; the first normal vector points from the outer wall surface of the vessel wall to the outer side of the vessel wall mesh, and the second normal vector points from the inner wall surface of the vessel wall to the outer side of the vessel wall mesh.

[0055] A vascular wall mesh is a model of the solid structure of a blood vessel within a local area. Optionally, the vascular wall mesh is based on medical image modeling. The vascular wall mesh consists of multiple mesh points, each of which can be used to establish a vascular coordinate system to accurately and comprehensively understand the condition of the blood vessel. The vascular wall mesh is as follows: Figure 3 As shown.

[0056] A reference point is used to establish the vascular coordinate system. It can be any grid point in the vascular wall mesh. During the process of establishing the coordinate system based on the reference point, it is necessary to select the corresponding companion point from the discrete points of the vascular centerline. This companion point is then used to establish a coordinate system that accurately reflects the actual vascular condition, thereby more accurately reflecting the various characteristics of the vascular system.

[0057] Each vessel wall grid corresponds to at least one vessel centerline, and the relationship between the two is as follows: Figure 4 As shown. The vascular centerline is an axis along the main trunk or major branches of a blood vessel in a vascular system, used to characterize the path of blood flow within a specific vascular region. A vascular centerline is a smooth line obtained by interpolating and fitting a set of discrete points. If multiple blood vessels exist in a vascular region, each vessel has its own vascular centerline, which is composed of a set of discrete points, as shown below. Figure 5 As shown.

[0058] The process of generating the vascular centerline includes: estimating the blood flow distance between the central axis and discrete points from the starting point (inlet / outlet) to the ending point; adjusting the central axis based on the shortest blood flow distance to obtain the vascular centerline between the starting and ending points. Thus, by determining the shortest blood flow distance through discrete points and adjusting the central axis, the vascular centerline more closely resembles the actual vascular image, increasing the model's accuracy.

[0059] Discrete points are blood flow path points obtained from sampling vascular images, used to represent the blood flow path within the blood vessels. Optionally, the size of each discrete point represents the radius of the blood vessel to which it belongs, and the density of each discrete point represents the number of sampling points. Optionally, the discrete points in each blood vessel centerline are a group of discrete points, and the group number of the blood vessel centerline to which each group of discrete points belongs corresponds to the blood flow outlet of the main blood vessel, with the group number increasing sequentially along the blood flow direction of the main blood vessel, and the discrete point numbers within each group of discrete points increasing sequentially from the discrete point numbers of the first group of blood vessel centerlines.

[0060] exist Figure 4In the abdominal aorta shown, blood flows from top to bottom from the entrance of the main artery: the first set of discrete points on the center line of the first vessel, globally numbered from 1 to M1; the second set of discrete points on the center line of the second vessel, globally numbered from M1+1 to M2, and so on, until the kth set of discrete points on the kth vessel center line, globally numbered from M... k-1 +1 starts, M ends k Where N is the center line of the last blood vessel, and k is an integer greater than 1 and less than N.

[0061] The inner wall of a blood vessel is the surface of the vessel lumen, and it is the side of the blood vessel wall closest to the center line. The outer wall of a blood vessel is the side of the blood vessel wall furthest from the center line. The inner and outer walls of the blood vessel wall are located on opposite sides of the blood vessel wall, and their thickness and shape information can be characterized by these surfaces.

[0062] The first and second normal vectors are both associated with the reference point. The information they represent pertains to the outer and inner surfaces of the vessel wall, respectively, allowing for a more accurate determination of the reference point's radial direction. The radial direction of the reference point indicates its orientation relative to the vessel wall. This radial direction is perpendicular to the vessel axis and characterizes the vessel wall's thickness, diameter, and other shape information in that direction.

[0063] Step 204: Based on the relative distance between the reference point and the vessel centerline, select the accompanying points of the reference point from the vessel centerline.

[0064] Relative distance refers to the Euclidean distance between a reference point and a discrete point on the vessel centerline, transformed based on a parameter representing the vessel as described by the reference point and the vessel centerline. When selecting accompanying points using relative distance, the corresponding discrete points of the reference point on the vessel centerline can be fully considered, so that the coordinate system generated by the accompanying points can more accurately represent the relevant information of the reference point.

[0065] The accompanying point is a discrete point selected from the centerline of the blood vessel based on relative distance. The coordinate system established for the accompanying point can more accurately reflect the information of the blood vessel where the reference point is located. Moreover, the amount of data required for modeling based on the accompanying point is small, and its modeling efficiency is high.

[0066] In one embodiment, companion points of reference points are selected from each vessel centerline based on the relative distance between the reference point and the vessel centerline. This includes: comparing the relative distances between the reference point in the vessel wall mesh and each discrete point in the vessel centerline to obtain a comparison result of the relative distances; and determining the companion points of the reference points at the discrete points indicated by the vessel centerline based on the comparison result. Thus, by comparing relative distances, the selection criteria for companion points are dynamically adjusted, improving the accuracy of companion point selection.

[0067] Step 206: Set a temporary axis along the accompanying point and the discrete points in the same group as the accompanying point; the discrete points in the same group and the accompanying point belong to the same vessel centerline.

[0068] The discrete points in the same group are discrete points within the centerline of the vessel to which the accompanying point belongs. The accompanying point and its group of discrete points are used to characterize the blood flow direction within the same vessel. The temporary axis is the blood flow direction set based on the accompanying point and its group of discrete points. This temporary axis is not adjusted based on the thickness or shape information of the vessel wall and can roughly reflect the length direction of the vessel.

[0069] In one embodiment, setting a temporary axis along the accompanying point and a set of discrete points in the same group as the accompanying point includes: selecting a neighboring point from the set of discrete points in the same group as the accompanying point to set the transition axis; and setting the temporary axis based on the accompanying point and the neighboring point. This allows for setting the axis with less data, resulting in a relatively high speed for setting the transition axis.

[0070] Step 208: Transform the coordinate system radially to the coordinate system circumferential direction, and calculate the coordinate system axis by combining the coordinate system radial and coordinate system circumferential directions.

[0071] The circumferential direction of the coordinate system is obtained through vector calculation using the radial and temporary axial directions of the coordinate system. The circumferential direction indicates the direction of the vessel around the location of a given point. Because the circumferential direction is obtained through a radial and temporary axial transformation, the shape information of the vessel wall in the radial direction can be temporarily corrected for the axial direction. This allows the circumferential direction to be adaptively adjusted based on the radial information, resulting in a more accurate circumferential direction.

[0072] The coordinate system axis is obtained by transforming the coordinate system radially and circumferentially. The coordinate system axis is adjusted to take into account the shape information in the radial direction. The coordinate system axis is more accurate than a temporary axis and can more accurately reflect the information of blood vessels in the direction of blood flow.

[0073] In the aforementioned method for constructing the vascular coordinate system, the radial direction of the reference point is calculated based on the first and second normal vectors associated with the reference point in the vascular wall mesh. The first normal vector points from the outer surface of the vascular wall to the outside of the vascular wall mesh, and the second normal vector points from the inner surface of the vascular wall to the outside of the vascular wall mesh, accurately reflecting the shape information such as the thickness of the vascular wall where the reference point is located. Based on the relative distance between the reference point and the vascular centerline, the accompanying points of the reference point are accurately and efficiently selected from the vascular centerline. Then, a temporary axis is set along the accompanying points and discrete points on the vascular centerline to which the accompanying points belong, initially reflecting the blood flow direction. Furthermore, the temporary axis is transformed from the radial direction to the circumferential direction of the coordinate system, using the shape information accurately reflected by the radial direction to make the circumferential direction more accurate. Finally, the axial direction is calculated using the radial and circumferential directions, adjusting it based on the shape information. Therefore, for any reference point in the vascular wall mesh, the radial, circumferential, and axial directions of the vascular coordinate system can be accurately constructed. This accuracy is particularly noticeable when there are many branches in the blood vessels and a high degree of curvature.

[0074] In one embodiment, the radial direction of the reference point is calculated based on the first and second normal vectors associated with the reference point in the vessel wall mesh, including: calculating each weight factor with negative distance correlation based on the distances from the reference point in the vessel wall mesh to the inner and outer surfaces of the vessel wall; and weighting the first and second normal vectors based on each weight factor to obtain the radial direction of the reference point.

[0075] The weighting factor is calculated based on the distances from the reference point to both the inner and outer surfaces of the blood vessel wall, and is negatively correlated with these distances. The weighting factor represents the proportional relationship between the distances from a discrete point to the inner and outer surfaces of the blood vessel wall.

[0076] In one embodiment, based on the distances from a reference point in the vessel wall mesh to the inner and outer surfaces of the vessel wall, respectively, weighting factors for negative distance correlation are calculated, including: calculating the distances from the reference point in the vessel wall mesh to the inner surface of the vessel wall, and calculating the distances from the reference point to the outer surface of the vessel wall; determining the weighting factors for negative distance correlation to the inner surface of the vessel wall, and determining the weighting factors for negative distance correlation to the outer surface of the vessel wall.

[0077] Correspondingly, the first normal vector and the second normal vector are weighted to obtain the radial direction of the reference point. This includes: weighting the first normal vector using a weighting factor that is negatively correlated with the distance to the inner wall of the blood vessel to obtain the weighted result of the outer wall of the blood vessel; weighting the second normal vector using a weighting factor that is negatively correlated with the distance to the outer wall of the blood vessel to obtain the weighted result of the inner wall of the blood vessel; and summing the weighted results of the inner wall of the blood vessel and the weighted results of the outer wall of the blood vessel to obtain the radial direction of the reference point.

[0078] For example, if the distance from the reference point to the inner wall of the blood vessel is greater than the distance from the reference point to the outer wall of the blood vessel, the first normal vector has a larger weighting factor; if the distance from the reference point to the inner wall of the blood vessel is less than the distance from the reference point to the outer wall of the blood vessel, the first normal vector has a smaller weighting factor. Specifically, the weighting factor is inversely proportional to the square of the distance to a certain surface, to ensure that the smaller the distance, the closer the surface is to the accompanying point, and the greater the influence of its normal vector.

[0079] The distances from the reference point to the inner wall of the blood vessel and the outer wall of the blood vessel are used to calculate and obtain various weighting factors that are negatively correlated with these distances. This allows the shape information of the blood vessel wall to be reflected through these weighting factors, thereby enabling the radial direction of the reference point to accurately reflect the shape information of the blood vessel wall.

[0080] In one embodiment, based on the relative distances between reference points in the vessel wall mesh and each discrete point, the accompanying points of the reference points are selected from each discrete point, including: obtaining the radius of the vessel to which each discrete point belongs; calculating the distance between the reference point in the vessel wall mesh and each discrete point to obtain the distance between each discrete point; calculating the relative distance between each discrete point based on the radius of the vessel to which each discrete point belongs and the distance between each discrete point; and selecting the accompanying points of the reference points from multiple discrete points based on the relative distances that satisfy the accompanying conditions of the reference points.

[0081] The radius of the blood vessel to which the discrete point belongs is the radius of the largest embedded sphere within the local blood vessel to which the discrete point belongs. Assuming the blood vessel is cylindrical, the local radius of the blood vessel can be characterized by the radius r of the largest embedded sphere tangent to the grid of the blood vessel lumen.

[0082] Discrete point distance is the Euclidean distance between a discrete point and a reference point. Each Euclidean distance represents the spatial distance between a given discrete point and the reference point. Discrete point distance reflects the positional relationship between the discrete point and the reference point in terms of spatial dimensions.

[0083] The reference point accompaniment condition is a relative distance index used to select accompaniment points for a reference point from multiple discrete points along the vessel centerline. When the relative distance between discrete points meets the reference point accompaniment condition, that discrete point can be used as an accompaniment point for the reference point.

[0084] By determining the relative distance between the radius of the blood vessel to which each discrete point belongs and the distance between the discrete points, this relative distance can accurately reflect the shape information such as the thickness of the blood vessel. This relative distance allows for a more robust selection of accompanying points, ensuring that the selected accompanying points more accurately represent the information required by the reference point. Therefore, whether establishing a coordinate system for blood vessels with many branches or those with significant curvature, the accompanying points of the reference point can be determined relatively accurately. This, in turn, determines the local radius of the blood vessel represented by the centerline of the accompanying point, resulting in higher accuracy in both the circumferential and axial directions of the coordinate system.

[0085] In one implementation, the relative distance between each discrete point is calculated based on the radius of the blood vessel to which each discrete point belongs and the distance between each discrete point, including: obtaining the relative distance between each discrete point based on the length relationship between the distance between each discrete point and the radius of the blood vessel to which each discrete point belongs.

[0086] Correspondingly, based on the relative distances that satisfy the accompanying conditions of the reference point, the accompanying points of the reference point are selected from multiple discrete points, including: based on the minimum relative distance among the relative distances of each discrete point, the discrete point with the minimum relative distance is selected from multiple discrete points as the accompanying point of the reference point.

[0087] The length relationship is determined by the distance between discrete points relative to the radius of their respective blood vessels. This length relationship is obtained by adaptively adjusting the distances between discrete points based on the radii of different blood vessels, ensuring that the relative distances reflect the structural information of the blood vessels at their local locations.

[0088] Minimum relative distance is a comparison result of relative distances, used to express the minimum relative distance between various offline points. Each relative distance is adaptively adjusted based on the radius of the blood vessel, incorporating the shape information of the blood vessel as one of the factors considered.

[0089] by Figure 6 Taking the vascular coordinate system established by reference point p in Figures (a) and (b) as an example, after comparing the relative distances of discrete points on the two vascular centerlines l1 and l2 in Figure (a), discrete point Q2 can be determined as the associated point of reference point p; after comparing the relative distances of discrete points on the two vascular centerlines l3 and l4 in Figure (b), discrete point Q2 can be determined as the associated point of reference point p. In this embodiment, the calculation expression is as follows:

[0090]

[0091] In this embodiment, the radius of the blood vessel to which the discrete point belongs is used as a reference for the distance between discrete points, so that the distance between discrete points is adjusted to a relative distance, thereby effectively improving the accuracy and computational efficiency of discretization. Moreover, the discrete point with the smallest relative distance is used as the companion point of the reference point, which can more accurately reflect the complex structure of the blood vessel, thus enabling accurate and efficient determination of the companion point of the reference point. The complex structure of blood vessels includes, but is not limited to, numerous branches and significant curvature.

[0092] In one embodiment, setting a temporary axis along the accompanying point and discrete points in the same group as the accompanying point includes: selecting neighboring points of the accompanying point from the discrete points in the same group as the accompanying point according to the order of discrete points corresponding to the blood vessel centerline to which the accompanying point belongs; and setting a temporary axis along the direction of the line connecting the accompanying point and the neighboring points.

[0093] The discrete point order characterizes the distribution order of discrete points. Discrete points within each vessel centerline are arranged sequentially according to their discrete point order, and this order can be used to determine discrete points within a certain range before and after an accompanying point. Optionally, the discrete point order on a vessel centerline is arranged along the blood flow direction of a local region of the vessel. Optionally, the discrete point order is set by discrete point numbering, with the numbering order reflecting the arrangement of discrete points along the blood flow direction of a local region.

[0094] A neighboring point is at least one discrete point located within a certain range from the accompanying point. Optionally, a neighboring point can be a discrete point preceding or following the accompanying point, or it can be multiple discrete points located within a certain distance range from the accompanying point. The neighboring point reflects the blood flow position before and after the accompanying point, and the direction of the line connecting the discrete point and the neighboring point reflects the blood flow direction. The direction of the line is the tangent direction between the accompanying point and the neighboring point, and can serve as a temporary axis.

[0095] The nearest neighbor of the accompanying point can be a neighboring point within the nearest distance range of the accompanying point; alternatively, the nearest distance range can be a certain distance interval or a number of distances within a certain range.

[0096] The adjacent points of the accompanying point are selected according to the discrete point sequence so that the temporary axis can more accurately reflect the blood flow direction at the reference point; and since the range of the same set of discrete points is narrowed down to the accompanying point and its adjacent points, the transition axis is efficiently set by the direction of the line connecting these two discrete points.

[0097] In one implementation, a temporary axis is defined along the line connecting the accompanying point and neighboring points, including: obtaining the tangent direction using curve fitting and differentiation, or directly estimating the tangent direction using the difference between adjacent points. Specifically, the fitted curve is a curve fitted using a fitting method (e.g., polynomial fitting, spline interpolation, etc.) based on a discrete set of points on the vessel centerline to which the accompanying point belongs. Obtaining the derivative means calculating the derivative of the curve at the accompanying point; finally, the tangent direction at the accompanying point is calculated using the aforementioned derivative to obtain the temporary axis.

[0098] In one embodiment, the process of selecting neighboring points of the accompanying point from the same group of discrete points of the accompanying point according to the order of discrete points corresponding to the center line of the blood vessel to which the accompanying point belongs includes: selecting the nearest neighboring point from the same group of discrete points of the accompanying point according to the blood flow direction indicated by the order of discrete points of the center line of the blood vessel to which the accompanying point belongs.

[0099] Correspondingly, a temporary axis is set along the line connecting the accompanying point and the neighboring point, including: determining the line connecting the accompanying point and the neighboring point according to the discrete point sequence; and setting the temporary axis according to the line connecting direction.

[0100] In one specific implementation, the direction of the connection between the accompanying point and the neighboring point is determined according to the discrete point sequence; this includes: when the discrete point sequence expresses the blood flow direction through discrete point numbers from small to large, determining the discrete point with the larger discrete point number and the discrete point with the smaller discrete point number from the accompanying point and the neighboring point; and setting the connection direction from the discrete point with the larger discrete point number to the discrete point with the smaller discrete point number. This allows for a more efficient acquisition of the temporary axis.

[0101] In this embodiment, the blood flow direction is indicated by the discrete point sequence to more efficiently determine the nearest neighboring point to the accompanying point. The neighboring point and the accompanying point themselves are used to characterize the blood flow direction, making the blood flow direction relatively more accurate. Furthermore, determining the direction of the line connecting the accompanying point and the neighboring point based on the discrete point sequence eliminates the need to limit the position of the accompanying point in the vessel centerline. Whether the accompanying point is the first point or the last point in the vessel centerline, the direction of the line can more accurately express the blood flow direction in the local vascular region, thereby setting the temporary axis more accurately.

[0102] In one embodiment, the temporary axis is transformed from the coordinate system radial direction to the coordinate system circumferential direction, and the coordinate system axis is calculated by combining the coordinate system radial direction and the coordinate system circumferential direction. This includes: performing a cross product operation on the coordinate system radial direction and the temporary axis to obtain the coordinate system circumferential direction; and performing a cross product operation on the coordinate system radial direction and the coordinate system circumferential direction to obtain the coordinate system axis.

[0103] By using cross product processing, the reference vectors of the coordinate system are transformed in different directions. This method is applicable to blood vessels of various types or shapes. It allows the radial, circumferential, and axial coordinate systems to be adaptively adjusted based on the shape information of the blood vessel wall, so as to better show the meaning of each direction and the geometric relationship of the blood vessel structure.

[0104] In a specific embodiment, a local coordinate system for the vessel wall is defined. This local coordinate system refers to generating three mutually orthogonal unit vectors at each point in the vessel wall mesh: radial, axial, and circumferential. Only by defining the local coordinate system can the fiber orientation be defined at each point in the vessel wall mesh, thereby defining the constitutive relation of the vessel wall's anisotropy. This is crucial for improving the physical realism of the computational model of the vascular system. The strategy of generating the local coordinate system based on the principal stress directions in static analysis is not used here because this strategy cannot be guaranteed to be stable and reliable when dealing with geometrically complex vessels. The strategy adopted in this invention can stably and efficiently handle arbitrarily complex spatial vessel wall models.

[0105] The radial coordinate system is defined as the weighted sum of the outward normal vectors from the inside of the blood vessel to the outside. These two surfaces are the inner and outer walls of the blood vessel. The weighting factor in the weighted sum is inversely proportional to the square of the distance to a given surface. This ensures that the closer the surface, the greater the proportion of the normal vector.

[0106] A temporary axis is defined as finding the accompanying point on the correct centerline and its nearest neighbor. The line connecting these two points approximates the tangent direction of the centerline at that point, pointing towards the exit direction. That is, the point with the smaller global number points to the point with the larger global number. Here, "temporary" means that the generated axis is not the final axis in the coordinate system; it is only used to obtain the circumferential direction by cross product with the radial direction.

[0107] The circumferential direction of the coordinate system is obtained by cross product of the radial vector and the temporary axial direction vector. The axial direction of the coordinate system is obtained by cross product of the radial vector and the circumferential direction vector, and is the final axial direction.

[0108] In a specific embodiment, the specific implementation process of this solution is described step by step from the perspective of the invention's objective:

[0109] This invention imports medical imaging data, such as two-dimensional tomographic images generated by imaging equipment, to create personalized three-dimensional computer-aided design (CAD) models of blood vessels. Based on these CAD models, a radius-based three-dimensional vascular mesh is then created. This meshing method not only provides high-quality meshes for numerical simulations of hemodynamics but also significantly reduces the overall simulation time, facilitating the efficient acquisition of precise physiological data of interest to clinicians. These physiological data, which are difficult to obtain through conventional measurement methods, can assist doctors in assessing the severity of cardiovascular disease and developing personalized treatment plans. Furthermore, they can provide a scientifically reliable basis for predicting potential complications and recurrence risks after surgical treatment, thereby reducing the medical burden on society, improving resource utilization efficiency, and benefiting the general public.

[0110] The largest proportion of deaths are due to cardiovascular disease, and this number is increasing year by year.

[0111] Ischemic heart disease and stroke are the first and second leading causes of death worldwide. According to the World Health Organization (WHO), in 2019, approximately 8.9 million people died from ischemic heart disease, accounting for 16% of all deaths globally; and 6.12 million people died from stroke, accounting for 11% of all deaths. The mortality rates of these two diseases have not decreased despite improved living standards and advancements in medical technology; on the contrary, they have been rising year by year.

[0112] The efficient diagnosis and treatment of cardiovascular diseases has enormous socio-economic significance.

[0113] Cardiovascular diseases are characterized by their insidious nature and rapid onset, and traditional diagnostic and treatment methods have many limitations. In clinical diagnosis, doctors often rely on observing two-dimensional tomographic images and their personal experience to make clinical diagnoses and formulate treatment plans. However, raw two-dimensional tomographic images contain many physiological organs besides the heart, leading to risks of misdiagnosis and missed diagnosis. Therefore, there is an urgent need for a precise assessment mechanism to quantify disease risk for doctors' reference.

[0114] Image-based blood flow modeling and numerical simulation are advanced techniques in scientific research and clinical practice.

[0115] In the preoperative stage, the rationality of diagnosis relies heavily on the doctor's experience and personal judgment, making this approach time-consuming and labor-intensive. Postoperatively, the ability to mitigate or even prevent complications is highly random, and catheter-based monitoring of key hemodynamic data can be complex and invasive. These risks and consequences primarily stem from the often-overlooked hemodynamic influences in vascular disease diagnosis and treatment. In fact, hemodynamic and biomechanical parameters within blood vessels have a direct causal relationship with the occurrence, evolution, and prognosis of vascular diseases. This invention provides personalized patient modeling and radius-based mesh generation, utilizing numerical simulation of hemodynamics and fluid-structure interaction analysis to assess relevant hemodynamic parameters. This method not only helps doctors determine the necessity of surgery but also allows for the virtual construction of surgical plans and the assessment of potential postoperative risks and complications. This hemodynamic and biomechanical-based auxiliary medical approach is of great significance for improving the diagnosis and treatment of vascular diseases.

[0116] In hemodynamic research methods, studying vascular wall lesions is a considerable challenge.

[0117] Image-based blood flow modeling began in the 1990s and has evolved to provide powerful tools for personalized patient care, virtual surgery, and optimized treatment planning. However, most of these blood flow models and numerical simulations simplify the vascular system. They often assume blood vessels are inelastic, rigid walls or uniformly thick, single-layered walls. This simplification leads to significant deviations between the model and reality, failing to accurately reflect the mechanisms of vascular diseases and their treatment outcomes.

[0118] Vascular system modeling, compared to blood flow modeling, can significantly improve reliability (due to the geometric complexity and multi-domain coupling of personalized models).

[0119] Modeling the vascular system refers to using physical and physiological models to describe physiological phenomena within blood vessels. This includes the blood within the lumen, the vessel wall, and pathological structures such as mural thrombi and aortic dissection. Using quantitative models can help analyze the physiological state of the vascular system more accurately and provide important references for designing treatment plans. In particular, existing research has confirmed that individual specificity has a significant impact on the reliability of the model. Therefore, it is necessary to consider personalized modeling for specific objects during the modeling process. Among various individual factors, geometric configuration has a significant impact on biomechanical modeling. When performing mesh generation, ensuring that the geometric configuration remains consistent with the original CAD model during discretization (without reducing computational accuracy) while reducing the complexity of the network structure (reducing unnecessary computational losses) is also a core issue considered in this work.

[0120] Fluid-structure interaction analysis requires that the meshes at the interface be compatible.

[0121] When performing fluid-structure interaction (FSI) analysis, the fluid and solid need to be coupled to accurately calculate fluid flow and solid deformation during the computation. This requires compatibility between the fluid and solid meshes, meaning that the nodes and elements of the fluid and solid must match at the interface. Otherwise, effective information exchange between the two physical fields is difficult to achieve.

[0122] Blood vessel walls possess extremely complex mechanical properties, primarily derived from their microscopic components such as smooth muscle cells, elastin networks, and collagen fibers. However, these mechanical properties cannot be directly obtained and set during medical image segmentation and CAD modeling. Therefore, when generating the finite element analysis mesh of the blood vessel wall, a local coordinate system needs to be defined for each mesh node to assign material properties (i.e., mechanical properties).

[0123] There are two strategies for defining the local coordinate system of the blood vessel wall. The first strategy is to perform linear elastic static analysis, using the direction of the maximum principal stress as the local circumferential direction, the direction of the minimum principal stress as the local radial direction, and the direction of the median principal stress as the local axial direction. However, this method has considerable limitations. First, using stress to determine the local coordinate system of the blood vessel geometry model requires considering parameter information of actual physiological pressure, which is difficult to obtain. This parameter information includes, but is not limited to, residual stress and steady-state stress, and the stress distribution largely depends on the way the load is applied and the material model of the blood vessel wall. The blood vessel geometry obtained from images actually has residual stress, making it difficult to simulate the image-modeled blood vessel load structure and make its stress state equal to the actual steady-state stress distribution under physiological pressure.

[0124] To simplify the analysis, the local coordinate system of the vessel wall can be defined using the principal stress axes, based on observational experience in ideal cylindrical vessel geometry. However, the logical connection between these axes lacks theoretical support, and their interpretability is often insufficient in real-world vessel geometries. Secondly, this strategy is inefficient for analyzing vessels beyond the ideal cylindrical shape, requiring challenging adaptations to actual geometries. For example, iterative methods are needed to obtain a steady-state stress distribution matching physiological pressure, and the subsequent generation of collagen fibers is highly random. For instance, after interpolation, the fiber orientation may be parallel or opposite, leading to erroneous results. Introducing additional procedures for aligning fiber orientations also increases computational cost and reduces efficiency. Finally, because stress analysis of complex vessel geometries is inherently challenging, the stress field and principal stress axis approach currently only handles vessels with ideal cylindrical geometries and aortic bifurcation geometries, such as the bifurcation of the carotid artery and the bifurcation of the common iliac artery within the abdominal aorta. Whether it remains applicable to more complex vessel shapes is unclear.

[0125] Morphological methods are suitable for analyzing complex, personalized vascular geometries. This approach primarily analyzes the morphological structure of blood vessels, offering the advantage of directly using image data to construct a 3D model of the vessel and generating a local coordinate reference system without considering material properties or residual stress. The tangent direction of the vessel lumen's centerline is defined as the local axial direction; the weighted surface normal pointing outwards at the vessel wall mesh nodes is defined as the local radial direction; and the cross product of the local axial direction and the local radial direction yields the local circumferential direction.

[0126] In particular, when dealing with vascular bifurcations with significant diameter differences, the larger diameter vessel may affect the centerline positioning of the smaller diameter vessel. To address this, various techniques have been designed to ensure that mesh nodes are positioned correctly along the vessel lumen centerline, thereby obtaining accurate local axial and circumferential coordinates. The specific technical field of this invention relates to the field of vascular fluid-structure interaction analysis based on medical imaging, and particularly to the definition of a local coordinate system in a patient-specific vascular wall mesh.

[0127] In a specific embodiment, the specific implementation process of this solution is explained step by step from the perspective of the overall inventive concept:

[0128] 1. Vascular imaging technology in medical imaging.

[0129] Currently, the medical imaging needed for diagnosing and treating vascular diseases mainly comes from vascular imaging techniques. These techniques primarily include magnetic resonance angiography (MRA), computed tomographic angiography (CTA), digital subtraction angiography (DSA), intravascular ultrasound (IVUS), and optical coherence tomography (OCT). These techniques differ in their principles, applicable scenarios, and respective advantages.

[0130] The advantages of MRA compared to CTA and DSA are that it is non-invasive, requires no contrast agent injection, and involves no radiation damage. The disadvantages are that the spatial resolution of the imaging results is lower, making it more prone to artifacts; the scanning time for patients is relatively longer, and they must endure greater noise; and no metal implants can be placed in the patient's body.

[0131] The advantages of CTA compared to MRA are significantly shorter detection time (usually just a few seconds), clearer imaging results, and the ability to display plaques within blood vessels. The disadvantages are that the injected contrast agent may affect the kidneys and there is radiation exposure.

[0132] The advantages of DSA compared to MRA and CTA are its higher resolution, lack of interference from overlapping tissues, clearer observation of lesions such as vascular stenosis, and reduced likelihood of missed or misdiagnosed cases. The disadvantages are that it requires arterial puncture and catheter insertion, making it an invasive procedure; the injected contrast agent may affect kidney function; and continuous X-ray imaging poses a radiation hazard to the patient.

[0133] IVUS and OCT are emerging tools for assessing vascular disease. Their advantage lies in their ability to display real-time, high-resolution cross-sectional images of blood vessels, thus compensating for the accuracy limitations and errors of previous vascular imaging techniques. However, both IVUS and OCT have limitations in imaging depth and range, typically confined to imaging a limited area of ​​a single vessel segment. They can only assess local features of diseased vessels, not provide a comprehensive evaluation of the entire vessel. While they can provide important information about diseased vessels, a comprehensive assessment of the entire vessel may require combining multiple imaging techniques. Furthermore, IVUS and OCT are invasive procedures requiring catheter insertion into the vessel. Catheter insertion can cause discomfort, bleeding, and other complications. Therefore, IVUS and OCT are not suitable for use in the initial screening stage. In summary, although IVUS and OCT are promising tools for assessing vascular disease, their limited imaging space and invasiveness in vivo must be considered when evaluating their practicality in clinical settings. Future research should focus on improving these imaging techniques and exploring their potential for combination with other imaging modalities to achieve a comprehensive assessment of vascular disease. 2. Vascular modeling and numerical simulation workflow based on medical imaging.

[0134] Identify the target blood vessel for the study, such as the coronary artery or the abdominal aorta.

[0135] Data on vascular structure and function are collected, including acquiring vascular morphology information using medical imaging techniques and acquiring functional information such as vascular flow and blood pressure using various measurement techniques. The output file formats of MRA and CTA, two vascular imaging techniques, are generally two: DICOM (Digital Imaging and Communications in Medicine) and NIFTI (Neuroimaging Informatics Technology Initiative).

[0136] Medical images are read and preprocessed using image processing tools. Preprocessing includes noise reduction, image enhancement, volumetric rendering, and visualization.

[0137] Modeling tools are used to reconstruct the vascular lumen in the preprocessed images in three dimensions to obtain a personalized vascular lumen model for each patient.

[0138] By combining functional information such as vascular flow and blood pressure obtained from previous measurement techniques, boundary conditions were set and simulations were performed. The final calculations yielded various physiological indicators that are impossible to measure in practice.

[0139] Finally, the calculation results are post-processed to extract various physiological and clinical data for doctors and researchers to analyze and study.

[0140] In a specific embodiment, the steps before and after constructing the vascular coordinate system are summarized: One of the key steps in the biomechanical analysis of vascular systems is applying an accurate constitutive model to the vascular wall mesh. In finite element analysis, the vascular wall mesh is assigned different mechanical response models and numerically simulated. However, real vascular tissue has extremely complex material properties, such as anisotropy, incompressibility, and high nonlinearity, which makes related computational research quite challenging. Furthermore, when the vascular system to be modeled and analyzed is larger and more complex, the special characteristics of arteries, such as the layered structure and complex geometry of the vessel wall, also increase the complexity of geometric modeling. In describing the anisotropic tissue properties of the vessel wall, it is necessary to generate a local coordinate system for any point in the vascular wall geometry model. This local Cartesian coordinate system gives the unit normal vectors in the axial, radial, and circumferential directions at that point. Based on this coordinate system, it is possible to generate descriptions of the orientation of collagen and smooth muscle. This is an essential input for defining the constitutive model of the vascular wall. Although biomechanicians have developed precise constitutive models of vascular anisotropy in the laboratory through measurements, there is still no good solution for generating local coordinate systems on personalized vascular wall geometry models for practical problems. Traditional methods for defining local coordinate systems for vascular wall volume meshes have limitations in handling complex vascular geometries. In contrast, the advantages of this invention lie in its coordinate system generation being based on geometric information, its robustness-ensuring mechanisms for complex vascular systems, and its better integration with subsequent vascular wall layering structure settings. Furthermore, this method offers numerous advantages such as low cost, convenience, and efficiency, and can be widely applied to the step of constructing local reference coordinate systems in various modeling processes. This research can provide clinicians with more accurate physiological indicators and will further promote the development of basic and translational research in vascular biomechanical modeling.

[0141] In one exemplary embodiment, the relevant steps before and after coordinate system construction are illustrated:

[0142] 1. Acquisition and preprocessing of medical images.

[0143] The medical images used here are not limited to angiography of a region of interest, but can also include whole-body angiography; nor are they limited to non-invasive angiography in the initial screening stage where vessel wall imaging is not possible, but can also include invasive angiography such as IVUS and OCT that can obtain cross-sectional information of blood vessels. After acquiring these necessary image data, image processing software is used to preprocess the images, such as noise removal, image smoothing, and histogram equalization. Then, volumetric rendering technology is used to convert the images into three-dimensional images, and the volumetric rendering parameters are adjusted as needed to obtain the best visualization effect for the blood vessels of interest.

[0144] 2. Vascular pathway planning.

[0145] This step aims to directly observe the blood vessels of interest by adjusting the volumetric rendering parameters of the image display and to create a path along the vessel's centerline. Specifically, the process involves: First, manually selecting points as close as possible to the vessel's centerline as "path points" using the marking function in an image processing tool. Then, interpolating splines from these path points yields the path of a single blood vessel. To improve the efficiency and accuracy of point selection, intelligent algorithms can be used to automatically select path points in subsequent improvements. Finally, the image can be re-sliced ​​along the current path to check the fit between the path and the vessel's centerline. If the fit is poor, the positions of the path points need to be adjusted for improvement. It is important to note that the quality of the point selection significantly impacts the path obtained from the interpolated spline calculation, which is crucial for subsequent two-dimensional segmentation along the path.

[0146] 3. Two-dimensional image segmentation along the path.

[0147] To create anatomical models based on medical imaging data, image segmentation is required to extract the geometry of the region of interest. This section focuses on the specific steps of two-dimensional image segmentation.

[0148] First, several sampling points are selected along the pre-planned blood vessel path. At each sampling point, the tangent vector along the blood vessel path is calculated, and these tangent vectors are used as the normal direction to generate the normal plane of the image data at the sampling point.

[0149] Secondly, image data containing the vessel cross-section can be obtained by processing the normal plane. To accurately extract the vessel geometry, the size of the normal plane needs to be adjusted to avoid interference from surrounding image data in segmenting the lumen of the vessel of interest. The adjusted normal plane will be used to segment the lumen within the vessel cross-section.

[0150] Finally, a suitable 2D image automatic segmentation technique needs to be selected to segment the lumen in the cross-section. Through long-term practical verification, two main methods have proven to achieve relatively stable segmentation: level set technology and thresholding technology. Level set technology initializes the segmentation with seed points; the lumen segmentation grows in the direction of intensity value change and stops at the point where the intensity value change is sharpest. This delineates the complete segmentation of the lumen. Thresholding technology uses a bilinear interpolation function to create contour lines with a specified threshold on the image based on the image intensity value at each pixel. These contour lines represent the potential segmentation of the lumen. Based on prior knowledge, the radius of the blood vessel corresponding to the current blood vessel path is preset. The smallest closed contour line that completely contains the circle corresponding to this blood vessel radius is the lumen segmentation. Using these methods, the geometry of the blood vessel cross-section can be extracted, thus providing crucial information for constructing anatomical models based on medical image data.

[0151] 4. Generate the contours of the blood vessel lumen and the blood vessel wall.

[0152] Two-dimensional image segmentation is one of the key tasks in the field of medical imaging. However, due to noise interference, the segmentation results may exhibit irregular shapes. To obtain a smoother contour, an appropriate sampling method can be selected to identify points, and interpolation splines can be calculated based on the selected points.

[0153] Next, the contours of the blood vessel lumen and the blood vessel wall need to be generated.

[0154] By smoothing the two-dimensional segmentation, the contour of the blood vessel lumen can be obtained.

[0155] Based on this, the thickness of the artificial blood vessel wall at different locations can be set according to existing physiological knowledge. For example, it can be assumed that the blood vessel wall thickness is uniformly distributed along the entire blood vessel, that is, the ratio of the wall thickness to the lumen radius in all radial directions originating from the centroid of the blood vessel lumen is isotropic. In addition, the blood vessel wall contour and wall thickness can be manually adjusted on each blood vessel cross-sectional view to adapt to local pathological conditions.

[0156] Based on the aforementioned assumptions about wall thickness distribution grounded in physiological common sense, the vessel wall contour can be automatically scaled up to generate an automated vessel wall contour. The scaling center is set as the centroid of the vessel lumen, which is the arithmetic mean of the coordinates of the sampling points on the contour.

[0157] The contour of a blood vessel wall can be obtained by enlarging the contour of the blood vessel lumen along the radial direction (i.e., from the centroid to a point on the contour) by a certain proportion. For example, according to common physiological knowledge, the thickness of the aorta wall is 0.2 times the radius of the lumen. Therefore, 1.2 can be used as the enlargement ratio for the aorta wall.

[0158] When medical imaging technology can display the blood vessel wall well (such as black blood images), the outer wall can be segmented directly, thus skipping the step of generating a hypothetical blood vessel wall contour.

[0159] Compared to traditional compression methods, the method of obtaining blood vessel wall contours through scaling is more robust, produces more uniform and accurate results, and is less prone to generating non-physiological features. In practical applications, it can significantly improve the accuracy and reliability of subsequent modeling and calculations.

[0160] 5. Loft the outline to generate a geometric solid.

[0161] To generate geometric entities corresponding to multiple contours of a blood vessel, four steps are required. First, the contours need to be resampled while maintaining an equal number of sampling points for each contour. Second, B-spline curve interpolation is performed on sampling points belonging to the same contour. Then, B-spline curves for different contours are made fully compatible through spline degree elevation and knot insertion. Finally, a smooth B-spline surface (i.e., the two-dimensional geometric entity describing the blood vessel) is created by lofting along these fully compatible B-spline curves. Using CAD tools and Boolean operations, the geometric entities corresponding to multiple blood vessels can be merged to generate a complete geometric model of the entire vascular system.

[0162] 6. The centerline and local radius of the blood vessel.

[0163] The vascular lumen surface mesh used in this step can be generated using a traditional uniform meshing strategy.

[0164] To better analyze the geometric properties of the vascular lumen surface mesh, a method based on solving the Eikonal equation using Voronoi diagrams was employed. This method can help accurately calculate important geometric properties such as the vessel centerline and the vessel radius represented by the maximum inset sphere.

[0165] The Voronoi diagram is a graph based on distances to a set of points, effectively outlining the central axis of a geometric shape. The Eikonal equation, on the other hand, is a nonlinear partial differential equation originally used to describe wave propagation in non-uniform media. By solving for the wave propagating from the inlet to the outlet of a blood vessel, the shortest distance of blood flow between the two points can be obtained, corresponding to the vessel's centerline between those two points.

[0166] Assuming the blood vessel is cylindrical, the local radius of the blood vessel can be characterized by the radius *r* of the largest inlaid sphere tangent to the vessel lumen mesh. The discrete points on the vessel centerline are the same set of discrete points as in the above embodiments.

[0167] 7. Generating surface meshes from geometric solid models. Although geometric solids contain the geometric and topological information of an object and can accurately distinguish object boundaries, they are not suitable for finite element calculations and need to be discretized for numerical simulation. During the previous generation of geometric solids, the use of Boolean operations resulted in sharp surface features near the branch regions of the geometric solids that do not conform to physiological reality. Therefore, it is necessary to smooth the mesh at the discretized branches to obtain surface meshes suitable for computation.

[0168] In the process of discretizing blood vessels, correctly setting the mesh size is crucial for the accuracy and computational efficiency of the model. However, traditional algorithms struggle to find the correct centerline and apply the recorded local vessel radius when dealing with blood vessels that have many branches and significant curvature. This is because existing shortest distance algorithms are not robust when handling such complex and variable vascular structures and are likely to find incorrect points, as shown in the attached figure. Figure 1 As shown in the figure. To address this issue, a new metric—"relative distance"—is proposed. Specifically, assuming there are several points in the region to be discretized, one of which is designated as point P; and a point Q on the centerline of the blood vessel, the relative distance is defined as the ratio between the Euclidean distance d between points P and Q and the radius r recorded at point Q. Point Q, with the smallest relative distance, is considered an "accompanying point" of point P, and the radius r recorded at the accompanying point is multiplied by an appropriate scaling factor to determine the desired grid size. This method can effectively improve the accuracy and computational efficiency of discretization, especially for blood vessels with complex structures.

[0169] The smoothing operation uses the Laplacian and Taubin smoothing algorithms, smoothing both the vessel and vessel lumen meshes together to ensure consistency. Laplacian smoothing is a simple algorithm that smooths the mesh by moving each vertex to the average position of its neighbors. The Laplacian operator is used to calculate the difference between a vertex and its neighbors, and then used to calculate the new position of the vertex. The smoothing process can be iterated to further improve mesh quality. Taubin smoothing is a modified version of Laplacian smoothing, designed to address the problem of mesh shrinkage. Taubin smoothing involves applying two consecutive Laplacian smoothing operations, one with a positive smoothing parameter λ and the other with a negative smoothing parameter μ. The negative smoothing parameter helps to counteract the shrinkage effect of the positive parameter.

[0170] The above-mentioned vascular lumen geometry is discretized and smoothed to generate a vascular lumen surface mesh.

[0171] The above-mentioned vascular geometry is discretized and smoothed to generate a vascular surface mesh.

[0172] It is important to understand that in the embodiment 7, generating a surface mesh from a geometric solid model, although the points in the vessel lumen surface mesh and the vessel surface mesh have discrete characteristics, they are not the discrete points found in other embodiments. Specifically, in steps 202-208, and in any step directly or indirectly referred to in steps 202-208, discrete points refer to points on the vessel centerline.

[0173] 8. Generate a volume mesh from a closed surface mesh.

[0174] To perform fluid-structure interaction (FSI) modeling, analysis, and computational simulation, it is necessary to construct separate meshes for the fluid and solid domains. The interfaces between each region must be compatible to ensure proper coupling during the FSI analysis. This section primarily explains the steps involved in generating the vessel cavity mesh (fluid) and the vessel wall mesh (solid), and points out the feasibility and advantages of the adopted method.

[0175] Vascular cavity mesh:

[0176] i. The Delaunay algorithm is used to generate tetrahedral elements to fill the closed blood vessel lumen mesh, resulting in the blood vessel lumen mesh. Specifically, the Delaunay algorithm can be used to generate a boundary layer mesh of a certain thickness to more accurately describe blood flow phenomena near the wall. Here, the boundary layer mesh thickness is defined as the surface mesh size multiplied by an appropriate ratio; the specific ratio needs to be calculated based on individual blood viscosity and flow velocity.

[0177] The generation of annular cylindrical meshes relies on well-defined annular cylindrical closed-face meshes. An annular cylindrical closed-face mesh generally consists of four sets of faces: an inlet annular face, an outlet annular face, an inner wall face, and an outer wall face. The inner ring of the inlet annular face is the unmagnified outline of the inlet vessel lumen, while the outer ring is the magnified outline of the inlet vessel wall; the inner and outer rings of the outlet annular face are defined similarly. The inner wall face is the inner wall face of the vessel, and the outer wall face is the outer wall face of the vessel.

[0178] Blood vessel wall mesh:

[0179] Remove the sealing mesh at the entrance and exit of the vessel lumen to obtain the inner wall surface of the vessel. Define the opening contour line at the entrance and exit as the inner ring.

[0180] Remove the sealing mesh at the entrance and exit of the blood vessel closure surface to obtain the outer wall surface of the blood vessel. Define the opening contour line at the entrance and exit as the outer ring.

[0181] At the blood vessel inlet and outlet, the annular surface of the inlet and outlet is defined by combining the aforementioned inner ring and outer ring.

[0182] Combining the aforementioned annular surface of the inlet / outlet, the inner wall surface of the blood vessel wall, and the outer wall surface of the blood vessel wall, a closed annular cylindrical surface mesh of the blood vessel wall is defined.

[0183] The Delaunay algorithm is used to generate a tetrahedral element mesh that fills the annular cylindrical closed-face mesh of the blood vessel wall, resulting in the blood vessel wall volume mesh. Simultaneously, the algorithm is forced to not modify the existing closed-face mesh during volume mesh generation.

[0184] The advantage of this method compared to methods with uniformly set mesh sizes is that it can accurately construct volume meshes with adaptive sizes. This significantly reduces the number of nodes and elements in the volume mesh without compromising its physical field description capabilities, thus greatly improving the speed of numerical simulations and facilitating rapid convergence, iteration, and the generation of hemodynamic parameters for physician reference. Specifically, the mesh for the vascular lumen closure surface used above is the mesh of the inner wall of the vessel; simultaneously, when generating the volume mesh for the outer wall of the vessel, the algorithm is required to maintain the already generated surface mesh. These two points ensure the compatibility of the interface mesh between the vessel wall and the vessel lumen, thereby ensuring the feasibility of subsequent coupled analysis.

[0185] 9. Definition of local coordinate system of blood vessel wall.

[0186] The local coordinate system of the blood vessel wall refers to generating three mutually orthogonal unit vectors at every point in the blood vessel wall mesh: radial, axial, and circumferential. Only by defining the local coordinate system can the fiber orientation be defined at each point in the blood vessel wall mesh, thereby defining the constitutive relation of the anisotropy of the blood vessel wall. This plays a crucial role in improving the physical realism of the computational model of the vascular system.

[0187] This invention does not employ the strategy of generating a local coordinate system based on the principal stress directions of static analysis, because such a strategy cannot be guaranteed to be stable and reliable when dealing with geometrically complex blood vessels (see the discussion in point 7 of the invention's objective above). The strategy employed in this invention can stably and efficiently handle spatially arbitrarily complex blood vessel wall models.

[0188] Radial: Radial is defined as the weighted sum of the outward normal vectors from the inside of the blood vessel to the outside. These two surfaces are the inner and outer walls of the blood vessel. The weighting factor in the weighted sum is inversely proportional to the square of the distance to a given surface. This ensures that the closer the surface, the greater the proportion of the normal vector.

[0189] Temporary axis: This is a transitional axis because it is not the axis in the final coordinate system; it is only used to obtain the circumferential axis by cross product with the radial axis. The temporary axis is defined as finding the accompanying point on the correct centerline and its neighboring points. The line connecting these two points approximates the tangent direction of the centerline at that point, pointing towards the exit direction. That is, a point with a smaller global number points to a point with a larger global number.

[0190] Circumferential: Cross product of radial vector and temporary axial vector;

[0191] Final axis: cross product of radial vector and circumferential vector.

[0192] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0193] Based on the same inventive concept, this application also provides a vascular coordinate system construction apparatus for implementing the above-described method for constructing a vascular coordinate system. The solution provided by this apparatus is similar to the implementation described in the above method. Therefore, the specific limitations of one or more embodiments of the vascular coordinate system construction apparatus provided below can be found in the limitations of the vascular coordinate system construction method described above, and will not be repeated here.

[0194] In one embodiment, such as Figure 7 As shown, a device for constructing a blood vessel coordinate system is provided, comprising:

[0195] The discrete point radial calculation module 702 is used to calculate the radial direction of the reference point based on the first normal vector and the second normal vector associated with the reference point in the blood vessel wall mesh; the first normal vector points from the outer wall surface of the blood vessel wall to the outside of the blood vessel wall mesh, and the second normal vector points from the inner wall surface of the blood vessel wall to the outside of the blood vessel wall mesh.

[0196] The accompanying point filtering module 704 is used to filter out the accompanying points of the reference point from the blood vessel centerline based on the relative distance between the reference point and the blood vessel centerline.

[0197] A temporary axis construction module 706 is used to set a temporary axis along the accompanying point and a set of discrete points in the same group as the accompanying point; the set of discrete points in the same group and the accompanying point belong to the same vascular centerline.

[0198] The coordinate system integration and construction module 704 is used to transform the temporary axis to the coordinate system circumferential direction through the coordinate system radial direction, and to calculate the coordinate system axis through the coordinate system radial direction and the coordinate system circumferential direction.

[0199] In one embodiment, the discrete point radial calculation module 702 is used for:

[0200] Based on the distances from the reference points in the vessel wall mesh to the inner and outer surfaces of the vessel wall, the weighting factors of the distance negative correlation are calculated.

[0201] The first normal vector and the second normal vector are weighted according to the respective weighting factors to obtain the radial direction of the reference point.

[0202] In one embodiment, the coordinate system integration construction module 704 is used for:

[0203] Obtain the radius of the blood vessel to which each of the discrete points belongs;

[0204] Calculate the distance between the reference point in the blood vessel wall mesh and each of the discrete points to obtain the distance between each discrete point;

[0205] The relative distance between each discrete point is calculated based on the radius of the blood vessel to which each discrete point belongs and the distance between each discrete point.

[0206] Based on the relative distance that satisfies the companion condition of the reference point, the companion point of the reference point is selected from multiple discrete points.

[0207] In one embodiment, the coordinate system integration construction module 704 is used for:

[0208] Based on the distance between each discrete point and the length of the blood vessel to which each discrete point belongs, the relative distance between each discrete point is obtained.

[0209] Based on the minimum relative distance among the relative distances of the discrete points, the discrete point with the minimum relative distance is selected from the plurality of discrete points as the companion point of the reference point.

[0210] In one embodiment, the temporary axial construction module 706 is used for:

[0211] Based on the order of discrete points corresponding to the blood vessel centerline to which the accompanying point belongs, the neighboring points of the accompanying point are selected from the same group of discrete points of the accompanying point.

[0212] A temporary axis is defined along the line connecting the accompanying point and the adjacent point.

[0213] In one embodiment, the temporary axial construction module 706 is used for:

[0214] Based on the blood flow direction indicated by the discrete point sequence of the vessel centerline to which the accompanying point belongs, the nearest neighboring point is selected from the same group of discrete points of the accompanying point;

[0215] The direction of the line connecting the accompanying point and the neighboring point is determined according to the order of the discrete points;

[0216] A temporary axial direction is set according to the direction of the connection.

[0217] In one embodiment, the coordinate system integration construction module 708 is used for

[0218] The circumferential direction of the coordinate system is obtained by performing a cross product operation on the radial direction of the coordinate system and the temporary axial direction.

[0219] The coordinate system axial direction is obtained by performing a cross product between the radial direction and the circumferential direction of the coordinate system.

[0220] Each module in the aforementioned vascular coordinate system construction device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0221] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 8As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When executed by the processor, the computer program implements a method for constructing a vascular coordinate system. The display unit of the computer device is used to form a visually visible image. It can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0222] Those skilled in the art will understand that Figure 8 The structure shown is only a block diagram of a part of the structure related to the present application and does not constitute a limitation on the computer device on which the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0223] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.

[0224] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0225] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0226] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data shall comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0227] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0228] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0229] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method of constructing a vascular coordinate system, characterized by, The method includes: Based on the distances from the reference point in the vessel wall mesh to the inner and outer surfaces of the vessel wall, the weighting factors of the distance negative correlation are calculated. Based on the weighting factors, the first normal vector and the second normal vector are weighted to obtain the radial direction of the reference point. The first normal vector points from the outer surface of the vessel wall to the outside of the vessel wall mesh, and the second normal vector points from the inner surface of the vessel wall to the outside of the vessel wall mesh. Based on the relative distance between the reference point and the vessel centerline, the accompanying points of the reference point are selected from the vessel centerline; the accompanying points are discrete points selected from the vessel centerline. A temporary axis is defined along the accompanying point and the discrete points in the same group as the accompanying point; the discrete points in the same group and the accompanying point belong to the same vessel centerline; the temporary axis is the blood flow direction defined based on the accompanying point and the discrete points in the same group as the accompanying point, and is used to represent the length direction of the vessel. The radial direction of the coordinate system and the temporary axial direction are cross-producted to obtain the circumferential direction of the coordinate system; the circumferential direction of the coordinate system is used to indicate the direction in which the location of the accompanying point surrounds the blood vessel. The coordinate system axial direction is obtained by performing a cross product between the radial direction and the circumferential direction of the coordinate system.

2. The method of claim 1, wherein, The step of filtering out the accompanying points of the reference point from the blood vessel centerline based on the relative distance between the reference point and the blood vessel centerline includes: Obtain the radius of the blood vessel to which each of the discrete points belongs; Calculate the distance between the reference point in the blood vessel wall mesh and each of the discrete points to obtain the distance between each discrete point; The relative distance between each discrete point is calculated based on the radius of the blood vessel to which each discrete point belongs and the distance between each discrete point. Based on the relative distance that satisfies the companion condition of the reference point, the companion point of the reference point is selected from multiple discrete points.

3. The method of claim 2, wherein, The step of calculating the relative distance between each discrete point based on the radius of the blood vessel to which each discrete point belongs and the distance between each discrete point includes: Based on the distance between each discrete point and the length of the blood vessel to which each discrete point belongs, the relative distance between each discrete point is obtained. The step of selecting the companion point of the reference point from multiple discrete points based on the relative distance that satisfies the companion condition of the reference point includes: Based on the minimum relative distance among the relative distances of the discrete points, the discrete point with the minimum relative distance is selected from the plurality of discrete points as the companion point of the reference point.

4. The method of claim 1, wherein, The step of setting a temporary axis along the accompanying point and the discrete points in the same group as the accompanying point includes: Based on the order of discrete points corresponding to the blood vessel centerline to which the accompanying point belongs, the neighboring points of the accompanying point are selected from the same group of discrete points of the accompanying point. A temporary axis is defined along the line connecting the accompanying point and the adjacent point.

5. The method of claim 4, wherein, The step of selecting neighboring points of the accompanying point from the same group of discrete points of the accompanying point according to the discrete point order corresponding to the blood vessel centerline to which the accompanying point belongs includes: Based on the blood flow direction indicated by the discrete point sequence of the vessel centerline to which the accompanying point belongs, select the nearest neighbor point from the discrete points in the vessel centerline to which the accompanying point belongs; The step of setting a temporary axis along the line connecting the accompanying point and the neighboring point includes: The direction of the line connecting the accompanying point and the neighboring point is determined according to the order of the discrete points; A temporary axial direction is set based on the direction of the connection.

6. The method of claim 4, wherein, The steps for generating the vascular centerline include: From the starting point of the blood vessel inlet and outlet to the ending point, estimate the blood flow distance between the central axis and discrete points between the starting point and the ending point; The central axis is adjusted according to the shortest blood flow distance among the various blood flow distances to obtain the vascular centerline between the starting point and the ending point.

7. A device for constructing a vascular coordinate system, characterized in that, The device includes: The discrete point radial calculation module is used to calculate the various weighting factors of the distance negative correlation based on the distance from the reference point in the vessel wall mesh to the inner and outer surfaces of the vessel wall, respectively; and to perform a weighted calculation on the first normal vector and the second normal vector based on the various weighting factors to obtain the radial direction of the reference point; the first normal vector points from the outer surface of the vessel wall to the outside of the vessel wall mesh, and the second normal vector points from the inner surface of the vessel wall to the outside of the vessel wall mesh; The accompanying point filtering module is used to filter out the accompanying points of the reference point from the blood vessel centerline based on the relative distance between the reference point and the blood vessel centerline; the accompanying points are discrete points filtered out by the blood vessel centerline. A temporary axis construction module is used to set a temporary axis along the accompanying point and a set of discrete points of the accompanying point; the set of discrete points and the accompanying point belong to the same vessel centerline; the temporary axis is the blood flow direction set based on the accompanying point and the set of discrete points of the accompanying point, and is used to represent the length direction of the vessel. The coordinate system integration and construction module is used to perform a cross product of the radial direction of the coordinate system and the temporary axial direction to obtain the circumferential direction of the coordinate system; the circumferential direction of the coordinate system is used to indicate the direction of the location of the accompanying point around the blood vessel; the cross product of the radial direction of the coordinate system and the circumferential direction of the coordinate system is performed to obtain the axial direction of the coordinate system. 8.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-7. When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program, characterized in that, When the computer program is executed, it implements the steps of the method according to any one of claims 1 to 6.

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