Method for measuring geometric morphology of carotid artery

Abstract

The invention provides a method for measuring the geometric morphology of a carotid artery. The method is used for carrying out quantitative analysis on a three-dimensional structure of the carotid artery. According to the method, an improved Fast Marching algorithm is utilized to automatically generate parameterized center lines of all blood vessel branches of the carotid artery bifurcation, a maximum inscribed sphere is defined on the center lines, the radius of the inscribed sphere is determined by calculating the minimum distance from each point on the center lines to the blood vessel wall, and the local blood vessel diameter is calculated based on the radius. A Gaussian weighted average method is adopted to obtain the blood vessel feature diameter; based on the parameterized center line and the weighted average diameter, a series of carotid artery geometric morphology parameters are calculated, and the carotid artery geometric morphology parameters comprise a weighted blood vessel diameter ratio, a bifurcation angle tensor and a normalized curvature index; the method is high in automation degree and high in reliability, manual measurement errors are reduced, and objective and accurate quantitative indexes are provided for early diagnosis and risk assessment of carotid artery diseases.

Description

Technical Field

[0001] The invention belongs to the technical field of medical image processing, and in particular relates to a method for measuring the geometric morphology of a carotid artery. Background Art

[0002] Carotid atherosclerotic lesions are closely related to cerebral stroke, so carotid atherosclerotic lesions have always been a hot topic in clinical research; a large number of studies have shown that the anatomy and geometry of blood vessels have a significant impact on hemodynamic characteristics, which may become an important risk factor for the early development of atherosclerotic diseases.

[0003] Atherosclerosis is prone to occur at bifurcations, bends, and stenosis of the arterial system. Due to its special geometric shape, the carotid bifurcation site has a complex and changeable blood flow state, making it a high-incidence area for the formation of atherosclerotic plaques. Different angles of carotid bifurcation can lead to differences in blood flow patterns, especially affecting the size and distribution of low shear stress areas. Low shear stress is considered to be one of the most dangerous hemodynamic factors in the development of arterial disease, thereby affecting the formation and stability of plaques.

[0004] Existing methods for measuring carotid artery geometry have multiple limitations: first, traditional two-dimensional measurements cannot fully reflect the three-dimensional geometric characteristics of the carotid artery; second, there are differences in the definition of measurement positions in different studies, resulting in a lack of comparability of the results; third, manual measurement is subjective, which increases measurement errors; more importantly, existing measurement methods often ignore the relationship between geometric parameters such as vessel diameter, bifurcation angle and tortuosity, and cannot provide a comprehensive assessment of vascular geometry.

[0005] Therefore, there is an urgent need to develop a standardized, automated quantitative measurement method for carotid artery geometry based on three-dimensional reconstruction to provide a more accurate and objective evaluation method and a more reliable basis for carotid atherosclerosis risk assessment and clinical decision-making. Summary of the invention

[0006] The present invention provides a method for measuring the geometric morphology of the carotid artery, which is based on three-dimensional vascular reconstruction and parameterized centerline extraction technology, and quantitatively analyzes the geometric characteristics of the carotid bifurcation through an automated algorithm, so as to achieve the purpose of accurately, objectively and repeatably evaluating the geometric morphology of the carotid artery and providing a scientific basis for clinical intervention decisions.

[0007] In order to achieve the above-mentioned invention object, the specific technical scheme is as follows: A method for measuring carotid artery geometry, the method comprising the following steps: Step S1, using an improved Fast Marching method to automatically generate parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation.

[0008] The center line is given by the function Indicates that is the parameterized length of the vessel centerline, The value range is , represents the total length of the centerline of the blood vessel to be measured, , , They respectively represent the coordinates of the center line in three-dimensional space.

[0009] Step S2, defining a maximum inscribed sphere on the center line of each blood vessel, wherein the radius of the maximum inscribed sphere is determined by calculating the minimum distance from each point on the center line to the blood vessel wall.

[0010] Radius function ,in, is a point on the blood vessel wall, Represents the distance from each point on the centerline to the vessel wall.

[0011] Step S3, calculating the local blood vessel diameter based on the maximum inscribed sphere radius function, and obtaining the characteristic diameter of the blood vessel by weighted average method; the local blood vessel diameter .

[0012] Step S4, calculating carotid artery geometric parameters based on the parameterized centerline and the weighted average diameter, wherein the geometric parameters include a weighted vessel diameter ratio, a bifurcation angle tensor, and a normalized tortuosity index.

[0013] Furthermore, the weighted average diameter in step S3 is calculated as follows: ;in, represents the weighted average diameter of the blood vessel segment to be measured, Indicates at location The local blood vessel diameter at is the weight function, which adopts the Gaussian weight function form: ,in, represents the center position of the center line of the blood vessel segment to be calculated, Represents the standard deviation of the Gaussian function, controls the width of the weight distribution, and has a value range of to .

[0014] Furthermore, the blood vessel diameter ratio in step S4 includes the inner-to-total diameter ratio Ratio of outer diameter to ; in, ; ; , and are the weighted mean diameters of the internal carotid artery, external carotid artery, and common carotid artery, respectively; Weighted mean diameter of the internal carotid artery The measurement range is the section from 5mm to 15mm distal to the center point of the largest inscribed sphere of the internal carotid artery; Weighted mean diameter of external carotid artery The measurement range is the section from 5mm to 15mm distal to the center point of the largest inscribed sphere of the external carotid artery; Weighted mean diameter of the common carotid artery The measurement range is the segment from 5mm to 15mm proximal to the center point of the largest internal inscribed sphere of the common carotid artery.

[0015] Furthermore, the bifurcation angle tensor in step S4 The calculation formula is: ;in, The angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the frontal projection plane, in degrees; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the frontal projection plane; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the lateral projection plane; represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the lateral projection plane; the tangent vector is the derivative vector of the centerline parameter length: .

[0016] Furthermore, the calculation of the normalized tortuosity index in step S4 includes: Calculate the local curvature: , represents the Euclidean norm of the second derivative vector of the centerline; calculate the total curvature index: , which represents the local curvature Integrate along the entire centerline; calculate the normalized tortuosity index: ;in, It is the straight-line distance between two points 1 cm above and below the carotid bifurcation, in millimeters; The actual length of the centerline between the blood vessels 1 cm above and below the carotid bifurcation, in millimeters; Normalized tortuosity index It is a dimensionless index, and the larger the value, the higher the degree of vascular tortuosity.

[0017] Furthermore, the specific steps of automatically generating the parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation using the improved Fast Marching method in step S1 include: Step S11, preprocessing the original three-dimensional blood vessel image, wherein the preprocessing includes noise reduction and blood vessel structure enhancement; Step S12, performing blood vessel segmentation based on the image grayscale value to obtain the blood vessel cavity volume; Step S13, selecting a starting point and an end point in the blood vessel cavity, the starting point being located at the proximal end of the common carotid artery, and the end points being located at the distal ends of the internal carotid artery and the external carotid artery respectively; Step S14, constructing a velocity field function based on the vascular cavity volume , so that the velocity is maximum near the center of the blood vessel and decreases toward the blood vessel wall; Step S15, using the velocity field The Fast Marching method is used to calculate the shortest time from the starting point to each point in the blood vessel. ; Step S16, from the end point along the shortest time graph The gradient direction Trace back to the starting point to obtain the initial path; Step S17, smoothing the initial path to obtain a parameterized center line ; Step S18, re-parameterize the center line by spline interpolation method to ensure that the parameters Directly proportional to the actual physical length of the centerline.

[0018] Furthermore, in step S11, the original three-dimensional vascular image is preprocessed, including: using an adaptive Gaussian filtering method to reduce noise on the original image, and automatically adjusting the filter kernel parameters according to the local vascular diameter; using a vascular enhancement algorithm based on multi-scale Hessian matrix eigenvalue analysis to improve the contrast between the blood vessel and the background; and using a histogram equalization method to adjust the image grayscale distribution and highlight the vascular structure.

[0019] Compared with the prior art, the present invention has the following beneficial effects: The present invention introduces the concept of the maximum inscribed sphere to measure the blood vessel diameter, and adopts the Gaussian weighted average method to calculate the characteristic diameter, which can more objectively reflect the real size of the blood vessel lumen and reduce the interference of local stenosis or dilation on the measurement result; the bifurcation angle is expanded from two-dimensional to three-dimensional space, and the three-dimensional geometric characteristics of the carotid artery bifurcation are fully captured through the combined description of the front and side angles; the geometric characteristics of the carotid artery are comprehensively evaluated by multiple parameters, which can more comprehensively reflect its hemodynamic characteristics and provide a more accurate basis for clinical risk assessment and intervention decision-making; the measurement method of the present invention can be applied to large-sample clinical research, and provides a reliable technical means for exploring the correlation between the geometric morphology of the carotid artery and diseases such as atherosclerosis and stroke. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart of a method for measuring carotid artery geometry of the present invention; DETAILED DESCRIPTION In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described implementation mode is a part of the present invention, not all implementation modes. Based on the implementation modes of the present invention, all other implementation modes obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] It should be noted that it is suitable for quantitative analysis of carotid artery geometry based on three-dimensional medical imaging data such as CT angiography (CTA), magnetic resonance angiography (MRA) or digital subtraction angiography (DSA), and can be widely used in clinical diagnosis, risk assessment and academic research of cerebrovascular diseases. Application scenarios include but are not limited to: clinicians' lesion risk assessment of patients with carotid atherosclerosis, vascular anatomy assessment before neurosurgery, vascular morphology analysis of stroke patients, and carotid artery morphology data collection and analysis in related clinical research. This measurement method can be integrated into the hospital's existing PACS system or independent medical image processing software to provide doctors with a convenient clinical auxiliary diagnosis tool.

[0022] like Figure 1 FIG. 1 is a flow chart of a method for measuring carotid artery geometry of the present invention, the method comprising the following steps: Step S1, using an improved Fast Marching method to automatically generate parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation; The center line is given by the function Indicates that is the parameterized length of the vessel centerline, The value range is , represents the total length of the centerline of the blood vessel to be measured, , , They respectively represent the coordinates of the center line in three-dimensional space.

[0023] The vascular centerline is a skeleton structure that describes the geometric morphology of the vascular lumen. Accurate centerline extraction is the basis for subsequent vascular morphology analysis. The parameterized centerline generated by the improved Fast Marching method in the present invention has the characteristics of continuity, smoothness, and being located in the center of the vascular lumen, and can accurately reflect the path of the blood vessel. In practical applications, for image data of different resolutions, the algorithm can adaptively adjust parameters to ensure the stability and accuracy of centerline extraction. For example, for CTA images with a resolution of 0.5mm×0.5mm×0.5mm, this method can complete the centerline extraction of the carotid bifurcation within 5-10 seconds, and the average positioning accuracy is better than 0.3mm.

[0024] The specific steps of automatically generating the parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation using the improved Fast Marching method include: Step S11, preprocessing the original three-dimensional blood vessel image, wherein the preprocessing includes noise reduction and blood vessel structure enhancement; Step S12, performing blood vessel segmentation based on the image grayscale value to obtain the blood vessel cavity volume; Step S13, selecting a starting point and an end point in the blood vessel cavity, the starting point being located at the proximal end of the common carotid artery, and the end points being located at the distal ends of the internal carotid artery and the external carotid artery respectively; Step S14, constructing a velocity field function based on the vascular cavity volume , so that the velocity is maximum near the center of the blood vessel and decreases toward the blood vessel wall; Step S15, using the velocity field The Fast Marching method is used to calculate the shortest time from the starting point to each point in the blood vessel. ; Step S16, from the end point along the shortest time graph The gradient direction Trace back to the starting point to obtain the initial path; Step S17, smoothing the initial path to obtain a parameterized center line ; Step S18, re-parameterize the center line by spline interpolation method to ensure that the parameters Directly proportional to the actual physical length of the centerline.

[0025] Preprocess the original 3D vascular image, including: The original image was denoised using an adaptive Gaussian filter, and the filter kernel parameters were automatically adjusted according to the local blood vessel diameter. A blood vessel enhancement algorithm based on multi-scale Hessian matrix eigenvalue analysis was used to improve the contrast between the blood vessels and the background. The histogram equalization method was used to adjust the image grayscale distribution and highlight the blood vessel structure.

[0026] The Hessian matrix eigenvalue analysis of the present invention is a powerful blood vessel enhancement technology that can selectively enhance according to the geometric characteristics of the blood vessel. Tubular structures (such as blood vessels) in three-dimensional images have specific local second-order structural characteristics, that is, the second-order derivative in the direction of the blood vessel is close to zero, while the second-order derivative perpendicular to the direction of the blood vessel has a large absolute value and the same sign. This feature can be identified by analyzing the eigenvalues ​​of the Hessian matrix, thereby selectively enhancing the blood vessel structure. In practical applications, for blood vessels of different diameters, convolution calculation of the Hessian matrix using Gaussian kernels of different scales can enhance the full range of blood vessel structures from large blood vessels (such as the common carotid artery, with a diameter of about 6-8mm) to small blood vessels (such as the distal branch of the external carotid artery, with a diameter of about 2-3mm), ensuring the integrity of subsequent analysis.

[0027] Step S2, defining a maximum inscribed sphere on the centerline of each blood vessel, wherein the radius of the maximum inscribed sphere is determined by calculating the minimum distance from each point on the centerline to the blood vessel wall; Radius function ,in, is a point on the blood vessel wall, Indicates the distance from each point on the centerline to the vessel wall; Step S3, calculating the local blood vessel diameter based on the maximum inscribed sphere radius function, and obtaining the characteristic diameter of the blood vessel by a weighted average method; The maximum inscribed sphere is a method that accurately expresses the local geometric characteristics of blood vessels. It can adapt to the irregularity of the cross-sectional shape of blood vessels and is more accurate than the traditional circular cross-sectional assumption. In practical applications, due to the influence of image resolution and noise, the direct calculation of the minimum distance from a point on the centerline to the blood vessel wall may fluctuate. The present invention uses a multi-directional ray method combined with gradient information for robust distance calculation, emitting rays from each point on the centerline in multiple directions (usually 32-64 directions) until the blood vessel wall is reached (determined by image gradient or threshold detection). This method has a strong fault tolerance for areas with vague definition of the blood vessel wall, and can significantly improve the accuracy and stability of distance measurement. Clinical verification shows that the consistency between the blood vessel diameter measured by this method and the measurement results of digital subtraction angiography (DSA) is better than 95%.

[0028] Local blood vessel diameter ; The weighted average diameter is calculated as: ;in, represents the weighted average diameter of the blood vessel segment to be measured, Indicates at location The local blood vessel diameter at is the weight function, which adopts the Gaussian weight function form: ,in, represents the center position of the center line of the blood vessel segment to be calculated, Represents the standard deviation of the Gaussian function, controls the width of the weight distribution, and has a value range of to .

[0029] Step S4, calculating carotid artery geometric parameters based on the parameterized centerline and the weighted average diameter, wherein the geometric parameters include a weighted vessel diameter ratio, a bifurcation angle tensor, and a normalized tortuosity index.

[0030] Geometric parameters are the core indicators of quantitative analysis of carotid morphology, which can comprehensively reflect the geometric characteristics of carotid bifurcation and its possible hemodynamic effects. The three core parameters (diameter ratio, angle tensor and curvature index) proposed in this invention describe the morphological characteristics of blood vessels from different dimensions, providing multi-dimensional quantitative indicators for subsequent clinical research and risk assessment. The combined analysis of these parameters can reveal the correlation between carotid morphology and disease. For example, a specific combination of diameter ratio and bifurcation angle may be correlated with the location of plaque formation, while a higher curvature index may be associated with blood flow disturbance and abnormal endothelial cell stress distribution. In a clinical study involving 200 carotid CTA images, the correlation analysis between these geometric parameters and plaque formation showed significant statistical significance (p<0.01).

[0031] Vessel diameter ratio includes internal to total diameter ratio Ratio of outer diameter to ;in, ; ; , and The weighted mean diameters of the internal carotid artery, external carotid artery and common carotid artery are respectively; the weighted mean diameter of the internal carotid artery is The measurement range is the section from 5mm to 15mm from the center point of the largest inscribed sphere of the internal carotid artery to the distal end; the weighted average diameter of the external carotid artery The measurement range is the section from 5mm to 15mm from the center point of the largest inscribed sphere of the external carotid artery to the distal end; the weighted average diameter of the common carotid artery The measurement range is the segment from 5mm to 15mm proximal to the center point of the largest internal inscribed sphere of the common carotid artery.

[0032] Bifurcation Angle Tensor The calculation formula is: ;in, The angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the frontal projection plane, in degrees; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the frontal projection plane; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the lateral projection plane; represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the lateral projection plane; the tangent vector is the derivative vector of the centerline parameter length: .

[0033] Traditional measurement methods often only consider the bifurcation angle in a single plane and cannot capture the three-dimensional characteristics of vascular bifurcations. The bifurcation angle has a significant impact on hemodynamics, especially on the flow field characteristics and wall shear force distribution at the bifurcation. Computer fluid dynamics (CFD) simulation studies have shown that larger bifurcation angles (especially >60°) is often accompanied by a large area of ​​low wall shear at the origin of the internal carotid artery, which is where plaque is prone to form.

[0034] The bifurcation angle tensor measurement method of the present invention is based on the calculation of the tangent vector of the parameterized centerline and has high stability and repeatability. In clinical applications, doctors can quickly identify patients who may have abnormal blood flow patterns through the value of the bifurcation angle tensor and conduct more detailed evaluation and follow-up.

[0035] The calculation of the normalized tortuosity index includes: Calculating the local tortuosity: , represents the Euclidean norm of the second derivative vector of the centerline; calculate the total curvature index: , which represents the local curvature Integrate along the entire centerline; calculate the normalized tortuosity index: ;in, It is the straight-line distance between two points 1 cm above and below the carotid bifurcation, in millimeters; The actual length of the centerline between the blood vessels 1 cm above and below the carotid bifurcation, in millimeters; Normalized tortuosity index It is a dimensionless index, and the larger the value, the higher the degree of vascular tortuosity.

[0036] This index combines the cumulative effect of local curvature (TCI) and the geometric characteristics of the overall curvature ( ), which fully captures the characteristics of vascular curvature. In clinical studies, it was found that patients with NCI values ​​greater than 1.4 had a significantly higher risk of plaque formation at the carotid bifurcation than those with NCI values ​​less than 1.2. This correlation remained significant after adjusting for traditional risk factors (such as hypertension, diabetes, smoking, etc.). This measurement method has good numerical stability, and the measurement error is usually controlled within 5% even in the case of poor image quality.

[0037] The histogram equalization method is used to adjust the grayscale distribution of the image to make the vascular structure more obvious; The Hessian matrix at Defined as image brightness function The second-order partial derivative matrix of : Hessian matrix Perform eigenvalue decomposition and obtain the eigenvalue ( ) and the corresponding eigenvector ; When the conditions are met ,and When , the point is judged to be a tubular structure, where The direction vector corresponding to the blood vessel; Constructing vascular enhancement response function based on eigenvalues : ; in, , , ; The control parameters are used to adjust the sensitivity of blood vessel recognition, the roundness requirement of the blood vessel cross section and the degree of suppression of background noise.

[0038] The velocity field function in step S14 The construction method is: Step S141, first calculate the distance mapping function from the vascular cavity volume to the vascular wall , represents the Euclidean distance from each point in the volume to the nearest blood vessel wall; Step S142, define the velocity field function: ; in, The maximum value of the intraluminal distance mapping function represents the radius of the thickest vessel segment; It is a parameter that controls the velocity distribution, and its value range is 1.0 to 5.0; Step S143, introducing additional constraints in the blood vessel bifurcation region to make the velocity field transition smoothly in the bifurcation region: ,in, It is a smoothing function in the bifurcation area. It takes a value of 1 in the non-bifurcation area and gradually increases in the bifurcation area according to the distance to the bifurcation center to ensure that the center line can smoothly pass through the bifurcation area.

[0039] The velocity field function is a key component in the Fast Marching method, which determines the characteristics of the path found by the algorithm. The velocity field function designed by the present invention has a maximum value near the center of the blood vessel and decreases toward the blood vessel wall, which ensures that the generated path tends to travel along the center of the blood vessel. Distance mapping function It is the basis for constructing the velocity field. It naturally forms a distribution with the center of the blood vessel as the maximum value by calculating the Euclidean distance from each point to the nearest blood vessel wall.

[0040] parameter Controls the rate at which the velocity decreases from the center to the wall. The value of will make the velocity field steeper near the center, enhancing the attraction of the centerline. In practical applications, for larger diameter vessels (such as the common carotid artery), A value close to 1.0 produces a smoother velocity field; for smaller diameter vessels (such as the distal external carotid artery), A value close to 5.0 can enhance the stability of the centerline. It is particularly noteworthy that the smoothing function introduced by the present invention in the bifurcation region This solves the instability problem of the traditional Fast Marching method when dealing with vascular bifurcations, ensures that the centerline can smoothly pass through the bifurcation area, and improves the accuracy of the overall geometric morphology measurement.

[0041] The carotid artery geometry measurement method proposed in the present invention realizes accurate quantitative analysis of the three-dimensional geometry of the carotid artery by constructing a complete automated processing flow. This method can not only be applied to clinical diagnosis and risk assessment, but also provide objective and reliable morphological data for the study of the mechanism of vascular diseases. Through innovative technologies such as parameterized centerline, maximum inscribed sphere, and weighted average diameter, this method solves the limitations of traditional two-dimensional projection measurement and provides a more comprehensive and accurate description of the morphological characteristics of the carotid artery.

[0042] Clinical validation showed that the geometric parameters measured by this method were significantly correlated with the risk of carotid atherosclerosis, providing new quantitative indicators for clinical risk stratification and intervention decisions.

[0043] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for measuring the geometric morphology of the carotid artery, characterized in that: The method comprises the following steps: Step S1, using an improved Fast Marching method to automatically generate parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation; The center line is given by the function Indicates that is the parameterized length of the vessel centerline, The value range is , represents the total length of the centerline of the blood vessel to be measured, , , They represent the coordinates of the center line in three-dimensional space respectively; Step S2, defining a maximum inscribed sphere on the centerline of each blood vessel, wherein the radius of the maximum inscribed sphere is determined by calculating the minimum distance from each point on the centerline to the blood vessel wall; Radius function ,in, is a point on the blood vessel wall, Indicates the distance from each point on the centerline to the vessel wall; Step S3, calculating the local blood vessel diameter based on the maximum inscribed sphere radius function, and obtaining the characteristic diameter of the blood vessel by a weighted average method; Local blood vessel diameter ; Step S4, calculating carotid artery geometric parameters based on the parameterized centerline and the weighted average diameter, wherein the geometric parameters include a weighted vessel diameter ratio, a bifurcation angle tensor, and a normalized tortuosity index.

2. The method for measuring carotid artery geometry according to claim 1, characterized in that: The calculation method of the weighted average diameter in step S3 is: ;in, represents the weighted average diameter of the blood vessel segment to be measured, Indicates at location The local blood vessel diameter at is the weight function, which adopts the Gaussian weight function form: ,in, represents the center position of the center line of the blood vessel segment to be calculated, Represents the standard deviation of the Gaussian function, controls the width of the weight distribution, and has a value range of to .

3. The method for measuring carotid artery geometry according to claim 2, characterized in that: The blood vessel diameter ratio in step S4 includes the inner diameter ratio Ratio of outer diameter to ; in, ; ; , and are the weighted mean diameters of the internal carotid artery, external carotid artery, and common carotid artery, respectively; Weighted mean diameter of the internal carotid artery The measurement range is the section from 5mm to 15mm distal to the center point of the largest inscribed sphere of the internal carotid artery; Weighted mean diameter of external carotid artery The measurement range is the section from 5mm to 15mm distal to the center point of the largest inscribed sphere of the external carotid artery; Weighted mean diameter of the common carotid artery The measurement range is the segment from 5mm to 15mm proximal to the center point of the largest internal inscribed sphere of the common carotid artery.

4. The method for measuring carotid artery geometry according to claim 3, characterized in that: The bifurcation angle tensor in step S4 The calculation formula is: ;in, The angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the frontal projection plane, in degrees; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the frontal projection plane; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the common carotid artery in the lateral projection plane; It represents the angle between the tangent vector of the centerline of the internal carotid artery and the tangent vector of the centerline of the external carotid artery in the lateral projection plane; The tangent vector is the derivative vector of the centerline parameter length: .

5. The method for measuring carotid artery geometry according to claim 4, characterized in that: The calculation of the normalized tortuosity index in step S4 includes: Calculate the local curvature: , represents the Euclidean norm of the second derivative vector of the centerline; calculate the total curvature index: , which represents the local curvature Integrate along the entire centerline; calculate the normalized tortuosity index: ;in, It is the straight-line distance between two points 1 cm above and below the carotid bifurcation, in millimeters; The actual length of the centerline between the blood vessels 1 cm above and below the carotid bifurcation, in millimeters; Normalized tortuosity index It is a dimensionless index, and the larger the value, the higher the degree of vascular tortuosity.

6. The method for measuring carotid artery geometry according to claim 1, characterized in that: The specific steps of automatically generating the parameterized center lines of each vascular branch of the three-dimensional carotid artery bifurcation using the improved Fast Marching method in step S1 include: Step S11, preprocessing the original three-dimensional blood vessel image, wherein the preprocessing includes noise reduction and blood vessel structure enhancement; Step S12, performing blood vessel segmentation based on the image grayscale value to obtain the blood vessel cavity volume; Step S13, selecting a starting point and an end point in the blood vessel cavity, the starting point being located at the proximal end of the common carotid artery, and the end points being located at the distal ends of the internal carotid artery and the external carotid artery respectively; Step S14, constructing a velocity field function based on the vascular cavity volume , so that the velocity is maximum near the center of the blood vessel and decreases toward the blood vessel wall; Step S15, using the velocity field The Fast Marching method is used to calculate the shortest time from the starting point to each point in the blood vessel. ; Step S16, from the end point along the shortest time graph The gradient direction Trace back to the starting point to obtain the initial path; Step S17, smoothing the initial path to obtain a parameterized center line ; Step S18, re-parameterize the center line by spline interpolation method to ensure that the parameters Directly proportional to the actual physical length of the centerline.

7. The method for measuring carotid artery geometry according to claim 6, characterized in that: In step S11, the original three-dimensional blood vessel image is preprocessed, including: The original image was denoised using an adaptive Gaussian filter, and the filter kernel parameters were automatically adjusted according to the local blood vessel diameter. A blood vessel enhancement algorithm based on multi-scale Hessian matrix eigenvalue analysis was used to improve the contrast between the blood vessels and the background. The histogram equalization method was used to adjust the image grayscale distribution and highlight the blood vessel structure.

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