Methods for simulating device deployment

Abstract

The present invention relates to a method for training a machine learning system, comprising: - based on at least one image data set (I) representative of at least one portion of a hollow structure, Compute the signed distance field for each part (S10), Calculating at least one geometric parameter of each part (S11); - generating an unfolded in-use representation of the device (S20) by calculating contact forces between the device and each part based on the signed distance field and applying said contact forces to a geometric representation of the device (S202); - training (S30) a machine learning system (ML) using each of the calculated geometric parameters as an input and the corresponding unfolded in-use representation as an associated target output; the resulting trained machine learning system being configured to receive as input at least one geometric parameter and provide as output a deployed in-use representation of the device; It concerns the method.

Description

[Technical field]

[0001] The present invention relates to a computer-implemented method for training a machine learning system configured to generate optimal deployment configurations of a device within a hollow structure of a subject for surgical planning.

[0002] The invention further relates to corresponding computer program products and devices.

[0003] The present invention relates to the field of surgical planning and navigation. [Background technology]

[0004] Expandable or deployable devices are used in a variety of situations where it is necessary to maintain or restore patency of a lumen in the body.

[0005] These devices include, for example, dilatation balloons and expandable stents, as well as combinations thereof (e.g., in angioplasty). While balloons are typically inserted into a narrowed lumen (e.g., a stenosed blood vessel), expanded with a pump, and then deflated and removed, stents are usually permanent structures that remain in place after insertion and expansion.

[0006] Expandable devices are essential to ensure patency of both vascular and non-vascular structures. Accurate insertion planning and prediction of in situ expansion are required to ensure efficiency and patient safety.

[0007] For this purpose, medical images are not sufficient due to their limited visibility.

[0008] Several techniques have been developed to simulate the deployment of expandable devices in the preoperative setting. Nevertheless, these techniques are complex and time-consuming and therefore not suitable for providing real-time information.

[0009] Although several attempts have been made to improve these methods, the proposed solutions typically involve oversimplification of the devices and / or anatomical structures and are not compatible with the standards of personalized and precision medicine. Moreover, these simplifications may lead to underestimation or overestimation of the risks associated with the surgical intervention.

[0010] It is an object of the present invention to provide a method for simulating extended device deployment that is fast, reliable and accurate. Summary of the Invention

[0011] To this end, the present invention provides a computer-implemented method of the type described above, comprising: - based on at least one image data set representative of at least one portion of a hollow structure of a plurality of reference subjects, calculating a signed distance field of at least one portion of a hollow structure of each of the plurality of reference subjects; - calculating at least one geometric parameter of at least one portion of a hollow structure of each of the plurality of reference subjects, the at least one geometric parameter being a set of geometric parameters defining a geometric model of a corresponding portion of a hollow structure of a particular reference subject of the plurality of reference subjects; - for each portion of at least one portion of a hollow structure of a plurality of reference subjects, calculating a contact force between the device and said portion of the hollow structure based on the corresponding calculated signed distance field; and applying said contact force to a geometric representation of a device; generating an expanded in-use representation of the device by - training a machine learning system with each of the calculated at least one geometric parameter as an input variable and the corresponding in-use representation of the device as an associated target output to obtain a trained machine learning system configured to receive as an input the at least one geometric parameter and to provide as output an in-use representation of the device for use in a method of generating an optimal deployed configuration of the device for surgical planning; The method includes:

[0012] The at least one image dataset may include a plurality of image datasets that together form an image database of the body lumen.

[0013] The signed distance field and at least one parameter are derived directly from the image dataset, thereby ensuring patient-specificity of the thus obtained in-use deployed representation of the device.

[0014] In particular, the at least one parameter represents the geometric shape of the hollow structure and defines a geometric model of the hollow structure. For example, the at least one parameter includes coordinates of points along a centerline of the hollow structure and control points that define cross sections of three-dimensional surfaces that delimit the hollow structure. Defining the hollow structure with a finite number of parameters can reduce the size of the database of digital models of hollow structures. Thus, when the parameters are to be used to train a machine learning system, training times are reduced.

[0015] As a result, the proposed invention provides a fast, reliable and accurate method for simulating extended device deployments.

[0016] Furthermore, contact forces are calculated from a signed distance field derived directly from the images, thus avoiding the introduction of spatial errors inherent in mesh generation algorithms.

[0017] Moreover, to generate an optimal deployment configuration C of device D by a trained machine learning system, there is no need to perform time-consuming steps such as running an iterative solution algorithm, a finite element method, calculating a signed distance field, etc. All of these steps are performed in advance.

[0018] According to other advantageous aspects of the invention, the method comprises one or more of the following features, taken alone or in any possible combination:

[0019] The hollow structure may be a blood vessel, a fistula, or a non-vascular vessel of the human body.

[0020] The method further comprises segmenting the at least one image dataset to obtain a segmented image dataset, and based on the segmented image dataset at least one geometric parameter and / or the signed distance field is calculated.

[0021] Segmenting includes applying a level set segmentation to the image dataset.

[0022] The method further comprises extracting a three-dimensional surface representing the hollow structure from the segmented image dataset, preferably using a marching cubes algorithm.

[0023] The segmenting includes an initialization phase to obtain a zero level set and an evolution phase, the initialization phase comprising: Selecting at least two points in at least one image data set; Running a colliding front algorithm using at least two points as seed points; Includes.

[0024] The segmented image data set comprises a set of points or a set of curves, and the calculation of the at least one geometric parameter comprises: Applying a point set registration to a set of points, or Applying a curve-based parameterization to a set of curves; Includes.

[0025] The geometric representation of the device includes beam elements, and the applying phase includes applying a co-rotational formulation to the beam elements.

[0026] The method further comprises, prior to training, reducing the order of the deployed in-use representation of the device to obtain a reduced order representation of the deployed device, during which the machine learning system is trained with the calculated geometric parameters as input variables and a subset of the features of the reduced order representation as associated target outputs, the reduced order representation of the deployed device allowing the total size of the training data to be reduced. As a result, the training data is created faster. Since the time of the training stage depends on the size of the training data, using training data of smaller size helps to improve and reduce the time of the training stage, especially for artificial neural networks. The reduction comprises applying a proper orthogonal decomposition algorithm to the deployed in-use representation of the device.

[0027] The at least one geometric parameter is a centerline, center, or radius of the hollow structure, points defining the centerline, control points defining a cross section of a three-dimensional surface representing the hollow structure, or a combination thereof.

[0028] The at least one geometric parameter includes three points defining a centerline of the hollow structure's vessel, three radii defining a cross section along said centerline, and two parameters defining an aneurysm associated with said vessel.

[0029] The method further includes generating a deformed representation of the device, the deformed representation representing a configuration of the device after implantation within a hollow structure of a subject, the deformed representation being a geometric representation of the device to which the contact force is applied.

[0030] Segmentation of the image dataset advantageously makes it possible to obtain both the signed distance field and the geometric parameters in a single operation.

[0031] Level set segmentation relies on spatial variations in image intensity rather than absolute intensity. Thus, level set segmentation is robust and less susceptible to variations in intensity of hollow structures in the image dataset (e.g., due to artifacts, contrast bolus dynamics, or partial volume effects). Furthermore, level set segmentation is highly reproducible since the number of user-dependent steps (e.g., manual definition of intensity thresholds) is minimized and it is based on uniquely definable criteria (e.g., gradient of image intensity).

[0032] By calculating at least one geometric parameter based on the segmented image data set, it is possible to obtain a parameter that is independent of the type and shape of the organ or hollow structure, in other words, the same parameter can be used to describe different anatomical regions or organs of the subject.

[0033] For example, the centerline is particularly useful for parameterizing hollow structures having a dimension that is greater than another dimension, such as a blood vessel or a tubular body passage, while the center and / or radius are particularly useful for parameterizing hollow structures having similar dimensions, such as an aneurysm.

[0034] The segmentation step usually includes an initialization phase and an evolution phase. The initialization phase based on the colliding front is particularly advantageous for obtaining a zero level set for hollow structures with a tubular shape, such as blood vessels. Indeed, in this case a first point may be selected at one end of the hollow structure and a second point may be selected at the opposite end of the hollow structure.

[0035] This three-dimensional surface of the hollow structure can be used for visualization purposes. Optionally, it can be used to derive one or more geometric parameters. Advantageously, the three-dimensional surface is obtained from the signed distance field and not vice versa. Thus, the loss of precision introduced by surface generation algorithms (such as marching cubes) is controlled to only affect the three-dimensional surface generation and not the signed distance field.

[0036] Beam elements make it possible to represent wire meshes that undergo large nonlinear deformations. They are therefore particularly suitable for representing devices such as knitted, braided or woven stents. For example, beam elements can also be modeled using a co-rotational formulation, which advantageously makes it possible to simulate large nonlinear deformations, as is the case for devices D that include a wire mesh (e.g., braided stents). Furthermore, the co-rotational formulation also makes it possible to reduce the computational load.

[0037] By inputting the reduced order representation into the machine learning system, one can obtain a trained machine learning system that can provide an evolved in-use representation of the device in an amount of time that is independent of the order or dimensionality of the representation. Indeed, based on the relationship between the reduced base and the corresponding geometric parameters, the trained machine learning system may derive the evolved in-use representation from a fixed number of reduced bases.

[0038] Furthermore, order reduction can reduce the computational cost required to provide a representation of the deployed device while controlling the final loss of precision.

[0039] For example, proper orthogonal decomposition can reduce the dimension of the deployed in-use representation of the device to a set of reduced bases.

[0040] The crimping and deformation steps can provide an initial configuration for the simulation step that is close to the actual position of the device immediately after implantation, and thus the resulting deployed in-use representation of the device closely replicates the actual deployed configuration of the device.

[0041] Deformation based on at least one geometric parameter ensures that the geometric representation fits the hollow structure (e.g., the crimping representation can be deformed to follow the centerline of the hollow structure), as in the case of a flexible device implanted within an organ.

[0042] Using a trained machine learning system according to any one of the above embodiments allows for accurate prediction of the deployed configuration of the device in real time, more precisely, the deployed representation is provided solely on the basis of geometric parameters derived from the images, without the need to perform operations such as evaluating the mechanical behavior by conventional finite element methods, generating a mesh of the organ, solving differential equations describing the contact between the device and the organ walls, etc.

[0043] Furthermore, the machine learning system is trained with input obtained through numerical simulations of stent deployment, rather than image-based simulations that do not take into account the mechanical behavior of the device.

[0044] The invention also relates to a non-volatile computer storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method according to any one of the above embodiments.

[0045] The present invention further provides a computer-implemented method for generating an optimal deployment configuration of a device in an organ of a subject for surgical planning, said method comprising: - calculating at least one geometric parameter of a hollow structure of the subject based on an image data set comprising at least the hollow structure; - generating an optimal deployment configuration for the device by inputting the calculated at least one geometric parameter into a machine learning system trained according to the method described above; The present invention relates to a method comprising the steps of:

[0046] The present invention further provides a device for training a machine learning system configured to generate an optimal deployment configuration of a device in a hollow structure of a subject for surgical planning, the device comprising: - based on at least one image data set representative of at least one portion of a hollow structure of a plurality of reference subjects, calculating a signed distance field of at least one portion of a hollow structure for each of the plurality of reference subjects; calculating at least one geometric parameter of at least one portion of a hollow structure of each of the plurality of reference subjects, the at least one geometric parameter comprising a set of geometric parameters defining a geometric model of a particular portion of a hollow structure of a particular reference subject of the plurality of reference subjects; - for each portion of at least one portion of a hollow structure of a plurality of reference subjects, calculating a contact force between the device and the one portion of the hollow structure based on the corresponding calculated signed distance field; and applying said contact force to a geometric representation of a device; generating an expanded in-use representation of the device by - training a machine learning system with each of the calculated geometric parameters as an input variable and the corresponding in-use deployed representation of the device as an associated target output to obtain a trained machine learning system configured to receive as an input at least one geometric parameter and to provide as output an in-use deployed representation of the device for use in a method of generating an optimal deployed configuration of the device for surgical planning; The present invention relates to a device comprising a processing unit configured to

[0047] The present invention further provides a device for generating an optimal deployment configuration of a device in an organ of a subject for surgical planning, said device comprising: - calculating at least one geometric parameter of a hollow structure of the subject based on an image data set comprising at least a hollow structure; - generating an optimal deployment configuration for the device by inputting the calculated at least one geometric parameter into a machine learning system trained according to the method described above; The present invention relates to a device comprising a processing unit configured to

[0048] The invention will be better understood with reference to the accompanying drawings. [Brief description of the drawings]

[0049] [Figure 1] FIG. 1 is a schematic diagram of a first embodiment of a device 1 for surgical planning according to the invention. [Diagram 2] FIG. 2 is a front view showing device D configured to be implanted within hollow structure H, device D being depicted in an unconstrained deployed configuration and a contracted configuration. [Diagram 3] 3A are images showing three-dimensional surfaces representing an exemplary hollow structure H and corresponding geometric parameters P. More precisely, Fig. 3A illustrates the three-dimensional surface of a blood vessel and its centerline, Fig. 3B further illustrates a geometric representation R1 of a device D within the hollow structure H of Fig. 3A, and Fig. 3C illustrates a corresponding deployed in-use representation R2 of said device D. [Figure 4] 1 is an image that diagrammatically illustrates an exemplary image dataset I that includes a hollow structure H. [Diagram 5] 5 is an image that diagrammatically illustrates an SDF generated from the image dataset of FIG. 4; [Figure 6] 1 is a flow chart illustrating a first embodiment of a method for training a machine learning system according to the present invention. [Figure 7] 3 is an image illustrating a geometric representation R1 of device D of FIG. 2 with a contact force applied thereto. [Figure 8] 1 is a flowchart illustrating a method for training the machine learning system of the present invention according to a first embodiment. [Figure 9] FIG. 1 is a schematic diagram of a device 1 for surgical planning according to the invention, according to a second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] For illustrative purposes, the present invention is shown in a preferred embodiment. However, it should be understood that the application is not limited to the exact arrangement, configuration, features, embodiments, and aspects shown. The drawings are not drawn to scale and are not intended to limit the scope of the claims to the depicted embodiments.

[0051] Surgical planning device1 A device 1 for surgical planning according to the invention is shown in FIG.

[0052] More precisely, the device 1 is configured to train a machine learning system ML configured to generate an optimal deployment configuration of the device D inside a hollow structure H of a subject. As will be explained later, the device 1 will process at least one image dataset comprising a plurality of image datasets forming together an image database of a lumen of the human body, in order to obtain training data dedicated to the training of the machine learning system ML.

[0053] The hollow structure H may be any lumen or cavity of the human body, including but not limited to blood vessels such as veins, arteries, or non-vascular structures such as fistulas, respiratory tract (e.g., trachea, bronchi, esophagus), digestive tract (e.g., colon), biliary tract, renal tract, or urinary tract.

[0054] All these hollow structures H are suitable for receiving a device D having an deployed configuration.

[0055] An example of a device D having a contracted or crimped configuration (diameter d1 and length L1) and a deployed or expanded configuration (diameter d2 and length L2) is shown in Figure 2. In particular, the device D is a braided stent.

[0056] Stents are tubular devices that allow the maintenance or restoration of luminal patency (e.g., to restore blood flow in a blood vessel, to prevent intraluminal growth of tumor tissue), and they can be made of a mesh of fibers or wires (e.g., braided stents, knitted stents, woven stents).

[0057] The deployed configuration of the stent in FIG. 2 (d2, L2) is the unconstrained deployed configuration.

[0058] More precisely, the term "unconstrained" refers to a configuration of device D that is influenced only by the intrinsic properties of device D (e.g., radius, material, Young's modulus, etc.) and not by external properties (e.g., presence, shape, mechanical properties of surrounding tissue).

[0059] Figure 3A illustrates one exemplary hollow structure H (a blood vessel), and Figures 3B and 3C illustrate contracted and expanded configurations, respectively, of a device D (in this case a braided stent) when implanted within hollow structure H. The bulge in the blood vessel in Figure 3 is an aneurysm A.

[0060] The deployed configuration of FIG. 3C is the deployed in-use configuration.

[0061] A further description of device 1 will now be provided.

[0062] As shown in FIG. 1, the device 1 includes an input section 10 for receiving at least one image dataset I at S01, and a processing unit 11 configured to train a machine learning system ML based on each received image dataset I.

[0063] Input section 10 As shown in Fig. 1, the inventive device 1 may comprise an input part 10 adapted to receive, during a receiving step S01, at least one image data set I. The image data set I comprises at least one part of a hollow structure H.

[0064] For example, the image dataset I may be stored in one or more local or remote database(s) 12. Alternatively or in addition, the input of the device 1 may be directly connected to an imaging apparatus 2 (FIG. 9).

[0065] The image dataset I preferably comprises a medical image, such as a Magnetic Resonance (MR) image, a Computed Tomography (CT) image, or a Rotational Angiography (RA) image. The image may be acquired with or without contrast enhancement.

[0066] The at least one image data set I may comprise a plurality of image data sets which together form an image database of a body lumen, each image data set representing at least a portion of a hollow structure of a reference subject.

[0067] One exemplary image dataset I is illustrated diagrammatically in Fig. 4. In this example, the hollow structure H includes a cerebral artery (exhibiting an aneurysm A) and its branches, and the image dataset I is a magnetic resonance angiography (or MRA) image including transverse, sagittal, and coronal sections (or slices) It, Is, Ic.

[0068] For purposes of clarity, only three orthogonal cross-sections of image dataset I are illustrated in FIG. 4, each cross-section including at least a portion of the aneurysm.

[0069] Processing Unit 11 As already mentioned, the device 1 comprises a processing unit 11 .

[0070] The processing unit 11 is configured to carry out a series of steps which will now be described in more detail, the main steps including a first calculation step S10, a second calculation step S11, a generation step S20 and a training step S30 (Figure 1).

[0071] Calculation of SDF S10 During a first calculation step S10, the processing unit 11 is configured to calculate a signed distance field (SDF) of at least one portion of the hollow structure H based on the image data set I. When the at least one image data set I comprises multiple image data sets corresponding to different reference subjects, the first calculation step S10 is performed for each image data set.

[0072] The SDF is a volume grid where each voxel is associated with a distance value from the target surface. The values ​​of the SDF are zero on the 3D surface (which forms the target surface), negative inside the 3D surface, positive outside the 3D surface, or vice versa.

[0073] One exemplary SDF is illustrated in Figure 5. The color bar illustrates the values ​​of the SDF (units: mm).

[0074] More precisely, two orthogonal cross sections of the SDF are illustrated here. For the sake of clarity, the three-dimensional surface of the hollow structure H is also illustrated.

[0075] Preferably, the processing unit 11 is configured to calculate the SDF from a set of points obtained by segmentation S02 of the image dataset I. This segmentation step S02 will be explained later.

[0076] Calculation of the geometric parameter(s) P S11 During a second calculation step S11, the processing unit 11 is configured to calculate at least one geometric parameter P of the portion of the hollow structure H based on the image dataset I. The at least one geometric parameter P will be used as input of a machine learning system that will be explained later. The at least one geometric parameter P to be calculated is intended to describe the geometric variability of the patient's vessels with a finite number of features.

[0077] When the at least one image data set I comprises a plurality of image data sets corresponding to different reference subjects, the second calculation step S11 is performed for each image data set.

[0078] The geometrical parameter(s) P and their calculation may be selected depending on the hollow structure H.

[0079] For example, the geometric parameters P may include one or more parameters such as the axis, centerline (FIG. 3), center (FIG. 3), or radius of the hollow structure H.

[0080] For example, the processing unit 11 may be configured to calculate the center of a spherical or quasi-spherical hollow structure H, such as an aneurysm A. As another example, the processing unit 11 may be configured to calculate the centerline of an elongated hollow structure H, such as a blood vessel.

[0081] For example, the centerline may be computed as the path defined on the Voronoi diagram sheet along which the integral of the radius of the largest inscribed sphere along that path is minimal.

[0082] Segmentation S02 Preferably, the processing unit 11 is configured to segment the image dataset I to obtain a segmented image dataset Is during a segmentation step S02 prior to the calculation steps S10, S11 for obtaining a segmented image dataset Is. In this case, the processing unit 11 is configured to calculate at least one geometric parameter P and / or a signed distance field SDF based on the segmented image dataset Is during the calculation steps S10, S11. When the at least one image dataset I comprises multiple image datasets corresponding to different reference subjects, the segmentation step S02 is performed for each image dataset.

[0083] The segmented image dataset Is comprises a surface or a set of curves that contain points (eg, corresponding to pixels or voxels having the same intensity).

[0084] For example, the surface or curve may include points obtained from segmentation step S02 based on a region growing algorithm from seed points (eg, from voxels selected by the user).

[0085] An example of the segmentation step S02 according to the invention is represented diagrammatically in FIG.

[0086] For example, during the segmentation step S02, the processing unit 11 may be configured to apply a level set segmentation to the image data set I. This makes it possible to generate the target surface or curve in an implicit form as an isosurface of the zero level set of a higher dimensional function called a "level set function". Applying the level set segmentation method will make it possible to obtain the information necessary to carry out the finite element analysis calculations that will be explained later.

[0087] As shown in FIG. 6, the segmentation step S02 may include an initialization phase S021 and an evolution phase S022.

[0088] In an initialization phase S021, the processing unit 11 is configured to define an initial curve or surface within the hollow structure H in the image data set I.

[0089] For example, in the case of level set segmentation, the first surface in the initialization phase S021 is the initial zero level set.

[0090] Advantageously, in level set segmentation, the initial zero level set is close to the target surface.

[0091] During the initialization phase S021, the processing unit 11 - Select at least two points in the image dataset, - Run the colliding front algorithm using at least two points as seed points, It is configured as follows.

[0092] This particular initialization phase S021 is preferred for hollow structures H having a tubular shape, such as blood vessels. In this case, a first point may be selected at one end of the hollow structure H, and a second point may be selected at an opposite end of the hollow structure H.

[0093] During an evolution phase S022 of the segmentation step S02, the processing unit 11 is configured to deform the predefined curve or surface (defined within the hollow structure H during the initialization phase S021) until it reaches the boundary of the hollow structure H. The segmented image data set Is then comprises the obtained deformed curve or surface.

[0094] For example, in level set segmentation, processing unit 11 is configured during evolution phase S022 to deform the initial zero level set by applying a set of partial differential equations to the initial zero level set to obtain a target surface. In this case, the segmented image data set Is includes the target surface. Processing unit 11 may further be configured to derive an SDF based on a relationship between the SDF and the target surface during the first calculation step S10. For example, processing unit 11 may be configured to select said target surface as the SDF.

[0095] Advantageously, level set segmentation minimizes the number of user-dependent steps and ensures that the segmentation step S02 is robust and reproducible, since it is based on intensity gradients rather than absolute intensities in the image dataset I.

[0096] However, the processing unit 11 may be configured to perform different initialization phases S021 and evolution phases S022, for example depending on the shape of the hollow structure H.

[0097] 3D Surface Extraction S03 As shown in Fig. 6, the processing unit 11 is configured to extract, during an optional extraction step S03, a three-dimensional surface representative of the hollow structure H from the segmented image data set Is. For example, said three-dimensional surface may be extracted using a marching cubes algorithm. When the at least one image data set I comprises multiple image data sets corresponding to different reference subjects, the extraction step S03 is performed for each segmented image data set.

[0098] A three-dimensional surface representing the hollow structure H can be output for visualization purposes.

[0099] Examples of such three-dimensional surfaces are shown in FIG. 3 (here superimposed on a representation R1, R2 of a device D and on the geometric parameters P) and in FIG. 4 (here superimposed on an image data set I).

[0100] Advantageously, it is the 3D surface that is obtained from the SDF, and not the other way around, so the loss of precision introduced by surface generation algorithms (such as the marching cubes algorithm) does not affect the computation of the SDF.

[0101] Advantageously, the centerline can be obtained from the segmentation step S02.

[0102] Calculation S11 of the geometric parameter(s) P based on the segmentation step S02 Following the segmentation step S02, a database of 3D surfaces associated with centerlines is obtained, the association of the 3D surfaces with the centerlines representing one model in the database.

[0103] To calculate the geometric parameters P, which correspond to the blood vessel having an aneurysm (hollow structure H) and represent the digital model Si of the blood vessel having an aneurysm, the centerline and the three-dimensional surface obtained from the segmentation step S02 are used as follows:

[0104] In the first step, the portion of the vessel covered by the stent deployment and the corresponding centerline of the vessel are isolated from the aneurysm. The centerline is interpolated using splines to control a number of points Nc along the centerline. For example, at least three points are used. When Nc is 3, nine parameters corresponding to the three-dimensional coordinates of the three points are obtained.

[0105] In the second step, cross sections of the vessel perpendicular to the centerline are calculated. Each cross section is interpolated using a spline to control the number of points Ns in each cross section. For example, when the cross sections are modeled as a circumference, the number of parameters of the cross section is 1, and the parameter corresponds to the radius of the circumference.

[0106] The aneurysm can then be parameterized by two parameters, for example the aneurysm neck is modeled as an ellipse, in this case the two parameters are the lengths of the major axes of the ellipse.

[0107] So, for example, if Nc is 3, and each cross section is parameterized with a single radius, the total number of parameters is 14. This is the minimum number of parameters P to model a blood vessel with an aneurysm.

[0108] In a more general parameterization, the number of parameters is N=Nc * Ns.

[0109] A reduction is possible if N is large. This reduction step is designed to obtain a high-fidelity digital model of the vessel, i.e. a compromise between accuracy, computation time, and memory size for storing the digital model.

[0110] For example, the PCA algorithm can be used to reduce the number of geometric parameters P. The PCA algorithm is mathematically similar to the POD (Proper Orthogonal Decomposition) algorithm.

[0111] Instead of using the PCA algorithm, an autoencoder can also be used to reduce the number of parameters.

[0112] Generation of transformation expressions S18 The processing unit 11 may advantageously be configured to generate a variant representation of the device D during a generation step S18.

[0113] The generation S18 of the transformed representation of device D is better illustrated in Figures 2 and 3. - applying a predetermined displacement (e.g. applying a radial displacement to each node of the mesh) to an unconstrained unfolded representation of the device D (e.g. configuration d2, L2 of FIG. 2) to obtain a shrunk or crimped representation of the same device (e.g. configuration d1, L1 of FIG. 2); and - Deforming a contracted representation of the device D based on the geometric parameters P of its hollow part H (FIG. 3A), It can be generated by:

[0114] For example, during said deformation, the processing unit 11 may be configured to deform the contracted representation of the device D to align it with the centre line of the hollow part H.

[0115] Various techniques may be used to modify the shrunk representation of the device D based on the geometric parameters P depending on the shape of the device D and / or the hollow structure H.

[0116] For example, in the case of a tubular device D, the transformation of the contracted representation may involve translating and / or morphing the initially straight centerline of the tubular device (FIG. 2) according to the centerline of the hollow structure H obtained during segmentation step S02 (FIG. 3A).

[0117] The deformed representation thus obtained (FIG. 3B) represents the configuration of the device D within the hollow structure H immediately after implantation.

[0118] Preferably, the processing unit 11 is configured to implement a finite element solver to perform this generating step S18.

[0119] In this case, processing unit 11 (e.g. a finite element solver) may be configured to iteratively apply incremental displacements to the unconstrained unfolded representation of device D until a predefined displacement is applied. More precisely, in each iteration, processing unit 11 is configured to apply predefined constraint components (e.g. radial displacements or forces) to the nodes of the mesh and to calculate the remaining (i.e. unconstrained) components associated with said constraints (e.g. longitudinal displacements).

[0120] Furthermore, the processing unit 11 may be configured to iteratively apply incremental deformations to the eroded representation of the device D until said eroded representation is contained within the hollow structure H. More precisely, at each iteration, the processing unit 11 is configured to apply certain constraint components (e.g. translations and / or rotations) to the nodes of the mesh and to calculate the remaining (i.e. unconstrained) components associated with said constraints.

[0121] In each of the above mentioned iterations, the processing unit 11 may be configured to input the calculated components into the next iteration to obtain updated boundary conditions.

[0122] This deformed representation may be used as an initial condition for a finite element solver configured to generate therefrom, during the generation step S20, an evolved working representation R2 (FIG. 3C).

[0123] Generation of the expanded representation R2 in use S20 During the generation step S20, the processing unit 11 is configured to generate, based on the calculated SDF and the centre line, an unfolded in-use representation R2 (FIG. 3C) of the device D. To this end, the generation step S20 advantageously comprises a contact force calculation phase S201 and a contact force application phase S202.

[0124] The step S20 of generating the evolved in-use representation R2 based on the SDF has several advantages.

[0125] First, contact search algorithms (ie, algorithms that find the closest points to a surface) and mesh generation algorithms are avoided, which allows the unfolded working representation R2 to be generated quickly in S20.

[0126] Furthermore, the introduction of spatial errors inherent in mesh generation algorithms is avoided.

[0127] Furthermore, since the deployed in-use representation R2 is generated based on an SDF derived directly from the image dataset I, the number of intermediate objects (and therefore numerical approximations and / or errors) between the initial image including the hollow structure H and the final representation (i.e. the deployed in-use representation R2) of the device D within said hollow structure H is minimized, thereby ensuring accuracy and patient specificity of the deployed in-use representation R2 thus obtained.

[0128] Preferably, the processing unit 11 is configured to implement a finite element solver to perform this generating step S20. For this purpose, any finite element solver can be implemented to generate the deployed in-use representation R2. For example, a finite element solver designed to numerically solve partial differential equations describing the interaction of wire-like structures (beam elements) with rigid surfaces can be used to generate the deployed in-use representation R2 of a vascular braided stent.

[0129] For example, implicit formulations for finite element simulations can be used. Implicit formulations allow larger time steps compared to explicit formulations, thus saving a lot of computation time. Implicit formulations require linearization, which results in the construction of large matrices that take into account all terms that affect the solution as the considered element (i.e. the beam) moves in space. For nonlinear problems, the use of signed distance fields makes the construction of implicit formulations easier, and improves computational speed and robustness.

[0130] The finite element solver may be configured to provide the deployed in-use representation R2 by numerically solving frictional contact dynamics equations. Frictional contact dynamics are particularly suitable for simulating the deployment of device D in contact with tissue, e.g., the inner wall of an organ or blood vessel.

[0131] Preferably, said identical finite element solver is the same as that which performs the generating step S18 above.

[0132] In this case, each iteration of the generation step S18 can result in intermediate node positions to which the contact forces calculated by the processing unit 11 during the corresponding iteration of the generation step S20 are applied.

[0133] Contact force calculation S201 More precisely, during a calculation phase S201 of the generation step S20, the processing unit 11 is configured to calculate a contact force between the device D and at least one part of the hollow structure H based on the SDF.

[0134] In other words, during this calculation phase S201, the processing unit 11 (e.g. a finite element solver) may be configured to iteratively determine the presence of contact between the device D and the hollow structure H by using the geometric representation R1 of the device D and the hollow structure H, which is implicitly described as an SDF. If the presence of contact is confirmed, the corresponding contact forces are calculated in S201.

[0135] The processing unit 11 may be configured to calculate said contact forces by applying friction contact dynamics equations based on said normal gap vectors.

[0136] The geometric representation R1 of the device D may be a mesh including nodes and geometric elements connecting the nodes. The mesh may be generated based on information of the device D such as the lengths L1, L2 or the diameters d1, d2.

[0137] For example, the geometric representation R1 of the device D may include beam elements. This geometric representation R1 is particularly suitable for a device D that includes a wire mesh. The beam elements of the geometric representation R1 may be defined based on information of the wire mesh, such as the radius of the wires.

[0138] 7 illustrates an exemplary geometric representation R1 of a device D. In this example, the geometric representation R1 of the device D is a mesh including beam elements. The mesh is within a hollow structure H (represented in grey) and the arrows represent contact forces applied to the nodes of the mesh during a contact force application phase S202 (as will be explained later). The color bar illustrates the magnitude (in N) of said contact forces.

[0139] For example, the calculation phase S201 may involve interpolating the SFD at a discrete number of points and calculating normal gap vectors at these points.

[0140] The result of the interpolation of this SDF represents the distance between the geometric representation R1 of the device D and the hollow structure H. In this case, the processing unit 11 is configured to calculate the magnitude of the contact force based on said distance.

[0141] By "normal gap vector" we mean a vector calculated as the gradient of the SDF at a particular interpolation point. The normal gap vector has a direction normal to the surface implicitly described by the SDF at the interpolation point and a magnitude equal to the above-mentioned distance. In this case, the processing unit 11 is configured to calculate the direction of the contact force based on the direction of the normal gap vector.

[0142] A contact threshold may further be defined: for example, the processing unit 11 may be configured to determine the presence of contact if the magnitude of the above-mentioned distance or normal gap vector is below said threshold.

[0143] Application of Contact Forces S202 During a contact force application phase S202 of the generation step S20, the processing unit 11 is configured to apply the calculated contact force to the geometric representation R1 of the device D.

[0144] The contact force application phase S202 may include using a co-rotational formulation for the dynamics of the beam element (eg, co-rotational dynamics for the frictional contact dynamics of the beam element against the surface).

[0145] During the contact force application phase S202, the processing unit 11 may be configured to iteratively apply the calculated contact force, for example by calculating a kinetic energy associated with the geometric representation R1 of the device D and applying the contact force to the geometric representation R1 of the device D until the kinetic energy falls below a predefined threshold.

[0146] FIG. 7 illustrates a portion of an exemplary geometric representation R1 of a device D obtained at the end of the iterations of the application phase S202.

[0147] As mentioned above, the processing unit 11 may be configured to generate, during the generating step S18, a deformed representation of the device D representative of its configuration immediately after implantation within the hollow structure H.

[0148] In this case, the geometric representation R1 of the device D to which the contact force is applied is the deformation representation (FIG. 3B).

[0149] Order reduction S28 As can be seen in FIG. 8, the processing unit 11 may further be configured to reduce the order of the evolved in-use representation R2 of the device D during an order reduction step S28 to obtain a reduced order representation roR2 thereof.

[0150] For example, the processing unit 11 is configured to obtain a reduced-order representation roR2 by applying a proper orthogonal decomposition algorithm (e.g., principal component analysis or PCA) to the unfolded in-use representation R2 of the device D (also called a “high-fidelity solution” or “snapshot”) obtained in the aforementioned generation step S20 to obtain a reduced base.

[0151] In this case, the reduced-order representation roR2 provides a description of the high-fidelity solution as a linear combination of a subset of the reduced bases.

[0152] Furthermore, the processing unit 11 may be configured to perform the aforementioned order reduction S28 in two separate stages: for example, the main features (e.g. principal components or reduced cardinalities) and their respective projection coefficients are computed in a first, offline stage, while the generation of an optimal unfolded configuration is performed in a second, online stage.

[0153] The term "online" generally encompasses any calculation that is performed by the processing unit 11 as input data for the calculation is received, i.e., performed in real time based on currently received input data.

[0154] The term “offline” generally encompasses any computation performed by processing unit 11 based on previously received or acquired input data (e.g., training a machine learning classifier on a stored data set).

[0155] As mentioned above, such a reduction step S28 comprising two separated stages advantageously enables the provision of a robust reduced-order representation roR2 since the online stage does not depend on the dimensions of the full-order model obtained in the generation step S20 (i.e. of the high-fidelity solution or the unfolded in-use representation R2).

[0156] Furthermore, in this case the online stage of the reduction step S28 may be implemented by a machine learning algorithm.

[0157] Preferably, the projection coefficients are calculated during an offline stage using one of Gaussian process regression, decision trees, or neural networks.

[0158] The order reduction step S28 allows for the compression of the data and therefore the reduction of memory space for storing the data. Furthermore, the total size of the training data is reduced since fewer calculations are required to obtain it. As a result, the training data is created faster.

[0159] Since the time of the training stage depends on the size of the training data, especially for artificial neural networks, using training data of smaller size helps to improve and shorten the training stage. Using reduced order models makes it possible to obtain direct control of the number of outputs that the neural network learns, and also of the error between the solution that the neural network predicts and the high fidelity solution. In other words, a smaller number of outputs leads to less training data and a shorter computational training time, but a higher error, and vice versa.

[0160] Training S30 The processing unit 11 is configured to train a machine learning system ML during a training step S30 using each of the calculated geometric parameters P as input variables and the corresponding evolved in-use representation R2 of the device D as an associated target output.

[0161] Preferably, the input variables of the machine learning system ML are vectors of geometric parameters (i.e., vectors of machine learning features). The vector of geometric parameters is the aforementioned N=Nc * It contains Ns parameters.

[0162] As mentioned above, the processing unit 11 may be configured to generate a reduced-order representation roR2 of the expanded in-use representation R2.

[0163] In this case, during the training step S30, the processing unit 11 may be configured to train a machine learning system with each geometric parameter P as an input variable and a subset of the features of the reduced-order representation roR2 (e.g. a subset of the reduced cardinality) as an associated target output.

[0164] The magnitude of the order reduction (e.g., the number of selected reduction bases input to the machine learning system) may be selected based on an error threshold. For example, in the case of an orthogonal decomposition, the optimal number of reduction bases (such as singular values ​​or principal components) may be selected based on the error of the reduction bases. Such error may be derived from the decay of the singular values.

[0165] Generate optimal deployment configuration As mentioned above, the device 1 of the present invention makes it possible to obtain a trained machine learning system configured to generate an optimal deployment configuration of the device D within the hollow structure H of a subject.

[0166] FIG. 9 is a schematic diagram of a device 1 of the invention showing a machine learning system ML receiving as input at least one geometric parameter P calculated in S10 from an image dataset I acquired by an imaging device 2 or from a segmented image dataset Is obtained by segmentation of the image dataset I.

[0167] In this example, the device 1 is operatively connected to an imaging apparatus 2 (eg an MRI or CT scanner). Alternatively, the acquired image data set I can be received via the input 10 as previously described.

[0168] In this example, the device 1 of the invention advantageously comprises a graphical user interface GUI in communication with a processing unit 11. Said graphical user interface GUI makes it possible to display in real time the deployment configuration of the device D to a user, for example a surgeon.

[0169] In this case, the processing unit 11 may be further configured to receive information from a user through the GUI, such as, for example, a selection of one or more seed points for initializing the segmentation of the image dataset I in S02.

[0170] Advantageously, the trained machine learning system of the present invention is configured to generate optimal deployment configurations for devices in real-time with high accuracy.

[0171] Indeed, as can be seen in FIG. 9 , the processing unit 11 is configured, during a second calculation step S11, to calculate at least one geometric parameter P of the hollow structure H from the image dataset I (for example via image segmentation based on the selected points), and the trained machine learning system ML is configured to generate therefrom directly an optimal deployment configuration C of the device D.

[0172] In other words, to generate the optimal deployment configuration C of the device D, there is no need to perform time-consuming and / or error-introducing steps such as mesh generation algorithms, iterative solution algorithms, running finite element methods, calculating SDFs, etc. All these steps are either avoided (e.g. in the case of generating the mesh of the hollow structure H) or performed in previous steps S10, S20, S30.

[0173] Notably, the number and complexity of calculations performed by the trained machine learning can be further reduced by implementing an order reduction step S28, which includes an offline stage and an online stage, as described above.

[0174] operation The operation of the device 1 according to the invention will now be described.

[0175] During step S01, the processing unit 11 receives at least one image data set I.

[0176] Then, during step S10, the processing unit 11 calculates S10 the SDF of at least one portion of the hollow structure H based on the image dataset I.

[0177] Furthermore, during step S11, the processing unit 11 calculates at least one geometric parameter P of the portion of the hollow structure H based on the image dataset I.

[0178] Alternatively, during step S02 prior to steps S10, S11, the processing unit 11 segments the image data set I. In this case, based on the segmented image data set Is, at least one geometric parameter P and / or the signed distance field SDF is calculated during steps S10, S11.

[0179] Then, during step S20, the processing unit 11 generates an evolved in-use representation R2 of the device D based on the calculated SDF.

[0180] For example, during a contact force calculation phase S201 of the generation step S20, the processing unit 11 calculates the contact force between the device D and at least one part of the hollow structure H based on the SDF.

[0181] Then, during a contact force application phase S202 of the generation step S20, the processing unit 11 applies said calculated contact force to the geometric representation R1 of the device D.

[0182] Preferably, the contact force is applied in a contact force application phase S202 to the deformed representation of the device D. In this case, such deformed representation of the device D is generated by the processing unit during an optional generation step S18 prior to step S20.

[0183] Then, during step S30, the processing unit 11 trains a machine learning system ML with each of the calculated geometric parameters P as input variables and the corresponding evolved in-use representation R2 of the device D as the associated target output.

[0184] Alternatively, during step S30, the processing unit 11 trains the machine learning system ML with the reduced-order representation roR2 of the device D as a target output. In this case, such reduced-order representation roR2 of the device D is generated during an optional order reduction step S28 prior to the training step S30.

[0185] Advantageously, the trained machine learning system generates an optimal deployment configuration D of the device within the hollow structure H of the subject based on the at least one geometric parameter P calculated during step S11.

[0186] Computer-Implemented Method The present invention also relates to a computer-implemented method for generating an optimal deployment configuration of a device 1 in an organ of a subject for surgical planning, the computer program comprising program code instructions which, when executed by a computer, cause the computer to carry out a method according to any one of the above embodiments.

[0187] storage medium The invention also relates to a non-volatile computer storage medium containing instructions which, when executed by a computer, cause the computer to carry out the steps of the method according to the invention.

[0188] Preferably, the computer readable storage medium is a non-transitory computer readable storage medium.

Claims

1. 1. A computer-implemented method for training a machine learning system configured to generate an optimal deployment configuration of a device within a hollow structure (H) of a subject for surgical planning, the method comprising: on the basis of at least one image data set (I) representative of at least one portion of a hollow structure (H) of a plurality of reference subjects, - calculating (S10) a signed distance field (SDF) of at least one portion of a hollow structure (H) of each of said plurality of reference subjects; - calculating (S11) at least one geometric parameter (P) of at least one portion of a hollow structure (H) of each of said plurality of reference subjects, said at least one geometric parameter being a set of geometric parameters defining a geometric model of a specific portion of a hollow structure of a specific reference subject of said plurality of reference subjects; for each portion of at least one portion of a hollow structure of a plurality of reference subjects, Calculating (S201) a contact force between the device (D) and said one part of the hollow structure (H) based on the corresponding calculated signed distance field (SDF); and applying (S202) said contact force to a geometric representation (R1) of a device (D); generating (S20) an expanded in-use representation (R2) of the device by training (S30) a machine learning system (ML) with each of the calculated geometric parameters (P) as an input variable and the corresponding deployed in-use representation (R2) of the device as an associated target output, to obtain a trained machine learning system configured to receive as input at least one geometric parameter (P) and to provide as output a deployed in-use representation (R2) of the device for use in a method for generating an optimal deployed configuration of the device (D) for surgical planning; A method comprising:

2. The method according to claim 1, wherein the hollow structure (H) is a blood vessel, a fistula or a non-vascular tube of the human body.

3. 3. The method according to claim 1 or 2, further comprising segmenting (S02) at least one image dataset (I) to obtain a segmented image dataset (Is), based on which at least one geometric parameter (P) and / or a signed distance field (SDF) are calculated (S10, S11).

4. The method of claim 3 , wherein the segmenting (S02) comprises applying a level set segmentation to the image dataset (I).

5. 5. The method of claim 4, further comprising extracting (S03) a three-dimensional surface representative of a hollow structure (H) from said segmented image data set (Is), preferably using a marching cubes algorithm.

6. The segmenting (S02) includes an initialization phase (S021) for obtaining a zero level set and an evolution phase (S022), the initialization phase (S021) including: selecting at least two points in at least one image data set (I); running a Colliding Front algorithm using the at least two points as seed points; The method of any one of claims 3 to 5, comprising:

7. The segmented image data set (Is) comprises a set of points or a set of curves, and the calculating (S11) of the at least one geometric parameter (P) comprises: applying a point set registration to the set of points; or applying a curve-based parameterization to the set of curves; The method of any one of claims 3 to 6, comprising:

8. 8. The method according to claim 1, wherein the geometric representation (R1) of the device (D) comprises beam elements, and the applying phase (S202) comprises applying a co-rotational formulation to the beam elements.

9. Prior to said training (S30), the method further comprises reducing (S28) the order of the expanded in-use representation (R2) of the device (D) to obtain a reduced order representation (roR2) of the expanded device; 9. The method according to any one of claims 1 to 8, wherein during the training (S30), the machine learning system is trained using the calculated geometric parameters (P) as input variables and a subset of features of a reduced-order representation (roR2) as associated target outputs.

10. The method of claim 9 , wherein the reducing (S28) comprises applying a proper orthogonal decomposition algorithm to the unfolded in-use representation (R2) of the device.

11. 11. The method according to any one of claims 1 to 10, wherein the at least one geometric parameter (P) is a centerline, a center, or a radius of a hollow structure (H), a point defining a centerline, a control point defining a cross section of a three-dimensional surface representing the hollow structure (H), or a combination thereof.

12. The method of any one of claims 1 to 11, further comprising generating (S18) a deformed representation of the device (D), the deformed representation representing a configuration of the device after implantation within a hollow structure (H) of a subject, the deformed representation being a geometric representation (R1) of the device (D) to which a contact force is applied.

13. 1. A computer-implemented method for generating an optimal deployment configuration of a device (D) in an organ of a subject for surgical planning, the method comprising: Calculating (S11) at least one geometric parameter (P) of a hollow structure (H) of a subject based on an image data set (I) including at least the hollow structure (H); - generating an optimal deployment configuration of the device by inputting the calculated at least one geometric parameter (P) into a machine learning system trained according to the method of any one of claims 1 to 12; A method comprising:

14. A device (1) for training a machine learning system configured to generate an optimal deployment configuration of a device (D) in a hollow structure (H) of a subject for surgical planning, the device (1) comprising: on the basis of at least one image data set (I) representative of at least one portion of a hollow structure (H) of a plurality of reference subjects, Calculating (S10) a signed distance field (SDF) of at least one portion of a hollow structure (H) for each of said plurality of reference subjects; - calculating (S11) at least one geometric parameter (P) of at least one portion of a hollow structure (H) of each of said plurality of reference subjects, said at least one geometric parameter comprising a set of geometric parameters defining a geometric model of a specific portion of a hollow structure of a specific reference subject of said plurality of reference subjects; for each portion of at least one portion of a hollow structure of a plurality of reference subjects, Calculating (S201) the contact forces between the device and said portion of the hollow structure (H) based on the corresponding calculated signed distance field (SDF); and applying (S202) said contact force to a geometric representation (R1) of the device; generating (S20) an expanded in-use representation (R2) of the device by training (S30) a machine learning system with each of the calculated geometric parameters (P) as an input variable and the corresponding deployed in-use representation (R2) of the device as an associated target output, to obtain a trained machine learning system configured to receive as input at least one geometric parameter (P) and to provide as output a deployed in-use representation (R2) of the device for use in a method of generating an optimal deployed configuration of the device for surgical planning; The device (1) comprises a processing unit (11) configured to:

15. A device (1) for generating an optimal deployment configuration of a device (D) in an organ of a subject for surgical planning, said device (1) comprising: Calculating (S11) at least one geometric parameter (P) of a hollow structure (H) of the subject based on an image data set (I) including at least the hollow structure (H), generating an optimal deployment configuration for the device by inputting the calculated at least one geometric parameter (P) into a machine learning system trained according to the method of any one of claims 1 to 12; The device (1) comprises a processing unit (11) configured to:

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