Computer-implemented method, computer program and imaging system for centerline calculation from 3D models of tubular structures

Abstract

A computer-implemented method according to the present invention, comprising receiving (100) a patient-specific volumetric image comprising structural information about the patient's vessels represented in voxels, including extracting and / or presenting patient-specific data using a centerline, comprises a correction step (150), which comprises an iterative process including at least an operation of centering (552) the points defining the centerline by further locating them from the most proximal plane defined in the geometry, and an operation of equalizing (553) the points defining the centerline by approximating each point to the average position of its neighbors. The present invention further relates to a computer program product and an imaging system.

Description

[Technical Field]

[0001] The present invention relates to a computer-implemented method, computer program product, and imaging system for centerline calculation from 3D models of tubular structures, which is particularly useful for simulating blood flow using computational fluid dynamics in vascular geometries extracted from medical 3D volumes of contrast-filled arteries and for enhancing visualization of blood vessels in medical 3D volumes. [Background technology]

[0002] Cardiovascular disease is one of the leading causes of death worldwide. The development of computed tomography (CT) has enabled a non-invasive approach for accurate diagnosis in patients with suspected ischemic heart disease.

[0003] CT scans are commonly represented as 3D volume images. Such 3D volume images represent a physical quantity as a function of three spatial coordinates. In a digital volume image, each sample (voxel) represents that quantity measured at a specific location. The image is composed of a series of 2D spatial slices through the object. A slice is generally represented as an image matrix of pixels (X and Y coordinates). The slice number indicates the Z coordinate.

[0004] Interpreting CT images and diagnosing cardiovascular diseases are challenging tasks that require highly trained physicians. A common problem is that interpretation of the projections visible on CT images requires highly skilled radiologists, while diagnosing cardiovascular diseases requires skilled cardiologists. There is a shortage of people with competence in both fields. Therefore, computer-assisted techniques are needed.

[0005] One method for computer-assisted diagnosis of cardiac pathologies is to generate 3D models of blood vessels for diagnostic support. In particular, in the field of cardiac pathology, detailed 3D models of coronary arteries are required. Detailed models enable highly accurate estimation of patient-specific anatomical and functional features, such as hemodynamic parameters. In the current state of the art, there are numerous techniques that utilize computational fluid dynamics (CFD) for blood flow simulation. The geometry of blood vessels presented in a 3D volumetric image can be represented as a subset of the 3D image's voxels, a surface mesh, a volume mesh, or a point cloud. An example of a CFD technique used to calculate fractional flow reserve (FFR) from a 3D model of the coronary arteries obtained by coronary computed tomography angiography (CCTA) is disclosed in U.S. Patent No. 5,649,999.

[0006] A centerline is defined as a polygonal chain of points, calculated at sub-voxel resolution. It represents the geometric location along the length of a vessel's cross-section center. It is used in the simulation and generation of vessel image representations. Methods for identifying centerlines have been widely developed and are known in the art, for example, from U.S. Patent Nos. 5,629,999; 5,629,999; 5,629,999; and 5,629,999.

[0007] Objects with curved 3D shapes, when represented in CT images with limited resolution, are prone to numerous artifacts that distort the shape of the centerline. One common artifact that adversely affects known algorithms for centerline identification is the so-called blooming artifact, which is caused by the high density of calcified atherosclerotic plaque and the high density of the contrast agent applied to the patient for imaging. The former is most severe when the contrast agent is concentrated in a specific region. Another common artifact is the so-called motion artifact, which frequently appears when imaging including the heart. Motion artifacts are caused by patient movement during the imaging process. Misregistration artifacts appear as blurring, streaks, or shadows. Blurring can also occur due to patient movement during a radiological examination, causing wave-like distortions in blood vessels.

[0008] Accurate 3D models of coronary arteries are crucial for accurate simulations that enable the diagnosis of cardiovascular disease. To achieve both accurate 3D modeling and accurate simulation, a method for centerline extraction from geometry is required. The centerline of a tubular object is defined as a polygonal chain, i.e., a curve, specified by a series of points (i.e., vertices) connected by edges. Because we consider only 3D models, these points always exist in 3D space. Both the geometry and the centerline are represented with subvoxel accuracy. The first and last points of the centerline must be at the beginning and end of the geometry, respectively. All points and their corresponding edges must be within and centered within the cross-section of the geometry. Because coronary arteries consist of multiple branches, so too must their 3D models. Therefore, multiple centerlines must be extracted for each coronary artery, one for each branch.

[0009] Centerline extraction is an important part of the 3D model creation process. The centerlines of 3D vascular models are used for segmentation tasks, topology analysis, and generating appropriate vascular representations called curved planar reconstructions (CPRs) that are used by physicians during diagnosis. Therefore, constructing appropriate centerlines for coronary arteries is important for diagnosing vascular diseases, estimating the size of coronary artery stenoses, and simulating blood flow.

[0010] One of the most common methods for calculating centerlines taking into account the geometry of blood vessels utilizes Voronoi diagrams of 3D geometric models, as disclosed in Non-Patent Document 1, and is provided as a practical computer program library documented and available online at http: / / www.vmtk.org / tutorials / Centerlines.html. The main advantage of this approach is that it provides high-quality, mathematically well-defined centerlines at the expense of providing a geometric model of the vessel. However, this method typically fails when the vessel is thin and curved.

[0011] Another approach consists in extracting the centerline directly from the provided image. This makes it possible to omit the geometric extraction step in the process, at the expense of the quality of the centerline. One example is a method disclosed in Non-Patent Document 2, which feeds local patches of the image to a neural network and attempts to identify the next point of the centerline, the bifurcation point of the vessel, and the possible end positions in an iterative process. Another example method disclosed in Patent Document 3 extracts the entire centerline by applying a filter to the image to identify the vessel position and then applying a thinning procedure (skeletonization) to find the centerline. Additional applicable methods are disclosed, for example, in Non-Patent Document 3. The main disadvantage of these methods is their high sensitivity to anatomical differences between patients and image acquisition. Non-Patent Document 4 discloses a computer-implemented method for identifying the centerline, which includes the steps of receiving a patient-specific volumetric image comprising structural information about the patient's vessels represented in voxels based on a cube model, recovering the three-dimensional geometry of at least one vessel, and extracting a skeleton graph from the geometry to identify the centerline. The method claims to operate directly on mesh regions, eliminating the need for image upsampling. [Non-Patent Document 5] discloses a geometry-based framework for extracting curve skeletons from mesh surfaces. The extraction is applied directly to mesh regions and does not require voxelization. This approach works well as long as the vessels fit well to an elliptical model. Otherwise, model inadequacies can introduce significant errors into the centerline trajectory.

[0012] Other related methods include US Pat. No. 6,269,649, which discloses a system for registering a vessel model from an image dataset based on a joint model with a reference object model and a vessel model from a centerline described by a plurality of control points.

[0013] Patent document 7 discloses an imaging system including a sub-resolution lumen narrowing detector that detects sub-resolution narrowing of a blood vessel lumen in an image volume by centerline profile analysis and calculates a sub-resolution determined diameter by correcting the approximate visible lumen diameter with the detected sub-resolution narrowing.

[0014] US Patent No. 6,269,649 discloses an image processing system configured to generate a model of a tubular object from a volumetric image, the system comprising a volume image acquisition unit, a geometry extraction unit and a centerline generator.

[0015] US Patent No. 6,299,643 discloses a system and method for identifying the centerline of a tubular structure from volumetric data of the vessel, where a contrast agent is injected into the bloodstream to enhance imaging of the centerline.

[0016] An active contour model is disclosed that can be applied to identify the contours of blood vessels defined within image data by normalizing the image data with respect to a starting point. [Prior art documents] [Patent documents]

[0017] [Patent Document 1] European Patent No. 3820357 [Patent Document 2] US Patent Application Publication No. 2017 / 0018116 [Patent Document 3] U.S. Patent No. 9,129,417 [Patent Document 4] Chinese Patent No. 108133478 [Patent Document 5] U.S. Patent No. 11,069,078 [Patent Document 6] European Patent No. 2074585 [Patent Document 7] European Patent No. 3245632 [Patent Document 8] European Patent No. 3723041 [License 9] U.S. Patent and Trademark Office Publication No. 2013 / 0064435 [Non-licensed literature]

[0018] [Non-licensed Document 1] Antiga, Luca. "Patient-specific modeling of geometry and blood flow in large arteries." Politecnico di Milano (2002) [Non-licensed Document 2] Zhang, Pengyue, Fusheng Wang and Yefeng Zheng. "Deep Reinforcement Learning for Vessel Centerline Tracing in Multi-modality 3D Volumes." MICCAI (2018) [Non-licensed Document 3] Xiong G, Sun P, Zhou H, Ha S, Hartaigh BO, Truong QA, Min JK. "Comprehensive Modeling and Visualization of Cardiac Anatomy and Physiology from CT Imaging and Computer Simulations." IEEE Trans Vis Comput Graph.2017 Feb;23(2):1014-1028.doi:10.1109 / TVCG.2016.2520946.Epub 2016 Feb 5.PMID:26863663;PMCID:PMC4975682 [Non-licensed Document 4] YIN WANG ET AL: "3-D Quantitative Vascular Shape Analysis for Arterial Bifurcations via Dynamic Tube Fitting", IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, IEEE, USA, vol.59, no.7, July 2012(2012-07), pages1850-1860,XP01 1447498,ISSN:0018-9294,DOI:10.1 109 / TBME.2011.2179654 [Non-patent document 5] OSCAR KIN-CHUNG AU ET AL: "Skeleton extraction by mesh contraction", ACM TRANSACTIONS ON GRAPHICS, ACM, NY, US, vol. 27, no. 3, August 2008 (2008-08), pages 1-10,XP058355353,ISSN:0730-0301,DOI:10.1145 / 1360612.1360643 Summary of the Invention [Problem to be solved by the invention]

[0019] Known methods of centerline generation and correction are prone to failure near bends, narrowing or other changes in dimensions, or other abnormalities that cause the vessel to differ significantly from the assumed model (e.g., elliptical cross section).

[0020] It is an object of the present invention to enhance known methods and improve the mechanism of centerline generation to reduce the need for manual correction. [Means for solving the problem]

[0021] A computer-implemented method according to the present invention comprises the steps of receiving a patient-specific volumetric image comprising structural information about the patient's blood vessels represented in voxels, recovering the three-dimensional geometry of at least one blood vessel, extracting a skeletal graph from the geometry, identifying end points of the at least one blood vessel to identify an inlet and at least one outlet, calculating at least one initial centerline of the at least one blood vessel, the at least one initial centerline being defined by points and calculated with sub-voxel resolution, correcting the at least one initial centerline with sub-voxel accuracy to obtain a corrected centerline, and outputting and using the corrected centerline to extract and / or present patient-specific data. According to the present invention, correcting the at least one initial centerline comprises an iterative process including operations of centering and equalizing at least the points defining the centerline. The centering points defining the centerline involve locating them away from the most proximal surface defined within the geometry. Equalization points, which define the centerline, involve moving each point closer to the average position of its neighbors. Centering and equalization are performed sequentially until a predetermined stopping condition is met. Centering keeps the centerline points equidistant to the vessel wall, i.e., at the center of the vessel. Equalization results in a centerline that better corresponds to the direction of blood flow and prevents shape assumptions (which can result in erroneous simulations). By sequentially performing the centering and equalization operations in an iterative manner, a centerline can be obtained, which is useful in fully or at least mostly automatic simulations.

[0022] The step of calculating at least one initial centerline includes the steps of checking the continuity of the skeleton graph and, if necessary, correcting the skeleton graph by connecting disconnected components, and identifying the initial centerline from the skeleton graph as the shortest path between the inlet and the outlet. This series of steps allows for the elimination of certain types of errors resulting from insufficient imaging. This approach does not rely on a vascular model and is therefore not affected by unusual or pathological shapes of blood vessels. In particular, the cross section of the blood vessel needs to be modeled as an ellipse.

[0023] Advantageously, the iterative process of correcting comprises applying an image force to the centerline points, centering comprises applying an image retraction force to the centerline points pushing the points away from the most proximal point of the geometric shape, and equalization consists of applying an image pulling force to the centerline points towards the adjacent points so that the points are pushed towards the average position of the two adjacent points.

[0024] The stopping condition is advantageously reaching a predetermined number of iteration steps. This type of stopping condition requires low power consumption when it is tested. An alternative stopping condition involves analysis of the point convergence to a stable position.

[0025] Advantageously, the step of recovering the three-dimensional geometry includes generating a surface mesh representation of the vessel from the volumetric image, which facilitates the calculations required for centering and facilitates presentation to the physician if manual enhancement is required. Alternative volumetric representations have advantageous effects that exist for use in simulating blood flow.

[0026] Advantageously, the step of extracting a skeleton graph from the geometry comprises the steps of voxelizing the geometry to obtain a volumetric representation of the vessel of interest, skeletonizing the volume to obtain a volumetric skeleton representation of the vessel, and creating a skeleton graph from the volumetric skeleton representation. In tests, this approach appears to be faster and more robust than Voronoi methods traditionally used in the art. This is particularly true in regions of vessel bends and vessel stenosis.

[0027] Advantageously, the identification of the endpoints involves an automatic breadth-first search of the geometric nodes and identifying vessel inlets and outlets using thickness gradients as a criterion, This approach allows for robust automatic or semi-automatic assignment of endpoints and orientation of the skeletal graph.

[0028] Advantageously, the user is prompted for the approximate location of the entrance, and the identification of the endpoints involves selection of the entrances aided by filtering the endpoint candidates based on the approximate location provided by the user, thus making the operation fast with very little effort from the user.

[0029] Advantageously, the corrected centerline points are subjected to post-processing comprising at least one operation selected from the group comprising: resampling the centerline, smoothing the positions of the centerline points in space, calculating metadata of the centerline points and pruning, where pruning reduces the memory consumption required to execute the method, while the metadata is useful for visualization of the 3D geometry.

[0030] A computer program product according to the invention comprises a set of instructions which, when loaded into a computer's memory, causes the computer to carry out the method according to the invention.

[0031] An image processing system according to the present invention, comprising a volumetric image acquisition unit, a geometry extraction unit, a centerline generator and a diagnostic assistance module, and configured to generate a model of a tubular object from a volumetric image, is adapted to implement the method according to the present invention.

[0032] Advantageously, the volumetric image acquisition unit is a computer module adapted to receive images via a telecommunications network.

[0033] The volumetric image acquisition unit is advantageously an imaging device, which is advantageously selected from the group comprising a computed tomography scanner, a photon counting computed tomography scanner, a magnetic resonance scanner, a positron emission tomography scanner, a single photon emission computed tomography scanner and an ultrasound imaging device.

[0034] The present invention will now be described in detail with reference to the following drawings: [Brief explanation of the drawings]

[0035] [Figure 1] 1 shows a flowchart of a method for generating a centerline. [Figure 2] 1 shows a flowchart of step 120 for extracting a skeletal graph from a geometry. [Figure 3] 1 shows a flow chart of step 130 for identifying entry and exit endpoints. [Figure 4] 1 shows a flowchart of step 140 for calculating an initial centerline. [Figure 5] 1 shows a flow chart of step 150 of the initial centerline correction. [Figure 6] 1 shows a flow chart of step 160 of centerline post-processing. [Figure 7a] 1 shows a surface mesh of the coronary arteries. [Figure 7b] Shown are surface meshes of coronary arteries and voxelized labels at three different image spacing values, d=1.0 mm. [Figure 7c] Shown are surface meshes of coronary arteries and voxelized labels at three different image spacing values, d=0.5 mm. [Figure 7d] Shown are surface meshes of coronary arteries and voxelized labels at three different image spacing values, d=0.15 mm. [Figure 8] The skeleton obtained from the voxelized mesh shown in Fig. 7b is shown. [Figure 9a] Shows the effect of connecting the initial centerlines. [Figure 9b] 1 illustrates the effect of a corrected centerline according to the present invention. [Figure 10a] 1 shows the effect of the corrected centerline before post-processing. [Figure 10b] The same centerline is shown after smoothing in a post-processing step. [Figure 11a] 1 shows an example of an arterial surface mesh with corresponding centerlines (white) identified by the present invention. [Figure 11b] 1 shows an example of an arterial surface mesh with corresponding centerlines (white) identified by the present invention. [Figure 11c] 1 shows an example of an arterial surface mesh with corresponding centerlines (white) identified by the present invention. [Figure 11d] 1 shows an example of an arterial surface mesh with corresponding centerlines (white) identified by the present invention. [Figure 12] 1 shows the mean and standard deviation of the voxelization time Tv (s) versus image spacing at voxel size d (mm) calculated for a set of 160 volumes of example data. [Figure 13] 1 shows the mean and standard deviation of the skeletonization time Ts (s) calculated for a set of 160 volumes of example data versus image spacing at voxel size d (mm). [Figure 14] The mean and standard deviation of correction time Tc (s) versus number of correction steps N(1 / 1) for a set of 160 volumes of example data are shown. [Figure 15a] The effect of the correction after five iteration steps is shown. [Figure 15b] The effect of the correction after 20 iteration steps is shown. [Figure 15c] The effect of the correction after 50 iteration steps is shown. [Figure 15d] The effect of the correction after 100 iteration steps is shown. [Figure 16a] 1 shows the effect of correction without tension. [Figure 16b] 1 shows the effect of correction without retraction force. DETAILED DESCRIPTION OF THE INVENTION

[0036] A high-level flowchart of the method of the present invention is shown in Figure 1. Solid arrows indicate the flow of the method, while double arrows indicate information provided by other steps. The method of the present invention begins in step 100 with receiving a patient-specific volumetric image comprising structural information about the patient's blood vessels. The volumetric image can be the result of any well-known imaging technique used to image blood vessels, including computed tomography (CT) scans, photon-counting computed tomography (PCCT) scans, computed tomography angiography (CTA) scans, coronary computed tomography angiography (CCTA) scans, magnetic resonance imaging (MRI) scans, positron emission tomography (PET) scans, ultrasound scans, or any other medical imaging modality that includes at least one blood vessel. The method has been tested and works very well with CCTA image series.

[0037] After the volumetric images are received, a three-dimensional (3D) geometry of at least one blood vessel is recovered from the images (110). The 3D geometry is a representation of at least one blood vessel. The 3D geometry is typically represented in the form of a graph, such as a surface mesh, but can also be represented in the form of a volume mesh or point cloud. The 3D representation is necessary for adequate modeling and accurate simulation of the blood vessel.

[0038] The 3D geometry can be recovered manually by an expert, such as a radiologist or trained technician, using computer segmentation software tools. In this embodiment, software tools that enhance 3D geometry creation include, but are not limited to, active contours, dynamic meshes, and machine learning. Active contours or dynamic meshes allow the creation and correction of 3D geometry by moving their edges toward contrast agents visible in the image. Machine learning methods are applied to generate an initial 3D geometry that can be further improved or accepted by an expert. The use of such software tools speeds up the geometry recovery step 110. Alternatively, fully automated tools are applied using machine learning, or artificial intelligence models trained by the radiologist-created geometry, to predict the presence of blood vessels in the 3D volume and convert it into a mesh.

[0039] The output 3D geometry of step 110 is represented in the form of a surface mesh. The resolution of the surface mesh is a hyperparameter of the method. Generally, setting a lower resolution increases the speed of operation at the expense of centerline quality. The 3D geometry is used to extract an undirected skeletal graph in step 120. In this embodiment, the undirected skeletal graph is created in three steps, as shown in Figure 2. · Voxelization 221, which involves converting the vessel geometry into voxels; Skeletonization with thinning 222, which creates a skeleton from voxels; · Creating an undirected skeleton graph from a skeleton223.

[0040] Voxelization 221 involves repartitioning 3D space, which may lead to an equal-divided grid of voxels or an octree of voxels. An octree is a tree data structure in which each internal node has only eight child nodes. Octrees are most often used to partition 3D space by recursively subdividing it into eight octants. An example of an efficient voxelization algorithm used for this purpose is the TriangleMeshToBinaryImageFilter method implemented in the ITK library. This converts a triangular mesh into a predefined volumetric representation by checking for each voxel whether it is inside the geometric mesh. However, those skilled in the art can easily find alternative algorithms for voxelization that provide nearly equally good results.

[0041] The skeletonization step 222 in this embodiment is realized by the medial axis transformation (MAT). The MAT identifies the nearest boundary point for each point of the vessel. An interior point belongs to the skeleton if it has at least two nearest boundary points. The formal definition of a skeleton is the locus of centers of all maximal inscribed spheres. An exemplary thinning algorithm that can be used in this step is Zhang's and Lee's.

[0042] An undirected skeletal graph is created from the skeletal volume in step 223 by rotating voxels into graph nodes and adding edges between connected voxels. For each node, its original position in the image is stored. Potentially separate graph components are then connected based on proximity. Identifying the endpoints of one vessel (130) results in locating the inlets and outlets. This is repeated for each vessel in the 3D geometry. In this embodiment, the approach described below with reference to Figure 3 is applied.

[0043] The vertices of the geometry are searched using a breadth-first search (BFS) algorithm to create a BFS graph in step 331. The algorithm starts at an arbitrary vertex. Because blood vessels tend to be quasi-tubular structures, connected vertices equidistant from the starting vertex should form a cross-sectional ring. The ring is advanced along the vessel in successive iterations of the BFS algorithm.

[0044] For each ring, the centroid of the vertices contained therein is calculated. An undirected graph is constructed with the centroids as nodes joined by edges based on the vertex connectivity of each ring.

[0045] The leaf nodes of the graph are expected to be located where the BFS algorithm cannot proceed further along the vessel, i.e., at potential extremities of the vessel geometry. These leaf nodes are then used to identify centerline endpoints (332).

[0046] The algorithm is particularly suited to semi-tubular structures, as structures of other shapes tend to misorient the rings.

[0047] The centerline endpoints are found using the leaf nodes of the BFS graph, the skeleton graph, and the geometry 332. The node of the skeleton graph closest to the leaf of the BFS graph is selected as the endpoint and projected onto the geometry surface.

[0048] An entrance is selected in step 333 under the assumption that blood vessels are thickest at the entrance and become thinner as each branch branches.

[0049] The diameter of the artery mesh at every node in the skeleton graph is calculated. The skeleton graph is then completely traversed starting from each endpoint, and the difference between the diameters at adjacent nodes is calculated. The calculation is assigned a positive sign if the adjacent node corresponds to a smaller diameter, and a negative sign otherwise. The differences are then added together. The largest resulting sum corresponds to the starting endpoint, for which the diameter decrease (gradient) is highest. This is the best candidate for the vessel entrance.

[0050] Optionally, the entrance is selected with the assistance of a user indicating an area in which the entrance is located, and the entrance is then selected by the above method from an end point located in the vicinity of the indicated area.

[0051] The remaining endpoints are considered as exits.

[0052] Step 140 results in at least one initial centerline of at least one vessel, the centerline being defined by points and calculated at sub-voxel resolution for the volumetric image.

[0053] Although there are vascular diagnostic methods based on 2D images and therefore 2D centerlines (eg, EP 3061015), accurate blood flow simulation requires a 3D representation.

[0054] The 3D display imposes the need to obtain a 3D centerline, which is required not only for the simulation itself but also for obtaining digitally rectified curved planar reconstruction (CPR) and arbitrary multiplanar reconstruction (MPR) views, specifically for calculating the cross-sectional planes along which the blood flow is modeled.

[0055] The 2D approach simplifies the identification of the centerline and reduces the required computational power, but does not provide sufficient accuracy of modeling and is not in accordance with the present invention.

[0056] In step 140 of calculating the initial centerline, the skeleton graph obtained at the points (120) is used to initialize the centerline. First, the disjoint skeleton graph parts are found and connected in step 441 to obtain a continuous graph.

[0057] Then, step 442 is performed to find the shortest path between the entry and exit nodes in the undirected skeletal graph. The shortest path is computed by a breadth-first search of the graph nodes.

[0058] The points of the shortest path are resampled to enforce the same distance between points. These points, along with information about the start (entry point) and end (exit point) of the vessel geometry, are used to create a directed graph consisting of many directed chains of points in volume coordinates. This gives only information about the location in space for each node of the centerline. Each centerline C m,n consists of the number of paths m and the number of points n. The paths are described in the form of a directed chain, and each path has an entry point p inlet From the exit point p m The path consists of many points up to . Points are shared among these paths, and each point in a path, other than an entry or exit, has only two neighbors. There are points one before and one after a point along the path. At the end of a point, the coordinates are converted to real coordinates to obtain an initial centerline. In step 445, the points are resampled at a desired interval. Centerline paths shorter than some specified threshold are removed in a centerline preprocessing step.

[0059] The step 150 of correcting at least one initial centerline with sub-voxel accuracy begins with step 551, in which the initial centerline and the 3D geometry are received. The correction of the at least one initial centerline then comprises an iterative process including at least an operation 552 of centering the points defining the centerline by further locating them from the most proximal plane defined in the geometry, and an operation 553 of equalizing the points defining the centerline by bringing each point closer to the average position of its neighbors, performed sequentially until a stopping condition 554 is met. The stopping condition can be a certain number of iterations or a specified measure of difference between subsequent steps. The result is output in step 555.

[0060] The calculation is convenient when the 3D geometry is a surface mesh, where the vessel surfaces within the voxelized geometry can be identified as the outer layer of voxels. If the geometry is represented as a cloud of points covering the vessel surface, the distance from the most proximal surface is the distance from the most proximal point.

[0061] The centering step 552 involves applying a retracting force to the centerline point that pushes the point away from the most proximal surface of the geometry.

[0062] The equalizing step 553 involves applying a pulling force to the centerline points towards their adjacent points so that each point is pushed towards the average position of its two adjacent points.

[0063] This process can be realized by the following procedure. [Table 1]

[0064] Good results were obtained with the following parameter values: n:int=100;n∈[1,1000] dt:float=0.5;dt∈[0,1] dr: float=0.02;dr∈[0,1] - represents the proportion of the vessel diameter at a given point on the centerline.

[0065] The corrected initial centerline is subjected to optional post-processing 160, which includes resampling 641 and 3D smoothing 642 of the entire path of the centerline.

[0066] In post-processing step 160, optional features of the vessel are calculated for the centerline points and added to the optional metadata 643. These features may include, but are not limited to, the normal vector to the centerline, the tangent to the centerline, the cumulative distance from the starting point, the diameter of a circle inscribed in the shape of the geometric surface, the diameter of a disk inscribed in the shape of the geometric surface, the semi-minor and semi-major axes of an ellipse inscribed in the shape of the geometric surface, the minimum distance to the most proximal vertex in the vessel geometry, and the radius of a disk with the same area as the area of ​​the shape specified by the vessel geometry in a plane perpendicular to the centerline at a given point.

[0067] Since all centerline paths start from the same entry point, they overlap and share many points. To combine them into a single centerline structure represented as a directed graph, branch pruning 644 is applied, removing overlapping parts and joining currently non-overlapping branches to edges.

[0068] The centerline is smooth, continuous, and geometrically centered - these properties are necessary for accurate CFD simulations and good MPR and CPR diagrams.

[0069] Finally, the centerline is output in step 170 and used in combination with conventional blood flow simulation (e.g., as disclosed in EP 3820357) to extract and / or present patient-specific data, or simply for visualization to the physician.

[0070] The computer program product according to the invention can be adapted to be run on a conventional computer supplied with volumetric images to simulate blood flow, the computer program product comprising a set of instructions which, when loaded into the memory of the computer, causes the computer to carry out the method according to the invention.

[0071] The program according to the present invention can be executed on a stand-alone computer or on a processing unit of a medical imaging device with integrated image processing means. Furthermore, the computer program product may also be provided in a software-as-a-service model, where volume images are uploaded by a user to a server, and centerlines and simulations are calculated on the server side, while the results are distributed to the user via a communication network.

[0072] The image processing system according to the present invention is configured to generate a model of a tubular object from a volumetric image, the system comprising a volumetric image acquisition unit, a geometry extraction unit, a centerline generator and a diagnostic support module adapted to implement the method according to the present invention, the diagnostic support module preferably comprising a blood flow simulator and a display module for presenting a diagram of the blood vessels to a physician.

[0073] The volumetric image acquisition unit may be a computer module adapted to receive images via a telecommunications network. Alternatively, if the system is implemented in an imaging device, the device itself is the volumetric image acquisition unit. Methods for geometry extraction, centerline generation and blood flow simulation that can be implemented on a computer to obtain a geometry extraction unit, a centerline generator and a blood flow simulator are described, for example, in EP 3820357. Implementation of the above-mentioned centerline generation and correction module makes it possible to obtain a system according to the present invention.

[0074] The imaging device can be any medical imaging device having a display and a processing unit, including, among others, a computed tomography scanner, a PCCT (photon counting computed tomography scanner), an MRI (magnetic resonance) scanner, a PET (positron emission tomography) scanner, a SPECT (single photon emission computed tomography scanner), an ultrasound scanner or any other related medical imaging device.

[0075] The method has been found to be useful over a wide range of parameters, examples of which are listed below, where a trade-off between computational power and accuracy must be made.

[0076] Figure 7a shows the geometric surface mesh of the coronary artery image acquired in the geometry recovery step 110. The step 120 of extracting a skeleton from the geometry requires voxelization 221. The image size in voxelization affects both the accuracy and the computation time in the various steps. Figures 7b-d show the results of voxelization 221 of the mesh shown in Figure 7a with different values ​​of image spacing (voxel size) d. Figure 7b shows the results of voxelization with d = 0.15 mm, Figure 7c shows the voxelization with d = 0.5 mm, and Figure 7d shows the voxelization with d = 1 mm.

[0077] FIG. 8 shows an example of a skeleton obtained in step 222, which is used to generate a skeleton graph (223), which is then used to generate an initial centerline.

[0078] Figure 9a shows an example of a portion of the initial centreline generated in step 140 of the method according to the invention, and Figure 9b shows a corrected centreline using the method according to the invention.

[0079] 10a and 10b show the results of post-processing at the edge of a vessel. FIG. 10a shows the centerline at the edge of the vessel before smoothing 642, and FIG. 10b shows the centerline after smoothing 642. Smoothing can consist in applying a relatively weak low-pass filter to the coordinates of the centerline points. In the example shown in FIG. 10b, Butterworth filtering was applied. Smoothing removes numerical artifacts, especially those correlated to specific geometric shapes that were not corrected earlier.

[0080] 11a-d show examples of coronary artery surface meshes with corresponding centerlines (white) identified by the present invention.

[0081] Figure 12 shows how the image spacing (voxel size) d [mm] affects the voxelization time Tv [s]. Data were acquired from 160 different patient images. As the number of voxels increases in three dimensions, a trade-off must be made between voxelization accuracy and duration. For the tested data, the value that met the best quality requirements and operating speed was d = 0.15 mm. With this value, voxelization took approximately 5 seconds on the test equipment.

[0082] Figure 13 shows the dependence of the skeletonization time Ts [s] on the image spacing d [mm]. The results were obtained using the scikit-image skeletonization algorithm, based on the method developed by Lee et al., in which the skeletonization iteratively removes wider voxels until only a single pixel representation remains. The higher the resolution, the more iterations of the algorithm are required to complete the task. For d = 0.15 mm, the skeletonization time is approximately 6 seconds.

[0083] Figure 14 shows the linear dependence between the number of correction iterations N[1 / 1] and the correction time Tc[s]. The relationship is approximately linear. As the time increases, the number of iterations makes a small difference to the centerline. More powerful computers can perform a large number of corrections by default, while slower machines, especially those integrated with older imaging devices, may default to fewer iterations and give the user the option to manually override and apply additional corrections if needed.

[0084] Figures 15a-d show the effect of correction after (i) 5, (b) 20, (c) 50, and (d) 100 correction iterations. We found that 100 iterations provided the best tradeoff between accuracy and processing time.

[0085] For example, the effect of applying equalization 553 by tension can be seen by comparing the image shown in Figure 15d with Figure 16a, which shows the centerline after the correction procedure without equalization 553. This form of centerline would not be useful because at least some of the properties calculated for each point, such as tangents, would be highly distorted.

[0086] For example, the effect of applying centering 552 with a retraction force can be seen by comparing the image shown in FIG. 15d with FIG. 16b, which shows the centerline after the correction procedure without centering 552. The centerline is smoother, but tends to be too close to the vessel wall. Also, it is unclear how many iterations should be used, since convergence typically occurs as the forces balance each other. Without the retraction force, the centerline does not converge, and increasing the number of iterations results in a successively straighter line.

[0087] The exemplary embodiments of the present invention described above are merely illustrative of the present invention and are not intended to be limiting. The present invention encompasses methods and systems for the calculation of centerlines of blood vessels, particularly coronary arteries, from surface meshes. Methods according to embodiments of the present invention are easy to implement and can produce robust and accurate segmentations, typically in less than 20 seconds, and with very limited time and memory costs, averaging 3 GB. Combining the above-described centerline identification method with current coronary artery segmentation methods and current methods for the calculation of hemodynamic factors can provide simulations of blood flow, enabling diagnosis with little or no intervention from a specialized operator.

[0088] In particular, the identification of sufficient centerlines can also be applied to modeling and simulating generally tubular objects based on the representation of the object in volumetric imaging. Thus, the present invention is applicable when modeling blood vessels other than coronary arteries, when modeling the digestive system or other tubular objects, especially those that conduct fluids of any kind.

[0089] A computer in the sense of the above description should be understood as a hardware device including a computer, a microcontroller, a signal processing, a programmable gate array, as well as a hardware computer, a graphics card, an application specific integrated circuit or other processing digital device used for image processing and a distributed solution including a cloud computing environment.

[0090] Those skilled in the art, in view of the teachings of the above description, can routinely propose multiple hardware and software solutions for the inventive device and for computer-implemented execution of the inventive method, as well as methods of obtaining training information.

[0091] The above description is merely illustrative of the invention, and those skilled in the art can suggest numerous alternative embodiments which are covered by the scope of protection defined in the appended claims.

[0092] In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The use of the verb "to comprise" does not imply that there are no elements or steps other than those stated in a claim. The article "a" or "an" preceding an element does not exclude the presence of a plurality of such elements.

Claims

1. The computer-implemented method comprises: receiving (100) a patient-specific volumetric image comprising structural information about the patient's blood vessels represented in voxels; recovering (110) the three-dimensional geometry of at least one blood vessel; Extracting (120) a skeletal graph from said geometry; Identifying end points of the at least one blood vessel to identify an inlet and at least one outlet (130); Calculating at least one initial centerline of at least one blood vessel, the at least one initial centerline being defined by points and calculated at sub-voxel resolution (140); a step (150) of correcting the at least one initial centerline with sub-voxel accuracy to obtain a corrected centerline, the step comprising an iterative process involving equalizing points by moving each point closer to the average position of its neighbors to define the centerline (553); outputting and using the corrected centerline to extract and / or present patient-specific data (170); Equipped with The step of calculating (140) at least one initial centerline comprises: checking the continuity of the skeletal graph and, if necessary, correcting the skeletal graph by connecting disconnected components; identifying the initial centerline from the skeletal graph as the shortest path between the entrance and the exit; Including, In the step of correcting (150) the at least one initial centerline, the iterative process further comprises an operation (552) of centering at least the points defining the centerline by further locating said points from the most proximal plane defined in the geometric shape; A computer-implemented method, wherein the centering (552) and the equalization (553) are performed sequentially until a predetermined stopping condition (554) is met.

2. The iterative process of the correcting step (150) includes applying image forces to the centerline points; the centering (552) includes applying an image retraction force to the point of the centerline that pushes the point away from the closest point of the 3D geometry; 2. The computer-implemented method of claim 1, wherein the equalization (553) consists in applying an image pulling force to the point on the centerline toward an adjacent point such that the point is pushed toward an average position of two adjacent points.

3. The computer-implemented method of claim 1 , wherein the stopping condition (554) is to run a simulation a predetermined number of times.

4. 3. The computer-implemented method of claim 1, wherein the step of recovering (110) the three-dimensional geometry comprises generating a surface mesh representation of the vessel from the volumetric image.

5. The step of extracting (120) the skeletal graph from the geometry comprises: voxelizing (221) the geometry to obtain a volumetric representation of the vessel of interest; skeletonizing (222) the volume to obtain a volumetric skeleton representation of the vessel; creating (223) the skeletal graph from the volumetric skeletal representation; 5. The computer-implemented method of claim 1, 2, 3 or 4, comprising:

6. 6. The computer-implemented method of claim 1, wherein identifying the endpoints comprises an automatic breadth-first search of nodes of the geometry and identifying vessel entrances and exits using thickness gradient as a criterion.

7. 7. The computer-implemented method of claim 1, wherein a user is prompted for the approximate location of the entrance, and wherein identifying the endpoint includes selecting the entrance aided by filtering endpoint candidates based on the approximate location provided by the user.

8. 8. The computer-implemented method of claim 1, wherein the points of the corrected centerline are subjected to post-processing including at least one operation selected from the group comprising: resampling the centerline (641), smoothing the positions of the centerline points in space (642), calculating metadata of the centerline points (643), and pruning (644).

9. A computer program product comprising a set of instructions which, when loaded into the memory of a computer, causes the computer to carry out the method of any one of claims 1 to 8.

10. 1. An image processing system configured to generate a model of a tubular object from a volumetric image, comprising: a volume image acquisition unit; a geometric shape extraction unit; a centerline generator; a diagnostic assistance module; and An image processing system adapted to implement a method as defined in any one of claims 1 to 8.

11. The image processing system of claim 10 , wherein the volumetric image acquisition unit is a computer module adapted to receive the images via a telecommunications network.

12. The image processing system according to claim 10 , wherein the volume image acquisition unit is an imaging device.

13. 13. The image processing system of claim 12, wherein the imaging device is selected from the group comprising a computed tomography scanner, a photon counting computed tomography scanner, a magnetic resonance scanner, a positron emission tomography scanner, a single photon emission computed tomography scanner, and an ultrasound imaging device.

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