METHOD FOR TRAINING A COMPUTER-IMPLEMENTED ARTIFICIAL DEEP NEURAL NETWORK FOR ESTIMATING A HEMODYNAMIC PARAMETER, AND COMPUTATIONAL SYSTEM

Abstract

A method of training of an artificial deep neural network (ADNN) for estimation of a hemodynamic parameter from a geometry of a blood vessel tree comprising a step of obtaining of a set of geometries of vessel trees, according to the invention is realized with the ADNN having an architecture adapted for point cloud processing with distance based point grouping. The distance is defined as geodesic distance along the blood vessel tree. A method of estimation of hemodynamic parameters from a geometry of a blood vessel tree using an ADNN, according to the invention, involves using ADNN adapted for point cloud processing with geodesic distance based point grouping. The invention concerns also a computer program products comprising a set of instruction that, when run on a computing system, cause it to realize the methods according to the invention. The invention concerns also a computer system adapted to realize methods according to the invention.

Description

1 / 24 “TRAINING METHOD FOR A COMPUTER-IMPLEMENTED ARTIFICIAL DEEP NEURAL NETWORK FOR ESTIMATING A HEMODYNAMIC PARAMETER, AND COMPUTATIONAL SYSTEM” FIELD OF THE INVENTION

[001] The invention relates to a method for training an artificial deep neural network to estimate a hemodynamic parameter, a method for estimating a hemodynamic parameter with an artificial deep neural network, computer program products implementing methods according to the invention, and computer systems adapted to implement a method according to the invention. BACKGROUND

[002] Cardiovascular diseases are one of the leading causes of death worldwide. With the development of Computed Tomography (CT), non-invasive approaches for accurate diagnosis in patients with suspected ischemic heart disease have become possible.

[003] Computed tomography scans are commonly represented as a 3D volume image. This 3D volume image represents a physical quantity as a function of three spatial coordinates. In a digital volume image, each sample (voxel) represents this quantity measured at a specific location. The image is made up of a spatial sequence of 2D slices that include the object of interest. Typically, a slice is represented as an image matrix of pixels (X and Y coordinates). The slice number indicates the Z coordinate.

[004] The interpretation of CT images and the diagnosis of cardiovascular diseases is a non-trivial task that requires highly trained physicians. A common problem is that the interpretation of visible projections in CT images requires a highly qualified radiologist, and the diagnosis of a cardiovascular disease requires a qualified cardiologist. People who have skills in both fields are scarce. Therefore, computer-aided techniques are necessary.

[005] One way to diagnose heart conditions, with the aid of a Petition 870250080152, dated 09 / 08 / 2025, p. 63 / 97 2 / 24 computer, is to produce a 3D model of blood vessels that aids diagnosis. Especially in the field of cardiac pathologies, a detailed 3D model of the coronary arteries is necessary. A detailed model allows for the precise estimation of specific anatomical and functional attributes of the patient, such as hemodynamic parameters. In the state of the art, there are numerous techniques that use computational fluid dynamics (CFD) for blood flow simulation. The geometry of a vessel tree, presented in the 3D volumetric image, can be represented as a subset of voxels of the 3D image, a surface mesh, a volumetric mesh, or as a point cloud. An example of a CFD technique used to calculate fractional flow reserve (FFR) from a 3D model of coronary arteries from Coronary Computed Tomography Angiography (CCTA) is disclosed in European patent EP3820357.Generally, CFD simulations are configured to return FFR or other hemodynamic parameters of a patient under test. Another example is given in an article, "Prediction of 3D Cardiovascular Hemodynamics Before and After Coronary Artery Bypass Surgery via Deep Learning," by Gaoyang Li et al., doi.org / 10.1038 / 542003-020-01638-1.

[006] CFD simulations are an excellent alternative to manual diagnoses made by physicians analyzing CT images or even for invasive procedures. CFD simulations are performed using geometric models of blood vessels or blood vessel trees. The geometric models need to be extracted from the patient's volumetric image, usually DICOM images (Digital Imaging and Communications in Medicine is the standard for the communication and management of medical image information and related data). There are known methods for automatic or semi-automatic extraction of geometric models from a 3D volumetric image of a patient, as well as methods for improving them.

[007] Patent application publication CN114399608 discloses a method for time-varying flux field super-resolution reconstruction for simulation. Petition 870250080152, dated 08 / 09 / 2025, page 64 / 97 3 / 24 hemodynamics. The method comprises the following steps: (1) dataset production: perform blood vessel simulation using SimVascular software and construct a time-varying flow field dataset through image acquisition, geometric modeling, grid generation, and simulation steps; (2) velocity field attribute extraction: extract attributes from the input dataset data using PointNet and generate a 1024-dimensional fv attribute vector; (3) time-value and resistance attribute extraction: extract time-value and resistance attribute vectors from the input data using a resistance-time-value encoder and generate a 1024-dimensional frt attribute vector; (4) attribute decoding is performed, and a high temporal resolution velocity field is reconstructed;(5) evaluate and analyze a reconstruction result, train the network using velocity field amplitude and direction loss functions, and evaluate and analyze the reconstruction result by means of a mean module length error and a relative error. The method of CN114399608 is demonstrated with respect to modeling an artery segment geometry, which is a relatively simple segment of a vessel tree suitable for modeling with a point cloud. It is a universally recognized truth that point clouds are difficult to process when they represent complex, elongated structures with multiple branches. It is especially problematic when at least two separate branches are spatially close to each other. The problem was discussed by: • Patryk Rygiel, Maciej Zieba, Tomasz Konopczynski in Eigenvector Grouping for Point Cloud Vessel Labeling, Proceedings of the First International Workshop on Geometric Deep Learning in Medical Image Analysis, PMLR 194:72-84, 202, • He, J. et al. (2020) Learning hybrid representations for automatic 3D vessel centerline extraction, arXiv.org. Available at: https: / / arxiv.org / abs / 2012.07262 (Accessed on: February 15, 2023).

[008] One disadvantage of CFD simulation is that it requires time and Petition 870250080152, dated 08 / 09 / 2025, pp. 65 / 97 4 / 24 considerable computational power is required to run this. Therefore, there is a need for an alternative. A promising alternative is a computational analysis of the tree of vessels geometry using artificial intelligence trained on real, artificial, or hybrid data. Real data comprises an actual tree of vessels geometry obtained from the patient and measured hemodynamic parameters. Artificial data includes computer-generated models of the tree of vessels geometry and simulated hemodynamic parameters. Hybrid data may include real tree of vessels geometries and simulated hemodynamic parameters. Another type of hybrid data comprises both real and artificial examples.

[009] Systems and methods for determining individual-specific blood flow characteristics, i.e., hemodynamic parameters, are disclosed in documents EP3218872, US2014073976 and US20160166209. The methods include, firstly, training an artificial deep neural network, including steps of acquiring an individual-specific geometric model, real or artificial, and blood flow characteristics of at least part of the individual's vascular system, creating an attribute vector corresponding to the geometric model, according to the predefined format, training an artificial deep neural network using said geometric model, said attribute vector and said blood flow characteristics.After training is complete, hemodynamic parameters can be estimated by extracting an attribute vector from the geometric model and using a trained artificial deep neural network fed with the attribute vector to obtain the hemodynamic parameter estimate. Generally, artificial intelligence is used to map certain predefined attributes extracted from the geometric model to a hemodynamic parameter. The attributes are related to geometry and include, but are not limited to, blood vessel dimensions, changes in diameter, lumen length size of narrow parts, etc. These attributes are a design choice of the method, and their specific definition is rarely shared publicly. Petition 870250080152, dated 08 / 09 / 2025, pp. 66 / 97 5 / 24 PROBLEM TO BE SOLVED

[010] It is observed that it is difficult and ineffective to try to train an artificial deep neural network using the entire geometry of the blood vessel tree only in its global context. On the other hand, using only a local context is also ineffective. Furthermore, it is difficult to use a predefined vector of physical attributes to be extracted from the blood vessel tree geometry, as this vector cannot be universally defined, suitable for all shapes, in all patients. In addition, the attribute extraction process is prone to numerical errors and the attributes need to be defined a priori. Furthermore, known attribute sets in the technique are usually assigned to certain candidate points along the vessel tree, and the candidate point selection process is also prone to errors. SUMMARY OF THE INVENTION

[011] A computer-implemented method for training an artificial deep neural network to estimate a hemodynamic parameter from a blood vessel tree geometry, for diagnosing a patient without invasive measurements, comprising, according to the invention, a step of obtaining a set of vessel tree geometries, a step of obtaining the hemodynamic parameter corresponding to the geometries within the set, a step of preparing the training data for the artificial deep neural network, and a step of training the artificial deep neural network. The artificial deep neural network according to the invention is an artificial deep neural network (ADNN) with an architecture adapted for point cloud processing with distance-based point clustering. The distance is defined as geodesic distance along the blood vessel tree.The step of preparing the training data for the artificial deep neural network involves representing the geometry as a point cloud and a centerline graph. The parameter or parameters used in the training set define the further use of the artificial deep neural network for estimating this hemodynamic parameter of other geometries. The use. Petition 870250080152, dated 08 / 09 / 2025, pp. 67 / 97 Using 6 / 24 of a geodesic distance to select and group neighbors within a point cloud representation allows for an elastic configuration that adapts to the real fluid dynamics in the vessel tree, without the need to use a predefined attribute set. This improves accuracy and eliminates errors related to attribute selection. Geodesic distance grouping allows for analysis of the vessel tree in both global and local contexts, and consequently, a specific attribute vector can be implicitly constructed by the deep artificial neural network itself. Thus, simulations are more reliable and accurate and less dependent on the vessel tree being typical. However, Euclidean distance point grouping does not work as well as geodesic distance, requiring more computing power.Using the centerline chart makes geodesic distance calculations faster and less dependent on patient-specific deviations in vessel geometry. Geodesic distance can be calculated along the centerline or main blood flow calculated using the centerline, or along a curve close to the centerline. Using centerlines reduces the risk of errors and shortcuts in vessel walls.

[012] Advantageously, the computer-implemented method comprises a step of obtaining a centerline graph of the blood vessel tree, where the geodesic distance along the blood vessel tree is measured along the centerline graph. The centerline graph is very suitable for calculating geodesic distance as it reflects the topology of the vessel tree and makes the flow simulation more accurate. Explicitly measuring the geodesic distance along the centerlines is the simplest way to use centerlines to improve geodesic distance calculation.

[013] Advantageously, obtaining hemodynamic parameter values ​​involves the use of computational fluid dynamics simulation. This approach allows the generation of a large training dataset without elaborate measurements. This allows for more efficient training. Training can be accelerated even further if artificial geometries are used. Hybrid approach, in Petition 870250080152, dated 08 / 09 / 2025, pp. 68 / 97 7 / 24 which real models and artificial models are used, can remedy this. Similarly, CFD simulation can be verified with the addition of real measurement data.

[014] A computer-implemented method for estimating hemodynamic parameters from a blood vessel tree geometry, to diagnose a patient without invasive measurements, according to the invention, involves the use of an artificial deep neural network, comprising a step of obtaining a blood vessel tree geometry and a step of applying an artificial deep neural network for estimating hemodynamic parameters. The artificial deep neural network, according to the invention, is an artificial deep neural network (ADNN), with an architecture adapted for point cloud processing, with distance-based point clustering. The distance is defined as geodesic distance along the blood vessel tree, and the geometry is represented as a point cloud and a centerline graph.The use of a point cloud allows for more elastic modeling of a geometry within an artificial deep neural network framework. Using a geodesic distance to select and group neighbors within a centerline point cloud representation enables an elastic configuration that adapts to the actual fluid dynamics in the vessel tree, without the need to use a predefined attribute set. This improves accuracy and eliminates errors related to attribute selection. Geodesic distance grouping allows for the analysis of the blood vessel tree in both global and local contexts, and consequently, a specific attribute vector can be implicitly constructed by the deep neural network itself.

[015] Advantageously, the geodesic distance along the blood vessel tree is measured along the centerline graph.

[016] Advantageously, the geometry acquisition step comprises loading the geometry from the mesh, a step transforming the geometry into a point cloud, and a step obtaining centerlines. Petition 870250080152, dated 08 / 09 / 2025, page 69 / 97 8 / 24

[017] Advantageously, processing with an artificial deep neural network comprises encoding with at least one centerline set abstraction block, decoding with at least one decoder block, processing with a shared multilayer perceptron block, and post-processing with a one-dimensional convolutional layer.

[018] A computer program product, according to the invention, comprises a set of instructions that, when executed on a computer system, cause it to perform the method of estimating hemodynamic parameters, according to the invention.

[019] A computer program product, consisting of a set of instructions which, when executed on a computer system, cause it to perform the training method of an artificial deep neural network, according to the invention.

[020] A computational system for extracting at least one estimate of hemodynamic parameters from a blood vessel tree geometry adapted to perform a method of estimating hemodynamic parameters, according to the invention.

[021] Advantageously, the system is further adapted to perform the training method according to the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[022] The invention is described in detail below, with reference to the following figures: Figure 1 presents a flowchart of one embodiment of a method for calculating hemodynamic parameters in which the invention is applicable; Figure 2 presents the architecture of the artificial deep neural network model for estimating hemodynamic parameters; Figure 3 presents a diagram of the abstraction block of the centerline assembly (CSA) that is used in the ADNN model applied in the embodiment of a method, according to the invention; Petition 870250080152, dated 09 / 08 / 2025, p. 70 / 97 9 / 24 Figure 4 presents a diagram of the decoder block that is used in the ADNN model applied in the embodiment of a method according to the invention; Figure 5 presents a block diagram of the shared multilayer perceptron (MLP) that is used in the ADNN model applied in the embodiment of a method, according to the invention; Figure 6 shows a diagram of the PointNet 305 block that is used, according to the invention; Figure 7 shows a specific architecture that was used for the experiments, according to the invention; Figure 8 presents a flowchart of one modality of the training method, according to the invention; Figure 9 presents an example of synthetic input data. DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[023] One embodiment of the method for estimating hemodynamic parameters from the geometry of a blood vessel tree, using an artificial deep neural network, according to the invention, is discussed below with reference to Figure 1, showing a general flowchart.

[024] First, in step 101, patient-specific metadata and patient-specific volume image data are received. Patient-specific metadata is optional but can improve accuracy. Patient-specific metadata may include, but is not limited to, attributes such as age, sex, non-invasive blood pressure monitoring, and medical history. Patient-specific volume image data is not optional and may be, but is not limited to: computed tomography (CT), computed tomography angiography (CTA), coronary computed tomography angiography (CCTA), and magnetic resonance imaging (MRI). Step 101 data retrieval may involve actual measurements or simply downloading data from an external source. It may be retrieved, for example, from an external drive, picture archiving and communication system (PACS), or any other means. Petition 870250080152, dated 08 / 09 / 2025, pp. 71 / 97 10 / 24

[025] The retrieved data is then loaded 102 into the computing system that executes the method. This system can be a general-purpose computer, dedicated computer, digital processing machine, distributed architecture, virtual machine, or cloud resource. It needs to be selected to complete the task within the desired time. In this embodiment, the Azure cloud environment is used.

[026] Within the computing system, an artery anatomy geometry is obtained in step 103. Step 103 of obtaining a geometry involves only loading a surface mesh. However, step 103 may involve transforming the geometric shape or even obtaining it through volume image segmentation.

[027] Step 103 of obtaining a geometry can be done manually by a human expert, or automatically by a computer algorithm, or semi-automatically with a computer algorithm and a human expert. The geometry of the inlet artery anatomy can be described as a surface mesh, point cloud surface, or any other relevant data structure. If the data structure is different from a point cloud surface, the data structure of the artery anatomy geometry should be transformed into a point cloud surface. The points in the point cloud have at least three parameters, which are coordinates in three-dimensional space and an additional number of attributes. Examples of attributes include, but are not limited to, distance to the centerline or geodesic distance from the vessel entrance (start). The surface mesh representation facilitates the determination of a centerline graph.

[028] In the next step 104, a centerline graph is then extracted from the geometry of the artery anatomy. The centerline graph can be extracted manually by a human expert, automatically by a computer algorithm, or semi-automatically with a computer algorithm and a human expert. The centerline graph is described as a connected polygonal chain of 3D points in space. As centerline graphs are Petition 870250080152, dated 08 / 09 / 2025, page 72 / 97 11 / 24 widely used for diagnosis, visualization, and analysis of blood vessel models, are often unavailable or need to be extracted for other applications anyway. Therefore, computational power is saved and reused. The use of centerlines saves the laborious calculation of geodesic distance.

[029] The centerline graph and the geometry of the artery anatomy are used for a deep learning artificial model described in the invention and discussed later with reference to Figures 2-7 to estimate the hemodynamic parameters of choice in a 105 step, especially FFR or pressure drop. Specifically, the 105 step is performed in steps 204, 205, 206 and 207.

[030] Hemodynamic parameters are calculated for each point of the artery anatomy geometry in the point cloud and can be plotted on the centerline graph and estimated for each point on the centerline. Hemodynamic parameters may be, but are not limited to, pressure drops, fractional flow reserve (FFR), or any other related hemodynamic parameter. FFR is defined as a ratio between the pressure at the beginning of the artery and the pressure at the measurement point.

[031] The result is then visualized and a report is produced and sent back or presented to the user in the output step 106.

[032] A general artificial deep neural network (ADNN) model architecture used in the present embodiment of the invention is shown in Figure 2. The ADNN model shown in Figure 2 is an example of an ADNN model with an architecture adapted for point cloud processing. The ADNN model comprises CSA blocks 204, decoder blocks 205, and shared MLP blocks 206. The CSA blocks are fed with a centerline graph 202 obtained in step 104 and the geometry of a blood vessel tree represented as a point cloud 203 and centerline graph. In the present embodiment, both the centerline graph 202 and the surface point cloud 203 are obtained from the geometry initially represented as a surface mesh 201. Petition 870250080152, dated 08 / 09 / 2025, pp. 73 / 97 12 / 24

[033] The CSA blocks 204 form an encoder module. The input to the CSA blocks is the centerline graph 202 and the surface point cloud 203. The CSA blocks return a vector representing the entire surface point cloud 203.

[034] Decoder blocks 205 are fed with the vector returned by CSA blocks 204 and with the surface point cloud 203 to return a decoded attribute point cloud.

[035] The cloud of decoded attribute points is fed into the blocks Shared MLP 206 for processing on selected hemodynamic parameters, for example, with a 1D convolution layer. Finally, the result is post-processed and generated in a block 207.

[036] The components of the general ADNN model architecture used in the present embodiment of the invention and shown in Figure 2 are shown in Figures 3-6. The corresponding Centerline Set Abstraction (CSA) block is shown in Figure 3, its corresponding decoder block is shown in Figure 4, and its corresponding Multilayer Shared Perceptron (MLP) block is shown in Figure 5. The PointNet 305 block shown in Figure 3 is described in detail with reference to Figure 6. The specific architecture configuration used for the other embodiment and specific experiments is shown in Figure 7.

[037] The specific modality is discussed below. In this modality, the model ADNN receives a centerline graph with V number of vertices and E number of edges, and a surface point cloud with Nin number of points and 203 with Fin per point as input attributes. In one embodiment, the centerline graph has an arbitrary number of vertices V and a corresponding number of edges E. The number of points Nin in the surface point cloud is also arbitrary and depends on the required resolution. The surface point cloud has Fin set to five. The first three describe the 3D spatial position, the fourth is the distance to the centerline, and the fifth is a geodesic distance from the point to the entrance, where the entrance is the beginning of the centerline. Both the centerline graph and the surface point cloud have Fin defined as five points. Petition 870250080152, dated 09 / 08 / 2025, p. 74 / 97 13 / 24 central as well as the surface point cloud are extracted from the geometry of the inlet vessel represented as a surface mesh 201.

[038] The CSA block is shown in Figure 3. The input to the CSA block is a surface point cloud input 301 and a centerline plot 303. The CSA block is parameterized with the number of representatives to be sampled Nout, grouping scales Di, D2, ..., Dn, number of points to be grouped for each scale Ki, K2, ..., Kn and PointNet settings 305. The number n can be selected empirically.

[039] The input surface point cloud 301 is first reduced to Point clustering is performed using the FPS (Farthest Point Sampling) algorithm 302. The FPS algorithm starts with the representative set R consisting of a single point P_0 chosen arbitrarily from the point cloud. The point furthest away, in the Euclidean sense of distance, from P_0 is extracted and added to the set R. The next point is chosen as the furthest away, in the Euclidean sense of distance, from all points in R. This procedure is repeated iteratively until the set R has the required size. The resulting point cloud should be called the representative point cloud. In centerline clustering 304, multiscale clustering is performed independently for each point in the representative point cloud. Multiscale clustering is defined as the execution of several independent clusterings with different parameterizations.Where a clustering is a procedure for finding Ki neighbors in the surface point cloud for the representative point cloud, according to the specified strategy. Where the strategy is a process of determining an order of some form of the points in the surface point cloud, according to the representative point, for which the clustering is performed.

[040] One of the possible clustering strategies is the centerline clustering discussed with reference to the present modality. A person skilled in the art, however, is able to suggest alternative clustering mechanisms. Petition 870250080152, dated 08 / 09 / 2025, pp. 75 / 97 14 / 24 local. The advantage of centerline-based clustering is that centerlines are also very useful in generating diagnostic images and are therefore often already available in the patient-specific geometry. Another advantage of centerlines is that they reflect information about vessel topology. In this strategy, all points in the surface point cloud and representative point cloud are assigned a centerline vertex, in the Euclidean distance sense. For each point in the representative point cloud, geodesic distances between the centerline vertex assigned to the representative point and all vertices in the centerline graph are calculated.

[041] The scale parameter Di is used to extract only centerline vertices for which the geodesic distance is less than Di. The centerline vertices extracted in this way are used to query all surface point cloud points that have been assigned these vertices. The surface point cloud points extracted in this way are considered a set of representative point neighbors. The set of neighbors is further subsampled or oversampled to the specified number of neighbors Ki. The clustering procedure is conducted in this way for each scale specified in the CSA parameterization.

[042] Neighbor sets extracted and at various scales are processed with PointNet 305 is used to obtain global neighborhood attribute vectors. For each scale, an independent PointNet block is used to extract an attribute vector of size Fi. The PointNet settings are passed as a parameterization to the CSA block. The outputs from each PointNet scale are concatenated point-to-point. The output surface point cloud 306 is of size Nout x (Fi + F2 + ... Fn). Where Fi, F2, ..., Fn are the attribute vector sizes of each clustering scale. The applicable PointNet processing method is known from the publication PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space by Charles R. Qi, Li Yi, Hao Su, Leonidas J. Guibas (https: / / doi.org / 10.48550 / arXiv.1706.02413) and also available in architecture of Petition 870250080152, dated 08 / 09 / 2025, pp. 76 / 97 15 / 24 software (https: / / github.com / charlesq34 / pointnet2). This, however, requires modifying the definition of distance to geodesic distance to use it in the embodiment of the invention. Notably, many other known PointNet-based architectures are not suitable for implementing distance point clustering and are therefore not suitable for use in the present invention, and implementing geodesic distance point clustering based on the centerline or other line that reflects the topology of the vase tree.

[043] The last CSA block groups all remaining points and creates a global embedding vector that represents the entire surface point cloud 203. This global embedding vector, together with the embedding vectors of the corresponding CSA blocks and the surface point cloud 203, are used as an input for the decoder blocks 205.

[044] The details of the PointNet block 305 are presented in Figure 6. The input to the PointNet block is an input surface point cloud 601 of spatial size N x F. The input surface point cloud is processed with several shared MLP blocks 602 of specified parameterization. The number of shared MLP blocks is a design option. The last shared MLP block generates a surface point cloud of spatial size N x Fout which is processed with Global Max Pooling 603 to produce a single attribute vector 604 representing a surface point cloud of size Fout.

[045] The number of CSA blocks used, their number of scales, corresponding distance parameters, and spatial dimension of the output are a design choice. Stacking more blocks offers greater generalization capabilities, at the cost of more weights and the risk of overfitting the entire model. Block stacking allows for the extraction of local features, capturing fine geometric structures of small neighborhoods in the first few blocks. Such local features are grouped into larger units in subsequent blocks and processed to produce higher-level features. It is common to gradually extend the number of output feature channels from previous blocks, usually by using the next powers of two or multiplying the Petition 870250080152, dated 08 / 09 / 2025, pp. 77 / 97 16 / 24 number of channels divided by two. The number of blocks with their corresponding number of scale and distance parameters should be selected so that the model takes into account the entire point cloud in the last CSA block. Only one block, at least in some vessel tree, may not be able to gather higher-level attributes, and too many blocks may lead to overfitting. In the embodiment described below, these settings were found empirically – as shown in Figure 7. In the specific embodiment discussed below, this number is equal to two: n=2, for all CSA blocks except the last. Thus, the blocks are parameterized with Di, D2, Ki, K2.

[046] Where the first CSA block 703 takes as input the centerline graph 701 and a surface point cloud 702. The parameters D1, D2 of block 703 are defined as 0.001 m, 0.002 m, respectively. The numbers Ki and K2 are defined as Ki=128, K2=256. The spatial dimension of the output point cloud for block 703 is defined as 2048 x (16 + 16).

[047] The next CSA 704 block receives as input the output of the previous block. 703 and the centerline graph 701. The parameters D1, D2 of block 704 are defined as 0.002 m, 0.004 m, respectively. The numbers K1 and K2 are defined as K1=16, K2=32. The spatial dimension of the outgoing point cloud for block 704 is defined as 1024 x (32 + 32).

[048] The next CSA 705 block receives as input the output of the previous block. 704 and the centerline graph 701. The parameters D1, D2 of block 705 are defined as 0.004 m, 0.008 m, respectively. The numbers K1 and K2 are defined as K1=16, K2=32. The spatial dimension of the outgoing point cloud for block 705 is defined as 512 x (64, 64).

[049] The next CSA 706 block receives as input the output of the previous block. 705 and the centerline graph 701. The parameters D1, D2 of block 706 are defined as 0.008 m, 0.012 m, respectively. The numbers K1 and K2 are defined as K1=16, K2=32. The spatial dimension of the outgoing point cloud for block 706 is defined as 256 x (128 + 128). Petition 870250080152, dated 08 / 09 / 2025, pp. 78 / 97 17 / 24

[050] The next CSA 707 block receives as input the output of the previous block. 706 and the centerline graph 701. The parameters D1, D2 of block 707 are defined as 0.012 m, 0.016 m, respectively. The numbers Ki and K2 are defined as Ki=16, K2=32. The spatial dimension of the outgoing point cloud for block 707 is defined as 128 x (128 + 128).

[051] The next CSA 708 block receives as input the output of the previous block. 707 and the centerline graph 701. The parameters D1, D2 of block 708 are defined as 0.016 m, 0.032 m, respectively. The numbers Ki and K2 are defined as Ki=16, K2=32. The spatial dimension of the outgoing point cloud for block 708 is defined as 64 x (128 + 128).

[052] The last CSA block 709 receives as input the output of the previous block 708 and the centerline plot 701. The parameter D1 708 is set to NONE, which is defined as grouping all remaining points. For the last CSA block n = 1. The last CSA block aggregates all remaining points and the number K1 is set to K1 = 64. The spatial dimension of the output point cloud for block 709 is set to 256.

[053] The decoder module is constructed from decoder blocks 205. The inputs for the decoder blocks are outputs from the CSA blocks 204 and, for the last decoder block, the surface point cloud 203 as well.

[054] The decoder block is shown in Figure 4. The input to the decoder block is a surface point cloud from the previous decoder block 401 and a surface point cloud from the respective CSA block 402. The decoder block is parameterized with the shared MLP configuration.

[055] The input surface point cloud of the previous decoder block 401 and the surface point cloud of the respective CSA block 402 are an input to the attribute interpolation block 403. In the attribute interpolation block 403, attributes per point of the input surface point cloud from the previous decoder block are interpolated based on three nearest neighbors, in Petition 870250080152, dated 08 / 09 / 2025, pp. 79 / 97 18 / 24 Euclidean distance sense, in the surface point cloud of the respective CSA 402 block. Where the surface point cloud of the respective CSA block with interpolated attributes is processed subsequently.

[056] The interpolated surface point cloud is processed with Shared MLP 404 to obtain the decoded attribute point cloud 405. The MLP block is one of the typical mechanisms used to extract attributes from a larger set of attributes - especially for data that are not linearly separable. The Shared MLP configuration is passed as a parameterization to the decoder block. The output surface point cloud, i.e., the decoded attribute point cloud 405, is of size Nout x Fout.

[057] The number of decoder blocks is a design option and depends on the number of CSA blocks. The spatial dimension of the output is also a design option. Each decoder block requires input from the corresponding CSA block. Therefore, in the present embodiment, the number of decoder blocks is seven.

[058] It is common to gradually reduce the number of output attribute channels from previous blocks, usually by using the next powers of two or by dividing the number of channels by two. In the present embodiment, seven decoder blocks are used, as shown in Figure 7.

[059] The first decoder block 716 receives an input from a previous decoder block 715 and from the surface point cloud 702. Its spatial output dimension is defined as 64 x 256.

[060] Decoder block 715 receives an input from a previous decoder block 714 and from CSA block 703. Its spatial output dimension is defined as 128 x 128.

[061] Decoder block 714 receives an input from a previous decoder block 713 and from CSA block 704. Its spatial output dimension is defined as 256 x 128.

[062] Decoder block 713 receives an input from a previous decoder block 712 and from CSA block 705. Its spatial output dimension is defined as Petition 870250080152, dated 08 / 09 / 2025, pp. 80 / 97 19 / 24 512 x 128.

[063] Decoder block 712 receives an input from a previous decoder block 711 and from CSA block 702. Its spatial output dimension is defined as 1024 x 64.

[064] Decoder block 711 receives an input from a previous decoder block 710 and from CSA block 707. Its spatial output dimension is defined as 2048 x 32.

[065] The last block of the 715 decoder receives an input from the CSA 708 block and the CSA 709 block. Its spatial output dimension is defined as Nn x 128.

[066] When the surface is fully decoded by the last block of the decoder, the point attributes are passed through the shared MLP blocks 206.

[067] The Shared MLP Block is shown in Figure 5. The input to the shared MLP Block is an input surface point cloud 501 of spatial size N x F. The input surface point cloud is processed with 1D convolution 502 of a specified number of output channels C. The output of the 1D convolution is then processed according to the 1D batch normalization layer 503, the activation function 504, and the dropout layer 505. The output surface point cloud 506 is of spatial size N x C. The estimated hemodynamic parameter is determined by the parameter used in the training dataset to train the network. If the ADNN is trained with FFR data – as in the present embodiment – ​​then it estimates the FFR data. On the other hand, the ADNN, according to the embodiment of the invention, can also be trained with other hemodynamic parameters, including pressure drops, wall shear stress, and others.

[068] The number of shared MLP blocks is a design choice.

[069] In one embodiment, only one shared MLP block 717 is used, as shown in Figure 7. In one embodiment, the number of convolutional channels is set to 128. Petition 870250080152, dated 08 / 09 / 2025, pp. 81 / 97 20 / 24

[070] The last step is to obtain the estimated output of hemodynamic attributes per point 207. This involves applying a series of post-processing procedures. In one embodiment, a single 1D convolutional layer 718 is used to convert the output into a required number of points Nn and generates it in step 719. Post-processing may include, as in one embodiment, casting estimated hemodynamic parameters from points in the point cloud to points on a centerline graph or using these estimated hemodynamic parameters for further calculations in a CFD algorithm.

[071] One embodiment of the ADNN training method, according to the invention, is discussed below, with reference to Figure 8. The method comprises a step of obtaining a set of training geometries in the form of surface mesh geometries or surface point cloud geometries.

[072] The hemodynamic parameters used in this modality are pressure drops or FFR. A pressure drop or FFR corresponding to individual points in each training geometry is determined in the CFD simulation to form a set of true values ​​of the training ground.

[073] Training data are formed by representing training geometries as centerline surface point clouds and assigning pressure drops or FFR values ​​to specific points in training geometries, and then used in training an ADNN model. Training datasets may include real data, artificial data, hybrid data, or a combination thereof, and include patient-specific images, artery geometries, and all related metadata.

[074] The training procedure is adapted to the estimation method. Generally, it involves a step of obtaining a set of vessel tree geometries—corresponding to real patients or artificial models, or both. Additionally, it includes obtaining parameter values ​​to be estimated by the trained network. The values ​​can be obtained from real measurements or CFD simulations, or both. Subsequently, the training data for the ADNN are prepared using the... Petition 870250080152, dated 08 / 09 / 2025, pp. 82 / 97 21 / 24 geometries and their corresponding parameters, including the representation of the geometries as a point cloud with a centerline graph. This is crucial to the invention, as the representation of the point cloud with geodesic distance clustering avoids the need to define arbitrarily selected parameters. Next, the ADNN is trained. The ADNN is an artificial deep neural network with an architecture adapted for point cloud processing with distance-based point clustering. The distance is defined as the geodesic distance along the blood vessel tree. The geodesic distance is preferably the distance along the centerline; therefore, a step is required to obtain a centerline graph of the blood vessel tree. A specific example of the training procedure is described below in detail with reference to Figure 8.It is observed, however, that several specific alternative forms of training are available to the person skilled in the art, which are applicable provided they meet the requirements set forth in claim 1.

[075] The training procedure is preceded by model initialization. 801 and by preparing the input data 804. The initialization of the model 801 includes the initialization of the ADNN model weights, which are sampled from an option distribution.

[076] In one embodiment, in the dataset loading step 804, the samples – input surface meshes or point clouds and hemodynamic attributes to be regressed – are loaded into memory. The samples are then preprocessed 805 – the meshes are decomposed into centerline plots and surface point clouds, if necessary. Then, additional attributes are calculated and incorporated into each point in the point cloud, as needed.

[077] After the data are preprocessed, data loaders are created 806 for both the training set 807 - in which the training is performed, and the validation set 815 - in which the model is evaluated during the training procedure. Petition 870250080152, dated 08 / 09 / 2025, pp. 83 / 97 22 / 24

[078] Model training comprises a set of operations that are repeated iteratively - one of these sets is called an epoch. Each epoch 802 starts from the training procedure 803 which uses the training data loader 807. The data loader produces batches of samples that are loaded into memory 808 and processed with the routing network procedure 809.

[079] When the network output is obtained, the loss function between the desired result and the generated result is calculated 810. In one embodiment, the loss function is the Mean Squared Error (MSE), and the loss is calculated for each point of the input surface point cloud and the result is calculated. Once the loss is calculated, its gradient is used to perform the backpropagation procedure 811, which estimates how much the network weights need to be adjusted to obtain a lower loss at the current epoch. According to the calculated loss gradients, the model parameters are updated 812.

[080] The set of instructions applied to the batch of data is called the training step. Training steps are repeated until there are no more batches of data in the training data loader 813.

[081] After the last training batch is processed, the validation procedure will begin 814. During the validation procedure, the model weights are not changed. The validation process is performed to evaluate and monitor the model's performance on data that was not included in the training set.

[082] The validation stage comprises instructions similar to those of the training stage - loading the next batch of data 816, executing the forward procedure 817 and calculating the loss function 818. The validation stage differs from the training stage in the absence of a backpropagation procedure and updating of the model parameters. The validation stages are performed iteratively until all validation batches have been generated 819.

[083] After the validation procedure is completed, the process requirements Petition 870250080152, dated 08 / 09 / 2025, pp. 84 / 97 23 / 24 of training are checked 820. Requirements may include checking if the validation loss has decreased compared to the lowest value previously. If so, the ADNN model is saved 821. Then, a stopping criterion 822 is checked. In one mode, the stopping criterion is defined as the number of epochs to be reached. If the stopping criterion is not met, the next epoch begins 802, otherwise, training ends 823.

[084] In the process of evaluating the invention, a dataset of 1,700 synthetically generated vessel geometries, in the form of a surface mesh, was used. The training, validation, and test sets consisted of 1,500, 100, and 100 samples, respectively. Figure 9 shows an example of a synthetic vessel. One sample consists of a centerline graph 901 (node ​​density shown in 902) and a mesh representing the vessel geometry 903.

[085] An attempt to use distance-based clustering with Euclidean distance instead of geodesic distance was unsuccessful and resulted in low correlation with CFD results and real data.

[086] Computers, as described above, should be understood as hardware devices, including computers, microcontrollers, signal processing, programmable gate arrays, understood as hardware computers, graphics cards, application-specific integrated circuits or other digital processing devices used for image processing, as well as distributed solutions, including cloud computing environments.

[087] Those skilled in the art, given the teachings of the above description, are able to routinely propose various hardware and software solutions for the device according to the invention, and for the execution of the computer-implemented method according to the invention, as well as methods for obtaining training information. Notably, training and estimation can be done on the same computer systems or on completely separate computer systems. The use of the trained system may include training Petition 870250080152, dated 08 / 09 / 2025, pages 85 / 97 24 / 24 additional of the same.

[088] It is noted that the invention described is applicable for estimating various hemodynamic parameters, while FFR and pressure drops have been given only as examples. The estimated parameters depend on the parameters provided in the training dataset.

[089] It should be noted that the above description is merely an illustration of the present invention and those skilled in the art may propose many alternative embodiments covered by the scope of protection as defined in the appended claims.

[090] In claims, any reference marks placed in parentheses should not be interpreted as limiting the claim. The use of the verb "to include" does not mean that there are no elements or steps beyond those stated in a claim. The use of the article "a," "an," or "the" preceding an element does not exclude the presence of a plurality of such elements. Petition 870250080152, dated 08 / 09 / 2025, pp. 86 / 97

Claims

1 / 3 CLAIMS 1. A method for training a computer-implemented artificial deep neural network to estimate a hemodynamic parameter from the geometry of a patient's blood vessel tree, wherein the method comprises: a step to obtain a set of vessel tree geometries, a step to obtain hemodynamic parameter values ​​corresponding to the geometries within the set, a step to prepare the training data for the artificial deep neural network, a step to train the artificial deep neural network, characterized in that the artificial deep neural network is an artificial deep neural network with an architecture adapted for point cloud processing with distance-based point clustering, wherein the distance is defined as geodesic distance along the blood vessel tree represented as a point cloud and a centerline graph,The step of preparing the training data for the artificial deep neural network includes representing the geometry as a point cloud and a centerline plot.

2. A computer-implemented method according to claim 1, characterized by comprising a step of obtaining a graph of the central line of the blood vessel tree, wherein the geodesic distance along the blood vessel tree is measured along the central line graph.

3. Computer-implemented method, according to claim 1 or 2, characterized by the obtaining of hemodynamic parameter values ​​comprising the use of computational fluid dynamics simulation in the geometries Petition 870250080152, dated 08 / 09 / 2025, pp. 93 / 97 2 / 3 within the set.

4. Computer-implemented method for estimating hemodynamic parameters from a blood vessel tree geometry for patient diagnosis using an artificial deep neural network, comprising a step of obtaining a blood vessel tree geometry (103) represented as a point cloud and a step (105) of applying an artificial deep neural network for estimating hemodynamic parameters, characterized in that the geometry is represented as a point cloud with a centerline graph, the artificial deep neural network is an artificial deep neural network with an architecture adapted for point cloud processing with distance-based point clustering wherein the distance is defined as geodesic distance along the blood vessel tree represented as a point cloud and a centerline graph.

5. A computer-implemented method according to claim 4, characterized in that the geodesic distance along the blood vessel tree is measured along the central line graph.

6. Computer-implemented method according to claim 5, characterized in that the geometry acquisition step comprises mesh geometry loading, a geometry transformation step into a point cloud and a centerline acquisition step (104).

7. A computer-implemented method according to claim 6, characterized by the use of an artificial deep neural network to comprehend, encode with at least one central line set abstraction block (204), decode with at least one decoder block (205), process with a shared multilayer perceptron block (206), and post-process with a one-dimensional convolutional layer (718). Petition 870250080152, dated 08 / 09 / 2025, pp. 94 / 97 3 / 3 8. Computer program product characterized by comprising a set of instructions that, when executed on a computer system, cause it to perform a computer-implemented method, as defined in any one of claims 1 to 3.

9. Computer program product characterized by comprising a set of instructions that, when executed on a computer system, cause it to perform a computer-implemented method, as defined in any one of claims 4 to 7.

10. A computational system for extracting at least one estimate of hemodynamic parameters from the geometry of a blood vessel tree, characterized by being adapted to perform a computer-implemented method as defined in any one of claims 4 to 7.

11. A computer system, according to claim 10, characterized by being adapted to perform a computer-implemented training method, as defined in claim 1, 2, or 3. Petition 870250080152, dated 08 / 09 / 2025, pp. 95 / 97

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