Left ventricular myocardium curved surface registration method based on two-dimensional parameter domain mapping

Abstract

The application discloses a left ventricular myocardium curved surface registration method based on two-dimensional parameter domain mapping. The method comprises the following steps: segmenting and reconstructing a dynamic three-dimensional curved surface sequence of left ventricular myocardium from a cardiac magnetic resonance short-axis image sequence, and then performing standardization processing on the dynamic three-dimensional curved surface sequence to obtain a target curved surface model; mapping a key frame curved surface in the target curved surface model to a pre-defined two-dimensional parameter domain to obtain global deformation parameters; and mapping the remaining frames of the target curved surface model in the whole cardiac cycle to the two-dimensional parameter domain according to the global deformation parameters. The method drives the mapping process of the whole sequence by using the global deformation parameters of a key frame curved surface, can establish stable space-time vertex corresponding relationships for the curved surfaces of all time frames on the two-dimensional parameter domain, realizes time sequence alignment of the curved surface sequence in the whole cardiac cycle and normalized registration of myocardium shapes among different cases, can effectively solve problems such as large shape difference among individuals and unclear characteristics, and realizes accurate registration of left ventricular myocardium curved surfaces.

Description

Technical Field

[0001] This disclosure relates to the field of medical image analysis technology, and in particular to a method for registration of left ventricular myocardial surface based on two-dimensional parameter domain mapping. Background Technology

[0002] Accurate assessment of left ventricular myocardial motion and deformation is crucial for quantitative analysis of cardiac function, early disease diagnosis, and evaluation of treatment effectiveness. The core technical challenge in achieving this goal lies in establishing a stable and precise spatiotemporal correspondence—i.e., surface registration—between images from different time frames or different individuals.

[0003] Currently, the main methods for left ventricular registration have several limitations. Manual registration heavily relies on physician experience for manual point plotting and alignment, which is tedious and highly subjective, and the accuracy of the calibration directly affects the reliability of subsequent analysis. Traditional point cloud registration algorithms based on Iterative Closest Point (ICP) are prone to getting trapped in local optima when the morphological features of the left ventricular surface are not significant, are sensitive to the initial position, and have poor robustness. Although machine learning-based methods can achieve automation, they rely on large-scale, high-quality labeled data and high computational resources, and the interpretability of the models is generally poor, making it difficult to guarantee the establishment of accurate, physically interpretable point-to-point correspondences when data is limited or individual differences are significant.

[0004] Most of the methods mentioned above perform registration and motion modeling directly in three-dimensional Euclidean space, failing to fully consider the geometric characteristics of the left ventricular myocardial surface as a two-dimensional Riemannian manifold. Although methods that treat the surface as a manifold for registration have gradually gained attention in recent years, in left ventricular myocardial motion modeling, how to utilize the homeomorphism of the left ventricular myocardium to establish a stable correspondence for this specific topological structure remains a challenge. Summary of the Invention

[0005] In view of this, the present disclosure provides a method for left ventricular myocardial surface registration based on two-dimensional parameter domain mapping, which can solve the problems of poor left ventricular registration accuracy, unstable results, and unreliability in the prior art.

[0006] This disclosure provides a method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping, employing the following technical solution: Dynamic three-dimensional surface sequences of left ventricular myocardium segmented and reconstructed from short-axis cardiac magnetic resonance imaging sequences; The dynamic three-dimensional surface sequence is standardized to obtain the target surface model; The keyframe surfaces in the target surface model are mapped to a predefined two-dimensional parameter domain to obtain global deformation parameters; Based on the global deformation parameters, the target surface model is mapped to the two-dimensional parameter domain for all remaining frames throughout the cardiac cycle.

[0007] Optionally, the dynamic three-dimensional surface sequence for segmenting and reconstructing the left ventricular myocardium from the short-axis image sequence of cardiac magnetic resonance imaging includes: Obtain a sequence of short-axis magnetic resonance images of the heart for a complete cardiac cycle; Left ventricular myocardial segmentation was performed on each frame of the cardiac magnetic resonance short-axis image sequence to obtain the myocardial boundary contour line; The myocardial boundary contours of all frames are reconstructed to generate a dynamic three-dimensional surface sequence of the left ventricular myocardium.

[0008] Optionally, the standardization process of the dynamic three-dimensional surface sequence to obtain the target surface model includes: Construct a pre-defined standard model; Based on the preset standard model, a feature point mapping relationship with consistent vertex indices is established between the dynamic three-dimensional surface sequence and the preset standard model. The preset standard model is then adjusted according to the feature point mapping relationship to obtain the target surface model.

[0009] Optionally, the construction of the preset standard model includes: A preset standard model is constructed based on a historical database. The preset standard model is a three-dimensional mesh with a preset number of vertices and a fixed topology, wherein each vertex has a unique index.

[0010] Optionally, the step of establishing a feature point mapping relationship with consistent vertex indices between the dynamic 3D surface sequence and the preset standard model based on the preset standard model, and adjusting the surface of the preset standard model according to the feature point mapping relationship to obtain the target surface model, includes: In the dynamic three-dimensional surface sequence, the feature points corresponding to the vertices are marked and denoted as target feature points; Based on the mapping relationship between the target feature points and the vertices, the preset standard model is surface-adjusted to obtain the target surface model.

[0011] Optionally, the vertex includes at least the apex and the mitral annulus.

[0012] Optionally, the step of adjusting the surface of the preset standard model according to the mapping relationship between the target feature points and the vertices to obtain the target surface model includes: Based on the mapping relationship between the target feature points and the vertices, the preset standard model is adjusted using rigid body transformation or non-rigid transformation methods to obtain the target surface model; The shape of the target surface model is consistent with the shape of the dynamic three-dimensional surface sequence, and the vertex index and topology of the target surface model are exactly the same as those of the preset standard model.

[0013] Optionally, mapping the keyframe surfaces in the target surface model to a predefined two-dimensional parameter domain to obtain global deformation parameters includes: A two-dimensional parameter domain is predefined that is topologically homeomorphic to the dynamic three-dimensional surface sequence; Determine the keyframe surfaces in the target surface model, wherein the keyframe surfaces are the left ventricular end-diastolic surface or the end-systolic frame surface; The keyframe surface is mapped to the two-dimensional parameter domain to obtain global deformation parameters.

[0014] Optionally, mapping the keyframe surface to the two-dimensional parameter domain to obtain global deformation parameters includes: Identify the boundary edges and internal edges on the keyframe surface to be mapped, and determine the total length of the output boundary and the cumulative length of each boundary vertex; Based on the total length of the boundary and the cumulative length of each boundary vertex, the boundary of the keyframe surface is mapped to the fixed boundary shape of the target two-dimensional parameter domain to obtain the predetermined coordinates of all boundary vertices in the two-dimensional parameter domain. Based on the predetermined coordinates and the Laplace-Beltrami operator, a system of linear equations is constructed regarding the coordinates of the interior vertices; Solve the system of linear equations to obtain the two-dimensional coordinates of all internal vertices in the two-dimensional parameter domain, and output the complete mapping relationship from the keyframe surface to the two-dimensional parameter domain; Based on the complete mapping relationship, the Beltrami coefficients of the mapping are obtained and used as global deformation parameters.

[0015] Optionally, mapping the target surface model to the two-dimensional parameter domain for all remaining frames throughout the cardiac cycle based on the global deformation parameters includes: Each remaining frame of the target surface model throughout the entire cardiac cycle is recorded as a target frame, and the global deformation parameters are used as the deformation descriptors for each target frame. Based on the geometric boundary conditions of each target frame and the deformation descriptor, the registration of each target frame with the two-dimensional parameter domain is performed.

[0016] The left ventricular myocardial surface registration method based on two-dimensional parameter domain mapping provided in this disclosure segmentes and reconstructs a dynamic three-dimensional surface sequence of the left ventricular myocardium from a short-axis image sequence of cardiac magnetic resonance imaging. The dynamic three-dimensional surface sequence is standardized to obtain a target surface model. Keyframe surfaces in the target surface model are mapped to a predefined two-dimensional parameter domain to obtain global deformation parameters. Based on the global deformation parameters, the remaining frames of the target surface model throughout the cardiac cycle are mapped to the two-dimensional parameter domain. This method, based on two-dimensional parameter domain mapping for left ventricular myocardial surface registration, drives the mapping process of the entire sequence by using the global deformation parameters of a keyframe surface mapping. It can establish a stable spatiotemporal vertex correspondence for the surfaces of all time frames in the two-dimensional parameter domain, thereby achieving temporal alignment of the surface sequence throughout the cardiac cycle and normalized registration of myocardial shapes between different cases.

[0017] The above description is merely an overview of the technical solution disclosed herein. In order to better understand the technical means of this disclosure and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this disclosure more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the left ventricular myocardial surface registration method based on two-dimensional parameter domain mapping provided in this embodiment of the disclosure.

[0020] Figure 2 This is a flowchart illustrating the method for reconstructing dynamic three-dimensional surface sequences provided in an embodiment of this disclosure.

[0021] Figure 3 This is a flowchart illustrating the method for obtaining a target surface model provided in an embodiment of this disclosure.

[0022] Figure 4 This is a flowchart illustrating the method for obtaining global deformation parameters provided in an embodiment of this disclosure.

[0023] Figure 5 A schematic flowchart illustrating the registration method for the remaining frames provided in this embodiment of the disclosure. Detailed Implementation

[0024] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0025] It should be understood that the following specific examples illustrate the implementation of this disclosure, and those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0026] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0027] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The drawings only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0028] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0029] Reference Figure 1 This application discloses a method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping, including: S100, a dynamic three-dimensional surface sequence for segmenting and reconstructing the left ventricular myocardium from a sequence of short-axis cardiac magnetic resonance images; S200 standardizes the dynamic three-dimensional surface sequence to obtain the target surface model; S300 maps the keyframe surfaces in the target surface model to a predefined two-dimensional parameter domain to obtain global deformation parameters; S400: Based on the global deformation parameters, the remaining frames of the target surface model throughout the cardiac cycle are mapped to the two-dimensional parameter domain; this step ensures that the mapping results of each frame are aligned with the keyframes in the parameter domain.

[0030] This application discloses a left ventricular myocardial surface registration method based on two-dimensional parameter domain mapping. By driving the mapping process of the entire sequence with the global deformation parameter of a keyframe surface mapping, a stable spatiotemporal vertex correspondence can be established for the surfaces of all time frames in the two-dimensional parameter domain. This enables temporal alignment of the surface sequence throughout the cardiac cycle and normalized registration of myocardial shapes among different cases. This method transforms the three-dimensional spatiotemporal registration problem into a stable correspondence establishment problem based on the same deformation parameter in the two-dimensional parameter domain. It can effectively overcome challenges such as large shape differences and indistinct features between individuals, providing a more robust and accurate geometric framework for left ventricular motion analysis. Compared with traditional registration methods in three-dimensional Euclidean space, this application avoids the registration challenges caused by individual anatomical differences and sparse surface features by transforming the three-dimensional spatiotemporal registration problem into a correspondence establishment problem in the two-dimensional parameter domain.

[0031] Among them, the global deformation parameter only needs to be calculated once, remains unchanged throughout the entire cardiac cycle, and serves as the uniform deformation generation kernel parameter throughout the cycle; the two-dimensional parameter domain serves as a standard motion representation space shared across cases, used for deformation data alignment and comparative analysis between different patients.

[0032] Reference Figure 2 The method S100, "Segmentation and Reconstruction of Dynamic Three-Dimensional Surface Sequences of Left Ventricular Myocardium from Short-Axis Cardiac Magnetic Resonance Image Sequences," specifically includes the following: S110, acquire a sequence of short-axis cardiac magnetic resonance images for a complete heartbeat cycle.

[0033] Among them, the cardiac magnetic resonance short-axis image sequence is a dynamic image sequence that contains images (usually 20-30 frames) at multiple time points throughout a complete cardiac cycle (from end-diastole to end-systole and back to end-diastole).

[0034] S120 performs left ventricular myocardial segmentation on each frame of the cardiac magnetic resonance short-axis image sequence to obtain the myocardial boundary contour.

[0035] Left ventricular myocardial segmentation is performed frame-by-frame. For each static image in this dynamic sequence, pixels belonging to the left ventricular myocardium are distinguished from other parts (such as blood, other heart structures, and the background) and marked. Specific segmentation methods can include: manual delineation (drawn manually by experienced physicians), semi-automatic interactive methods (the algorithm provides an initial outline, which is then manually corrected and confirmed), and fully automatic segmentation algorithms (completely performed by computer algorithms, such as deep learning networks based on U-Net).

[0036] In this embodiment, the myocardial boundary contour line includes the endocardial boundary contour line and the epicardial boundary contour line; the endocardial boundary contour line is the inner edge of the junction between the left ventricular cavity and the myocardium, and the epicardial boundary contour line is the outer edge of the junction between the myocardium and the pericardium or surrounding tissues. These two lines together define the boundary and thickness of the myocardial wall.

[0037] S130 uses a surface reconstruction algorithm to reconstruct the myocardial boundary contours of all frames, generating a dynamic three-dimensional surface sequence of the left ventricular myocardium.

[0038] In this embodiment, the obtained dynamic three-dimensional surface sequence is raw data, without parameterization, and each frame is independent. Specifically, the dynamic three-dimensional surface sequence is {S1,..., St..., ST}, where St represents the left ventricular surface at time point t.

[0039] Reference Figure 3 The method for "standardizing the dynamic three-dimensional surface sequence to obtain the target surface model" in S200, specifically the method for obtaining the target surface model, includes: S210, construct a preset standard model.

[0040] Specifically, a preset standard model is constructed based on a historical database. The preset standard model is a three-dimensional mesh with a preset number of vertices and a fixed topology. Each vertex has a unique index (i.e., a standard position). In other words, the preset standard model is a predefined three-dimensional mesh template for the left ventricle. It not only has the correct topology (a zero-genus surface with two openings), but also has predefined feature points and an inherent vertex index order.

[0041] The vertices include at least the apex and the mitral valve annulus. The historical database can be an average cardiac geometry model based on a large amount of population data.

[0042] S220: Based on a preset standard model, establish a feature point mapping relationship with consistent vertex indices between the dynamic three-dimensional surface sequence and the preset standard model, and adjust the surface of the preset standard model according to the feature point mapping relationship to obtain the target surface model.

[0043] The specific steps include: S221, marking the feature points corresponding to the vertices in the dynamic three-dimensional surface sequence, and recording them as target feature points; S222, adjusting the surface of the preset standard model according to the mapping relationship between the target feature points and the vertices to obtain the target surface model, that is, finding a unique corresponding position for each vertex S[i] in the preset standard model on the surface of the dynamic three-dimensional surface sequence.

[0044] For S222, specifically, it includes: adjusting the surface of a preset standard model using rigid body transformation or non-rigid transformation methods based on the mapping relationship between target feature points and vertices to obtain a target surface model. The shape of the target surface model is consistent with the shape of the dynamic 3D surface sequence, and the vertex indices and topological structure in the target surface model are completely identical to those of the preset standard model.

[0045] For example, a predefined number of vertices in the preset standard model includes 5 points: one apex (the lowest vertex of the ventricle) and typically 4 mitral valve annulus points, namely the midpoints of the anterior, posterior, lateral, and septal walls. This step is usually completed in one go when creating the standard model. Then, the positions of the target feature points with the same definition are identified on the dynamic 3D surface sequence through manual interactive clicking or automatic detection algorithms. That is, the obtained target feature points also include 5 points, and the order is consistent with the vertices in the preset standard model.

[0046] The method of adjusting the surface of a preset standard model using rigid body transformation to obtain the target surface model specifically includes: using Protodyakonov analysis or the least squares method to calculate an optimal rigid transformation (rotation R, translation T, uniform scaling s). The objective is to minimize... After R, T, s transformation and The positional error between them, find R, T, s so that Minimum.

[0047] The calculated rigid transformation is applied to all vertices of the entire preset standard model to obtain a preliminarily aligned target surface model; S1: S1=s R S+T. At this point, the target surface model and the dynamic 3D surface sequence are basically aligned at the anatomical landmarks, providing a good initial position for the next step of non-rigid registration and avoiding getting trapped in local optima.

[0048] Among them, the non-rigid deformation registration method is a method for adjusting the surface of a preset standard model to obtain a target surface model. The specific iterative steps are as follows: 1) For each vertex v of the preset standard model i Find the geometrically closest point c on the surface of a dynamic three-dimensional surface sequence. i1) KD-tree can be used to accelerate the process; 2) Remove obviously unreasonable pairs (e.g., distances exceeding a threshold, opposite normal directions); 3) Solve for deformation, the goal is to find a set of vertex displacements {d}. i}, so that: v i + d i Get as close to c as possible i (That is, ensure it fits the target) and minimize the displacement between adjacent vertices (keep the surface smooth and prevent excessive folding). 4) Calculate the displacement {d} i} Add to all vertices of the preset standard model; 5) Repeat the above steps until the overall displacement is less than a certain threshold, or the maximum number of iterations is reached, to obtain the target surface model. The shape of the target surface model is highly similar to the dynamic three-dimensional surface sequence, but its vertex index and connection topology are completely consistent with the preset standard model. At this time, it means that the correspondence has been established, that is, the final position of the i-th vertex S[i] in the target surface model is its corresponding anatomical position on the surface of the dynamic three-dimensional surface sequence.

[0049] Reference Figure 4 The S300 method of "mapping the keyframe surfaces in the target surface model to a predefined two-dimensional parameter domain to obtain global deformation parameters" includes the following methods for obtaining global deformation parameters: S310, a predefined two-dimensional parameter domain that is topologically homeomorphic to dynamic three-dimensional surface sequences.

[0050] The two-dimensional parameter domain can be a unit topological disk, a unit topological sphere, or a planar topological rectangle. Specifically, based on the topological structure of the left ventricular myocardium, which is a zero-genus surface with a boundary, a two-dimensional parameter domain that is topologically homeomorphic to it can be defined. Typically, a unit disk can be chosen; for closed surfaces, a unit sphere can also be used; other domains such as planar rectangles are also applicable.

[0051] S320, determine the key frame surface in the target surface model. The key frame surface is either the left ventricular end-diastolic surface or the end-systolic frame surface.

[0052] S330 maps the keyframe surface to the two-dimensional parameter domain to obtain global deformation parameters.

[0053] For the S330, specifically including: S331, identify the boundary edges and internal edges on the keyframe surface to be mapped, and determine the total length of the output boundary and the cumulative length of each boundary vertex.

[0054] Specifically, the boundary edges and internal edges on the triangular mesh surface of the keyframe to be mapped are identified, and the ordered set of its boundary vertices is determined. Based on the set of boundary vertices, the length of each boundary edge is calculated, and the cumulative total length of the entire surface boundary is calculated accordingly. The total boundary length and the cumulative arc length of each boundary vertex are then output.

[0055] S332, based on the total length of the boundary and the cumulative length of each boundary vertex, map the boundary of the keyframe surface to the fixed boundary shape of the target two-dimensional parameter domain, and obtain the predetermined coordinates of all boundary vertices in the two-dimensional parameter domain.

[0056] Specifically, for the case where the two-dimensional parameter domain is a unit disk, each boundary vertex is assigned a unique central angle based on the proportion of its cumulative arc length to the total length, and its two-dimensional coordinates on the unit circle are calculated. The predetermined coordinates of all boundary vertices on the two-dimensional parameter domain are then output.

[0057] S333, based on predetermined coordinates and the Laplace-Beltrami operator, constructs a system of linear equations about the coordinates of the interior vertices.

[0058] The coefficient matrix of the linear equation system is constructed by calculating the cotangent weight of each edge in the triangular mesh, and the right-hand side of the equation is determined by the known coordinates of the boundary vertices.

[0059] S334 solves the system of linear equations to obtain the two-dimensional coordinates of all internal vertices in the two-dimensional parameter domain, and outputs the complete mapping relationship from the keyframe surface to the two-dimensional parameter domain.

[0060] S335, based on the complete mapping relationship, obtain the Beltrami coefficients of the mapping and use them as global deformation parameters.

[0061] Specifically, local isothermal coordinates are introduced on the surface and in the parameter domain, respectively. A differential operator is constructed by calculating the partial derivatives of the mapping with respect to the isothermal coordinates. Based on the ratio of the differential operator, the complex-valued Beltrami coefficient μ(z) defined at each point on the surface is calculated to quantify the local angular distortion characteristics of the mapping at various points globally. This application elevates the Beltrami coefficient from a mapping description parameter to a parameter generated by surface deformation in a regular parameter domain, ensuring the temporal consistency of the registration results and improving the overall accuracy of the method. It provides a stable and reliable data foundation for myocardial strain analysis, cardiac function assessment, and computer-aided diagnosis, and has significant application value in the fields of medical image analysis and computational cardiology.

[0062] Specifically, taking the case where the keyframe is the end-diastolic frame and the parameter domain is the unit disk as an example, firstly, a graph search algorithm is used to identify the internal edges and boundary edges in the triangular mesh. Let the set of boundary points of the left ventricular surface be... Then calculate the total boundary length according to the first formula. The first formula is: ,in Indicates connection to vertices and The length of the boundary edge, where n is the total number of fixed anatomical points. Let i be the i-th fixed dissection point. Then, calculate the central angle corresponding to each boundary vertex according to the second formula. The second formula is: , ,in To start from the beginning To the top The cumulative boundary length, Indicates connection to fixed anatomical points and The length of the boundary edge, For the first A fixed anatomical point, For the first A fixed anatomical point.

[0063] After setting the boundary conditions, the discrete differential geometry method of the Laplace-Beltrami operator is used to calculate the coordinates of the internal vertices on the target disk using the cotangent weights.

[0064] Wherein, the cotangent weight matrix of edge (i,j) for: .in, , Let (i,j) be the two opposite angles of the edge (i,j) in two adjacent triangles. An interior edge is an edge whose two vertices are not on the boundary. , These are the two opposite angles of the side (i,j) (i.e., the angles opposite the side in the two triangles to which the side belongs). A boundary edge is an edge with at least one vertex on the boundary; in this case, the edge usually belongs to only one triangle. Let be the angle opposite to a side in the triangle.

[0065] Linear system: Let the mapping f map vertex i to two-dimensional coordinates. For each internal vertex Its parameter coordinates satisfy: , Let i be the set of neighborhood points of point i, i.e., satisfying and .

[0066] For boundary vertices, The boundary of the unit disk is fixed (i.e., the boundary of the unit disk is known). Solving this sparse linear system with respect to coordinates u and v yields the parametric coordinates of all internal vertices, i.e., the coordinates (u, v) of each vertex on the unit disk. Specifically, the above formula, after simplification, becomes: A·U=B u and A·U=B v Where A is an (M×M) sparse coefficient matrix (M is the number of interior points), U is the u coordinate of the interior point (to be solved), and V is the v coordinate of the interior point (to be solved). By sparsely solving the linear equation system, the parametric coordinates of all interior vertices are obtained, that is, the coordinates (u, v) of each vertex on the unit disk.

[0067] By solving a linear system, the quasi-conformal mapping of the left ventricular myocardial surface is transformed into a unit topological disk. For this mapping, the corresponding Beltrami coefficients can be calculated. This coefficient is a complex function describing the local angular distortion of the quasi-conformal mapping, and its specific calculation method is as follows: Let... Left ventricular curved surface To topological disk The mapping on the surface Introducing isothermal coordinates above On the disk Introducing isothermal coordinates above And define the following differential operator: , For about The conjugate derivative of , For about The derivative of .

[0068] In this application, the Beltrami coefficient (A complex-valued function) is defined by the following equation: .

[0069] Reference Figure 5 For the S400 method of "mapping the target surface model to the two-dimensional parameter domain for all remaining frames in the entire cardiac cycle based on global deformation parameters", the registration method for the remaining frames specifically includes: S410, each remaining frame of the target surface model throughout the entire cardiac cycle is recorded as the target frame, and the global deformation parameters are used as the deformation descriptors for each target frame.

[0070] S420 performs registration between each target frame and the two-dimensional parameter domain based on the geometric boundary conditions and deformation descriptors of each target frame.

[0071] Specifically, S420 includes: S421, acquire each target frame The set of boundary vertices.

[0072] S422, based on the boundary vertices of the keyframe surface in the two-dimensional parameter domain The mapping position on the surface determines the target position of the corresponding boundary vertex of the current frame surface (the current target frame) in the two-dimensional parameter domain. S423, based on the deformation descriptor and target position, establish a Beltrami equation for the mapping from the current frame surface to the two-dimensional parameter domain, requiring that the local deformation mode of the mapping remains consistent with the keyframe. This equation is based on the mapping... The specific form of expression is an unknown quantity; S424, Solve the Beltrami equation to obtain the Beltrami coefficients. Quasi-conformal mapping of (i.e., deformation descriptors) and boundary conditions Output the quasi-conformal mapping from the current frame surface to the two-dimensional parameter domain. .

[0073] Obtain the Beltrami coefficients of keyframes Then, this coefficient is fixed as the global conformal deformation parameter driving the registration of all subsequent frames. For each remaining frame surface... Mapping it to the same two-dimensional parameter domain When this happens, the Beltrami coefficient of the keyframe is used directly. As a known deformation descriptor, combined with the geometric boundary conditions of the current frame, its quasi-conformal mapping is determined by solving the mapping equation. This process eliminates the need to recalculate the Beltrami coefficients for each frame. Through the same coefficient-driven mechanism described above, the mapping of all frames is uniformly constrained by... Under the defined local angular distortion pattern, all mappings naturally achieve vertex alignment in the two-dimensional parameter domain when all mappings are complete, thus automatically and accurately establishing the spatiotemporal correspondence throughout the entire cardiac cycle. This method allows for precise mapping of each frame... A mapping can be found for each. This ensures that the deformation descriptors are all identical and that the boundary conditions corresponding to each frame are satisfied, i.e., the conditions of each target frame are satisfied. Boundary points mapped to the two-dimensional parameter domain The specified locations on the boundary (these locations are the same as the boundary point mapping locations of the keyframe).

[0074] In this embodiment, the Beltrami equation establishes a mathematical relationship between local deformation features (μ) and global mapping (f). Knowing μ(z) is equivalent to knowing the local mapping specification, and knowing the boundary conditions is equivalent to knowing the boundary. By solving the equation, it is possible to determine how to determine the mapping that satisfies the specification within the entire two-dimensional parameter domain. Here, the boundary conditions are the fixed positions of the current frame boundary in the two-dimensional parameter domain D.

[0075] This method generates a unified parametric mapping for surfaces with different geometries in each frame by fixing local deformation features and boundary conditions. Although all frames share the same local deformation pattern, the surface geometry of each frame is different (like a heart contracting / diffusing). In this embodiment, the boundary conditions ensure that the mapping boundary correspondences are consistent, meaning that the boundary vertices of all frames are mapped to the same position in the parameter domain, while adapting to the current geometry; that is, the mapping needs to adapt to the actual 3D shape of the surface in the current frame.

[0076] In this application, by using the fixed Beltrami coefficient as the driving parameter, the present invention not only ensures the consistency and stability of the registration results in time, but also significantly improves the accuracy and robustness of the overall method, thereby providing a stable and reliable data foundation for myocardial strain analysis, cardiac function assessment and computer-aided diagnosis, and has important application value in the fields of medical image analysis and computational cardiology.

[0077] The method disclosed in this application can normalize all information to the same two-dimensional parameter domain D, and only requires one time-consuming optimization in the keyframe. The remaining frames solve a linear or nonlinear system, which is extremely fast. At the same time, it effectively ensures that the mapping of all frames shares the same local deformation pattern. Regardless of the case, whether the actual shape of the left ventricle is ellipsoidal or more complex, it will eventually be mapped onto the same coordinate paper. Deformation parameters (such as strain) of different patient groups (such as healthy vs. heart failure) can be compared in the same region on D. The average deformation pattern of healthy people at each coordinate point on D can be calculated as a standard template, and then the data of new patients can be mapped onto it for comparison, intuitively identifying local abnormal areas.

[0078] This invention establishes a parameterized template aligned with a standard model and, for the first time, uses the Beltrami coefficient as a single deformation-driving parameter shared throughout the entire cardiac cycle, creating a consistent surface correspondence across the entire cycle within a unified two-dimensional parameter domain. Compared to existing frame-by-frame independent registration methods, this invention avoids parameter redundancy and error accumulation caused by repeatedly solving for deformation locations, achieving a more stable temporal correspondence. It transforms the three-dimensional spatiotemporal registration problem into a consistency constraint problem in the two-dimensional parameter domain, fully utilizing the geometric characteristics of the left ventricular myocardial surface as a two-dimensional Riemannian manifold, thus improving registration accuracy, robustness, and computational efficiency. The motion representation model constructed in the unified parameter domain makes deformation data comparable across different time frames and cases, providing a unified geometric basis for myocardial strain analysis and clinical quantitative assessment.

[0079] Furthermore, in the unified parameter domain, based on the established vertex correspondence, the displacement vector field of the corresponding vertices in the parameter domain between each time frame can be calculated, and a two-dimensional deformation distribution map of the left ventricular myocardium in a complete cardiac cycle can be constructed accordingly, realizing a unified motion representation across time frames and across cases.

[0080] Since each frame mapping establishes a consistent correspondence of vertex indices driven by fixed Beltrami coefficients, for any vertex in the parameter domain... Each has a corresponding keyframe vertex position. Let the vertex mapping of the keyframe be... Then in the parameter domain In the middle, the relative displacement vector: By analyzing the parameter domain By performing the above calculations on all vertices, the first... Two-dimensional displacement vector field of a frame relative to a keyframe Furthermore, by repeating the above calculations for all time frames within the entire cardiac cycle, a two-dimensional displacement vector sequence of the complete cardiac cycle can be obtained. ,in This represents the total number of frames in a cardiac cycle. In real-world data, a cardiac cycle typically consists of 19-35 frames.

[0081] Because a stable vertex correspondence is established for each time frame within a unified parameter domain, the displacement vector field is unaffected by rigid displacement or rotation in the three-dimensional Euclidean space. This eliminates the temporal drift problem caused by independent frame-by-frame optimization and allows for direct use in motion alignment and comparative analysis between different time frames and different cases. Through this method, the present invention achieves a structured characterization of left ventricular myocardial motion within a unified two-dimensional parameter domain, providing a stable and consistent geometric basis for subsequent strain analysis and clinical quantitative assessment.

[0082] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0083] The basic principles of this disclosure have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this disclosure are merely examples and not limitations, and should not be considered as essential features of each embodiment of this disclosure. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the scope of this disclosure to the necessity of employing the aforementioned specific details for implementation.

[0084] In this disclosure, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The block diagrams of devices, apparatuses, devices, and systems involved in this disclosure are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as "comprising," "including," "having," etc., are open-ended terms meaning "including but not limited to," and are used interchangeably with them. The terms "or" and "and" as used herein refer to the terms "and / or," and are used interchangeably with them unless the context clearly indicates otherwise. The term "such as" as used herein refers to the phrase "such as but not limited to," and is used interchangeably with it.

[0085] Additionally, as used herein, the "or" used in a list of items beginning with "at least one" indicates a separate list, such that a list of, for example, "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not imply that the described example is preferred or better than other examples.

[0086] It should also be noted that in the systems and methods of this disclosure, the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered as equivalent solutions to this disclosure.

[0087] Various changes, substitutions, and modifications can be made to the technology described herein without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of this disclosure is not limited to the specific aspects of the processes, machines, manufactures, events, means, methods, and actions described above. Currently existing or later-developed processes, machines, manufactures, events, means, methods, or actions that perform substantially the same function or achieve substantially the same result as the corresponding aspects described herein can be utilized. Therefore, the appended claims include such processes, machines, manufactures, events, means, methods, or actions within their scope.

[0088] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of this disclosure. Therefore, this disclosure is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0089] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this disclosure to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping, characterized in that, include: Dynamic three-dimensional surface sequences of left ventricular myocardium segmented and reconstructed from short-axis cardiac magnetic resonance imaging sequences; The dynamic three-dimensional surface sequence is standardized to obtain the target surface model; The keyframe surfaces in the target surface model are mapped to a predefined two-dimensional parameter domain to obtain global deformation parameters; Based on the global deformation parameters, the target surface model is mapped to the two-dimensional parameter domain for all remaining frames throughout the cardiac cycle.

2. The method for registration of left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 1, characterized in that, The dynamic three-dimensional surface sequence for segmenting and reconstructing the left ventricular myocardium from short-axis cardiac magnetic resonance imaging sequences includes: Obtain a sequence of short-axis magnetic resonance images of the heart for a complete cardiac cycle; Left ventricular myocardial segmentation was performed on each frame of the cardiac magnetic resonance short-axis image sequence to obtain the myocardial boundary contour line; The myocardial boundary contours of all frames are reconstructed to generate a dynamic three-dimensional surface sequence of the left ventricular myocardium.

3. The method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 1, characterized in that, The standardization process for the dynamic three-dimensional surface sequence to obtain the target surface model includes: Construct a pre-defined standard model; Based on the preset standard model, a feature point mapping relationship with consistent vertex indices is established between the dynamic three-dimensional surface sequence and the preset standard model. The preset standard model is then adjusted according to the feature point mapping relationship to obtain the target surface model.

4. The method for registration of left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 3, characterized in that, The construction of the preset standard model includes: A preset standard model is constructed based on a historical database. The preset standard model is a three-dimensional mesh with a preset number of vertices and a fixed topology, wherein each vertex has a unique index.

5. The method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 4, characterized in that, The step of establishing a feature point mapping relationship with consistent vertex indices between the dynamic 3D surface sequence and the preset standard model based on the preset standard model, and adjusting the surface of the preset standard model according to the feature point mapping relationship to obtain the target surface model includes: In the dynamic three-dimensional surface sequence, the feature points corresponding to the vertices are marked and denoted as target feature points; Based on the mapping relationship between the target feature points and the vertices, the preset standard model is surface-adjusted to obtain the target surface model.

6. The method for registration of left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 5, characterized in that, The apex includes at least the apex of the heart and the mitral valve annulus.

7. The method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 5, characterized in that, The step of adjusting the surface of the preset standard model according to the mapping relationship between the target feature points and the vertices to obtain the target surface model includes: Based on the mapping relationship between the target feature points and the vertices, the preset standard model is adjusted using rigid body transformation or non-rigid transformation methods to obtain the target surface model; The shape of the target surface model is consistent with the shape of the dynamic three-dimensional surface sequence, and the vertex index and topology of the target surface model are exactly the same as those of the preset standard model.

8. The method for registration of left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 1, characterized in that, The step of mapping the keyframe surfaces in the target surface model to a predefined two-dimensional parameter domain to obtain global deformation parameters includes: A two-dimensional parameter domain is predefined that is topologically homeomorphic to the dynamic three-dimensional surface sequence; Determine the keyframe surfaces in the target surface model, wherein the keyframe surfaces are the left ventricular end-diastolic surface or the end-systolic frame surface; The keyframe surface is mapped to the two-dimensional parameter domain to obtain global deformation parameters.

9. The method for registering left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 8, characterized in that, The step of mapping the keyframe surface to the two-dimensional parameter domain to obtain global deformation parameters includes: Identify the boundary edges and internal edges on the keyframe surface to be mapped, and determine the total length of the output boundary and the cumulative length of each boundary vertex; Based on the total length of the boundary and the cumulative length of each boundary vertex, the boundary of the keyframe surface is mapped to the fixed boundary shape of the target two-dimensional parameter domain to obtain the predetermined coordinates of all boundary vertices in the two-dimensional parameter domain. Based on the predetermined coordinates and the Laplace-Beltrami operator, a system of linear equations is constructed regarding the coordinates of the interior vertices; Solve the system of linear equations to obtain the two-dimensional coordinates of all internal vertices in the two-dimensional parameter domain, and output the complete mapping relationship from the keyframe surface to the two-dimensional parameter domain; Based on the complete mapping relationship, the Beltrami coefficients of the mapping are obtained and used as global deformation parameters.

10. The method for registration of left ventricular myocardial surfaces based on two-dimensional parameter domain mapping according to claim 9, characterized in that, The step of mapping the target surface model to the two-dimensional parameter domain for all remaining frames throughout the cardiac cycle based on the global deformation parameters includes: Each remaining frame of the target surface model throughout the entire cardiac cycle is recorded as a target frame, and the global deformation parameters are used as the deformation descriptors for each target frame. Based on the geometric boundary conditions of each target frame and the deformation descriptor, the registration of each target frame with the two-dimensional parameter domain is performed.

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